Answers
Answer:
The slope of the line tangent to the function at x = 1 is 2.01 ≅2.Step-by-step explanation:
Using the formula of derivative, it can be easily shown that, [tex]\frac{d f(x)}{dx} = 2[/tex] where [tex]f(x) = x^{2}[/tex].
Here we need to show that as per the instructions in the given table.
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = [tex](1 + 0.01)^{2} - 1^{2} = 0.0201[/tex].
In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.
Hence, dividing Δy by Δx, we get, [tex]\frac{0.0201}{0.01} = 2.01[/tex].
Let's examine this taking a smaller value.
If we take Δx = 0.001, then Δy = [tex]1.001^{2} - 1^{2} = 0.002001[/tex].
Thus, [tex]\frac{0.002001}{0.001} = 2.001[/tex].
The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.
We can see here that the slope of the line tangent to the function at x = 1 is 2.001 ≅ 2.
How we arrived at the solution?We can use the formula of derivative: [tex]\frac{df(x)}{dx} = 2[/tex]
Looking at the instructions in the given table, we have:
Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = (1 + 0.01)² - 1² = 0.0201
In the above written equation, x = 1 because we need to find the slope of the line tangent at x = 1.
Thus, Δy divided by Δx, we get, 0.0201/0.01 = 2.01
If we take Δx = 0.001, then Δy = 1.001² - 1² = 0.002001
So, we have: 0.002001/0.001 = 2.001
We can see here that the more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.
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Related Questions
An atomic nucleus has a charge of +40e. What is the magnitude of the electric field at a distance of 1.0 m from the center of the nucleus?
Answers
Answer:
[tex]E=5.76\times 10^{-8}N/C[/tex]
Step-by-step explanation:
We are given that
Charge of atomic nucleus,q=+40 e=[tex]40\times 1.6\times 10^{-19}C[/tex]
Because
1 e=[tex]1.6\times 10^{-19} C[/tex]
Charge of atomic nucleus=[tex]64\times 10^{-19}C[/tex]
Distance of charge form the center of nucleus=r=1 m
We have to find the magnitude of electric field at distance r
[tex]E=\frac{Kq}{r^2}[/tex]
Where K=[tex]9\times 10^9Nm^2/C^2[/tex]
Using the formula
[tex]E=\frac{9\times 10^9\times 64\times 10^{-19}}{1}=576\times 10^{-10}N/C[/tex]
[tex]E=\frac{576}{100}\times 10^2\times 10^{-10}=5.76\times 10^{2-10}=5.76\times 10^{-8}N/C[/tex]
Using identity[tex]a^x\cdot a^y=a^{x+y}[/tex]
Hence, the magnitude of electric field=[tex]E=5.76\times 10^{-8}N/C[/tex]
General Motors wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 30 customers and asks them about their level of satisfaction with the company. What type of sampling is used? Cluster Convenience Simple random Systematic Stratified
Answers
Answer: Simple random
Step-by-step explanation:
Since , the company randomly selects customers and asks them about their level of satisfaction with the company.
So the chances for each customer to get selected are equal.
This technique of sampling is known as simple random sampling .
Definition:
A simple random sampling is a sampling technique in which the researcher randomly selects individuals from the whole population of interest for his sample.Here , the probability for each individual to get selected is equal as [tex]\dfrac{1}{N}[/tex] , where N = Population size.
In the rest of sampling method (convenience , systematic , stratified and cluster) , the individuals in the population do not have equal chances to get selected. .
The type of sampling used is Cluster Sampling.
Explanation:The type of sampling used in this scenario is Cluster Sampling.
Cluster sampling involves dividing the population into smaller groups or clusters, and then selecting a random sample of clusters to survey.
In this case, the customers are grouped based on their respective clusters in the customer database, and then a random sample of 30 clusters is selected to participate in the satisfaction survey.
The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for e ≤ t ≤ 2e?
Answers
Answer:
[tex]V_{avg} = \frac{ln2}{e} = 0.255fts^{-1}[/tex]
Step-by-step explanation:
The question asks for the average velocity and not the instantaneous velocity (which would have meant to differentiate). So, the right formula is
[tex]V_{avg} = \frac{s(t_{2}) - s(t_{1} ) }{t_{2} -t_{1} } =[/tex]
From the question, [tex]t_{1}[/tex] corresponds to e seconds and [tex]t_{2}[/tex] corresponds to 2e seconds. So, we have
[tex]V_{avg} = \frac{ln(2e) - ln(e)}{2e - e}[/tex]
One of the laws of logarithms says that
[tex]ln(\frac{a}{b} )= ln(a) - ln(b). \\\\ Therefore, ln(2e) - ln(e) = ln(\frac{2e}{e} ) = ln(2)[/tex]
[tex]V_{avg} = \frac{ln(2)}{e} = 0.2550fts^{-1}[/tex] ≅ [tex]0.255fts^{-1}[/tex]
3.) Fill in the blank.
___ + 1 = sec^2 0
A.) 1
B.) tan^2 0
C.) -cos^2 0
D.) 0
E.) sec^2 0
Answers
Answer:
The answer to your question is tan²Ф
Step-by-step explanation:
Trigonometric identities are equalities that relate trigonometric functions and are true for every value of it. There are many trigonometric functions and are useful in trigonometry.
The trigonometric identity that is the answer to this question is tan²Ф.
tan²Ф + 1 = sec²
CHECK MY ANSWERS ASAP
2. which equation is equivalent to -3x+y=5
y=5 - 3x
y=-3x -5 *
y=5+3x
y=3x-5
3. -5x+5= -40?
-15
9 *
7
-65
* is my answer
Answers
Question 1:
For this case we must rewrite the following equation:
[tex]-3x + y = 5[/tex]
If we add 3x to both sides of the equation we have:
[tex]y = 5 + 3x[/tex]
Thus, we have that an equivalent expression is option C.
Answer:
Option C
[tex]y = 5 + 3x[/tex]
Question 2:
For this case we must solve the following equation:
[tex]-5x + 5 = -40[/tex]
Subtracting 5 from both sides of the equation we have:
[tex]-5x = -40-5\\-5x = -45[/tex]
Dividing between -5 on both sides of the equation we have:
[tex]x = \frac {-45} {- 5}\\x = 9[/tex]
Answer:
Option B
A pizza factory has come out with two kinds of pizzas.A square pizza of side 45 cm costs rs.450 and a circular pizza of diameeter 50 cm costs rs.480.Which pizza is a better deal
Answers
Answer:
The answer to your question is the Square pizza is a better deal.
Step-by-step explanation:
Data
Square pizza
side = 45 cm
cost = 450
Circular pizza
diameter = 50 cm
cost = 480
Process
1.- To solve this problem calculate the area of both pizzas
Area square pizza = side x side
= 45 x 45
= 2025 cm ²
Area of circular pizza = π(50/2)²
= 1962.5 cm²
2.- Compare the area of the pizza to its cost
Square pizza = 2025 / 450 = 4.5
Circular pizza = 1962.5 / 480 = 4.1
From this data we conclude that the square pizza is a better deal.
(30 Points, please explain your answer)
Data were collected and showed an increase in ice cream sales as the weather gets warmer.
Which of the following best describes this situation?
Based on the data, this is an example of correlation.
Based on the data, this is an example of causation.
Based on the data, this is not an example of causation or correlation.
Answers
Answer:
B: Based on the data, this is an example of correlation.
Step-by-step explanation:
It's the correct answer because there somewhat related and as the ice cream trucks get more sales the weather gets warmer. They both have a positive increase.
Based on the data, this is an example of correlation and causation. Option A is correct
Correlation is defined as the two things depends on each other.
Here,
People would like to buy ice cream in warm weather this statement is correlation and causation is people would like to by ice cream cause the increase in temperature.
Thus, Based on the data, this is an example of correlation and causation.
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Given the equation y = 4x - 3.A) If x increases by 1 unit, what is the corresponding change in y? B) If x decreases by 5 units, what is the corresponding change in y?
Answers
A) When x increases by 1 unit, y increases by 4 units.
B) When x decreases by 5 units, y decreases by 20 units.
Use the concept of linear equation defined as:
The equation having degree one is called a linear equation.
The point-slope of the linear equation is:
y = mx + c
The given equation is:
y = 4x - 3
A) To find the corresponding change in y when x increases by 1 unit,
Use the given equation y = 4x - 3.
By substituting x+1 in place of x, we get
y = 4(x+1) - 3.
Simplifying this expression,
y = 4x + 4 - 3,
y = 4x + 1.
Comparing this equation with the original equation,
That the coefficient of x is the same (4),
Which means that the rate of change remains constant.
Therefore, when x increases by 1 unit, y will increase by 4 units.
B) Similarly, to find the corresponding change in y when x decreases by 5 units,
Substitute x-5 in place of x in the original equation.
This gives us y = 4(x-5) - 3.
Simplifying further, we get
y = 4x - 20 - 3,
y = 4x - 23.
Comparing this equation with the original equation,
Again the coefficient of x remains the same (4), indicating a constant rate of change.
Therefore, when x decreases by 5 units, y will decrease by 20 units.
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Final answer:
For the equation y = 4x - 3, an increase of x by 1 unit results in an increase of y by 4 units, and a decrease of x by 5 units results in a decrease of y by 20 units, due to the slope of the line being 4.
Explanation:
The equation in question is y = 4x - 3.
A) Change in y when x increases by 1 unit:
For the linear equation given, the coefficient in front of x represents the slope of the line, which is 4. This indicates that for every 1 unit increase in x, y will increase by 4 units (since the slope is the rate of change of y with respect to x). Therefore, if x increases by 1 unit, y will increase by 4 units.
B) Change in y when x decreases by 5 units:
If x decreases by 5 units, we again use the slope of the line to determine the change in y. Since the slope is 4, a decrease in x by 5 units will result in a decrease in y by 20 units (5 units × 4 = 20 units).
Mary the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 7 clients who did Plan A and 9 who did Plan B. On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Mary trained her Wednesday clients for a total of 12 hours and her Thursday clients for a total of 6 hours. How long does each of the workout plans last?
Answers
Mary's Plan A and Plan B workout sessions both last 0.75 hours, or 45 minutes each. This was determined by setting up a system of equations based on the number of clients and total hours trained on Wednesday and Thursday, and solving for the duration of each plan.
To determine how long each of Mary's workout plans lasts, we need to set up a system of equations based on the information given. Let Plan A be x hours per session, and Plan B be y hours per session.
On Wednesday, Mary had 7 clients who did Plan A and 9 clients who did Plan B for a total of 12 hours. Thus, we have the equation:
7x + 9y = 12.
On Thursday, there were 5 clients who did Plan A and 3 who did Plan B for a total of 6 hours, leading to the equation:
5x + 3y = 6.
We can now solve the system of equations. Multiplying the second equation by 3 gives us:
7x + 9y = 12
15x + 9y = 18
Subtracting the first equation from the second equation, we get:
8x = 6
x = 6÷8
x = 0.75 hours (or 45 minutes).
Now, using the value of x, we can solve for y in either equation. We'll use the first equation for simplicity:
7(0.75) + 9y = 12
5.25 + 9y = 12
9y = 12 - 5.25
9y = 6.75
y = 6.75/9
y = 0.75 hours (or 45 minutes).
Therefore, both Plan A and Plan B last 0.75 hours, or 45 minutes, per session.
The rectangle ABCD is centered at the origin. C has the coordinates (W-V). Determine the coordinates of A, B, and D.
A. Al-W, -V), B(-W, V), D(W, V)
B. Al-W,-V), B(w,V), D(-W,V)
C. A(W, V), B(-W,-V), D(-W,-1)
D. A(-W, V), B(W,V), D(-W,-V)
Answers
Answer:
Option D.Step-by-step explanation:
The co-ordinates of C is (W, -V).
The co-ordinate of C indicates that it is in the fourth quadrant.
A lies diagonally opposite to that of C, that is A is in the second quadrant.
Since, the rectangle is centered at the origin, the mod values of the points' co-ordinates will be same.
Hence, the co-ordinates of A will be (-W, V), as it is in the second quadrant.
Only the option D tells the same.
Answer:
D
Step-by-step explanation:
In a study of the effect of handedness on athletic ability, participants were divided into three groups: right-handed, left-handed, and ambidextrous. Athletic ability was measured on a 12-point scale. The dependent variable is:_______.
A. Discrete and quantitative.B. Qualitative and continous.C. Discrete and qualitative.D. Discrete and continuous.
Answers
Final answer:
The dependent variable in the study of the effect of handedness on athletic ability, which is measured on a 12-point scale, is A. Discrete and quantitative since it cumulates as whole-number scores.
Explanation:
In the study of the effect of handedness on athletic ability, the dependent variable is athletic ability measured on a 12-point scale. The nature of this variable can be determined by considering how the data behaves. Since athletic ability is rated using a numerical score on a fixed scale, it is a quantitative type of data. Furthermore, because the scores are given as whole numbers on a scale (from 1 to 12), they are discrete values, which refer to data that result from counting.
Therefore, the dependent variable in this study is A. Discrete and quantitative. This conclusion is based on the information that the athletic ability is measured numerically and cannot take infinitely varying values but is rather confined to integer values on the scale.
Theresa is planning on making a fleece blanket for her nephew. She learns that the fabric she wants to use is $7.99 per yard . Find the total cost of 4 yards of fabric
Answers
In a certain state the maximum speed permitted on freeways is 75 mi/h and the minimum speed is 50 mi/h. The fine for violating these limits is $25 for every mile per hour above the maximum speed or below the minimum speed. Express the amount of the fine F as a function of the driving speed x.
Answers
Answer: The amount of fine F as a function of the driving speed x would be
[tex]25(50-x)\ ;\ 0\leq x<50\\\\0\ ;\ 50\leq x\leq 75\\\\25(x-75)\ ;\ x> 75[/tex]
Step-by-step explanation:
Since we have given that
Maximum speed = 75 mi/hr
Minimum speed = 50 mi/hr
Fine for every mile per hour above the maximum speed or below the minimum speed = $25
So, Amount of fine for below the minimum speed would be
[tex]25(50-x)\ ;\ 0\leq x<50[/tex]
Amount of fine for above the maximum speed would be
[tex]25(x-75)\ ;\ x> 75[/tex]
There will be no fine in between the following range:
[tex]0\ ;\ 50\leq x\leq 75[/tex]
Hence, the amount of fine F as a function of the driving speed x would be
[tex]25(50-x)\ ;\ 0\leq x<50\\\\0\ ;\ 50\leq x\leq 75\\\\25(x-75)\ ;\ x> 75[/tex]
The function that represents the given situation is required.
The required function is
[tex]f(x)=\begin{cases}25(50-x) & \text{ if } 0\leq x<50 \\0 & \text{ if } 50\leq x\leq75\\25(x-75) & \text{ if } x>75 \end{cases}[/tex]
Let [tex]x[/tex] be the speed of the car
Maximum speed limit is 75 mi/h
Minimum speed limit is 50 mi/h
Any speed above the maximum speed and any speed below the minimum speed the fine is $25 dollar per mile per hour.
[tex]f(x)=25(50-x),\ 0\leq x<50[/tex]
[tex]f(x)=25(x-75),\ x>75[/tex]
There is no fine if the speed is between the given limits.
[tex]f(x)=0,\ 50\leq x\leq75[/tex]
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All the students you know taking a biology class are going to a picnic hence you concluded all students in the biology class are going for picnic This type of reasoning is an example of
a) Deduction
b) Induction
c) Inaccurate information
d) None of the above
Answers
Answer:
Induction
Step-by-step explanation:
This is an example of induction. When you take a (possibly false) conclusion according to the information you know. In this case, since you dont know of any case of a biology student not going for picnic, then you conclude that every biology student go for picnic .
It isnt deduction because the reasoning is not based on logic, rather, it is based on the partial information you know. You can argue that, since you know many students that went for a picninc, then the whole class should go to the picnic because they organized it that way, however you might need a bit more of information to reach this conclussion, for example, that the teacher went with them. Maybe, for example, a small group of students decided to go elsewhere instead.
There isnt inaccurate information here. It is incomplete, yes, but it doesnt lack accuracy: all you know is true. There isnt innacurate information.
When it is 11:00 a.m. in Riyadh, it is 4:00 p.m. in Manila. If your flight from Riyadh to Manila lasts 11 hours and 40 minutes, and you land at 2:00 a.m. on Monday (Manila time), what time was it in Riyadh when you left?
Answers
Final answer:
The departure time in Riyadh when flying to Manila can be calculated by subtracting the flight duration from the arrival time in Manila.
Explanation:
To determine the time in Riyadh when you left for Manila, we need to calculate the time difference between the two cities. We know that when it's 11:00 a.m. in Riyadh, it's 4:00 p.m. in Manila, giving us a time difference of 5 hours. Since your flight duration is 11 hours and 40 minutes, we need to subtract this time from the arrival time in Manila to find the departure time in Riyadh. Subtracting 11 hours and 40 minutes from 2:00 a.m. on Monday gives us 2:00 p.m. on Sunday. Therefore, it was 2:00 p.m. on Sunday in Riyadh when you left for Manila.
The entomologist estimates that the fourth colony of termites most likely have about 4 million termites in it. Is the entomologist estimation correct? The population of New York City is estimated at eight The population of New York City is estimated at 8(10) to the power of six people. How many colonies of true minds would be needed to represent the population of New York City?
Answers
Answer:
fyfyfiulhvt
Step-by-step explanation:
xerytuyuytref
Gayle,Irma and when'll each made a cake.Gayle used 3 1/4 cups of flour,Irma used 2 2/3 cups of flour,and wynell used 4 1/2 cups of flour.How much total flour did the three ladies use?
Answers
Answer: the total cups of flour that the three ladies used is 10 5/12 cups
Step-by-step explanation:
Gayle used 3 1/4 cups of flour.
Converting 3 1/4 cups of flour to improper fraction, it becomes 13/4 cups of flour.
Irma used 2 2/3 cups of flour. Converting 2 2/3 cups of flour to improper fraction, it becomes 8/3 cups of flour.
Wynell used 4 1/2 cups of flour. Converting 4 1/2 cups of flour to improper fraction, it becomes 9/2 cups of flour.
Therefore, the total number of cups of flour that Gayle, Wynell and Irma used would be
13/4 + 8/3 + 9/2 = (39 + 32 + 54)/12
= 125/12 = 10 5/12 cups of flour.
Answer:
The three ladies used 10 5/12 of flour total!
Step-by-step explanation:
A 28ft boat ramp makes a 10 degree angle with water. What is the height of the ramp above the water at the highest point?
Answers
Answer: the height of the ramp above the water at the highest point is 2.0832ft
Step-by-step explanation:
The ramp makes an angle of 10 degrees with water and forms a right angle triangle.
The height of the ramp above the water at the highest point represents the opposite side of the right angle triangle.
The length of the ramp represents the hypotenuse of the right angle triangle. Therefore, to determine the height of the ramp above the water at the highest point, h , we would apply the Sine trigonometric ratio.
Sin θ = opposite side/hypotenuse. Therefore,
Sin 10 = h/12
h = 12Sin10 = 12 × 0.1736
h = 2.0832
The height of the ramp above the water at the highest point is approximately 4.87ft.
Explanation:To find the height of the ramp above the water at the highest point, we can use trigonometry. The height of the ramp is represented by the opposite side of the angle, while the adjacent side is the length of the ramp. We can use the formula: Opposite = Adjacent * tan(Angle). Plugging in the values, we get: Opposite = 28ft * tan(10 degrees). Evaluating this expression on a calculator, we find that the height of the ramp above the water at the highest point is approximately 4.87ft.
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A manufacturing operations consists of 13 operations. However, five of the 13 machining operations must be completed before any of the remaining operations can begin. Within each of these two sets, operations can be completed in any order. How many different production sequences are possible?
Answers
Answer: Possible production sequences= 4,838,400
Step-by-step explanation: Total machine operation =13
Machines divided into 2 sets.
Set 1= 5 machines
Set 1=5!= 5×4×3×2×1=120 ways
Set 2= 13-5 =8 machines
Set 2= 8!=8×7×6×5×4×3×2×1=40,320 ways
Total number of ways to sort the two sets =120×40,320= 4,838,400
Select all polynomials that are divisible by (x-1).
Choose all answers that apply:
*A(x)=3x^3+2x^2-x
*B(x)=5x^3-4x^2-x
*C(x)=2x^3-3x^2+2x-1
*D(x)=x^3+2x^2+3x+2
Answers
Answer:
The answer to your question is below
Step-by-step explanation:
*A(x)=3x³ + 2x² - x This polynomial is not divisible by (x - 1)
Factor completely 3x(x + 1)(3x - 1)
*B(x)=5x³ - 4x² - x This polynomial is divisible by (x - 1)
factor completely 3x(x - 1)(5x + 1)
*C(x)=2x³ - 3x² + 2x - 1 This polynomial is divisible by (x - 1)
Synthetic division 2 - 3 + 2 -1 1
2 -1 1
2 -1 1 0
*D(x)=x³ + 2x² + 3x + 2 This polynomial is not divisible by (x - 1)
Synthetic division 1 2 3 2 1
1 3 6
1 3 6 8
Answer:
B(x) and C(x)
Step-by-step explanation:
B(x) and C(x)
Select the graph of the solution set that would represent the following expression. 3(x - 2) = 5 (x + 1)
Answers
The solution set is [tex]x=-\frac{11}{2}[/tex]
Step-by-step explanation:
The given expression is [tex]3(x-2)=5(x+1)[/tex]
Multiplying the terms, we get,
[tex]3x-6=5x+5[/tex]
Subtracting 3x from both sides of the equation,
[tex]-6=2x+5[/tex]
Subtracting 5 from both sides of the equation,
[tex]-11=2x[/tex]
Dividing both sides by 2, we get,
[tex]-\frac{11}{2} =x[/tex]
Thus, the solution set is [tex]x=-\frac{11}{2}[/tex]
The graph the solution set [tex]x=-\frac{11}{2}[/tex] is to plot this value in the number line.
The graph for the solution set [tex]x=-\frac{11}{2}[/tex] is attached below:
Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles. (Enter your answers in set notation. Enter EMPTY or ∅ for the empty set.)(a) List all outcomes in the event A that all three vehicles go in the same direction.A = (b) List all outcomes in the event B that all three vehicles take different directions.B = (c) List all outcomes in the event C that exactly two of the three vehicles turn right.C = (d) List all outcomes in the event D that exactly two vehicles go in the same direction.D = (e) List outcomes in D'.D' = List outcomes in C ∪ D.C ∪ D = List outcomes in C ∩ D.C ∩ D =
Answers
Answer:
a. A = {RRR,LLL,SSS}
b. B = {RLS, RSL, LSR, LRS, SRL, SLR}
c. C = {RRS, RRL, RSR, RLR, LRR, SRR}
d. D = {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}
e. C U D= {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}
C n D = {RRS, RRL, RSR, RLR, LRR, SRR}
Step-by-step explanation:
a..
All three vehicles go in the same direction
This means that all the three vehicles either go straight, or right or left at the same time.
So, A { {RRR, LLL, SSS}
b..
All three vehicles take different directions
Thus means that all the vehicle take different routes
If a vehicle takes the the straight direction, the other 2 vehicles take right and left directions respectively
So, B = {RLS, RSL, LSR, LRS, SRL, SLR}
c..
Exactly two of the three vehicles turn right
This means that two vehicles take right direction while the last vehicle either tske the straight route or left route.
C = {RRS, RRL, RSR, RLR, LRR, SRR}
d..
Exactly two vehicles go in the same direction.
The means that if two vehicles pass straight direction then the third vehicle takes either the right or left direction.
Also, if two vehicles pass right direction, the third vehicle either takes the left direction or straight direction
Lastly, if two vehicles pass left direction then the third vehicle either pass the straight direction or right direction.
D = {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}
e. C U D = the union of items in C and D without repetition
So,
C U D= {RRS, RRL, RSR, RLR, LRR, SRR, SSR, SSL, SRS, SLS, LSS, RSS, LLS, LLR, LRL, LSL, SLL, RLL}
C n D = Common items in C and D
C n D = {RRS, RRL, RSR, RLR, LRR, SRR}
List outcomes in D'.D' = List outcomes in C ∪ D.C ∪ D = List outcomes in C ∩ D.C ∩ D =
The question presents various scenarios of successive vehicles choosing directions. Outcomes are determined in cases where all vehicles choose the same direction, all choose different directions, exactly two choose right, exactly two choose the same direction (any), and the negation of the latter case. The outcomes of combining these scenarios (union and intersection) are also defined.
Explanation:The events refer to the outcomes of the directions three successive vehicles could potentially take. There are three possibilities: right (R), left (L), or straight (S).
(a) Event A where all three vehicles go in the same direction, would include these outcomes: A = {RRR, LLL, SSS}.
(b) Event B where all three vehicles take different directions, would look like this: B = {RLS, RSL, LRS, LSR, SRL, SLR}.
(c) Event C where exactly two of the three vehicles turn right would include these outcomes: C = {RRS, RRL, SRR, LRR, RSR, RLR}.
(d) Event D where exactly two vehicles go in the same direction, would include these outcomes: D = {RRS, RRL, SRS, SSL, LRL, LLR, RRS, RLS, RSS, LSS, SLL, LLS, SSR, SRL, SRR, LLR, LRS, LRR}.
(e) Event D' which stands for everything that's not in event D, includes these outcomes: D' = {RLS, SLR, LRS, RSL, LSR, SRL}.
The union of events C and D, C ∪ D, combines the outcomes of both C and D, but without repetition: C ∪ D = {RRS, RRL, SRS, SSL, LRL, LLR, RRS, RLS, RSS, LSS, SLL, LLS, SSR, SRL, SRR, LLR, LRS, LRR, RSR, RLR}.
Finally, the intersection of event C and D, C ∩ D, includes only outcomes common to both C and D: C ∩ D = {RRS, RRL, SRR, LRR, RSR, RLR}.
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Evaluate the expression when x = -1 and y = 4. 9x^-5y^-2y
A) 9/64
B) 9/16
C) -9/64
D) -9/16
Answers
Answer:
The correct option is D) -9/16
Therefore the final expression when X is equal to -1 and Y is equal to 4 is
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
Step-by-step explanation:
Given:
[tex]9x^{-5}y^{-2}[/tex]
Evaluate when x = -1 and y = 4
Solution:
When x = -1 and y = 4 we hane
[tex]9x^{-5}y^{-2}=9(-1)^{-5}(4)^{-2}[/tex]
Identity we have
[tex]x^{-a}=\dfrac{1}{x^{a}}[/tex]
As we know minus sign multiplied by odd number of times the number is multiplied and the assign remain same that is minus. Therefore,
[tex](-1)^{5}=-1\times -1\times -1\times -1\times -1\\(-1)^{5}=-1[/tex]
Now using the above identity we get
[tex]9x^{-5}y^{-2}=\dfrac{9}{(-1)^{5}}\times \dfrac{1}{(4)^{2}}[/tex]
[tex]9x^{-5}y^{-2}=\dfrac{9}{-1}\times\dfrac{1}{16}[/tex]
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
Therefore the final expression when X is equal to -1 and Y is equal to 4 is
[tex]9x^{-5}y^{-2}=-\dfrac{9}{16}[/tex]
ASAP!!! help its emergent
Answers
Answer:
Step-by-step explanation:
F(x)=(5 t^2+t )x to x+3
=5((x+3)^2-x^2)+(x+3-x)
=5(x^2+6x+9-x^2)+3
=5 (6x+9)+3
=30x+48
F'(x)=30
Select the margin of error that corresponds to the sample mean that corresponds to each population: A population mean of 0.45, a standard deviation of 0.001, and margin of error of 0.5%
A)0.44
B)0.46
C)0.45
Answers
Answer:
C) 0.45
Step-by-step explanation:
Given that a population mean is 0.45, standard deviation is 0.001 and margin of error stands at 0.5% we have the following
0.45 + 0.001 = 0.451
Population mean with standard deviation is 0.451.
0.451 * 0.5% = 0.448745
We now reduce the number to two decimals and get the final marigin of error
0.45 as result
Answer:
Confirmation it is 0.45
Step-by-step explanation:
HELP! What does X equal? WILL GIVE BRAINLIEST!
Answers
Answer:
110
Step-by-step explanation:
triangle = 180° total so
180- 82 = 98
98 ÷ 2 = 49
y = 49
4 sided shape = 360° total
35 + 35 + 49 + 49 + 82 = 250
360 (total) - 250 = 110
hope this helps
40 points!! The first term of an arithmetic sequence is -12. The common difference of the sequence is 7. What is the sum of the first 30 terms of the sequence?
Answers
Answer: 2685
==========================================
Explanation:
When we want to add up the first n terms of an arithmetic sequence, the formula to use is
S = (n/2)*( 2*a+d(n-1) )
where
S = sum of the first n terms
n = number of terms
a = first term
d = common difference
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In this case,
S = unknown
n = 30
a = -12
d = 7
which means,
S = (n/2)*( 2*a + d*(n-1) )
S = (30/2)*( 2*(-12) + 7*(30-1) )
S = 15*(-24 + 7*29)
S = 15*(-24 + 203)
S = 15*(179)
S = 2685
This answer is confirmed using a spreadsheet. Basically I had the spreadsheet generate 30 terms based on a pattern I gave it of the first two terms. Then I used the "SUM" function to add up all 30 terms quickly getting 2685.
----------------------------
Side note:
Another formula we could use is
S = (n/2)*(a_1 + a_n)
where
a_1 = first term
a_n = nth term, when n = 30 this is the 30th term
The a_n part is equal to a_n = a_1 + d(n-1), and when you add this to the a_1 already in the S formula, that accounts for the 2*a_1 back in the first formula mentioned at the top of the page.
Answer:sum of the first 30 terms is 2685
Step-by-step explanation:
The formula for determining the sum of n terms of an arithmetic sequence is expressed as
Sn = n/2[2a + (n - 1)d]
Where
n represents the number of terms in the arithmetic sequence.
d represents the common difference of the terms in the arithmetic sequence.
a represents the first term of the arithmetic sequence.
From the information given,
n = 30 terms
a = - 12
d = 7
Therefore, the sum of the first 30 terms, S30 would be
S30 = 30/2[2 × - 12 + (30 - 1)7]
S30 = 15[- 24 + 203)
S30 = 15 × 179 = 2685
Feather color in budgies is determined by two different genes, Y and B, one for pigment onthe outside and one for the inside of the feather. YYBB, YyBB, or YYBb is green; yyBB or yyBbisblue; YYbb or Yybb is yellow; and yybb is white. A blue budgie is crossed with a white budgie.Which of the following results is NOT possible?
A) green offspring only
B) yellow offspring only
C) blue offspring only
D) green and yellow offspring
Answers
Answer:
Therefore, the following results are not possible:
A) green offspring only
B) yellow offspring only
D) green and yellow offspring.
Step-by-step explanation:
We know that feather color in budgies is determined by two different genes. For blue color are combinations yyBB or yyBb. For white color is combination yybb.
By combining these two colors we can not get green and yellow.
Because green and yellow colors are in this form:
Green: YYBB, YyBB, or YYBb
Yellow: YYbb or Yybb.
Therefore, the following results are not possible:
A) green offspring only
B) yellow offspring only
D) green and yellow offspring.
Amanda can spend no more than $85 to rent a car for day trip. A rental car cost 35 per day plus $20 per mile. Write and solve an inequality to find the possible distance in miles and the Amelia can drive without exceeding her budget
Answers
Answer: 2miles/ 2.5miles.
Step-by-step explanation:
If rentals for a car costs $35
subtracting this $35 from budget of $85 gives us
$85-$35= $50
By travelling one mile, we subtract $20, we're then left with
$50 - $20 = $30.
By travelling another mile, we subtract another $20, which gives
$30-$20= $10.
Since this $10 is not enough to cater for another mile, the maxmimum number of miles is 2miles.
But if allowed in halves, the $10 can cover half a mile and the longest possible distance she can travel is 2.5miles
Georgia pay $2.75 for four granola bars and one apple. Addison paid $2.25 for two granola bars and three apples find a cost of one granola bar in the cost of one apple.
Answers
The cost of one granola bar is $0.60 and cost of one apple is $0.35
Step-by-step explanation:
Let,
Cost of one granola bar = x
Cost of one apple = y
According to given statement;
4x+y=2.75 Eqn 1
2x+3y=2.25 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(2x+3y=2.25)\\4x+6y=4.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 1 from Eqn 3
[tex](4x+6y)-(4x+y)=4.50-2.75\\4x+6y-4x-y=1.75\\5y=1.75[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{1.75}{5}\\y=0.35[/tex]
Putting y=0.35 in Eqn 2
[tex]4x+0.35=2.75\\4x=2.75-0.35\\4x=2.40[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{2.4}{4}\\x=0.60[/tex]
The cost of one granola bar is $0.60 and cost of one apple is $0.35
Keywords: linear equation, elimination method
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The cost of one granola bar is $0.60, and the cost of one apple is $0.35.
To solve the problem, we need to set up a system of linear equations based on the information given:
Georgia paid $2.75 for 4 granola bars and 1 apple.
Addison paid $2.25 for 2 granola bars and 3 apples.
Let G be the cost of one granola bar and A be the cost of one apple.
4G + A = 2.75
2G + 3A = 2.25
Multiply the first equation by 3
3(4G + A = 2.75)
=> 12G + 3A = 8.25
(12G + 3A) - (2G + 3A) = 8.25 - 2.25
10G = 6
G = 0.60
Substitute the value of G back into the first equation,
4(0.60) + A = 2.75
2.40 + A = 2.75
A = 0.35
Therefore, the cost of one granola bar is $0.60 and the cost of one apple is $0.35.