Answer: Total amount invested in both accounts is $1875
Step-by-step explanation:
Let x represent the amount invested at 11%.
Let y represent the amount invested at 5%.
She invests four times as much in an account paying 11% as she does in an account paying 5%. This means that
x = 4y
The formula for determining simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents the rate of investment
T represents the time in years.
Considering the amount invested at 11%,
I = (x × 11 × 1)/100 = 0.11x
Considering the amount invested at 5%,
I = (y × 5 × 1)/100 = 0.05y
If she earns $183.75 in interest in one year from both accounts combined, it means that
0.11x + 0.05y = 183.75 - - - - - - - - - -1
Substituting x = 4y into equation 1, it becomes
0.11 × 4y + 0.05y = 183.75
0.44y + 0.05y = 183.75
0.49y = 183.75
y = 183.75/0.49
y = 375
x = 4y = 375 × 4
x = 1500
Total amount invested in both accounts is
1500 + 375 = $1875
Amy invested a total of $1875 in both simple interest accounts. She placed $375 into the account with a 5% interest rate and $1500 into the account with an 11% interest rate to achieve the total interest income of $183.75 in one year.
Explanation:Amy invests money in two simple interest accounts. One account pays 11% interest, while the other pays 5%. If she puts four times as much into the 11% account as the 5% account, we can set up the following equations to find out how much she invested altogether:
Let x represent the amount invested at 5%.Then 4x will represent the amount invested at 11%.The total interest from both accounts is $183.75 for one year.We can use the formula for simple interest which is Interest = Principal × Rate × Time, where the principal is the initial amount of money invested, the rate is the interest rate, and the time is the period of time over which the money is invested.
So, the total interest earned from both accounts is:
Interest from 5% account + Interest from 11% account = $183.75
(x × 0.05 × 1) + (4x × 0.11 × 1) = $183.75
0.05x + 0.44x = $183.75
0.49x = $183.75
Now, solve for x:
0.49x = $183.75
x = $183.75 / 0.49
x = $375
Since x represents the amount invested at 5%, Amy invested $375 in the 5% account. To find the total investment:
Total investment = x + 4x
Total investment = $375 + 4(×$375)
Total investment = $375 + $1500
Total investment = $1875
A ball is thrown 178 m upward and then falls back to earth. Neglecting air resistance, how long will it be in the air? The acceleration of gravity is 9.8 m/s 2 .
After calculating the initial velocity with which the ball was thrown upwards, the time taken for the ball to reach its peak and fall back to earth was calculated to be approximately 38 seconds.
Explanation:In order to find out how long the ball will be in the air, we are essentially dealing with an example of free fall in Physics. When the ball reaches its maximum height, its velocity will be zero and it will have spent a certain amount of time t to reach there. But the total time it will be in the air is twice this amount, as it will take the same amount of time to go up and come back down.
Using the second equation of motion, v = u + gt (where v = final velocity, u = initial velocity, g = acceleration due to gravity and t = time), when the ball reaches maximum height, its final velocity (v) is zero. If we rearrange this equation, we get t = (v - u) / -g.
As the problem doesn't state the initial velocity with which the ball is thrown upward, we need to find it first. We can do this by applying the equation of motion: v² = u² + 2gs, where s = displacement. If we set v = 0 at maximum height, the equation becomes u = √(2gs). Given s = 178 m and g = 9.8 m/s², we find u ≈ 186.26 m/s. Substituting these values into our time equation, we get t ≈ 19 seconds for the time to reach maximum height. As mentioned, the ball will take the same time to fall back, hence the total time in air will be around 38 seconds.
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Rebecca and dan are biking in a national park for three days they rode 5 3/4 hours the first day and 6 4/5 hours the second day how long do they need to ride on the third day to make their goal of biking a total of 20 hours in the park
Answer:
Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.
Step-by-step explanation:
Given:
Goal of Total number of hours of biking in park =20 hours.
Number of hours rode on first day = [tex]5\frac34 \ hrs.[/tex]
So we will convert mixed fraction into Improper fraction.
Now we can say that;
To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.
[tex]5\frac34 \ hrs.[/tex] can be Rewritten as [tex]\frac{23}{4}\ hrs[/tex]
Number of hours rode on first day = [tex]\frac{23}{4}\ hrs[/tex]
Also Given:
Number of hours rode on second day = [tex]6\frac45 \ hrs[/tex]
[tex]6\frac45 \ hrs[/tex] can be Rewritten as [tex]\frac{34}{5}\ hrs.[/tex]
Number of hours rode on second day = [tex]\frac{34}{5}\ hrs.[/tex]
We need to find Number of hours she need to ride on third day in order to achieve the goal.
Solution:
Now we can say that;
Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.
framing in equation form we get;
Number of hours she need to ride on third day = [tex]20-\frac{23}{4}-\frac{34}{5}[/tex]
Now we will use LCM to make the denominators common we get;
Number of hours she need to ride on third day = [tex]\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}[/tex]
Now denominators are common so we will solve the numerator we get;
Number of hours she need to ride on third day =[tex]\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.[/tex]
Hence Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.
Final answer:
Rebecca and Dan need to ride for 7 9/20 hours on the third day to reach their goal of biking a total of 20 hours in the national park, having already biked 5 3/4 hours on the first day and 6 4/5 hours on the second day.
Explanation:
Rebecca and Dan are biking in a national park and want to achieve a goal of biking a total of 20 hours over three days. They biked 5 3/4 hours on the first day and 6 4/5 hours on the second day. To find the time they need to bike on the third day, we first convert the hours they biked into improper fractions:
First day: 5 3/4 hours = (5×4 + 3)/4 = 23/4 hoursSecond day: 6 4/5 hours = (6×5 + 4)/5 = 34/5 hoursNext, we add these two amounts together:
(23/4) + (34/5) = (23×5 + 34×4) / (4×5) = (115 + 136) / 20 = 251/20 hours.
Now we convert 251/20 hours to a mixed number:
251/20 = 12 11/20 hours
They have biked a total of 12 11/20 hours over the first two days. Their total goal is 20 hours, so we need to subtract the time already biked from the total goal:
20 hours - 12 11/20 hours = (20×20 - 12×20 - 11)/20 = (400 - 240 - 11)/20 = 149/20 hours.
Finally, we convert 149/20 hours back to a mixed number to find out how long they need to ride on the third day:
149/20 hours = 7 9/20 hours.
So, Rebecca and Dan need to ride for 7 9/20 hours on the third day to meet their goal of biking a total of 20 hours in the park.
At Joe's Pizza a 16 inch diameter pizza and a 12-inch-diameter pizza cost the same per square inch of top surface area. If the cost of a large pizza is 9.60, what is the cost, in dollars, of the small pizza?
Answer:
5.4
Step-by-step explanation:
Surface area of the large 16 in diameter pizza is
[tex]A = \pi(d/2)^2 = \pi8^2 = 64\pi[/tex]
Cost per unit surface area is
[tex]c = \frac{9.6}{64\pi} = \frac{0.15}{\pi}[/tex]
Surface area of the small 12-in diameter pizza is
[tex]a = \pi(12/2)^2 = \pi6^2 = 36\pi[/tex]
So the total cost for that much surface area of pizza is
[tex]ac = 36\pi*\frac{0.15}{\pi} = 5.4[/tex]
Start of Questions
Write sinπ/5cosπ/8+cosπ/5sinπ/8 as a trigonometric function of one number. Keep π in your answer. Be sure to PREVIEW your answer before submitting!
Answer:
sin(13π/40)
Step-by-step explanation:
The given expression matches the pattern ...
sin(a)cos(b) +cos(a)sin(b) = sin(a+b)
Then ...
sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)
= sin(13π/40)
_____
π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)
The trigonometric expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 can be simplified to sin(13π/40) by using the sine addition formula.
Explanation:The expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 resembles the formula for the sine of a sum, sin(a+b) = sin(a)cos(b) + cos(a)sin(b). By applying this trigonometric identity, we can rewrite the expression as the sine of a single angle. Therefore, sinπ/5 cosπ/8 + cosπ/5 sinπ/8 is equivalent to sin(π/5 + π/8). To simplify it further, we must find a common denominator for the two angles, π/5 and π/8, which is 40. Thus, we get sin((8π + 5π)/40), which simplifies to sin(13π/40).
find the equation of the line that is perpendicular to y=3x and passes through the point (4,-2)
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
y = 3x
Comparing with the slope intercept form, slope = 3
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.
Therefore, the slope of the line passing through (4,-2) is - 1/3
To determine the intercept, we would substitute m = - 1/3, x = 4 and
y = -2 into y = mx + c. It becomes
- 2 = - 1/3 × 4 + c = 4/3 + c
c = - 2 + 4/3 = - 2/3
The equation becomes
y = - x/3 - 2/3
The high school debate team is developing a logo to represent their club. A scale drawing of the logo design is presented below, where each unit of the grid represents 3 inches in length. The team is printing out an enlargement of the new logo, where the enlargement has a height of 105 inches. The area of the enlargement will be inches2, which is times the size of the original scale drawing.
Answer:
c
Step-by-step explanation:
Answer:
The enlargement will be 2,250 which is 25 the times
Step-by-step explanation:
In the provided scale drawing, each unit represents 3 inches in length. Use this scale to add the real world measurements to the scale drawing as shown.
It can be seen from the figure that the total height of the scale drawing is 9 in + 3 in + 9 in = 21 in. It is given that the enlargement has a height of 105 inches. Find the scale factor between the scale drawing and the enlargement by dividing as shown.
The scale factor of 5 means that each dimension of the enlargement will be 5 times larger than the matching dimension of the scale drawing. So, the dimensions of the enlarged figure are shown below.
The logo is made up of three polygons: two triangles and one square. To find the total area of the logo, the area of each region must be found and added together.
To calculate the area of a triangle, use the formula below where b is the length of the base of the triangle and h is the height of the triangle.
To calculate the area of a square, use the formula below, where s is the length of the side of the square.
Now, calculate the areas of of the two logos.
Finally, determine how many times larger the area of the enlargement is than the scale drawing by dividing, as shown below.
Therefore, the area of the enlargement will be 2,250 inches2, which is 25 times the size of the original scale drawing.
Please help me, i am horrible at geometry.
Answer:
m<BCD is equivalent to 148*
Step-by-step explanation:
We know this due to the inscribed angle always being congruent to the angle that it inscribes. Hope this helps
Answer:
106°
Step-by-step explanation:
m arc BCD=148
∠A=1/2*148=74°
∠BCD=180-74=106°
How do you do this question?
Step-by-step explanation:
The integral is the area under the curve. When the curve is above the x-axis, the area is positive. When the curve is below the x-axis, the area is negative. The integral equals 0, so we want to find the value of b such that the area of the quarter circle is canceled out by the area of the triangle.
Area of the quarter circle is:
A = π/4 r²
A = 9/4 π
Area of the triangle is:
A = ½ bh
9/4 π = ½ (b − 3) (b − 3)
9/2 π = (b − 3)²
b − 3 = 3√(π/2)
b = 3 + 3√(π/2)
b = 6.760
Determine the point of discontinuity if it exists
v(x)=x^2-25/2x^2+13x+15
Answer:
x=-5 and x=-1.5
Step-by-step explanation:
The given function is
[tex]v(x) = \frac{{x}^{2} - 25}{2 {x}^{2} + 13x + 15} [/tex]
The points of discontinuity occurs at where the denominator is zero.
[tex]2 {x}^{2} + 13x + 15= 0[/tex]
We solve by factoring.
We first split the middle term:
[tex]2 {x}^{2} + 3x + 10x + 15= 0[/tex]
We factor by grouping:
[tex]x(2x + 3) + 5(2x + 3)= 0[/tex]
[tex](x + 5)(2x + 3) = 0[/tex]
The points of discontinuity occur at x=-5, and x=-1.5
Final answer:
The function v(x) has discontinuities at x = -3 and x = -5/2.
Explanation:
A point of discontinuity in a mathematical function refers to a location where the function fails to be continuous. In other words, it's a point at which the function exhibits a break or abrupt change in its behavior.
The point of discontinuity for the function [tex]v(x) = (x^2-25)/(2x^2+13x+15)[/tex] can be found by setting the denominator equal to zero and solving for x. In this case, the denominator factors to (x+3)(2x+5), indicating discontinuities at x = -3 and x = -5/2. These are the points where the function is not defined.
Points of discontinuity are essential to understanding the behavior and properties of functions, particularly in areas like calculus and real analysis. They are critical in identifying where a function fails to meet the criteria for continuity and in analyzing the behavior of functions in various contexts.
PLEASE HE LPPP!!! QUESTION AND ANSWERS IN PICTURE !!2
Answer:
Line ED
Explanation:
Opposite side is EF (because its opposite to the angle)
Hypotenuse side id FD (opposite of right angle)
Adjacent is the line leftover
Answer:
B
Step-by-step explanation:
Adjacent is the one with 90° and the angle, theta
ED in this case
Since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year. Predict the number of cases that will be reported in 2020 and the trend continues
Answer:
20,158 cases
Step-by-step explanation:
Let [tex]t=0[/tex] represent year 2010.
We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.
Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.
We can represent this information in an exponential decay function as:
[tex]F(t)=102,390(1-0.15)^t[/tex]
[tex]F(t)=102,390(0.85)^t[/tex]
To find number of cases in 2020, we will substitute [tex]t=10[/tex] in our decay function as:
[tex]F(10)=102,390(0.85)^{10}[/tex]
[tex]F(10)=102,390(0.1968744043407227)[/tex]
[tex]F(10)=20,157.970260446597\approx 20,158[/tex]
Therefore, 20,158 cases will be reported in 2020.
1. New Jersey Lottery Let A denote the event of placing a $1 straight bet on the New Jersey Pick 3 lottery and winning. There are 1000 different ways that you can select the three digits (with repetition allowed) in this lottery, and only one of those three-digit numbers will be the winner. What is the value of P1A2? What is the value of P1A2?
Answer:
P1A2= 0.001
P1A'2=0.999
Step-by-step explanation:
Probability = number of ways A occurs/ number of different simple events
P1(A2) =1/1000=0.001
P1A2 = 1-(1/1000)= 999/1000 = 0.999
Probabilities are used to determine the outcome of an event.
The probability of winning is 0.001
Given
[tex]n = 1000[/tex] --- ways
Only one of the 1000 digits is a winning digit.
So, the probability of winning, P(A) is:
[tex]P(A) = \frac{1}{n}[/tex]
So, we have:
[tex]P(A) = \frac{1}{1000}[/tex]
Express as a decimal
[tex]P(A) = 0.001[/tex]
Hence, the probability of winning is 0.001
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If Alex and Brandon work together, they will finish cleaning the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself?
Answer:
Alex can do the job in 60 days alone.
Step-by-step explanation:
Alex and Brandon working together, they can finish the job of cleaning the school in 15 hours. Brandon alone in 20 hours can finish the job.
So, Brandon can complete [tex]\frac{1}{20}[/tex] part of the job in one hour.
Let, Alex alone can finish the same job in x hours.
So, Alex can complete [tex]\frac{1}{x}[/tex] part of the job in one hour.
So, working together they do [tex](\frac{1}{20} + \frac{1}{x}) = \frac{x + 20}{20x}[/tex] part of the whole job in one hour.
Hence, from the conditions given we can write
[tex]\frac{x + 20}{20x} = \frac{1}{15}[/tex]
⇒ 15x + 300 = 20x
⇒ 5x = 300
⇒ x = 60 days.
Therefore, Alex can do the job in 60 days alone. (Answer)
Please assist me with this problem
Answer:
The answer to your question is 90 dB
Step-by-step explanation:
Data
I = 10⁻³
I⁰ = 10⁻¹²
Formula
Loudness = 10log ([tex]\frac{I}{Io}[/tex])
Process
1.- To solve this problem, just substitute the values in the equation and do the operations.
2.- Substitution
Loudness = 10 log [tex](\frac{10^{-3}}{10^{-12}} )[/tex]
3.- Simplify
Loudness = 10log (1 x 10⁹)
Loudness = 10(9)
Loudness = 90
a wise man once said, “ 400 reduced by 3 times my age is 163”. what is his age?
Answer:
79 years old
Step-by-step explanation:
Let his age be x
400-3x=163
400-163=3x
237=3x
Divide both side by 3
237/3 =3x/3
79=x
The man's age (x) =79 years old
Which of the following variables are qualitative and which are quantitative? If the variable is quantitative, then specify whether the variable is discrete or continuous.a. Points scored in a football game.b. Racial composition of a high school classroom.c. Heights of 15-year-olds.
Quantitative in general involves number while qualitative does not involves number. For example, you can count the point scored in a football game which is considered as quantitative. While you cannot count racial composition because it involves different quality or type.
Quantitative is further divided into two type; discrete and continuous. Discrete variable involves integers while in between two values of a continuous variable, there are an infinite number which is valid and this is not the case for discrete variables.
Qualitative is variable something that you cannot count.
Answer:
A. Points scored in a football game - Quantitative; discrete
B. Racial composition of a high school classroom - Qualitative
C. Heights of 15-year-olds - Quantitative; continuous
Points scored in a football game is a discrete quantitative variable, racial composition of a high school classroom is a qualitative variable, and heights of 15-year-olds is a continuous quantitative variable.
Explanation:The variables given in this question can be classified as either qualitative or quantitative.
Points scored in a football game: This is a quantitative variable as it involves numerical measurements. Moreover, since points scored in a game can only take on whole number values (for example, you cannot score 2.5 points in a football game), it is specifically a discrete variable.Racial composition of a high school classroom: This is a qualitative variable as it involves non-numerical categories or types, namely, different races.Heights of 15-year-olds: This variable is quantitative, as it involves measurement of a physical characteristic (height). Furthermore, since height can take on any value within a certain range (for example, a 15-year-old could be 1.52 meters tall or 1.523 meters tall), this is a continuous variable.Learn more about Qualitative vs Quantitative Variables here:https://brainly.com/question/31565073
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Ruben has his dad are building a tree house the treehouse . The tree house has an area of 384 square feet the width of the tree house is 3/8 its length.What is the length of the treehouse
Answer:
12.25 ft
Step-by-step explanation:
(3/8)x + (5/8)x = √384
0.375x + 0.625x = 19.6
x = 19.6
Since L = 5/8 * 19.6 = 12.25 ft
The length of the treehouse, we use the area (384 square feet) and the given ratio (width is 3/8 the length). After setting up the equation, we solve for the length to find that the length of the treehouse is 32 feet.
The length of the treehouse, we can set up an equation using the given area and the relationship between the width and length. Let L represent the length and W represent the width. According to the problem, W = {3}/{8}L.
The area of the treehouse is given as 384 square feet. The formula for the area of a rectangle is Area = Length imes Width, so we have:
L times W = 384 square feet
L times {3}/{8}L = 384
{3}/{8}L² = 384
L² = rac{384 times 8}{3}
L² = 128 times 8
L² = 1024
L =[tex]\sqrt{1024}[/tex]
L = 32 feet
Therefore, the length of the treehouse is 32 feet.
The average radius of Jupiter is 4.34 x 10^4 miles. The average sun radius of the sun is 4.32 x 10^5. How many times greater is the average radius of the sun?
Answer:
The average radius of sun is approximately 9.95 times the average radius of Jupiter.
Step-by-step explanation:
We are given the following in the question:
Average radius of Jupiter =
[tex]4.34\times 10^{4}\text{ miles}[/tex]
Average radius of the sun =
[tex]4.32\times 10^{5}[/tex]
Relation between average radius of sun and average radius of Jupiter =
[tex]\displaystyle\frac{\text{Average radius of Sun}}{\text{Average radius of Jupiter}}\\\\= \frac{4.32\times 10^{5}}{4.34\times 10^{4}}\\\\\displaystyle\frac{\text{Average radius of Sun}}{\text{Average radius of Jupiter}} = 9.953917\\\\\text{Average radius of Sun} \approx 9.95\times \text{(Average radius of Jupiter)}[/tex]
Thus, the average radius of sun is approximately 9.95 times the average radius of Jupiter.
To determine how many times greater the Sun's radius is compared to Jupiter, divide the Sun's radius (695,700 km) by Jupiter's radius (71,400 km), resulting in the Sun being approximately 9.75 times greater than Jupiter in size.
Explanation:The question asks how many times greater the average radius of the Sun is compared to that of Jupiter. To find this, we will divide the Sun's radius by Jupiter's radius. The radius of Jupiter is given as 71,400 km, while the radius of the Sun is much larger at 695,700 km.
Calculating the ratio, we get:
Radius of the Sun / Radius of Jupiter = 695,700 km / 71,400 km.This simplifies to approximately 9.745.Therefore, the average radius of the Sun is roughly 9.75 times greater than that of Jupiter.
A street lamp casts a shadow 31.5 feet long, while an 8 foot-tall street sign casts a shadow of 14 feet long. What is the length and height of the lamp?
Answer:
The answer to your question is the height of the lamp is 18.2 ft
Step-by-step explanation:
Data
Street lamp shadow = 31.5 ft
Street sign height = 8 ft
Street sign shadow = 14 ft
Street lamp height = x
Process
1.- To find the height of the lamp use proportions. In this kind of problem, we do not look for the length, but the shadow.
Street lamp height/street lamp shadow = street sign height/street sign
shadow
Substitution
x / 31.5 = 8 / 14
Solve for x
x = (31.5)(8) / 14
Simplification
x = 254.4 / 14
Result
x = 18.2 ft
To find the length and height of the lamp, set up proportions using the shadow lengths and given values, then solve for the lamp height and length based on the information provided.
Explanation:The length of the lamp:
Set up a proportion using the shadow lengths:
What is the probability of rolling a die twice, and having it land on a number greater than 1 both times?
Answer: 25/36
Step-by-step explanation:
A die has six faces, therefore its sample space S is 6
Since we are rolling a die twice(at different times), the probability of one turning up the first time is 1/6(i.e expected outcome/total outcome)
Similarly, if we throw the die the second time, the probability of one turning up the second time is also 1/6
The probability of having number greater than 1 land at each time will be (1- 1/6) which is 5/6.
Therefore the probability of having number greater than 1 land at "both times" will be 5/6×5/6 = 25/36
Students who attend Washington Middle School are either in seventh or eighth grade. At the end of the first semester 25% of the students at Washington Middle School were on the honor roll. Seventh graders represented 60% 60 % of the students on the honor roll. If 124 124 students on the honor roll were in eighth grade, how many students attend Washington Middle School? There are students who attend Washington Middle School.
Answer:
There are 1240 students who attended Washington Middle School.
Step-by-step explanation:
Given:
Students who attend Washington Middle School are either in seventh or eighth grade.
At the end of the first semester 25% of the students at Washington Middle School were on the honor roll.
Seventh graders represented 60% of the students on the honor roll.
If 124 students on the honor roll were in eighth grade.
Now, to find the students attend Washington Middle School.
Let the total number of students be [tex]x.[/tex]
So, the students at Washington Middle School were on the honor roll:
25% of [tex]x[/tex]
[tex]=\frac{25}{100} \times x[/tex]
[tex]=\frac{25x}{100}[/tex]
[tex]=\frac{x}{4}[/tex]
As, given seventh graders represented 60% of the students.
So, the students on the honor roll represented as seventh graders:
[tex]60\%\ of\ \frac{x}{4}[/tex]
[tex]=\frac{60}{100} \times \frac{x}{4}[/tex]
[tex]=0.6\times \frac{x}{4}[/tex]
[tex]=\frac{0.6x}{4}[/tex]
As, 124 students on the honor roll were in eighth graders.
Thus,
According to question:
[tex]\frac{x}{4} -\frac{0.6x}{4} =124[/tex]
[tex]\frac{x-0.6x}{4} =124[/tex]
[tex]\frac{0.4x}{4} =124[/tex]
Multiplying both sides by 4 we get:
[tex]0.4x=496[/tex]
Dividing both sides by 0.4 we get:
[tex]x=1240.[/tex]
Therefore, there are 1240 students who attended Washington Middle School.
What is the repulsive force between two pith balls that are 13.0 cm apart and have equal charges of −24.0 nC?
Answer:
The repulsive force is [tex]3.067\times10^{-4}N[/tex].
Step-by-step explanation:
Consider the provided information.
The coulomb's law to calculate the repulsive force: [tex]F=\frac{kQ_1Q_2}{r^2}[/tex]
Where the value of k is 9.00×10⁹ Nm²/C²
Substitute the respective values in the above formula.
[tex]F=\frac{9\times10^9\frac{N\cdot m^2}{c^2} \times(-24\times10^{-9}C)^2}{[(13 cm)(\frac{1m}{100cm} )]^2}[/tex]
[tex]F=\frac{9\times10^9\frac{N\cdot m^2}{c^2} \times(-24\times10^{-9}C)^2}{(0.13 m)^2}[/tex]
[tex]F\approx0.0003067N[/tex]
[tex]F=3.067\times10^{-4}N[/tex]
Hence, the repulsive force is [tex]3.067\times10^{-4}N[/tex].
Newton’s law of cooling states that for a cooling substance with initial temperature T0 , the temperature T(t) after t minutes can be modeled by the equation T(t)=Ts+(T0−Ts)e−kt , where Ts is the surrounding temperature and k is the substance’s cooling rate.A liquid substance is heated to 80°C . Upon being removed from the heat, it cools to 60°C in 12 min.What is the substance’s cooling rate when the surrounding air temperature is 50°C ?The substances cooling rate when the surrounding air temperature is 50C is 0.0916.0.06870.07320.08130.0916
Answer:
k = 0.0916
Step-by-step explanation:
T(t) = [tex]T_{s} + ( T_{o} - T_{s} )e^{-kt}[/tex]
from question; t = 12 mins , [tex]T_{s}[/tex] = 50 C , [tex]T_{o}[/tex] = 80 C , T = 60 C
60 = 50 + (80 - 50) [tex]e^{-12k}[/tex]
60-50 = 30 [tex]e^{-12k}[/tex]
10/30 = [tex]e^{-12k}[/tex] (Taking natural Log of both sides)
In(0.3333) = In [tex]e^{-12k}[/tex]
-1.0986 = -12k
k = 0.0916
An isosceles triangle has exactly two sides that are equal in length (congruent). If the base (the third side) measures 46 inches and the perimeter is 119 inches, find the length of the two congruent sides, called legs.
Answer:
36.5 Inches
Step-by-step explanation:
The perimeter of the triangle is the sum of all three(3) sides.
let the length of one congruent side be 'a', Therefore;
a + a + 46 = 119
2a = 119 - 46
a = 73/2
a = 36.5 inches.
Describe and sketch the surface in R^3 represented by the equation x + y = 2
Answer:
The Surface in R^3
Step-by-step explanation:
Represented by the equation x+y=2
when y=0
then 0=2-x
x=2
similarly
when x=0
then 0=2-y
y=2
the sketch and description is in attached file
Answer: The equation is a plane.
Graph is attached.
The equation [tex]x + y = 2[/tex] is an equation of a plane in [tex]R^3[/tex].
z can take any value and x and y must satisfy the equation [tex]x + y = 2[/tex].
3 such points are: [tex]A = (0, 2, 0), B = (2, 0, 0), C = (1, 1, 3)[/tex].
Then we plot the points and draw a plane through them.
Learn more: https://brainly.com/question/1655368
A 72.5-foot rope from the top of a circus tent pole is anchored to the ground 44.4 feet from the bottom of the pole. What angle does the rope make with the pole? (Assume the pole is perpendicular to the ground.
The CEO of a large electric utility company claims that 80 percent of his 1,000,000 customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. After performing the appropriate statistical test, they find the p-value to be 0.894. What conclusion can we make?
Answer:
Conclusion: The proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.
Step-by-step explanation:
To test the claim made by the CEO of a large electric utility company the newspaper must conduct a hypothesis test for one proportion.
Assumption:
The significance level (α) of the test can be assumed to be 5%.
Hypothesis:
[tex]H_{0}:[/tex] The proportion of customers satisfied with the service they receive is 0.80, i.e. [tex]p=0.80[/tex]
[tex]H_{a}:[/tex] The proportion of customers satisfied with the service they receive is different from 0.80, i.e. [tex]p\neq 0.80[/tex]
Decision Rule:
If the p-value of the test is less than the significance level (α) then the null hypothesis may be rejected. But if the p-value is more than the significance level (α) then we cannot reject the null hypothesis.
Test Statistics:
As the sample size is large, i.e.n = 100 > 30, then according to the central limit theorem sampling distribution of sample proportion will follow the normal distribution.
The test statistic used is:
[tex]z=\frac{\hat p-p}{\frac{\sqrt{p(1-p)}} {n} }[/tex]
Given:
The p-value of the hypothesis test is computed to be 0.894.
That is:
[tex]p-value=0.894>\alpha =0.05[/tex]
This implies that we fail to reject the null hypothesis at 5% level of significance.
Conclusion:
The null hypothesis was failed to be rejected at 5% level of significance.
Thus, concluding that the proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.
Red apples cost $1.20 per pound green apple cost 1.50$ per pound what is the total cost if you buy 3 pounds of red apples and 2 pounds of green apples
6.60 would be the total cost for both 3 pounds and two pounds :D
Answer:
$6.60
Step-by-step explanation:
multiply 1.20 (red apples) by 3 (lbs) = 3.6
and 1.50 (green apples) times 2 (lbs) = 3
then add the two totals = $6.60
I was doing my math homework and I was clueless when it came to this question, my best friend and I both came up with 30 and Get More Math Said it was incorrect. Can you help?
to find the probability of flipping heads at least once if you flip a coin two times. The possible outcomes (we don't care about the order) are (each equally likely) TT, TH, HT, HH. Three out of four have an H in them, so the probability is 34. Is this correct? Is there a better and efficient way (especially when dealing with a higher number of flips? Please use only very basic terminology and concepts from probability because I've never taken a class.
Answer:
The probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].
Step-by-step explanation:
The probability of an event, say E, is the ratio of the favorable outcomes to the total number of outcomes, i.e.
[tex]P (E) = \frac{Favorable\ outcomes}{Total\ outcomes}[/tex]
The sample space of flipping two coins is:
S = {HH, HT, TH and TH}
Total number of outcomes = 4
Compute the probability of flipping Heads at least once as follows:
Let X = heads.
P (X ≥ 1) = P (X = 1) + P (X = 2)
[tex]=\frac{2}{4}+\frac{1}{4} \\=\frac{3}{4}[/tex]
Thus, the probability of flipping Heads at least once is [tex]\frac{3}{4}[/tex].
The experiment of flipping a coin is a binomial experiment.
Since there are only two outcomes of the experiment, either a Heads or a Tails.
So if X is defined as the number of heads in n flips of a coin then the random variable X follows a binomial distribution with probability p = 0.5 of success.