Twice a number is equal to 35 more than 7 times the number. Find the number.

T is a linear combination of independent standard normal and  square random variables, it follows a Student's t distribution with n + m - 2 degrees of freedom. This completes the proof.

We have the statistic w defined as:

w = (-3X1 - X2 + 5Y1) / √(0.1/n + 0.2/m)

Since X1, X2, ..., Xn are independent and identically distributed normal random variables with mean μ1 = 41 and variance σ1^2 = 0.1, we know that the sum of these variables is also a normal random variable with mean nμ1 = 41n and variance nσ1^2 = 0.1n. Similarly, the mean and variance of Y1, Y2, ..., Ym are μ2 = H and σ2^2 = 0.2.

Using these properties, we can express w as a linear combination of two independent standard normal random variables Z1 and Z2 as follows:

w = (-3/√0.1)Z1 - (1/√0.1)Z2 + (5/√0.2)(H-41)/√m

where Z1 ~ N(0,1) and Z2 ~ N(0,1) are independent standard normal random variables.

Therefore, w follows a standard normal distribution with mean 0 and variance 1. The degrees of freedom of the distribution is n + m - 1, since we have n + m independent observations.

We have the statistic T defined as:

T = (-18X1 - X2 + 19Y1) / {√[s^2(1/n + 1/m)]}

where s^2 = [(n-1)S1^2 + (m-1)S2^2] / (n+m-2) is the pooled sample variance, S1^2 and S2^2 are the sample variances of X and Y, respectively.

Using the same steps as in part (a), we can express T as a linear combination of two independent standard normal random variables and a chi-square random variable with n + m - 2 degrees of freedom:

T = (-18/√s^2)(Z1) - (1/√s^2)(Z2) + (19/√s^2)(H-41)/√m

√{[(n+m-2)/s^2] / X^2(n+m-2)}

where X^2(n+m-2) ~ χ^2(n+m-2) is a square random variable with n + m - 2 degrees of freedom, independent of Z1 and Z2.

Since T is a linear combination of independent standard normal and chi-square random variables, it follows a Student's t distribution with n + m - 2 degrees of freedom. This completes the proof.

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To construct a 95% confidence interval estimate of the mean time required for all college students to earn bachelor's degrees, we can use the given sample data.

The sample mean (x) is calculated by summing up all the values and dividing by the sample size. In this case, the sample mean is approximately 7.75 years. The sample standard deviation (s) can be calculated as the square root of the sum of squared deviations from the mean divided by the sample size minus one. In this case, the sample standard deviation is approximately 5.55 years. The margin of error (E) for a 95% confidence interval is then calculated as 1.96 times the standard deviation divided by the square root of the sample size. In this case, the margin of error is approximately 3.33 years. Therefore, the 95% confidence interval estimate for the mean time required for all college students to earn bachelor's degrees is approximately (4.42, 11.08) years.

Based on the confidence interval, it does not appear that college students typically earn bachelor's degrees in four years since the lower bound of the interval is greater than four. The data suggests that the mean time required is likely to be between 4.42 and 11.08 years, which indicates that students may take longer than four years on average to earn their bachelor's degrees.

However, there are some factors to consider that might suggest the confidence interval may not be a good result. First, the sample size is relatively small, which may lead to a larger margin of error and less precise estimates. Second, the data shows some variability with a range from 4 to 22 years, indicating a wide range of completion times among the sample. This variability can affect the accuracy of the confidence interval estimate. It is important to gather a larger and more representative sample to improve the precision of the estimate and provide a more reliable conclusion about the mean time required for college students to earn bachelor's degrees.

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Answer:

Following are the responses to the given question:

Step-by-step explanation:

\(\to y=(\frac{1}{2})(x-4)(x+4)\\\\\to y=(\frac{1}{2}) (x^2-16)\\\\\to y=(\frac{1}{2})(x-0)^2-8\\\\vertex \to (0,-8)\)

The general x-intercept parabola equation \(y=k(x-4)(x+4)\)

Parabola crosses the dot (2,-12)

\(\to k(2-4)(2+4)=-12\\\\\to k(-2)(6)=-12\\\\\to -12k=-12\\\\\to k=\frac{-12}{-12}\\\\\to k=1\)

The parabolic equation which crosses the position \((2,-12)\) is\(y=(x-4)(x+4)\)

\(\to y=(x-4)(x+4)\\\\\to y=x^2-16\\\\\to y=(x-0)^2-16\\\\vertex \to (0,-16)\)

The distance among the vertices of the two parabolas:

\(= \sqrt{(0 - 0)^2+(-8-(-16))^2}\\\\ = \sqrt{0+(-8+16))^2}\\\\ =\sqrt{0+(8)^2}\\\\=\sqrt{(8)^2}\\\\= 8\\\\\)

Answer:

$28.84 with the sale

Step-by-step explanation:

good luck! Brianliest?

well, since we know the diameter points, half-way in between is the center

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-25}~,~\stackrel{y_2}{-11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -25 -1}{2}~~~ ,~~~ \cfrac{ -11 -1}{2} \right)\implies \left(\cfrac{-26}{2}~~,~~\cfrac{-12}{2} \right)\implies (-13~~,~~-6)\)

and its radius will be half the length of the diameter

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-25}~,~\stackrel{y_2}{-11})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-25 - (-1)]^2 + [-11 - (-1)]^2}\implies d=\sqrt{(-25+1)^2+(-11+1)^2} \\\\\\ d=\sqrt{(-24)^2+(-10)^2}\implies d=\sqrt{676}\implies d=26~\hfill \stackrel{half~that}{r=13}\)

\(\rule{34em}{0.25pt}\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-13}{ h},\stackrel{-6}{ k})\qquad \qquad radius=\stackrel{13}{ r} \\\\[-0.35em] ~\dotfill\\\\\ [x-(-13)]^2~~ + ~~[y-(-6)]^2~~ = ~~13^2\implies (x+13)^2~~ + ~~(y+6)^2~~ = ~~169\)

Tn = a + ( n- 1 ) d

T 26 = -33 + ( 26 - 1 ) 4

T 26 = -33 + ( 25 x 4 )

= -33 + 100

= 67.............. Option D

The payment amount for the loan is approximately $832.54.

To calculate the payment amount for a loan, we can use the formula for the present value of an annuity. The formula is as follows:

\[ P = \frac{A \times r}{1 - (1 + r)^{-n}} \]

Where:

- P is the loan principal (initial amount borrowed)

- A is the payment amount

- r is the interest rate per period (expressed as a decimal)

- n is the total number of periods

In this case, the loan principal (P) is $3500, the interest rate (r) is 9% (or 0.09 as a decimal), and the number of periods (n) is 4 (since payments are made annually for 4 years). We need to solve for A, the payment amount.

Plugging in the given values into the formula, we get:

\[ 3500 = \frac{A \times 0.09}{1 - (1 + 0.09)^{-4}} \]

To solve for A, we can rearrange the equation:

\[ A = \frac{3500 \times 0.09}{1 - (1 + 0.09)^{-4}} \]

Let's calculate the value of A using this equation:

\[ A = \frac{3500 \times 0.09}{1 - (1.09)^{-4}} \]

\[ A \approx \frac{315}{0.3781} \]

\[ A \approx \$832.54 \]

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Answer:

Well, make brainlist okay

1) FH = JH ( GIVEN) Side

2) FG = JK (GIVEN) side

3) GH = HK ( MIDPOINT) side

AND BOOM

FGH = JKH ( from SSS, mention eq)

S mean side

The top of a building 40 feet above the ground a construction worker locates a rock at a 12 degree angle of depression is the rock from the building. So, 188.1848 far is the rock from the building.

The top of a building 40 feet above the ground a construction worker locates a rock at a 12 degree angle of depression.

based on the given conditions, formulate:

Calculate the approximate value:

= 40/tan 12°

= 40/0.2125

= 188.1848

Therefore, the closest integer: 188.18

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Answer: 14

Step-by-step explanation: 9 small squares with one teddy bear in each, 4 medium squares with 4 bears in each medium square, and 1 big square for the entire thing.

The total number of square is 14

In the counting of figures, you have a shape or a figure. From the given shape you will have to identify a given known shape and count the number of times it is present in the given shape.

According to the question

9 small squares with one teddy bear in each,

4 medium squares with 4 bears in each medium square.

1 big square for the entire thing.

Total square = 9 + 4 + 1

                     = 14

Hence, the total number of square is 14

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180 people would the elevator carry than if all the passengers were​ adults.

What is the meaning of times?

The mathematical symbol is used to represent the multiplication operation and the consequent product. It is often referred to as the times sign or the dimension sign.

Given an elevator can carry 25 adults or 30 children at one time.

One day the elevator carries a full passenger load 36 times.

If the elevator carries all adults, then it carries (25 × 36) = 900 adults.

If the elevator carries all children, then it carries (30 × 36) = 1080 adults.

If all the passengers were​ children, then the elevator carry more than (1080 - 900) = 180 people if all the passengers were​ adults.

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Answer:

x≤7

Step-by-step explanation:

Start by solving for x

-12+4x≤16

4x≤28

x≤7

see pic below for the second part

Regardless of the block's dimensions, there are 6.90 x 10²² atoms of lead-206 present in it.

We can calculate the number of lead-206 atoms present in the block. We can assume that the block's mass is 100 grams.

To begin, we need to know the atomic mass of lead-206. It is 206 grams/mole.

1 mole of lead-206 contains 6.022 x 10²³ atoms.

We can use these numbers to calculate the number of atoms present in the block as follows:

Number of moles of lead-206 present = (23.6/100) x (100/206) = 0.1146 moles

Number of atoms of lead-206 present = 0.1146 x 6.022 x 10²³ = 6.90 x 10²² atoms

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Answer:

i dont

Step-by-step explanation:

thanks for points thoo

Normal quantile plot is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution.

What is a Normal Quantile Plot?

A normal quantile plot is a graphical tool used to determine whether a data set is normally distributed or not.

It plots sample data versus a theoretical normal distribution.

In general, the points on the plot should form a straight line if the data is normally distributed. If the data is not normally distributed, the points on the plot will not form a straight line.

A normal quantile plot can be used to evaluate the following:

The normal quantile plot of the residuals is the most important diagnostic tool for examining whether the assumptions of a linear regression model have been met.

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Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.

To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.

The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.

The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.

Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.

Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.

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The solution of the differential equation for the given initial conditions is x = e^-2t (-1/2 cos(3t) + sin(3t))

The equation of motion of the spring-mass-damper system is given by2x'' + 8x' + 26x = 0

            where x is the displacement of the mass from its equilibrium position, x' is the velocity of the mass, and x'' is the acceleration of the mass.

The characteristic equation for this differential equation is:

                          2r² + 8r + 26 = 0

Dividing by 2 gives:r² + 4r + 13 = 0

Solving this quadratic equation, we get the roots: r = -2 ± 3i

The general solution of the differential equation is:

                    x = e^-2t (c₁ cos(3t) + c₂ sin(3t))

where c₁ and c₂ are constants determined by the initial conditions.

Using the initial conditions x(0) = -1 m and x'(0) = 2 m/s,

we get:-1 = c₁cos(0) + c₂

              sin(0) = c₁c₁ + 3c₂ = -2c₁

              sin(0) + 3c₂cos(0) = 2c₂

Solving these equations for c₁ and c₂, we get: c₁ = -1/2c₂ = 1

Substituting these values into the general solution, we get:x = e^-2t (-1/2 cos(3t) + sin(3t))

The solution of the differential equation for the given initial conditions is x = e^-2t (-1/2 cos(3t) + sin(3t))

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what do you want me to answer?

Answer:

Answer is on the picture

Step-by-step explanation:

Answer is on the picture

The successive approximations are x_1 = 1.2900, x_2 = 1.2898, and x_3 = 1.2898.

So, the method yields a positive root of the polynomial 5 + 4x - 6 to be x = 1.2898 (rounded to 5 decimal places). The number 22 and 23 are not relevant to this problem.

To use Newton's method to find the positive root of the polynomial 5 + 4x - 6, we need to use the following iteration formula:

x_(n+1) = x_n - f(x_n)/f'(x_n)

where f(x) = 5 + 4x - 6 and f'(x) = 4.

Starting with x_0 = 1.32, we have:

x_1 = x_0 - f(x_0)/f'(x_0) = 1.32 - (5 + 4(1.32) - 6)/4 = 1.2900
x_2 = x_1 - f(x_1)/f'(x_1) = 1.2900 - (5 + 4(1.2900) - 6)/4 = 1.2898
x_3 = x_2 - f(x_2)/f'(x_2) = 1.2898 - (5 + 4(1.2898) - 6)/4 = 1.2898

The successive approximations are x_1 = 1.2900, x_2 = 1.2898, and x_3 = 1.2898.

So, the method yields a positive root of the polynomial 5 + 4x - 6 to be x = 1.2898 (rounded to 5 decimal places). The number 22 and 23 are not relevant to this problem.

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Answer:

i hope this will help u

Step-by-step explanation:

if p(0) so answer is 0

if p(1) so answer is 7/2 or 3.5

In order to transform linear regression into polynomial regression, certain polynomial terms are added to it due to the non-linear relationship between the dependent and independent variables.

Let's say we have independent data X and dependent data Y. In the preprocessing stage, we turn the input variables into polynomial terms to some extent before feeding the data to a mode.

As a specific example of multiple linear regression, polynomial regression is a type of linear regression that estimates the connection as an nth degree polynomial. The performance can also be negatively impacted by the existence of one or two outliers since Polynomial Regression is sensitive to outliers.

The connection between the dependent and independent variables is best approximated by polynomial. It may be used for a wide range of functions. In general, polynomial suits a large range of curvature.

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Answer:

the answe

Step-by-step explanation:

If B is the midpoint of AC and C is the midpoint of BD, then AB=CD.

Given that B is midpoint of AC and C is the midpoint of BD.

We are required to prove that AB is equal to CD.

Midpoint is the point which divides the line segment into two equal parts.

If B is midpoint of AC then,

2AB=AC-----1

2BC=AC-----2

If C is midpoint of BD then,

2BC=BD-----3

2CD=BD-----4

From 1 & 2

2AB=2BC

AB=BC

Put the value of BC from 3.

AB=BD/2

Now put the value of BD from 4.

AB=2CD/2

AB=CD

Hence proved

Hence if B is the midpoint of AC and C is the midpoint of BD, then AB=CD.

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The approximate percentage of students who hope to own a house someday is between 78.4% and 81.6% calculated at a 68% confidence.

What is confidence level in statistics?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. At a chosen confidence level, a confidence interval is calculated.

From the given question, we can write

The proportion of students who hope to own a house p' = \(\frac{480}{600}\) = \(\frac{4}{5}\) = 0.8

The proportion of students who does not hope to own a house q' = 1-p'

                                                                                                = 1-0.8=0.2

Since the requested confidence level is CL = 0.68, then

\(\frac{\alpha }{2}\) = 0.68/2 = 0.32

\(z_{\frac{\alpha }{2} }\) = 0.92 ( From standard normal distribution table)

So, approximate percentage is

p' - \(z_{\frac{\alpha }{2} }\)\(\sqrt{\frac{p'q'}{n} }\) ∠ p ∠ p' +  \(z_{\frac{\alpha }{2} }\)\(\sqrt{\frac{p'q'}{n} }\) ( n is the total population)

= 0.8 - 0.92\(\sqrt{\frac{0.8 * 0.2}{600} }\) ∠ p ∠ 0.8 + 0.92\(\sqrt{\frac{0.8 * 0.2}{600} }\)

= 0.784 ∠ p ∠ 0.816

Therefore the approximate percentage of students who hope to own a house someday calculated at a 68% confidence is between 78.4% and 81.6%.

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Answer: Point C is (0, -7)

Step-by-step explanation:

For a general line y = a*x +b

A perpendicular line to this one will have a slope equal to -(1/a)

First, for a line y = a*x + b that passes through points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Then for a line that passes through the points A (-4, 5) and B (5, 8) the slope is:

a = (8 - 5)/(5  - (-4))  = 3/9 = 1/3

a = 1/3

Then, a line perpendicular to this one will have the slope:

a' = -(1/(1/3) = -3

Then the perpendicular line is something like:

y = -3*x + b

Now we know that this line passes through point A, then when x = -4, we have y = 5

if we replace these values we get:

5 = -3*(-4) + b

5 = 12 + b

5 - 12  = b

-7 = b

Then our line is:

y = -3*x - 7

This line intersects the y-axis at point C, we know that the y-axis corresponds to x = 0.

Then:

y = -3*0 - 7

y = -7

The point C is (0, -7)

The linear equation that can be used to find the height considering all the information is h2 = h1 + (-0.5)(t2 - t1)

The height of a candle can be modeled by a linear function with a slope of -0.5 cm/hour.

If the height of the candle after t1 hours is h1 centimeters, then the height of the candle after t2 hours is given by h2 = h1 + (-0.5)(t2 - t1).

So, if the height of the candle after t1 hours is h1 centimetres, and after t2 hours is h2 centimeters, we have:

h2 = h1 + (-0.5)(t2 - t1)

We can use the given information to find the value of h1, and then use the equation above to find the value of h2.

However, the information given in the question is not enough to solve for h1 and h2. We need more information such as the height of the candle after a certain number of hours.

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