A store dedicated to removing stains from suits claims that a new stain remover product will remove more than 70% of the stains on which it is applied. To verify this statement, the stain remover product will be used on 12 randomly chosen stains. If fewer than 11 of the spots are removed, the null hypothesis that p = 0.7 will not be rejected; otherwise, we will conclude that p > 0.7. (tables are not allowed in this problem)
a) Evaluate the probability of making a type I error if p = 0.7.
b) Evaluate the probability of committing a type II error, for the alternative p = 0.9.
Use four decimal places for the calculation* NO Excel*

Answer: before I answer this do you need it in cubic feet or inches?

Step-by-step explanation:

Answer:

1,415.09 ft3

Step-by-step explanation:

First you would start off by finding the area of the circle. 13 squared is 169. Then you would multiply it by 3.14. You now have 530.66. Then you multiply it by 8 giving you 4,245.28. Then multiply that number by 1/3 which gives you 1,415.09 ft3.

Hope this helps!

The values of  that make the inequality v < 1  true are

{0 , -1 , -2,, -3, -4....}. An equivalent inequality, in terms of v, is v < 1.

In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size. There are several notations used to represent various types of inequalities.

In both cases a is not equal to b. These relationships are known as strict inequalities. This means that a is either strictly less than or strictly greater than b. Equivalents are excluded.

There are two types of inequality relations that are not strict, as opposed to strict inequalities.

The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or equivalently greater than max b or b).

The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or equivalently at least greater than or equal to b or b). The not-greater-than-relation can also be represented by the "greater than" symbol a ≯ b, split in two by a forward slash "not". The same is true if it is not less than a ≮ b.

The notation a ≠ b means that a is not equal to b. This inequality is sometimes considered a strict inequality .

To get the values that make the inequality true, we have to solve the inequality for . This will also give an equivalent inequality in terms of v < 1.

     \(\frac{v}{1} > \frac{1}{1}\)

⇒ v >-1

the solution set is the set of values {0, 1 ,2,3,4,5...} . In other words,  v can take up values less or equal to -1  to make the inequality -v > -1  true

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We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

The correct interpretation of a 99% confidence interval is that we are 99% confident that the true population mean falls in it.

The probability that it contains the true population mean is 99%.

Given  99% confidence interval : 4.1 < μ < 5.6

Then, the correct interpretation is we are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

Hence the answer is We are​ 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of mu.

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Answer:

Distribute 2 to (x + 6) and 3 to (x – 4).

Step-by-step explanation:

While solving for:

2(x+6) = 3(x-4) + 5

Firstly, we need to open the parenthesis. For this, we've to distribute 2 to (x+6) and 3 to (x-4).

\(\rule[225]{225}{2}\)

Hope this helped!

Approximately 25% of the values in the dataset are above the third quartile.

The third quartile, also known as the upper quartile, is the value below which 75% of the data lies. Therefore, if approximately 25% of the values are above the third quartile, it implies that the remaining 75% of the values are below or equal to the third quartile.

To calculate the third quartile, we need to sort the dataset in ascending order and find the median of the upper half. Once we have the third quartile value, we can determine the percentage of values above it by counting the number of values in the dataset that are greater than the third quartile and dividing it by the total number of values.

For example, if we have a dataset with 100 values, we would find the third quartile, let's say it is 80. Then we count the number of values greater than 80, let's say there are 20. So the percentage of values above the third quartile would be (20/100) * 100 = 20%.

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Answer:

the shape could be congruent or similar to its preimage. There are basically four types of transformations: Rotation; Translation; Dilation; Reflection; Definition of Transformations. Transformations could be rigid (where the shape or size of preimage is not changed) and non-rigid (where the size is changed but the shape remains the same).

Step-by-step explanation:

Answer:

16.7 units

Step-by-step explanation:

its a 45°-45°-90° right triangle, so n1=4.9

r=4.9\(\sqrt{2}\) =6.9

perimeter = 4.9+4.9+6.9=16.7 units

Option C is correct. No, the least value is smaller than the critical value.

Null hypothesis (H₀): The average first-year teacher salary is $52,000.

Alternative hypothesis (Ha): The average first-year teacher salary is not $52,000.

The significance level is 5% (or 0.05), which means we will reject the null hypothesis if the probability of obtaining the observed result is less than 5%.

Calculate the standard error of the mean:

Standard Error = Standard Deviation / √n

where n is the number of samples (n = 25 in this case).

Standard Error = $1500 / √25

= $1500 / 5

= $300

Now, perform the hypothesis test using a t-test since the sample size is relatively small (n < 30) and the population standard deviation is unknown.

t-score = (Sample Mean - Population Mean) / Standard Error

t-score = ($52,525 - $52,000) / $300

t-score = $525 / $300

t-score = 1.75

To find the critical value at a 5% significance level with 24 degrees of freedom (n - 1), we can consult a t-table. At a 5% significance level (two-tailed test), the critical t-value is approximately ±2.064.

Since the calculated t-score (1.75) is not greater than the critical t-value (2.064), we fail to reject the null hypothesis.

Therefore, option C is correct. No, the least value is smaller than the critical value.

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Complete question:

The average first year teacher salary in a certain state is known to be $52,000 with a standard deviation of $1500. A researcher tests this claim by averaging the salaries of 25 first year teachers and finding their average salary to be $52,525. Is there significant evidence to suggest that the claim is wrong at the 5% significance level?

A. Yes, the least value is greater than the critical value

B. No, the least value is larger than the critical value

C. No, the least value is smaller than the critical value

D. yes, the least value is smaller than the critical value

Answer:

20

Step-by-step explanation:

All you are doing is taking the accuracy of how many balls Cody can hit or the chances that he will hit the ball, then you take that and multiply it by the amount of times he is hitting the ball, in which it would be 30 x 6.5 = 19.5, but you would round to the nearest whole number, being 20.

Answer:

we convert 65% to decimal format. It will be .65 this is the percentage that he will sink the ball.

Multiply 30(.65)=19.5 since a ball throw cannot be a fraction round off the number. Therefore it would be 20 balls that he sinks.

In case this was not clear if he sunk 50% it would be .5(30)=15

Answer:

Step-by-step explanation:

y + 1 = -3(x - 2)

y + 1 = -3x + 6

y = -3x + 5

Answer:

1. 942.48

Step-by-step explanation:

Input the numbers in the formula.

Answer:

(-1, -5)

Step-by-step explanation:

That is the intersection point of the two equations when put on a graph.

See picture

The percent yield is calculated as the ratio of the actual yield to the theoretical yield, multiplied by 100.

Percent yield is a measure of how efficient a chemical reaction or process is in producing the desired product.

The formula for percent yield is:

Percent Yield = (Actual Yield / Theoretical Yield) * 100

The actual yield is the amount of product obtained from the reaction or process, typically measured in grams or moles. It represents the actual amount of product obtained in the laboratory.

The theoretical yield, on the other hand, is the maximum amount of product that can be obtained based on stoichiometry and other factors. It is calculated using balanced chemical equations and the starting amounts of reactants.

By dividing the actual yield by the theoretical yield and multiplying by 100, we get the percent yield, which is expressed as a percentage.

This value provides insight into the efficiency of the reaction or process, with a higher percent yield indicating a more efficient conversion of reactants into products.

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Differentiate y with respect to x for y = sin(cos x) and y = sin x cos x is that in the first function, we apply the chain rule, whereas in the second function, we apply the product rule.

When we differentiate a function, we find the rate at which the function changes at each point.

We can differentiate a function with respect to different variables.

In this case, we have to differentiate the given functions with respect to x.

Now, let's differentiate the two given functions one by one:

For the function y = sin(cos x)

The function y = sin(cos x) can be rewritten as:

y = sin u, where u = cos x

The derivative of the function y = sin(cos x) can be found by applying the chain rule.

The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by:

dy/dx = dy/du * du/dx

Here, f(u) = sin u and g(x) = cos x.

So,

dy/dx = (cos u)(-sin x)

dy/dx = -cos x sin(cos x)

We know that u = cos x, so cos u = cos(cos x).

So,

dy/dx = -cos x sin(cos x)

For the function y = sin x cos x

We can use the product rule to differentiate the function y = sin x cos x.

The product rule states that if y = f(x)g(x), then the derivative of y with respect to x is given by:

dy/dx = f(x)g'(x) + f'(x)g(x)

Here, f(x) = sin x and g(x) = cos x.

So,dy/dx = sin x(-sin x) + cos x cos xdy/dx

= -sin2 x + cos2 x

We can use the trigonometric identity cos2 x + sin2 x = 1 to simplify ;

So,

dy/dx = -sin2 x + cos2 xdy/dx

= cos2 x - sin2 x

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The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289.

What is a sequence?

A sequence is a function from natural numbers to the set of real numbers. it maps the set of number numbers on the set of real numbers.

We are given a sequence 8, 5,2, -1,.....

Now the first term of the sequence is 8 and common difference is -3.

As the difference between 2 consecutive terms is same, the given sequence is arithmetic.

now substituting this in the standard equation

we get,

t(n) = a+ (n-1)d

t(n)= 8+(n-1)(-3)

t(n) = 8-3n+3

t(n) = 11-3n                           (1)

Now we have to find the 5th, 6th, 7th term of the sequence

We substitute n=5, n=6, n=6 in equation 1

We get

t(5) = 11-3(5)

t(5) = 11-15

t(5) = -4

And,

t(6) = 11-3(6)

t(6) = 11-18

t(6) = -7

And,

t(7) = 11-3(7)

t(7) = 11-21

t(7) = -10

Hence the next three terms are -4, -7, -10.

The equation is t(n) = 11-3n

The 100th term would be given as

t(100)  = 11-3(100)

t(100)  = 11-300

t(100) = -289

Hence, The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289

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(a) The probability that at least n-1 flips come up heads in n flips of a fair coin can be expressed as 1/2^(n-1).  (b) The probability that there are at least two consecutive flips that are the same in n flips of a fair coin can be expressed as 1 - (1/2)^n.

(a) To calculate the probability that at least n-1 flips come up heads, we need to consider the complement event, which is the probability that fewer than n-1 flips come up heads. In a fair coin flip, the probability of getting heads or tails is 1/2. Therefore, the probability of getting fewer than n-1 heads in n flips is (1/2)^(n-1). Taking the complement, we get the probability that at least n-1 flips come up heads as 1 - (1/2)^(n-1). Simplifying further, we have 1/2^(n-1).

(b) To calculate the probability that there are at least two consecutive flips that are the same, we can consider the complement event, which is the probability that all flips have alternating outcomes (heads followed by tails or tails followed by heads). In each flip, the probability of getting a different outcome from the previous flip is 1/2. Therefore, the probability of having all flips with alternating outcomes is (1/2)^n. Taking the complement, we get the probability that there are at least two consecutive flips that are the same as 1 - (1/2)^n.

The probability that at least n-1 flips come up heads is 1/2^(n-1), and the probability that there are at least two consecutive flips that are the same is 1 - (1/2)^n.

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Answer: No

Step-by-step explanation: No because the table doesn’t give us an exponential equation. Even though the factors are close, they’re not the same.

Answer:

no

Step-by-step explanation:

Answer:

Step three

Step-by-step explanation:

She placed the point on C when it was supposed to be on E

Answer:

If `r` and `R` and the respective radii of the smaller and the bigger semi-circles then the area of the shaded portion in the given figure is: (FIGURE) `pir^2\ s qdotu n i t s` (b) `piR^2-pir^2\ s qdotu n i t s` (c) `piR^2+pir^2\ s qdotu n i t s` (d) `piR^2\ s qdotu n i t s`

Step-by-step explanation:

Answer:C

Step-by-step explanation:Because I did this

The equation of the parabola represented by the graph is y = 9x²

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

Point = (2, 36)

See attachment for the graph

This means that

(x, y) = (2, 36)

The vertex of the parabola is represented as

(h, k) = (0, 0)

The equation of the parabola is represented as

y = a(x - h)² + k

When the vertices are substituted, we have

y = a(x - 0)² + 0

So, we have

y = ax²

Using the point, we have

a * 2² = 36

So, we have

a = 9

Hence, the equation of the parabola is y = 9x²

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To determine the minimum speed of a particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k, we need to find the magnitude of the velocity vector, which is the derivative of the position vector with respect to time.

v(t) = r'(t) = 2ti + 6j + (2t - 24)k

The speed of the particle at any given time t is the magnitude of the velocity vector, which is:

|v(t)| = √(4t^2 + 36 + (2t - 24)^2) = √(4t^2 + 4t^2 - 96t + 576) = √(8t^2 - 96t + 576)

To find the minimum speed, we need to find the minimum value of |v(t)|. We can do this by finding the vertex of the parabolic function 8t^2 - 96t + 576, which corresponds to the minimum value of the function.

The vertex of a parabola of the form ax^2 + bx + c is at x = -b/2a. In this case, a = 8, b = -96, and c = 576, so the vertex is at t = -b/2a = 96/16 = 6.

So the minimum speed of the particle is:

|min speed| = |v(6)| = √(8(6)^2 - 96(6) + 576) = √(288) = 12√2

Therefore, the minimum speed of the particle moving in 3-space with position function r(t) = t^2 i + 6t j + (t^2 - 24t) k is approximately 16.97 units/sec (rounded to two decimal places). Option 4, min speed = 17 units/sec, is the closest answer.

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Note that the the five-number summary and interquartile range for each data set are:

Let's say the distances recorded for each airplane are:

Andre's: 18, 20, 22, 25, 28, 29, 30, 31, 32, 35

Lin's: 15, 16, 18, 20, 21, 22, 23, 25, 30, 33

Noah's: 10, 12, 13, 15, 18, 20, 21, 22, 23, 25

To find the five-number summary for each data set, we need to find the minimum, maximum, median, and quartiles. We can start by ordering the data sets from smallest to largest:

Andre's: 18, 20, 22, 25, 28, 29, 30, 31, 32, 35

Lin's: 15, 16, 18, 20, 21, 22, 23, 25, 30, 33

Noah's: 10, 12, 13, 15, 18, 20, 21, 22, 23, 25

Minimum:

Andre's: 18

Lin's: 15

Noah's: 10

Maximum:

Andre's: 35

Lin's: 33

Noah's: 25

Median:

Andre's: (28 + 29) / 2 = 28.5

Lin's: (21 + 22) / 2 = 21.5

Noah's: (18 + 20) / 2 = 19

First Quartile (Q1):

Andre's: (22 + 25) / 2 = 23.5

Lin's: (18 + 20) / 2 = 19

Noah's: (12 + 13) / 2 = 12.5

Third Quartile (Q3):

Andre's: (31 + 32) / 2 = 31.5

Lin's: (23 + 25) / 2 = 24

Noah's: (22 + 23) / 2 = 22.5

Interquartile Range (IQR):

IQR = Q3 - Q1

Andre's: 31.5 - 23.5 = 8

Lin's: 24 - 19 = 5

Noah's: 22.5 - 12.5 = 10

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Answer:

3x+14

Step-by-step explanation:

remove parenthses

6x+8-3x+6

3x+14

Answer:

3x+14

Step-by-step explanation:

2(3x+4)-3(x-2)

6x+8-3x+6

3x+14

Hey there!

A = ½ (a + b) h,

⇒ A = ½(8+16)14

⇒ A = ½(24)14

⇒ A = (12)(14)

⇒ A = 168

Therefore, Area of trapezoid is 168 sq. un

Check the picture below.

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ h=14\\ a=16\\ b=8 \end{cases}\implies \begin{array}{llll} A=\cfrac{14(16+8)}{2}\implies A=\cfrac{14(24)}{2} \\\\\\ A=7(24)\implies A=168 \end{array}\)

Step-by-step explanation:

The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011. The Riemann hypothesis, a famous conjecture, says that all non-trivial zeros of the zeta function lie along the critical line.

s

SO, LAST IS CORRECT

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The practical range of the function is between $100 and $625.

This can be calculated using the formula y=10x, where x is the number of subscriptions sold each week and y is the amount of money earned. To calculate the amount of money earned for selling t subscriptions each week, we can use the formula y = 10t. This can be interpreted as saying the amount of money (y) is equal to 10 times the number of subscriptions sold (t). For example, if Clarence sells 15 subscriptions each week, then we can calculate the amount of money he earns by plugging in t = 15. y = 10(15) = 150. This means Clarence earns $150 each week by selling 15 subscriptions. For example, if Clarence sells 10 subscriptions each week, he would earn $100 (10 x 10 = 100). If he sells 25 subscriptions each week, he would earn $625 (25 x 25 = 625). The practical range of the function is therefore $100 to $625.

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Answer:

y= 6x - 30

Step-by-step explanation:

First yu would take the 30 dollars you spent then you will subtract 6 times  how many cars you have done.

Answer:

Step-by-step explanation:

True. The function appears to be f(x) = x/4.