consider the multiple regression model predicting graduating gpa using both the sat critical reading score and the sat math score. computer output of the model gpa

To justify the statement ln(17) = 2.833 mathematically, we can use the definition of the natural logarithm function.

The natural logarithm of a number x, denoted as ln(x), is defined as the exponent to which the base e (approximately 2.71828) must be raised to obtain the number x.

In this case, we have ln(17) = 2.833. To justify this statement mathematically, we can rewrite it using the definition of the natural logarithm:

e^(2.833) = 17

Here, e represents the base of the natural logarithm function, which is approximately 2.71828. By raising e to the power of 2.833, we should obtain the value of 17.

So, the mathematical equation to justify the statement ln(17) = 2.833 is e^(2.833) = 17.

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9514 1404 393

Answer:

  A)  29/40

Step-by-step explanation:

The formula for this is ...

  P(A or B) = P(A) + P(B) - P(A and B)

Filling in the given values, you have ...

  P(A or B) = 9/20 +1/2 - 9/40

  P(A or B) = 18/40 +20/40 -9/40 = (18+20-9)/40

  P(A or B) = 29/40 . . . . matches choice A

a. The probability that difference in sample proportions is more than 6% is 0.1056.

b. There is a 0.2677 probability that the sample proportion from School A is greater than 5% than that from School B.

a. We must first determine the standard error of variation between the two sample proportions in order to determine the probability that the difference in sample proportions is greater than 6:

SEp1-p2 = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }

where,

P1 = 57% of students are from school A.

p2 = 61% of students are from school B.

Sample sizes from schools A and B were 75 and 80, respectively.

SEp1-p2 = sqrt{ [(0.57)(0.43)/75] + [(0.61)(0.39)/80] }

= sqrt{ 0.00233 + 0.00240 }

= 0.0803

Now, we can find the Z-score as:

Z = (p1 - p2 - D) / SEp1-p2

where,

D = 6% = 0.06

Z = (0.57 - 0.61 - 0.06) / 0.0803

= -1.248

Using a standard normal distribution table, we can find the probability that Z < -1.248 is 0.1056.

Therefore, the probability that difference in sample proportions is more than 6% is 0.1056.

b. To find the probability that School A sample proportion is more than 5% higher than School B, we need to find the standard error of the difference between the two sample proportions:

SEp1-p2 = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }

where,

57% of the population in p1 is from school A.

61% of those in p2 are from school B.

75 were included in the sample from school A, while 80 were included in the sample from school B.

SEp1-p2 = sqrt{ [(0.57)(0.43)/75] + [(0.61)(0.39)/80] }

= sqrt{ 0.00233 + 0.00240 }

= 0.0803

Now, we can find the Z-score as:

Z = (p1 - p2 - D) / SEp1-p2

where,

D = 5% = 0.05

Z = (0.57 - 0.61 - 0.05) / 0.0803

= -0.621

We can get the probability that Z -0.621 is 0.2677 by using a standard normal distribution table.

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The function we have is:

The steps to find the inverse function are:

Step 1. Solve for x.

In this case, we solve for x by dividing both sides of the equation by 4:

Step 2. Change f(x) for x, and x for the inverse function f^-1(x):

If we call this inverse function h(x) we get the result:

Answer:

Shown below.

Step-by-step explanation:

Test Marks          Tally          Frequency          Percentage

1                                                    8                   8/60 = 0.133

2                                                   6                   6/60 = 0.100

3                                                   5                   5/60 = 0.083

4                                                   5                   5/60 = 0.083

5                                                   5                   5/60 = 0.083

6                                                   8                   8/60 = 0.133

7                                                   6                   6/60 = 0.100

8                                                   7                   7/60 = 0.116

9                                                   4                   4/60 = 0.066

10                                                 5                   5/60 = 0.083

Total                                            59                 59/60 = 0.983

For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.

Answer:

It angle one I think

Step-by-step explanation:

The proportions of parts produced within specifications by the two shifts at a 4% significance level with the help of an equation.

A formula exists in every equation. Some equations do not have formulae. Equations are designed to be solved for a variable.

(a) To estimate the difference in proportions of parts produced within specifications by the two shifts, we need to calculate the confidence interval.

First, we can calculate the sample proportions of parts produced within specifications for each shift:

For the day shift, the sample proportion is:

p1 = 188/200 = 0.94

p2 = 180/200 = 0.90

p1 - p2 = 0.94 - 0.90 = 0.04

To calculate the confidence interval, we can use the following formula:

(point estimate) ± (critical value) x (standard error)

We will use a 96% confidence level, so our critical value is z* = 2.05 (from the z-table).

The standard error can be calculated as follows:

SE = sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2))

where n1 and n2 are the sample sizes.

Substituting in our values, we get:

SE = sqrt((0.94*(1-0.94)/200) + (0.90*(1-0.90)/200))

SE = 0.040

Now we can calculate the confidence interval:

0.04 ± 2.05(0.040)

The confidence interval is (0.003, 0.077).

Therefore, we are 96% confident that the true difference in proportions of parts produced within specifications by the two shifts is between 0.003 and 0.077.

(b) To determine whether the difference in proportions of parts produced within specifications by the two shifts is significantly different from 0, we need to check if 0 is within the confidence interval we calculated.

Since the confidence interval does not include 0, we can conclude that the difference in proportions of parts produced within specifications by the two shifts is significantly different from 0 at a 96% confidence level.

(c) The hypotheses of interest for the significance test are:

H0: p1 - p2 = 0 (There is no difference in proportions of parts produced within specifications by the two shifts)

Ha: p1 - p2 ≠ 0 (There is a difference in proportions of parts produced within specifications by the two shifts)

We will use a significance level of α = 0.04.

To perform the significance test, we need to calculate the test statistic:

z = (p1 - p2 - 0) / SE

where p1, p2, and SE are the same as calculated in part (a).

Substituting in our values, we get:

z = (0.94 - 0.90 - 0) / 0.040

z = 1.00

Using a z-table, we find that the p-value for a two-tailed test with z = 1.00 is approximately 0.317.

Since the p-value is greater than our significance level of 0.04, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that there is a difference in proportions of parts produced within specifications by the two shifts at a 4% significance level.

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Answer:d

Step-by-step explanation:

16-4=12 and 16+4=20

We know that the triangle is an isosceles triangle because the base angles are the same.

Therefore, the answer is 'x = 2'

Hoped this helped.

\(BrainiacUser1357\)

Answer to the question is D.  \sqrt6/2

The quotient of the given expression is √6/2. Therefore, option D is the correct answer.

The given expression is √12/2√2.

We need to find the equivalent quotient to the given expression.

In Mathematics, surds are the values in the square roots that cannot be further simplified into whole numbers or integers. Surds are irrational numbers.

Now, √12/2√2

We can write √12 as √4×3

Then, we get 2√3/2√2

Further, rationalise the denominator

A fraction whose denominator is a surd can be simplified by making the denominator rational. This process is called rationalising the denominator.

That is √3×√2/√2×√2=√6/2

Therefore, option D is the correct answer.

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Answer:

(6^2)3n

Step-by-step explanation:

6 to the 2nd is 6^2, and since it's hard to tell whether the *n is part of the exponent, I put parentheses around the 6^2. Then just multiply by 3 by adding a 3 to the n.

Answer:

Step-by-step explanation: Raising 6 to the second power means 6 squared, then you multiply it by n so it would be n x 6^2, and then you multiply all of that by 3 so 3(n x6^2)

Answer:

57.98 yards

Step-by-step explanation:

When the ball is on the ground, the height is \(y=0\), therefore:

\(y=-0.017x^2+0.98x+0.33\)

\(0=-0.017x^2+0.98x+0.33\)

\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \)

\(x=\frac{-0.98\pm\sqrt{0.98^2-4(-0.017)(0.33)}}{2(-0.017)} \)

\(x_1=57.98184919\)

\(x_2=-0.3347903693\)

Since distance cannot be negative, the ball landed 57.98 yards down the field from where the goalie kicked the ball.

Answer:

77/125 = 37/60?

If this is a true or false problem it would be marked false.

Answer:

what grade are u in

Step-by-step explanation:

bc I have no idea what u are doing

Answer:

18 square centimeters

Step-by-step explanation:

YW :)

a) The marginal probability mass function for X is P(X) = {0.5, 0.3, 0.2}, for Y is P(Y) = {0.6, 0.3, 0.1}. b) The expectation for X is 1.0, and the variance for X is 0.1. The expectation for Y is 0.5, and the variance for Y is 0.45. c) The covariance between X and Y is -0.2, and the correlation between X and Y is approximately -0.632. They are negatively correlated. d) The weather in two consecutive days is not independent.

(a) Marginal probability mass functions for X and Y:

To find the marginal probability mass function for X, we sum the probabilities across each row:

P(X = 0) = 0.3 + 0.1 + 0.1 = 0.5

P(X = 1) = 0.2 + 0.1 + 0 = 0.3

P(X = 2) = 0.1 + 0.1 + 0 = 0.2

The marginal probability mass function for X is:

P(X) = {0.5, 0.3, 0.2}

To find the marginal probability mass function for Y, we sum the probabilities down each column:

P(Y = 0) = 0.3 + 0.2 + 0.1 = 0.6

P(Y = 1) = 0.1 + 0.1 + 0.1 = 0.3

P(Y = 2) = 0.1 + 0 + 0 = 0.1

The marginal probability mass function for Y is:

P(Y) = {0.6, 0.3, 0.1}

(b) Expectation and variance for X and Y:

The expectation (mean) for X can be calculated as follows:

E(X) = ∑(x * P(X = x))

= (0 * 0.5) + (1 * 0.3) + (2 * 0.2)

= 0.5 + 0.3 + 0.4

= 1.0

The expectation (mean) for Y can be calculated similarly:

E(Y) = ∑(y * P(Y = y))

= (0 * 0.6) + (1 * 0.3) + (2 * 0.1)

= 0.0 + 0.3 + 0.2

= 0.5

To calculate the variance for X, we can use the formula:

Var(X) = E(X²) - [E(X)]²

E(X²) = ∑(x² * P(X = x))

= (0² * 0.5) + (1² * 0.3) + (2² * 0.2)

= 0 + 0.3 + 0.8

= 1.1

Var(X) = E(X²) - [E(X)]²

= 1.1 - 1.0²

= 1.1 - 1.0

= 0.1

Similarly, the variance for Y can be calculated:

E(Y²) = ∑(y² * P(Y = y))

= (0² * 0.6) + (1² * 0.3) + (2² * 0.1)

= 0 + 0.3 + 0.4

= 0.7

Var(Y) = E(Y²) - [E(Y)]²

= 0.7 - 0.5^2

= 0.7 - 0.25

= 0.45

The expectation for X is 1.0, and the variance for X is 0.1.

The expectation for Y is 0.5, and the variance for Y is 0.45.

(c) Covariance and correlation between X and Y:

The covariance between X and Y can be calculated using the formula:

Cov(X, Y) = E(XY) - E(X)E(Y)

E(XY) = ∑(xy * P(X = x, Y = y))

= (0 * 0 * 0.3) + (1 * 0 * 0.1) + (2 * 0 * 0.1) + (0 * 1 * 0.2) + (1 * 1 * 0.1) + (2 * 1 * 0) + (0 * 2 * 0.1) + (1 * 2 * 0.1) + (2 * 2 * 0)

= 0 + 0 + 0 + 0 + 0.1 + 0 + 0 + 0.2 + 0

= 0.3

Cov(X, Y) = E(XY) - E(X)E(Y)

= 0.3 - (1.0 * 0.5)

= 0.3 - 0.5

= -0.2

The correlation between X and Y can be calculated as:

Cor(X, Y) = Cov(X, Y) / (√(Var(X)) * √(Var(Y)))

Cor(X, Y) = -0.2 / (√(0.1) * √(0.45))

≈ -0.632

(d) Independence of the weather in two consecutive days:

To determine if the weather in two consecutive days is independent, we check if the joint probability distribution can be factored into the product of the marginal probability distributions.

If X and Y are independent, then P(X, Y) = P(X) * P(Y) for all values of X and Y.

Let's compare the joint probabilities with the product of the marginal probabilities:

P(X = 0, Y = 0) = 0.3

P(X = 0) * P(Y = 0) = 0.5 * 0.6 = 0.3

P(X = 1, Y = 0) = 0.2

P(X = 1) * P(Y = 0) = 0.3 * 0.6 = 0.18

P(X = 2, Y = 0) = 0.1

P(X = 2) * P(Y = 0) = 0.2 * 0.6 = 0.12

...

We observe that the joint probabilities do not match the product of the marginal probabilities for all values of X and Y. Therefore, the weather in two consecutive days is not independent.

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then for 5 tablespoons you use 12.5 ounces of milk

Answer:

(-2,5)

Step-by-step explanation:

From the figure in the attachment it is clear that when point B will be reflected about the line y= -1. The point B becomes (-2,5)

Answer:b-(-2,5)

Step-by-step explanation:

Answer:

I was born in California and then moved to Texas bt Im indian because my parents are indian

Answer:

please

Step-by-step explanation:

follow me

please

please

please

Answer: hope this help u to find the answer

Step-by-step explanation:Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.The verbal expression for 2x is: "Two times some value." or "The product of two and some value.

Answer:

2(x + 2y)

Step-by-step explanation:

2x + 4y

=> 2(x + 2y)

A measure of the probability that the sample's average IQ is below 987 is 44.70 %.

The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a specific data point deviates from the mean.

The Z-standard score's deviation measure, which the p-value is, can be regarded of as a percentile expression. So they do have p-values.

Given: IQ scores are frequently described as having a normal distribution with a mean of 100.0 and a standard deviation of 15.0. A sample of 57 persons is chosen at random.

Z-score = (X- μ)/σ

             = (98-100)/15

             = -0.1333

P value for this z score equals 0.4470 which is 44.70 %

Therefore, the probability that the average IQ of the sample's population is lower than 987 is 44.70 %.

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Answer:

-1

Step-by-step explanation:

-7=n-6

n=-7+6

n=-1

Please mark me as Brainliest if you're satisfied with the answer.

The Power series representation of f(x) = \(x^8tan^-^1x^3\) is \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

The Maclaurin series expansion method can be used to get the power series of such functions if the function has a composite part, such as the multiplication or quotient form.

An infinite series in mathematics known as a "power series" can be compared to a polynomial with an infinite number of terms.

The Maclaurin series will be used in this instance to expand the function:

\(tan^-^1x\) = \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^2^n^+^1}{2n+1}\)

and for    \(tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{(x^3)^2^n^+^1}{2n+1}\)

=>  \(tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}\)  -------(i)

and f(x) = \(x^8tan^-^1x^3\)

now we need to multiply \(x^8\) in the above equation to get the power series expansion of f(x)

\(x^8tan^-^1x^3\) = \(x^8\) \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}\)

=> \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3^+^8}{2n+1}\)

=>  \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

so the expansion of f(x) = \(x^8tan^-^1x^3\) is \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

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Answer: Initial height before launch

Step-by-step explanation:

Given

The equation \(y=-9.8t+109.7t+7.4\)  the height of toy rocket after t sec

when the rocket is launched, time is \(t=0\)

Substituting 0 for \(t\) in the equation

\(\Rightarrow y(0)=-9.8(0)+109.7(0)+7.4\\\Rightarrow y(0)=7.4\)

Here, \(7.4\) represents that rocket is already at a height of \(7.4\) m before the launch.

Answer:

many

a = 0.2

b = 0.7

Step-by-step explanation:

if a÷b is less than 1, then a must be smaller than b, so you can use any two decimals as long as a is the smaller of the two.

Answer:

answer is 10 (very easy)

Answer:

380. 1

Step-by-step explanation:

A=π r2=π. 11^2= 380.13271