State a research question, null hypothesis, and alternate hypothesis for gpa anc Step 2: Write Section 2 of the DAA: Testing Assumptions Test for one of the assumptions of correlation - normality. • Create a descriptive statistics table in statistical software to assess normality. Th include the four variables named above, including skew and kurtosis for each va • Paste the table in the DAA Template. • Interpret the skewness and kurtosis values and determine whether the assumpti normality was violated or not violated. Step ​

The combination is evaluated to give 20

From the information given, we have the expression as;

⁵C₁

The formula for calculating combination is expressed as;

ⁿCᵣ = n! / (r!(n-r)!)

Such that the parameters of the formula are expressed as;

Now, substitute the values into the formula, we have;

⁵C₁ = 5! / (1!(5-1)!)

= 5! / (1! × 4!)

Find the permutation, we have;

= (5 × 4 × 3 ×2 × 1) / (1 × (4 × 3 × 2 × 1))

Divide the values, we get;

= 20 / 1

Find the value

= 20

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Given two points (7,-2) and (-3,-10), we can determine the slope of the line passing through them as follows:

slope = (y2 - y1) / (x2 - x1)

slope = (-10 - (-2)) / (-3 - 7)

slope = -8 / -10

slope = 4 / 5

Since we want a line perpendicular to this line, we need to find its negative reciprocal. The negative reciprocal of 4/5 is -5/4.

Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the point (-8,-12), we can substitute the values into the equation:

y - (-12) = -5/4(x - (-8))

y + 12 = -5/4(x + 8)

Simplifying, we get:

y + 12 = -5/4x - 10

y = -5/4x - 22

Therefore, the equation of the perpendicular line passing through the point (-8,-12) is y = -5/4x - 22 in point-slope form.

Measure of one exterior angle = 30 degree

Measure of one interior angle = 150 degree

In the given regular pentagon

Number of terms = 12

We know that,

Sum of all exterior angles = 360 degree

To find one exterior angle,

Divide the complete angle by number of terms

Therefore,

One exterior angle = 360/12  =  30 degree

Since,

Sum of all interior angles = 180 degree

And To find one interior angle,

subtract the interior  angle by one exterior angle

Therefore,

One exterior angle = 180 - 30  =  150 degree

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The solution of the system of equations is (-3, 1)

Here we want to solve the system of equations:

y = (2/3)x + 3

y = - (4/3)x - 3

To do it, we need to graph both of the lines in the same coordinate axis and find the point where the two lines intersect.

In the image at the end you can see the graph of the system, there we can see that the lines intercept at the point (-3, 1), so that is the solution of the system

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The area of the given triangle, given the height and the type of triangle would be E. 16 cm ²

To find the area of an equilateral triangle when given just the height, the formula is:

= ( height ² x  √ 3 ) / 2

We are given a height of 4 cm.

The area of the triangle is therefore :

= ( height ² x  √ 3 ) / 2

= ( 4 cm ² x  √ 3 ) / 2

= ( 16 x  √ 3 ) / 2

=  27. 712 / 2

= 13. 85

The closest option is 16 cm ² so this is the answer.

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Answer:

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Step-by-step explanation:

Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:

In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.

The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.

Which of these could be a step to prove that BC2 = AB2 + AC2?

Answer:

x < 6

Step-by-step explanation:

3x < 18 ( divide both sides by 3 )

x < 6

An equation relating to P to N include the following: P(N) = 16.75N - 650.

In Mathematics, profit is a measure of the amount of money generated when the selling price is deducted from the cost price of a good or service, which is usually provided by producers.

Mathematically, the amount of profit made from selling x number of books can be calculated by using the following function:

Profit made = Revenue earned – Cost of production (cost price)

P(N) = R(N) - C(N)

P(N) = 33.70N - (650 + 16.95N)

P(N) = 33.70N - 650 - 16.95N

P(N) = 16.75N - 650

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Answer:

The correct answer is b) f^-1(n)= 4/-n-1 +1.

b

Step-by-step explanation:

I think parentheses are missing :

y = -4/(n-1)  - 1       switch n and y   then solve for y

n = -4/(y-1) - 1         add 1 to both sides of the equation

n+1 = - 4/(y-1)         multiply through by y -1

(y-1)(n+1) = - 4         divide through by (n+1)

y -1   = - 4/ (n+1)      add 1 to both sides

y = - 4/ (n+1 )  + 1     <=====this is the inverse function  y = -4/(n-1) -1

   equivalent to   4 / (-1-n)  + 1        by putting the ' - ' in the denominator

The variables for this problem are given as follows:

a = 16, [tex]b = 16\sqrt{2}[/tex] , c = 16, d = 16.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For side lengths a and c, we have a right triangle with angles of 45º, hence using the 45-45-90 Triangle Rule, with the hypotenuse of [tex]16\sqrt{2}[/tex], the lengths a and c are given as follows:

a = c = 16.

The length a is also the geometric mean of the lengths c and d, hence:

16² = 16d

d = 16.

Then the length b is obtained applying the Pythagorean Theorem as follows:

b² = 16² + 16²

[tex]b = \sqrt{2 \times 16^2}[/tex]

[tex]b = 16\sqrt{2}[/tex]

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1. The area of the fort is 27 square feet.

2. No, Carlos was not correct

3.  The correct way to determine the area is to multiply the length and width, not add them. Carlos' mistake was in incorrectly calculating the area of the fort.

1. The area of the fort can be calculated by multiplying the length and width of the rectangle. In this case, the length is 6 feet and the width is 4.5 feet. Therefore, the area can be calculated as:

Area = Length × Width

= 6 feet × 4.5 feet

= 27 square feet

So, the area of the fort is 27 square feet.

2. No, Carlos was not correct. The actual area of the fort is 27 square feet, not 13.5 square feet as he determined.

3. Carlos made a mistake in his calculation. Instead of multiplying the length and width together, he likely mistakenly multiplied them as if he was finding the perimeter or added them together. The correct way to determine the area is to multiply the length and width, not add them. Carlos' mistake was in incorrectly calculating the area of the fort.

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The flux of material past x = 0 is zero for all times.

The flux of material past x = 0 can be calculated by integrating the product of density and velocity over the spatial domain.

This is calculated as;

Φ = ∫ ρv dx

ρ = exp[cos(t − x)]

v = sin(t − x)

where;

The flux of material past x = 0 is calculated as;

Φ = ∫ exp[cos(t − x)] sin(t − x) dx

∫ exp[cos(t − x)] sin(t − x) dx, is the integration of an odd function over a symmetric interval [-π, π] which is zero.

Φ = ∫ exp[cos(t − x)] sin(t − x) dx = 0

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The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.

The Central limit theorem is used to find the probability

Data given:

sample size = 5.

mean, μ = 9.70 ounces

standard deviation, σ = 0.03 ounce.

To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.

x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

For the sample mean of 9.65 ounces in 5 boxes:

z = (9.65 - 9.70) / (0.03 / √5)

z ≈ -0.05 / (0.03 / √5)

Using a calculator, we find that the probability is approximately 0.4801.

Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.

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Hello!

It's a division.

17  I  6

-12 I   2

  5

the dividende = 17

the divider = 6

the quotient = 2

the rest = 5

17 = 2 x 6 + 5

Answer:

A

Step-by-step explanation:

We can factor 625x^4 - 81 by recognizing it as the difference of two squares:

625x^4 - 81 = (25x^2)^2 - 9^2

This can be further simplified using the formula for the difference of squares, which states that:

a^2 - b^2 = (a + b)(a - b)

In this case, a = 25x^2 and b = 9, so we have:

(25x^2 + 9)(25x^2 - 9)

We can then use the difference of squares formula again to factor 25x^2 - 9:

25x^2 - 9 = (5x)^2 - 3^2 = (5x + 3)(5x - 3)

Substituting this into our original expression, we get:

625x^4 - 81 = (25x^2 + 9)(25x^2 - 9) = (25x^2 + 9)(5x + 3)(5x - 3)

Therefore, the fully factored form of 625x^4 - 81 is (25x^2 + 9)(5x + 3)(5x - 3). Answer: (A) (5x - 3)(5x - 3)(25x² + 9)

The solution is: the interest rate and principal is 6% and Rs 65,000

The interest rate, r = 6% and the principal, P = Rs 65,000

Here, we want to find the interest rate and principal

Compound interest:

A = P(1 + r/n)^t

Simple interest :

I = P * r * t

Simple interest for 2 years = Rs 7800

Simple interest for 1 year = Rs 7800 / 2

= Rs 3900

Compound interest for 2 years = Rs 8034

Compound interest for the second year = Rs 8034 - Rs 3900

= Rs 4134

Interest on Rs 3900 = Rs 4134 - Rs 3900

= Rs 234

Therefore,

Interest rate, r = 234/3900 × 100

= 0.06 × 100

r = 6%

Recall,

Simple interest :

I = P * r * t

Then,

P = I / r * t

= 3900 / 6% * 1

= 3900 / 0.06

= 65,000

P = Rs 65,000

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complete question:

compound interest on a sum of money for 2 years compounded annually is Rs 8034 simple interest on the same sum for the same period and at the same rate is Rs 7800 find the sum and the rate of interest​

The mass of the 405 cm³ milk is 417.15 grams.

Density is simply  the mass of a substance per unit volume.

It is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

Density of the milk p =  1.03g/cm³

Volume of the milk v = 405 cm³

Mass m = ?

Plug the values into the above formula and solve for mass m.

p = m / v

m = pv

m = 1.03g/cm³ × 405 cm³

m = 417.15 g

Therefore, the value of the mass is 417.15 grams.

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The probability that at least one barrel develops a leak over a 20-year period is approximately 0.1813 or 18.13%.

Since leaks in different barrels are independent, the probability that none of the 10,000 barrels develops a leak in a given year is:

0.99999¹⁰⁰⁰⁰ = 0.9048

Therefore, the probability that at least one barrel develops a leak in a given year is:

1 - 0.9048 = 0.0952

Now we can use the same approach to find the probability that no barrel develops a leak in 20 years:

0.99999²⁰⁰⁰⁰⁰ = 0.8187

Therefore, the probability that at least one barrel develops a leak over a 20-year period is:

1 - 0.8187 = 0.1813

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We can see here the proof of complex functions to geometry was contributed by the Norwegian mathematician Caspar Wessel.

A complex function is one that accepts a complex number as input and outputs another complex number. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain.

Wessel demonstrated in his article that complex functions and complex numbers may both be used to represent curves and points in the plane. This research was a significant advancement in the field of complex analysis and opened the path for its growth into a potent instrument for addressing geometric problems.

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The perimeter of the square that is given in the diagram above would be = 96cm

To calculate the perimeter of a square, the formula for the perimeter of a square should be used and this is given below.

That is ;

perimeter = 4a

where ;

a = side length = 24cm

Perimeter = 4× 24 = 96cm

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The value of angle ABC in the equilateral triangle formed by points D, E, and C, given angle EAB is 80°, is 50°.

Let's solve the problem step by step:

In an equilateral triangle, all three angles are equal. Let's denote the measure of angle ABC as x.

Since the triangle is equilateral, angle BAC is also equal to x.

The sum of angles in a triangle is

=180°

Therefore, we can write the equation:

= x + 80 + x = 180.

Simplifying the equation, we have:

= 2x + 80 = 180.

Subtracting 80 from both sides:

= 2x = 100.

Dividing both sides by 2:

=x = 50.

Thus, angle ABC measures 50°.

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The complete question is:

The shaded triangle formed by points D, E and C is equilateral. If angle EAB is 80°, then what is the value of angle ABC? Give your answer in degrees (°).

a. The standard deviation of the tuition is  $150.

b. The shape of this distribution is a normal distribution, which is a bell-shaped curve.

(a) The mean tuition is $100 per credit hour * 15 credit hours per semester + $150 lab fee = $1650 per semester.

The standard deviation of the tuition is l:

= ✓(100² + 150²) =

= ✓22500

= $150.

(b) The shape of this distribution is a normal distribution, which is a bell-shaped curve. The mean is the center of the distribution, and the standard deviation is the width of the distribution. The majority of the tuitions will be close to the mean, with fewer and fewer tuitions as you move further away from the mean.

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The graph of the function |x| + 1 < 3 is plotted and attached

The graph is an absolute value graph merged with inequality. hence the attributes of inequality which involves shading of the graph will be seen in the graph

To create a table of values for the inequality |x| + 1 < 3, we can evaluate the inequality for each value of x within that range.

For x = -2:

|(-2)| + 1 < 3

2 + 1 < 3

3 < 3

This inequality is not true for x = -2.

For x = -1:

|(-1)| + 1 < 3

1 + 1 < 3

2 < 3

This inequality is true for x = -1.

For x = 0

|(0)| + 1 < 3

0 + 1 < 3

1 < 3

This inequality is true for x = 0.

For x = 2:

|(2)| + 1 < 3

2 + 1 < 3

3 < 3

This inequality is not true for x = 2.

Therefore, the values of x  that satisfy the inequality |x| + 1 < 3 are: x = -1 and x = 0.

the graph is attached

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We can see that (a^2+b^2)(x+y) - (a^2y+b^2x) simplifies to zero, which means the expression is true. Therefore, the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x) holds.

To verify the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x), we need to simplify the expression on both sides and show that they are equal.

Expanding (a^2+b^2)(x+y) using the distributive property, we get:

(a^2+b^2)(x+y) = a^2x + a^2y + b^2x + b^2y

Expanding (a^2y+b^2x), we have:

(a^2y+b^2x)

Now, let's subtract (a^2y+b^2x) from (a^2x + a^2y + b^2x + b^2y):

(a^2x + a^2y + b^2x + b^2y) - (a^2y+b^2x)

We can observe that the terms involving 'x' and 'y' cancel each other out:

(a^2x - b^2x) + (a^2y - a^2y) + (b^2y - b^2y)

= 0 + 0 + 0

= 0

We can see that (a^2+b^2)(x+y) - (a^2y+b^2x) is being simplified to zero, which means that the expression is true. Therefore, the polynomial identity (a^2+b^2)(x+y) - (a^2y+b^2x) holds.

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The surface area of the prism given is 362 m².

Given is a prism.

We have to find the total surface area of the prism.

The given prism has to be divided in to various other known figures to find the total area.

By drawing a line vertically through the top of the prism, we get two rectangular prism.

Surface area of a rectangular prism = 2 [lw + wh + lh], where l, w and h are length, width and height respectively.

Surface area of big rectangular prism = 2[(6 × 6) + (6 × 7) + (6 × 7)]

                                                               = 240 m²

Surface area of smaller rectangular prism = 2[(3 × 4) + (4 × 7) + (3 × 7)]

                                                                      = 122 m²

Total area of the prism = 240 m² +  122 m²

                                      = 362 m²

Hence the surface area is 362 m².

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Answer:

1500

Step-by-step explanation:

Hello!

x = number of caps of Mel

36 - x = 2(12 + x)

36 - x = 24 + 2x

36 - 24 = 2x + x

12 = 3x

x = 12/3

x = 4

The answer is 4.

verification:

36 - 4 = 32

12 + 4 = 16

16 x 2 = 32 or 32/2 = 16

it's correct.

Answer:

79632 cu ft

Step-by-step explanation:

The volume of a rectangular prism is length x width x height. We are given the values 158 ft by 80 ft by 6.3 ft. All we do is multiply all 3 values by each other, (158)(80)(6.3). The answer after multiplying is 79632 cubic feet.

The different features for the graphs of f(x) and g(x) is given as follows:

C. y-value when x = 5.

To obtain the numeric value of a function or even of an expression, we must substitute each instance of the variable of interest on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The numeric value for the function f(x) at x = 5 is given as follows:

f(5) = 5² = 25.

The numeric value for the function g(x) at x = 5 is given as follows:

g(5) = 3 x 5² = 75.

The options are given as follows:

A. location of the vertex

B. axis of symmetry

C. y-value when x = 5

D. direction parabola opens

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