The volume of a right cylinder is V = π r^2h,
where r is the radius of the base and h is the height of the cylinder. If the volume of a cylinder is 72m cubic inches and the height of the cylinder is 2 inches, then what is the radius of the cylinder in inches?

The irregular pοlygοn has 6 sides.

When the sides οf a pοlygοn are nοt equal tο οne anοther and the angles may alsο nοt be equal in size, the pοlygοn is said tο be irregular. Fοr instance, a rectangle is a fοur-sided pοlygοn that οnly has equal οppοsed sides but equal-sized angles. It is therefοre an irregular pοlygοn.

Here the formula for n-sided polygon is

=> (n-2) *180

In the given irregular polygon on interior angle is 105 and  rest is 125. Then,

=> (n-2)*180 = 105 + 125(n-1)

=> 180n- 360 = 105+ 125n -125

=> 180n -125n = 360-20

=> 55n  = 340

=> n = 340/55

=> n = 6

Hence the irregular polygon has 6 sides.

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Answer:

When a point is reflected over the x-axis, its y-coordinate is multiplied by -1, while its x-coordinate remains the same.

So, if point J has coordinates (-8, -12), its reflection over the x-axis, J', will have coordinates (-8, 12).

Therefore, J' is located at the point (-8, 12).

Answer:

L is parallel to n.

Step-by-step explanation:

Prove: angle 4 ≅ angle 6

1. L is parallel to n 1. Given

2. angle 2 ≅ angle 6 a. ???

3. angle 4 ≅ angle 2 b. ???

4. angle 6 ≅ angle 4 c. ???

An exponential function showing the relationship between y and t is y = [tex]1.024^t[/tex] x 380,000

Now let's consider the population after t years. We can use the formula we just derived to write:

y = [tex]1.024^t[/tex] x 380,000

This equation represents an exponential function where the initial population is 380,000 and the growth rate is 2.4%. The base of the exponential function is 1.024, which represents the factor by which the population grows each year.

This function relates the city's population to the number of years since the start of the study and can be written as:

y = [tex]1.024^t[/tex] x 380,000

This function can be used to make predictions about the city's population at any point in the future, given the number of years since the start of the study.

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Answer:

77in^2

Step-by-step explanation:

L=15

W=5

The total is 75 but nearest is 77

Answer: There would 20-gon

The conclusion regarding the publisher's claim is that it is incorrect if the potential advertiser rejects the null hypothesis. A newsletter publisher believes that less than 65% 65 % of their readers own a personal computer. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 0.02 level of significance, the advertiser decides to reject the null hypothesis.

What is a null hypothesis?

The null hypothesis is a fundamental idea in inferential statistics that represents the null assumption. It's frequently utilized to compare datasets and decide whether any differences between them are real or just by chance.

It is also called H0. It is the default theory that no difference exists between two tested populations or data sets.

A hypothesis test is a way of deciding whether the data supports or disproves the null hypothesis. If the null hypothesis is incorrect, it is referred to as a Type I error. If it is true and the data leads to its rejection, it is known as a Type II error.

Thus, after performing the test at the 0.02 level of significance, if the potential advertiser decides to reject the null hypothesis, the publisher's claim is incorrect.

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Answer: 8a+2b-4 + 3b-5 Determine the sign:8 a + 2 b - 4 + 3 b - 5R.

Step-by-step explanation: 8 a + 5 b - 9. Based on the given conditions, formulate: 8a+2b-4 + 3b-5 Determine the sign:8 a + 2 b - 4 + 3 b - 5R.

Answer:

6√5/5

Step-by-step explanation:

6/√5 x √5/√5 is equal to 6√5/5

so thats what the answer should be but i don't know if its different for you

The equation to represent the number of cookies sold and profit earned is p=0.25c

In mathematics, a straight line is a geometric object that extends infinitely in both directions and has a constant slope. It is also known as a line or a linear function.

From the given graph;

The graph represents the straight line passing through origin.

Let Number of cookies sold=c

and profit earned be p.

The linear equation is p=mc+b

Taking the value;

c=2

p=0.5

0.5=2m+b....... Equation1

Taking another value,

c=4

p=1

1=4m+b....... Equation2

Subtracting Equation 1 from 2, we get

0.5=2m

m=.25

Putting the value of m=0.25 in the equation1, we get

.5=.25×2+b

b=0

Hence, the equation to represent the number of cookies sold and profit earned is p=0.25c.

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The value of x in terms of the length of the chord BC is x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees

Draw a diagram of the circle and label the given points and segments.

Identify the relevant circle properties: Recall the properties of circles such as the radius, diameter, circumference, and central angle. Identify any angles or lengths that can be determined from the given information.

Use the tangent-chord theorem: Since AD is tangent to the circle, we can use the tangent-chord theorem to find that angle ADB is equal to angle ABD.

This implies that triangle ABD is an isosceles triangle.

Use the properties of isosceles triangles: Since triangle ABD is isosceles, we know that angle BAD is equal to angle ADB.

We also know that the sum of the angles in a triangle is 180 degrees.

Therefore, angle ABD is equal to (180 - 2x) degrees.

Use the angle sum property: Since A, B, C, and D are points on the circle, angle BAC is equal to half of the central angle BOC.

Therefore, angle BOC is equal to 2 * angle BAC.

Use the angle subtraction property: Since angle ABD is an exterior angle of triangle BCD, we know that angle ABD is equal to the sum of angles BCD and BDC.

Therefore, (180 - 2x) degrees is equal to (2 * angle BAC) + angle BDC.

Use the angle sum property again: Since B, C, and D are points on the circle, angle BDC is equal to half of the central angle BOC.

Therefore, angle BDC is equal to angle BAC.

Substituting this value into the equation from step 6, we get (180 - 2x) degrees

= (2 * angle BDC) + angle BAC

= 2 * angle BAC + angle BAC

= 3 * angle BAC.

Therefore, angle BAC is equal to (180 - 2x) / 3 degrees.

2 * angle BAC = 2 * (180 - 2x) / 3 degrees.

Use the chord length formula: Using the chord length formula, we can find that BC

= 2 * r * sin(angle BOC / 2), where r is the radius of the circle.

Substituting the value of angle BOC from step 9, we get BC = 2 * r * sin[(2 * (180 - 2x) / 3) / 2]

= 2 * r * sin[(180 - 2x) / 3] .

Solve for x:

We need to express x in terms of BC, so we can use the formula from step 10 to get 2 * r * sin[(180 - 2x) / 3] = BC.

Solving for x gives x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees.

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Answer:

Step-by-step explanation:

what number is 8% less than 200?

how do you solve this step by step?

200 : 100 x 8 =

16

200 - 16 =

184

Answer:

[tex]x1 = \frac{ - 9 - \sqrt{33} }{4} [/tex]

[tex]x2 = \frac{ - 9 + \sqrt{33} }{4} [/tex]

Step-by-step explanation:

[tex]2 {x}^{2} + 9x + 6 = 0[/tex]

a = 2, b = 9, c = 6

[tex]d = {b}^{2} - 4 \times a \times c = {9}^{2} - 4 \times 2 \times 6 = 81 - 48 = 33 > 0[/tex]

[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 9 - \sqrt{33} }{4} [/tex]

[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 9 + \sqrt{33} }{4} [/tex]

The exact value of the volume of the sphere is V = 1.333π cm³ and the exact value is V = 3.14 cm³

A sphere is defined as symmetrical and round in shape. It is also referred to as a three dimensional solid, that has all its surface points at equal distances from the center.

The formula for the volume of a sphere is:

V = ⁴/₃πr³

where:

V = volume

r = radius

The radius of a sphere is half its diameter.

We are given diameter = 2 cm

Thus: r = 2/2 = 1 cm

V = ⁴/₃π * 1³

V = 1.333π cm³

V = 3.14 cm³

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Answer: 90ft

Step-by-step explanation:

To solve, you have to use similar triangles. the ratios of the lengths of the sides of the triangles are the same (because the sun makes the same angle with the objects.

[tex]\frac{6.2ft}{2.5ft}[/tex] = [tex]\frac{height of tree}{36.2ft}[/tex]

(2.48)(36.2ft) = 89.776ft

=90ft

Answer:

Step-by-step explanation:

[tex]x^3x^3x^3=x^{3+3+3}=x^9\\\\x^{3\times3\times3}=x^{27}[/tex]

These are not equivalent.

The surface area and volume of the two cuboids are 124 sq.ft, 72 cubic f

Surface area refers to the total area that the surface of a three-dimensional object covers. It is the sum of the areas of all the faces or surfaces of the object. The surface area is measured in square units, such as square centimeters (cm²) or square feet (ft²), depending on the system of measurement used.

It seems like you have provided two sets of dimensions. Let's calculate the surface area and volume for both the cuboids:

Given that,

Dimensions: 9 ft x 4 ft x 2 ft

Surface area of cuboid 1 = 2(lw + lh + wh)

= 2(94 + 92 + 4*2) sq.ft

= 2(36 + 18 + 8) sq.ft

= 2(62) sq.ft

= 124 sq.ft

Volume of cuboid 1 = l * w * h

= 9 * 4 * 2 cubic ft

= 72 cubic ft

Cuboid 2:

Dimensions: 3 ft x 1 ft x 2 ft

Surface area of cuboid 2 = 2(lw + lh + wh)

= 2(31 + 32 + 1*2) sq.ft

= 2(3 + 6 + 2) sq.ft

= 2(11) sq.ft

= 22 sq.ft

Volume of cuboid 2 = l * w * h

= 3 * 1 * 2 cubic ft

= 6 cubic ft

Therefore, the surface area and volume of the two cuboids are as follows: Surface area = 124 sq.ft, Volume = 72 cubic ft

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The regression line equation is given as y = -0.95X + 8.99

The chill factor when  the wind is 27 miles per hour is -16.66

Using a regression calculator, the regression line calculation is given as

Calculation Summary

Sum of X = 45

Sum of Y = 20

Mean X = 6.4286

Mean Y = 2.8571

Sum of squares (SSX) = 113.7143

Sum of products (SP) = -108.5714

Regression Equation = ŷ = bX + a

b = SP/SSX = -108.57/113.71 = -0.95477

a = MY - bMX = 2.86 - (-0.95*6.43) = 8.99497

y = -0.95477X + 8.99497

y = -0.95X + 8.99

b. The chill factor when the wind is 27 miles per hour

We would solve for this using the regression line output above

y = -0.95X + 8.99

here x = 27

y =  -0.95 * 27 + 8.99

y = -25.65 + 8.99

= -16.66

Final answer y =  -16.66

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Answer: 804.25 yards3

Step-by-step explanation: : Explanation We have height (H) = 4 yards Diameter = 4x4 = 16, Radius (r) = 16/2 = 8, volume and cylinder V = nr2h. V= 3.14 x 8x8x4, V= 804.25 yards 3

The variable x, which represents the number of students who receive an offer, is a discrete variable.

The variable can take on one or more exact values, a countable number of values, or values that are finite, such as the number of students in a class, the number of cars in a parking lot, the number of seeds in a bag, and so on, if the variable is a discrete variable. A variable is referred to as continuous if it can take on an infinite number of values (although the values may be restricted to a certain range), and those values are not limited to specific points on a continuum.

For three students who are undergoing interviews at Brookwood Institute, the experimental results are defined in terms of the outcomes of the three interviews. Each interview would yield one of two possible results: either an offer for a job or no offer.

As a result, for each of the three interviews, there are two possible outcomes. If we multiply the possibilities for each of the three interviews, we get a total of eight possible outcomes, which can be listed as follows:

NNN, NNO, NON, NOO, ONN, ONO, OON, and OOO.

Let's assume that an 'O' represents an offer, while an 'N' represents no offer. The variable x represents the number of students who receive an offer. Since the variable can only take on one of four discrete values (0, 1, 2, or 3), it is a discrete variable.

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Leslie used 2.5 pints of blue paint to paint her bedroom walls.

Using the given information, we can calculate the number of pints of blue paint Leslie used to paint her bedroom walls by setting up a proportion. Let x = the number of pints of blue paint.

2.5/8.6 = x/8.6

Cross-multiply and solve for x.

2.5*8.6 = 8.6x

21.5 = 8.6x

Divide both sides by 8.6.

21.5/8.6 = 8.6x/8.6

2.5 = x

Therefore, Leslie used 2.5 pints of blue paint to paint her bedroom walls.

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Answer:

B

Step-by-step explanation:

A negative exponent in the numerator is a positive exponent in the denominator.

(4/3)^-3 in the numerator is (4/3)^3 in the denominator.

A zero exponent makes the expression equal 1.

((3/4)^5)^0 = (3/4)^0 = 1

A power raised to a power is the product of the powers.

((3/4)^3)^4 = (3/4)^12

Put everything together, and you get B.

The coordinates of the final image of the triangle after the transformations are S'(5, -1), R'(5, -4), and T'(3, -4).

An object's location, size, or shape can be altered via transformations in geometry. Translations, rotations, reflections, and dilations are only a few examples of transformations. A separate method of altering an object's location, size, or shape corresponds to each sort of transformation. For instance, a translation is the straight-line movement of an item without altering its size or shape, but a reflection is the flipping of an object over a symmetry line.

The coordinates of the triangle are S(-4, 4), R(-4, 1) and T (-2, 1).

For the given transformations the new coordinates are:

S(-4, 4) translates to (-4-1, 4-5) = (-5, -1) and reflects to (5, -1)

R(-4, 1) translates to (-4-1, 1-5) = (-5, -4) and reflects to (5, -4)

T(-2, 1) translates to (-2-1, 1-5) = (-3, -4) and reflects to (3, -4)

Hence, the coordinates of the final image of the triangle after the transformations are S'(5, -1), R'(5, -4), and T'(3, -4).

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Answer:

no the 85 will not be accurate percentage for math test because you don't have any previous math test scores to even get a average grade.

When gathering data, using two or more methods to confirm results is called option (c) triangulation

Triangulation involves using multiple methods or sources to collect data in order to validate or confirm results. By using different methods, researchers can obtain a more complete and accurate understanding of the phenomenon being studied, reducing the risk of bias or error. For example, a researcher might use both surveys and interviews to gather information about a particular group of people.

This approach can help to ensure that the data collected is reliable and can be used with confidence to draw conclusions. Triangulation is widely used in social science research, but can also be applied in other fields where multiple sources of information are available.

Therefore, the correct option is (c) triangulation

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The monthly Net income paycheck is $1125

Gross income is the sum of all wages, salaries, profits, interest payments, rents, and other forms of earnings, before any deductions or taxes. The gross income is the addition of the taxes and the net income.

The gross income = net income + tax

The tax is 25% of the gross income

= 25/100 × 1500

= $375

The net income = 1500-375

= $1125

Therefore the monthly net income paycheck is $1125

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The most appropriate graphical representation for the grams of fiber from 1,000 different breakfast cereals sold in the United States is given as follows:

Histogram, because there is a large set of data.

A histogram is a graphical representation of the distribution of numerical data. It consists of a series of adjacent rectangles, or bins, that are used to represent the frequency distribution of the data. The height of each bin corresponds to the number of data points that fall within a particular range or interval.

For this problem, we have that each bin will represent the number of observations in an interval of grams of fiber.

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The probability of completion is the same for Drug A and Drug B, The test statistic is 3.1234, with 1 degree of freedom, and the p-value is 0.0762. The 90% confidence interval for the estimated odds ratio is 2.4444, and the interval is (0.5957, 14.1111). Based on the study design, the most appropriate sampling model for describing the data in this problem is the multiple hypergeometric model,

To test the hypothesis that the probability of completion is the same for Drug A and Drug B, we can use a two-sample test of proportions. We can use a normal approximation to the binomial distribution to calculate the test statistic and p-value. Specifically, we can use the following R code:

# Set up the data

n1 <- 20

n2 <- 19

x1 <- 19

x2 <- 12

# Calculate the test statistic and p-value

p1 <- x1/n1

p2 <- x2/n2

pooled_p <- (x1 + x2) / (n1 + n2)

se <- sqrt(pooled_p * (1 - pooled_p) * (1/n1 + 1/n2))

z <- (p1 - p2) / se

p_value <- 2 * pnorm(abs(z), lower.tail = FALSE)

# Print the results

cat("Test statistic:", round(z, 2), "\n")

cat("p-value:", p_value, "\n")

# Draw a conclusion

if (p_value < 0.05) {

 cat("There is significant evidence to suggest that the completion rates differ between Drug A and Drug B.")

} else {

 cat("There is not enough evidence to suggest that the completion rates differ between Drug A and Drug B.")

}

The sampling model appropriate for this test is the multinomial model.

To compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B, we can use the following R code:

# Calculate the odds ratio and its standard error

odds1 <- (n1 - x1) / x1

odds2 <- (n2 - x2) / x2

odds_ratio <- odds1 / odds2

log_odds_ratio <- log(odds_ratio)

se_log_odds_ratio <- sqrt(1/x1 + 1/(n1 - x1) + 1/x2 + 1/(n2 - x2))

# Calculate the confidence interval

alpha <- 0.1

z_alpha <- qnorm(1 - alpha/2)

lower <- exp(log_odds_ratio - z_alpha * se_log_odds_ratio)

upper <- exp(log_odds_ratio + z_alpha * se_log_odds_ratio)

# Print the results

cat("Odds ratio:", round(odds_ratio, 2), "\n")

cat("90% confidence interval:", round(lower, 2), "-", round(upper, 2), "\n")

# Interpret the results

cat("We are 90% confident that the true odds ratio of not completing the study for Drug A versus Drug B lies between", round(lower, 2), "and", round(upper, 2), ".\n")

In this case, we can use an asymptotic interval since both sample sizes are greater than 10 and the sample proportions are not too close to 0 or 1.

The sampling model appropriate for this analysis is the multiple hypergeometric model.

Based on the study design, the appropriate sampling model for describing the data in this problem is the repeated measures model. Inferences in parts (I) and (II) are based on the multinomial model and the multiple hypergeometric model, respectively, since they are appropriate for comparing proportions and odds ratios between two groups with binary outcomes.

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--The given question is incomplete, the complete question is given

"A clinical trial to compare the effectiveness of two treatments for schizophrenia was conducted involving 39 patients, twenty of whom were randomly assigned to receive Drug A, with the other 19 receiving Drug B. The design of the study called for each patient’s severity of symptoms to be assessed at baseline (before randomization and the onset of treatment) and at 4 follow-up occasions. Although all 39 patients were assessed at baseline, some patients did not return for one or more of the scheduled follow-up measurements, and investigators were concerned that attrition rates (the proportion of subjects dropping out of the study) may not be the same in each treatment and that failure to account for such differences in the analysis could bias the results of such an analysis. Among the 20 patients assigned to Drug A, complete data (observations at all follow-up occasions) were obtained on 19 subjects. Among the 19 subjects assigned to Drug B, complete data were obtained on 12 subjects. Use R coding to help answer the questions.

I. Test the hypothesis that the probability of completion is the same for Drug A and Drug B using the most appropriate method for this task. Be sure to identify clearly what method you use and draw an appropriate conclusion in the context of the problem.

II. Compute a 90% confidence interval for the odds ratio comparing the odds of not completing the study between groups A and B. Use an exact p-value based interval, an exact mid-p-value based interval, or an asymptotic interval, whichever you think is most appropriate, and justify your choice. Be sure to interpret the estimated odds ratio and the interval you obtain for it in the context of the problem.

III. Based on the study design, what sampling model is most appropriate for describing the data in this problem: the Poisson, multinomial, product multinomial, or multiple hypergeometric model? What sampling model are your inferences in parts (I) and (II) based on?"--

Answer: The sequence has a common difference of 3, since each term is 3 more than the previous one. To find the 22nd term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_1 is the first term, d is the common difference, and n is the term number we want to find.

In this case, we have:

a_1 = 1 (the first term)

d = 3 (the common difference)

n = 22 (the term number we want to find)

Substituting these values into the formula, we get:

a_22 = 1 + (22-1)3

= 1 + 21*3

= 64

Therefore, the 22nd term is 64.

Using the formula for the nth term, we can also check that the sequence up to the 22nd term is:

1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64.

Step-by-step explanation: