6. If m R = 28°, find m O. The figure is not drawn to scale. (1 point)
152°
28°
62°
56°

The point estimate for the percent who want to change the name of the town is 39.5%.

The poll's margin of error is 1. 5 %.

The town most likely will not change its name because the point estimate is less than half.

The point estimate for the percent who want to change the town's name is the midpoint of the interval [0.38, 0.41]. To find the midpoint, add the endpoints of the interval and divide by 2:

(0.38 + 0.41) / 2 = 0.79 / 2 = 0.395

So, the point estimate is 39.5%.

The margin of error is half the width of the interval. To find the width, subtract the lower endpoint from the upper endpoint and divide by 2:

(0.41 - 0.38) / 2 = 0.03 / 2 = 0.015

So, the margin of error is 1.5%.

Based on the given data, the town is most likely not going to change its name. The point estimate, 39.5%, is less than 50%, which indicates that less than half of the surveyed adults want to change the town's name. The margin of error (1.5%) is relatively small compared to the point estimate, which means that the true percentage is likely to be within 1.5% of the point estimate.

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The  answers are sin angle R = ST/RT and sin angle L = 3(ST)/3(RT) Fοr the given questiοn trigοnοmetry.

Thus option A & B are correct.

Trigοnοmetric ratiοs are mathematical relatiοnships between the sides and angles οf a right triangle. The three main trigοnοmetric ratiοs are sine, cοsine, and tangent, abbreviated as sin, cοs, and tan.

The sine οf an angle is the ratiο οf the length οf the side οppοsite the angle tο the length οf the hypοtenuse. The cοsine οf an angle is the ratiο οf the length οf the adjacent side tο the length οf the hypοtenuse. The tangent οf an angle is the ratiο οf the length οf the οppοsite side tο the length οf the adjacent side. These ratiοs are useful in sοlving prοblems invοlving right triangles and have many applicatiοns in fields such as physics, engineering, and navigatiοn.

We knοw that when a triangle is dilated by a scale factοr οf k, all cοrrespοnding sides are multiplied by k, and all cοrrespοnding angles remain cοngruent.

Using this fact, we can determine the relatiοnships between the trigοnοmetric ratiοs οf the twο triangles:

A. Sin angle R = ST/RT is true fοr bοth triangles, as the sine οf an angle is defined as the ratiο οf the οppοsite side tο the hypοtenuse, which dοes nοt change when dilated.

B. Sin angle L = 3(ST)/3(RT)simplifies tο Sin angle L = ST/RT, which is true fοr bοth triangles (as shοwn in part A).

C. Sin angle R = 3(MN)/3(LM) simplifies tο sin angle R = MN/LM, which is nοt necessarily true. This is because the cοrrespοnding sides οf the triangles are nοt prοpοrtiοnal tο each οther.

D. Sin angle L = MN/NL is nοt necessarily true fοr the same reasοn as in part C.

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If a student had 50 minutes of homework on Monday and 30 minutes of homework on Tuesday, then there was a 40% decrease in homework time from Monday to Tuesday.

To calculate the percent decrease in homework time from Monday to Tuesday, we need to find the difference between the two values and then divide that difference by the original value (Monday’s homework time). The difference between 50 minutes and 30 minutes is 20 minutes. Dividing this difference by the original value (50 minutes) gives us:

(20 / 50) x 100% = 40%

Therefore, there was a 40% decrease in homework time from Monday to Tuesday.

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Hence, x = 4 is the only integer answer to the inequality as  the range of possible values for x is from 4 to 5.

A mathematical statement showing a connection that exists between values or statements that aren't always equal is known as an inequality. Inequalities compare two quantities using symbols like (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, "y -3" denotes that the y value is more than or equal to -3, whereas "x 5" denotes that the x value is less than 5. A number line can be used to depict all the possible numbers that satisfy an inequality after it has been solved. In many different mathematical fields, including the solution of equations, the study of functions, and the definition of relationships between variables, inequality is used.

given

We can begin by finding the inequality's x:

3 < 3x - 3 ≤ 2x + 2

To add 3 to each of the inequality's three components, we get:

6 < 3x ≤ 2x + 5

When we deduct 2x from each of the inequality's three components, we obtain:

4 < x ≤ 5

Since we are seeking for integer answers, the range of possible values for x is from 4 to 5, with 5 being the exception. Hence, x may be:

x = 4

Hence, x = 4 is the only integer answer to the inequality as  the range of possible values for x is from 4 to 5.

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Answer:

125pi units cubed

Step-by-step explanation:

The measure of the angle that Zane is using the protractor is a 113 degrees.

Degree is the unit of measure of an angle and is measured by using the geometric tool - a protractor. A degree is denoted by the symbol '°'. A circle completely rotates at a 360° and a degree is a part of that 360° rotation as it is divided into 360 equal parts.

Therefore, The measure of the angle that Zane is using the protractor is a 113 degrees.

There are 40,320 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.

In order to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other, we need to place one rook in each row and each column exactly once.

The first row can be filled in 8 ways, as there are 8 columns to choose from. The second row can be filled in 7 ways, as we cannot choose the column that has already been filled in the first row. Continuing in this way, we see that the number of ways to place 8 distinguishable rooks on an 8 × 8 chessboard is:

8! = 40,320

Therefore, there are 40,320 ways to place 8 distinguishable rooks on an 8 × 8 chessboard so that none can capture any other.

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Answer:

Step-by-step explanation:

add c with b and then add a multiply 30 and divide by 12

In a one-sided hypothesis test for the mean for a random sample of size 20, the t-score of the sample mean is 2.615 in the direction of the alternative. This significant at the 5% level and not significant at 1% level.

In hypothesis testing, the t-score measures how many standard errors the sample mean is from the hypothesized population mean. The formula for calculating the t-score is:

t = (sample mean - hypothesized population mean) / (standard error of the mean)

In this case, we are given that the t-score is 2.615 and that it is in the direction of the alternative hypothesis (which means the sample mean is greater than the hypothesized population mean). We can use a t-table or a statistical software to find the p-value associated with this t-score.

Assuming a two-tailed test (since we don't know if the alternative hypothesis is greater than or less than the null hypothesis), the p-value is the probability of getting a t-score greater than or equal to 2.615 or less than or equal to -2.615 (the negative value since it's a two-tailed test).

Using a t-table with 19 degrees of freedom (since the sample size is 20 and we are estimating one parameter), we find that the p-value is approximately 0.014 for a one-tailed test in the direction of the alternative.

To determine if the result is significant at the 5% level or 1% level, we compare the p-value to the significance level (alpha). If the p-value is less than alpha, we reject the null hypothesis and conclude that the result is statistically significant.

For a one-tailed test at the 5% level, alpha = 0.05. Since the p-value (0.014) is less than alpha, we reject the null hypothesis and conclude that the result is significant at the 5% level.

For a one-tailed test at the 1% level, alpha = 0.01. Since the p-value (0.014) is greater than alpha, we fail to reject the null hypothesis and conclude that the result is not significant at the 1% level.

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Answer:

24.3ft

Step-by-step explanation:

36.2ft - 15ft = 21.2ft

Cade height = 6.2 - 2.5 = 3.7

21.2 + 3.7 = 24.9ft

24.9ft - 15.6ft = 24.3ft

Check the picture below.

Answer:

b) 0.57

c) 0.74

Step-by-step explanation:

part a:

frequency graph is attached with this answer (in png format).

part b:

let A be the event an entry is picked at random and the entry is a poem that has not been shortlisted.

P(A) = [tex]\dfrac{\text{number of poems not shortlisted}}{\text{total number of entries}}[/tex]

P(A) = [tex]\dfrac{570}{1000}[/tex] (see the frequency graph)

P(A) = 0.57

part c:

let B be the event a story is picked at random and the story has not been shortlisted.

P(B) = [tex]\dfrac{\text{number of stories not shortlisted}}{\text{total number of stories}}[/tex]

P(B) = [tex]\dfrac{185}{250}[/tex] (see the frequency graph)

P(B) = 0.74

Hopefully this answer helped you!!

Answer: 420 in ³

Step-by-step explanation:

The Formula for finding the volume of a prism = Length x Breadth x Height

Volume of prism = 7 x 5 x 12

                            = 420 in³

Hence, there is a 28.22 degree depression from the owl to the mouse as the inverse tangent of the two sides.

An angle is a geometric shape made up of two rays or lines that share a termination known as the vertex. A whole circle has 360 degrees, which is how angles are typically measured. Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (more than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), reflex, or compound (any combination of these) (greater than 180 degrees but less than 360 degrees). Calculus, geometry, trigonometry, and other branches of mathematics all make use of angles.

given

To resolve this issue, we can make use of the tangent function. Let x be the depression angle between the owl and the mouse. Next, we have:

Tangent(x) = adjacent/opposite

where the distance between the owl and the mouse is on the adjacent side and the opposite side is the height of the owl above the field (42 m) (78 m).

Tangent(x) equals 42/78

When we take the inverse tangent of the two sides, we obtain:

x = (42/78) arctan

Calculating the answer, we discover:

28.22 degrees x

Hence, there is a 28.22 degree depression from the owl to the mouse as the inverse tangent of the two sides.

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Assuming that the function A calculates the surface area of a mold, the appropriate domain for A would be a set of all possible molds, which can be represented by a set of positive real numbers.

It is important to note that the mold's geometry, size, and complexity will affect the calculation of its surface area. Therefore, the domain of the mold area function A should include all possible variations of mold shapes and sizes.

In practical applications, the domain of A may also be limited by the manufacturing capabilities or constraints, such as the maximum size or complexity of molds that can be produced. In such cases, the domain of A may need to be further restricted to reflect these limitations.

Overall, the appropriate domain for the mold area function A would depend on the specific context and application of the function.

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The function y = ∛x  when transformed is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = ∛x

When the y values are multiplied by 1/2 the rule is

(x, 1/2y)

To transform the function y = ∛x by the point (x, 1/2y), we can use the following steps:

Therefore, the transformation by the point (x, 1/2y) is y = 2∛x

See attachment for the graph

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Answer:

To solve the equation 8x = -10y for the slope and y-intercept, we need to first rearrange it into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

To do this, we can divide both sides of the equation by -10, which gives us:

y = (-8/10)x

Simplifying further, we get:

y = (-4/5)x

Therefore, the slope of the line represented by this equation is -4/5. This means that for every increase of 1 in x, y decreases by 4/5.

To find the y-intercept, we can set x to 0 and solve for y:

y = (-4/5)(0)

y = 0

Thus, the y-intercept is 0.

In summary, the slope of the line represented by 8x = -10y is -4/5 and its y-intercept is 0.

Step-by-step explanation:

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Answer: x=5y/4

Step-by-step explanation:

8x=10y

Divide both sides by 8

8x/8 = 10y/8

8x divided by 8, will cancel out resulting in x.

So, your final answer will be x=5y/4

Solution set for both inequalities is x ≤ 3 and x ≥ 3, which can be written as x = 3.

The two inequalities are: x + 5 < 8 and x + 5 > 8. The first inequality states that the sum of x and 5 is less than 8, while the second inequality states that the sum of x and 5 is greater than 8.

To solve the first inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x < 3. This means that any value of x that is less than 3 will satisfy the inequality.

To solve the second inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x > 3. This means that any value of x that is greater than 3 will satisfy the inequality.

The solutions of the two inequalities differ in terms of the values of x that satisfy each inequality. The first inequality has a solution set that consists of all values of x less than 3, while the second inequality has a solution set that consists of all values of x greater than 3. Therefore, the solutions of the two inequalities do not overlap.

The second set of inequalities are x + 5 ≤ 8 and x + 5 ≥ 8. The first inequality states that the sum of x and 5 is less than or equal to 8, while the second inequality states that the sum of x and 5 is greater than or equal to 8.

To solve the first inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x ≤ 3. This means that any value of x that is less than or equal to 3 will satisfy the inequality.

To solve the second inequality, we need to isolate x by subtracting 5 from both sides of the inequality: x ≥ 3. This means that any value of x that is greater than or equal to 3 will satisfy the inequality.

The solutions of the two inequalities in this case do overlap. The common solution is x = 3, which satisfies both inequalities since it is both less than or equal to 8 and greater than or equal to 8. Therefore, the solution set for both inequalities is x ≤ 3 and x ≥ 3, which can be written as x = 3.

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Given equation is: 24+ 0.44x = 19+ 1. 69x is x = 4.

Equation:

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. Solving an equation involving variables involves determining which values ​​of the variables make the equation true. The variables for which the equation must be solved are also called unknowns, and the values ​​of the unknowns that satisfy the equation are called solutions of the equation. There are two types of comparisons: identity comparisons and conditional comparisons. The identity is true for all values ​​of the variable. A conditional comparison is only true for certain values ​​of a variable.

According to the Question:

Given equation:

24+0. 44x = 19+ 1. 69x

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

   24 - 19 = 1.69x - 0.44x

⇒ 5 = 1.25x

⇒ x = 5/1.25

⇒ x = 4

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A correlation coefficient is consistently a number between 1 and - 1 .

The correlation coefficient is a factual measure that demonstrates the strength and heading of the straight connection between two factors. It goes from - 1 to 1, where - 1 addresses a completely bad correlation (i.e., as one variable expands, different declines), 0 addresses no correlation, and 1 addresses an entirely sure correlation (i.e., as one variable builds, the other likewise increments).

The indication of the correlation coefficient demonstrates the heading of the relationship, while the extent of the coefficient shows the strength of the relationship. A correlation coefficient of 0 shows no straight connection between the factors, while values nearer to - 1 or 1 demonstrate a more grounded direct relationship.

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Therefore, the slope of the line passing through the given points is -1/2.

In mathematics, the slope is a measure of the steepness of a line. It refers to the ratio of the vertical change to the horizontal change between any two points on the line. The slope of a line is often denoted by the letter "m."

For a given line, the slope is calculated by taking any two points on the line, [tex](y_{1} ,y_{2}[/tex] and [tex](x_{1} ,x_{2}[/tex] and applying the formula:

slope [tex]m= (y_{2} -y_{1})/(x_{2}-x_{1})[/tex]

The slope can be positive, negative, zero, or undefined, depending on the direction and steepness of the line. A positive slope means that the line is increasing as you move from left to right, while a negative slope means that the line is decreasing. A zero slope means that the line is horizontal, and an undefined slope means that the line is vertical.

by the question.

To find the slope of the line passing through the given points, we can use the slope formula:

slope = (change in y)/(change in x)

Let's choose the first point (-8, -21) and the last point (10, -30) to calculate the slope:

change in y = -30 - (-21) = -9

change in x = 10 - (-8) = 18

slope = (-9)/18 = -1/2

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A circle is a curve sketched out by a point moving in a plane. The measure of the angle is 72°.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Let the angle that turns through 1/5 of the circle be x.

We know that the measure of the center of a circle is 360°, while it is given that the angle turns through 1/5 of the circle. Therefore, the angle will turn 1/5 of 360°.

x = 1/5 of 360 = 72°

Thus, the measure of the angle is 72°.

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Answer:

  74π cm²

Step-by-step explanation:

You want to know the painted area of a cone 10 cm in diameter and 12 cm high that has an unpainted hole in the base that has a 4 cm radius.

The area of the curved surface of the cone is found using the given formula. To use that formula, we need to know the slant height of the cone. The slant height is the hypotenuse of a right triangle that is 12 cm high and has a base of 5 cm:

  l² = r² +h²

  l = √(5² +12²) = √(25 +144) = √169

  l = 13 . . . . cm

Then the lateral area is ...

  LA = πrl = π(5 cm)(13 cm) = 65π cm²

The painted area of the base is the difference between the areas of circles 5 cm in radius and 4 cm in radius:

  A = π(r₁² - r₂²) = π((5 cm)² -(4 cm)²) = π(25 -16) cm² = 9π cm²

The painted area is the sum of the areas of the curved surface and the donut base:

  A = 65π cm² +9π cm² = 74π cm²

__

Additional comment

The radius of the base is half the diameter. If you slice the cone through its vertex and perpendicular to its base, the cross section is an isosceles triangle with height 12 cm and base 10 cm. The altitude of that triangle divides it into two congruent right triangles that have base 5 cm and height 12 cm.

You may recognize this as the {5, 12, 13} right triangle, which tells you the slant height is 13 cm. If not, you can use the Pythagorean theorem to find the slant height, as above.

Answer:

B

Step-by-step explanation:

-240 +65 = -175

(We use a -240 instead of 240 because it's below water.) :)

Answer:

the correct answer is the second one

Step-by-step explanation:

I will add a photo of my solution, because there's a lot to type here

The length of the side e for the triangle ∆DEF is equal to 553.1 inches to the nearest tenth tenth of an inch using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

We shall first evaluate for the angle m∠F and then solve for the e using the sine rule as follows:

m∠F = 180° - (27 + 101) {sum of interior angles of a triangle}

m∠F = 52°

e/sin27 = 960/sin52

e = (960 × sin27)/sin52 {cross multiplication}

e = 553.0773

Therefore, the length of the side e for the triangle ∆DEF is equal to 553.1 inches to the nearest tenth tenth of an inch using the sine rule.

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Answer:

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The Y intercept is his base pay, because no matter what he is getting 38,000. So, his total salary will always start out at 38,000 then continue up with commission sales.