A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:

Education 3 4 6 2 5 4 8 0

Salary $40 36 56 35 72 47 107 52

a) Find the sample regression equation for the model: Salary = ?0 + ?1Education + ?. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.)

b) Interpret the coefficient for education.

c) What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)

Step-by-step explanation:

She has 1050

400 of that is the DB fee

Now she has 650 dollars

650/50 per person is 13

She can have 13 people

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

D

Step-by-step explanation:

Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica

Answer:x=-7

Step-by-step explanation:

Step-by-step explanation:

I'm not sure it's probably x=-2

Answer:

Hello there, lol.

Adjacent = Opposite/ Tan(35)

Adjacent = 4.3

Answer:

4.28

Step-by-step explanation:

basically using the sine ratios :

a/sinA = b/sinB = c/sinC

so, let's call the known side a (3) and its opposing angle A (35 degrees).

and we know C is 90 degrees.

sin(90) = 1

b = the missing side AC.

and because the sum of all angles in a triangle is always 180 degrees, the missing angle B is

B = 180 - 90 - 35 = 55

AC/sin(55) = 3/sin(35)

AC = b = sin(55) × 3/sin(35) = 4.28

a little more practice and calculate also c that way :

3/sin(35) = c/1

c = 3/sin(35) = 5.23

Answer:

Step 4 is incorrect ⇒ C

Step-by-step explanation:

Let us check step by step

∵ sin(x + y)

∵ sin(z) = cos(\(\frac{\pi}{2}\) - z)

→ Replace z by (x + y)

∴ sin(x + y) = cos(\(\frac{\pi }{2}\) - [x + y])

∴ Step 2 is correct

∵ cos(\(\frac{\pi }{2}\) - [x + y]) = cos(\(\frac{\pi }{2}\) - x - y])

∵ take [\(\frac{\pi }{2}\) - x] as the 1st angle and y as the 2nd angle

∴ cos(\(\frac{\pi }{2}\) - x - y]) = cos([\(\frac{\pi }{2}\) - x] - y)

∴ Step 3 is correct

∵ cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

→ Replace a by ([\(\frac{\pi }{2}\) - x] and b by y

∴ cos([\(\frac{\pi }{2}\) - x] - y) = cos(\(\frac{\pi }{2}\) - x)cos(y) + sin(\(\frac{\pi }{2}\) - x)sin(y)

∴ Step 4 is incorrect, the second angle is y not (-y)

∵ cos(\(\frac{\pi }{2}\) - x) = sin(x)

∵ sin(\(\frac{\pi }{2}\) - x) = cos(x)

∴ cos(\(\frac{\pi }{2}\) - x)cos(y) + sin(\(\frac{\pi }{2}\) - x)sin(y) = sin(x)cos(y) + cos(x)sin(y)

∴ Step 5 is correct

Answer:

C. Step 4

Step-by-step explanation:

got it right on edge :)

Answer:

n=49

Step-by-step explanation:

|z|= 2 √(5), |2z|=4 √(5)  and |3z|=6 √(5).  |2z|= 2|z|  this relationship holds true.

In mathematics, the modulus, also known as the absolute value or magnitude, is a function that returns the positive value of a number regardless of its sign. The modulus function is denoted by the vertical bars surrounding the number or expression, for example, |x| or |a-b|.

The modulus of a number is defined as the distance of that number from zero on the number line. For example, the modulus of 5 is 5, while the modulus of -5 is also 5. This is because both 5 and -5 are located at a distance of 5 units from zero on the number line.

The modulus function can also be used to express the distance between two numbers. For example, the modulus of the difference between two numbers a and b is written as |a-b|. This gives the distance between the two numbers on the number line, regardless of their signs.

We are given that z = 4 - 2i.

The magnitude (absolute value) of a complex number a + bi is given by |a + bi| = √(a² + b²).

Therefore, we have:

|z| = |4 - 2i| = √(4² + (-2)²) = √20) = 2 √(5)

To find |2z| and |3z|, we multiply z by 2 and 3, respectively, and then take the magnitude:

|2z| = |2(4 - 2i)| = |8 - 4i| = √(8² + (-4)²) = √(80) = 4 √(5)

|3z| = |3(4 - 2i)| = |12 - 6i| = √(12² + (-6)²) = √(180) = 6 √(5)

Finally, we can investigate if |2z| = 2|z|:

|2z| = 4 √(5)

2|z| = 2(2 √(5)) = 4 √(5)

Since |2z| = 2|z|, this relationship holds true.

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The answer to the integral is (1/10) * x³ + (1/2) * x⁴ + C, where C is the constant of integration.

To evaluate the integral ∫(3x²/10 + 2x³) dx, we can apply the power rule of integration. The power rule states that the integral of x^n with respect to x is (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.

Using the power rule, we integrate each term separately:

∫(3x²/10) dx = (3/10) * ∫(x²) dx = (3/10) * (1/3) * x³ + C₁ = x³/10 + C₁

∫(2x³) dx = (2/1) * ∫(x³) dx = (2/1) * (1/4) * x⁴ + C₂ = (1/2) * x⁴ + C₂

Combining the integrals, we get:

∫(3x²/10 + 2x³) dx = x³/10 + (1/2) * x⁴ + C

Simplifying this expression, we can rewrite it as:

(1/10) * x³ + (1/2) * x⁴ + C

Therefore, the answer is B) (10 + 2x³)^(5/4) + C, which corresponds to (1/10) * x³ + (1/2) * x⁴ + C when expanded.

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a)  The general solution is expected to have terms proportional to x^(±1/2) and x^(±1).

b) The integration interval depends on the problem, but for this Sturm-Liouville problem it is typically taken to be [-1, 1].

c)   Cn is a normalization constant that ensures the polynomials are orthogonal

d)  We get:  Cn = [∫_{-1}^1 (4x² - 1)^(-1/2) [(d/dx)^n (x² - 1)^n]^2 dx]^(-1/2)

(a) For the differential equation (4x² - 1)y'' - 4xy' + λy = 0 to have at least one polynomial solution, we need to find values of λ such that the solutions are polynomials. One way to do this is by using the indicial equation:

r(r-1) + (-4x/r) + λ/(4x²-1) = 0

where r is the root of the indicial equation and represents the power of x in the solution. Solving for r, we get:

r = ± 1/2, ± 1

So the general solution is expected to have terms proportional to x^(±1/2) and x^(±1). To have at least one polynomial solution, we need to choose λ such that the term proportional to x^(±1/2) disappears. This happens when λ = n(n+1) for some non-negative integer n.

(b) The orthogonality condition for the eigenfunctions yn(x) is given by:

∫w(x) ym(x) yn(x) dx = 0

where w(x) is a weight function that satisfies certain conditions (for example, w(x) > 0 for all x in the integration interval). The integration interval depends on the problem, but for this Sturm-Liouville problem it is typically taken to be [-1, 1].

(c) Rodrigues' formula for the polynomials yn(x) is:

yn(x) = Cn (4x² - 1)^(-1/4) d^n/dx^n (x² - 1)^n

where Cn is a normalization constant that ensures the polynomials are orthogonal.

(d) To derive a general expression for yn(x), we need to determine the normalization constant Cn. This can be done using the orthogonality condition:

∫w(x) ym(x) yn(x) dx = δnm

where δnm is the Kronecker delta (equal to 1 if n = m and 0 otherwise). Using the weight function w(x) = (4x² - 1)^(-1/2), we have:

∫_{-1}^1 (4x² - 1)^(-1/2) ym(x) yn(x) dx = δnm

Substituting the expression for yn(x) from Rodrigues' formula and using integration by parts, we can show that:

Cn² ∫_{-1}^1 (4x² - 1)^(-1/2) [(d/dx)^n (x² - 1)^n]^2 dx = δnm

Solving for Cn, we get:

Cn = [∫_{-1}^1 (4x² - 1)^(-1/2) [(d/dx)^n (x² - 1)^n]^2 dx]^(-1/2)

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Answer:

x = 2

Step-by-step explanation:

3(5x + 2) = 8x + 20

open the parenthesis

15x + 6 = 8x + 20

subtract 8x from both sides of the equation

15x - 8x + 6 = 8x - 8x + 20

7x + 6 = 20

subtract 6 from both sides of the equation

7x + 6 - 6 = 20 - 6

7x = 20 - 6

7x = 14

divide both sides of the equation by 7

7x/7 = 14/7

x = 14/7

x = 2

Answer:

x=2

Step-by-step explanation:

3(5x+2)=8x+20

First, we distribute the 3.

15x+6=8x+20

Now we can subtract 8x from both sides of the equation.

7x+6=20

Next, we subtract 6 from both sides.

7x=14

Finally, we divide both sides by 7.

x=2

HTH :)

Answer: diamond

Step-by-step explanation:

The diamond symbol is used to indicate a condition that must be tested in a flowchart. It is used to represent a decision point, where the flow of the process will depend on the outcome of the test. The diamond symbol is typically used in conjunction with other symbols, such as arrows or ovals, to show the flow of the process.

Answer:

Step-by-step explanation:

(12-5)x4=28

The equation of the intersection of the sphere and the plane is:

(x-1)^2 + (y+5)^2 = 27.

The given equation of the sphere is:

(x-1)^2 + (y+5)^2 + (z-9)^2 = 36

The equation of the plane is:

z = 10

To find the equation of the intersection of the sphere and the plane, we substitute z = 10 into the equation of the sphere:

(x-1)^2 + (y+5)^2 + (10-9)^2 = 36

Simplifying:

(x-1)^2 + (y+5)^2 = 27

This equation represents a circle in the plane z = 10, where (x-1)^2 + (y+5)^2 = 27 is in the form of a circle equation: (x-a)^2 + (y-b)^2 = r^2. Here, (a, b) represents the center of the circle and r is the radius.

By comparing the given equation (x-1)^2 + (y+5)^2 = 27 with the standard form of a circle equation, we can conclude that the equation (x-1)^2 + (y+5)^2 = 27 represents the intersection of the sphere and the plane.

Therefore, the equation of the intersection of the sphere and the plane is:

(x-1)^2 + (y+5)^2 = 27.

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Answer:

.

Step-by-step explanation:

there has to be more to this question you csnt just guess the minutes

Answer:

What is the rate

Step-by-step explanation:

Answer:

Step-by-step explanation:

y= 20x+40

y- is the cost of rental

x-number of days

20 is the slope

40-flat rate and the y-intercept is at (0,40)

Answer:

A

Step-by-step explanation:

The correct inequality that represents the given situation is: A.) n - 87 < 320.

The situation states that Samuel played a video game and gained some points. Let's represent the points he gained as 'n'.

Next, it is mentioned that he lost 87 points. To represent this in the inequality, we subtract 87 from the initial points gained, which gives us 'n - 87'.

Finally, the situation specifies that Samuel finished with less than 320 points. This means that the final score, represented by 'n - 87', is less than 320.

This inequality represents that the initial points gained by Samuel (n) minus 87 points is less than 320 points, indicating that his final score is less than 320 points after losing 87 points.

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Answer:

the subtraction property of equality

Step-by-step explanation:

trust

Answer:

Subtraction

Step-by-step explanation:

1. Calculating the yearly and monthly property tax to determine if it will be a better deal to continue to rent or to purchase this home based on the monthly cash output is as follows:

2. To continue renting at $1,500 is less costly per month than buying the house with a monthly cash outflow of $1,525.50.

But the difference between renting and buying is minimal unless you factor in future maintenance costs.

The property tax per year is based on the assessed value multiplied by the mill rate and divided by 1,000.

The annual property tax is then divided by 12 to obtain the monthly property tax.

Home value = $248,000

Assessed value = $71,920 ($248,000 x 29%)

Mill rate = 32.45%

Yearly property tax = $2,334 ($71,920 x 32.45/$1,000)

Monthly property tax = $194.50 ($2,334/12)

                                       Renting     Purchase

Monthly payment           $1,500       $1,331

Property tax                                          194.50

Total monthly payment $1,500      $1,525.50

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QUESTION 17

STEP - BY - STEP EXPLANATION

What to find?

a12

Given:

a1= -8 d=-2

Step 1

Recall the nth formula for calculating the nth term.

n= 12

Step 2

Substitute the values into the formula and simplify.

ANSWER

-30

The empirical rule can be used to estimate the percentage of vehicles that are traveling between certain speeds on a highway. This rule is a statistical method for determining the proportion of data that lies within a certain number of standard deviations from the mean.

For normally distributed data, the empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
In this case, the mean speed of the sample of vehicles along the highway is miles per hour with a standard deviation of miles per hour. To estimate the percentage of vehicles whose speeds are between miles per hour and miles per hour, we need to determine how many standard deviations from the mean these speeds are.
First, we need to calculate the z-scores for the speeds of miles per hour and miles per hour.

The z-score for miles per hour is:
\(z = (x - μ) / σ = (55 - 60) / 5 = -1\)
The z-score for miles per hour is:

\(z = (x - μ) / σ = (65 - 60) / 5 = 1\)
These z-scores tell us how many standard deviations from the mean these speeds are. A z-score of -1 means that the speed of miles per hour is one standard deviation below the mean, while a z-score of 1 means that the speed of miles per hour is one standard deviation above the mean.
Since the data is bell-shaped and we are looking at speeds that are within two standard deviations from the mean, we can use the empirical rule to estimate the percentage of vehicles that are traveling between miles per hour and miles per hour.

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Answer:

y=4x+1

Step-by-step explanation:

I’m guessing the equation needed to be in the y=Mx+b form. If so, m is your slope and b is your y-intercept.

Answer:

y - 1 = 4 ( x - 0 )

Step-by-step explanation:

point slope form

Below is the picture attached for the five vectors in span {bold v1 v1, bold v2 v2}.

Given a subspace S, every basis of S contains the same number of vectors; this number is the dimension of the subspace. To find a basis for the span of a set of vectors, write the vectors as rows of a matrix and then row reduce the matrix. The span of the rows of a matrix is called the row space of the matrix.

Then any linear combination of all three vectors is also a linear combination of the first two, so the span of all three is the same as the span of the first two, i.e. it is the set of all vectors in the plane. Case 3: no plane contains all three vectors. (So the vectors are all 3-space vectors.)

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The value of the test statistic used to test the claim is -2.00.

And, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

Now, If a two-sided test of hypothesis is conducted at a 0.05 level of significance and the test statistic resulting from the analysis was 1.23, the potential type of statistical error is Type II error.

A Type II error occurs when we fail to reject a false null hypothesis, meaning that we conclude there is no significant difference or effect when there actually is one.

To answer the second question, we can perform a one-sample t-test to test the claim that the mean GPA for Psychology students at a certain college is less than 3.2.

The hypotheses are:

H₀: μ = 3.2

Ha: μ < 3.2

where μ is the population mean GPA.

We can use the t-statistic formula to calculate the test statistic:

t = (x - μ) / (s / √n)

where, x is the sample mean GPA, s is the sample standard deviation, n is the sample size, and μ is the hypothesized population mean.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

Therefore, the value of the test statistic used to test the claim is -2.00.

Since this is a one-tailed test with a significance level of 0.05, we compare the t-statistic to the critical t-value from a t-table with 48 degrees of freedom.

At a significance level of 0.05 and 48 degrees of freedom, the critical t-value is -1.677.

Since the calculated t-statistic (-2.00) is less than the critical t-value (-1.677), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean GPA for Psychology students at the college is less than 3.2.

To calculate the p-value of the test, we can perform a one-sample t-test using the formula:

t = (x - μ) / (s / √n)

where x is the sample mean GPA, μ is the hypothesized population mean GPA, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

The degrees of freedom for this test is 49 - 1 = 48.

Using a t-distribution table or calculator, we can find the probability of getting a t-value as extreme as -2.00 or more extreme under the null hypothesis.

Since this is a two-sided test, we need to find the area in both tails beyond |t| = 2.00. The p-value is the sum of these two areas.

Looking up the t-distribution table with 48 degrees of freedom, we find that the area beyond -2.00 is 0.0257, and the area beyond 2.00 is also 0.0257. So the p-value is:

p-value = 0.0257 + 0.0257

p-value = 0.0514

Rounding to three decimal places, the p-value of the test is 0.051.

Therefore, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

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Answer:

22

Step-by-step explanation:

You use the order of operations: PEMDAS.

Sooo...

4*6-8/4=

24-8/4=

24-2=

22

Answer: 24

Step-by-step explanation:

We can use the pythagorean theorem to solve for the missing side.

Let the missing side be x.

Then, x^2 + 10^2 = 26^2.

x^2 + 100 = 676

Subtract 100 from both sides:

x^2 = 576

Square root both sides:

x = 24

Answer:

24

Step-by-step explanation:

~ Formula ~

a² + b² = c ²

Solve:

Let,

a² = 10

c² = 26

Thus,

a² + b² = c²

10² + b² = 26²                                 { ² means # × # Not # × 2 }

100 + b² = 676                                {Subtract both sides by 100}

b² = 576                                       {Square Root}

576 = 24²

= √24 ²

Apply radical rule - n √aⁿ = a

√24 ² = 24  

Answer = 24

Check Answer:

a² + b² = c²

10² + 24² = 26²

100 + 576= 676 ☑

Kavinsky