A researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆ y = 2 − 4 x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way:When amount of schooling increases by one year, the number of pregnancies increases by 2.When amount of schooling increases by one year, the number of pregnancies increases by 4.When amount of schooling increases by one year, the number of pregnancies decreases by 2.When amount of schooling increases by one year, the number of pregnancies decreases by 4

Answer:

Yes

Step-by-step explanation:

5% of 70,000 is 3,500 (70,000 x 0.05 = 3,500)

That means she is earning at least $3,500 a month from interest.

$3,500 is plenty to cover the monthly payment of $280.

You know what, I think Jessica should get a brand new car instead.

Yes, her monthly interest will cover the cost of the down payment and Jessica should get a brand-new car instead.

If n is the number of times the interest is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

\(a = p(1 + \dfrac{r}{n})^{nt}\)

We have given that Jessica has $70,000 in the bank and is earning 5% compounded monthly.

And the down payment is $500 and the monthly payments are $280

5% of 70,000 = 3,500

70,000 x 0.05 = 3,500

That means that she is earning at least $3,500 per month from interest.

$3,500 is plenty of amounts to cover the monthly payment of $280.

Therefore, Yes her monthly interest will cover the cost of the down payment and Jessica should get a brand-new car instead.

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(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

Answer:

-1.875

Step-by-step explanation:

1. Write the problem: -2(5x + 8) = 14 + 6x

2. Multiply -2 by 5 and 8 to get: -10x - 16 = 14 + 6x

3. Combine like terms: -16x - 16 = 14

4. Repeat step 3: -16x = 30

5. Divide -16 by 30 to get the answer which is -1.875.

Hope this helped!

Answer:

\(\boxed{\sf 200\pi}\)

Step-by-step explanation:

We know that the volume of a cone:-

\(\boxed{\sf \pi r^2\cfrac{h}{3}}\)

(r = 10) (h = 6)

\(\sf \pi \times 10^2\times\cfrac{6}{3}\)

Divide numbers:-

\(\sf \cfrac{6}{3}=\boxed{2}\)

\(\sf 10^2\times \:2\pi\)

\(\sf 100\times \:2\pi\)

Multiply numbers:-

\(\boxed{\sf 200\pi}\)

Therefore, your answer is 200π³

We could also multiply 200 by 3.14 which will give you 628 units³.

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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The side labeled "a" is made the longer side. These are the two congruent sides. So a > b.

We are told that the longer side is 6.3, so a = 6.3, meaning that

2a+b = 15.7

2(6.3)+b = 15.7

12.6+b = 15.7

b = 15.7-12.6

b = 3.1

The triangle has sides of: 6.3, 6.3, 3.1

The perimeter is 6.3+6.3+3.1 = 15.7

Going back to the question "which equation can be used to find the length of the base?", it sounds like either you were given a list of multiple choice answers, or you just fill in the blank. If multiple choice, then try to see which answer matches with what I wrote above. If fill in the blank, then I would just enter either 2(6.3)+b = 15.7 or 12.6+b = 15.7

Answer:

2(6.3)+b = 15.7 or 12.6+b = 15.7

Step-by-step explanation:

Answer:

We are 95% confident that the proportion of American voters who favor congressional term limits is 64 percent with a difference of 3% for small sample size.

Step-by-step explanation:

95 % confidence means that we are 95 % confident that the the proportion of American voters who favor congressional term limits is 64 percent.

95 % confidence  means that of all the sample about 95 %  values are within in the given range.

And only 5% sample are not included in the given parameter.

Margin of error is the amount of miscalculation or difference in change of circumstances from the obtained data.

3% margin of error usually occurs when the data size is small.

As the data size increases the margin of error decreases.

So this statement tells us that we are 95% confident that the proportion of American voters who favor congressional term limits is 64 percent with a difference of 3% for small sample size.

Margin of error= z *σ/√n→

This indicates that as the sample size decreases the margin of error increases and vice versa.

Answer:

y = -4/3 - 1

Step-by-step explanation:

Step 1

Step 2

Step 3

You have now solved the problem.

The formula for volume of a hemisphere is: V = 2/3 * π * r³

Volume = 2/3 x 3.14 x 150^3

Volume = 7,065,000 cubic feet.

Multiply the cost per cubic foot by the volume:

7,065,000 x 0.05 = 353,250

The total cost was $353,250

Therefore , the value of the given problem of linear equation comes out to be  x = -250.

In algebra, a mathematical model is just one that of the form y=mx+b. The slope is B, and the y-intercept is m. Since x and y are variables, the previous sentence is frequently referred to as a "mathematical expression with 2 variables." Bivariate linear equations are linear equations with two variables. Linear equations can be found in many different situations. Once an issue has the formula y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.

Here,

Given : 70.50 - 45.50 + 0.15x - 0.09x =0

To find the value of x,

Thus,

We do : 70.50 - 45.50 + 0.15x - 0.09x =0

=> 15 + 0.06x =0

=> 6/100 *x = -15

=> 6x = -1500

=> x = -1500/6

=> x = -250

Therefore , the value of the given problem of linear equation comes out to be  x = -250.

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Answer:

36

Step-by-step explanation:

tan(41π/36) can be written in terms of the tangent of a positive acute angle as (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

To express tan(41π/36) in terms of the tangent of a positive acute angle, we need to find an angle within the range of 0 to π/2 that has the same tangent value.

First, let's simplify 41π/36 to its equivalent angle within one full revolution (2π):

41π/36 = 40π/36 + π/36 = (10/9)π + (1/36)π

Now, we can rewrite the angle as:

tan(41π/36) = tan((10/9)π + (1/36)π)

Next, we'll use the tangent addition formula, which states that:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = (10/9)π and B = (1/36)π.

tan(41π/36) = tan((10/9)π + (1/36)π) = (tan((10/9)π) + tan((1/36)π)) / (1 - tan((10/9)π)tan((1/36)π))

Now, we need to find the tangent values of (10/9)π and (1/36)π. Since tangent has a periodicity of π, we can subtract or add multiples of π to get equivalent angles within the range of 0 to π/2.

For (10/9)π, we can subtract π to get an equivalent angle within the range:

(10/9)π - π = (1/9)π

Similarly, for (1/36)π, we can add π to get an equivalent angle:

(1/36)π + π = (37/36)π

Now, we can rewrite the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Since we are looking for an angle within the range of 0 to π/2, we can further simplify the expression as:

tan(41π/36) = (tan((1/9)π) + tan((37/36)π)) / (1 - tan((1/9)π)tan((37/36)π))

Therefore, tan(41π/36) can be written in terms of the tangent of a positive acute angle as the expression given above.

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Answer:

a) 39 meters

b) t = 1.8 seconds

Step-by-step explanation:

a)

To find the starting height of the riders, we just need to use the value of t = 0 in the equation of h(t):

h(0) = -9.8*0^2 - 5*0 + 39

h(0) = 39 meters

b)

To find when the height will be equal 0, we just need to use the value of h(t) = 0 and then find the value of t:

0 = -9.8*t^2 - 5*t + 39

Delta = b^2 - 4ac = 25 + 4*39*9.8 = 1553.8

sqrt(Delta) = 39.418

t1 = (5 + 39.418)/(-2*9.8) = -2.2662 s (A negative value for the time is not suitable for the problem)

t2 = (5 - 39.418)/(-2*9.8) = 1.756 s

Rounding to nearest tenth, we have t = 1.8 s

If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be: D. .95.

A confidence interval is also referred to as level of confidence and it can be defined as a range of estimated values that defines the probability that a population parameter would fall or lie within it.

For instance, the confidence interval at 95% is given by p - E < p < p + E

Since the confidence interval for the mean of a population is at 95%, the confidence coefficient would be calculated by simply dividing the confidence interval by 100:

Confidence coefficient = 95/100

Confidence coefficient = 0.95

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The middle point of the given numbers are 6 .

The median or the middle value is the number in the middle {2, 3, 11, 13, 26, 34, 47}, which in this instance is 13 since there are three numbers on either side.

To find the median value in a list with an even amount of numbers, one must determine the middle pair, add them, and divide by two.

The middle point of two numbers usually refers to the average of them .

thus the given numbers are - 24 and 36

This can be calculated by :

=> - 24 + 36 / 2

=> 12 / 2

=> 6  

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Answer:

$96.15

Step-by-step explanation:

Given data

markup = 30%

cost price= $125

let the cost price before markup be x

125-30/100*x= x

125-0.3x= x

125= x+0.3x

125= 1.3x

divide both sides by 1.3

x= 125/1.3

x= $96.15

Hence the price before markup is $96.15

The percentage mark-up of the goods is 69 percent.

The mark-up percentage is calculated by subtracting the unit cost from the selling price, dividing by the unit cost and multiplying times 100.

Therefore, the buyer for a chain of stores purchased tables in bulk, paying $200 each. The stores will sell each table for $338.

Hence, the percentage mark-up can be calculated as follows:

percentage mark-up = 338 - 200 / 200 × 100

percentage mark-up = 138 × 100 / 200

percentage mark-up = 13800 / 200

percentage mark-up = 138 / 2

percentage mark-up = 69 %

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For simple exponential smoothing, the needed element to find the future forecast value is the historical values. This means that all the previous values in the time series data are required to compute the forecast for the future.

Simple exponential smoothing is a time series forecasting method that uses weighted averages of past observations to predict future values. The forecast at each time period is calculated based on the previous forecast and the actual observation for that period. The weight assigned to each historical value decreases exponentially as the observations become more distant in the past.

By considering all the historical values, the exponential smoothing algorithm can capture the trend and seasonality patterns in the data, enabling it to make accurate predictions for future values.

It's worth noting that historical forecasts are not directly used in the computation of future forecasts in simple exponential smoothing. Instead, they are used to update the weight given to each observation. Therefore, only the historical values are necessary to find the future forecast value.

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Answer:

what is the question...

Step-by-step explanation:

7 bills of $5 and 20 bills of $10

Explanation

Step 1

Let

Malick has $235=total = 235

total=235

number of bill $5= x

number of bill $10=y

He has one less than three times as many $10 bills than $5 bills=

3x=y+1

Step 2

the total is 235, so

total for $ 5 bills= 5* number of bills $5=5x

total for $ 10 bills= 10* number of bills $10=10x

Step 2

using equation (1I and (2) solve for x and y

isolate, y in equation (1)

replace the value of x in equation (2)

replace the value of y in equation (1) to fin d x

so, the answer is

7 bills of $5 and 20 bills of $10

Answer:

D 11/18 11:18 11 to 18

Step-by-step explanation:

Because there are eleven technicians, our numerator is 11. Then, because there are 18 total helpers our denominator is 18.

Answer:

1

2,3,4

Step-by-step explanation: to

when the number of football is 1 is less expensive than basketball

The surface area and volume of a cube with different edge length are

When a cube with edge length 4inches ,

Surface area = 96 square inches and Volume =64 cubic inches.

Cube dilated by scale factor 0.25 ,  

Surface area = 6 square inches and Volume =1 cubic inches.

The surface area of a cube is = 6 times the area of one face.

Each face of this cube has an area equals to

= (4 inches) x (4 inches)

= 16 square inches,

So the total surface area is,

Surface area

= 6 x 16 square inches

= 96 square inches

The volume of a cube =  length of one edge cubed.

Here, the edge length is 4 inches,

Volume

= (4 inches)^3

= 64 cubic inches

When a cube is dilated by a scale factor of 0.25, all of its edges are multiplied by 0.25.

This implies,

The edge length of the image cube is

0.25 x 4 inches = 1 inch.

Surface area of the image cube =  6 times the area of one face.

Each face of the image cube has an area of

= (1 inch) x (1 inch)

= 1 square inch,

So the total surface area is,

Surface area

= 6 x 1 square inch

= 6 square inches

Volume of the image cube = length of one edge cubed.

Here, the edge length is 1 inch,

Volume

= (1 inch)^3

= 1 cubic inch

Therefore, the surface area and volume for the given dimensions are

For edge length 4inches , Surface area = 96 square inches and Volume =64 cubic inches.

For scale factor 0.25 ,  Surface area = 6 square inches and Volume =1 cubic inches.

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Answer:

switch the position

1/3πr²h=v

multiply all through by 3

3•1/3πr²h=3•v

3 will cancel out 3

πr²h=3v

divide both sides by πh

r²=3v/πh

root both sides

r=±√3v/πh

Answer:

ba.80 5. Area =72 5. Perimeter =44 6b.36

Step-by-step explanation:

ba. b*h is the formula the base is 10 and the height is 8 multiplied is 80.

Explanation=in the comments

Answer:

-9. 125

Step-by-step explanation:

.

Answer:

Step-by-step explanation

Given

Total number of pages to complete the packet = 6400 pages

If each ream contains 500pages, then:

Total number of reams needed = Total pages/number of pages per ream

Total number of reams needed = 6400/500

Total number of reams needed = 12.8

Hence you will need about 13 reams for all the packets

Answer:

Total number of Hardcover books is TWO while the number of Paperback books is FIVE

Step-by-step explanation:

No. of hardcover book = x

No. of paperback book = y

Cost of one hardcover book = $8

Cost of one paperback book = $5 We are given that:

x+y=7 (Equation 1)

8x+5y=41 (Equation 2)

We can find out value of x and y by solving both equations simultaneously.

Hence, Total number of Hardcover books is TWO while the number of Paperback books is FIVE

Step-by-step explanation: