61 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows:

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Lower limit = 0.45 - (1.96 * 0.121855) = 0.2209. This means that we can be 95% confident interval that the true slope coefficient lies between 0.2209 and 0.45.

1. The standard error of the slope coefficient can be calculated by dividing the sample standard deviation of the residuals (obtained from the regression output) by the square root of the sample size.

2. The lower limit of the 95% confidence interval of the slope coefficient can be calculated by subtracting 1.96 times the standard error of the slope coefficient from the coefficient itself.

Lower limit = 0.45 - (1.96 * 0.121855) = 0.2209

Interpretation

The lower limit of the 95% confidence interval for the slope coefficient of the regression of kinesthetic VARK scores on the visual VARK scores for biology students is 0.2209. This means that we can be 95% confident that the true slope coefficient lies between 0.2209 and 0.45.

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Answer:

-6.13406 and 61.13406

Step-by-step explanation:

x + y = 55

x × y = -375

y = 55 - x

x × (55 - x) = -375

55x -x² = -375

x² - 55x - 375 = 0

solution of a quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

a=1

b=-55

c=-375

x = (55 ± sqrt(55² + 4×375))/2 = (55 ± sqrt(4525))/2 =

= (55 ± sqrt(25 × 181))/2 = (5×11 ± 5×sqrt(181))/2 =

= 5/2 × (11 ± sqrt(181)) =

= 61.13406... or -6.13406...

y = 55 - 5/2×(11 ± sqrt(181)) = 55/2 ± 5/2×sqrt(181) =

= -6.13406... or 61.13406...

The dimensions of the fencing that will minimize the cost of the fence are 50 feet by 100 feet.

The area of the total lot with all three pens is 5000 square feet, which means that the total area of the fencing is also 5000 square feet.

Let's say the length of the fencing is x feet and the width of the fencing is y feet. We can write the following equation to represent the area of the fencing:

xy = 5000

The cost of the horizontal fencing (length) is $26 per foot, so the total cost of the horizontal fencing is 26x. The cost of the vertical fencing (width) is $12 per foot, so the total cost of the vertical fencing is 12y. The total cost of the fencing is the sum of these two costs, so we can write the following equation to represent the total cost of the fencing:

26x + 12y = C

Where C is the total cost of the fencing.

We want to minimize the total cost of the fencing, so we want to find the values of x and y that minimize the value of C We can do this by setting up a system of equations and solving for x and y.

xy = 5000

26x + 12y = C

We can solve this system of equations using the substitution method. First, we can solve the first equation for y:

\($y = \frac{5000}{x}$\)

Substituting this expression for y into the second equation, we get:

\($26x + 12(\frac{5000}{x}) = C$\)

Solving for x, we get:

\($x = \sqrt{625} = 25$\)

Substituting this value for x into the first equation, we get:

\($y = \frac{5000}{25} = 200$\)

Therefore, the dimensions of the fencing that will minimize the cost of the fence are x = 25 feet and y = 200 feet, which is a fencing with a length of 50 feet and a width of 100 feet.

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Answer:

6/24

Step-by-step explanation:

Answer:

Explicit formula *******

Jaidee's printing company LLC has 8 of Model A and 5 of Model B press, respectively.

We can find each type of press with the help of the substitution method.

Let Model A = x presses

Model B = y presses

According to the question, the company owns 13 total printing presses, then

x + y = 13

x = 13 - y

Also, according to the question

80x + 30y = 790

Put the value of x = 13 - y in the above equation

80(13 - y) + 30y = 790

1040 - 80y + 30y = 790

1040 - 790  = 80y - 30y

50y = 250

y = 250/50 = 5

Now, put the value of y in x = 13 - y

x = 13 - 5

x = 8

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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No, the line x=1-2t, y=2+5t, z=-3t is not parallel to the plane 2x+y-z=8 as their dot product is not zero.

To determine if the line x = 1 - 2t, y = 2 + 5t, z = -3t is parallel to the plane 2x + y - z = 8, we can find the direction vector of the line and check if it is orthogonal to the normal vector of the plane.

The direction vector of the line is given by the coefficients of t in each component, which is (-2, 5, -3).

The normal vector of the plane is given by the coefficients of x, y, and z in the plane's equation, which is (2, 1, -1).

To check if the direction vector is orthogonal to the normal vector, we can take their dot product and see if it is zero:

(-2, 5, -3) * (2, 1, -1) = -4 + 5 + 3 = 4

Since the dot product is not zero, the direction vector of the line and the normal vector of the plane are not orthogonal, which means the line is not parallel to the plane.

The line x = 1 - 2t, y = 2 + 5t, and z = -3t is not parallel to the plane 2x + y - z = 8, hence the answer is no.

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Answer:

x>-5 x ≤10

Step-by-step explanation:

-35/7=-5

7x/7=x

3x/3=x

30/3=10

Answer: -5 < x _< 10

Step-by-step explanation:

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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Steps to solve:

7x + 24 + 19x + 33

~Combine like terms

26x + 57

Best of Luck!

Answer: 26x+ 57

Step-by-step explanation:

Combine like terms; 7x + 19x = 26x

33+24= 57 which gives us “26x + 57” as our final answer :)

Stay safe! Good Luck!

Answer:

y-9=-4(x+2)

Step-by-step explanation:

The point-slope formula is:

y-y1=m(x-x1)

m=-4 and use the point (-2, 9)

                                       x1    y1

Plug in the information.

y-9=-4(x+2)

This is the equation written in point-slope form using the point (-2, 9).

Hope this helps!

I believe that it is 31.4, but please correct me if I'm wrong.

The required area of the sculpture that is shaped like a circle is \(78.5m^{2}\).

Given that,

Jessie designed a sculpture that is shaped like a circle,

The circumference of the sculpture is 10π meters.

We have to determine,

Which measurement is closest to the area of the sculpture in square meters.

According to the question,

Circumference of the circle = \(2\pi r\)

Where, circumference = \(10\pi\)

Then,

\(10\pi =2\pi r \\\\r = \dfrac{10\pi }{2\pi }\\\\r = 5m\)

Therefore,

Jessie designed a sculpture that is shaped like a circle.

Area of the circle = \(\pi r^{2}\)

Where, r = 5m

Then,

Area of the circle is given by,

\(= \pi r ^{2}\\\\= 3.14 \times (5)^{2}\\\\= 3.14 \times 25\\\\= 78.5m^{2}\)

Hence, The required area of the sculpture that is shaped like a circle is \(78.5m^{2}\).

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The vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0 is r(t) = <0, 2, 0> - t<1, -1, 0>.

To find a vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0, we can solve the system of equations formed by the planes.
First, let's solve for y in terms of x and z from the equation x + y + z = 2. Rearranging the equation, we have y = 2 - x - z.
Now, substitute this expression for y in the equation x + z = 0. We have x + (2 - x - z) + z = 2, which simplifies to 2 - z = 2.
Solving for z, we find z = 0.
Substituting z = 0 into the equation x + z = 0, we have x = 0.
Now that we have the values of x, y, and z, we can form a vector equation for the line of intersection as follows:
r(t) =  = <0, 2 - x - z, 0> = <0, 2, 0> - t<1, -1, 0>.

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Answer:

6 is b, 7 is c

Step-by-step explanation:

Answer:

#6 wants you to find out what answer from the 4 expressions gives you the least or smallest number. For #7, you need to follow PEMDAS in order to get the right answer.

Step-by-step explanation:

#6, the answers you get are 8, -9, -3, and 9. You need to choose the smallest number. Negative numbers are smaller than positive numbers, so you can immediately eliminate 8 and 9. You have to be careful when comparing negative numbers because the larger negative number is actually smaller than the smaller negative number since it is further away from the zero. So, negative -9 would be smaller than -3 in this case.

#7, I would divide the -720/12 first. This results in -60. Then, divide the -60 by -10. This gives you an answer of positive 6.

ANSWERS:

#6 : B

#7 : C

The expression giving the enrollment t years from now can be found by integrating P'(t) with respect to t.

Given that P'(t) = 2000(15t + 1)^(3/2) represents the rate at which the student enrollment is growing per year, we can find the expression for the enrollment t years from now by integrating P'(t) with respect to t. The integration of P'(t) will yield the original function P(t) that represents the student enrollment at a given time. Integrating 2000(15t + 1)^(3/2) with respect to t will result in the expression for the enrollment t years from now. It is important to note that the initial condition, P(0) = 1200, should be taken into account when integrating to find the constant of integration. Thus, by integrating P'(t) and considering the initial condition, we can determine the expression for the enrollment t years from now.

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The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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The ball traveled approximately \(26.27\) units in total.

To calculate the distance the ball traveled, we can use the distance formula between two points in a Cartesian coordinate system.

Distance = \(\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1} )^{2} }\)

Let's calculate the distance between Player A and Player B first:

Distance_AB =

\(\sqrt{((16-2)^{2}+(9-4)^{2}) }\)

\(= \sqrt{(14^{2}+5^{2} ) } \\= \sqrt{(196 +25)} \\= \sqrt{221} \\= 14.87\)

Now, let's calculate the distance between Player B and Player C:

Distance_BC =

\(\sqrt{ ((25 - 16)^2 + (16 - 9)^2)}\\= \sqrt{ (9^2 + 7^2)}\\= \sqrt{(81 + 49)}\\= \sqrt{130}\\=11.40\)

Finally, we can calculate the total distance traveled by adding the distances AB and BC:

Total distance = Distance_AB + Distance_BC

\(= 14.87 + 11.40 \\= 26.27\)

Starting from Player A at \((2, 4),\) it was thrown to Player B at \((16, 9),\) covering a distance of about \(14.87\) units. From Player B, the ball was then thrown to Player C at \((25, 16),\) covering an additional distance of approximately \(11.40\) units.

Combining these distances, the total distance the ball traveled was approximately \(26.27\) units.

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Answer: about a 13% increase

Step-by-step explanation:

2750/3162.50 is 0.87 so the profit before was 87% of what it is now

1-0.87 is 0.13 so it increased by 13%

8 students made 4 mistakes or more

The  rate of change of Wayne's hours of sleep with respect to each day is  5  hours per day.

The rate of change of Wayne's hours of sleep with respect to each day is calculated as follows;

Mathematically, the formula is given as;

rate of change of sleep = change in sleep / change in time of sleep

The change in the sleep pattern = 30 - 15 = 15 hours

The change in the time of sleep = 6 - 3 = 3 days

The  rate of change of Wayne's hours of sleep with respect to each day is calculated as

rate of change of sleep = ( 15 hours ) / ( 3 days )

rate of change of sleep = 5  hours per day

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Answer:

the answer is C I got you :)

Given:

\(\Delta FUN\cong \Delta TEA\)

To find:

Identify the congruent corresponding parts of \(\angle N\cong \angle \_\_\).

Solution:

We have,

\(\Delta FUN\cong \Delta TEA\)

We know that corresponding parts of congruent triangles are congruent.

\(\angle F\cong \angle T\)

\(\angle U\cong \angle E\)

\(\angle N\cong \angle A\)

Therefore, the required corresponding part is  \(\angle N\cong \angle A\).

Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50

Step-by-step explanation: i dont know what to write??

The equation of the line that contains the point P(4, 5) and is parallel to the graph of 5x + y = -4 is y = -5x + 25.

To find the equation of a line parallel to the graph of 5x + y = -4 and passing through the point P(4, 5), we need to determine the slope of the given line and then use the point-slope form of a linear equation.

The equation 5x + y = -4 is in the standard form Ax + By = C, where A = 5, B = 1, and C = -4. To find the slope of this line, we can rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope:

5x + y = -4

y = -5x - 4

From this form, we can see that the slope of the given line is -5.

Since the line we are looking for is parallel to this line, it will have the same slope of -5. Now we can use the point-slope form of a linear equation to find the equation of the parallel line:

y - y₁ = m(x - x₁)

Substituting the values of the point P(4, 5) and the slope m = -5, we have:

y - 5 = -5(x - 4)

Simplifying:

y - 5 = -5x + 20

Now, we can write the equation in slope-intercept form:

y = -5x + 25

Therefore, the equation of the line that contains the point P(4, 5) and is parallel to the graph of 5x + y = -4 is y = -5x + 25.

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When using the normal distribution as an approximation, the value of the standard deviation is typically chosen based on the specific context and requirements of the problem at hand.

In many cases, a commonly used rule of thumb is to approximate the standard deviation by dividing the range (difference between the maximum and minimum values) by 4.

However, it's important to note that this rule of thumb is not universally applicable and may not provide an accurate approximation in all scenarios. The choice of the standard deviation should ideally be based on a careful analysis of the data or knowledge of the underlying distribution.

Additionally, in some cases, standard deviation may already be known or given, and there may be specific guidelines or formulas available for determining the appropriate standard deviation for approximation. Therefore, it is crucial to consider the specific context and consult relevant resources or statistical techniques to determine the most suitable standard deviation for the normal distribution approximation.

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