a right triangle's height is 5 times the length of its base. if the area of the triangle is 160, what is its height?

Reducing the variation of a process will increase the width of a given confidence interval relative to that process.

Option C is correct .

In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as a confidence interval. By employing the dimensions of values used in the computation of the intervals, it is simple to establish the link between components of two confidence intervals. The width is a fundamental component in these range estimates, which are affected by sample size, etc.

Hence, reducing the variation of a process will increase the width of a given confidence interval relative to that process is false.

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The required question of the given problem are solved below.

A distance-time graph shows how far an item has gone in a given time. It is a straightforward line diagram that signifies distance versus time discoveries on the chart. Distance is plotted on the Y-pivot. Time is plotted on the X-pivot.

1) he take 20 minutes to get to his friends house.

2) he stayed 60 - 20 = 40 minutes at his first friends house.

3) he take 70 - 60 = 10 minutes to ride his bike from his first friends house to his second friends house.

4) 30 minutes, he stayed his second friend

Then

Difference = 40 - 30 = 10 minutes

So, he stay 10 minutes longer than first friend.

5) In part E, he is riding towards his home.

6) In part A of the graph he is travelling faster.

7) he went 10 kilometer away from his house.

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The expression that would be easier to simplify if you used the associative property to change the grouping is D. (160 + 40) + 27.

The associative property of some binary operations in mathematics means that rearranging the parentheses in an expression will not change the result. Associativity is a valid rule of replacement for expressions in logical proofs in propositional logic.

This law simply states that when adding and multiplying numbers, you can change the grouping of the numbers in the problem and the answer will not change.

Addition and multiplication are both affected by the associative property. The reason for this is that you are combining numbers to get a total in both of these operations. You are combining values with addition. It makes no difference how you group these to put them together. The associative property of addition states that the addends can be grouped in various ways without changing the outcome.

In this case, (160 + 40) + 27 can simply be (40 + 160) + 27.

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The correct option is (B) generated randomly from probability distributions.

The values for random variables in a Monte Carlo simulation are generated randomly from probability distributions.

A frequency distribution that has been idealized is a probability distribution. An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each possible value of a variable appears. The probability of occurrence of a value determines how frequently it appears in a sample.

A random variable can have any number of alternative values and likelihoods within a particular range, and a probability distribution is a statistical function that captures all of these possibilities. This range will be constrained by the minimum and maximum possible values, but the location of the possible value on the probability distribution will rely on a number of other variables.

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Answer:

I don’t know

Step-by-step explanation:

There is not sufficient evidence to support the power company's claim.

According to the information given in the question, we can frame the hypothesis as follows-

Null hypothesis ⇒ :  H = 10400

Alternate hypothesis ⇒ Ha:  > 10400

This is the right-tailed test.

Test statistic = z

[(x - μ)√n]/ σ

where x ⇒ sample mean = 10,782

σ ⇒ standard deviation = 2768

= (10782 - 10400)√163/ (2768)

= 382* 12.76/(2768)

= 1.76

⇒ Test statistic z = 1.76

Now, P( z > 1.76) = 1 - P( z < 1.76)

= 1 - 0.9608

= 0.0392

using z tables-

p-value = 0.0392

a = 0.01

we see that p-value > a

Thus, we fail to reject our null hypothesis.

Therefore, there is not sufficient evidence to support the  power company's claim.

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the null hypothesis the company will​ use p =0.44.

What is z test?

If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.

Here the data is normally distributed and using the sample mean.

This is the right-tailed test.

The null  hypothesis is

H0 :  p =0.44

Hence, the null hypothesis the company will​ use p =0.44.

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The 4 different types of items will be selected.

What is the combination?

Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. In combinations, you can select the items in any order.

[tex]nCr = \frac{n!}{(n - r)! \ r!}[/tex]

This formula to find the number of combinations by using r objects from the n objects is also referred as the ncr formula.

so, we have 4 items and a person randomly selects 3.

[tex]nCr = (n, r) = (4, 3)[/tex]

[tex]= \frac{4!}{3!(4 - 3)!}[/tex]

= 4! / 3!

= 4

Hence, The 4 different types of items will be selected.

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The length of the other leg of the right triangle, rounded to the nearest whole number, is 10 units.

To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the length of the other leg as x. Given that one leg is 6 units long and the hypotenuse is 12 units long, we can set up the equation:

6^2 + x^2 = 12^2

Simplifying this equation, we have:

36 + x^2 = 144

Subtracting 36 from both sides, we get:

x^2 = 108

Taking the square root of both sides, we find:

x = √108

Rounding this value to the nearest whole number, we have:

x ≈ 10.392

The length of the other leg of the right triangle, rounded to the nearest whole number, is 10 units.

The correct option is: 10 units.

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Answer:

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

Step-by-step explanation:

1/4 / 3/5

To divide fractions we flip the second one and then multiply them both and this method works for any number

1/4 x5/3

5/12

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The new position of the anchor is 7 1/5 below the surface of the ocean

Initially the anchor is located 15 3/5 m below the surface of the ocean, this is same as = -15 3/5 m

The anchor is further lowered and the position now is

=   -15 3/5 m - 4 1/5 m

= -99 /5 m

Then the anchor is pulled up 12 3/5 m  the new position now is

= -99 /5 m + 12 3/5 m

= -36/5

= -7 1/5

= -7.2

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A test's standard deviation is 5 and its mean is 85. scores is within one standard deviation of the mean is 25/n^12.

The square root of the variance of a random variable, sample, mean ,statistical population, data set, or probability distribution is that variable's standard deviation. Although less robust in practice, it is algebraically simpler than the average absolute deviation.The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, is a useful characteristic of the statistic.

variance = 5^2 = 25

standard deviation of the mean = ( variance / n )^1/2

= (25/n)^1/2

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If a categorical independent variable contains 4 categories, then four dummy variables will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4

How many dummy variables are needed to represent the categorical variable?

We need 1 less dummy variable than outcomes for the categorical variable.

categorical variable has 2 outcomes

So, we need 2-1 = 1 dummy variable.

Note: If our categorical variable had 5 outcomes, we would need 5-1 = 4 dummy variables.

b. Write the multiple regression equation relating the dependent variable to the independent variables.

Note: Depending your your professor, this can be written one of the following ways...

yhat = a + b1 x1 + bx2

yhat = b0 + b1 x1 + b2 x2

yhat = beta0hat + beta1hat x1 + betahat2 x2

where x1 is the ratio variable

and x2 is the dummy variable

c. Interpret the meaning of the coefficients in the regression equation.

b0 = the predicted value of y when x1 and x2 both equal 0.

b1 = the change in y when x1 increases by 1 unit holding x2 constant.

b2 = the predicted difference in y between the two possible outcomes of the categorical variable holding x1 constant

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The average number of rounds fired each day is 140.

The average number of rounds fired by each gun during the eight days is 1122.

A mean simply means the average of the set of numbers. It is calculated by adding the numbers and then dividing.

In this situation, the British bombarded the German trenches for eight days and some 1,537 British guns fired 1,723,873 rounds without letting up. The average will be:

= 1,723,873 / 1,537

= 1122 rounds .

The average per day will be

= Average / Number of days

= 1122 / 8

= 140 per day.

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Answer: 11.9 pounds

Step-by-step explanation:

142.5 - 130.6 = 11.9

The total number of possible legitimate license plate numbers possible are (15)⁵.

The license plate has a length of 7 character for the legitimate license plates.

So, there are a total 7 position, in these positions, on has to be a upper case vowel and one has to be an integer digit.

Now, we have only 5 position are left.

There are only 5 vowels and 10 integers digits.

So, we are assuming that the repetition is allowed because nothing else is mentioned.

So, total possible combinations are 1 x 1 x 15 x 15 x 15 x 15 x 15.

Because repetition is allowed, we don't have to consider the factor of internal arrangement.

So, the total number of legitimate license plates possible are (15)⁵.

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The value of E(XY) is equivalent or equal to -1 according to the joint pdf having function f(x, y) = xe^−x(1 + y) x ≥ 0 and y ≥ 0 0.

Given that:

f(x,y) = xe^-x(1+y), where x ≥ 0 and y ≥ 0 0.

E(XY) = ∫∞ ∫∞ xy. xe^−x(1 + y) dx dy

            0   0

E(XY) = ∫∞ ∫∞ x^2y . e^−x(1 + y) dx dy

            0   0

E(XY) = ∫∞ x^2 . e^−x (∫∞ y e^-xy dy) dx

             0                     0

E(XY) = ∫∞ x^2 . e^−x (-1/x) dx

             0

E(XY) = - ∫∞ x . e^−x dx

               0

E(XY) = - 1

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y are equal to i.e. E(XY) = -1.

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 When a  null hypothesis is not rejected, a type ii error has occurred.

A null hypothesis being a statistical hypothesis, states that no statistical significance can be present in a set of observations. Usually, hypothesis testing is a method used to judge the veracity of a given sample.

Sometimes, it is called just null, or even it has a symbol, viz, [tex]H_0[/tex].

We consider generally 4 cases:

According to the given question, we have not rejected the null hypothesis.

Thus,  we have two options present, either the type ii error has occurred and null hypothesis is not present, or the null hypothesis is present.

Concluding, when a null hypothesis is accepted, it is possible that a type ii error has occurred.

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its the second oneee

the length of the confidence interval is 12.8

You have a 5% chance of being incorrect with a 95% confidence interval. You have a 10% chance of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.

The likely location of the population parameter is shown by a confidence interval. For instance, the population mean is between 9 and 11, according to the 95% confidence interval of the mean [9 11].

​According to the question,

Length of confidence interval = 2*(6.4)

Length of confidence interval = 12.8

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The percentage error is 8.3%

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, Akira is redecorating her bedroom. She misread the markings on her ruler and thought a picture frame she bought was 5.2 centimetres wide. The frame's actual width was 4.8 centimetres.

Percentage Error = ((Estimated Number – Actual Number)/ Actual number) x 100.

= (5.2-4.8)/4.8x100 = 8.3%

Hence, The percentage error is 8.3%

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The measure of angle < HEB = 60 degrees.

Given:

if you draw square abcd and extend the sides by equal lengths to form square efgh.

so that the area of abcd is half the area of efgh.

Let AB = x and HA = x

so area of square ABCD = x * x

= x^2

< HEB = 60 so < BHE = 30

EB = y

HE = 2y

HB = x + y

so x + y = [tex]\sqrt{3}[/tex] y

x = [tex]\sqrt{3}[/tex] y - y

x = ([tex]\sqrt{3}[/tex] - 1 ) y

y = x /  ([tex]\sqrt{3}[/tex] - 1 )

squaring on both sides

y^2 =  x^2 /  ([tex]\sqrt{3}[/tex] - 1 )^2

= x^2 / 3 - 1

= x^2 / 2

Area of EFGH = (2y)^2 = 4y^2 = 2x^2 = 2 * area of ABCD.

Therefore < HEB = 60 degrees.

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Answer:

1.41 inches per hour

Step-by-step explanation:

volume of water for 3 hrs=4.23 inches

v of water for 1 hours=4.23/3=1.21inches

This enabled the borrower to obtain 90 percent financing while avoiding the additional cost of pmi. these loans are more commonly referred to as  piggyback mortgage loans.

A loan is the lending of cash via one or more individuals, organizations, or different entities to other individuals, corporations, etc. The recipient incurs a debt and is normally susceptible to pay hobby on that debt till it is repaid as well as to repay the foremost amount borrowed.

A mortgage is a shape of debt incurred by using an character or different entity. The lender—commonly a business enterprise, economic organization, or authorities—advances a amount of money to the borrower. In return, the borrower agrees to a sure set of phrases together with any finance charges, hobby, repayment date, and different situations.

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The interest rate is 4.17%, according to the question.

What do you mean by interest rate?

An amount that a borrower must pay to a lender as interest during the course of a loan, stated as a percentage of the loan amount is called interest rate.

According to data in the given question,

We have the given values:

Amount to be invested/Principal: 2,400

Amount of Interest: 800

Time: 8 years

Now, we will calculate the rate,

Solve for the rate:

Interest = Principal × Rate × Time

Derive the equation for rate:

Rate = [Interest ÷ (Principal × Time)] × 100

Substitute the given values:

Rate = [800 ÷ (2,400 × 8)] × 100

Rate = [800 ÷ 19,200] × 100

Rate = 0.04167 × 100

Rate = 4.17 %

Therefore, the rate is 4.17%.

Check:

800 = 2,400 × 8 × 0.04167

800 = 800.064

800 = 800

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Answer:

slope = 3

y-intercept = 0

Step-by-step explanation:

The number of defectives follows binomial distribution with parameters (n,p) and if n>30 then binomial distribution goes to the Normal' approximation.

Given that,

We have to find which of the following approximation approaches is adequate in a test of the equality of the percent defectives from two populations when the sample sizes are big (> 30).

We know that,

The normal curve is roughly followed by the sample distribution of averages or proportions from numerous independent experiments. The population value that corresponds to a sample proportion or average is its expectation.

Therefore, the number of defectives follows binomial distribution with parameters (n,p) and if n>30 then binomial distribution goes to the Normal' approximation.

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Answer:

1. $105

2. $144

Step-by-step explanation:

For the first question:

4.20 × 25 = 105

For the second question:

4.80 × 30 = 144

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If the R is an equivalence relation then for every a and b in set R , if a = b then aRb exists.

If R is an equivalence relation on set A, a and b are in A and [a]=[b]

By the definition of the equivalence relation we can say that R is reflexive

Hence aRa and so by definition of equivalence class a ∈ [a] .

Since [a] = [b] and a ∈ [a] we can say that a ∈ [b] by the definition of set equality.

Now we will use the definition of equivalent class we can say that aRb .

An equivalence relation is a reflexive, symmetric, transitive binary link. The relationship of equipollence between line segments in geometry is one example of an equivalence relation.

Each equivalence relation separates the underlying set into distinct equivalence classes. Two items in the given set are only comparable to one another if and when they belong to the same equivalence class.

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The required function of the line would be y = 2x + 1.

The slope-intercept form is one rule to represent linear function rules.

f(x) = mx+b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.

Linear equations, or straight-line equations, can be quickly recognized as they have no terms with exponents in them. For example, you will find an x or a y , but never an x². Each linear equation describes a straight line, which can be expressed using the slope intercept form equation.

According to the given question,

The coordinates of the y-intercept would be (0, 1).

The value of the x-coordinate is 1 when y-coordinate is 3.

Here the line passes through points (0, 1) and (1, 3).

Let the required linear function would be

     y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = 1

x₂ = 1, y₂ = 3

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]

⇒ y - 3 = (2)[x -1]

⇒ y - 3 = 2x - 2

⇒ y = 2x - 2 + 3

⇒ y = 2x + 1

Therefore, the required function of the line would be y = 2x + 1 which is shown in the given question.

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