Write an equation in point-slope form for the given point and slope:
Point: (4, -6)
Slope: 2

Answer:

I think it's

Step-by-step explanation:

usually involves reading the pattern on the table while keeping in mind that x goes on top and y on

The shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.

The mean of the sampling distribution of the sample mean height for samples of size 10 will also be 40 inches.

The standard deviation of the sampling distribution of the sample mean height can be calculated as:

σ/sqrt(n) = 5.2/sqrt(10) = 1.645

So, the shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.

The variability of the sampling distribution is smaller than the variability of the population distribution, because the standard error is smaller than the population standard deviation. This means that the sample means are more likely to be closer to the population mean than the individual heights in the population.

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a)  The test was designed to have a 5% chance of making a Type I error. b) Reject H0 since p-value < significance level. c) Type I error (false positive) if H0 is true and rejected.

A significance test is used to determine whether there is sufficient evidence to reject a null hypothesis, which is a statement about a population parameter, such as a proportion, mean, or standard deviation. The significance level, often denoted by α, is the probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. The commonly used significance level is 0.05, which means that the test is designed to have a 5% chance of making a Type I error.

In this scenario, the sample proportion is 0.12 and the p-value is 0.03, which is the probability of observing a sample proportion as extreme as 0.12 or more extreme, assuming that the null hypothesis is true. Since the p-value is less than the significance level, we have strong evidence against the null hypothesis, and we reject it. Therefore, we conclude that the proportion is significantly different from the hypothesized value.

If the null hypothesis is actually true, and we reject it based on the sample data, we have made a Type I error. In other words, we have falsely concluded that there is a difference when there is not. False positive is another name for this mistake. Conversely, a Type II error occurs when we fail to reject the null hypothesis when it is actually false, and this error is also known as a false negative.

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The complete question is:

A significance level of 0.05 is used when conducting a proportion-related significance test. 0.12 is the sample statistic. P-value equals 0.03.

a) What chance of a Type I error was the test designed for, if H0 were true?

b) What judgement would you draw on this test (reject or fail to reject)?

c) What kind of error, if any, was there as a result of this test?

Answer:

Step-by-step explanation:

The vertex of the equation y = |x - 2 + 1| is (2, 1). The range of the equation depends on the value of x. When x < 2, the equation becomes y = -x + 1, which gives us a line with a slope of -1 that intersects the y-axis at (0,1) and has a minimum value of 1. When x >= 2, the equation becomes y = x - 1, which gives us a line with a slope of 1 that intersects the y-axis at (0,-1) and has no minimum value. Therefore, the range of the equation y = |x - 2 + 1| is [1, infinity).

The solutions of the given absolute value equation |4/3 x + 2| - 6 = 0 are x = 3 and x = -6.

Absolute value equations are kind of equations which includes the absolute value symbol in the expression.

For example : |x - 5| = 4 is an absolute value equation.

The given absolute value equation is,

four thirds times x plus 2 end quantity minus 6 equals 0.

|4/3 x + 2| - 6 = 0

Isolating the absolute value quantity on one side,

|4/3 x + 2| - 6 + 6 = 0 + 6

|4/3 x + 2| = 6

This can be written as,

4/3 x + 2 = 6 and 4/3 x + 2 = -6

Solving each of these,

4/3 x + 2 = 6

4/3 x = 4

x = 3

4/3 x + 2 = -6

4/3 x = -8

x = -6

Hence the value of x are 3 and -6.

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The area of the shaded portion is 6x^2

How to determine this?

The area of the shaded portion = Area of big rectangle - Area of small rectangle.

To get the area of big rectangle = L * B

A = 2x * 4x

A = 8x^2

To get area of small rectangle = L * B

A = 2x * x

A = 2x^2

To get the area of shaded portion ,

= 8x^2 - 2x^2

= 6X^2

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

5x - y = 2 ( subtract 5x from both sides )

- y = - 5x + 2 ( multiply through by - 1 )

y = 5x - 2 ← in slope- intercept form

with slope m = 5

(a)

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{5}[/tex] , then

y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation

to find c substitute (15, 2 ) into the partial equation

2 = - [tex]\frac{1}{5}[/tex] (15) + c = - 3 + c ( add 3 to both sides )

5 = c

y = - [tex]\frac{1}{5}[/tex] x + 5 ← in slope- intercept form

(b)

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

y = - [tex]\frac{1}{5}[/tex] x + 5 ( multiply through by 5 to clear the fraction )

5y = - x + 25 ( add x to both sides )

x + 5y = 25 ← in standard form

The scale factor of the smaller figure to the larger figure in the first instance is 1. 25 .

The scale factor in the second instance is 3. 75 .

To find the scale factor, the formula is :

= Length of side of larger figure / Length of corresponding side of smaller figure

The scale factor in the first instance is :

= 30 / 24

= 1. 25

The scale factor in the second instance is :

= 15 / 4

= 3. 75

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Answer:

180 most likely

The second statement in your question is the correct response.

What is the sampling distribution?

A sampling distribution is the probability distribution of a statistic (such as the sample mean or sample proportion) based on all possible random samples of a fixed size from a population.

The following statement must be true for an estimator of a population parameter to be unbiased:

The expected value of the estimator is equal to the population parameter.

Hence, the second statement in your question is the correct response.

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Answer:

You are correct it is 12.

Step-by-step explanation:

Answer: Square root of 288, or estimated 16.97

Step-by-step explanation:

Conveniently, the points form a diagonal line as you show, so we can use the Pythagorean Theorem to find the distance.

The x-component of this is the distance between -6 and 6, which is 12, and the y-component is again the distance between -6 and 6, which is also 12.

Therefore, the distance is the square root of 12^2 + 12^2, or the squareroot of 288.

There are infinitely many possible locations for your house that would allow you to travel one mile south, one mile east, and one mile north and end up back at your starting point.

As per the question given,  

This is a classic puzzle known as the "One-Mile Puzzle". There are actually infinitely many possible locations for your house that satisfy these conditions.

One way to think about it is to consider the fact that the one-mile distances you traveled form the sides of a triangle. Since you traveled one mile due south, one mile due east, and one mile due north, the triangle you formed is an isosceles right triangle, with the right angle at the point where you ended up.

If you let (x, y) be the coordinates of your house, then the point where you ended up after traveling one mile south, one mile east, and one mile north is (x, y-1) + (1, y) + (x, y+1), which simplifies to (2x+1, 2y).

So, any point (x, y) that satisfies the equation 2x + 1 = 2y will work as a possible location for your house. For example:

If x = 0, then y = 1/2, so your house could be located at (0, 1/2).

If x = 1, then y = 3/2, so your house could be located at (1, 3/2).

If x = -1, then y = -1/2, so your house could be located at (-1, -1/2).

And so on...

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Hi there, here's your answer:

Given two trapeziums, ABCD and WXYZ, where ABCD ~ WXYZ.

To find:

Value of v.

Solution:

We see that 2 sides are equal for both the trapeziums and it appears that

when comparing these sides, the bigger sides which are equal are always a multiple of 5 of the smaller side.

Applying this to find the similarity of the other two sides which are not equal, we find that on comparing the sides that are known, the similar side for AB is WX and AB = 5 × WX.

Thus, using this we can find the value of v to be YZ × 5 = 10 × 5 = 50m

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The required probability that X is less than 16 is approximately 0.15866 or 15.86%.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

Here,
We can use the standard normal distribution to find the probability that a normally distributed random variable, X, is less than a certain value. To use the standard normal distribution, we need to standardize X by subtracting the mean and dividing by the standard deviation:

Z = (X - μ) / σ

In this case, X has a mean of 25 and a standard deviation of 9,

Z = (16 - 25) / 9
z = -1

To find the probability that X is less than 16, we need to find the corresponding value of Z using the standard normal distribution table or a calculator.

P(Z < -1) ≈  0.15866

Therefore, the probability that X is less than 16 is approximately 0.15866 or 15.86%.

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Answer:

C.

Step-by-step explanation:

Multiply then divide

The exponent of g, r, is -65536.

The exponent of y, s, is 1.

The leading coefficient, k, is 4.

Note: The expression 4^65536g³y² √√/65536g³y² is not equal to kg³y³, but instead represents the value of 4 raised to the power of 65536 times g raised to the power of -65536, divided by the square root of 65536 times g raised to the power of -65536 times y squared. The square root symbol is used twice, which is equivalent to taking the square root of the square root, or the fourth root.

The values in the missing observation are:

X1    X2

76 22  

82 25

91 32

101    41

88 28

An expression contains terms with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x1 x2

76 22  

82 __

91 32

__    41

88 28

The difference between each row are:

76 - 22 = 54

82 - 25 = 57

91 - 32 = 59

101 - 41 = 60

88 - 28 = 60

We see that,

57 - 54 = 3

59 - 57 = 2

60 - 59 = 1

60 - 60 = 0

So,

The difference between the numbers is consecutive as 3, 2, 1, 0.

Thus,

The missing values of X1 and X2 are 101 and 25.

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X = 11 when y = 4 when X=a+b+4 and a directly proportional to y squared , b is inversely proportional to y.

Given that a is directly proportional to y^2 and b is inversely proportional to y, we can write the following two relationships:

[tex]a = k * y^2[/tex]

[tex]b = m / y[/tex]

where k and m are constants. From the first equation, we can find the value of k when y = 2:

[tex]a = k * 2^2[/tex]

[tex]k = a / 4[/tex]

And from the second equation, we can find the value of m when y = 2:

[tex]b = m / 2[/tex]

[tex]m = 2b[/tex]

Substituting these values into the equation X = a + b + 4, we can find X when y = 2:

[tex]X = (k * 2^2) + (m / 2) + 4[/tex]

[tex]X = (a / 4) * 4 + 2b + 4[/tex]

[tex]X = a + 2b + 4[/tex]

[tex]X = 18[/tex]

We can now use the value of k and m to find X when y = 4:

[tex]X = (k * 4^2) + (m / 4) + 4[/tex]

[tex]X = (a / 4) * 16 + (2b) / 4 + 4[/tex]

[tex]X = 4a + 2b + 4[/tex]

Substituting the value of X = 18 when y = 2, we can solve for a and b:

18 = 4a + 2b + 4

14 = 4a + 2b

7 = 2a + b

Solving the system of equations for a and b, we find:

a = 5

b = 2

Finally, substituting these values into the equation X = a + b + 4, we can find X when y = 4:

X = (5) + (2) + 4

X = 11

Therefore, X = 11 when y = 4.

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The probability of selecting three numbers in increasing order is 1/3, which means that in one out of every three trials, we will select three numbers in increasing order.

Probability is a branch of mathematics that deals with the measurement of the likelihood or chance of an event occurring. In this problem, we are asked to find the probability of selecting three numbers in increasing order from a range of 0 to 1.

Let's compute the probability of selecting three numbers in increasing order. Since the total number of possible outcomes is infinite, we need to use a continuous probability distribution to compute the probability. In this case, we can use the uniform distribution, which assumes that each number between 0 and 1 is equally likely to be selected.

The probability of selecting "a" as the smallest number is a/1 = a.

The probability of selecting "a" as the largest number is (1-a)/1 = 1-a.

The probability of selecting "a" as the middle number is 2(1-a)a, which is the product of the probability of selecting "a" and the probability of selecting "b" or "c" from the remaining range.

Therefore, the probability of selecting three numbers in increasing order is the sum of these probabilities:

P(increasing order) = ∫₀¹ (a * (1 - a) + (1 - a) * a + 2a(1 - a))da

P(increasing order) = ∫₀¹ 2a(1 - a)da

P(increasing order) = 2∫₀¹ a - a²da

P(increasing order) = 2[(a²/2) - (a³/3)] from 0 to 1

P(increasing order) = 2[(1/2) - (1/3)] = 1/3

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Answer:

A. First, outer, inner, last.

Step-by-step explanation:

The radius of the circle is 2.8feet (nearest tenth)

Arc length is the distance between two points along a section of a curve.

The length of an arc is expressed as ;

L = (tetha) / 360 × 2πr

L is the length of the arc

tetha is the angle made by the two radii and the arc.

In radian 360° = 2π

therefore ;

8 = 2.9/ 2π × 2πr

8 = 2.9 r

r = 8/2.9

r = 2.76 ft

therefore the radius of the circle is 2.8 feet( nearest tenth) .

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Answer:

hope this helps!

Step-by-step explanation:

Answer: 78.39 thousand, (78,390)

Step-by-step explanation:

Using the quadratic formula with this gives us two answers, 78.39 and -65.39. Since a negative answer doesnt make sense in this context, we will go with 78.39 thousand pens, (78,390 pens). The limit on x however doesn't seem to make sense as it says x </= 25 and x>/= 0. The only two answers are both above and below this limit.

Answer:its hard to say

Answer: 4

Step-by-step explanation:

Answer: A. [tex]92cm^{3}[/tex]

Step-by-step explanation:

[tex]V= \frac{4}{3} \pi r^{3}[/tex]

[tex]V=\frac{4}{3}\pi 2.8^{3}[/tex]

[tex]4/3=1.33333333333[/tex]

calculate in calculator

[tex]1.33333333333\pi 2.8^3=91.9523225755[/tex]

round to nearest ones (9 tells 1 to go to 2)

Therefore, A. 92cm^3

The highest score obtained in this group of 12 scores is 19

What is the distribution in statistics?

In statistics, a distribution refers to the way in which a variable is spread out or distributed across different values. A distribution describes the probability of different outcomes for a variable, and can be visualized using graphs such as histograms, box plots, and probability density functions.

The distribution in Table 2-3 shows frequency (f) for different score ranges (x). Without knowing the exact scoring system, we can't say for certain what the highest score obtained in this group of 12 scores is. However, we can determine the upper limit of the highest score range by multiplying the upper limit of the range by its frequency:

Upper limit of 20-24 range = 24

Frequency of 20-24 range = 2

Upper limit of 15-19 range = 19

Frequency of 15-19 range = 5

Upper limit of 10-14 range = 14

Frequency of 10-14 range = 4

Upper limit of 5-9 range = 9

Frequency of 5-9 range = 1

To find the highest score, we need to determine the upper limit of the score range that has the highest frequency. In this case, the highest frequency is 5, which corresponds to the range 15-19.

Hence, the highest score range is 15-19, and the highest score within that range is the upper limit of that range, which is 19. So, the highest score obtained in this group of 12 scores is 19 (assuming the scoring system is such that higher scores correspond to higher ranges).

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When the residual is negative it represents the predicted value is very much high.

Therefore, the negative residual value on the regression line represents the predicted value is very much high.

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Chandra spends 3 minutes on each math problem if she spends a total of 15 minutes on math problems and spends the same amount of time on each problem

Chandra spends the same amount of time on each math problem. Let's call the amount of time she spends on each problem "t".

We know that Chandra spends a total of 15 minutes on math problems. If she spends the same amount of time on each problem, then the total time spent on all the problems is equal to the number of problems multiplied by the time spent on each problem.

So, we can write the following equation:

total time spent on all problems = number of problems * time spent on each problem

We know that the total time spent on all problems is 15 minutes, so we can substitute this into the equation:

15 = number of problems * t

We don't know the number of problems, but we can solve for t by rearranging the equation:

t = 15 / number of problems

So, the amount of time Chandra spends on each math problem is equal to 15 divided by the number of problems.

For example, if Chandra works on 5 math problems, then the amount of time she spends on each problem is:

t = 15 / 5 = 3

So, Chandra spends 3 minutes on each math problem if she spends a total of 15 minutes on math problems and spends the same amount of time on each problem.

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