A simple random sample of men is obtained and the elbow-to-fingertip length of each man is measured. The population of those lengths has a distribution that is normal. The sample statistics are
n=31,
x=14.1,
s=0.7.
Determine the critical value of t and the margin of error, and then construct the 95% confidence interval estimate for the population mean.
the critical value is t =?

Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.

The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).

Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.

In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.

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To solve the equation 1/2 + a = 1 3/4, we need to convert the mixed number 1 3/4 to an improper fraction:

1 3/4 = 4/4 + 3/4 = 7/4

Now we can rewrite the equation as:

1/2 + a = 7/4

To isolate the variable a, we need to subtract 1/2 from both sides:

a = 7/4 - 1/2

To add these two fractions, we need to find a common denominator, which is 4:

a = (7/4 - 2/4)

a = 5/4

Therefore, a = 5/4.

To solve the equation 1/2 + ? = 7, we can follow a similar approach. We need to isolate the variable on one side of the equation, so we need to subtract 1/2 from both sides:

? = 7 - 1/2

We need to find a common denominator to add these two fractions, which is 2:

? = (14/2 - 1/2)

? = 13/2

Therefore, the missing number is 13/2.

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The statement "When plotting an ogive graph, the plotted points have x coordinates that are equal to the upper limits of each class" is True because the y coordinate of each point represents the cumulative frequency corresponding to upper limits of each class.

An ogive graph is used to display cumulative frequency distributions and provide a visual representation of the data. When plotting an ogive, the x-coordinates of the plotted points represent the upper limits of each class or category, while the y-coordinate of each point represents the cumulative frequency or cumulative percentage of the data corresponding to the upper limit of each class. The cumulative frequency is calculated by adding up the frequencies of all the data points up to and including the current class.

In this way, the ogive graph provides a visual representation of the cumulative distribution of the data, showing how the cumulative frequency or cumulative percentage increases as the class intervals increase.

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Answer:

x=1

Step-by-step explanation:

Answer:

1. 28

2. 53

Step-by-step explanation:

1. The angle CFD is a straight line, this means that the measure is 180. This means, using the angle addition postulate, you can set up the equation \(180=x+152\). Then, subtract 152 from both sides to get \(x=28\).

2. The question states that the two angles are complementary. This means that they summate to 90 degrees. So using the angle addition postulate again, you can set up the equation, \(90=x+37\). Finally, subtract 37 from both sides to get \(x=53\).

Answer:

D.

Step-by-step explanation:

\(\frac{\sqrt{a} }{\sqrt{b} } =\sqrt{\frac{a}{b} }\)

There is a rule like this, so answer is D.

Answer:

n = 20

Step-by-step explanation:

\(\frac{n+4}{6}\) = 4

You need to get rid of the 6 in the denominator on the left hand side to make it easier to solve, so multiply both sides by 6. So you would get:

( \(\frac{n+4}{6}\) ) × 6 = 4 × 6

n+4 = 24

Then just rearrange for n by subtracting 4 on both sides.

n+4 = 24

n= 24-4

n=20

Answer:

10/3

Step-by-step explanation:

1. Divide:

\(\frac{n+4}{6}=4\)

\(\frac{n+2}{3} =4\)

2. Subtract \(\frac{2}{3}\) from both sides of the equation

3. simplify

Answer: N = \(\frac{10}{3}\)

The required solution for the hypothesis testing is shown.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
Part A:

The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.

The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.

H0: p ≤ 0.05

Ha: p > 0.05

where p represents the proportion of defective batteries.

Part B:

A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.

A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.

Part C:

If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.

Part D:

If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.

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For a quadratic function if the value of the coefficient is far away from zero, the parabola looks thin or narrow.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

If the value of the coefficient of the squared variable in a quadratic function is far away from zero, the parabola looks narrow or thin.

This is because the coefficient of the squared variable determines the "steepness" of the curve of the parabola.

For example, consider the equation y = 2x².

This parabola is narrow because the coefficient of x² is 2, which is far away from 0.

On the other hand, if we consider the equation y = (1/2)x², the parabola is wider because the coefficient of x² is 1/2, which is closer to 0.

In general, the closer the coefficient of the squared variable is to 0, the wider the parabola will be.

Conversely, the farther the coefficient is from 0, the narrower or thinner the parabola will be.

Therefore, the parabola looks thin.

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The coefficient of the squared variable determines how wide or narrow a parabola is.

If the value of the coefficient is far away from zero, the parabola looks?

a. 80% of 90 is the same as of 90 - False

b. 45% of 60 is 27 - True

c. 20% of 90 is the same as as of 90- True

d. 25 is 35% of 80 -False

a. 80% of 90 is not the same as 90. To find 80% of 90, we multiply 90 by 0.8, which gives us 72. Therefore, the statement is false.

b. To find 45% of 60, we multiply 60 by 0.45, which gives us 27. Therefore, the statement is true.

c. 20% of 90 is the same as of 90. To find 20% of 90, we multiply 90 by 0.2, which gives us 18. Therefore, the statement is true.

Lastly, for question d. 25 is not 35% of 80. To find 35% of 80, we multiply 80 by 0.35, which gives us 28. Therefore, the statement is false.

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Answer:

X = C - B

--------

A

Step-by-step explanation:

Solving for X is pretty much getting X alone on one side of the equal sign. That's when we would do the "opposite" of what the original equation is showing. And we do that to both sides.

For example, we see +b. The opposite of addition is subtraction, so we do just that. We do -b on BOTH sides of the equal sign. b -b = 0. It cancels it out. c-b is just as it says. So now we have ax = c-b.

Now we see ax are right next to each other with no symbol, which means they are being multiplied. The opposite of multiplication is division. So we'll do that exactly. We will divide A on both sides. ax/a gets rid of that a and leaves the x alone. Dividing c-b/a gives you just that, making the answer X = C-B/A

The equation for the line tangent to the graph of f(x) = x²+ 3 at the indicated point (4,19) is y = 8x - 13.

What is the equation for the line tangent to the graph of f(x) = x²+ 3 at the indicated point (4,19)?

To find the equation for the line tangent to the graph of the function f(x) = x² + 3 at the indicated point (4,19), we need to use the concept of the derivative. The derivative of f(x) is given by f'(x) = 2x.

At the indicated point (4,19), the derivative f'(x) evaluated at x = 4 gives us the slope of the tangent line: f'(4) = 2(4) = 8.

Now, we can use the point-slope form of a line to find the equation of the tangent line. The point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that the point (4,19) is on the tangent line, and we just found that the slope of the tangent line is 8.

Plugging in these values, we get:

y - 19 = 8(x - 4)

Simplifying this equation, we get:

y = 8x - 13

Therefore, the equation for the line tangent to the graph of f(x) = x²+ 3 at the indicated point (4,19) is y = 8x - 13.

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Answer:

x = 2x

x + 20 = 2x + 20

And,

1.5(x + 20) = 2x + 20

x = 20 i.e. Alexis

And, Jelani be 40

Step-by-step explanation:

Given that

Jelani has twice as much as Alexis

And, both can added $20

Jelani will have 1.5 times as much on his pass on Alexis

We need to write an equation also the amount does Jelani and Alexis have

So,

Let us assume the alexis be x

And, Jelani be 2x

Now

x = 2x

x + 20 = 2x + 20

And,

1.5(x + 20) = 2x + 20

1.5x + 30 = 2x + 20

-0.5x = -10

x = 20 i.e. Alexis

And, Jelani be 40

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

To determine if a function is linear, we need to verify if it satisfies the linearity property, which states that for any x and y in the domain of the function and any scalars α and β, the function should satisfy f(αx + βy) = αf(x) + βf(y).

Let's examine each function and determine if it is linear:

f(x) = 3x - 2

To check linearity, we need to verify if f(αx + βy) = αf(x) + βf(y). Let's substitute the values:

f(αx + βy) = 3(αx + βy) - 2

= 3αx + 3βy - 2

On the other hand:

αf(x) + βf(y) = α(3x - 2) + β(3y - 2)

= 3αx - 2α + 3βy - 2β

Comparing the two expressions, we can see that they are not equal, so the function f(x) = 3x - 2 is not linear.

f(x) = 2x²

Using the same logic, let's check linearity:

f(αx + βy) = 2(αx + βy)²

= 2(α²x² + 2αβxy + β²y²)

= 2α²x² + 4αβxy + 2β²y²

On the other hand:

αf(x) + βf(y) = α(2x²) + β(2y²)

= 2αx² + 2βy²

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

In conclusion, neither of the given functions is linear since they do not satisfy the linearity property.

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The probability that the score of a randomly selected examinee is more than 50 is approximately 1, as the minimum possible score is 0 and all examinees' scores are above 50.

The probability that the score of a randomly selected examinee is between 400 and 480 can be found by calculating the area under the normal curve between those scores.

To do this, we need to standardize the scores using the z-score formula and then use the standard normal distribution table or statistical software to find the corresponding probabilities.

For a score of 400, the z-score is :

= (400 - 420) / 32

= -0.625,

and for a score of 480, the z-score is :

= (480 - 420) / 32

= 1.875.

Using the standard normal distribution table or statistical software, we can find the cumulative probabilities for these z-scores and subtract them to find the probability.

To find the probability of a certain score range in a normal distribution, we need to standardize the values by converting them into z-scores. The formula for calculating the z-score is (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

In this case, we have a normal distribution with a mean of 420 and a standard deviation of 32.

By plugging in the values and calculating the z-scores for the given scores, we obtain -0.625 for 400 and 1.875 for 480.

To find the probabilities, we refer to the standard normal distribution table or use statistical software to look up the cumulative probabilities corresponding to these z-scores. We then subtract the lower cumulative probability from the higher cumulative probability to find the probability between the two scores.

In this case, the probability that the score of a randomly selected examinee is between 400 and 480 can be found by subtracting the cumulative probability of -0.625 from the cumulative probability of 1.875.

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If the mean of a statistic's sample distribution perfectly matches the actual value of the parameter being evaluated, the statistic is said to be unbiased. The population proportion p is best estimated objectively using the sample proportion (p hat) from an SRS.

If the expected value of an estimate for a given parameter is the same as the parameter's true value, the estimator is said to be impartial. To put it another way, an estimator is impartial if it generates parameter estimates that are generally accurate.

The mean of a sample taken from a population is calculated to produce a point estimate of the population mean. The mean is calculated by dividing the total sample values by the total number of values.

Hence we get the required answer.

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Answer:

8.2

Step-by-step explanation:

x=10 1/4=41/4

we have to do  Unitary method.

when x=15 then y=12

when x=1 the y=12/15

when x=41/4 then y=(12*(41/4))/15

Answer:

center = \((-4,8)\)

Radius = 7 units

Step-by-step explanation:

Given: Equation of circle is \(x^2+y^2+8x-16y+31=0\)

To find: Radius and center of the circle

Solution:

Equation of circle is \((x-a)^2+(y-b)^2=r^2\)

Here, \((a,b)\) is the center and r is the radius.

\(x^2+y^2+8x-16y+31=0\\\left [ x^2+2(4)x+4^2 \right ]+\left [ y^2-2(8)y+8^2 \right ]+31=4^2+8^2\)

Use formula \((u+v)^2=u^2+v^2+2uv\)

\((x+4)^2+(y-8)^2=16+64-31\\(x+4)^2+(y-8)^2=49=7^2\)

On comparing this equation with equation of circle,

center = \((-4,8)\)

Radius = 7 units

Answer:

center: (4,-4)

Radius: 9

Step-by-step explanation:

KHAN ACADEMY

Answer:

BAC=15

Step-by-step explanation:

angle BOA= 180-30= 150

triangle BAO is   isosceles because it has two equal sides, radii of a circumference so the angles ABO=BAO=(180-150)/2=15

The expression in terms of m and h is D = m/h if the expression is hD = m; the answer is D = m/h.

What exactly is a phrase?

It is described as blending mathematical operators, constants, and variables.

It follows that:

The sentence is:

hD = m

To account for D Declare D as the subject.

As we know, an arithmetic operation can be defined as an operation in which we add, subtract, multiply, and divide integers. It has four basic operators that are +, -, ×, and ÷.

By dividing both sides by h:

hD/h = m/h

Here h ≠ 0

D = m/h

As a result, if the statement is hD = m, then the expression in terms of m and h is D = m/h, and the solution is D = m/h.

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An isomorphism is a concept in mathematics that relates to the similarities between two mathematical structures. It emphasizes the idea that two structures can be considered essentially the same if there is a bijective function, called an isomorphism, that preserves their operations and structure.

Regarding groups, a fundamental concept in algebra, we can determine whether two groups are isomorphic by finding a bijective function between them that preserves their group operations. In other words, if we can find a function that maps each element of one group to a unique element in the other group, while also preserving the group operation, then the two groups are considered isomorphic.
In the given question, it states that the groups Z4 and Us are isomorphic. To illustrate this, we can create side-by-side Cayley tables that show the group operation for each element of both groups. The Cayley table will demonstrate the matching between the elements of Z4 and Us. It's important to note that there can be more than one way to create these Cayley tables, as long as the overlay-matching between the elements is evident.
To summarize, an isomorphism is a bijective function that preserves the operations and structure of mathematical structures. In the context of groups, two groups are isomorphic if there exists an isomorphism between them. The Cayley tables help illustrate this isomorphism by showing the matching between the elements of the groups.

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The balance increase for card i is $89.24 greater than the balance increase for card h. Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt)

Given, Card h has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually.

Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt),

where A = final amount, P = principal (initial balance), r = annual interest rate (as a decimal), n = number of times compounded per year, t = time (in years)

For card h,

A = 1186.44(1 + 0.1474/1)^(1*3)

A = 1883.99

For card i, A = 1522.16(1 + 0.1205/12)^(12*3)

A = 1973.23

Therefore, the balance for card i will have increased more than that of card h, and the difference in the increase is: 1973.23 - 1883.99 = 89.24

The balance increase for card i is $89.24 greater than the balance increase for card h. Hence, the required answer is card i.

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Answer:

it would be 2.33 I divided it I hope I'm right :)

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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The given distribution is Normal with a mean of μ = 140 and a standard deviation of σ = 10. Using the empirical rule, we can find the percentage of the total credits earned by students that are less than 140 credits.

The given distribution is Normal with a mean of μ = 140 and a standard deviation of σ = 10. Using the empirical rule, we can find the percentage of the total credits earned by students that are less than 140 credits:

68% of the total credits lie within one standard deviation of the mean. Therefore, the percentage of total credits that are less than 140 credits is 50%. The empirical rule is also called the 68-95-99.7 rule. The empirical rule is a statistical concept that indicates the proportion of the data that falls within certain standard deviations from the mean of a normal distribution. Therefore, the percentage of total credits that are less than 140 credits is 50%.

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