Find the rejection region for a one-dimensional chi-square test of a null hypothesis concerning p1, p2, . . . pk if k = 4 and ? = .01.
a ?2 > 15.086
b ?2 > 0.115
c ?2 > 13.277
d ?2 > 11.345

The expansion of Cos(A-B) is:

We are provided with the following:

We will have to obtain the values of Cos B and Sin A. Thus, we have:

To be obtain Sin A, we have to get the value of the third side, which is the opposite side, by applying the pythagoras theorem. Thus, we have:

To be obtain Cos B, we have to get the value of the third side, which is the adjacent side, by applying the pythagoras theorem. Thus, we have:

Now that we have obtained the values of Cos B and Sin A, we can then go on to solve the original problem.

The sample mean does not consistently overestimate or underestimate the population mean. It provides an accurate estimate of the population mean.

The statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean is that the sample mean is equal to the population mean on average. In other words, the sample mean does not consistently overestimate or underestimate the population mean. It provides an accurate estimate of the population mean.

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Answer:

The sequence is that, for every page 999 stars are drawn.

Step-by-step explanation:

999

999

999

999

3996

--

The evolution of 999 began when artist Juice WRLD decided to turn the evil number 6 into good... making and upside down 6 become a 9. Think of it as, "turn that frown upside down", or "turn evil into good".

Answer:

See below

Step-by-step explanation:

Looks like positive linear to me....slope is up and to the right (positive) and the line drawn shows it ot be approx linear

Answer:

From the given figure we can see that :---

MN||PO, MN=PO and MP=NO

Therefore, angle M=angle N (adjacent sides of the trapezoid)

\((8x - 16) = (6x + 20) \\ 2x = 36 \\ \boxed{x = 18}\)

angle M=angle N= (6×18)+20=108+20 =128°

angle O =(180°-128°)=52°

Answer:

a(n) = -20 + 3(n - 1)

Step-by-step explanation:

a(n) = -20 + 3(n - 1)

Step-by-step explanation:

I need help to...

I keep putting it in and no one has ever answered it and I'm struggling and getting stressed.

The graph with slope 3/4 is shown below.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

y= 3/4x -3

From the above equation we can see that

slope, m= 3/4

which shows the rise of 3 units and horizontal unit and run of 4 units,

The following graph represent the slope 3/4.

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Answer:

\(x = 15.\)

Step-by-step explanation:

\(4x/5-x=X/10-9/2 = > \\ \frac{4x}{5 - x} = \frac{x}{10} - \frac{9}{2} \\ (20)4x = 2x(5x - x) - 10(5x - x) \\ 80x = 10 {x}^{2} - {2x}^{2} - 50x + 10x \\ 8 {x}^{2} - 120x = 0 \\ {x}^{2} = 15x \\ x = 15.\)

\(f(0) = 60(0) = 0 \\ f(1) = 60(1) = 60 \\ f(2) = 60(2) = 120 \\ f(3) = 60(3) = 180 \\ f(3.5) = 60(3.5) = 210\)

So we conclude that f(x) does not necessarily equal multiples of 60 only and f(x) cannot be negative hence all real numbers is an exaggeration, Finally

\(f(x) \geqslant 0\)

Answer:

5.7

Step-by-step explanation:

Equilateral triangle means all the sides are the same length. So each side is basically \(\sqrt{11}\) times 2

After we know that, we then look to the Pythagorean theorum:

a^2 + b^2 = c^2

Before that, we have to find what the length of the hypotenuse is. 90 degrees equals \(\sqrt{11}\) times 2. So plug this info into the equation:

\(\sqrt{11}\)^2 + b^2 = \(2\sqrt{11}\)^2

11 + b^2 = 4(11)

11 + b^2 = 44

b^2 = 33

b = \(\sqrt{33}\)

b = 5.744 = 5.7

a. The distribution of XX, denoted as X ~ N(270, 45^2), is a normal distribution with a mean of 270 feet and a standard deviation of 45 feet. b. The probability that a randomly hit fly ball travels less than 234 feet is 0.2119. c. The 70th percentile for the distribution of distance of fly balls is approximately 293.60 feet.

a. The distribution of XX, denoted as X ~ N(270, 45^2), is a normal distribution with a mean of 270 feet and a standard deviation of 45 feet.

b. To find the probability that a randomly hit fly ball travels less than 234 feet, we need to calculate the cumulative probability using the normal distribution.

First, we standardize the value 234 feet using the formula:

Z = (X - μ) / σ

where X is the observed value, μ is the mean, and σ is the standard deviation.

In this case, X = 234, μ = 270, and σ = 45. Substituting these values into the formula, we get:

Z = (234 - 270) / 45 = -0.8

Next, we look up the cumulative probability for Z = -0.8 in the standard normal distribution table or use a statistical calculator. The cumulative probability is approximately 0.2119.

Therefore, the probability that a randomly hit fly ball travels less than 234 feet is 0.2119 (rounded to 4 decimal places).

c. To find the 70th percentile for the distribution of the distance of fly balls, we need to determine the value at which 70% of the data falls below.

We can use the inverse of the cumulative distribution function (CDF) for the normal distribution to find this percentile. Alternatively, we can also use the Z-score formula.

Using a standard normal distribution table or a statistical calculator, we find that the Z-score corresponding to a cumulative probability of 0.70 is approximately 0.5244.

Now, we can use the Z-score formula to find the corresponding value in the original distribution:

Z = (X - μ) / σ

0.5244 = (X - 270) / 45

Solving for X, we get:

X - 270 = 0.5244 * 45

X - 270 = 23.5956

X = 270 + 23.5956 = 293.5956

Rounded to two decimal places, the 70th percentile for the distribution of distance of fly balls is approximately 293.60 feet.

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Rounded to two decimal places, the 70th percentile for the distribution of distance of fly balls is approximately 293.60 feet.

a. The distribution of XX, denoted as X ~ N(270, 45^2), is a normal distribution with a mean of 270 feet and a standard deviation of 45 feet.

b. To find the probability that a randomly hit fly ball travels less than 234 feet, we need to calculate the cumulative probability using the normal distribution.

First, we standardize the value 234 feet using the formula:

Z = (X - μ) / σ

where X is the observed value, μ is the mean, and σ is the standard deviation. In this case, X = 234, μ = 270, and σ = 45. Substituting these values into the formula, we get:

Z = (234 - 270) / 45 = -0.8

Next, we look up the cumulative probability for Z = -0.8 in the standard normal distribution table or use a statistical calculator. The cumulative probability is approximately 0.2119.

Therefore, the probability that a randomly hit fly ball travels less than 234 feet is 0.2119 (rounded to 4 decimal places).

c. To find the 70th percentile for the distribution of the distance of fly balls, we need to determine the value at which 70% of the data falls below.

We can use the inverse of the cumulative distribution function (CDF) for the normal distribution to find this percentile. Alternatively, we can also use the Z-score formula.

Using a standard normal distribution table or a statistical calculator, we find that the Z-score corresponding to a cumulative probability of 0.70 is approximately 0.5244.

Now, we can use the Z-score formula to find the corresponding value in the original distribution:

Z = (X - μ) / σ

0.5244 = (X - 270) / 45

Solving for X, we get:

X - 270 = 0.5244 * 45

X - 270 = 23.5956

X = 270 + 23.5956 = 293.5956

Rounded to two decimal places, the 70th percentile for the distribution of distance of fly balls is approximately 293.60 feet.

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Answer:

False.

Step-by-step explanation:

The ratio is 1:500, which means that the model will be 500 times smaller than the real deal.

The real airplane is 50 metres, or 5,000 centimetres. The model is 50 cm. 5,000 / 50 = 1,000 / 10 = 100 / 1 = 100. Since 100 is NOT equal to 500, the answer is false.

Hope this helps!

Answer:

49

Step-by-step explanation:

A= a^2 = 7^2 =49

Answer:

  4x -10

Step-by-step explanation:

You want the side length of a square whose perimeter is (16x -40) feet.

The four sides of a square are all the same length. The perimeter is the sum of those lengths, so is 4 times the side length. Conversely, the side length is 1/4 of the perimeter.

  s = P/4 = (16x -40)/4

  s = 4x -10

The side length of the square table is 4x -10 feet.

Therefore, In the figure, a∥b  angle m∠7 = 34° .

An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.

Here,

Given that a and b are parallel lines,

∠3 and ∠7  are corresponding angles and congruent

m∠3 = 34°

thus ,m∠7 =m∠3 = 34°

so, m∠7 = 34°

Therefore, In the figure, a∥b  m∠7 = 34° .

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Answer:

there I'd an app to subtract and add and multiply and divide fractions or you can just google

11.is using subtraction

12.is using division

13.is using division

14.is using subtraction

Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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Vertex is slang for a corner or a place where two lines converge.The four corners of a square, for instance, are each referred to as a vertex.

The graph of g is a vertical stretch by a factor of 2 followed by a translation of 3 units down of the graph of f(x) = (x-1)²then the function g(x) = 2(x+4)²

f(x) =x²-2x+1 The graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of  .f(x) =x²-2x+1

Rewrite the given function f(x).

f(x) =  (x-1)²

Now, the graph is stretched vertically by a factor of 2.

= 2(-x-1)²

reflect the graph about the y-axis.

2(x+1)²

move to the left by 3 units.

= 2(x+3+1)²

=2(x+4)²

The function g(x) =2(x+4)²

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The rejection region is t > 1.761.

To test the hypothesis that the mean fee for car washers (including tips) is greater than $12, we can perform a one-sample t-test.

Sample mean \(\bar{x}\)  = $14.9

Sample standard deviation (s) = $6.75

Sample size (n) = 15

Significance level (α) = 0.05 (5%)

Since the sample size is small (n < 30) and the population standard deviation is unknown, we will use the t-distribution for inference.

Define the null and alternative hypotheses:

Null hypothesis (H₀): μ ≤ $12 (Mean fee for car washers is less than or equal to $12)

Alternative hypothesis (H₁): μ > $12 (Mean fee for car washers is greater than $12)

Determine the critical value (rejection region) based on the significance level and degrees of freedom.

The degrees of freedom (df) for a one-sample t-test is calculated as df = n - 1 = 15 - 1 = 14.

Using a t-table or statistical software, we find the critical t-value for a one-tailed test with α = 0.05 and df = 14 to be approximately 1.761.

Calculate the test statistic:

The test statistic for a one-sample t-test is given by:

t = (\(\bar{x}\)  - μ) / (s / √n)

Plugging in the values:

t = ($14.9 - $12) / ($6.75 / √15) ≈ 2.034

Make a decision:

If the test statistic t is greater than the critical t-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value (2.034) is greater than the critical t-value (1.761), indicating that it falls in the rejection region.

State the conclusion:

Based on the test results, at the 5% significance level, we have enough evidence to reject the null hypothesis.

We can infer that the mean fee for car washers (including tips) is greater than $12.

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Given:

Graph is given.

Option B is the final answer.

Answer:

The dilation will create a similar rectangle with sides of half the length of the original rectangle

Answer:

Its B for the people who dont know what the other guy was talking about

Step-by-step explanation:

The p-value from the hypothesis test is 0.142 i.e., greater than the given significance level of 0.05. So, the null hypothesis is not rejected. The z-score for the given sample is 1.471.

The decision rule based on p-value states,

Since it is given that the valve would produce a mean pressure of 5.4 pounds/square inch. I.e., μ = 5.4 p/si

So, Defining the hypothesis:

Null hypothesis H0: μ = 5.4

Alternative hypothesis Ha: μ ≠ 5.4

It is given that,

The valve was tested on 24 engines. I.e., Sample size n = 24

The sample mean X = 5.7

Standard deviation σ = 1.0 and

The significance level = 0.05

Since the population distribution is approximately normal,

the test statistic is calculated as follows:

z = (X - μ)/(σ/\(\sqrt{n}\))

On substituting the value,

z = (5.7 - 5.4)/(1.0/\(\sqrt{24}\))

  = (0.3)/0.204

  = 1.471

Fron this z-score, the p-value is calculated as 0.142.

Since, the value of p > 0.05 (significance level), the null hypothesis is not rejected.

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The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

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The correct statement is: P(A and B) <= 0.3 * 0.5 = 0.15.

The probability of A and B both occurring is denoted by P(A and B). If A and B are independent events, then the probability of both events occurring is given by the product of their individual probabilities, that is P(A and B) = P(A) * P(B). Therefore, P(A and B) = 0.3 * 0.5 = 0.15.

To understand why this statement is correct, we need to understand the concept of independence and multiplication rule of probability.  When two events are independent, the occurrence of one event does not affect the occurrence of the other. In other words, the probability of one event occurring is not affected by the occurrence of the other event.
The multiplication rule of probability states that if two events A and B are independent, then the probability of both events occurring together is given by the product of their individual probabilities, that is P(A and B) = P(A) * P(B).
In this case, we are given that events A and B are independent, and their individual probabilities are P(A) = 0.3 and P(B) = 0.5. Therefore, we can calculate the probability of both events occurring together as follows:
P(A and B) = P(A) * P(B)
= 0.3 * 0.5
= 0.15
This means that the probability of both events occurring together is less than or equal to 0.15. This statement is correct because the multiplication of probabilities can never result in a probability greater than the smaller of the two individual probabilities.

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Answer:

40

Step-by-step explanation:

The two angles form a right angle

A right angle has a measure of 90 degrees meaning that the sum of the two angles is 90

a + 50 = 90

90 - 50 = 40

Thus, a = 40

missing angle is (40⁰) :)

Answer:

an equivalent expression: -14(-8x+12y)=112x-168y

factor of an equivalent expression: 36a−16=4(9a-4)

The distance of the plane from the point (1,2,2) is \(7 / \sqrt(3)\) units.

The distance of a plane from a point can be determined by finding the perpendicular distance between the point and the plane. To find the distance of the plane from the point (1,2,2) in this case, we first need to determine the equation of the plane that passes through (1,-2,1) and is perpendicular to the given planes 2x-2y+z=0 and x-y+2z=4.

To find the equation of the plane, we need to find the normal vector of the plane. Since the plane is perpendicular to the given planes, the normal vector should be perpendicular to the normal vectors of the given planes. The normal vectors of the given planes are (2,-2,1) and (1,-1,2). To find a vector that is perpendicular to both of these vectors, we can take their cross product.

Taking the cross product of (2,-2,1) and (1,-1,2), we get the vector (-3,-3,-3). This vector represents the normal vector of the plane we are looking for. We can then write the equation of the plane in the form ax + by + cz + d = 0, where (a,b,c) is the normal vector and (x,y,z) represents a point on the plane.

Using the point (1,-2,1) and the normal vector (-3,-3,-3), we can substitute these values into the equation and solve for d. The equation becomes -3(1) - 3(-2) - 3(1) + d = 0, which simplifies to d = -6.

Therefore, the equation of the plane passing through (1,-2,1) and perpendicular to the given planes is -3x - 3y - 3z - 6 = 0.

To find the distance between the plane and the point (1,2,2), we can use the formula for the distance between a point and a plane. The formula is given by the absolute value of (ax + by + cz + d) divided by the square root of \((a^2 + b^2 + c^2)\), where (a,b,c) is the normal vector of the plane, and (x,y,z) is a point on the plane.

Using the equation of the plane -3x - 3y - 3z - 6 = 0, and substituting the coordinates of the point (1,2,2), we have\(|-3(1) - 3(2) - 3(2) - 6| / \sqrt((-3)^{2} + (-3)^{2} + (-3)^{2})\)

Simplifying this expression, we get

\(|-3 - 6 - 6 - 6| / \sqrt(9 + 9 + 9) = 21 / \sqrt(27) = 7 / \sqrt(3)\)

Therefore, the distance of the plane from the point (1,2,2) is\(7 / \sqrt(3)\) units.

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Answer:

C

Step-by-step explanation:

it is stretched