Use spherical coordinates.
Evaluate ∭E^xe^(x2+y2+z2) dV∭, where E id the portion of the unit ball x2+y2+z2≤1that lies in the first octant.

The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

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To find the volume of the gift box, we need to multiply the length, width, and height together.First, let's convert all the dimensions to improper fractions:

Length: 14 1/4 = 57/4,

Width: 9 1/4 = 37/4, 

Height: 1 7/8 = 15/8

Now we can multiply them together:

57/4 * 37/4 * 15/8 = 31,635/128

To write this as a mixed number in simplest form, we need to divide the numerator by the denominator and express the result as a mixed number:

31,635/128 = 247 with remainder of 19

So, the volume of the gift box is 247 19/128

The online retailer will make $4 on a sale of $80. This is calculated by multiplying the cost of the sale ($80) by the retailer's percentage (5%).

The first step in calculating the retailer's profit is to identify the cost of the sale. In this case, the cost of the sale is $80.

The next step is to identify the percentage of the cost that the retailer will receive. In this case, the retailer will receive 5% of the cost of the sale.

The third step is to calculate the retailer's profit. This can be done by multiplying the cost of the sale ($80) by the retailer's percentage (5%). This calculation results in $4, which is the retailer's profit for this sale. Hence, the online retailer will make $4 on a sale of $80.

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Answer:

(2a + 3b)² = 121

Step-by-step explanation:

given 4a² + 9b² = 25 and ab = 8

(2a + 3b)² ← expand using FOIL

= 4a² + 6ab + 6ab + 9b²

= 4a² + 9b² + 12ab ← substitute given values from above

= 25 + 12(8)

= 25 + 96

= 121

Answer:

Step-by-step explanation: The answer is 115+2c+5c.

Friday the reception desk which gives her 115 dollars.

Thursday and Saturday she cut hair for 2 hrs and 5 hrs respectively.so if she earns ‘c’ dollars per hour for cutting hair it is 2c and 5c respectively.

so the total amount of money is 2c+115+5c

For the first question, the correct graph would be option B (b-a)², as the water level decreases at a constant rate and then remains constant, which would result in a diagonal line followed by a horizontal line on a graph.

An expression is a combination of symbols and/or numbers that can be evaluated or simplified to obtain a numerical or symbolic result. Expressions can be composed of one or more terms, which are separated by arithmetic operations, such as addition, subtraction, multiplication, or division.

For the second question, the area of the smaller square can be calculated using the expression (c - b)² or option C. This is because the length of the side of the larger square is c, and one side of the smaller square is equal to the difference between the side length of the larger square and the length of the smallest side of one of the congruent triangles, which is c - b.

Taking the square of this difference gives the area of the smaller square. Option D (a-b)² and option E b(c-b) are not correct expressions for the area of the smaller square, and option A does not provide enough information to calculate the area of the smaller square. Option (c - b)² is equivalent to option F.

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29. The correct graph would be option B (b-a)², as the water level decreases at a constant rate and then remains constant.

30. The area of the smaller square can be calculated using the expression (c - b)² or option C.

An expression is a combination of symbols and/or numbers that can be evaluated or simplified to obtain a numerical or symbolic result. Expressions can be composed of one or more terms, which are separated by arithmetic operations, such as addition, subtraction, multiplication, or division.

For the first question, the correct graph would be option B (b-a)², as the water level decreases at a constant rate and then remains constant, which would result in a diagonal line followed by a horizontal line on a graph.

For the second question, the area of the smaller square can be calculated using the expression (c - b)² or option C. This is because the length of the side of the larger square is c, and one side of the smaller square is equal to the difference between the side length of the larger square and the length of the smallest side of one of the congruent triangles, which is c - b.

Taking the square of this difference gives the area of the smaller square. Option D (a-b)² and option E b(c-b) are not correct expressions for the area of the smaller square, and option A does not provide enough information to calculate the area of the smaller square. Option (c - b)² is equivalent to option F.

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The equation of Basanta's walking route is: y = -2x + 10

We can find the equation of Basanta's walking route by using the slope-intercept form of a linear equation:

y = mx + b

where m is the slope of the line and

b is the y-intercept.

To find the slope of Basanta's walking route, we can use the coordinates of two points on the line, namely B(6, -2) and K(4, 2):

slope = (y2 - y1) / (x2 - x1)

= (2 - (-2)) / (4 - 6)

= 4 / (-2)

= -2

To find the y-intercept, we can use the coordinates of one of the points on the line, for example, B(6, -2):

y = mx + b

-2 = (-2)(6) + b

-2 = -12 + b

b = 10

Therefore, the equation of Basanta's walking route is: y = -2x + 10

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The measure of angle A is 112 degrees. Hence, option d is correct.

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Similarly, since the angle of the cut is 36 degrees, the angle opposite it (angle BCD) is also 36 degrees. Since angles BCD and BDC add up to 90 degrees (because triangle BCD is a right triangle), angle BDC measures 54 degrees (90 - 36 = 54).

Now, we can find angle BDA by subtracting angle ADB and angle BDC from 180 degrees:

angle BDA = 180 - angle ADB - angle BDC

= 180 - 58 - 54

= 68

Finally, we can find angle A by subtracting angle BDA from 180 degrees:

angle A = 180 - angle BDA

= 180 - 68

= 112

Therefore, the measure of angle A is 112 degrees. Hence, option d is correct.

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Complete question:

the mean of the data is 0.54,the median of the data is 0.6.and  the mode(s) of the data are 0.4 and 0.6.

what is median ?

The median is a measure of central tendency that represents the middle value in a dataset when the data are arranged in numerical order. It is a value that separates the dataset into two equal halves.

In the given question,

To find the mean of the data, we add up all the values and divide by the total number of values:

Mean = (0.4 + 0.6 + 0.6 + 0.9 + 0.4 + 0.5 + 0.8) / 7

Mean = 3.8 / 7

Mean = 0.54

Therefore, the mean of the data is 0.54.

To find the median of the data, we first need to put the values in order:

0.4, 0.4, 0.5, 0.6, 0.6, 0.8, 0.9

Since there are an odd number of values, the median is the middle value, which is 0.6.

Therefore, the median of the data is 0.6.

To find the mode(s) of the data, we look for the value(s) that appear most frequently:

0.4 appears twice

0.6 appears twice

Therefore, the mode(s) of the data are 0.4 and 0.6.

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Check the picture below.

so the volume of each green box will be 1x1x1, and the volume of the whole rectangular prism on the back of Nico's truck is 7x4x8.

Now, let's get the volume of the containing rectangular prism, and then the volume of each box and do a division, namely, "how many times does the volume of a box go into the volume of the prism?"

[tex]\stackrel{\textit{volume of the prism}}{(7)(4)(8)}\div \stackrel{\textit{volume of one box}}{(1)(1)(1)}\implies \cfrac{(7)(4)(8)}{(1)(1)(1)}\implies \cfrac{224}{1}\implies \stackrel{ boxes }{\text{\LARGE 224}}[/tex]

Perimeter = 2(3 mi + 1 mi) = 8 miles.

A coefficient is a numerical factor that is multiplied by a variable or a term in an algebraic expression. In mathematics, coefficients are commonly used in polynomial functions, where they determine the degree of the polynomial and the specific values of the function.

For example, in the polynomial function [tex]f(x) = 3x^2 + 2x - 1[/tex], the coefficients are 3, 2, and -1. The coefficient 3 is multiplied by the variable [tex]x^2[/tex], the coefficient 2 is multiplied by the variable x, and the coefficient -1 is the constant term.

by the question.

If you are referring to a rectangle, then the perimeter would be:

Perimeter = 2(length + width)

Assuming the 3 mi and 1 mi are the length and width respectively, then the perimeter would be:

Perimeter = 1 mile + 1 mile + unknown length of the third side

Perimeter = 2(3 mi + 1 mi) = 8 miles

perimeter = 8 mi.

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Complete question -

Find the perimeter of following -

3 mi. 1l mi.​

Answer:

Step-by-step explanation:

Answer:

25.1

Step-by-step explanation:

formula for circumfrance is 2piR

so (2pi)(4)= 25.1

:)

Answer: x=1 y=6

Step-by-step explanation:

The polynomial function of least degree possible using the given information.

Real roots: −1 (with multiplicity 2), 1 and (2,

f(2)) = (2, 7) is f(x) = x³ - 3x² + 3x - 1.

Since the polynomial function has real roots at -1 (with multiplicity 2) and 1, we know that the factors of the polynomial are (x + 1)² and (x - 1).

Let the polynomial be of the form f(x) = ax³ + bx² + cx + d. We know that f(2) = 7, so:

a(2³) + b(2²) + c(2) + d = 7

8a + 4b + 2c + d = 7

Now we need to use the fact that the roots are -1 (with multiplicity 2) and 1. Since the polynomial has factors of (x + 1)² and (x - 1), we can write the polynomial as:

f(x) = a(x + 1)²(x - 1)

Expanding this expression, we get:

f(x) = a(x² - 2x + 1)(x - 1)

f(x) = ax³ - 3ax² + 3ax - a

Now we can equate the coefficients of this expression with the coefficients of our assumed polynomial f(x) = ax³ + bx² + cx + d:

a = a

-3a = b

3a = c

-a = d

Therefore, our polynomial function is:

f(x) = x³ - 3x² + 3x - 1

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After calculation, we know that rate of growth of the seed is 2/9 feet in 1 month which is in proper fraction.

Take the current number and subtract it from the prior value to determine the growth rate.

The growth rate is then expressed as a percentage by multiplying the difference by the previous number and dividing by 100.

The three types of growth identified by the Harrod-Domar model are warranted growth, real growth, and the natural rate of growth.

The economy cannot continue to develop at this rate indefinitely or without experiencing a downturn, which is known as the warranted growth rate.

The annual increase in a country's real GDP rate is known as actual growth.

So, we know that the seed grows:

2/3 foot in 3 months

Then, the rate of growth in 1 month was:

= 2/3 ÷ 3

= 2/3 ÷ 3/1

= 2/3 * 1/3

= 2/9 foot

Therefore, after calculation, we know that rate of growth of the seed is 2/9 feet in 1 month which is in proper fraction.

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Since I and m are in direct proportion, we can write:

I = km

where k is the constant of proportionality.

From the given equation of proportionality, we have:

I/m = 9

Multiplying both sides by m, we get:

I = 9m

So, the constant of proportionality is k = 9.

If m increases from 4 to 7, then we can find the increase in I as follows:

ΔI = I2 - I1

where I1 is the initial value of I when m = 4, and I2 is the final value of I when m = 7.

From the equation of proportionality, we have:

I1 = km1 = 9(4) = 36

I2 = km2 = 9(7) = 63

Therefore, the increase in I is:

ΔI = I2 - I1 = 63 - 36 = 27

So, if m increases from 4 to 7, then I increases by 27.

After answering the provided question, we can conclude that which  slope equals m = 1/2. As a result, the second line's equation is y - 2 = (1/2)(x - 2), or y = (1/2)x + 1.

In mathematics, the slope-intercept form of a linear equation is an equation of the form y = mx + b, where m is the line's gradient and b is the más, which is the point on the line where it intersects the y-axis. Because it allows you to speedily see the line and ascertain its slope and y-intercept, the slope-intercept form is a useful way to represent a line's equation. The slope of the line indicates its steepness, while the esta indicates in which the line intersects the y-axis.

To answer these questions, we must first determine the equation of the line depicted in the graph. Assume the line is in slope-intercept form, y = mx + b, with m representing the slope and b representing the y-intercept.

where m is the slope to be found. Because we want this line to intersect the given line at (4, 3), we can plug those values into both equations and solve for m: Because y = (1/4)x + 1, we get 3 = (1/4)(4) + 1 = 2 + 2m, which equals m = 1/2. As a result, the second line's equation is y - 2 = (1/2)(x - 2), or y = (1/2)x + 1.

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After simplifying this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 so the answer is 19/15.

Suppose there are two pizza slices on a plate. One slice is divided into 3 equal parts, and the other slice is divided into 5 equal parts. If you eat 2 out of the 3 parts of the first slice and 3 out of the 5 parts of the second slice, what fraction of the total pizza have you eaten?

To solve the problem, we need to add the fractions together. The fraction of the first slice eaten is 2/3, and the fraction of the second slice eaten is 3/5. We must identify a common denominator in order to add these fractions. In this case, the least common multiple of 3 and 5 is 15. So we need to convert both fractions so that they have a denominator of 15.

To convert 2/3 to a fraction with a denominator of 15, we need to multiply both the numerator and denominator by 5. This gives us 10/15. To convert 3/5 to a fraction with a denominator of 15, we need to multiply both the numerator and denominator by 3. This gives us 9/15.

We can now put the two fractions together because they both have the same denominator. This results in:

10/15 + 9/15 = 19/15

By dividing the denominator and numerator by their 1 greatest common factor, we may simplify this fraction. The final response is thus: 19/15

To act out this problem, we can draw a pizza with two slices, one divided into 3 parts and the other divided into 5 parts. We can then shade in the parts that have been eaten (2 out of 3 for the first slice and 3 out of 5 for the second slice), and count the total number of shaded parts. We can then convert this count into a fraction and simplify it if necessary.

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The distance north of Helicopter A from helicopter B is 1. 03 km.

The shortest distance between the polar bear and the conservationists is 9.36 km.

To find the distance from Helicopter A to Helicopter B in the north direction, we can use trigonometry. We can create a right triangle with the north direction as one side, the distance between the helicopters as the hypotenuse, and the angle of 122° between them.

Let N be the north distance between A and B. We can use the sine function:

sin(angle) = opposite side / hypotenuse

sin(122°) = N / 1.2 km

Now, solve for N:

N = 1.2 km x sin (122°) = 1.03 km

The polar bear's position is given as 3 km eastward and on a bearing of 104°. To find the shortest distance between the polar bear and the conservationists, we need to consider the right triangle formed by the eastward direction, the north direction, and the distance between the polar bear and the conservationists as the hypotenuse.

Let D be the shortest distance between the polar bear and the conservationists. We can use the cosine function:

cos(angle) = adjacent side / hypotenuse

cos(104°) = 3 km / D

Now, solve for D:

D = 3 km / cos(104°) = 9.36 km

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The group of friends can consist of up to 10 people if they want to stay within their budget of $152.75 for parking and admission.

Total cost = parking cost + ticket cost

The ticket cost for x people can be expressed as:

Ticket cost = x × $14.25

the cost of each ticket is $14.25.

the total cost for x people can be expressed as:

= $10.25 + x × $14.25

the group has a budget of $152.75 to spend on parking and admission, so we can set up

$152.75 = $10.25 + x × $14.25

Now we can solve for x by first subtracting $10.25

$152.75 - $10.25 = x × $14.25

Simplifying:

$142.50 = x × $14.25

Finally, we can solve for x

x = $142.50 ÷ $14.25

x = 10

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Let us consider the ratio to be x

So, as per the question's statement, we can write it as;

[tex]5x+4x=36[/tex]

[tex]\implies 9x=36[/tex]

We will divide 9 on both the sides, we get;

[tex]\implies x=\dfrac{36}{9} =4[/tex]

So, for getting the number of puppy sold we have to multiply it with 5, we get:

[tex]5x=5\times4=20[/tex]

They have sold 20 puppies.

Hence, the answer is [tex]20[/tex] puppies.

Divide data A by data B to find your ratio. In the example above, 5/10 = 0.5. Multiply by 100 if you want a percentage. If you want your ratio as a percentage, multiply the answer by 100.

Ratios can be fully simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided any more.

a. The median attendance is 796, and the IQR is 229. b. the museum should schedule 37 staff members. c. A scatterplot is not an appropriate display of this data because it is not continuous data, but rather discrete data.

The interquartile range (IQR) is a statistical measure that represents the spread or variability of a dataset. It is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset.

To find the interquartile range, the dataset is first arranged in order from smallest to largest. The median of the dataset is then found, and the data is split into two halves: the lower half, which contains all the data points less than or equal to the median, and the upper half, which contains all the data points greater than or equal to the median.

a. To find the median and interquartile range (IQR), we first need to arrange the attendance numbers in order from lowest to highest:

400, 593, 680, 731, 861, 870, 940

The median is the middle number, or the average of the two middle numbers. In this case, the median is:

Median = (731 + 861) / 2 = 796

To find the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data. To find Q1, we take the median of the numbers below the median:

400, 593, 680, 731

Q1 = (593 + 680) / 2 = 636.5

To find Q3, we take the median of the numbers above the median:

861, 870, 940

Q3 = (870 + 861) / 2 = 865.5

The IQR is the difference between Q3 and Q1:

IQR = Q3 - Q1 = 865.5 - 636.5 = 229

Therefore, the median attendance is 796, and the IQR is 229.

b. To find the number of staff members needed each week, we divide the total attendance by 150:

(870 + 940 + 731 + 400 + 861 + 680 + 593) / 150 ≈ 36.54

Rounding up to the nearest whole number, we get 37 staff members. Therefore, the museum should schedule 37 staff members to work each week to meet their goal of having approximately one staff member for every 150 visitors.

c. A scatterplot is not an appropriate display of this data because it is not continuous data, but rather discrete data. Attendance is measured in whole numbers of visitors, and there are only 7 data points in this set. A scatterplot is typically used to display continuous data, where there are many data points and each data point can take on any value within a certain range. Instead, a bar chart or a histogram would be a more appropriate display for this data set.

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The complete question is:

During a given week, the museum had attendance as shown in the table at right. a. Numerically summarize the center and spread of attendance by finding the median and interquartile range (IQR). b. The museum management needs to tell the staff members their work schedules a week in advance. The museum wants to have approximately one staff member for every 150 visitors. How many staff members should be scheduled to work each week? Explain your reasoning. c. Why is a scatterplot not an appropriate display of this data?

Day           Attendance

1              870

2              940

3              731

4              400

5              861

6              680

7              593

Answer:

Yes

Step-by-step explanation:

Unit circle is the circle whose center is at origin (0, 0) and radius r = 1 unit.

equation of this circle is,

[tex]x^2 + y^2 = 1[/tex]

point P(24/25, 7/25) lies on the above curve (substitute and check).

therefore point P lies on unit circle.

Hopefully this answer have helped you!

Answer:(3x−y+5)(3−+5)

Step-by-step explanation:

the polar coordinates of P are: (r, θ) = ([tex]\sqrt{(81 +\pi ^{2} /25)}[/tex], -0.3586 + 2πk) for all integers k. There are an infinite number of polar coordinates for P, corresponding to different values of k.

To express the point P = (9, -π/5) in polar coordinates, we need to find its distance from the origin and the angle it makes with the positive x-axis.

The distance from the origin to P can be found using the formula:

r = [tex]\sqrt{(x^2 + y^2)}[/tex]

where x and y are the Cartesian coordinates of the point. Substituting the values for P, we get:

r = [tex]\sqrt{9^2}[/tex]

The angle θ that P makes with the positive x-axis can be found using the formula:

θ = atan(y/x)

where atan is the arctangent function. Substituting the values for P, we get:

θ = atan((-π/5)/9) ≈ -0.3586 radians

Note that the angle is negative because the point is in the fourth quadrant.

Therefore, the polar coordinates of P are:

(r, θ) = ([tex]\sqrt{(81 +\pi ^{2} /25)}[/tex], -0.3586 + 2πk) for all integers k.

There are an infinite number of polar coordinates for P, corresponding to different values of k.

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The value of x in the similar triangles are:

a. x = 80 ft.

b. x = 16 ft.

Similarity among two or more triangle is a common relations when the properties of the triangles are compared. But in this case, the triangle are NOT congruent.

Considering the triangles in the given question,

1. Comparing the properties of the similar triangles, we have;

So that,

30/ x = 50/ 80

50x = 4000

x = 4000/ 50

  = 80

x = 80 ft.

2. Comparing the properties of the two triangles, we have;

4.5/ 12 = 6/ x

4.5x = 72

x = 72/ 4.5

  = 16

x = 16 ft

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Step-by-step explanation:

K = G = 45°

L = H = 75 °

M = J =  180° - 45 - 75  = 60°     ( because three angles sum to 180 degrees)

Answer: The probability of a student taking the SATs is p = 0.61. Let's consider the first student we sample. The probability that this student does not take the SATs is q = 1 - p = 0.39.

If the first student does not take the SATs, we need to sample another student. The probability that the second student does not take the SATs, given that the first student did not take the SATs, is still q = 0.39.

Similarly, if the second student also does not take the SATs, we need to sample a third student. The probability that the third student does not take the SATs, given that the first two students did not take the SATs, is still q = 0.39.

We continue this process until we find the first student who takes the SATs. Let X be the number of students we sample until we find the first student who takes the SATs. Then X can take on the values 1, 2, 3, and so on.

The probability that we find the first student who takes the SATs on the first try is p = 0.61. The probability that we find the first student who takes the SATs on the second try is (q)(p) = (0.39)(0.61) = 0.238.

Similarly, the probability that we find the first student who takes the SATs on the third try is (q)(q)(p) = (0.39)(0.39)(0.61) = 0.147.

In general, the probability that we find the first student who takes the SATs on the kth try is (q)^(k-1)(p).

Therefore, the probability that we find the first student who takes the SATs in exactly k tries is:

P(X=k) = (q)^(k-1)(p)

We want to find the probability of sampling five successive students at random until we find the first student to take the SATs. So we want to find:

P(X=1) ∗ P(X=2) ∗ P(X=3) ∗ P(X=4) ∗ P(X=5)

= p ∗ (q)(p) ∗ (q)(q)(p) ∗ (q)(q)(q)(p) ∗ (q)(q)(q)(q)(p)

= (0.61) ∗ (0.39)(0.61) ∗ (0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.39)(0.61)

= 0.61 ∗ 0.238 ∗ 0.147 ∗ 0.0905 ∗ 0.0554

≈ 0.00028

Therefore, the probability of sampling five successive students at random until you find the first student to take the SATs is approximately 0.00028 or 0.028%.

Step-by-step explanation: