If the area of a semi - circle is 308 cm square, calculate its radius. ( use pi = 22/7)​

The perimeter of the right triangle ABD is 31 units.

Given is right triangle ADB, we need to find the perimeter of the triangle,

So, according to properties of a triangle we have,

x² = 9 × 4

x = √36

x = 6

Now using Pythagoras theorem,

6² + 4² = AD²

AD = 7.2

Similarly,

BD² = 6² + 9²

BD = 10.8

So, we know that the perimeter of a polygon is the sum of all its sides,

So,

P = AD + BD + AB

= 10.8 + 7.2 + 9 + 4

= 31 units.

Hence the perimeter of the right triangle ABD is 31 units.

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Answer:

-7x=-31+3

-7x=-28

÷ by -7 both sides

x=3

The Surface area of the rectangular prism is 1232 square inches

To find the surface area of a rectangular prism, we need to find the areas of all six faces and add them together.

The two faces that have dimensions of 14 inches by 16 inches have a combined area of 2(14 in)(16 in) = 448 square inches.

The other four faces are all rectangles with dimensions of 14 inches by 14 inches, giving us a total area of 4(14 in)(14 in) = 784 square inches.

Therefore, the surface area of the rectangular prism is:

448 + 784 = 1232 square inches.

So the surface area of the rectangular prism is 1232 square inches.

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Answer:

x = 5  or x = -3

Step-by-step explanation:

2(x-1)^2 +7= 39

Subtract 7 from each side.

2(x-1)^2 +7-7= 39 -7

2(x-1)^2 = 32

Divide each side by 2.

2/2(x-1)^2 = 32/2

(x-1)^2 = 16

Take the square root of each side.

sqrt((x-1)^2)= sqrt(16)

x-1 = ±4

Add 1 to each side.

x =   ±4 +1

x = 5  or x = -3

Answer:

x = 5 or x = -3

Step-by-step explanation:

We know that,

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

Accordingly, let us solve this.

2 ( x - 1 )² + 7 = 39

First, solve the brackets.

2 ( x² - 2x + 1 ) + 7 = 39

2x² - 4x + 2 + 7 = 39

Subtract 39 from both sides.

2x² - 4x - 30 = 0

Divide the whole equation by 2.

x² - 2x - 15 = 0

Solve the quadratic equation.

x² + 3x - 5x - 15 = 0

x ( x + 3 ) - 5 ( x + 3 ) = 0

( x - 5 ) ( x + 3 ) = 0

∴ x - 5 = 0                      x + 3 = 0

   x = 5          or              x = -3

Answer: C

Step-by-step explanation:

You are trying to find the number of muffins Nola started the day with.

When she baked 21 muffins she gained 21 muffins (addition)

When she gave away 30 muffins she lost 30 muffins (subtraction)

The third equation has her gaining 21 muffins and losing 30 muffins for a final amount of 44 so it must be C

Answer:

1a. Let’s assume that the length of the north side of the house is represented by ‘x’. Then the polynomial that represents the length of the north side of the house is x.

1b. There is no expression to simplify.

2a. Your cousin is not correct.

2b. The length of the north side of the house is represented by ‘x’ and not by ‘9y+2y’. Therefore, your cousin is not correct.

The polynomial stated by the cousin as the length of the north side of the house, 9y + 2y, simplifies to 11y. Thus, the cousin is not correct. Polynomials and simplifying expressions are part of basic algebra skills.

Based on your cousin's statement, the polynomial representing the length of the north side of the house is 9y + 2y. To determine the correctness of this polynomial, we must first simplify the expression. By combining like terms (terms with the same variable and exponent), the expression simplifies to 11y. So, the length of the north side is represented by 11y, not 9y + 2y. Hence, your cousin's statement is not correct.

Understanding how to combine like terms, simplify expressions, and handle polynomials is an important part of basic algebra skills. Polynomials can be used to represent many real world quantities such as the length of a side of a house as in this problem. Remember that it is crucial to perform all calculations accurately to avoid errors.

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None of the postulates given can prove that the two triangles are congruent.

According to the Side-side-angle (SSA) Congruence Theorem, if two triangles have two corresponding sides and a non-included sides that are congruent, then both triangles are congruent to each other.

In the image given, the information in the diagram shows that both triangles have two pairs of corresponding sides that are congruent and a pair of non-included sides that are congruent, therefore, they are congruent based on the SSA congruence theorem.

None of the options given proves that the triangles are congruent.

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Calculating this expression, we find that the probability of exactly 4 arrivals in a one-minute period is approximately 0.0902.

The probability of at least 4 arrivals in a one-minute period is approximately 0.8571.

The probability of exactly 4 arrivals in a one-minute period can be calculated using the Poisson distribution formula. With a mean arrival rate of 2 customers per minute, we can substitute λ = 2 into the formula. The probability of exactly 4 arrivals is given by:

P(X = 4) = (e^(-λ) * λ^4) / 4!

Substituting λ = 2:

P(X = 4) = (e^(-2) * 2^4) / 4

The probability of at least 4 arrivals in a one-minute period can be calculated by summing the probabilities of having 4, 5, 6, and so on, arrivals. Using the same Poisson distribution formula, we can calculate the individual probabilities and sum them up.

P(X ≥ 4) = 1 - P(X < 4)

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Substituting λ = 2 into the Poisson formula, we can calculate each individual probability and sum them up.

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No, the variances are not similar enough to use the pooled t test. The ratio of the two variances (25/8) is greater than 3, which is the typical cutoff for determining similarity of variances. Therefore, an alternative method such as the Welch's t-test or a non-parametric test should be used to compare the means.

To determine if the variances are similar enough to use a pooled t-test, you can perform an F-test for equality of variances. Follow these steps:

1. Calculate the F statistic by dividing the larger variance by the smaller variance: F = var2 / var1 = 25 / 8 = 3.125.

2. Determine the degrees of freedom for each group: df1 = 10 - 1 = 9 and df2 = 10 - 1 = 9.

3. Check the F critical value for the given degrees of freedom and chosen significance level (e.g., 0.05) using an F-distribution table or a calculator. For df1 = 9 and df2 = 9 at a 0.05 significance level, the F critical value is approximately 3.18.

4. Compare the calculated F statistic to the F critical value: 3.125 < 3.18.

Since the F statistic is less than the F critical value, we fail to reject the null hypothesis that the variances are equal. Therefore, the variances are similar enough to use the pooled t-test to evaluate differences in the means. The answer is yes.

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The median annual salary would be more useful to Jaime in making the decision between pursuing graduate studies or applying for a job.

The median annual salary represents the middle value in a salary distribution, which indicates the typical or central salary of college graduates in that profession. It is less affected by extreme values or outliers in the data. Therefore, the median provides a more reliable measure of the average salary that Jaime can expect as a college graduate. On the other hand, the mean annual salary can be influenced by a few individuals with exceptionally high or low salaries, which may not accurately reflect the typical salary range. Hence, the median salary would be a better indicator for Jaime to make an informed decision.

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The function that represents the situation is,

y = 1049(1.080)ˣ.

To determine the equation which closely models the data, we need to first plot the data points on a graph and analyze the trend.

Year Population

1 1049

2 1137

3 1229

4 1326

5 1434

6 1542

7 1662

We can see that the population is increasing each year, so we can assume that it follows an exponential growth pattern.

To find the equation that models the data, we can use the exponential growth formula:

y = abˣ

where y is the population, x is the year, a is the initial population, and b is the growth factor.

Using the data for year 1 and year 7, we can find the values of a and b:

a = 1049

y = abˣ

1662 = 1049b⁷

b = (1662/1049)¹/⁷ = 1.080

Now we can substitute the values of a and b into the formula:

y = 1049(1.080)ˣ.

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The value of the original side length is, 6 m

Here, We have to given that;

All the sides of a square have lengthened by,

⇒ 3 m

And, the area of a square becomes,

⇒ 81 m²

Since, We know that;

A square is a two dimension figure with 4 equal sides, 4 corners and 4 right angles. The sides of the square are equal and parallel to each other.

Now, We can assume that,

the original side length is,

⇒ x

Hence, We can formulate by given condition,

⇒ (x + 3)² = 81

Taking square root both side,

⇒ x + 3 = √81

⇒ x + 3 = 9

Subtract 3 both side,

⇒ x = 9 - 3

⇒ x = 6 m

Therefore, We get;

The solution of the original side length is,

⇒ 6 m

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Both of Nick's bags weigh 41 kilograms combined.

In mathematical terms, if we let W1 be the weight of the first bag and W2 be the weight of the second bag, then the total weight of both bags can be expressed as W1 + W2.

Substituting the given values, we get:

Total weight of both bags = 24 + 17 = 41 kilograms.

This is a simple addition problem that involves adding the weights of two bags to find the total weight.

The complete question is:

Nick is going on vacation. one of his bags weighs 24 kilograms. the other bag weighs 17 kilograms. how much do both of nick's bags weigh combined?

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By finding the inverses we can see that:

Two functions g(x) and g⁻¹(x) are inverses if:

g⁻¹(g(x)) = x

Here we know that the function g is defined by:

g={(-8, -3), (-3, 2), (3, 0), (5, 6)}

And we want to find:

g⁻¹(-3)

On the table we can see that g(-8) = -3, then:

g⁻¹(-3) = -8

And we have:

h(x) = -2x + 13

Evaluating on the inverse we should get:

h(h⁻¹(x)) = x

            = -2*h⁻¹(x)   + 13 = x

Solving for the inverse:

h⁻¹(x) = (x - 13)/-2

Now we can get the product:

(h⁻¹*h)(3) = (-2*3 + 13)(3 - 13)/-2

              = 7*5 = 35

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The function g(f(x)) is √(3x + 1).

We have,

This is a composite function.

To find g(f(x)), we need to substitute the function for f(x) into g(x) wherever we see x:

g(f(x)) = g(3x + 2)

Then, we substitute the function for g(x).

g(f(x)) = √(3x + 2 - 1)

Simplifying the expression inside the square root.

g(f(x)) = √(3x + 1)

Therefore,

g(f(x)) = √(3x + 1).

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Answer: 54, 63, 72

Step-by-step explanation: Well let's multiply 9 till 75 so 9(1), 18(2), 27(3), 36(4), 45(5), 54(6), 63(7), 72(8). The underlined numbers are ones that are divisible by 3. Hope this helps! :)

option "The population is the number of people in the town of Westingbrook, and the sample is the number of people who go to the mall" is correct

The probability of selecting a P on the first draw and a V on the second draw is 2/4950

From the question, we are to determine the probability of selecting a P on the first draw and a V on the second draw.

From the formula for probability, we have that

P(A) = Number of favorable outcomes to A / Total number of possible outcomes

From the given tiles,

Number of favorable outcomes to P = 2

Total number of possible outcomes = 100

Thus,

Probability of selecting a P on the first draw = 2/100

On the second draw

Number of favorable outcomes to V = 2

Total number of possible outcomes = 99

Thus,

Probability of selecting a V on the second draw = 2/99

Now,

The probability of selecting a P on the first draw and a V on the second draw is

P(1st P and 2nd V) = 2/100 × 2/99

P(1st P and 2nd V) = 1/50 × 2/99

P(1st P and 2nd V) = 2/4950

Hence, the probability is 2/4950

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The coordinates of point P that represents the weighted average of the set of points are (-8/5, y).

Given that point A weighs 3 times as much as point C. This implies that the weight of point C is 1, and the weight of point A is 3.

To find the weighted average of the points, we can use the formula:

[tex]P = \dfrac{(w_1 \times A + w_2 \times B + w_3 \times C)}{(w_1 + w_2 + w_3)}[/tex]

where P is the weighted average point, w₁, w₂, and w₃ are the weights of points A, B, and C, respectively, and A, B, and C are the coordinates of the points.

Substituting the given values, we have:

P = (3 × (-5) + 0 + 1 × 7) / (3 + 1 + 1)

P = (-15 + 7) / 5

P = -8/5

Therefore, the coordinates of point P that represents the weighted average of the set of points are (-8/5, y).

The y-coordinate cannot be determined without additional information.

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There is about 295.11335 cubic inches of space left in the container, not including the balls.

We must first determine the cylinder's total volume before deducting the volume of the 25 spheres in order to determine the amount of space still inside the container.

The formula for calculating a cylinder's volume is V_cylinder = * r2 * h, where V_cylinder denotes the cylinder's volume, r stands for the cylinder's radius, and h denotes the cylinder's height.

The cylinder's radius (r) in this instance is specified as 3 inches, while its height (h) is specified as 12 inches. We may determine the volume of the cylinder by entering these values into the formula.

V_cylinder equals 3.14159 * 3 2 * 12 V_cylinder is 339.292 in3 in volume.

Next, we must determine the volume of each sphere. The following equation determines a sphere's volume:

Where: V_sphere = (4/3) * * (r3) V_sphere is the sphere's volume, is a mathematical constant roughly equal to 3.14159, and r is the sphere's radius.

The spherical balls' diameter (d) in this instance is 1.5 inches, which means the radius (r) is equal to half of the diameter.

r = 1.5/2d/2 = 0.75 inches.

We may get the volume of each spherical ball using this value as a plug-in in the formula.

V_sphere is equal to 4.33 * 3.14159 * 0.75.

1.7671459 in3 V_sphere

The volume of one sphere is multiplied by the quantity of spheres in order to determine the combined volume of the 25 spherical balls.

V_total_spheres is calculated as V_sphere * 25 V_total_spheres 44.17865 in3.

Finally, we can determine how much room is still in the container by deducting the volume of the 25 spheres from the cylinder's volume.

Space left is equal to V_cylinder - V_total_spheres.

339.292 - 44.17865 space_left

295.11335 in3 of space is remaining.

Without accounting for the balls, there is approximately 295.11335 cubic inches of empty space in the container.

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The 90% confidence interval suggests that we are 90% confident the proportion of disapproving small-business owners is between 69.2% and 74.8%.

To compute the 90% confidence interval for the population proportion of small-business owners who do not approve of the changes, we can use the sample proportion and the properties of confidence intervals.

Given that the sample size is 570 and the sample proportion is 72%, we can calculate the standard error using the formula:

Standard Error = [tex]sqrt((p * (1 - p)) / n)[/tex]

where p is the sample proportion and n is the sample size.

Substituting the values, we get:

Standard Error = [tex]sqrt((0.72 * (1 - 0.72)) / 570)[/tex] ≈ 0.017

Next, we can calculate the margin of error by multiplying the standard error by the appropriate z-score for a 90% confidence level. For a 90% confidence level, the z-score is approximately 1.645.

Margin of Error = z * Standard Error = 1.645 * 0.017 ≈ 0.028

Finally, we can construct the confidence interval by subtracting and adding the margin of error from the sample proportion:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.72 ± 0.028

Therefore, the 90% confidence interval for the population proportion of small-business owners who do not approve of the changes is approximately 0.692 to 0.748 (rounded to 3 decimal places). This means we can be 90% confident that the true proportion of small-business owners who do not approve of the changes lies between 69.2% and 74.8%.

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Answer:

THE CORRECT ANSWER IS C. "The description does not show a linear relationship or a proportional relationship."

Step-by-step explanation:

The statistic that indicates how much scores differ from each other is Standard deviation.

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

To calculate the standard deviation, you must first calculate the mean of the data set. This is done by adding up all the values in the data set and dividing by the number of values. Once you have the mean, you must subtract it from each value in the data set and square the result.

Then, you must add up all of the squared values, divide by the total number of values, and take the square root of that number. The result is the standard deviation.

Standard deviation is important because it can be used to compare the data to its mean and can help determine the amount of risk associated with a particular data set. Standard deviation is a measure of how spread out a data set is from its mean or average. It is used to measure the amount of variability or dispersion for a given data set.

Thus, The statistic that indicates how much scores differ from each other is Standard deviation.

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Answer: C

Step-by-step explanation:

The standard deviation measures the amount of variation or dispersion of a set of scores from the mean. Therefore, the correct answer is C.

0 5/3 21 On the number line, we need to position three numbers: 0, 5/3, and 21.

The number 0 is the starting point and should be placed on the leftmost box. Next, we have the number 5/3. To determine its placement, we can convert it to a decimal. Dividing 5 by 3 yields 1.666..., which is approximately 1.67.

Since 5/3 is greater than 1 but less than 2, it falls between 1 and 2 on the number line. Finally, we have the number 21, which is significantly larger than 5/3. It should be placed on the rightmost box, well past the midpoint between 0 and 5/3. Therefore, the correct placement along the number line would be: 0, 5/3, 21.

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Approximately 13 percent  of the student body in the 9th grade don't play a sport.

To find the percentage of the student body in the 9th grade who don't play a sport, we need to calculate the number of 9th-grade students who don't play a sport and divide it by the total number of students, then multiply by 100 to get the percentage.

From the table, we can see that the number of 9th-grade students who don't play a sport is 32. The total number of students is 240.

Percentage = (Number of 9th-grade students who don't play a sport / Total number of students) * 100

= (32 / 240) * 100

= 0.133333 * 100

≈ 13.33

Rounded to the nearest whole number, the percentage is 13.

Therefore, approximately 13% of the student body in the 9th grade don't play a sport.

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The length of AB is 6 units.

Given that two congruent circles, we need to find the distance AB,

Let the point where AB and CD intersects be O,

According to the property of circle, AB⊥CD, and CO = OD.

Therefore, using the Pythagorean theorem,

AC² = OC² + AO²

AO = √5²-4²

AO = 3

Since the circles are congruent then AO = OB = 3

AB = OA + OB

AB = 6 units.

Hence the length of AB is 6 units.

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Answer:

This graph is a negative linear association. C is the correct answer.

The center is (1,0), thus the center lies on the x-axis, the radius is 3 units and the radius of the circle is the same with x² + y² = 9.

The radius is half the diameter of a circle and the center of the circle is a point from which all distance to the edge of the circle is equal.

The equation that represents the center of the circle equation is (x - h)² + (y - k)² = r², where h,k represents the center and r is the radius.

Our circle in this form is: (x − 1)² +(y − 0)² = 3. Thus, h = 1, k = 0, r = 3. The standard form is y² + (x − 1)² = 9.

We can conclude that the center is (1,0), thus the center lies on the x-axis, the radius is 3 units and the radius of the circle is the same with x² + y² = 9.

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