A normal population has known mean u = 75 and variance o = 5. What is the approximate probability that the sample variance is greater than or equal to 7.442 less than or equal to 2.56? For a random sample of size a. n= 16 b. n=30 c. Compare your answers to parts (a)-(b) for the approximate probability that the sample variance is greater than or equal to 7.44. Explain why this tail probability is increasing or decreasing with increased sample size. d. Compare your answers to parts (a)-(b) for the approximate probability that the sample variance is less than or equal to 2.56. Explain why this tail probability is increasing or decreasing with increased sample size.

From the given information provided, the equation of the line using slope form method is y = -2x.

Equation of the line using the two point slope form:

(0,0) and (4, -2)

The two-point slope form is a method for finding the equation of a straight line given two points on the line.

Let (x₁, y₁) and (x₂, y₂) be two points on a line, and let m be the slope of the line. The equation of line in the slope-intercept form is given by:

y - y₁ = m(x - x₁)

y - 0/x - 0 = 4-0/ -2-0

y/x = -2

y = -2x

option b, y = -2x

Question - What is equation of following line? see all answer options. a. y = -1/4x b. y = -2x c. y = -1/2x d. y = 4x y = 1/2x?

Learn more about slope here: brainly.com/question/3493733

#SPJ4

Answer: 1. 64 | 2. 32

Step-by-step explanation:

Formula for a rectangle is Area = Length*Width

Therefore: 8*8 = 64

Formula for a triangle is Area = 1/2*Base*Height, which is also 1/2*length*width

Therefore: 1/2*8*8 = 32

Hope this helps :)

Answer:

-2

Step-by-step explanation:

From the graph, it appears that (0, 2) and (2, -2) are points on the line.  (Othere points will work, as well; you just need two points.)

Slope = (difference between the y coordinates) / (difference between the x coordinates)

One phrase to remember this is slope = "rise over run"  (vertical change divided by horizontal change from point to point).

Slope = (-2 - 2) / (2 - 0) = -4 / 2 = -2

The slope is -2.

Variance is a useful tool for gaining a deeper understanding of a dataset beyond just the mean.

Variance is a measure of how far the individual values in a set of data are from the average value.

The variance is calculated by first finding the difference between each value in the dataset and the mean, squaring these differences, and then averaging the squared differences.

The result is a non-negative number that indicates how far, on average, each value deviates from the mean. If the variance is small, it means that most of the values are close to the mean, while a large variance indicates that the values are widely spread out.

One important use of variance is in statistical inference, where it is used to make predictions about a population based on a sample of data. Variance also plays a role in hypothesis testing, where it is used to determine whether the differences between two sets of data are statistically significant.

To know more about average here

https://brainly.com/question/16956746

#SPJ4

A = 42°

B= 23°

F = 115°

Step-by-step explanation:

The required measures of the three angles in triangle ABF are A = 23°, B = 42°, and F = 115°.

Alternate Interior Angles are defined as the pair of angles created on the inner side of the parallel lines

Given that Lines AB and CD are parallel.

To determine the measures of the three angles in triangle ABF.

For finding ∠F,

∠CDF = 180° - 157° = 23°

∠F = 180° - ∠C - ∠CDF

∠F = 180° - 42° - 23°

∠F = 115°

However, if a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

So ∠A = ∠CDF = 23°

And ∠B = ∠C = 42°

Thus, the required measures of the three angles in triangle ABF are A = 23°, B = 42°, and F = 115°.

Learn more about Alternate Interior Angles here:

brainly.com/question/2125016

#SPJ2

Answer:

Cost of car including VAT = $17,700

Step-by-step explanation:

Given:

Cost of car without VAT = $15,000

Rate of VAT = 18%

Find:

Cost of car including VAT

Computation:

Cost of VAT = Cost of car without VAT x Rate of VAT

Cost of VAT = 15,000 x 18%

Cost of VAT =  15,000 x 18

Cost of VAT = $2,700

Cost of car including VAT = Cost of car without VAT + Cost of VAT

Cost of car including VAT = 15.000 + 2700

Cost of car including VAT = $17,700

Answer: he is correct

Step-by-step explanation:

40 x 1.2 = 48        

40:48  

divided by 8

=5.6

Answer:

1st. 1/4

2nd. Not proportional

Step-by-step explanation:

Answer:

both are not proportional

Step-by-step explanation:

16 : 4 = 16/4 = 4

20 : 5 = 20/5 = 4

9 : 36 = 9/36 = 1/4

not the same so NOT proportional

4 : 12 = 4/12 = 1/3

5 : 20 = 5/20 = 1/4

9 : 45 = 9/45 = 1/5

not the same so NOT proportional

The number of potatoes peeled by Tom was 36 potatoes after peeling a pile of 64 potatoes

An equation is an expression that shows the relationship between two or more variables and numbers.

Let t represent the time after Tom joined.

number of potatoes peeled by Ben = 2(5 minutes) + 2t = 2t + 10

number of potatoes peeled by Tom = 4t

Since they are 64 potatoes, hence:

2t + 10 + 4t = 64

t = 9 minutes

number of potatoes peeled by Tom = 4(9) = 36 potatoes

The number of potatoes peeled by Tom was 36 potatoes after peeling a pile of 64 potatoes

Find out more on equation at: https://brainly.com/question/2972832

The independent variable in either a before/after t-test or a within-subjects ANOVA is always measured on a nominal or categorical scale.

This is because these statistical tests are used to compare means of two or more related groups, where the independent variable represents the different conditions or time points in which the dependent variable is measured.

For example, in a before/after t-test comparing the effectiveness of a medication, the independent variable would be the two time points (before and after), which are categorical in nature. Similarly, in a within-subjects ANOVA comparing three different treatment conditions, the independent variable would be the three treatment conditions, which are nominal in nature.

Learn more about statistical tests

https://brainly.com/question/14128303

#SPJ4

The number of voters that should be sampled for a confidence interval depends on the desired level of confidence and the margin of error.

A larger sample size generally leads to a smaller margin of error and a higher level of confidence in the accuracy of the results. However, the relationship between sample size and margin of error is not linear, meaning that doubling the sample size will not necessarily halve the margin of error.
To calculate the required sample size, a formula can be used that takes into account the margin of error, level of confidence, and population size.
the number of voters that should be sampled for a confidence interval depends on several factors and cannot be determined without more information.
To determine the required sample size, you can use the following formula:
n = (Z^2 * p * (1-p)) / E^2

Where:
- n is the sample size
- Z is the Z-score (usually 1.96 for a 95% confidence interval)
- p is the estimated proportion of the population (usually 0.5 for the worst-case scenario)
- E is the margin of error (in decimal form)

Hence, without the specific margin of error, we cannot provide the exact sample size needed.

learn more about confidence interval click here:

https://brainly.com/question/20309162

#SPJ11

Answer:

15x^3 - 28x^2 + 18x -4

Step-by-step explanation:

(3x-2) (5x^2-6x+2)

\(15x^3 -18x^2 +6x - 10x^2 + 12x - 4\)

\(15x^3 - 28x^2 + 18x -4\)

Answer:

I just wanna steal your points :)

Step-by-step explanation:

The correct answer is (C) g'(-6).

We have to use the Chain Rule of Differentiation in order to find h'(-2).

Therefore, we have:

h(x) = f(g(x))

So,

h'(x) = f'(g(x)) \cdot g'(x)

The expression above can be written as:

h'(x) = f'(u) \cdot g'(x)

where $u = g(x)$.

Now, let's find h'(-2):

h'(-2) = f'(u) \cdot g'(-2)

We have been given that g(-2) = 6 and g'(-2) = 8.

However, we still need to know f'(u) in order to calculate h'(-2).

Therefore, the correct answer is (C) g'(-6).

Know more about Differentiation here:

https://brainly.com/question/954654

#SPJ11

Answer:

- The angles in the triangle DEF must all be acute angles- angles smaller than a right angle (90 degrees) to prove an acute isosceles triangle. - The angles in the triangle DEF must all be acute angles- angles smaller than a right angle (90 degrees) to prove an acute isosceles triangle

Answer:

Question: Which characteristics will prove that ΔDEF is an acute, isosceles trianglle?

Step-by-step explanation:

Correct Choice: segment DE and segment EF are congruent to each other but not to segment DF, and their slopes are not related.

I took the test and got it right.

Step-by-step explanation:

wow, how complicated can one phrase this ...

the point being :

1 ft = 12 in and vice versa (1 in = 1/12 ft)

so, any measurements given in feet but needed in inches need to be multiplied by 12.

and any measurements given in inches but needed in feet need to be divided by 12.

so,

3.5 ft = 3.5×12 = 7/2 × 12 = 7×6 = 42 in

27 in = 27/12 = 9/4 = 2 1/4 or 2.25 ft

Answer:When converting from inches to feet, the measurement in inches, m, of an object varies directly with its measurement in feet, f, with the constant of variation being 12.

What is the equation relating these two quantities?

✔ m = 12f

How many inches would a 3.5-foot object measure?

✔ 42

inches

How many feet would a 27-inch object measure?

✔ 2.25

feet

Step-by-step explanation:

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

Learn more about line tangent: brainly.com/question/30162650

#SPJ11

The element of the discrete sequence corresponding to the given function is 7n + 15.

Given, T = 1.4 sec and f(t) = 5t with k = 3.

So, we need to find the element of the discrete sequence corresponding to the given function.

We know that the formula for the nth term of a discrete sequence is given by:

\($$a_n = f(nT + k)$$\)

Here, T = 1.4 sec and k = 3

Substituting these values in the above formula, we get:

\($$a_n = f(nT + k)$$$$a_n = f(n(1.4) + 3)$$ $$a_n = 5(n(1.4) + 3)$$ $$a_n = 7n + 15$$\)

Therefore, the element of the discrete sequence corresponding to the given function is 7n + 15.

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

X is an algebraic variable which has no defined value. X is kind of universe variable taken in most of the equations.

The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.

Solution:

Given: - 5x - 15 > 10 + 20x

Let us solve the inequality by isolating the variable x.

Add 5x on both sides

- 5x - 15 + 5x > 10 + 20x + 5x

- 15 > 10 + 25x

Subtract 10 from both sides

- 15 - 10 > 10 - 10 + 25x

- 25 > 25x

Divide both sides by - 25

-1 > x

x < - 1

The value of x in the solution set of - 5x - 15 > 10 + 20x is x < - 1 and the required value from the solution set is -2.

To learn more about algebraic variable visit:

https://brainly.com/question/10638093

#SPJ4

Answer:

-2

Step-by-step explanation:

i did it

Answer:

    (a, b) ∈ {(1, 729), (3, 243), (9, 81), (27, 27), (81, 9), (243, 3) (729, 1)}

Step-by-step explanation:

\(\sqrt{a\cdot b}=27\\\\(\sqrt{a\cdot b})^2=27^2\\\\a\cdot b=729\\\\\\729=27\cdot27=9\cdot81=3\cdot243=1\cdot729\)

So:

(a, b)∈{(1, 729), (3, 243), (9, 81), (27, 27), (81, 9), (243, 3) (729, 1)}

By using concept of interior angle we find the value of X is -7.14 degrees.

The above problem involves finding the value of x in a triangle with two known angles measuring 78° and 152°.

The sum of the interior angles of any triangle is always 180°, so we can use this fact to set up an equation involving the third angle, which is given as 7x +3 degrees.

To solve for x, we first simplify the equation by combining the known angles:

78° + 152° + (7x + 3)° = 180°

Next, we can simplify by adding the two known angles:

230° + 7x° = 180°

This simplifies to:

7x° = -50°

Finally, we can solve for x by dividing both sides by 7:

x =  \(\frac{-50^\circ}{7}$$\)

Therefore, x is approximately -7.14 degrees.

To learn more about interior angles refer here:

https://brainly.com/question/10638383

#SPJ11

Answer:

A. y= 1x + 5

Step-by-step explanation:

Answer:

A. y=x+5

Step-by-step explanation:

(0,5):

x=0

y=(0)+5=5

(3,8):

x=3

y=(3)+5=8

I hope this help you

The "hypothesis of no change," "status quo," and "conventional wisdom" are all alternative names for the null hypothesis. Unless there is overwhelming evidence to the contrary, the null hypothesis is assumed to be correct.

H0: u = 1: u ≠ 1,400

When testing hypotheses with the P value, the null hypothesis is rejected if?

The evidence against the null hypothesis is stronger when the p-value is smaller (closer to 0).If the p-esteem is not exactly or equivalent to the predetermined importance level α, the invalid speculation is dismissed;The null hypothesis is not rejected otherwise.

A statement of expectation or prediction that will be tested by research is called a research hypothesis. Read up on the subject that interests you before coming up with your research hypothesis.

Learn more about hypothesis here:

https://brainly.com/question/13025783

#SPJ4

Where C1 and C2 are constants that can be determined from initial conditions.

a(d^2y/dt^2) + b(dy/dt) + cy = 0

where a, b, and c are constants.

To solve this equation, we assume that the solution has the form:

y = e^(rt)

where r is a constant. We substitute this form of the solution into the differential equation and get:

a(r^2)e^(rt) + b(re^(rt)) + ce^(rt) = 0

We can factor out e^(rt) from this equation to get:

e^(rt)(ar^2 + br + c) = 0

Since e^(rt) is never zero, we can divide both sides of the equation by e^(rt) to get:

ar^2 + br + c = 0

This is called the characteristic equation of the differential equation. We can solve for r by using the quadratic formula:

r = (-b ± sqrt(b^2 - 4ac)) / 2a

There are three possible cases for the roots of the characteristic equation:

If the discriminant (b^2 - 4ac) is negative, then the roots are complex conjugates of the form r = α ± iβ, where α and β are real numbers. In this case, the general solution is:

y = e^(αt)(C1cos(βt) + C2sin(βt))

If the discriminant is zero, then the roots are repeated and of the form r = -b / 2a. In this case, the general solution is:

y = e^(rt)(C1 + C2t)

If the discriminant is positive, then the roots are real and distinct. In this case, the general solution is:

y = C1e^(r1t) + C2e^(r2t)

where r1 and r2 are the roots of the characteristic equation.

Now let's apply this method to the given differential equation:

d^2y/dt^2 - 2(dy/dt) + 5y = 0

The coefficients are a = 1, b = -2, and c = 5. The characteristic equation is:

r^2 - 2r + 5 = 0

Using the quadratic formula, we get:

r = (2 ± sqrt(4 - 4(1)(5))) / 2

r = 1 ± 2i

Since the roots are complex conjugates, the general solution is:

y = e^t(C1cos(2t) + C2sin(2t))

Therefore, the general solution to the differential equation is:

y = C1e^(2t)sint + C2e^(2t)cost

where C1 and C2 are constants that can be determined from initial conditions.

To learn more about discriminant visit:

https://brainly.com/question/15884086

#SPJ11

Answer:

If Kiran is 15 years old: His aunt is 32

If Kiran is 30 years old: His aunt is 47

If Kiran is x years old: His aunt is x + 17

If Kiran's aunt is 60 years old: Kiran is 43

Step-by-step explanation:

Hello!

We know that Kiran's aunt is 17 years older than Kiran. So their difference in ages is 17 years.

A)

If Kiran is 15, Kiran's aunt will be his age plus 17 years, so:

If Kiran is 30, Kiran's aunt will be his age plus 17 years, so:

If Kiran is x years old, Kiran's aunt will be his age plus 17 years, so:

Nothing can be simplified further

If Kiran's aunt is 60, Kiran will always be 17 years younger than his aunt.

So:

Kiran would be 43 years old.

Answer:

\(12x^{2}+272x+320=10560\)

Step-by-step explanation:

Start by setting the width = x.

Length is equal to x+20.

We know the cost of the land was $12 per square foot (area) and the cost of the fence around the perimeter is equal to $8 per foot.  This gives us two equations we need to work with.

$12(x*(x+20)) + $8((2*x)+(2*(x+20))) = 10560.  It looks a little difficult to read but as we distribute the cost throughout the equations, we see it start to take shape.

12(x^2+20x) + 8(2x+2x+40) = 10560

12x^2+240x+16x+16x+320 = 10560

12x^2+272x+320=10560

The roots of our equation here are x=20, and x = -128/3

Since we know that area is not negative, our answer is x=20.

Check the work: 12(20)^2 + 272(20) +320 = 10560

Answer:

this is a positive correlation

Step-by-step explanation:

it is going up so its positive

Answer:

  y = 4·4^x

Step-by-step explanation:

We can write the exponential function in the form ...

  y = a·b^x

The y-value for x=0 is 4, so that is the multiplier 'a' in our equation.

The ratio of values between x=1 and x=0 is 16/4 = 4, so that is the value of 'b' in the equation. The equation is ...

  y = 4·4^x

_____

Additional comment

This could also be written ...

  y = 4^(x+1)

__

Consider the values for x=0 and x=1.

  x=0: y = a·b^0 = a

  x=1: y = a·b^1 = ab

Then the ratio of values is (ab)/(a) = b.

This is the fact that we used in the above working.

Answer: 5

Step-by-step explanation: