A store can print your soccer team's name on 12 T-shirts in 10 minutes you want to buy 30 T-shirts how long will it take the store to print 30 T-shirts if the T-shirts are always printed at the same rate

we can purchase a maximum of 23 hats if we buy them for $3.50 each, or a maximum of 27 hats if we buy them for $2.97 each.

Two or more expressions with an Equal sign is called as Equation.

Function to represent the total cost of the order in terms of the number of hats ordered:

C(n) = {3.50n, if n < 25;

2.97n, if n >= 25}

where n is the number of hats ordered, and C(n) is the cost of the order.

If the budget for hats is $80, we can set C(n) equal to 80 and solve for n:

3.50n = 80, if n < 25;

2.97n = 80, if n >= 25

For n < 25, we get:

n = 80/3.50 ≈ 22.86 =23

if the budget is $80 and the hats cost $3.50 each, we can buy a maximum of 23 hats.

For n >= 25, we get:

n = 80/2.97 ≈ 26.96

So if the budget is $80 and the hats cost $2.97 each, we can buy a maximum of 27 hats.

Therefore, we can purchase a maximum of 23 hats if we buy them for $3.50 each, or a maximum of 27 hats if we buy them for $2.97 each.

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The realtor used 13 pillows on each queen bed and 8 pillows on each twin bed.

Simultaneous equations are any one or more equations that can have the same number of unknowns and be solved concurrently. The system of equations is a simultaneous equation.

Given:

A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed.

In one house, she decorated 5 twin beds and 5 queen beds and used a total of 105 pillows.

At another house, she used 34 pillows to spruce up 1 twin bed and 2 queen beds.

Let x be the number of twin beds and y be the number of queen beds.

Now, we have a system of equations,

x + 2y = 34   {equation 1}

5x + 5y = 105  

Simplifying,

x + y = 21   {equation 2}

Subtracting equation 1 to equation 2,

we get,

y = 13 and x = 8.

Therefore, y = 13 and x = 8.

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The probability that a randomly chosen fitness club member signs up for a free running session is 0.12 or 12%.

What is probability ?
Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. For example, if the probability of an event is 0.5, it means that there is a 50% chance that the event will occur.

Given by the question:

There are a total of 100 members in the fitness club, and 30 members have signed up for the free session. Let's call the number of members who signed up for the weightlifting session "x", so the number of members who signed up for the running session and the swimming session each is "2x".

The total number of members who signed up for the free session is:

x + 2x + 2x = 5x

We know that 30 members signed up for the free session, so we can set up the following equation:

5x = 30

Solving for x, we get:

x = 6

Therefore, 6 members signed up for the weightlifting session, and 12 members signed up for each of the running and swimming sessions.

The probability of a randomly chosen member signing up for a free running session is the number of members who signed up for the running session divided by the total number of members:

P(Running) = 12/100

P(Running) = 0.12

Therefore, the probability that a randomly chosen fitness club member signs up for a free running session is 0.12 or 12%.

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At a significance level of 0.01, the hypothesis that the average number of dropouts in the high school is 21 is not refutable based on the available data.

To determine if the average number of dropouts in the high school is 21, we need to conduct a one-sample t-test. The null hypothesis is that the average number of dropouts is 21, and the alternative hypothesis is that it is not 21.

We can use statistical software or a calculator to find the test statistic and p-value. With a sample size of 17, the degree of freedom is 16. Assuming a significance level of 0.01, the critical t-value is ±2.921.

The calculated t-value for this sample is -0.294, and the p-value is 0.773. Since the calculated t-value is not in the rejection region, we fail to reject the null hypothesis. This means that we do not have sufficient evidence to claim that the average number of dropouts is different from 21.

In conclusion, at a significance level of 0.01, the hypothesis that the average number of dropouts in the high school is 21 is not refutable based on the available data.

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The statements are classified as follows:

7. Never true.

8. Never true.

9. Never true.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

Hence statement 9 is false.

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

Hence statements 7 and 8 are false.

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The correlation coefficient is 0.053, Bettina has not yet found a perfect positive relationship.

The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative relationship and +1 indicates a perfect positive relationship.

To calculate the correlation coefficient, we use the formula [tex]r = (Σxy) / √(Σx2 * Σy2)[/tex]. Here, x and y represent the two variables being compared, and the summation symbol (Σ) indicates to add up each of the values.

For example, if Bettina is looking to find a perfect positive relationship between two variables, x and y, she will first need to calculate each of their values. Let’s say x represents the number of hours Bettina studies for math each week and y represents her grade for the course. Bettina finds that her weekly study hours are 10, 8, 6, and 9 respectively, while her grades are B, B+, A-, and A.

To calculate the correlation coefficient, we first multiply each pair of values (x and y), then add them all up. In this example, that would be [tex](10*B) + (8*B+) + (6*A-) + (9*A) = 94[/tex]. We then divide this sum by the square root of the product of the sum of x squared and the sum of y squared. In this example, that would be[tex](10^2 + 8^2 + 6^2 + 9^2) * (B^2 + B+^2 + A-^2 + A^2) = 1764[/tex]. When we divide 94 by 1764, we get 0.053.

Since the correlation coefficient is 0.053, Bettina has not yet found a perfect positive relationship.

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The system of equations representing this movie theater scenario is B:

A system of equations involves two or more equations whose solutions are determined concurrently or at the same time.

A system of equations is otherwise called simultaneous equations.

The total sales revenue = $63

The total number of tickets sold = 29

The cost per unit of children tickets = $3

The cost per unit of adult tickets = $2

The cost per unit of senior tickets = $2

Let the number of children tickets sold = 3c

Let the number of adult tickets sold = a

Let the number of senior tickets sold = s

c + a + s =29 Total number of tickets sold

3c+2a+2=63 Total amount realized from the ticket sales

3a=c

Thus, the correct system of equations is Option B.

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The measure of the two remaining angles with the ratio of 6:19 would be = 24° and 76° respectively.

The total angle that makes up a triangle of any type = 180°

The value of one angle as given = 80°

Therefore the remaining total of two angles= 180-80 = 100°

The angle with the ratio of 6= 6/25×100= 600/25 = 24°

The angle with the ratio of 19 = 19/25× 100/1

= 1900/25

= 76°

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Answer:

36.75 points the first game, 26.25 points the second game, which makes 63 points he scored

Step-by-step explanation:

He must be a pro lol but anyways,

75% x 49 = 36.75

75% x 35 = 26.25

36.75+26.25=63

Case 1: x = - 11 (Correct choice: B)

Case 2: x = - 11 (Correct choice: D)

Case 3: x = - 10 (Correct choice: C)

Case 4: x = - 8 (Correct choice: B)

Case 5: x = - 6 (Correct choice: A)

Case 6: m ∠ E' = 33° (Correct choice: D)

Case 7: m ∠ C' = 41° (Correct choice: C)

In this problem we find five cases of similar triangles. Two triangles are similar when their angles are congruent and sides are not congruent though proportional. Now we proceed to determine the value of variables associated with each system of proportional triangles by means of proportionality formulas:

Case 1

(2 · x + 30) / (x + 27) = 1 / 2

2 · (2 · x + 30) = x + 27

4 · x + 60 = x + 27

3 · x = - 33

x = - 11

Case 2

(2 · x + 31) / (x + 29) = 1 / 2

2 · (2 · x + 31) = x + 29

4 · x + 62 = x + 29

3 · x = - 33

x = - 11

Case 3

(2 · x + 27) / (x + 24) = 1 / 2

2 · (2 · x + 27) = x + 24

4 · x + 54 = x + 24

3 · x = - 30

x = - 10

Case 4

(x + 19) / (x + 30) = 1 / 2

2 · (x + 19) = x + 30

2 · x + 38 = x + 30

x = - 8

Case 5

(x + 18) / (x + 30) = 1 / 2

2 · (x + 18) = x + 30

2 · x + 36 = x + 30

x = - 6

The next two cases are quadrilaterals formed by two congruent triangles. Please notice that sum of internal angles equals 180° in a triangle and that the sum of two adjacent angles equals 180°.

Case 6

m ∠ E = 180° - m ∠ D

m ∠ E = 180° - 75°

m ∠ E = 105°

m ∠ E' = 105° - 72°

m ∠ E' = 33°

Case 7

m ∠ C = 180° - m ∠ B

m ∠ C = 180° - 88°

m ∠ C = 92°

m ∠ C' = 92° - 51°

m ∠ C' = 41°

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Answer: To find the GDP per capita, we need to divide the total GDP by the population:

$50.3 billion ÷ 732,670 people = $68,547.32 per person

Rounding to the nearest hundredth:

$68,547.32 per person ≈ $68,547.32 per person

So the GDP per capita in Alaska in 2021 was $68,547.32 per person.

Step-by-step explanation:

The formula for distance between two points d = √(c- a)² + (d -b)².

To derive the formula, let us consider two points in 2D plane A (a, b) and B(c, d) is d = √(c- a)² + (d -b)².

Given:

The Euclidean distance formula is another name for the formula used to calculate the separation between two points on a two-dimensional plane.

To derive the formula, let us consider two points in 2D plane A (a, b) and B(c, d)

By the Pythagoras theorem,

d²= (c- a)² + (d -b)²

d = √(c- a)² + (d -b)²

For example, Find the distance between the points (-2, 3), and (5, 6).

d = √(c- a)² + (d -b)²

d= √(5 -(-2))² + (6 -3)²

d= √7² + 3²

d= √49+ 9

d= √58

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The female volleyball player is taller in relation to the distribution of heights based on gender.

The mean height of a man is 69 inches and the standard deviation is 2.25 inches. The mean height of a woman is 64 inches and the standard deviation is 2 inches.

To compare the heights of the female volleyball player and the male soccer player, we need to convert their heights to inches.

6 feet 2 inches is equal to 74 inches.

The female volleyball player is 10 inches taller than the mean height for women in the United States, while the male soccer player is 5 inches taller than the mean height for men in the United States.

To determine who is taller in relation to the distribution of heights based on gender, we need to compare the difference between their heights and the mean height for their respective gender in terms of the standard deviation.

For the female volleyball player, the difference is 10 inches - 64 inches (the mean height for women) = 6 standard deviations (since the standard deviation for women is 2 inches).

For the male soccer player, the difference is 10 inches - 69 inches (the mean height for men) = 4.4 standard deviations (since the standard deviation for men is 2.25 inches).

Therefore, the female volleyball player is taller in relation to the distribution of heights based on gender.

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Subsets of the given set. {b, j, v} is. {}, {b}, {j}, {v}, {b, j}, {b, v}, {j, v}, {b, j, v}, so correct option is A.

subsets of {b, j, v}

{}

{b}

{j}

{v}

{b, j}

{b, v}

{j, v}

{b, j, v}

The empty set and the original set itself are included in the power set, which is a set that contains all other subsets as well. P is typically used to indicate it. The number of subsets that can be generated from a given set determines the cardinality of a power set. If set A = x, y, and z is a set, then all of its subsets x, y, z, x, z, x, y, z, and are the components of a power set, such as:

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Let's denote the width of the rug by x.

The dimensions of the rug to the nearest tenth of a foot are:

Width ≈ 6.7 feet

Length ≈ 11.7 feet

Since the rug is 5 feet longer than it is wide, its length can be expressed as (x+5).

We know that the diagonal of the rug is 12 feet. We can use the Pythagorean theorem to set up an equation relating the length, width, and diagonal:

(diagonal)^2 = (length)^2 + (width)^2

Substituting the values we know, we get:

12^2 = (x+5)^2 + x^2

Simplifying this equation gives:

144 = 2x^2 + 10x + 25

2x^2 + 10x - 119 = 0

Using the quadratic formula, we can solve for x (the width of the rug):

x = (-10 ± √(10^2 - 4(2)(-119))) / (2(2))

x ≈ 6.7 feet (rounded to the nearest tenth)

Now we can use the expression we found for the length (x+5) to find the length of the rug:

length ≈ 11.7 feet (rounded to the nearest tenth)

The rug measures 6.7 feet wide by 11.7 feet long, to the nearest tenth of a foot.

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A tree diagram to calculate the probability of each of the four possible outcomes are 0.8, 0.8, 0.1, 0.06.

Bag A contains one red ball and one blue ball, whereas bag B contains two white balls and three black balls.

P(A) = 0.2

P(B) = 0.8

Probability of getting one red is 1/1 = 1

Probability of getting one blue is 1/1 = 1

Probability of getting one white ball is 1/2

Probability of getting 1 black ball is 1/3

Therefore, by tree diagram we get four possible probability that is  

0.8, 0.8, 0.1, 0.06.

A probability tree illustration is used to represent the probability of circumstance of events without using complicated formulas. It displays all the possible issues of an event. The purpose of a probability tree is that it shows all the possible issues of an event and calculates the probability of these issues. A probability tree illustration can either represent a series of independent events or it can be used to denote tentative chances.

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Answer:

Step-by-step explanation:

6w + 18 = 330

18 -18

6w = 312

6          6

w = 52 yards, which is the width.

l = 2(52) + 9 = 113 yards, which is the length.

When estimating the population average using the sample mean, adding observations to a sample will always decrease the standard error of your estimate is random sampling variability.

In statistical analysis, estimating the population average is a common task. One way to estimate this is by using the sample mean. However, as more observations are added to the sample, the standard error of the estimate decreases. Let's explore why this is the case.

The standard error of the mean (SEM) is a measure of the amount of variability in a sample mean from one sample to another. It can be calculated using the formula:

SEM = standard deviation / square root of sample size

As we can see, the SEM is inversely proportional to the square root of the sample size. This means that as we increase the sample size by adding more observations, the denominator of the SEM formula increases, causing the SEM to decrease.

Now, let's consider how this affects our estimate of the population average. The sample mean is an unbiased estimate of the population mean. This means that on average, the sample mean will equal the population mean. However, due to random sampling variability, the sample mean can differ from the population mean.

The standard error of the mean gives us an idea of how much the sample mean can vary from one sample to another.

Therefore, adding more observations to a sample decreases the SEM, making our estimate of the population average more precise. This is because the average of a larger sample is more representative of the population average, as it is less affected by random sampling variability.

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The points (0, 0), (0, 3), (4, 0): A. points are vertices of a right triangle.

The points (1, 2), (3, 0), (3, 3): B. points are not vertices of a right triangle.

The midpoint between the two points (2, 2) and (6, 4) is [4, 3].

The midpoint between the two points (2, 3) and (4, 1) is [3, 2].

The company's sales in 1997 is equal to $610,000.

In order to determine the straight-line distance from your starting point, we would apply Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

c² = a² + b²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

c² = 12² + 2²

c² = 144 + 4

c = √148

c = 12.17 miles.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(6 + 2)/2, (4 + 2)/2]

Midpoint = [8/2, 6/2]

Midpoint = [4, 3]

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(2 + 4)/2, (3 + 1)/2]

Midpoint = [6/2, 4/2]

Midpoint = [3, 2]

By applying the midpoint formula, the sales for 1997 can be calculated as follows;

Sales = (1996 sales + 1998 sales)/Number of years

Sales = ($500,000 + $720,000)/2 years

Sales = $1,220,000/2

Sales = $610,000.

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Context, it is not clear what is meant by "j(0,0)" or what the function's codomain being [tex]R^2[/tex] signifies.

It is not clear what you mean by "b" and "j". However, I can provide a general answer on how to find a holomorphic function.

A holomorphic function is a complex-valued function that is complex differentiable in a neighborhood of each point in its domain. This means that the function must satisfy the Cauchy-Riemann equations, which relate the partial derivatives of the function with respect to the real and imaginary parts of its input.

To find a holomorphic function, one approach is to use the power series representation of complex analytic functions. If a function f(z) is analytic at a point z0, then it has a power series expansion of the form:

f(z) = ∑n=0∞ [tex]c_n (z - z0)^n[/tex]

where [tex]c_n[/tex] are complex coefficients that depend on the function and z0. This power series converges in a neighborhood of z0, and the coefficients can be calculated using complex integration techniques.

Another approach is to use the Cauchy integral formula, which expresses the value of a holomorphic function at a point in terms of an integral over a closed curve that encloses the point. This formula allows one to compute the function at any point in its domain using complex integration techniques.

Without more information about "b" and "j", it is not possible to determine if a holomorphic function exists or what its properties might be. Similarly, without more context, it is not clear what is meant by "j(0,0)" or what the function's codomain being [tex]R^2[/tex] signifies.

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Answer:

3² +2³= 9+8=17

2¹ - 3²= 2-9=8

Step-by-step explanation:

Answer:

1-7

Step-by-step explanation:

[tex]3^{2}[/tex] + [tex]2^{2}[/tex] (3x3) + (2x2x2) = 9 + 8 = 17

[tex]2^{1}[/tex] - [tex]3^{2}[/tex] = 2 - (3x3) = 2 - 9 = -7

The form of the function that most quickly reveals the y-intercept is m(c) = 2 + 6(x + 2), and the y-intercept is 14.

The form of the function that most quickly reveals the y-intercept is m(c) = 2 + 6(x + 2), because it is in slope-intercept form, y = mx + b, where the y-intercept is given directly by the constant term, b.

To find the y-intercept of this function, we can substitute x = 0, since the y-intercept occurs when x = 0:

m(0) = 2 + 6(0 + 2) = 2 + 12 = 14

Therefore, the y-intercept of the function is 14.

Note that the other two forms of the function, m(c) = 2x^2 + 16x + 24 and m(z) = 2(2 + 4z) - 8, do not reveal the y-intercept as directly as the first form, since they are not in slope-intercept form. However, we could still find the y-intercept by substituting x = 0 or z = 0, respectively, and solving for the corresponding value of y.

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The summation of permutations of the n-1 rolls that contain at least one 6.

Permutation refers to the arrangement of a set of objects in a specific order or sequence. It is a mathematical concept that involves counting the number of ways in which a set of objects can be ordered or arranged.

However, we need to exclude the sequences that already contain a 6 before the nth roll. These sequences do not belong in event E n . Therefore, we need to find the number of permutations of the n-1 rolls that contain at least one 6.

Let's first consider the case where there is exactly one 6 in the sequence. We have n-1 slots for the rolls, and we need to choose one of them to be a 6. There are (n-1) ways to choose the position of the 6, and the remaining (n-2) slots can be filled with any of the remaining 5 numbers. Therefore, there are

=> [tex](n-1) * 5^{n-2}[/tex]

ways to have exactly one 6 in the sequence.

Now let's consider the case where there are two 6s in the sequence. We have n-1 slots for the rolls, and we need to choose two of them to be 6s. There are (n-1) choose 2 ways to choose the positions of the 6s. For the remaining (n-3) slots, we can fill them with any of the remaining 4 numbers. Therefore, there are

=> [tex](n-1 choose 2) * 4^{n-3}[/tex]

ways to have exactly two 6s in the sequence.

We can continue this pattern for the case where there are k 6s in the sequence. There are (n-1) choose k ways to choose the positions of the k 6s. For the remaining (n-k-1) slots, we can fill them with any of the remaining 6-(k+1) = 5-k numbers. Therefore, there are

=> [tex](n-1 choose k) * (5-k)^{n-k-1}[/tex]

ways to have exactly k 6s in the sequence.

To get the total number of outcomes in event E n , we need to sum up the number of outcomes for each possible number of 6s in the sequence. Therefore, we have:

[tex]|E n | = 6^{(n-1) - (n-1)} * 5^{(n-2) + (n-1 choose 2)} * 4^{(n-3)} - ... + (-1)^{(n-1) * (n-1 choose n-1)} * 1^{(n-n)}[/tex]

This is a formula for the total number of outcomes in event E n .

We use permutations to count the number of ways to arrange the rolls, and we use the principle of inclusion-exclusion to exclude the sequences that contain a 6 before the nth roll.

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The school newspaper reporter wants to find out how many students will attend Tet festivities. She randomly surveys 13 students and knows that 24% of students typically attend the festivities. We are interested in the probability of the number of students who will attend.

The probability that at most 4 students will attend is 0.4936 and the probability that more than 3 students will attend is 0.5064. Calculating these probabilities can be done using the binomial probability formula. First, calculate the probability of exactly 4 students attending. This probability is [tex]0.24^4 * 0.76^9 = 0.0038[/tex]. Then, calculate the probability of 3 students or fewer attending by adding the probabilities of 0, 1, 2, and 3 students attending, which is 0.0013 + 0.0358 + 0.1045 + 0.2696 = 0.4113. Finally, subtract 0.4113 from 1 to get 0.4936. We are interested in the probability of the number of students who will attend. To calculate the probability of more than 3 students attending, subtract 0.4113 from 1 to get 0.5064.

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The equation of the relationship between glucose left (g) and time elapsed (t) is found and intercepts are also found.

What is an equation?

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Given, the drip rate of glucose = 1.02 cc/min

Total glucose given = 120cc

Time taken to given 120cc glucose  = 120/1.02  = 117.6 minutes ≈ 118 minutes

a) We will use g for glucose left and t for the time in minutes.

When t = 0 ,  g = 120

When t = 20, g = 120 - (1.02 * 20) = 99.6cc

when t = 40, g = 120 - (1.02 * 40)  = 79.2cc

Similarly, we fill up the table as below:

t     0         20       40       60         80       100     120    

g    120    99.6    79.2     58.8     38.4       18        0

b) We know in 1 minute = 1.02 cc glucose is used

  So the glucose left after 1 minute = 120 - 1.02 * 1

From option (a), we can see that for 20 minutes

  g = 120 - (1.02 * 20)

So for t minutes, glucose left can be represented by the equation:

g = 120 - 1.02t

c) from the above equation, we can find :

       t intercept

g = 0

0 = 120 - 1.02t

120 = 1.02t

t = 117.6 minutes

   g- intercept

t = 0

 g = 120 - 1.02*0 = 120 cc

Now the graph is a straight line passing through (0,120) and (117.6,0).

Therefore the equation of the relationship between g and t is found and intercepts are found.

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To find:-

Answer:-

We need to evaluate,

[tex]\implies \displaystyle\sum_{k=1}^5(3-k) \\[/tex]

Substitute k = 1 , 2 , 3 , 4 and 5 in the expression 3-k and then add them .

[tex]\implies (3-1)+(3-2)+(3-3)+(3-4)+(3-5)\\[/tex]

[tex]\implies 2 + 1 + 0 -1 -2 \\[/tex]

[tex]\implies 0\\[/tex]

Hence option A is the correct choice.

and we are done!

The population will decrease. Thus, the correct option is A.

Let a be the initial value and x be the power of the exponent function and b be the factor.

The exponent is given as

y = a(b)ˣ

The equation is modeled as,

M(r) = 945 × (0.935)ⁿ

Where 'n' is the number of years since 2010.

There are three conditions exist which are as follows:

On comparing, the value of 'b' is 0.0935 which is less than one. Then the population will decrease. Thus, the correct option is A.

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The missing options are given below.

A. The population is decreasing.

B. The population is increasing.

C. The population remains constant.

D. None of the above.

Number of adult tickets that Paige sold is 350 and the number of children tickets that she sold is 105.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Let x be the number of adult tickets and y be the number of children tickets.

Total number of tickets sold = 455

So, x + y = 455

Cost of each adult ticket is $8 and cost of each children ticket is $5 and the total cost is $3,325.

8x + 5y = 3325

So we got a system of two linear equations.

x + y = 455 ⇒ y = 455 - x

8x + 5y = 3325

Substituting y = 455 - x in 8x + 5y = 3325,

8x + 5(455 - x) = 3325

Solving,

8x + 2275 - 5x = 3325

3x = 1050

x= 350

y = 455 - 350 = 105

Hence number of adult tickets Paige sold is 350 and that of children tickets is 105.

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Between 7.7 weeks and 68.5 weeks search times does chebyshev's theorem guarantee that we will find at least 89% of the graduates.

Chebyshev's theorem states that for any distribution, at least 1 - 1/k^2 of the data will fall within k standard deviations from the mean.

To find the bounds for at least 89% of the graduates, we need to find the value of k that satisfies this condition.

Using Chebyshev's theorem, we have:

1 - 1/k^2 = 0.89

Solving for k, we get:

k = sqrt(1/0.11) ≈ 3.3

Therefore, at least 89% of the graduates will have job search times between:

38.1 - 3.3 x 10.1 ≈ 7.7 weeks

38.1 + 3.3 x 10.1 ≈ 68.5 weeks

Rounding to the nearest tenth, we get:

between 7.7 weeks and 68.5 weeks.

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