Select the correct answer.
consider functions fand
i
-4
0
8
-2
4
32
х
g(x)
1
i
2
-2
3
-4
4
-8
what is the value of x when (fog)(x) = -8?

We need at least 7 terms of the series to be certain that the partial sum Sn is within 1/100 of the sum.

We want to find the smallest value of n such that the absolute value of the difference between the sum of the first n terms and the sum of the entire series is less than 1/100.

The sum of the first n terms of the series is given by:

Sn = ∑_(k=1[tex])^n[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex]

We can write the sum of the entire series as:

S = ∑_(k=[tex]1)^∞[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex]

The absolute value of the difference between the sum of the first n terms and the sum of the entire series is:

|S - Sn| = |∑_(k=n+1[tex])^∞[/tex] [tex](-1)^(k+1)/2^k|[/tex]

We want to find the smallest value of n such that |S - Sn| < 1/100.

Let's start by evaluating the sum of the series:

S = ∑_(k=1) (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex] = 1/2 - 1/4 + 1/8 - 1/16 + ...

This is a geometric series with first term a = 1/2 and common ratio r = -1/2. The sum of the series is:

S = a/(1-r) = (1/2)/(1+1/2) = 1/3

Now we can write:

|S - Sn| = |∑_(k=n+1[tex])^∞[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k|[/tex] <= 1/[tex]2^(n+1)[/tex]

The last inequality is true because the terms of the series are decreasing in absolute value, and we are summing an infinite number of terms.

Therefore, we need to find the smallest value of n such that 1/2^(n+1) < 1/100. This gives:

n+1 > log2(100)

n > log2(100) - 1

n > 6.64

The smallest integer value of n that satisfies this inequality is n = 7.

Therefore, we need at least 7 terms of the series to be certain that the partial sum Sn is within 1/100 of the sum.

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Reflection across the y-axis is the transformation used to the polygon ABCD. The type of transformation shown is a horizontal translation.

A polygon is closed geometric shape that is made up of straight line segments connected end to end. It is  two-dimensional shape that has three or more sides, angles, and vertices.

In a polygon, sides do not cross each other and vertices are points where two sides meet.

1)  The type of transformation shown in the image is a Horizontal translation, because the second polygon A'B'C'D' is moved horizontally to the right of the original polygon ABCD while maintaining its size and shape.

2) 90° clockwise rotation

3)  90° counterclockwise rotation.

4)  Reflection across the x-axis.

5)  Reflection across the y-axis.

6)  Reflection across the y-axis

7)  the correct answer is 180° clockwise rotation.

The type of transformation shown is a horizontal translation, since the image has been shifted horizontally from the original position.

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complete question -

The product (k/3) x 12 is greater than 12 for values of k greater than 3.

To determine the values of k for which the product (k/3) x 12 is greater than 12, follow these steps:

Step 1: Set up the inequality:
(k/3) x 12 > 12

Step 2: Simplify the inequality by dividing both sides by 12:
(k/3) > 1

Step 3: Multiply both sides by 3 to solve for k:
k > 3

So, the product (k/3) x 12 is greater than 12 for values of k greater than 3.

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The volume of cement in cubic feet that will be needed is 45 cubic feet.

Volume is the space occuppied by an object.

To calculate the volume of cement in cubic feet that will be needed, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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a. By central limit theorem, P(XB- XA >= 0. 2) is approximately 0.0228 under the condition that μA=μB.

b. Yes, we can conclude that the observed difference in sample means does provide evidence that the two population means for the two machines are different.

a. Using the central limit theorem, we know that the sampling distribution of the difference in means (XB - XA) is approximately normal with mean (μB - μA) and standard deviation (σ/√n), where σ is the population standard deviation (σ=1 ounce) and n is the sample size (n=36 for both machines).

So, P(XB - XA >= 0.2) can be calculated by standardizing the difference in means:

Z = (XB - XA - (μB - μA)) / (σ/√n)
Z = (4.7 - 4.5 - 0) / (1/√36)
Z = 2

Looking up the probability of Z being greater than or equal to 2 in a standard normal distribution table, we find P(Z >= 2) = 0.0228.

Therefore, P(XB - XA >= 0.2) is approximately 0.0228 under the condition that μA=μB.

b. The difference in sample means (XB - XA = 0.2) is relatively small compared to the population standard deviation (σ=1 ounce). However, the calculated probability in part a (0.0228) suggests that the observed difference in sample means is statistically significant at a significance level of 0.05 (since P(XB - XA >= 0.2) < 0.05).

Therefore, we can conclude that the observed difference in sample means does provide evidence that the two population means for the two machines are different. However, further testing or analysis may be necessary to confirm this conclusion.

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a. The equation to solve for x is given as follows: 2x + 8 = 42.

b. The solution for x is given as follows: x = 17.

The value of x is obtained applying the angle bisection theorem, which divides an angle into two angles of equal measure, hence the opposite segments also have equal length.

The segments for this problem, along with their lengths, are given as follows:

Hence the equation is given as follows:

2x + 8 = 42.

The value of x is given as follows:

2x = 34

x = 17.

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The statement''El 91 no es un número primo porque tiene más divisores que el 1 y el 91''  is true because  91 is not a prime number.

A prime number is a positive integer that has only two divisors, 1 and itself. To check if 91 is a prime number, we need to find its divisors. We can start by dividing 91 by 2, but we find that 2 is not a divisor of 91. Next, we can try dividing it by 3, and we get 30 with a remainder of 1. This means that 3 is not a divisor of 91 either.

We continue dividing by 4, 5, 6, and so on until we reach 13, which gives us 7 as a quotient and 0 as a remainder. Therefore, the divisors of 91 are 1, 7, 13, and 91, which means that 91 is not a prime number because it has more than two divisors. Hence, the statement is true.

91 ÷ 2 = 45 r 1

91 ÷ 3 = 30 r 1

91 ÷ 4 = 22 r 3

91 ÷ 5 = 18 r 1

91 ÷ 6 = 15 r 1

91 ÷ 7 = 13 r 0

Since 91 has more than two divisors, it is not a prime number.

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He must sell the car at R80,625 to make an overall profit of 25%

To find the selling price of the car that gives a 25% profit, we need to use the following steps:

Calculate the total cost of buying and transporting the car to Durban:

Total cost = Cost of car + Cost of transportation

Total cost = R60,000 + R4,500

Total cost = R64,500

Calculate the desired profit:

Profit = 25% of total cost

Profit = 0.25 x R64,500

Profit = R16,125

Calculate the total amount that the car needs to be sold for:

Total amount = Total cost + Profit

Total amount = R64,500 + R16,125

Total amount = R80,625

Therefore, the man needs to sell the car for R80,625 to make an overall profit of 25%.

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The budgeted ending raw material inventory for May is 2,560 pounds, calculated by taking 25% of the next month's budgeted production (12,800 units) multiplied by 2 pounds per unit.

To solve this problem, we need to calculate the budgeted production and raw material inventory for June, July, and August.

Budgeted production = 12,800 units + 30% * 16,800 units = 17,440 units

Raw material inventory = 25% * 17,440 units * 2 pounds = 8,720 pounds

Budgeted production = 16,800 units + 30% * 14,800 units = 20,840 units

Raw material inventory = 25% * 20,840 units * 2 pounds = 10,420 pounds

Budgeted production = 14,800 units + 30% * 20,840 units = 20,632 units

Raw material inventory = 25% * 20,632 units * 2 pounds = 10,316 pounds

To find the budgeted ending finished goods inventory for June, we need to subtract the budgeted sales for June from the budgeted production for June and add the budgeted ending finished goods inventory for May:

Budgeted ending finished goods inventory for June = 17,440 units - 12,800 units + 3,840 units = 8,480 units

Similarly, we can find the budgeted ending finished goods inventory for July and August:

Budgeted ending finished goods inventory for July = 20,840 units - 16,800 units + 8,480 units = 12,520 units

Budgeted ending finished goods inventory for August = 20,632 units - 14,800 units + 12,520 units = 18,352 units

Therefore, the budgeted ending finished goods inventory for June, July, and August are 8,480 units, 12,520 units, and 18,352 units, respectively. The budgeted raw material inventory for June, July, and August are 8,720 pounds, 10,420 pounds, and 10,316 pounds, respectively.

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Answer:

Step-by-step explanation:

If there are 180 degrees in a triangle total and in this problem we know that one angle is 49 and the other is 39, we can assume that subtracting 39 and 49 from 180 will find x. In this case, x will be 92.

Answer:

C) 1,050

Step-by-step explanation:

We can see that to get from 8.4 to 42 and to get from 42 to 210, we have to multiply by 5.

To complete the sequence, multiply 210 by 5

210·5

=1,050

Hope this helps!

Answer:

if the two angles are equal

we use sss therom to solve it

2ft/6ft=24ft/xft

x=(6*24)/2

=72

The angle of elevation of the room is approximately 19.1 degrees.

To determine the angle of elevation of the room, we need to use trigonometry. The angle of elevation is the angle between the horizontal plane and the line of sight from the rover to the room. We can use the tangent function to find this angle:

tan(angle of elevation) = opposite/adjacent

In this case, the opposite side is the vertical distance of 65 meters and the adjacent side is the horizontal distance of 180 meters. So we have:

tan(angle of elevation) = 65/180

To find the angle of elevation, we can take the inverse tangent (or arctan) of both sides:

angle of elevation = arctan(65/180)

Using a calculator, we get:

angle of elevation = 19.1 degrees (rounded to the nearest thousands of degree)

Therefore, the angle of elevation of the room is approximately 19.1 degrees.

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We are not given the distance between the spheres, so we cannot calculate the force without that information.

To calculate the electrostatic force between the two charged spheres, we can use Coulomb's law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Mathematically, we can express this as:

F = k * (q1 * q2) / r^2

Where F is the electrostatic force, k is Coulomb's constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges of the spheres, and r is the distance between their centers.

We are given the charges of the two spheres: sphere A has a charge of +1.0 x 10^-6 C, and sphere B has a charge of -1.6 x 10^-6 C.

However, we are not given the distance between the spheres, so we cannot calculate the force without that information.

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If c represents the cost per pound for the plums, the cost per pound for the plums is $0.90.

First, we need to determine the total cost of the plums before the coupon was applied.

4 1/5 pounds can be written as a mixed number:

4 1/5 = 21/5

So, the total cost of the plums without the coupon can be found by multiplying the cost per pound (c) by 21/5:

Total cost = c * 21/5

Now we can create an equation to represent the total cost after the coupon was applied:

Total cost - coupon = $3.23

Substituting the expression for total cost:

c * 21/5 - 0.55 = 3.23

To solve for c, we can start by adding 0.55 to both sides:

c * 21/5 = 3.78

Then, we can isolate c by multiplying both sides by the reciprocal of 21/5:

c = 3.78 / (21/5)

c = 0.90

Therefore, the cost per pound for the plums is $0.90.

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To find the equation of the plane that passes through the point (0, 9, 0) and is perpendicular to the vector n = -2i ÷ 4k, we first need to find the normal vector of the plane.

Since the plane is perpendicular to the given vector, the normal vector will be parallel to it. So, we can take the given vector and multiply it by -1 to get a vector in the opposite direction, which will be normal to the plane.

n = -2i ÷ 4k = -1/2i ÷ k

Multiplying by -1 gives us:

n = 1/2i ÷ k

Now we can use the point-normal form of the equation of a plane:

r · n = d

where r is the position vector of any point on the plane, n is the normal vector, and d is the distance of the plane from the origin (since the normal vector is normalized, d will be the signed distance of the plane from the origin).

Substituting the given point (0, 9, 0) and the normal vector n = 1/2i ÷ k into the equation, we get:

(0, 9, 0) · (1/2i ÷ k) = d

0 + 9(1/2) + 0 = d

d = 4.5

So the equation of the plane is:

x/2 + z/2 = 4.5

or, multiplying by 2 to eliminate fractions:

x + z = 9

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Sally Rose's new balance is $3,282.35, and option (b) is the correct answer.

Sally Rose's charge account statement contains information about her previous balance, finance charge, new purchases, and payment. To determine her new balance, we need to take the previous balance, add the finance charge and new purchases, and then subtract the payment.

Starting with the previous balance of $6,472.82, we add the finance charge of $12.95 and new purchases of $1,697.08 to get a total of:

$6,472.82 + $12.95 + $1,697.08 = $8,182.85

Next, we subtract the payment of $4,900.50 to get the new balance:

$8,182.85 - $4,900.50 = $3,282.35

It's important to keep track of credit card balances to avoid accumulating too much debt and paying high interest charges. When making credit card payments, it's a good idea to pay more than the minimum amount due, which can help reduce the balance faster and save money on interest charges over time. The answer is option b).

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The area of a rectangle can be found by multiplying its length and width.

To find the area of rectangles with different perimeters, we need to use the formula:

Area = length x width

Possible dimensions:

Length = 5 cm, Width = 3 cm

Length = 4 cm, Width = 4 cm

Area of the first rectangle = 5 cm x 3 cm = 15 cm²

Area of the second rectangle = 4 cm x 4 cm = 16 cm²

Possible dimensions:

Length = 6 cm, Width = 4 cm

Length = 5 cm, Width = 5 cm

Area of the first rectangle = 6 cm x 4 cm = 24 cm²

Area of the second rectangle = 5 cm x 5 cm = 25 cm²

Possible dimensions:

Length = 4 cm, Width = 3 cm

Area of the rectangle = 4 cm x 3 cm = 12 cm²

Therefore, the areas of the possible rectangles with perimeters 16cm, 20cm, and 14cm are:

For perimeter 16cm: 15 cm² and 16 cm²

For perimeter 20cm: 24 cm² and 25 cm²

For perimeter 14cm: 12 cm²

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The function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20).

To answer this question, we need to identify the function that best models the number of game consoles sold in millions x years since 2010.

Option A can be simplified to g(x) = 30, which is a constant function. This means that it does not depend on the value of x and is not a good model for the number of game consoles sold over time.

Option B can be simplified to g(x) = 3x, which is a linear function. This means that the number of game consoles sold increases at a constant rate over time. This could be a good model for the number of game consoles sold, but we need to compare it to the other options.

Option C can be simplified to g(x) = 0.03x, which is also a linear function. However, the rate of increase is much slower than in option B. This is not a good model for the number of game consoles sold.

Option D can be simplified to g(x) = 300, which is a constant function like option A. Again, this is not a good model for the number of game consoles sold over time.

Therefore, the function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20). This is a linear function that represents a constant rate of increase in the number of game consoles sold over time.

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complete question:

Based on this information, which function best models the number of game consoles

sold in millions x years since 2010?

A- g(x) = 0.15(20)^x

B- g(x) = 20(0.15)^x

C- g(x) = 20(1.5)^x

D- g(x) = 0.15(.2)^x

The number of bases, faces, edges and vertices are;

7. 2, 4, 6, 6

8. 6, 5, 10, 10

9. 1, 4, 5, 5

10. 1, 5, 7 , 7

11. 1, 5, 7, 7

12. 1, 3, 4 , 4

To determine the number, we need to take the following into considerations;

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Answer:

This function is an exponential function because the base is a constant and the exponent is a variable.

Answer: -40

Step-by-step explanation:

Rate of change is calculated as the slope. The formula for Slope is:

S = [tex]\frac{x_{1}-x_{2} }{ y_{1}-y_{2}}[/tex]

The two points we have are when x = 3 and 6.

the points are (3, 120) and (6, 0), as we can see.

plugging into the slope formula:

S = [tex]\frac{120-0 }{ 3-6}[/tex]

S = 120/-3

S = -40

Which hopefully makes sense, because the slope is negative, (the graph is falling).

The probability values when calculated are

From the question, we have the following parameters that can be used in our computation:

Cards = {1, 2, 3, 4, 5}

Selecting two cards without replacement

So, we have

P(2 numbers greater than 3) = 2/5 * 1/4

P(2 numbers greater than 3) = 0.1

P(2 even numbers) = 2/5 * 4/4

P(2 even numbers) = 0.4

P(2 cards with same numbers) = 1/5 * 0/4

P(2 cards with same numbers) = 0

P(1 card is 3) = 2 * 1/5 * 3/4

P(1 card is 3) = 0.3

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An equation to model this situation will be S(t) = 4 * 10^(t). The average rate of change for the number of shares from 2 minutes to 4 minutes is approximately 19,800 shares per minute.

a. Let S(t) be the number of shares of the video at time t in minutes after Steph Curry shared it with his friends. The initial number of shares is 4 (the 4 friends he shared it with), and the number of shares increases by a factor of 10 every minute. Therefore, we can model this situation with the exponential function:

S(t) = 4 * 10^(t)

b. The average rate of change for the number of shares from 2 minutes to 4 minutes can be calculated by finding the slope of the line connecting the points (2, S(2)) and (4, S(4)) on the graph of S(t). Using the equation S(t) = 4 * 10^(t), we have:

S(2) = 4 * 10^(2) = 400

S(4) = 4 * 10^(4) = 40,000

The slope of the line connecting these two points is:

(S(4) - S(2)) / (4 - 2) = (40,000 - 400) / 2 = 19,800

Therefore, the average rate of change for the number of shares from 2 minutes to 4 minutes is approximately 19,800 shares per minute.

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The mean absolute deviation is 6.25.

To find the mean absolute deviation (MAD), we first need to find the mean of the scores:

Mean = (68 + 76 + 63 + 58 + 64 + 75 + 78 + 78) / 8 = 69.5

Next, we need to find the absolute deviation of each score from the mean. The absolute deviation is the absolute value of the difference between the score and the mean.

For example, the absolute deviation of the first score (68) is:

|68 - 69.5| = 1.5

We can calculate the absolute deviation for each score:

|68 - 69.5| = 1.5

|76 - 69.5| = 6.5

|63 - 69.5| = 6.5

|58 - 69.5| = 11.5

|64 - 69.5| = 5.5

|75 - 69.5| = 5.5

|78 - 69.5| = 8.5

|78 - 69.5| = 8.5

To find the MAD, we take the average of the absolute deviations:

MAD = (1.5 + 6.5 + 6.5 + 11.5 + 5.5 + 5.5 + 8.5 + 8.5) / 8 = 6.25

Therefore, the mean absolute deviation is 6.25.

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The height of the triangle is 2 meters.

Para encontrar la altura del triángulo, podemos utilizar la fórmula para calcular el área de un triángulo:

Área = (base x altura) / 2

Sabemos que el área es de 1.5 m² y que la base mide 1.5 m, por lo que podemos despejar la altura de la siguiente manera:

1.5 m² = (1.5 m x altura) / 2

Multiplicando ambos lados por 2:

3 m² = 1.5 m x altura

Despejando la altura:

altura = 3 m² / 1.5 m

altura = 2 m

Por lo tanto, la altura del triángulo que representa al pino en el periódico mural es de 2 metros.

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Answer:

a)  15, 18, 27, 48, 52, 86, 103

b)  Minimum number = 15

c)  Maximum number = 103

d)  Median = 48

e)  First quartile = 18

f)  Third quartile = 86

g)  Interquartile range = 68

Step-by-step explanation:

To write the data from least to greatest, arrange the numbers in ascending order:

[tex]\hrulefill[/tex]

The minimum number in a set of data is the smallest value.

Therefore, the minimum number of animals is 15.

[tex]\hrulefill[/tex]

The maximum number in a set of data is the greatest value.

Therefore, the maximum number of animals is 103.

[tex]\hrulefill[/tex]

The median of a set of data is the middle value when all data values are placed in order of size.  

[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &&&\uparrow&&&\\&&&\sf median&&&\end{array}[/tex]

Therefore, the median is the fourth number, which is 48.

[tex]\hrulefill[/tex]

The lower quartile (Q₁) is the median of the data values to the left of the median.  

[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &\uparrow &&\uparrow&&&\\&\sf Q_1&&\sf median&&&\end{array}[/tex]

Therefore, the median of the first half of the data is 18.

[tex]\hrulefill[/tex]

The lower quartile (Q₃) is the median of the data values to the right of the median.  

[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &&&\uparrow &&\uparrow&\\&&&\sf median&&\sf Q_3&\end{array}[/tex]

Therefore, the median of the second half of the data is 86.

[tex]\hrulefill[/tex]

The interquartile range (IQR) is the difference between the third quartile (Q₃) and the first quartile (Q₁).

[tex]\begin{aligned}\sf IQR &=\sf Q_3 - Q_1 \\&= \sf 86 - 18 \\&= \sf 68\end{aligned}[/tex]

Therefore, the interquartile range is 68.

The number of triangles formed or the interior angle sum should be matched to each regular polygon as follows;

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon can be calculated by using this formula:

Sum of interior angles = 180 × (n - 2)

1,440 = 180 × (n - 2)

1,440 = 180n - 360

180n = 1,440 + 360

n = 1,800/180

n = 10 (decagon).

Sum of interior angles = 180 × (n - 2)

1,800 = 180 × (n - 2)

1,800 = 180n - 360

180n = 1,800 + 360

n = 2,160/180

n = 12 (dodecagon).

Generally speaking, the number of triangles in a regular polygon (n-gon) can be calculated by using this formula;

Number of triangles = n - 2

4 = n - 2

n = 4 + 2 = 6 (regular hexagon).

Number of triangles = n - 2

6 = n - 2

n = 6 + 2 = 8 (regular octagon).

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Answer:

0,8

Step-by-step explanation:

Answer:

x^2 / 81 + y^2 / 56 = 1

Step-by-step explanation:

The center of the ellipse is at the midpoint of the foci, which is (0,0). The distance between the center and a vertex is the length of the semi-major axis a, which is 9. The distance between the center and a focus is c, which is 5. The equation for the ellipse is:

(x-0)^2 / 9^2 + (y-0)^2 / b^2 = 1

where b is the length of the semi-minor axis. To find b, you use the relationship:

b^2 = a^2 - c^2

b^2 = 9^2 - 5^2

b^2 = 56

Therefore, the equation for the ellipse is:

x^2 / 81 + y^2 / 56 = 1

We know that by solving for t, you can find the amount of time Roger spent answering phone calls

You can use the equation t + 40 = 90, where t represents the amount of time Roger answers phone calls at the information desk.

This equation takes into account that Roger spends 40 minutes delivering flowers and the total time he volunteers at the hospital is 90 minutes.

By solving for t, you can find the amount of time Roger spent answering phone calls.

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