Prove the following:

(2cos x) / (cos 2x + 1) = sec x

The mean value is 6.5.

Given, z = 2.25, x = 14.6, σ = 3.6

The formula to calculate the z-score is,

z-score, z = (x - μ) / σOn

substituting the given values in the above formula, we get

2.25 = (14.6 - μ) / 3.6

Multiplying both sides by 3.6, we get,

2.25 * 3.6 = 14.6 - μ8.1 = 14.6 - μ

Subtracting 14.6 from both sides, we get,

-6.5 = -μOn multiplying both sides by -1, we get,

μ = 6.5

Hence, the mean value is 6.5.

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The decimal place z -score formula, z=x−μσ z = x − μ σ the mean (μ) is 6.5.

To find the mean (μ) using the z-score formula the Solve for μ

z = (x - μ) / σ

substitute the given values into the equation

2.25 = (14.6 - μ) / 3.6

solve for μ:

2.25 × 3.6 = 14.6 - μ

8.1 = 14.6 - μ

To isolate μ, subtract 14.6 from both sides:

8.1 - 14.6 = -μ

-6.5 = -μ

multiplying both sides by -1 gives

6.5 = μ

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Answer:

1 km

Step-by-step explanation:

According to the unit of conversion in every 1 kilometer, there is a total of 100 000 centimeters. Now, the given value of centimeters is equals to 52 800 => 1 km = 100 000 cm => 52 800 cm is less than the value of 100 000 cm which is equivalent to 1 km. Thus, the given is not correct.

In spherical coordinates (ρ, θ, ϕ), the point (0, -5, 0) can be represented as (5, π/2, π/2).

To convert from rectangular coordinates to spherical coordinates, we use the following formulas:

ρ = √(x² + y² + z²)

θ = arctan(y / x)

ϕ = arccos(z / √(x² + y² + z²))

In this case, since the point lies on the negative y-axis, the x-coordinate is 0, and the y-coordinate is -5. Therefore, we have:

ρ = √(0² + (-5)² + 0²) = √25 = 5

Since the point lies in the negative y-axis, the angle θ is π/2.

Since the point lies on the xz-plane, the z-coordinate is 0. Therefore, we have:

ϕ = arccos(0 / √(0² + (-5)² + 0²)) = arccos(0 / 5) = arccos(0) = π/2

Combining these values, the point (0, -5, 0) in rectangular coordinates is equivalent to (5, π/2, π/2) in spherical coordinates.

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If the graph represents the perimeter (y) in units for an equilateral triangle, we can determine the relationship between the perimeter and the side length of the triangle.

In an equilateral triangle, all three sides are equal in length. Let's denote the side length of the equilateral triangle as x.

The perimeter (P) of an equilateral triangle is given by the formula:

P = 3 * x

Therefore, the relationship between the perimeter (y) and the side length (x) of the equilateral triangle is:

y = 3x

So, if the graph represents the perimeter (y) in units for an equilateral triangle, it would be a linear function with a slope of 3 and the side length (x) as the independent variable.

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Answer:

17/27

Step-by-step explanation:

Since there are 10 blue marbles, and 27 total marbles, the probability of not choosing a blue marble is 17/27 because you subtract the amount of blue marbles (10) from the amount of total marbles (27).

The probability of not choosing a blue marble is 17/27.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Number of red marbles = 4

Number of blue marbles = 10

Number of green marbles = 7

Number of yellow marbles = 6

The event is the probability of not choosing a blue marble is

⇒ [tex]\frac{red+green+yellow}{Total marbles}[/tex]

⇒ [tex]\frac{4+7+6}{27}[/tex]

⇒ [tex]\frac{17}{27}[/tex]

Hence we can conclude that the the probability of not choosing a blue marble is 17/27.

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The p-value for the two-tailed t-test with degrees of freedom (df) = 19 and a sample t-value of -0.36 is greater than the significance level of α = 0.01. Therefore, we retain the null hypothesis.

In a two-tailed t-test, the null hypothesis (H₀) states that there is no significant difference between the population mean (µ) and a hypothesized mean (µo). The alternative hypothesis (H₁) states that the population mean is not equal to the hypothesized mean.

To determine the p-value, we compare the absolute value of the sample t-value (-0.36 in this case) with the critical t-value for the given degrees of freedom (df = 19). Since the sample t-value falls within the acceptance region, we find the probability of obtaining a t-value as extreme as -0.36 (or more extreme) assuming the null hypothesis is true.

If the p-value is less than the significance level (α = 0.01), we reject the null hypothesis. However, if the p-value is greater than the significance level, we retain the null hypothesis. In this case, since the p-value is greater than 0.01, we do not have sufficient evidence to reject the null hypothesis. Therefore, we retain it.

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After 1 minute, the mass of salt in the tank will be 3.072 kg. The concentration of salt in the tank will reach 0.01 kg/L after approximately 31 minutes.

To determine the mass of salt in the tank after 1 minute, we need to consider the inflow and outflow of the brine solution. The rate of inflow is 8 L/min, and the initial concentration of salt in the solution is 0.03 kg/L. Therefore, after 1 minute, 8 L of brine solution with a concentration of 0.03 kg/L will enter the tank, resulting in an additional mass of salt of 0.24 kg (8 L * 0.03 kg/L).

Since the solution inside the tank is well stirred and flows out at the same rate, the outflow rate is also 8 L/min. Thus, after 1 minute, 8 L of the brine solution will leave the tank, taking away 0.24 kg of salt.Considering the initial mass of salt in the tank (3 kg) and the change in mass due to the inflow and outflow after 1 minute, the mass of salt in the tank after 1 minute will be 3 kg + 0.24 kg - 0.24 kg = 3.0 kg.

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The question is incomplete:

Two ovens have measurements as shown. Which oven has a greater volume? How much greater is its volume?

The image with the information is below.

Answer:

-Oven B has a greater volume.

-Its volume is greater by 768 in³.

Step-by-step explanation:

First, you have to calculate the volume of each oven by multiplying the area of the base by the height:

Oven A: 576 in²*15 in= 8640 in³

Oven B: 672 in²*14 in= 9408 in³

Now, you have to calculate the difference between the volumes:

9408-8640=768

According to this, the answer is that oven B has a greater volume. Its volume is greater by 768 in³.

Answer:

Step-by-step explanation:

Question says that it uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides. Putting this into equation, we have something like this.

120 = L + 2W

Where

LW = area.

Again, in order to maximize the area with the given fencing, from the equation written above, then Width, w must be = 30 feet and length, l must be = 60

On substituting, we have

A = LW = (120 - 2W) W

From the first equation, making L the subject of the formula, we have this

L = 120 - 2W, which then we substituted above.

On simplification, we have

L = 120W -2W²

Differentiating, we have

A' = 120 - 4W = 0

Remember that W = 30

So therefore, L = 120 - 2(30) = 60 feet

The required length of the rectangular garden is 60 feet

According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.

Substitute into the perimeter of the rectangle will give:

120 = L + 2W

Area = LW

In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60

On substituting, we have;

A = LW = (120 - 2W) W

L = 120 - 2W,

On simplification, we have

L = 120W -2W²

Differentiating, we have

A' = 120 - 4W = 0

Remember that W = 30

So therefore, L = 120 - 2(30) = 60 feet

Hence the required length of the rectangular garden is 60 feet

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Answer:

The median of plot A is greater that the median of plot B

Step-by-step explanation: the median on plot A is 45 and the median on plot B is 15

1)The mean of the data in plot A is greater than the

mean of the data in plot B.

2) The median of the data in plot A is greater than the

median of the data in dot plot B.

3) The range of the data in plot A is greater than the

range of the data in plot B.

The median is the middle number in a sorted, ascending, or descending, list of numbers.

Let us arrange the data of plot A in ascending order:

30,35,35,40,40,40,40,45,45,45,45,50,55,55,60

Number of observations = 15

Mean of the plot A = 44

Median will be the middle observation i.e. 8th observation i.e. 45

Let us arrange the data of plot A in ascending order:

5,5,5,10,10,10,10,15,15,15,20,20,25,30,35

Number of observations = 15

Mean of the plot B = 15.33

Median will be the middle observation i.e. 8th observation i.e. 15

Therefore,1)The mean of the data in plot A is greater than the

mean of the data in plot B.

2) The median of the data in plot A is greater than the

median of the data in dot plot B.

3) The range of the data in plot A is greater than the

range of the data in plot B.

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Answer:

B is not true

Step-by-step explanation:

8+7= 15 and 14+3= 17

15 is not equal to 17

Answer:

B is the one equation that is NOT true.

Step-by-step explanation:

A: 9+4 is 13, and 17-4 is 13 as well. This equation is true, 13=13.

B: 8+7 is 15, and 14+3 is 17. This equation is false, because 15 is not equal to 17. Although we have our answer, we need to still check the other equations.

C: 11 is, well, 11, because nothing changed on that side of the equation. 19-8 is 11, so this is true because 11=11.

D: 5+8 is 13, and 20-7 is 13. This equation is also true, because 13=13.

The only equation that is not true, is B. (8+7 = 14+3)

Answer: C

Step-by-step explanation:

21x+9-3x = 18x + 9

If you factor out the 9, you would be left with

9 (2x+1)

Answer: A. 9(2x - 1)

Step-by-step explanation:

combine like terms

21x+9-3x

21x-3x

18x+9

Factor the expression

factor out 9 from the expression

you get 9(2x - 1)

Answer:you cross multiply

Step-by-step explanation:

i hate tacos

The cutoff sample score is therefore:40 - 2.326(1.5811) ≈ 36.59

The research hypothesis and null hypothesis about the populations can be restated as follows:Population 1: The population of people who have not received the new stress-reduction method training.Population 2: The population of people who have received the new stress-reduction method training.Research hypothesis: The new stress-reduction method training has reduced stress levels in the population that has received it compared to the population that has not.Null hypothesis: The new stress-reduction method training has not reduced stress levels in the population that has received it compared to the population that has not.7. The comparison distribution in this case is the distribution of means from samples of the population that has not received the new stress-reduction method training. This distribution has a mean (μ) equal to the population mean of 40 and a standard deviation (σ) equal to the population standard deviation divided by the square root of the sample size, which is σ/√n = 10/√40 = 1.5811.8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01, we need to find the z-score corresponding to a probability of .01 in the right tail of the distribution. This is given by:z = invNorm(0.99) ≈ 2.326Therefore, if the sample mean of the population that has received the new stress-reduction method training is more than 2.326 standard errors below the mean of the comparison distribution (which is 40), the null hypothesis can be rejected at the 0.01 level of significance.

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6. Restate question as a research hypothesis and a null hypothesis about the populations.

Population 1: The population of people who do not follow the stress-reduction method.

Population 2: The population of people who are trained in the stress-reduction method.

Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.

Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.

7. The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).

8. The Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.

6. Restate question as a research hypothesis and a null hypothesis about the populations.

Population 1: The population of people who do not follow the stress-reduction method.

Population 2: The population of people who are trained in the stress-reduction method.

Research hypothesis: The mean score of population 2 is significantly less than the mean score of population 1, indicating that the stress-reduction method is effective in reducing stress levels.

Null hypothesis: There is no significant difference between the mean score of population 1 and population 2, indicating that the stress-reduction method is not effective in reducing stress levels.

7. To determine the characteristics of the comparison distribution.

The comparison distribution is the distribution of sample means if we drew all possible samples of the same size from the population of interest.

In this case, we have a sample of 40 people who were trained in the stress-reduction method, so the comparison distribution will be a distribution of sample means of size 40 from the population of people who follow the stress-reduction method.

The mean of the comparison distribution will be equal to the mean of the population of people who follow the stress-reduction method (which is 40), and the standard deviation of the comparison distribution will be equal to the standard deviation of the population of people who follow the stress-reduction method (which is 10 / sqrt(40) = 1.58).

8. To determine the cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01.

To find the cutoff sample score (or Z score), we need to calculate the Z score of the sample mean (36) using the formula:

Z = (X - μ) / (σ / sqrt(n))

Z = (36 - 40) / (10 / sqrt(40))

Z = -2.52

The cutoff sample score (or Z score) on the comparison distribution at which the null hypothesis should be rejected at p < .01 is the Z score that corresponds to a probability of .01 in the upper tail of the distribution, which is equal to 2.33.

Therefore, if the Z score of the sample mean is less than -2.33, we can reject the null hypothesis at p < .01. Since the Z score of the sample mean is -2.52, we can reject the null hypothesis at p < .01.

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The statement  if /[tex]\sqrt{25}[/tex]∉Q, then it is the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q is false.

To disprove the statement, we need to provide a counter example where [tex]\sqrt{25}[/tex] ∉ Q (irrational) and [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∉ Q (also irrational).

Let's consider [tex]\sqrt{25}[/tex] = 5, which is a rational number since it can be expressed as a ratio of two integers (5/1).

In this case, [tex]\sqrt{25}[/tex] ∉ Q is false since it is a rational number.

Furthermore, [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] = 5 - [tex]\sqrt{17}[/tex] is also irrational since it cannot be expressed as a ratio of two integers.

Therefore, we have found a counterexample that disproves the statement, showing that if [tex]\sqrt{25}[/tex] ∉ Q, then it is not necessarily the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q.

Hence, the statement is false.

Question: Prove or disprove, using any method, that if /[tex]\sqrt{25}[/tex]∉Q, then it is the case that [tex]\sqrt{25}[/tex] – [tex]\sqrt{17}[/tex] ∈ Q.

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Answer:

Step-by-step explanation:

The scale factor of a dilation is the ratio of the corresponding side lengths of the image triangle to the original triangle. In this case, the image triangle is triangle A' B' C' and the original triangle is triangle ABC.

To find the scale factor, we can compare the corresponding side lengths of the two triangles. Let's denote the lengths of the corresponding sides as follows:

Side AB corresponds to side A'B'

Side BC corresponds to side B'C'

Side CA corresponds to side C'A'

The scale factor is then given by:

Scale factor = Length of corresponding side in image triangle / Length of corresponding side in original triangle

To find the scale factor, you can calculate the ratio of the corresponding side lengths. For example, if the length of AB is 4 units and the length of A'B' is 8 units, then the scale factor would be 8/4 = 2.

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Answer:

Step-by-step explanation:

b

Question

Marcus asked 10 people at a juggling festival what age they were when they started to juggle. Which interval contains the median age?

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]n = 10[/tex]

Required

The median interval

The question is incomplete, as the required data is not given.

To solve this question, I will use the following assumed dataset.

[tex]Age:17\ 17\ 18\ 20\ 21\ 22\ 22\ 24\ 28\ 28[/tex]

First, calculate the median position.

[tex]Median = \frac{n+1}{2}\ th[/tex]

[tex]Median = \frac{10+1}{2}\ th[/tex]

[tex]Median = 5.5\ th[/tex]

This implies that the median is the mean of the 5th and 6th data

So, we have the interval to be.

[tex]Median = [5th, 6th][/tex]

[tex]Median=[21,22][/tex]

Generally, the median of 10 data set is located at interval 5 to 6

Answer:

20

Step-by-step explanation:

Find the difference of the smallest value and the largest value.

Answer:

30 minus 10 then the range is 20

Step-by-step explanation:

We first Find the Slope of the line y=2x+3

The Slope Intercept Form of the equation of a given line is:

y=mx+c

where m is the Slope of that line, and c is the Y intercept.

For this line, the Slope is 2

So the Slope of the line PARALLEL to y=2x+3 will also be 2. And we are given that it passes through the point (2,6)

The Point-Slope form of the Equation of a Straight Line is:

(y−k)=m⋅(x−h)

m is the Slope of the Line

(h,k) are the co-ordinates of any point on that Line.

Here, we have been given the coordinates (h,k) of 1 point on that line as (2,6)

And the Slope m is 2

Substituting the values of h,k and m in the Point-Slope form, we get

(y−2)=(2)⋅(x−6)

(y−2)=2⋅(x-6)

y−2=2x -12

y=2x -12 +2

y=2x-10

The graph will look like

graph{y=2x -10 10 [10, -10, 5, - 5]}

Step-by-step explanation:

Surface Area of Figure = Area of 4 triangular sides + Area of Base

=

[tex]4 \times ( \frac{1}{2} \times base \times height) + (length \: \times \: width) \\ = 4 \times ( \frac{1}{2} \times 10 \times 12.1) + (10 \times 10) \\ = 4 \times 60.5 + 100 \\ = 242 + 100 \\ = 342 {yd}^{2} [/tex]

Answer:

The answer is A. y <= -3x + 3

Answer:

[tex]4\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]4\frac{3}{4} -\frac{1}{3} \\\\\frac{19}{4} -\frac{1}{3} \\\\\frac{57}{12} -\frac{4}{12} \\\\\frac{53}{12} \\\\4\frac{5}{12}[/tex]

Answer:

leon's older brother is 4 5/12 feet tall

Step-by-step explanation:

4 3/4 - 1/3

= 4 5/12

Answer:

3 units down

Step-by-step explanation:

got it right on edg

Answer: (a) $424.8

Step-by-step explanation:

Answer:

(0,6), (6,0)

Step-by-step explanation:

Answer:

Whatttttttttttttttttt

Answer:

y - 6 = -1 (x+5)

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1} \\[/tex]. Substitute the x and y values of (-5,6) and (0,1) into the formula and simplify like so:

[tex]m = \frac{(1)-(6)}{(0)-(-5)} \\m = \frac{1-6}{0+5} \\m = \frac{-5}{5} \\m = -1[/tex]  

So, the slope of the line is -1.

2) Now we have enough information to write the equation of the line in point-slope form. Use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] and substitute real values for the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].

Since [tex]m[/tex] represents the slope of the line, substitute -1 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (-5, 6) in those places as well. This gives the following equation and answer:

[tex]y-6 = -1(x+5)[/tex]