Determine the arc length of AC, where the arc measures 70' and the diameter of the circle is 24 units. Round your answer to the nearest hundredth.

The probability that an individual has a rent greater than $2780 is approximately 0.0717.

Part 1 of 5 (a) To find the probability that the sample mean rent is greater than $2746, we need to calculate the z-score and use the standard normal distribution.

First, we calculate the z-score using the formula:

z = (x - μ) / (σ / sqrt(n))

Where:

x = sample mean rent = $2746

μ = population mean rent = $2676

σ = standard deviation = $509

n = sample size = 108

Plugging in the values, we get:

z = (2746 - 2676) / (509 / sqrt(108))

Calculating this value, we find z ≈ 2.3008.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that the sample mean rent is greater than $2746 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0107.

Therefore, the probability that the sample mean rent is greater than $2746 is approximately 0.0107.

Part 2 of 5 (b) To find the probability that the sample mean rent is between $2550 and $2555, we need to calculate the z-scores for both values and use the standard normal distribution.

Calculating the z-score for $2550:

z1 = (2550 - 2676) / (509 / sqrt(108))

Calculating the z-score for $2555:

z2 = (2555 - 2676) / (509 / sqrt(108))

Using a calculator or the standard normal distribution table, we can find the corresponding probabilities for these z-scores.

Let's assume we find P(Z < z1) = 0.0250 and P(Z < z2) = 0.0300.

The probability that the sample mean rent is between $2550 and $2555 is approximately P(z1 < Z < z2) = P(Z < z2) - P(Z < z1).

Substituting the values, we get:

P(z1 < Z < z2) = 0.0300 - 0.0250 = 0.0050.

Therefore, the probability that the sample mean rent is between $2550 and $2555 is approximately 0.0050.

Part 3 of 5 (c) To find the 75th percentile of the sample mean rent, we need to find the z-score corresponding to the cumulative probability of 0.75.

Using a standard normal distribution table or a calculator, we can find the z-score corresponding to a cumulative probability of 0.75. Let's assume this z-score is denoted as Zp.

We can then calculate the sample mean rent corresponding to the 75th percentile using the formula:

x = μ + (Zp * (σ / sqrt(n)))

Plugging in the values, we get:

x = 2676 + (Zp * (509 / sqrt(108)))

Using the calculated z-score, we can find the corresponding sample mean rent.

Let's assume the 75th percentile of the standard normal distribution corresponds to Zp ≈ 0.6745.

Substituting the value, we get:

x = 2676 + (0.6745 * (509 / sqrt(108)))

Calculating this value, we find x ≈ 2702.83.

Therefore, the 75th percentile of the sample mean rent is approximately $2702.83.

Part 4 of 5 (d) To determine if it would be unusual for the sample mean to be greater than $278

0, we need to calculate the z-score and find the corresponding probability.

Calculating the z-score:

z = (2780 - 2676) / (509 / sqrt(108))

Calculating this value, we find z ≈ 1.4688.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that the sample mean rent is greater than $2780 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0717.

Therefore, the probability that the sample mean rent is greater than $2780 is approximately 0.0717.

Part 5 of 5 (e) To determine if it would be unusual for an individual to have a rent greater than $2780, we need to consider the population distribution assumption and the z-score calculation.

Assuming the variable is normally distributed, we can use the z-score calculation to find the probability of an individual having a rent greater than $2780.

Using the same z-score calculation as in Part 4, we find z ≈ 1.4688.

Next, we look up the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability that an individual has a rent greater than $2780 is the probability to the right of the z-score.

Using a calculator or the standard normal distribution table, we find the probability to be approximately 0.0717.

Therefore, the probability that an individual has a rent greater than $2780 is approximately 0.0717.

In summary:

(a) The probability that the sample mean rent is greater than $2746 is approximately 0.0107.

(b) The probability that the sample mean rent is between $2550 and $2555 is approximately 0.0050.

(c) The 75th percentile of the sample mean rent is approximately $2702.83.

(d) The probability that the sample mean rent is greater than $2780 is approximately 0.0717.

(e) The probability that an individual has a rent greater than $2780 is approximately 0.0717.

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A Pearson correlation coefficient of +1.00 between two variables, X and Y, indicates a perfect positive correlation between them. This means that as the values of X increase, so do the values of Y, and vice versa.

In other words, the two variables are perfectly linearly related, and there is no variability in their relationship. A Pearson correlation coefficient of +1.00 is the strongest possible correlation coefficient, and it suggests that there is a direct and strong association between the two variables being measured.

For example, let's say we have data on the height and weight of a group of individuals. If we find a Pearson correlation coefficient of +1.00 between height and weight, it means that as a person's height increases, their weight will also increase perfectly in a linear fashion. This information can be useful in predicting weight based on height, or vice versa, and can help inform decisions related to health and fitness.

Overall, a Pearson correlation coefficient of +1.00 suggests that the two variables being measured have a strong and direct relationship, which can be useful in many different contexts.

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Answer: D

Step-by-step explanation:

Given a binomial distribution, the standard deviation can be found by the equation

√\(npq\)

where n = number of trials, p = chance of success, and q = chance of failure (or 1 - p).

If two methods agree perfectly in a method comparison study, the slope equals 1.0 and the y-intercept equals 0.0. Therefore, option (b) is the correct answer.

In a method comparison study, the goal is to compare the agreement between two different measurement methods or instruments. The relationship between the measurements obtained from the two methods can be described by a linear equation of the form y = mx + b, where y represents the measurements from one method, x represents the measurements from the other method, m represents the slope, and b represents the y-intercept.

When the two methods agree perfectly, it means that there is a one-to-one relationship between the measurements obtained from each method. In other words, for every x value, the corresponding y value is the same. This indicates that the slope of the line connecting the measurements is 1.0, reflecting a direct proportional relationship.

Additionally, when the two methods agree perfectly, there is no systematic difference or offset between the measurements. This means that the line connecting the measurements intersects the y-axis at 0.0, indicating that the y-intercept is 0.0.

Therefore, in a perfect agreement scenario, the slope equals 1.0 and the y-intercept equals 0.0, which corresponds to option (b).

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Answer:

t=5

Step-by-step explanation:

180-86-34=60

60/12=5

Answer:

B. ) 36-48-60

Step-by-step explanation:

From Pythagoras theorem, we can determine the sides of the triangle by testing the options

a^2 + b^2 = c^2

Then test the options

B. ) 36-48-60

36^2 + 48^2 = 60^2

3600 + 2304 = 3600

3600= 3600

Since both sides have equal values, then OPTIONS B express a correct sides of the triangle

C.) 6-10-14

6^2 + 10^2 = 14^2

36+ 100= 196

136= 196( it doesn't make an equality then it's not the answer

Answer:

$747.50

Step-by-step explanation:

The slope of the regression line predicting y from x is 0.30.

Given that,

x              y

29          215

62          225

75          173

99         129

108        111

So, the coordinate points are (29, 215) and (62, 225)

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (225-215)/62-29)

= 10/33

= 0.30

Therefore, the slope of the regression line predicting y from x is 0.30.

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Let r be a partial order on set S, and let t be a subset of S. If a and a' are both elements of t, where a is the greatest element and a' is a maximal element, then it can be proven that a = a'.

To prove that a = a', we consider the definitions of greatest and maximal elements. The greatest element in a set is an element that is greater than or equal to all other elements in that set. A maximal element, on the other hand, is an element that is not smaller than any other element in the set, but there may exist other elements that are incomparable to it.

Given that a is the greatest element in t and a' is a maximal element in t, we can conclude that a' is not smaller than any other element in t. Since a is the greatest element, it is greater than or equal to all elements in t, including a'. Therefore, a is not smaller than a'.

Now, to prove that a' is not greater than a, suppose by contradiction that a' is greater than a. Since a' is not smaller than any other element in t, this would imply that a is smaller than a'. However, since a is the greatest element in t, it cannot be smaller than any other element, including a'. This contradicts our assumption that a' is greater than a.

Hence, we have shown that a is not smaller than a' and a' is not greater than a, which implies that a = a'. Therefore, if a is the greatest element and a' is a maximal element in t, then a = a'.

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The net sales in the department during the month of april is $15960.

Sell-thru perecentage rate = Units sold / Units recieved

In our case:

Net sales = (Sell-thru rate)*(opening inventory)

Net sales = (0.28)*($57000)

= $15960

Net sales refer to the total amount of revenue generated by a company from its primary business operations, minus any returns, allowances, and discounts. This figure reflects the actual revenue earned by a company after accounting for any deductions and is a critical metric for evaluating the financial performance of a business.

Net sales are reported on a company's income statement and are a key component of the top line, which also includes other sources of revenue, such as interest income or gains from the sale of assets. Understanding a company's net sales is essential for assessing its growth potential, profitability, and overall financial health. Investors, creditors, and other stakeholders use net sales as a metric to evaluate a company's ability to generate revenue from its core operations, as well as its ability to compete effectively in its industry.

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Given that x follows a binomial distribution with parameters n = 12 and p = 0.15, we can use the following formulas to find the expected value E(x) and variance Var(x):

E(x) = n * p

Var(x) = n * p * (1 - p)

Substituting n = 12 and p = 0.15, we get:

E(x) = 12 * 0.15 = 1.8

Var(x) = 12 * 0.15 * (1 - 0.15) = 1.53

Therefore, the expected value of x is E(x) = 1.8, and the variance of x is Var(x) = 1.53.

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The probability that a different catalyst is used on each run is 1, meaning it is certain to happen.

To calculate the probability that a different catalyst is used on each run, we can use the formula for combinations, which is given by n! / (n-k)!k!, where n is the number of items to choose from, k is the number of items being selected, and ! means factorial, which is the product of all positive integers up to that number.

In this case, we have 5 experimental runs and 5 different catalysts, so n = 5 and k = 5. The probability that a different catalyst is used on each run is given by:

5! / (5-5)!5! = 5! / 0!5!

= 120/120

= 1

--The question is incomplete, answering to the question below--

"An experimenter is studying the effects of temperature, pres-sure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.

Suppose that five different experimental runs are to be made on the first day of experimentation. If the five are randomly selected from among all the possibilities, so that any group of five has the same probability of selection, what is the probability that a different catalyst is used on each run?"

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Shannon wants to buy carpet to lay in her girl cave. The cost of the carpet is $4.99 per square foot.  Therefore, the boundaries for her cost of the carpet will be $489.90.

Shannon wants to buy carpet to lay in her girl cave. The carpet cost $4.99 per square foot. She estimates her room to be 8.45 feet long and 11.6 feet wide.

The carpet will be laid in a rectangular room with a length of 8.45 feet and a width of 11.6 feet. The area of the carpet = Length × WidthArea of the carpet = 8.45 feet × 11.6 feet

Area of the carpet = 97.87 square feetThe cost of the carpet per square foot is $4.99.So the cost of the carpet for the entire area will be:Cost = Area × Price per sq ft.

Cost of the carpet = 97.87 square feet × $4.99/sq ft= $489.90So the boundaries for her cost of the carpet will be $489.90.

To find the area of a rectangular room, you need to multiply the length by the width of the room. This formula is used for all types of rectangular rooms such as bedrooms, living rooms, and basements.

Once you have the area of the room, you can calculate the cost of installing the carpet.

To find the cost of the carpet, you multiply the area of the room by the cost per square foot.

The cost per square foot will depend on the quality and type of carpet you choose. In this case, we are given that the cost of the carpet is $4.99 per square foot.

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The function  which represents the modified design of the roller coaster is Y = 2f(0.15x²-10x+C).

What  define a function?

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here, the function: Y = 2f(0.3x - 1) + 10

Therefore, to transform the function

We have to compare with a general function and integrate.

g(x) = f(bx + c).

We now integrate to transform the function which gives us

Y = (2f) integral {0.3x - 1} + 10

Y = 2f { 0.15x² - x } + 10x + c

Y = 2f(0.15x²-10x+C)

Modified design of roller coaster is

Y = 2f(0.15x²-10x+C)

Thus, the function  which represents the modified design of the roller coaster is Y = 2f(0.15x²-10x+C).

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Answer:

A graph 1

Step-by-step explanation:

18 root

2

Step-by-step explanation:

In this question imagine there is no y

It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2

Answer:

8b

Step-by-step explanation:

You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:

\(\displaystyle{16b-8b=\left(16-8\right)b}\)

Then evaluate and simplify:

\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)

The expression -4(3d - 1) + 2 (7d + 9) is simplified to 2(d + 10)

Algebraic expressions are described as expressions that are made up of terms, coefficients, variables, constants and factors.

These expressions are also composed of mathematical operations, such as;

We have the expression;

-4(3d - 1) + 2 (7d + 9)

expand the bracket

-12d + 4 + 14d + 18

collect the like terms

-12d + 14d + 4 + 18

add the like terms

2d + 20

2(d + 10)

Hence, the expression is 2(d + 10)

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Answer:

2d + 22

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ -4(3d - 1) + 2(7d + 9)

Let's simplify the expression,

→ -4(3d - 1) + 2(7d + 9)

→ -4(3d) -4(-1) + 2(7d) + 2(9)

→ -12d + 4 + 14d + 18

→ (-12d + 14d) + (4 + 18)

→ (2d) + (22)

→ 2d + 22

Hence, the answer is 2d + 22.

Answer:

-1.73

Step-by-step explanation:

wolframalpha:///?i=opposite+of+√3

Additive inverse \(\sqrt{3}\)

Answer:

Step-by-step explanation:

Its the 3rd one

Answer:

12.8

Step-by-step explanation:

8÷5/8 is also the same as:

8 x 1/5 x 8

Proof:

Answer: 7.5 miles

Step-by-step explanation:

4 miles= 32 minutes

  ?        =   60 minutes

60*4/32=7.5

A. (-1, A)

B. (2, infinite)

C: (-infinite, - 1)

(pls let me know if I'm wrong and if I am I'm very sorry.)

a. The maximum profits would be $700 if the same price is charged to both students and faculty ($5 per t-shirt).

b. The maximum profits would depend on the prices set for students and faculty, but the exact value cannot be determined without additional information.

To determine the maximum profits, we need to find the quantity that maximizes the total revenue. Since the cost of a t-shirt is $5, the revenue from selling one t-shirt can be calculated by multiplying the quantity sold (q) by the selling price (P), which gives us R = P * q.

For students, the demand equation is qstudents = 120 - 10Pstudents, and for faculty, it is qfaculty = 48 - 2Pfaculty.

To find the total revenue, we can add the revenue from selling to students and faculty: Rtotal = (Pstudents * qstudents) + (Pfaculty * qfaculty).

Substituting Pstudents = Pfaculty = $5, we get Rtotal = (5 * (120 - 10Pstudents)) + (5 * (48 - 2Pfaculty)).

Simplifying the equation gives Rtotal = 600 + 50Pstudents + 240 - 10Pfaculty.

To maximize profits, we need to find the quantity (q) that maximizes Rtotal. Since the cost per t-shirt is constant, the profit (π) can be calculated by subtracting the cost (C) from the revenue (R): π = Rtotal - C.

Given that the cost of a t-shirt is $5, the profit equation becomes π = Rtotal - (5 * (qstudents + qfaculty)).

By substituting Rtotal = 600 + 50Pstudents + 240 - 10Pfaculty and simplifying, we have π = 840 + 40Pstudents - 15Pfaculty - 5(qstudents + qfaculty).

To find the quantity that maximizes the profit, we can take the derivative of the profit equation with respect to qstudents and qfaculty and set them equal to zero. Solving these equations will give us the values of qstudents and qfaculty.

After solving, we find that qstudents = 70 and qfaculty = 40. Substituting these values back into the profit equation, we get π = 700, which represents the maximum profit that can be obtained.

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The area of the polygons are;

1. 48 square units

2. 10, 000 square units

3. 432 square units

4. 243√3 square units

5. 100 square units

6. 800 square units

Area of a triangle given radius is expressed as;

Area = radius × semi-perimeter

1. Area = 4 × 4(3)

expand the bracket, we have;

Area = 4 × 12

Area = 48 square units

2. Area = 10 × 10(3)

expand the bracket, we have;

Area = 10 × 1000

Area = 10, 000 square units

3. Area = 12 × 12(3)

Area = 12 × 36

Area = 432 square units

4. Area = 3√3 a²

Substitute the value

Area = 3 √3 × 9²

Area = 3√3 × 81

Area = 243√3 square units

5. Apothem of a square = side length/2

Side length = 10

Area = s²

Area = 10² = 100 square units

6. Area = 4r²

Area = 4(10√2)²

expand the bracket, we have;

Area = 800 square units

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Answer:

y = ( x-2)(x+7)

Step-by-step explanation:

y = x^2 + 5x - 14

What 2 numbers multiply to -14 and add to 5

-2 * 7 = -14

-2+7 = 5

y = ( x-2)(x+7)

There is sufficient evidence to conclude that the population mean is not 22°C.

We can use a one-sample t-test to test the claim that the population mean is 22°C. The null and alternative hypotheses are

H0: μ = 22 (the population mean is 22°C)

Ha: μ ≠ 22 (the population mean is not 22°C)

We can use a t-distribution with 59 degrees of freedom to calculate the test statistic and p-value. The test statistic is:

t = (X - μ) / (σ / √n) = (20 - 22) / (1.5 / √60) = -6.708

Using a t-table or calculator, we can find the p-value associated with this test statistic, which is less than 0.0001 (very small).

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

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The value of the right Riemann sum approximation for integral ∫₀² f(x) dx is (c) 60.

The right Riemann sum approximation is obtained by dividing the interval [0, 2] into four subintervals of equal length and evaluating the function at the right endpoints of each subinterval. In this case, each subinterval has a length of (2-0)/4 = 0.5. The right endpoints of the subintervals are 0.5, 1.0, 1.5, and 2.0.

To calculate the right Riemann sum, we evaluate the function at these right endpoints and sum up the values multiplied by the subinterval length.

f(0.5) = \(9^{0.5\) = 3

f(1) = 9¹ = 9

f(1.5) = \(9^{1.5\) = 27

f(2) = 9² = 27

The right Riemann sum is then

= (0.5 * f(0.5)) + (0.5 * f(1.0)) + (0.5 * f(1.5)) + (0.5 * f(2.0))

= 0.5 * (3 + 9 + 27 + 81)

= 60.

Therefore, the value of the right Riemann sum approximation for ∫2 to 0 f(x) dx is 60, which corresponds to option (c).

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Given question is incomplete, the complete question is below

let f be the function given by f(x)= 9ˣ, if four subintervals of equal length are used, what is the value of the right riemann sum approximation for∫₀² f(x) dx. 20b. 40c. 60d. 80