Ernesto takes a sheet of paper and makes a diagonal cut from one corner to the opposite corner, making two triangles. The cut he makes is 20 inches long and the width of the paper is 16 inches. What is the paper's length?

The 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.

The following formula is used to calculate a confidence interval for the proportion of all American adults who support same-sex marriage

KI = p ± z*(√(p*(1-p)/n))

where:

p = percentage of respondents who support same-sex marriage

n = sample size (total number of respondents)

z = z-score for the desired confidence level

substitute all the values in the above formula,

CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/n))

To compute confidence intervals, we need to know the sample size (n). the sample size is large, so we can use the normal distribution.

the random sample size of 1000 is taken as no sample size is specified.

For n = 1000,

CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/1000))

= 0.517 ± 0.032

Therefore, the 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.

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The expected value of the sample mean of mpg derived from a random sample of four passengers is 30.5 mpg.

The expected value of the sample mean can be calculated using the formula

E(x) = μ

where x is the sample mean, and μ is the population mean.

In this case, the population mean is given as 30.5 mpg. The standard deviation of the population is also given as 4.1 mpg.

The standard deviation of the sample mean can be calculated using the formula

σx = σ/√n

where σ is the population standard deviation and n is the sample size.

Substituting the given values, we get:

σx = 4.1/√4 = 2.05

So the expected value of the sample mean is

E(x) = μ = 30.5 mpg.

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The rate that would result in a single investment doubling in 3 years with annual compound interest can be calculated using the rule of 72.

The rule of 72 states that if you divide 72 by the annual interest rate (as a percentage), you get the approximate number of years it takes for an investment to double in value.

So, to find the annual interest rate that would result in a single investment doubling in 3 years, we need to solve the equation: 72 / r = 3 where the r is the annual interest rate (as a percentage).

Simplifying the equation, we get:

r = 24

Therefore, the annual interest rate that would result in a single investment doubling in 3 years is 24%.

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Answer:

84.3.

Step-by-step explanation:

To find the range of the given data, we need to subtract the smallest value from the largest value in the set.

The smallest value in the set is 11.2 and the largest value is 95.5. Therefore, the range is:

Range = Largest value - Smallest value

= 95.5 - 11.2

= 84.3

the range of the given data is 84.3.

Answer:

15.5 feet

Step-by-step explanation:

12 (each foot have 12 inches) × 8 (two 4-foot pieces of rope) = 96

6 (six pieces of rope) × 15 (each rope have fifteen inches long) = 90

90 + 96 = 186

186 ÷ 12 = 15.5

12 × 15.5 = 186

Patty need 15.5 feet.

The probability that the website has fewer than 8 million visitors in a single day is 0.2061 or 20.61%.Hence, option C is correct.

The traffic to the web site of Made by Charmz, LLC which sells customized mugs, follows a normal distribution,

with a mean of 8.5 million visitors per day and a standard deviation of 610,000 visitors per day.

The problem asks us to find the probability that the website has fewer than 8 million visitors in a single day.

Therefore, we need to find P(X < 8 million).

Using the Z-score formula, we have;

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Where X = 8 million, μ = 8.5 million and σ = 610,000.

Substituting the given values in the formula, we get:

[tex]Z=\frac{8-8.5}{0.61}=-0.8197[/tex]

Using a standard normal table, the probability corresponding to Z-score = -0.8197 is 0.2061.

Therefore, the probability that the website has fewer than 8 million visitors in a single day is 0.2061 or 20.61%.Hence, option C is correct.

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The solution is A. 3/8. We can calculate it in the following manner.

According to the general equation for conditional probability,

P(A|B) = P(A and B) / P(B)

We are given that P(A|B) = 3/10 and P(B) = 2/5.

We need to find P(A and B) to solve for P(A|B).

Using the formula for conditional probability, we can rearrange the equation as:

P(A and B) = P(A|B) * P(B)

Substituting the given values, we get:

P(A and B) = (3/10) * (2/5) = 6/50 = 3/25

Now, we can find P(A|B) using the first equation:

P(A|B) = P(A and B) / P(B) = (3/25) / (2/5) = (3/25) * (5/2) = 3/10

Therefore, the answer is A. 3/8.

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Based on the sample, the number of people whose favorite snack is cake are 589.

We learn languages ​​to communicate. In the world of mathematics, we express language based on algebraic formulas. Algebraic Expressions Simply put, defining an algebraic expression means combining numbers, letters, and operators to convey instructions or explanations. This is similar to forming sentences as a child learns to express himself in sentences.

Let,

The number of people whose favorite snack is cake = 31x

The number of people whose favorite snack is pretzels = 25x

The number of people whose favorite snack is cookies = 53x

The number of people whose favorite snack is other = 60x

Since the reception is been planned for 3200 people:

31x + 25x + 53x + 60x = 3200

169x = 3200

x = 3200/169

x = 18.93

x ≈ 19

As, The number of people whose favorite snack is cake:

= 31x

= 31 × 19

= 589

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After solving (d + 3)(d² - 4d + 1) by using the FOIL method we get d³ - d² - 11d + 3.

The foil method is a strategy for organising your memory of the steps

needed to multiply two binomials. First, outer, inner, and last are the

letters that make up the acronym F-O-I-L.

To solve the given expression using the FOIL method, you have to follow the below steps:

F: Multiply the First terms (d x d²)

O: Multiply the Outer terms (d x -4d)

I: Multiply the Inner terms (3 x d²) and

L: Multiply the Last terms (3 x 1)

Finally, combine the like terms to get the answer

(d + 3)(d² - 4d + 1)= d(d² - 4d + 1) + 3(d² - 4d + 1)

                           = d³ - 4d² + d + 3d² - 12d + 3

                           = d³ - d² - 11d + 3

Thus, (d + 3)(d² - 4d + 1) equals d³ - d² - 11d + 3.

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The 90% confidence interval for bmi is:  (27.998, 28.302)

The correct answer is an option (d) (27.97, 28.33)

We know that the formula for the confidencce interval is,

CI = [tex](\bar{x}\pm z\frac{s}{\sqrt{n} })[/tex]

where, Ci is the confidence interval

[tex]\bar{x}[/tex] is the sample mean

z is the confidence level value

s = sample standard deviation

n = sample size

Here we need to find 90% confidence interval for bmi in a sample of 3,326 adults, the mean bmi was 28.15 and the sample standard deviation was 5.32

n = 3326,  [tex]\bar{x}[/tex]  = 28.15 and σ = 5.32

We know that 1 - α = confidence interval

1 - α = 0.90

so, α = 0.10

α/2 = 0.05

And from the standard normal table [tex]z_{\alpha /2}[/tex] = 1.64

Using above formula of confidence interval,

CI = [tex](28.15 \pm 1.64\frac{5.32}{\sqrt{3326} } )[/tex]

CI = (28.15 ±0.152)

CI = (27.998, 28.302)

Therefore, the correct answer is an option (d) (27.97, 28.33)

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With little knowledge of the square shape, we know that the area of the shaded region is (B) x² - 2y².

A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles.

It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.

As we previously stated, a square is nothing more than a rectangle with equally long neighboring sides.

The area of a rectangle is therefore expressed as Area = Length Breadth.

So, according to the given figure:
The area of the shaded region would be:

x² - y²

But as we know that 2 triangles make up 1 small square, so the formula can be molded as:

x² - 2y²

Therefore, with little knowledge of the square shape, we know that the area of the shaded region is (B) x² - 2y².

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Answer:

Yes, the graph of y = -2x^2 + 5 is different from the graph of y = -2x^2. Both equations are quadratic functions with a leading coefficient of -2, which means that they have the same shape of a downward-facing parabola.

However, the graph of y = -2x^2 + 5 is shifted upwards by 5 units compared to the graph of y = -2x^2. This means that for any given value of x, the y-value of y = -2x^2 + 5 will be 5 units higher than the y-value of y = -2x^2.

If repeats are forbidden, the provided letters u, v, w, x, y, and z can be used to create 8 lists of length 3, each of which has a w or u in the second entry.

We can apply the inclusion-exclusion concept to resolve this issue.

First, let's determine how many total lists of length three can be created using the provided letters without any limitations. There are six options for the first submission, five for the second (since it must be either w or u), and four for the third (since no characters can be repeated). Thus, there are a total of the following lists:

6 × 5 × 4 = 120

Next, let's count the number of lists of length 3 that do not have a w or u in the second entry. We have 6 choices for the first entry, 4 choices for the second entry (since we can't choose w or u), and 4 choices for the third entry (since we can't repeat any letters). Thus, the total number of such lists is:

6 × 4 × 4 = 96

Similarly, we can tally the number of lists of length 3 lacking a w or u in the first entry as well as the number of lists of length 3 lacking a w or u in either the first or second entry. Which are:

4 × 5 × 4 = 80 (no w or u in first entry)

4 × 4 × 4 = 64 (no w or u in first or second entry)

Finally, we can use the principle of inclusion-exclusion to count the number of lists that have a w or u in the second entry. This is:

120 - 96 - 80 + 64 = 8

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The Statements 1,2 and 4 are true about quadratic function. So, the right answer for this problem is options (1), (2) and (4).

Quadratic function is defined as a function whose highest power of exponent is 2.

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Answer:

angleC = 35°

Step-by-step explanation:

Because AC is the diameter of the circle, angle B = 90°

Then we can use the idea that there are 180° in a triangle to find angle C.

55 + 90 + c = 180

145 + c = 180

c = 35

The measure of angleC = 35°

Consumer surplus and deadweight loss have decreased due to the price floor of $9.00 set by the government. The correct option is c.

To answer this question, we need to first understand what a price floor is and how it affects the market.

A price floor is a government-imposed minimum price that must be paid for a good or service.

In the context of a market, a price floor that is set above the equilibrium price will create a surplus of the good or service.

This is because the price floor creates a situation where the quantity supplied exceeds the quantity demanded.

Now, let's examine the diagram:

           ^

        | P=$9.00  <- price floor

  S    |  / \

        |  /  \

$10  | /     \

        |/        \

 $8   /           \

         |               \

$6   /|_________\

        |                      \

        |       Qd   Qs   |

        |___________|

                 Q

In this diagram, the price floor is set at $9.00, which is above the equilibrium price of $8.00.

As a result, there is a surplus of the good, with quantity supplied (Qs) exceeding quantity demanded (Qd).

Now, let's consider the impact on consumer surplus, producer surplus, and deadweight loss:

Consumer surplus is the difference between the price consumers are willing to pay and the actual price they pay. In this case, the price consumers are willing to pay is below the price floor, so consumer surplus is reduced. Therefore, option c.) "Consumer surplus and deadweight loss" is the correct answer.

Producer surplus is the difference between the price producers receive and the minimum price they are willing to accept. In this case, the price producers receive is above the equilibrium price, so producer surplus is increased. Therefore, option b.) "Consumer surplus and producer surplus" is incorrect.

Deadweight loss is the loss of economic efficiency that occurs when the quantity of a good that is bought and sold is below or above the equilibrium quantity. In this case, the price floor creates a surplus, which leads to deadweight loss. Therefore, option d.) "Only deadweight loss" is incorrect.

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Consider the diagram below. Which of the variables (consumer surplus, producer surplus, and deadweight loss) have decreased due to the price floor of $9.00 set by the government?

a.) Producer surplus and deadweight loss

b.) Consumer surplus and producer surplus

c.) Consumer surplus and deadweight loss

d.) Only deadweight loss

Answer:

Quintic

Step-by-step explanation:

the degree of a polynomial is determined by the variable with the largest exponent in the expression.

3h³ ← is of degree 3

6 ← is of degree 1

4h² ← is of degree 2

4[tex]h^{5}[/tex] ← is of degree 5

then the degree of the polynomial is 5 , or a Quintic

Answer:

100

Step-by-step explanation:

its impossable

The new volume of the cylinder is $100$ cubic feet.

Let the original radius and height of the cylinder be $r$ and $h$, respectively. Therefore, the original volume of the cylinder is given by $\pi r^2 h = 100$. After the radius decreases by $10%$ and the height increases by $10%$, the new radius and height become $0.9r$ and $1.1h$, respectively. The new volume of the cylinder can be calculated as $\pi (0.9r)^2 (1.1h) = 0.891\pi r^2 h$. Since $0.891\pi r^2 h = 100$, the new volume of the cylinder is $100$ cubic feet.

Therefore, the new volume of the cylinder is the same as the original volume, i.e., $100$ cubic fee

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The recent study says 24% wage gap between nonmetropolitan and metropolitan workers can be attributed to differences in job opportunities, education and skill levels, cost of living, and economic development.

According to a recent study, the median earnings of nonmetropolitan workers in the United States was 24% less than the median earnings of metropolitan workers.

The most likely explanation for this phenomenon can be attributed to several factors.
1. Job opportunities: Metropolitan areas tend to have a higher concentration of job opportunities, particularly in higher-paying industries such as finance, technology, and professional services.

In contrast, nonmetropolitan areas often have fewer job options and may be dominated by lower-paying industries such as agriculture, retail, and hospitality.
2. Education and skill levels: Metropolitan areas generally have a larger pool of highly educated and skilled workers, which can lead to higher salaries.

Nonmetropolitan areas may have lower levels of education and skill among the workforce, which can result in lower earnings.
3. Cost of living: The cost of living is generally higher in metropolitan areas, which can lead to higher salaries to offset these expenses.

In nonmetropolitan areas, the cost of living is typically lower, which can result in lower wages as employers do not need to pay as much to maintain a reasonable standard of living for their workers.
4. Economic development: Metropolitan areas tend to have more robust economies with higher levels of economic development.

This can create a more competitive job market, which can lead to higher salaries for workers. Nonmetropolitan areas often have less economic development, which can result in fewer high-paying jobs and lower wages overall.
In summary, the 24% wage gap between nonmetropolitan and metropolitan workers can be attributed to differences in job opportunities, education and skill levels, cost of living, and economic development.

These factors contribute to the higher median earnings of metropolitan workers compared to their nonmetropolitan counterparts.

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The numerical value of x rounded to the nearest tenth is 7.5.

The Midsegment Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

Hence:

the smaller segment = half the third side

From the diagram;

The smaller segment = x

The larger third side = 15

Using the Midsegment Theorem

x = half of 15

Solve for x

x = 1/2 × 15

x = 15/2

x = 7.5

Therefore, the value of x is 7.5.

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Answer:

O y = 15x + 10 is the only linear function

Hope this helps!!!

The range of a set of numbers measures the spread or dispersion of the values in the set, and in the given set of numbers, the range is 4.1.

The range of a set of numbers is the difference between the largest and smallest numbers in the set.

The range can be a useful measure of the variability of a dataset, as it can tell us if the values are tightly clustered or widely spread out. However, the range can be influenced by extreme values, also known as outliers, which can distort the measure.

In the given set of numbers:

9, 6.9, 8.1, 7, 7.9, 7.1, 9, 7.6, 4.9

The largest number is 9, and the smallest number is 4.9.

So, the range is:

9 - 4.9 = 4.1

Therefore, the range of the given set of numbers is 4.1.

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Answer:

To find out how much more Joi paid than Adelyn for each fidget popper, we need to know how much Adelyn paid for each fidget popper.

If we assume that Adelyn bought the same set of fidget poppers as Joi at the regular price of $20 without tax, then we can calculate how much Adelyn paid for each fidget popper by dividing the total price by the number of fidget poppers in the set.

Let’s say that there are 10 fidget poppers in the set. Then, Adelyn paid $20 / 10 = $2 per fidget popper.

Joi bought the same set of fidget poppers at the regular price of $20 plus 8% sales tax. To find out how much Joi paid for each fidget popper, we can add the sales tax to the regular price and then divide by the number of fidget poppers in the set.

The sales tax is 8% of $20, which is $1.60. So, Joi paid a total of $20 + $1.60 = $21.60 for the set.

If there are 10 fidget poppers in the set, then Joi paid $21.60 / 10 = $2.16 per fidget popper.

To find out how much more Joi paid than Adelyn for each fidget popper, we can subtract Adelyn’s price per fidget popper from Joi’s price per fidget popper:

$2.16 - $2 = $0.16

Therefore, Joi paid $0.16 more than Adelyn for each fidget popper

Answer:

Nn

Step-by-step explanation:

The value of x from the given triangle is 55°.

What is an exterior angle?

The angle between any side of a shape and a line that extends from the next side is known as the exterior angle. the angle formed by a shape's side and a line that extends from another side.

Here, we have

Given: A side of the triangle below has been extended to form an exterior angle of 125°.

We have to find the value of x.

From the given figure, the exterior angle of the triangle is 125° and x is the exterior angle to that.

Now, 125°+x=180°

x=180°-125°

x=55°

Hence, the value of x from the given triangle is 55°.

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First, we need to calculate the monthly interest rate by dividing the APR by 12:

11.99% / 12 = 0.9992%

Next, we can use the formula for monthly interest on credit cards, which is:

(balance x monthly interest rate) + (payment - (balance x monthly interest rate)) = new balance

We can solve for the new balance each month, and then use the new balance to calculate the interest for the following month. Here's how it works:

Month 1:

(balance x 0.9992%) + ($350 - (balance x 0.9992%)) = $7,219.17 (new balance)

Month 2:

($7,219.17 x 0.9992%) + ($350 - ($7,219.17 x 0.9992%)) = $6,870.19 (new balance)

Month 3:

($6,870.19 x 0.9992%) + ($350 - ($6,870.19 x 0.9992%)) = $6,516.76 (new balance)

Month 4:

($6,516.76 x 0.9992%) + ($350 - ($6,516.76 x 0.9992%)) = $6,158.68 (new balance)

Month 5:

($6,158.68 x 0.9992%) + ($350 - ($6,158.68 x 0.9992%)) = $5,795.73 (new balance)

Month 6:

($5,795.73 x 0.9992%) + ($350 - ($5,795.73 x 0.9992%)) = $5,427.67 (new balance)

Month 7:

($5,427.67 x 0.9992%) + ($350 - ($5,427.67 x 0.9992%)) = $5,054.24 (new balance)

Month 8:

($5,054.24 x 0.9992%) + ($350 - ($5,054.24 x 0.9992%)) = $4,675.18 (new balance)

Month 9:

($4,675.18 x 0.9992%) + ($350 - ($4,675.18 x 0.9992%)) = $4,290.23 (new balance)

Month 10:

($4,290.23 x 0.9992%) + ($350 - ($4,290.23 x 0.9992%)) = $3,899.12 (new balance)

Month 11:

($3,899.12 x 0.9992%) + ($350 - ($3,899.12 x 0.9992%)) = $3,501.61 (new balance)

At the end of the 11th month, the balance is paid down to $3,501.61, and then at the end of the 12th month, it is paid off completely.

To calculate the total interest paid, we can add up the interest for each month:

$7,568.19 - $7,219.17 = $349.02

$7,219.17 - $6,870.19 = $348.98

$6,870.19 - $6,516.76 = $353.43

$6,516.76 - $6,158.68 = $358.08

$6,158.68 - $5,795.73 = $362.95

$5,795.73 - $5,427.67 = $368

I explained step by step.

Answer:

368

Step-by-step explanation:

Answer:

I think second one is the answer

Step-by-step explanation:

if a number is raised to a negative power u put 1 as the numerator and the number with a positive power and for p3 it stays the same

Answer:

[tex]\frac{p^3}{n^6}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

[tex]n^{-6}[/tex] p³

= [tex]\frac{1}{n^{6} }[/tex] × p³

= [tex]\frac{p^3}{n^6}[/tex] ( with positive exponents )

If the number of degrees of freedom for a chi-square distribution is 81, then the population mean and standard deviation is calculated to be 81 and 12.7279 respectively.

For a chi-square distribution with k degrees of freedom, the population mean and standard deviation are:

Population Mean = k

Population Standard Deviation = √(2k)

Therefore, for a chi-square distribution with 81 degrees of freedom:

Population Mean = k = 81

Population Standard Deviation = √(2k) = √(2×81) = √(162)

Population Mean = 81

Population Standard Deviation = 12.7279 (rounded to four decimal places)

So the population mean is 81 and the population standard deviation is approximately 12.7279.

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1.a) The total revenue received for CD sales was $12,090,000.

1.b) The total revenue received for downloads was $2,499,000.

1.c) The total amount that Craze-K received in royalties last year was $1,240,065.

2) The total royalties that Mr. Pambruccian received last year were $45,210.01.

Commission = 8.5%

                                               CDs         Downloads      Total

Number of items sold     1.86 million      2.1 million

Selling price per unit       $6.50             $1.19

Total sales revenue      $12,090,000   $2,499,000   $14,5898,000

                                  (1.86 m x $6.50)  (2.1 m x $1.19)

Sales commission =      $1,027,650      $212,415        $1,240,065

Royalties = 4%

Selling price per book = $45.99

The total number of books sold = 24,576

The total revenue (sales) = $1,130,250,24 (24,576 x $45.99)

Royalties received = $45,210.01 ($1,130,250.24 x 4%)

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Point E: (7, 3), Point F: (1, 3), Point G: (1, -2) and Point H: (7, -2) are the coordinates of each point.

To translate a point in the (x, y) coordinate plane, we add the translation distances to the x-coordinate and the y-coordinate of the point.

For each point in the quadrilateral EFGH, we can apply this translation as follows:

Point E: (4, 5) + (3, -2) = (7, 3)

Point F: (-2, 5) + (3, -2) = (1, 3)

Point G: (-2, 0) + (3, -2) = (1, -2)

Point H: (4, 0) + (3, -2) = (7, -2)

Therefore, after the translation of 3 units right and 2 units down, the coordinates of the points in quadrilateral EFGH are:

Point E: (7, 3)

Point F: (1, 3)

Point G: (1, -2)

Point H: (7, -2)

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