The vertices of a rectangle are plotted on the coordinate grid shown.

A graph with the both the x and y-axes numbered starting from negative 8 with units of one up to 8. There are points plotted at negative 4, 5, at 5, 5, at negative 4, negative 4, and at 5, negative 4.

What is the area of the rectangle shown?

81 square units
80 square units
40.5 square units
40 square units

The total value of the prize is $936,000.

The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.

The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:

=  $900/week x 52 weeks/year x 20 years

= $936,000.

We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r

Plugging in the values:

PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154

PV = $900 x 657.221075423

PV = $591,498.968.

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1a. Inferring from the facts that Sample 2—which is larger than Sample 1—received the most votes,

we may infer that "Butterflies and Ladybirds" would be the most widely chosen option for the spring window show.

1b. This hypothesis is plausible given that a bigger sample size often yields more accurate results and can more accurately reflect the population as a whole.

Furthermore, the fact that "Butterflies and Ladybirds" garnered the most votes across the board implies that it is a widely accepted pick.

2a. The statistics should not be used to draw the conclusion that the spring window displays "Flower Garden" and "April Showers" are unpopular options.

They got fewer votes than "Butterflies and Ladybirds," but they still got a lot of votes from both samples.

2b. This conclusion should not be drawn since the data only reflects the opinions of the chosen samples and might not fairly represent the opinions of the general community.

Personal prejudices and preferences may have also had a role in the outcomes, and there may be more variables (such as cost or availability) that might have an impact on the decision about the spring window display.

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Complete question:

Two random samples of people were selected to help choose a spring window display for a department store. The results are shown in this table.

"Flower Garden"

Number of Votes from Sample 1 =35

Number of Votes from Sample 2=21

"April Showers"

Number of Votes from Sample 1 =16

Number of Votes from Sample 2=15

"Butterflies and Ladybugs"

Number of Votes from Sample 1 =27

Number of Votes from Sample 2=42

1a. What prediction can you make from the data?

1b. Explain why your prediction is reasonable.

2a. What conclusion should not be made from the data?

2b. Explain why the conclusion should not be made.

To factor 20w+30, we can first factor out the greatest common factor, which is 10:

20w+30 = 10(2w+3)

So the factored form of 20w+30 is 10(2w+3).

Answer:

10(2w+3)

Step-by-step explanation:

Answer: 1:4

Step-by-step explanation:

In order to do this, we have to know that the octagon has an area which is four times less than the other area. Because of this, it shuld be 1:4

Answer:

Therefore, the percentage change from 20 to 50 is an increase of 150%.

Step-by-step explanation:

To work out the percentage change from 20 to 50, we can use the following formula:

((New Value - Old Value) / Old Value) x 100%

Plugging in the numbers, we get:

((50 - 20) / 20) x 100%

= (30 / 20) x 100%

= 1.5 x 100%

= 150%

Using the system of equations, the number of adults and the number of children who were committed are 140 and 104 respectively.

Given that,

The admission fee at an amusement park is $1.50 for children and $4 for adults.

Let x be the number of adults and y be the number of children who were admitted.

On a certain day, 244 people entered the park, and the admission fees collected totaled 716.00 dollars.

We get a system of equations,

x + y = 244

4x + 1.5y = 716

From the first equation,

y = 244 - x

Substituting this to second equation,

4x + 1.5(244 - x) = 716

4x + 366 - 1.5x = 716

2.5x = 350

x = 140

y = 244 - x = 104

Hence the number of children equals 104 and the number of adults equals 140.

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Answer:

648ft

Step-by-step explanation:

18 multiplied by 36 is 648

Answer:

648 ft ^2

Step-by-step explanation:

A = L * W A = 18 ft * 36 ft A = 648 ft^2

The resulting number is the area of the rectangle, which is expressed in square units. So the area of the figure is 648 square feet

The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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The rates that would fill Paige's boxes per minute is

15 boxes in 75 minutes

12 boxes in 75 minutes

1 box in 6 minutes

Given data ,

The rate at which Paige worked can be calculated by comparing the number of boxes filled by Paige with the time Paige worked.

Now , Andrew filled 5 boxes in 35 minutes,

So , The rate of Andrew = Number of boxes filled / Time taken = 5 boxes / 35 minutes = 1/7 boxes per minute

And , Paige worked for 75 minutes at a faster rate than Andrew, so Paige's rate must be greater than 1/7 boxes per minute

A. 15 boxes in 75 minutes:

Rate of Paige = Number of boxes filled / Time taken = 15 boxes / 75 minutes = 1/5 boxes per minute

B. 10 boxes in 75 minutes

Rate of Paige = Number of boxes filled / Time taken = 10 boxes / 75 minutes = 2/15 boxes per minute

C. 12 boxes in 75 minutes

Rate of Paige = Number of boxes filled / Time taken = 12 boxes / 75 minutes = 4/25 boxes per minute

D. 1 box in 6 minutes

Rate of Paige = Number of boxes filled / Time taken = 1 box / 6 minutes = 1/6 boxes per minute

E. 1 box in 9 minutes

Rate of Paige = Number of boxes filled / Time taken = 1 box / 9 minutes = 1/9 boxes per minute

Based on the calculations, options A, C, and D could be Paige's rates, as they are greater than 1/7 boxes per minute

Hence , the equations are solved

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Answer: Jonick Company's margin of safety as a percentage of current sales is 26.05%.

Step-by-step explanation:  To find the margin of safety as a percentage of current sales, we need to first calculate the margin of safety, which is the amount of sales above the break-even point:

Margin of safety = Actual sales - Break-even point

We know that actual sales are $740,000 and the break-even point is $547,600, so:

Margin of safety = $740,000 - $547,600

Margin of safety = $192,400

Now that we know the margin of safety, we can calculate it as a percentage of current sales:

Margin of safety % = (Margin of safety / Actual sales) x 100

Plugging in the numbers, we get:

Margin of safety % = ($192,400 / $740,000) x 100

Margin of safety % = 26.05%

Therefore, Jonick Company's margin of safety as a percentage of current sales is 26.05%. This means that sales can drop by 26.05% before the company starts to incur losses.

The measures of the angles are 33°, 105° and 42°

We can call the top angle P, the bottom left angle Q, and the bottom right angle R. We are also given that angle P is (x - 9) degrees, angle Q is (x + 63)  degrees, and angle R is x degrees.

Now, we can use the fact that the sum of the angles in a triangle is 180 degrees to set up an equation:

Angle P + Angle Q + Angle R = 180

To find Angle, we can use the fact that the sum of the angles in a straight line is 180 degrees. We can see that Angle and Angle A are on a straight line, so we have:

(x – 9) + ( x + 63) +  x = 180

=> 3x + 54 = 180

=> 3x = 126

=> x = 42

We can now use this value to find the measures of the angles.

Angle P is (x -9) degrees, so Angle P = 42 - 9 = 33 degrees.

Angle Q is (x + 63) degrees, so Angle Q = 42 + 63 = 105 degrees.

Angle R is x degrees, so Angle R = 42 degrees.

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The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.

We have,

To eliminate the y-terms in this system of equations, we can multiply the second equation by 2 and add it to the first equation.

This will result in the y-terms canceling out, and we will be left with only x-terms on one side of the equation, which we can then solve for x.

So, multiplying the second equation by 2, we get:

2(3x + 4y) = 2(5)

6x + 8y = 10

Now, adding this to the first equation, we get:

4x - 8y + 6x + 8y = 20 + 10

10x = 30

Dividing both sides by 10, we get:

x = 3

Now, we can substitute this value of x back into either of the original equations to solve for y.

4x - 8y = 2

So,

4(3) - 8y = 20

12 - 8y = 20

-8y = 8

y = -1

Therefore,

The solution to the system of equations is (x, y) = (3, -1).

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Answer:

Step-by-step explanation:

1. the initial population at t=0 is 1

2. 16

1) b. quota

2) d. they make foreign products cheaper to U.S. shoppers

3) a. it sets the value of its currency in relation to a specific amount of gold

4) c. $3,040 per person

5) b. low population growth

We have,

1)

A limit imposed by the government on the quantity of a good or product that can be brought into the country is called a quota.

Tariffs, on the other hand, are taxes imposed on imported goods, while foreign bills of exchange refer to payment methods in international trade, and value-added tax (VAT) is a tax on the value added to goods and services.

2)

The argument that enacting trade restrictions makes foreign products cheaper to U.S. shoppers is not effective because it is contradictory.

Trade restrictions, such as tariffs or quotas, are intended to make foreign products more expensive and protect domestic industries from foreign competition.

3)

If a country is on the gold standard, it means that it sets the value of its currency in relation to a specific amount of gold.

The value of the currency is directly linked to the amount of gold held in reserves by the government and can be exchanged for gold at a fixed rate.

4)

Economists tend to classify a country as less developed if the country's average level of income is less than $3,040 per person.

This is the World Bank's definition of low-income countries, which are typically characterized by high levels of poverty, limited access to education and healthcare, and underdeveloped infrastructure.

5)

Low population growth is not considered a barrier to economic development.

In fact, some economists argue that high population growth can put a strain on resources and hinder economic development.

Barriers to economic development typically include factors such as political corruption, lack of investment capital, and low levels of education and human capital.

Thus,

1) b. quota

2) d. they make foreign products cheaper to U.S. shoppers

3) a. it sets the value of its currency in relation to a specific amount of gold

4) c. $3,040 per person

5) b. low population growth

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Answer:

it is 3/3 3/6 I hope this helped

The value of n is given as follows:

n = 53.3 years.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

The interest rate for this problem is given as follows:

r = 0.03.

Then the amounts are given as follows:

The ratio is given as follows:

A(n + 1)/A(n) = 1.01875.

Hence the value of n is obtained as follows:

(n + 1)/n = 1.01875 (0.03P is simplified as it is common to both expressions)

1.01875n = n + 1

0.01875n = 1

n = 1/0.01875

n = 53.3 years.

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The concentration (C) in ounces of sugar per ounce of milk will be C = 10/(10/t + 1) + 1

The domain is all real numbers except t = 0.

The concentration (C) in ounces of sugar per ounce of milk will be

C = S/M

C = (10 + 10t)/(10 + t)

C = 10/(10/t + 1) + 1

The concentration after five minutes, will be:

C = 10/(10/5 + 1) + 1

C = 10/3

C ≈ 3.33 ounces of sugar per ounce of milk

The time it takes to reach a concentration of 8 ounces of sugar per ounce of milk, will be:

8 = 10/(10/t + 1) + 1

7 = 10/(10/t)

70/t = 10

t = 7 minutes

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The solution is the area of triangle ABC is 9.56 square units .

Given:

The objective is to find the area of triangle ABC

Explanation:

The general formula to find the area of a triangle is,

A = 1/2 *b*h

To find the area of triangle ABC:

The height of the triangle DC can be calculated using the Pythagorean theorem of triangle ADC.

DC  = √ 9 - 6.25

      =1.65

On plugging the given values in equation

Thus, the height of triangle ABC is 2.5

So the base of the triangle CB = 6 + 1.65 = 7.65.

Now, substitute the obtained values in equation

area = 1/2 * 7.65 * 2.5

        = 9.56

Hence, the area of triangle ABC is 9.56 square units .

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The additive inverse of the polynomial is A' = - ( 1.3t³ - 0.2t² - 6t - 8 )

Given data ,

Let the polynomial be represented as A

Now , the value of A is

A = ( 1.3t³ + 0.4t² - 24t ) - ( 0.6t² + 8 - 18t )

On simplifying the equation , we get

A = 1.3t³ + 0.4t² - 24t - 0.6t² - 8 + 18t

A = 1.3t³ - 0.2t² - 6t - 8

Now , the additive inverse of the polynomial is

A' = - ( 1.3t³ - 0.2t² - 6t - 8 )

Hence , the polynomial is solved

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We can write the pull force of the magnet as [tex]2 \frac{1}{5} pounds[/tex].

A mixed number refers to number that contains both an integer (whole number) and a proper fraction (a fraction whose numerator is less than its denominator).

To represent the pull force as a mixed number, we must to convert the decimal 0.2 to a fraction. Since 0.2 is equal to 1/5, we can write it as 2 and 1/5 pounds/ Therefore, the mixed number representation of the magnet's pull force of 2.2 pounds is 2 1/5 pounds.

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Answer:

We can use the binomial probability formula to find the probability of getting exactly 3 blue marbles in two draws:

P(X=3) = (2 choose 3) * (0.6)^3 * (0.4)^(-1) = 0.288

However, since we are asked for the probability of the random variable having an outcome of 3 (i.e. getting exactly 3 blue marbles), we can simply use this probability:

P(X=3) = 28.8%

Therefore, the answer is (a) 24%.

The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.

We have,

The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.

a)

Potential problem:

Age can be a confounding variable, affecting the occurrence of injuries due to muscle damage. Solution: Randomly assign people to stretch or not stretch after exercising without considering their age.

Improved design:

The researcher selects 400 people who exercise on a regular basis. The people are randomly assigned to stretch after exercising or to not stretch. The people's occurrence of injuries due to muscle damage is monitored.

b)

Potential problem:

The people in the two groups may not be comparable, leading to a biased result. Solution: Randomly assign people to stretch or not stretch after exercising.

Improved design:

The researcher randomly selects 150 people who exercise on a regular basis. Half of them are assigned to stretch after exercising, and the other half are assigned to not stretch. The number of injuries due to muscle damage is monitored for both groups.

Thus,

The research topic of whether stretching after exercising decreases the number of injuries due to muscle damage can be best investigated through an experimental study.

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Answer: A

Step-by-step explanation:

Goes down to the integer 1. B is the only one that makes sense subtracting doesn't work 87654321 goes from the 2 half line.

Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.

For test the claim that half of all teens have made new friends online, we can use a hypothesis test.

Null hypothesis:

The proportion of teens who have made new friends online is equal to 0.5.

Alternative hypothesis:

The proportion of teens who have made new friends online is not equal to 0.5.

We will use a one-sample proportion test with a significance level of 0.01.

For calculate the test statistic, we can use the formula:

z = (p - P₀) / sqrt(P₀ * (1 - P₀) / n)

where p is the sample proportion, P₀ is the hypothesized proportion (0.5), and n is the sample size.

Using the given information, we have:

p = 0.57

P₀ = 0.5

n = 1060

Plugging these values into the formula, we get:

z = (0.57 - 0.5) / sqrt(0.5 x 0.5 / 1060)

z = 4.39

Hence, Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.

Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that more than half of all teens have made new friends online.

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In order to decrease the margin of error, the best option in this instance is by decreasing the confidence level would make the interval to be narrower.

The correct option is D.

The margin of error, also known as the confidence interval, provides information on how closely your survey results will likely reflect the opinions of the general community.

The margin of error is a measure of the potential uncertainty in your survey results. It is more likely that the results will deviate from the "true figures" for the entire population the wider the margin of error.

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The possible values of a are:

(i) A unique solution: a such that a² ≠ 5

(ii) Infinitely many solutions: a such that a² = 5

(iii) No solution: for all other values of a.

To solve this system of linear equations, use Gaussian elimination to reduce the augmented matrix to row echelon form. Then, examine the resulting matrix to determine the number of solutions.

The augmented matrix for the system is:

[1  2  -3  | 4 ]

[3  -1  5  | 2 ]

[4  1  a²-14 | a+2]

Using row operations, transform the matrix as follows:

[1  2  -3  | 4 ]

[0  -7  14 | -10]

[0  -7  a²-2 | a-6]

The third row is a linear combination of the first two rows, so we can eliminate it. This gives us:

[1  2  -3  | 4 ]

[0  -7  14 | -10]

Further simplify this matrix by dividing the second row by -7:

[1  2  -3  | 4 ]

[0  1  -2  | 10/7]

Use back-substitution to solve for the variables, start with the second row:

y - 2z = 10/7

Rearranging this equation:

y = 2z + 10/7

Substituting this into the first row:

x + 2(2z+10/7) - 3z = 4

Simplifying this equation:

x + (4/7)z = 18/7

So, the solution to the system is:

x = (18/7) - (4/7)z

y = 2z + 10/7

z is free

Now, examine the possible values of a:

(i) A unique solution: If the system has a unique solution, then there can be no free variables. From our solution above, we see that z is a free variable. Therefore, the system can have a unique solution only if a is such that the third row in the original augmented matrix does not reduce to a multiple of the first two rows. This is equivalent to the condition -7 ≠ a² - 2, or a² ≠ 5.

(ii) Infinitely many solutions: If the system has infinitely many solutions, then there must be at least one free variable. From our solution above, we see that z is a free variable. Therefore, the system can have infinitely many solutions for all values of a such that a² = 5.

(iii) No solution: If the system has no solution, then there must be a row in the reduced row echelon form that has all zeros except in the last column. However, our reduced matrix does not have this form. Therefore, the system has no solution for any value of a.

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Answer:

The correct operator for the exponential expression 3^5 ? 4^6 is > (greater than), because we can compare the values of the two exponents:

3^5 = 243

4^6 = 4096

Since 4096 is greater than 243, we can write:

3^5 < 4^6

or

4^6 > 3^5

Therefore, the correct operator for the exponential expression 3^5 ? 4^6 is > (greater than).