13. Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
amplitude: 4, period 4 phase shift = vertical shift = -2
Answers
Answer:
[tex]y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2[/tex]
Step-by-step explanation:
Let's start with the original function.
[tex]y=a sin\frac{2\pi t}{T}[/tex]
We can immediately fill in the amplitude 'a' and period 'T' , as the question defines these for us, and provides values for 'a' and 'T', 4 and 4[tex]\pi[/tex] respectively.
[tex]y=4sin(\frac{2\pi t}{4\pi } )[/tex]
Now we only have phase shift and vertical shift to do. Vertical shift is very easy, you can just add it to the end of the right side of the expression. A positive value will shift the graph up, while a negative value will move shift the graph down. We have '-2' as our value for vertical shift, so we can add that on as so:
[tex]y=4sin(\frac{2\pit }{4\pi } )-2[/tex]
Now phase shift the most complicated of the transformations. Basically, it is just movement left or right. A negative phase shift moves the graph right, a positive phase shift moves the graph left (I know, confusing!). Phase shift applies directly to the x variable, or in this case the t variable. To achieve a -4/3 pi phase shift, we need to input +4/3 pi into the function, because of the aforementioned negative positive rule. Here is what the function looks like with the correct phase shift:
[tex]y=4sin(\frac{2\pi(t+\frac{4}{3}\pi ) }{4\pi } )-2[/tex]
This function has vertical shift -2, phase shift -4/3 [tex]\pi[/tex], amplitude 4, and period 4[tex]\pi[/tex].
Desmos.com/calculator is a great tool for learning about how various parts of an equation affect the graph of the function, If you want you can input each step of this problem into desmos and watch the graph change to match the criteria.
Related Questions
PLLLZ HELP HAVE A DEADLINE 30 POINTS Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cot θ= - 3/7 . Find the exact values of the five remaining trigonometric functions of θ.
Answers
Answer:
answer is the first option
Step-by-step explanation:
GASB requires a budget to actual comparison in the financial statements for the general fund and the ________.
Answers
Answer: Major special revenue funds with legally adopted budgets.
Step-by-step explanation: GASB ( Governmental accounting standards board) is a private organization based in Norwalk,that tries to regulates Government accounting process in the United States of America by giving specific standards to ensure proper accounting.
Governmental accounting standards board (GASB) requires a budget to actual comparison in the financial statements for the general fund and major special revenue funds with legally adopted budgets.
Abigail"s parents pay her $5 an hour for weeding the yard and pay her little sister $3 an hour for raking leaves. Write and expression two different ways to represent the amount for parents will pay Abigail and her sister from work you same amount of hours
Answers
Final answer:
To represent the total amount Abigail's parents will pay both Abigail and her sister for working the same number of hours, you could use the algebraic expressions 5h + 3h or (5 + 3)h, where h is the number of hours worked.
Explanation:
Abigail's parents pay her for weeding the yard and pay her little sister for raking leaves. If both of them work for the same amount of hours, we can represent the total amount their parents will pay using algebraic expressions. Let h be the number of hours they work.
One way to write the expression is: 5h + 3h, where 5 represents the dollars per hour for Abigail and 3 represents the dollars per hour for her sister.
Another way to represent this is: (5 + 3)h, which simplifies the expression by adding the hourly wages first and then multiplying by the number of hours worked, h.
Both expressions will give us the total amount paid to Abigail and her sister for the same number of hours worked, h.
Which sentence below represents the number of test questions in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. If the test has 25 questions, how many multiple choice questions are there?
A. The number of multiple-choice questions plus the number of short-answer questions is 25.
B. The number of multiple-choice questions times the number of short-answer questions is 25.
C. The number of multiple-choice questions minus the number of short-answer questions is 80.
D. The number of multiple-choice questions plus the number of short-answer questions is 80.
Answers
Answer: there are 10 multiple choice questions and 15 short-answer questions
Step-by-step explanation:
Let x represent the number of multiple choice questions in the test.
Let y represent the number of short-answer questions in the test.
If the test has 25 questions, it means that
x + y = 25
Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. The test is worth a total of 80 points. It means that
2x + 4y = 80 - - - - - - - -1
Substituting x = 25 - y into equation 1, it becomes
2(25 - y) + 4y = 80
50 - 2y + 4y = 80
- 2y + 4y = 80 - 50
2y = 30
y = 30/2 = 15
x = 25 - y = 25 - 15 = 10
A. The number of multiple-choice questions plus the number of short-answer questions is 25.
Answer:
A makes the most sense
Step-by-step explanation:
as if you don't get tricked and notice that C and D are not true but between A and B are two answers but B isn't correct if you go over what it means without getting tricked and A is to be the right answer
The yearbook was sold for $26 at the beginning of the year.Since the price has increased to $28.What was the percent of increase in price (round to the hundredths place
Answers
Answer:the percent of increase in price is 7.69%
Step-by-step explanation:
The yearbook was sold for $26 at the beginning of the year. This means that the initial price of the year book was $26.
The price has increased to $28. The amount by which it was increased would be the current price - the initial price. It becomes
28 - 26 = $2
The percent of increase in price would be
Increase/initial price × 100
It becomes
2/26 × 100 = 7.69%
A certain tennis player makes a successful first serve 6969% of the time. Suppose the tennis player serves 9090 times in a match. a) What's the mean and standard deviation of the number of good first serves expected? b) Determine if you can use a normal model to approximate the distribution of the number of good first serves. c) What's the probability she makes at least 7272 first serves?
Answers
Answer:
a) 4.387
b) Yes, because np & npq are greater than 10.
c) = 0.017
Step-by-step explanation:
Give data:
p = 0.69
n = 90
a) a
E(X) = np = 62.1
[tex]SD(X) = \sqrt{(np(1-p))}[/tex]
[tex]=\sqrt{90\times 0.69(1- 0.69)}[/tex]
= 4.387
b)
np = 62.1
q = 1 - p = 1 - 0.69 = 0.31
npq = 19.251
Yes, because np & npq are greater than 10.
c.
[tex]P(X \geq 72 ) = P(X > 71.5)[/tex] [continuity correction]
[tex]= P(Z> \frac{((71.5-62.1)}{ 4.387})[/tex]
= P(Z> 2.14 )
= 1 - P(Z<2.14)
= 1 - 0.983 (using table)
= 0.017
Final answer:
The tennis player is expected to have an average of 62.1 successful first serves with a standard deviation of 4.573 in 90 attempts. A normal model is appropriate for this distribution. The probability that she makes at least 7272 first serves is approximately [tex]\( 1 - 0.9908 \approx 0.0092 \)[/tex], or about 0.92%.
Explanation:
A certain tennis player makes a successful first serve 69% of the time. If the tennis player serves 90 times in a match, we can calculate the mean and standard deviation of the number of good first serves expected, and determine if a normal model can be used to approximate the distribution.
a) Mean and Standard Deviation
The mean (μ) of the number of successful first serves can be calculated using the formula μ = n*p, where n is the total number of serves, and p is the probability of success on each serve. For 90 serves with a 69% success rate, the mean is 90*0.69 = 62.1 serves.
The standard deviation (σ) can be calculated using the formula σ = √(n*p*(1-p)). Therefore, the standard deviation for our scenario is √(90*0.69*0.31) = 4.573.
b) Normal Model Appropriateness
To determine if a normal model can approximate the distribution, we check if np and n(1-p) are both greater than 10. Here, np = 62.1 and n(1-p) = 27.9, both of which are greater than 10, indicating a normal model is appropriate.
c) Probability of At Least 72 First Serves
Given the large number of trials (9090) and the high probability of success (0.6969), we can approximate the binomial distribution with a normal distribution using the central limit theorem. The mean of the binomial distribution is [tex]\( \mu = np = 9090 \times 0.6969 \approx 6340.8841 \)[/tex] and the standard deviation is [tex]\( \sigma = \sqrt{np(1-p)} = \sqrt{9090 \times 0.6969 \times (1-0.6969)} \approx 39.9549 \).[/tex]
Now, to find the probability that she makes at least 7272 first serves, we'll use the normal approximation with continuity correction. We'll first standardize X = 7272 to find the corresponding z-score:
[tex]\[ z = \frac{X - \mu}{\sigma} = \frac{7272 - 6340.8841}{39.9549} \approx 2.3333 \][/tex]
Using a standard normal distribution table or calculator, the probability associated with z = 2.3333 is approximately 0.9908.
Thus, the probability that she makes at least 7272 first serves is approximately [tex]\( 1 - 0.9908 \approx 0.0092 \)[/tex], or about 0.92%.
Volleyball A volleyball is hit when it is 4 ft above the ground and 12 ft from a 6-ft-high net. It leaves the point of impact with an initial velocity of 35 ft>sec at an angle of 27° and slips by the opposing team untouched.
a. Find a vector equation for the path of the volleyball.
b. How high does the volleyball go, and when does it reach maximum height?
c. Find its range and flight time.
d. When is the volleyball 7 ft above the ground? How far (ground distance) is the volleyball from where it will land?
e. Suppose that the net is raised to 8 ft. Does this change things? Explain. 38. Shot put In
Answers
Answer:
a) the vector equation is r(x,y) = (35cos27°t, 16t^2 -35sin27° - 4)
b) Maximum height = 7.945ft
c) Time of flight = 1.201 secs and range = 37.45ft
d) when t = 0.74, the distance above the ground = 14.37ft
When t = 0.254, the distance above the ground = 26.53ft
e) if the ball is raised to 8ft, the ball won't be able to reach it. This is because the maximum height is 7.954ft
Step-by-step explanation:
a) From the diagram
x0 = 0
y0= 4
V0(initial velocity) = 35
α= 27°
y = 4 + 35sin27°t - 16t^2
y = -16t^2 + 35sin27°t+ 4
y = 16t^2 - 35sin27°t - 4
x = 35cos27°t
Vector equation for the path of the volleyball = r(x,y)
r(x,y) = (35cos27°t, 16t^2 -35sin27° - 4)
b) the ball reaches maximum when dy/dt = 0
y = 16t^2 - 35sin27°t - 4
dy/dt = 32 - 35sin27°
0 = 32 - 35sin27°t
-32 = -35sin27°t
t = -32 / -35sin27°
t = 0.4966 seconds
Put t = 0.4966 into y = 16t^2 - 35sin27°t - 4
y = 16(0.4966)^2 - 35sin27°(0.4966) - 4
y = 7.945 ft
The maximum height is 7.945 ft
c) To find the range and flight time, put y= 0
0 = 16t^2 - 35sin27°t - 4
0 = 16t^2 - 15.89t - 4
Using quadratic equation general formula,
[-b +/- √b^2 -4ac] / 2a
a = 16, b = -15.89, c = -4
= [-(-15.89) +/- √ (-15.89)^2 - 4(16)(-4)] /2(16)
= [15.89 +/- √(15.89)^2 + 256] / 32
= (15.59 +/- 22.55) / 32
= (15.89 + 22.55) / 32 or (15.89 - 22.55) / 32
= 1.201 or -0.208
Time of flight = 1.201 secs
Range = x = 35cos27°t
Range = 32cos27°(1.201)
= 37.45 ft
d) when the volley is 7ft above ground, y = 7
Recall that y = 16t^2 - 35sin27°t - 4
7 = 16t^2 - 35sin27°t - 4
0 = 16t^2 - 35sin27°t - 4 +7
0 = 16t^2 - 35sin27°t + 3
0 = 16t^2 - 15.89t + 3
Using quadratic equation general formula,
[-b +/- √b^2 -4ac] / 2a
a = 16, b = -15.89, c = 3
= [-(-15.89) +/- √ (-15.89)^2 - 4(16)(3)] /2(16)
= [15.89 +/- √(15.89)^2 - 192] / 32
= (15.59 +/- 7.7778) / 32
= (15.89 + 7.7778) / 32 or (15.89 - 7.7778) / 32
= 0.74 or 0.254
When t = 0.74,
x = 35cos27°t
x = 35cos27°(0.74)
x = 23.08 ft
Therefore , R - x(0.74)
= 37.45 - 23.08
= 14.37ft
When t = 0.254,
x = 35cos27°t
x = 35cos27°(0.254)
x = 7.92 ft
Therefore R - x(0.254) =
37.45 - 7.92 = 29.53ft
e) if the ball is raised to 8ft, the ball won't be able to reach it. This is because the maximum height is 7.954ft
This activity will help you meet these educational goals:
You will create a function to model a fireworks show and examine the attributes of the function.
You’re in charge of planning a fireworks show. The company you hire proposes using fireworks called mortar fireworks. These fireworks are placed in a tube that sits on the ground or a flat surface and are shot from the tube with an initial velocity that propels them into the sky.
Mortar fireworks have two fuses that are lit at the same time. The first fuse burns fastest and causes the initial force that launches the firework into the sky. The second fuse takes longer to burn. When the second fuse reaches the middle of the firework, the firework explodes and we see the light show in the sky. This second fuse does not add any extra propulsion to the firework while it’s in the air.
You plan to have the company light the fireworks from the ground. Based on information provided by the company, you’ve determined that the fireworks will have an initial velocity of 192 feet/second.
The formula for the vertical motion of an object is h = -16t2 + v0t + h0, where h is the height of the object, h0 is the initial, or starting, height, v0 is the initial velocity, and t is the time in seconds.
Part A
Create a function to model the height of a firework when shot in the air. Explain whether the function will have a maximum or a minimum value.
Part B
Using the equation representing the height of the firework (h = -16t2 + v0t + h0), algebraically determine the extreme value of f(t) by completing the square and finding the vertex. Interpret what the value represents in this situation.
Answers
Answer:
A
[tex]h = -16t^2 + 192t[/tex]
B
Vertex=(6,576)
Step-by-step explanation:
The problem gives us the following data:
[tex]v_o=192\ ft/s,\ h_o=0[/tex]
A.
Thus the function is
[tex]h = -16t^2 + 192t[/tex]
The graph of h has the shape of an inverted parabola. Recall if the coefficient of the quadratic term is negative, the parabola is concave down, so it has a maximum value.
Part B
Let's take the function of h
[tex]h = -16t^2 + 192t[/tex]
Factoring by -16
[tex]\displaystyle h = -16(t^2 - 12t)[/tex]
Completing squares
[tex]\displaystyle h = -16(t^2 - 12t+36-36)[/tex]
[tex]\displaystyle h = -16(t^2 - 12t+36)+576[/tex]
Factoring
[tex]\displaystyle h = -16(t-6)^2+576[/tex]
Rearranging
[tex]\displaystyle h -576= -16(t-6)^2[/tex]
We can get the coordinates of the vertex from this standard form of the parabola.
Vertex=(6,576)
The maximum value means that at t=6 seconds, the firework will be 576 feet high and then it will start falling back to the ground.
question 1. Enter the ratio equivalent to sin(B)
question 2. Consider this a right triangle. enter the measure of angle CAB to the nearest hundredth degree.
question 3. Suppose angle A is an angle such that angle cosA < sinA. select ALL angle measures that are possible values for angle A. 25, 35, 45, 55, 66, 75.
Answers
Answer:
The three questions about the given triangle has been answered below.
Step-by-step explanation:
We are given a right angled triangle whose sides are of length 20, 21 and 29.
(1) sin(B) = [tex]\frac{side opposite to B}{hypotenuse}[/tex]
= [tex]\frac{21}{29}[/tex]
= 0.72
(2) sin(A) = [tex]\frac{20}{29}[/tex]
sin(A) = 0.689
∠CAB = [tex]sin^{-1}(0.689)[/tex]
∠CAB = 43.551°
(3) We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.
From the given options the angles that satisfy this are 55 , 66 and 75.
45 is not included as then sinA = cosA and that condition is not there.
We can use sine and cosine trigonometric ratios to calculate the ratio and measures of angles.
A: The ratio equivalent to sin(B) is [tex]\dfrac{21}{29}[/tex]
B: The measure of angle ∠CAB is [tex]43.6^\circ[/tex]
C: The possible measures of angle A can be: 55, 66 or 75
Given that:AB = 29 unitsBC = 20 unitsCA = 21 unitsUsing definitions of specific trigonometric ratios:A: The ratio equivalent to sin(B) is:
[tex]sin(B) = \dfrac{CA}{AB} = \dfrac{21}{29}\\[/tex]
B: The measure of angle ∠CAB is calculated as:
[tex]sin(A) = \dfrac{CB}{BA} = \dfrac{20}{29} = 0.69\\\\A = arcsin(0.69) = 43.6^{\circ}\\\\\angle CAB = 43.6^{\circ}[/tex]
C: When sin A > cos A, the measures of angle A from 25,35,45,55,66,75 are:
55, 65 and 75:
The reason for the angles possible are 55, 66 ,75 is that:
[tex]\theta \leq 45\\sin(\theta) \leq cos(\theta)[/tex]
Thus, we have:
A: The ratio equivalent to sin(B) is [tex]\dfrac{21}{29}[/tex]
B: The measure of angle ∠CAB is [tex]43.6^\circ[/tex]
C: The possible measures of angle A can be: 55, 66 or 75
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Which numerical setup can be used to calculate the heat energy required to completely melt 100 grams?
Answers
Answer:
Multiplying the mass of ice by the specific latent heat of fusion of ice
Step-by-step explanation:
The heat energy required to completely melt 100 grams can be calculated by multiplying the mass of ice (100g) by the specific latent heat of fusion of ice (336J/g)
Robert's dog is 4 years older than Karen's cat. In 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. How old is Robert's dog right now?
Answers
Answer:
5.5 years old.
Step-by-step explanation:
Let D represent present age of Robert's dog and C represent present age of Karen's cat.
We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:
[tex]D=C+4...(1)[/tex]
We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be [tex]D+3[/tex] and [tex]C+3[/tex] respectively.
We can represent this information in an equation as:
[tex]D+3+C+3=13...(2)[/tex]
From equation (1), we will get:
[tex]C=D-4[/tex]
Upon substituting this value in equation (2), we will get:
[tex]D+3+D-4+3=13[/tex]
Combine like terms:
[tex]2D+2=13[/tex]
[tex]2D+2-2=13-2[/tex]
[tex]2D=11[/tex]
[tex]\frac{2D}{2}=\frac{11}{2}[/tex]
[tex]D=5.5[/tex]
Therefore, Robert's dog is 5.5 years old right now.
Lee can purchase gas for his rental car for $3.25 per gallon. It will cost him $96 to rent the car. How much will it cost Lee if he purchases 160 gallons of gas? Write your answer in proper money form.
Answers
Answer:
It will cost him $616 for 160 gallons of gas.
Step-by-step EXPLANATION FIRST YOU HAVE TO MULTIPLY 3.25 BY 160 TO GET $520, THEN JUST ADD IT BY $96 TO GET $616.
It will cost Lee $520 to purchase 160 gallons of gas.
What are arithmetic operations?
The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division. The priority of these opeartors in a given expression can be determined by PEDMAS. Each letter represents one operation as P for Parenthesis, E for exponential, D for division, M for Multiplication, A for Addition and S for Subtraction.
The price of gas per gallon is $3,25.
The cost of 160 gallons can be calculated as follows,
Number of gallons × Price per gallon
⇒ 160 × 3.25
⇒ 520
Hence, the price of 160 gallons is given as $520.
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Roddy Richards invested $12014.88 in Wolverine Meat Distributors (W.M.D.) five years ago. The investment had yearly arithmetic returns of minus9.7%, minus8.1%, 15%, 7.2%, and 15.4%. What is the arithmetic average return of Roddy Richard's investment?
Answers
Answer:
The arithmetic average return would be 3.96%
Step-by-step explanation:
Given,
The returns in 5 years are,
-9.7%, -8.1%, 15%, 7.2%, and 15.4%
We know that,
[tex]\text{Arithmetic average}=\frac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]
Hence,
The arithmetic average return of the investment = [tex]\frac{-9.7-8.1+15+7.2+15.4}{5}[/tex]
[tex]=\frac{19.8}{5}[/tex]
= 3.96%
A postal worker counts the number of complaint letters received by the United States Postal Service in a givenday. Identify the type of data collected.
A) quantitative
B) qualitative
Answers
Answer:
A) quantitative
Step-by-step explanation:
A data that can be counted or expressed numerically constitute quantitative data. Quantitative data collection method is capturing statistical data in numbers, figures, or values. Quantitative data collection usually answered the questions of “how many?”, "how much?" and “how often?” are the occurrence of a particular data. These questions are quantitative data collection methods based on numbers and mathematical calculations. Quantitative data collection methods are based on random sampling and structured data collection. Some of the quantitative data collection methods are surveys, questionnaires, quizzes, interviews and direct observation.
Water pump A, B and c could empty a pool for 6 hours, a and b pump could empty a pool for 8 hours how long (to the nearest minute) will it take to drain the pool if both pumps are used simultaneously?
Answers
Answer:
3.4286 hours or 3 hours 26 minutes
Step-by-step explanation:
Well, it is considered that there are 5 different pumps (A, B, C, a and b). Pumps A and B are not same with pumps a and b.
Let us solve it. Well, it says a and b pump could empty a pool for 8 hours. So in 1 hour, pumps a and b empty 1/8 part of the pool.
And pumps A, B and C could empty a pool for 6 hours. Then A, B and C pumps empty 1/6 part of pool in 1 hour.
5 pumps (A, B, C, a and b) altogether can empty 7/24 parts (1/6+1/8=7/24) of a pool in 1 hour.
To drain whole pool, it will take 24/7=3.4286 hours or 3 hours 26 minutes.
A circle has a radius of 5 inches (What is the measure, in radians, of this central angle?
Answers
Answer:
Step-by-step explanation:
Given
Circle has radius [tex]r=5 in.[/tex]
Area of the sector is given by
[tex]A_s=\frac{\theta }{2\pi }\times \pi r^2[/tex]
if [tex]A_s[/tex] is one-sixth of area of circle then
[tex]A_s=\frac{\pi r^2}{6}[/tex]
[tex]\frac{\pi r^2}{6}=\frac{\theta }{2\pi }\times \pi r^2[/tex]
[tex]\theta =\frac{2\pi }{6}=\frac{\pi }{3}\ radian[/tex]
If [tex]A_s[/tex] is one-fourth of area of circle then
[tex]A_s=\frac{\pi r^2}{4}[/tex]
[tex]\theta =\frac{2\pi }{4}[/tex]
[tex]\theta =\frac{\pi }{2}[/tex]
Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?
Answers
Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.
Let x represent the number of boxes of cookies bought by Kendal.
Each box has 12 cookies, hence:
number of cookies = 12x
Kendal brings 60 cookies to the party. She keeps 2 boxes for herself. To find the number of boxes we use:
12x = 60 + 12(2)
12x = 84
x = 7
Therefore Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.
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Final answer:
To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. The equation (x - 2) * 12 = 60 can be used to find the number of boxes Kendal bought.
Explanation:
To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. Kendal initially buys x boxes of cookies. Each box contains 12 cookies. She decides to keep two boxes for herself and brings 60 cookies to the party.
The number of cookies Kendal brings to the party can be calculated by multiplying the number of boxes she bought minus the number of boxes she kept for herself by the number of cookies in each box. So, the equation to find x would be:
(x - 2) * 12 = 60
Solving this equation will give us the value of x, which represents the number of boxes Kendal bought.
Two trains leave a town at the same time heading in opposite directions. One train is traveling 12 mph faster than the other. After two hours, they are 232 miles apart. What is the average speed of each train?
Answers
Answer:
Step-by-step explanation:
I'm going to paint you a picture in words of what this looks like on paper. We have a train leaving from a point on your paper heading straight west. We have another train leaving from the same point on your paper heading straight east. This is the "opposite directions" that your problem gives you.
Now let's make a table:
distance = rate * time
Train 1
Train 2
We will fill in this table from the info in the problem then refer back to our drawing. It says that one train is traveling 12 mph faster than the other train. We don't know how fast "the other train" is going, so let's call that rate r. If the first train is travelin 12 mph faster, that rate is r + 12. Let's put that into the table
distance = rate * time
Train 1 r
Train 2 (r + 12)
Then it says "after 2 hours", so the time for both trains is 2 hours:
distance = rate * time
Train 1 r * 2
Train 2 (r + 12) * 2
Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r. The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24. The distance between them (which is also the length of the whole entire arrow) is 232. Thus:
2r + 2r + 24 = 232 and
4r = 208 so
r = 52
This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph
Answer: its A ^3^❤
Step-by-step explanation:
that guy above me probably got yall confused
Suppose that y varies directly as the square root of x, and that y=21 when x=361. What is y when x=247? (Round off your answer to 2 decimal places.)
Answers
Answer:
17.37
Step-by-step explanation:
y varies inversely as the square root of x
Mathematically:
y = k.root x
We first find k here
To find k, we were made to know that y is 21 and x = 361
k = y/root.x
k = 21/root. 361
k = 21/19
now what is y when x = 247
From y = k.root x
y = 21/19 * root 247
y= 21/19 * 15.72
y = 17.37
Sales variances may be computed in a manner similar to cost variances–that is, computing both price and volume variances.
Answers
Answer:
The answer is True.
Step-by-step explanation:
Sales variance is computed in same manner as cost variance that is computing both price and volume variance. However interpretation of end result will not be same. For example in material price variance if
A = actual purchase price = $ 4, B = standard purchase price= $ 5 and Qt= quantity purchased = 500 units then
Material price varaince = 500 (5-4) = 500,
This gives us favourable price variance of 500 dollars. However in sales price variance if
A = actual sales price = $ 4, B = standard sale price= $ 5 and Qt= quantity sold = 500 units then
Sale price varaince = 500 (5-4) = (500)
This gives us unfavourable sales price variance of 500 dollars.
This show that formulas to compute variances are same but sale price decrease give us un favorable variance and cost price decrease gives us favorable price variance and vice versa.
What is the solution for t in the equation?
Answers
Answer:
The answer to your question is letter C. [tex]t = \frac{30}{7}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} t - \frac{1}{5} t = 2[/tex]
[tex]\frac{10t - 3t}{15} = 2[/tex]
[tex]\frac{7t}{15} = 2[/tex]
7t = 30
[tex]t = \frac{30}{7}[/tex]
Answer:
14.5
Step-by-step explanation:
PLS MARK BRAINLIEST
A Chinese restaurant has a large goldfish pond. Suppose that an inlet pipe and a hose together can fill the pone in 9 hours. The inlet pipe alone can Complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job aloneThe time that the hose can complete the job alone is______ hour The time that the inlet pipe can complete the job alone is______ hours.
Answers
Answer:
The time that the hose can complete the job alone is 18.513 hour.
The time that the inlet pipe can complete the job alone is 17.513 hours.
Step-by-step explanation:
Let the number of hours required to fill the pond by hose alone = x
Then the number of hours required to fill the pond by inlet pipe alone = x-1
This means that in 1 hour, the hose alone can fill 1/x of the pond.
Similarly, in 1 hour, the inlet pipe can fill 1/(x-1) if the pond.
Taken together,in 1 hour, the hose and inlet pipe can together fill:
[tex]\[\frac{1}{x} + \frac{1}{(x-1)}\][/tex] of the pond.
But this actually corresponds to 1/9 of the pond.
[tex]\[\frac{1}{x} + \frac{1}{(x-1)} = \frac{1}{9}\][/tex]
Solving:
[tex]\[\frac{x-1+x}{x(x-1)} = \frac{1}{9}\][/tex]
=> [tex]\[18x-9 = x^{2}-x\] [/tex]
=> [tex]\[x^{2}-19x+9=0\][/tex]
=> x= 18.513,0.486 ( roots of the quadratic equation)
Of these values, x=18.513 is relevant since x-1 must be non-negative.
So, the number of hours required to fill the pond by hose alone is 18.513 hours
Similarly, the number of hours required to fill the pond by inlet pipe alone is 17.513 hours
The time that the hose can complete the job alone is (-9 + √(109))/18 hour. The time that the inlet pipe can complete the job alone is (-9 + √(109))/18 + 1 hours.
Explanation:Let x be the time it takes for the hose alone to complete the job. Therefore, the inlet pipe can complete the job in x + 1 hour.
From the given information, we know that the inlet pipe and the hose together can fill the pond in 9 hours.
Using the formula for work done, we can set up the following equation:
1/((x + 1) + 1/((1/x)) = 1/9
Simplifying the equation, we get:
1/(x + 1) + x = 1/9
Multiplying all terms by 9(x + 1) to eliminate the fractions, we get:
9 + 9x(x + 1) = (x + 1)
Simplifying further, we get:
9 + 9x(x + 1) = (x + 1)
9x^2 + 9x - 7 = 0
Using the quadratic formula, we can solve for x:
x = (-b ± √(b^2 - 4ac))/(2a) = (-9 ± √(9^2 - 4(-7)))/(2(9))
Simplifying, we get:
x = (-9 ± √(81 + 28))/18 = (-9 ± √(109))/18
Since the time cannot be negative, we take the positive square root:
x = (-9 + √(109))/18
Therefore, the time that the hose can complete the job alone is (-9 + √(109))/18 hour.
The time that the inlet pipe can complete the job alone is (x + 1) = (-9 + √(109))/18 + 1 hours.
Six hundred chances are sold at $3 apiece for a raffle. There is a grand prize of $700, two second prizes of $200, and five third prizes of $50. First calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair.
Answers
Answer:
Expected net gain is -$0.75. Not a fair game. Appropriate price is $2.25.
Step-by-step explanation:
There is 1 in 600 chance to win the grand price (1/600)
There are 2 in 600 chance to win the 2nd price (2/600 = 1/300)
There are 5 in 600 chance to win the 3rd price (5/600 = 1/120)
We can use these probability to calculate the expected gain from this game
[tex]E_g = 700\frac{1}{600} + 200*\frac{1}{300} + 50*\frac{1}{120} = \$2.25[/tex]
Since the cost to play is $3, the expected net gain from this game is
$2.25 - $3 = -$0.75
So this game is not fair as the player is losing money. The appropriate price should instead be $2.25
The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.
Calculate the total amount collected from selling all tickets: 600 tickets × $3 = $1800.Calculate the expected value by taking into account the probabilities of winning and the respective prizes: ($700 × 1/600) + ($200 × 2/600) + ($50 × 5/600) = $1.91.Determining Fairness:
The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.
welp! help! brainly deleted my last question so here's this!
Answers
Answer:
Part 1) [tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]
Part 2) [tex]\frac{a}{b}=\frac{2}{3}[/tex]
Part 3) [tex]\frac{a^3}{b^3}=\frac{8}{27}[/tex]
Step-by-step explanation:
Part 1) Find the ratio Area I/Area II
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
The ratio of the areas is equal to divide the surface area cylinder I by the surface area cylinder II
Let
a^2 -----> the surface area cylinder I
b^2 ----> the surface area cylinder II
we have
[tex]a^2= 8\pi\ in^2[/tex]
[tex]b^2= 18\pi\ in^2[/tex]
Find the ratio
[tex]\frac{a^2}{b^2}=\frac{8\pi }{18\pi}[/tex]
Simplify
[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]
That means
[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex] --->[tex]4b^2=9a^2[/tex]
Four times area cylinder II is equal to nine times the surface area of cylinder I.
Part 2) Find the ratio a/b
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor.
In this problem
[tex]\frac{r_1}{r_2}=\frac{h_1}{h_2}=\frac{a}{b}[/tex] ----> scale factor
we have
[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]
so
square root both sides
[tex]\frac{a}{b}=\frac{2}{3}[/tex]
That means
[tex]\frac{r_1}{r_2}=\frac{2}{3}[/tex] --->[tex]2r_2=3r_1[/tex]
Two times radius cylinder II (r_2) is equal to three times radius cylinder I (r_1)
[tex]\frac{h_1}{h_2}=\frac{2}{3}[/tex] --->[tex]2h_2=3h_1[/tex]
Two times height cylinder II is equal to three times height cylinder I
Part 3) Find the ratio Volume I/Volume II
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
we have
[tex]\frac{a}{b}=\frac{2}{3}[/tex] ----> scale factor
[tex]\frac{Volume\ I}{Volume\ II}=\frac{a^3}{b^3}[/tex]
substitute the values
[tex]\frac{Volume\ I}{Volume\ II}=\frac{2^3}{3^3}[/tex]
[tex]\frac{Volume\ I}{Volume\ II}=\frac{8}{27}[/tex]
[tex]8Volume\ II=27Volume\ I[/tex]
8 times volume cylinder II is equal to 27 times volume cylinder I
The manager of an industrial plant is planning to buy a new machine. For each day’s operation, the number of repairs X, that the machine needs is a Poisson random variable with mean 0.96 repairs per day. The daily cost of operating the machine is C = 160 + 40X2 . Find the expected value of the daily cost of operating the machine.
Answers
Answer: Expected value of the daily cost of operating the machine is 235.264.
Step-by-step explanation:
Since we have given that
E[x]= 0.96 repairs per day
And Var[x] = 0.96 repairs per day.
[tex]C=160+40x^2[/tex]
[tex]E[c]=160+40E[x^2]\\\\E[c]=160+40(Var[x]+(E[x])^2)\\\\E[c]=160+40(0.96+0.96^2)\\\\E[c]=235.264[/tex]
Hence, Expected value of the daily cost of operating the machine is 235.264.
The expected value of the daily cost of operating the machine is $235.264.
Explanation:To find the expected value of the daily cost of operating the machine, we need to calculate the expected value of C = 160 + 40X^2, where X is the number of repairs the machine needs per day. Since X follows a Poisson distribution with a mean of 0.96, we can use the formula for the expected value of a function of a random variable:
E(C) = E(160 + 40X^2) = 160 + 40E(X^2)
To calculate E(X^2), we need to find the variance of X first.
The variance of X is Var(X) = λ = 0.96.
Then, E(X^2) = Var(X) + [E(X)]^2 = 0.96 + (0.96)^2 = 0.96 + 0.9216 = 1.8816.
Now, we can calculate the expected value of the daily cost:
E(C) = 160 + 40E(X^2) = 160 + 40(1.8816) = 160 + 75.264 = 235.264.
Therefore, the expected value of the daily cost of operating the machine is $235.264.
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Given the function h(x) = 3(2)x, Section A is from x = 1 to x = 2
and Section B is from x = 3 to x = 4.
Part A: Find the average rate of change of each section.
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.
Answers
Answer:
A: 6 and 24
B: 4 times as great; the rate of change increases exponentially
Step-by-step explanation:
Part A: The average rate of change on the interval [a, b] is given by ...
average rate of change = (h(b) -h(a))/(b -a)
On the interval [1, 2], the rate of change is ...
(h(2) -h(1))/(2 -1) = (12 -6)/1 = 6
On the interval [3, 4], the rate of change is ...
(h(4) -h(3))/(4 -3) = (48 -24)/1 = 24
For Section A, the average rate of change is 6; for Section B, the average rate of change is 24.
__
Part B: The ratio of the rates of change on the two intervals is ...
(RoC on [3,4]) / (RoC on [1,2]) = 24/6 = 4
The average rate of change of Section B is 4 times that of Section A.
__
The rate of change is exponentially increasing, so an interval of the same width that starts at "d" units more than the previous one will have a rate of change that is 2^d times as much.
An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4H, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct the sample space S and then find the probability of getting an even number on the die followed by one head. 3/18 6/18 3/12 6/12
Answers
Answer:
[tex]\Omega = \{ 1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T,\\5HH , 5HT, 5TH, 5TT, 6H, 6T \}[/tex]
The probability is 3/12. The third option is correct.
Step-by-step explanation:
The sample space is
[tex]\Omega = \{ 1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T,\\5HH , 5HT, 5TH, 5TT, 6H, 6T \}[/tex]
Note that this sample space is not equally probable.
The probability of getting a given number followed is the probability of getting an even number from the 6 numbers (3/6) multiplied by the probability of getting a head after getting that even number, that is 1/2, because is equally probable to get heads or tails from one single coin toss (note that we are assuming that the dice was even, thats why there is a single coin toss).
Therefore, the probability of getting an even number and a head is
P( D in {2,4,6} , H = 1) = P(D in {2,4,6}) * P(H=1 | D in {2,4,6}) = 3/6 * 1/2 = 3/12.
The sample space S can be constructed by listing all possible outcomes. The probability of getting an even number on the die followed by one head is 1/4.
Explanation:The sample space S can be constructed by listing all possible outcomes. Since there are 6 possible outcomes for the die and 2 possible outcomes for the coin flip, the total number of outcomes is 6 * 2 = 12. The sample space S is {1HH, 1HTT, 2H, 2HTT, 3HH, 3HT, 4H, 4HTT, 5HH, 5HTT, 6H, 6HTT}.
The probability of getting an even number on the die followed by one head can be found by counting the number of favorable outcomes (even number on the die followed by one head) and dividing it by the total number of outcomes. From the sample space, we can see that there are 3 favorable outcomes: 2H, 4H, and 6H. Therefore, the probability is 3/12, which can be simplified to 1/4.
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The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekendis $600 or less. Amember of the hotel’s accounting staff noticed that the total chargesfor guest bills have been increasing in recent months. The accountant will use a sample ofweekend guest bills to test the manager’s claim.a. Which form of the hypotheses should be used to test the manager’s claim? Explain.$H0:μ≥600Ha:μ<600H0:μ≤600Ha:μ>600H0:μ=600Ha:μ≠600$b. What conclusion is appropriate when H0 cannot be rejected?c. What conclusion is appropriate when H0 can be rejected?
Answers
Answer:
[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]
Step-by-step explanation:
We are given the following in the question:
Manager's claim: The mean guest bill for a weekend is $600 or less.
A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months.
A sample of weekend guest bills were collected to test the manager’s claim.
We design the null and alternate hypothesis in the following manner:
[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]
Conclusion when null hypothesis cannot be rejected:
When we fail to reject the null hypothesis and accept the null hypothesis, thus, we have enough evidence to support the manager's claim that the mean guest bill for a weekend is $600 or less.
Conclusion when null hypothesis can be rejected:
When the null hypothesis is rejected, we accept the alternate hypothesis.
Thus, there are not sufficient evidence to support the manager's claim that the mean guest bill for a weekend is $600 or less.
The ratio of corresponding side lengths of two similar MP3 players is 4:3. The area of the larger MP3 player is 8 square inches. What is the area of the smaller MP3 player?
Answers
The area of smaller mp3 player is 4.5 square inches
Solution:
Given that ratio of corresponding side lengths of two similar MP3 players is 4:3
The area of the larger MP3 player is 8 square inches
To find: area of the smaller MP3 player
If two MP3 players are similar, then their corresponding sides are proportional.
To find the area ratios, raise the side length ratio to the second power
[tex]\frac{\text {area of larger mp3}}{\text {area of smaller mp3}}=\left(\frac{4}{3}\right)^{2}[/tex]
From given information,
area of larger mp3 = 8 square inches
Let the area of smaller mp3 = x
So the above ratio becomes,
[tex]\frac{8}{x}=\left(\frac{4}{3}\right)^{2}\\\\\frac{8}{x} = \frac{16}{9}\\\\16x = 9 \times 8\\\\16x = 72\\\\x = 4.5[/tex]
Thus the area of smaller mp3 player is 4.5 square inches
Final answer:
The area of the smaller MP3 player is 128/9 square inches.
Explanation:
The area of the larger MP3 player is 8 square inches and the ratio of corresponding side lengths of the two MP3 players is 4:3. To find the area of the smaller MP3 player, we need to use the ratio of the side lengths squared. Since the ratio is 4:3, the area ratio will be (4/3)^2 = 16/9. Given that the area of the larger MP3 player is 8 square inches, we can find the area of the smaller MP3 player by multiplying 8 by the area ratio: (8) * (16/9) = 128/9 square inches.
Which of the following is the simple interest paid on a loan of $354 at 6% for six months?
$12.74
$12.47
$10.26
$10.62
Answers
Answer:
12.47 is the correct answer