Find the x- and y-intercepts of the graph of x + 4y = 20. State each answer as an I refer or an improper fraction in simplest form.

The slope in a least-squares regression line of the form y = a bx is equal to the coefficient b. This coefficient represents the rate of change in the dependent variable (y) for every one unit increase in the independent variable (x).

Specifically, it represents the change in y divided by the change in x, as b is calculated as the covariance between x and y divided by the variance of x.

This slope is important in understanding the relationship between the variables being studied and can help to make predictions about future values of the dependent variable based on changes in the independent variable.

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For function f(x, y, z) = -6xy - 4xz - 10yz, we need to evaluate the value of f(8, -12, 14). The function takes three variables as input, we substitute the given values into the function to obtain the numerical result.

The explanation below will provide the step-by-step process to calculate the value of f(8, -12, 14).To find the derivative of h(x) = (5x)(-x^2 + 5)^4, we'll use the power rule and the chain rule. Let's start by applying the power rule to the outer function:

h'(x) = 5(-x^2 + 5)^4 * (d/dx) (5x)

Next, we differentiate the inner function, d/dx (5x) = 5. Substituting this into the equation, we have:

h'(x) = 5(-x^2 + 5)^4 * 5

Simplifying further, we obtain:

h'(x) = 25(-x^2 + 5)^4

Therefore, the derivative of h(x) is 25(-x^2 + 5)^4.

To calculate the value of f(8, -12, 14) for the function f(x, y, z) = -6xy - 4xz - 10yz, we substitute x = 8, y = -12, and z = 14 into the function:

f(8, -12, 14) = -6(8)(-12) - 4(8)(14) - 10(-12)(14)

Evaluating this expression, we get:

f(8, -12, 14) = 576 - 448 - 1680

f(8, -12, 14) = -1552

Therefore, the value of f(8, -12, 14) is -1552.

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The step in showing that\(n^3+2n\) is divisible by 3 by mathematical induction is: Prove that the statement is true when n = k. Option B

This step involves substituting k for n in the expression \(n^3+2n\) and showing that the result is divisible by 3. In other words, we need to show that:

\(k^3 + 2k\) is divisible by 3.

If we assume that the statement is true for n = k, then we can substitute k+1 for n in the expression \(n^3+2n\) and simplify:

=\((k+1)^3 + 2(k+1) = k^3 + 3k^2 + 3k + 1 + 2k + 2\)

= \(k^3 + 3k^2 + 5k + 3\)

= \((k^3 + 2k) + (3k^2 + 3k)\)

Since we assumed that the statement is true for n = k, we know that \(k^3 + 2k\) is divisible by 3. Also, \(3k^2 + 3k\) is divisible by 3 because it has a factor of 3. Therefore, the entire expression \((k+1)^3 + 2(k+1)\)is also divisible by 3.

This completes the inductive step, and we can now conclude by mathematical induction that the statement \(n^3+2n\) is divisible by 3 is true for all positive integers n.

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Answer:

v=πr^2(h)

Step-by-step explanation:

the general formula is this

Answer:

16642.1 feets

Step-by-step explanation:

Given :

Elevation of Mt. Wilson = x

If the elevation of snow crest = y

Snow crest = 11,508.21 feet higher than Mt. Wilson

Hence, y = 11,508.21 + x

The elevation of Mt. Wilson, x = y - 11,508.21  feets

From the table, elevation of Snow crest = 28,150.31 feets = y

Hence, The elevation of Mt. Wilson, x = y - 11,508.21  feets

x = 28,150.31 - 11,508.21

x = 16642.1 feets

Answer:

6720

Step-by-step explanation:

⁸P5 = 8! / (8 - 5)!

⁸P5 = 8! / 3!

⁸P5 = 6720

Answer:

it should be 15

Step-by-step explanation:

Answer:

15 units

Step-by-step explanation:

Since the x- coordinates of both points are the same, then calculate the distance between the y- coordinates using the absolute value, that is

d = | - 8 - 7 | = | - 15 | = 15 , or

d = | 7 - (- 8) | = | 7 + 8 | = | 15 | = 15

The critical points are (2,1) and (0,0). Given, z = 3x² - xy + 2y² - 4x - 7y + 12.1. Find the critical points at which the function may be optimized.

To find the critical points, we need to solve the following system of equations: ∂z/∂x = 0, ∂z/∂y = 0∂z/∂x = 6x - y - 4 = 0∂z/∂y = -x + 4y - 7 = 0By solving these equations, we get two critical points: (2,1) and (0,0).2. Determine whether at the computed points, the function takes on its maximum or minimum value.

To determine whether each critical point is a maximum, minimum, or saddle point, we need to compute the second partial derivatives of z: ∂²z/∂x² = 6, ∂²z/∂y² = 4, ∂²z/∂x∂y = -1At the point (2,1), the second partial derivatives satisfy the condition (∂²z/∂x²)(∂²z/∂y²) - (∂²z/∂x∂y)² = (6)(4) - (-1)² = 25 > 0 and ∂²z/∂x² > 0, so z has a minimum value at this point.At the point (0,0), the second partial derivatives satisfy the condition (∂²z/∂x²)(∂²z/∂y²) - (∂²z/∂x∂y)² = (6)(4) - (-1)² = 25 > 0 and ∂²z/∂x² > 0, so z has a minimum value at this point.Therefore, the function z = 3x² - xy + 2y² - 4x - 7y + 12 is optimized at (2,1), where the minimum value is z = 3(2)² - (2)(1) + 2(1)² - 4(2) - 7(1) + 12 = -10.

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Answer:

convert 10 hours 30 minutes to hours= 10.5

683/10.5

=65.04km/h

Answer:

-0.5 (-1/2)

Step-by-step explanation:

Answer:

m= -1/2

Step-by-step explanation:

Slope formula

m= y2-y1/x2-x1

plug the given points in which are (7,-4) (5,-3)

m= -3-(-4)/ 5-7

m= 1/-2 which can be rewritten as -1/2

Two Spiteful Uncles Walking to the Beat

A Short Story

by Grim

Lee Changseon had always loved deprived Falmouth with its magnificent, mutated mountains. It was a place where he felt delighted.

He was a down to earth, splendid, squash drinker with ruddy eyes and handsome ankle. His friends saw him as a bad, breakable barndon harera. Once, he had even helped a silky chicken cross the road. That's the sort of man he was.

Lee walked over to the window and reflected on his creepy surroundings. The snow flurried like thinking puppies.

Then he saw something in the distance, or rather someone. It was the figure of Morwenna Thornton. Morwenna was a sympathetic friend with skinny eyes and tall ankle.

Lee gulped. He was not prepared for Morwenna.

As Lee stepped outside and Morwenna came closer, he could see the squashed smile on her face.

Morwenna gazed with the affection of 747 sinister ordinary owls. She said, in hushed tones, "I love you and I want Internet access."

Lee looked back, even more sneezy and still fingering the cursed gun. "Morwenna, I just don't need you in my life any more," he replied.

They looked at each other with ecstatic feelings, like two hurt, handsome horses drinking at a very brutal snow storm, which had piano music playing in the background and two spiteful uncles walking to the beat.

Lee regarded Morwenna's skinny eyes and tall ankle. "I feel the same way!" revealed Lee with a delighted grin.

Morwenna looked jumpy, her emotions blushing like a narrow, nosy newspaper.

Then Morwenna came inside for a nice beaker of squash.

THE END lol

The expected value for Game 1 is $14.50, you would be willing to pay up to $14.50 to participate in the game. For Game 2, with an expected value of $50, you would be willing to pay up to $50 to participate in the game.

To determine how much you would pay or have to be paid to take part in either Game 1 or Game 2, we need to calculate the expected value of each game. The expected value is the average outcome of the game if it were played many times, and it's calculated using the probabilities and potential winnings or losses.

For Game 1, the expected value (EV1) can be calculated as follows:

EV1 = (Win amount x Probability of winning) + (Loss amount x Probability of losing)
EV1 = ($30 x 0.5) + (-$1 x 0.5)
EV1 = $15 + (-$0.50)
EV1 = $14.50

For Game 2, the expected value (EV2) can be calculated similarly:

EV2 = (Win amount x Probability of winning) + (Loss amount x Probability of losing)
EV2 = ($2000 x 0.5) + (-$1900 x 0.5)
EV2 = $1000 + (-$950)
EV2 = $50

Now that we have the expected values, we can determine how much to pay or be paid to take part in each game. Since the expected value for Game 1 is $14.50, you would be willing to pay up to $14.50 to participate in the game. For Game 2, with an expected value of $50, you would be willing to pay up to $50 to participate in the game.

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An increasing exponential function is defined as follows:

y = a(1 + r)^x.

In which:

For this problem, the function is given as follows:

y = 20000(1.14)^t.

In which the parameters are given as follows:

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Answer:

x = 146°

Step-by-step explanation:

(all angles in a triangle add up to 180°)

180 - 115 - 31 = 34

(supplmentary angle)

180 - 34 = 146°

Step-by-step explanation:

The area of the triangular base is: 19

square units

How to calculate the base area

The given parameters are:

Volume = 27.36 cubic units

Height = 2.88 unit

The volume of a triangular prism is:

V = 0.5 * B *h

Where B represents the base area.

So, we have:

27.36 = 0.5 * B * 2.88

27.36 B * 1.44 -

Solve for B

B = 19

Hence, the area of the triangular base is: 19 square units

the sixteenth term of the series is 85.25.

To determine the sixteenth term of the series, we need to find the common difference (d) between consecutive terms.

Let's denote the first term of the series as a₁ and the common difference as d.

Given that the 7th term of the series is 29, we have:

a₇ = a₁ + 6d = 29   ------(1)

And given that the 11th term of the series is 54, we have:

a₁₁ = a₁ + 10d = 54   ------(2)

To find the value of the sixteenth term, we can use the value of d obtained from equations (1) and (2).

Subtracting equation (1) from equation (2), we get:

a₁₁ - a₇ = (a₁ + 10d) - (a₁ + 6d)

54 - 29 = 4d

25 = 4d

Dividing both sides by 4, we find:

d = 25/4 = 6.25

Now that we have the common difference, we can find the first term (a₁) by substituting d into equation (1):

a₇ = a₁ + 6d = 29

a₁ + 6(6.25) = 29

a₁ + 37.5 = 29

a₁ = 29 - 37.5

a₁ = -8.5

Now, we can find the sixteenth term (a₁₆) by using the formula for the nth term of an arithmetic series:

a₁₆ = a₁ + (n - 1)d

a₁₆ = -8.5 + (16 - 1)(6.25)

a₁₆ = -8.5 + 15(6.25)

a₁₆ = -8.5 + 93.75

a₁₆ = 85.25

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The probability of one color coming up three times in a row when a 5 color wheel is spun is (1/5)³ or 0.008 which is equivalent to 0.8%.

The probability of getting a specific color on any spin is 1/5. Since you're spinning a 5-color wheel, the probability of spinning the same color three times in a row can be calculated using the multiplication rule of probability, which says that the probability of two independent events occurring together is the product of their individual probabilities.

Let's assume that the first spin lands on one of the colors. Then the second spin has a 1/5 probability of landing on the same color as the first spin, and the third spin also has a 1/5 probability of landing on that same color. Therefore, the probability of spinning one color three times in a row is:

(1/5) × (1/5) × (1/5) = (1/125) = 0.008 or 0.8%.

Therefore, the probability of spinning one color three times in a row on a 5-color wheel is 0.8%.

If you spin a 5-color wheel, the likelihood of getting one color three times in a row is slim. It is just 0.8 percent, which means that you are very unlikely to get that result.

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Answer: -3

Step-by-step explanation: Plug the points into rise over run and solve

hope this helps;)

Answer:

15x^9

Step-by-step explanation:

A=l x w

5x^4 times 3x^5 is basically 3*5*x^4*x^5

when you multiply exponents with the same base, you add the exponents, so it becomes 15x^9

Answer:2/9

Step-by-step explanation:

Answer:

Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

Answer:

b^20

Step-by-step explanation:

(b^4)^5 = b^4*5

\(\huge\text{Hey there!}\)

\(\mathtt{(b^4)^5}\\\mathtt{\rightarrow b^{4\times5}}\\\mathtt{\rightarrow b^{4 + 4 + 4 + 4 + 4}}\\\mathtt{\rightarrow b^{8 + 8 + 4}}\\\mathtt{\rightarrow b^{16 + 4}}\\\mathtt{\rightarrow b^{20}}\\\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathtt{Option\ D. b^{20}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

2 imaginary solutions

Step-by-step explanation:

The composition functions are fog(x) = x² + 4x + 5 and gof(x) = x² + 3.

The given functions are f(x) = x² + 1 and g(x) = x + 2.

To find fog(x) (also written as f(g(x))), substitute g(x) into f(x):
fog(x) = f(g(x)) = f(x + 2)

Replace x in f(x) with (x + 2):
fog(x) = ((x + 2)²) + 1

Simplify the expression:
fog(x) = (x² + 4x + 4) + 1

= x² + 4x + 5

So, fog(x) = x² + 4x + 5.

Now, let's find composition function gof(x) (also written as g(f(x))):

Substitute f(x) into g(x):
gof(x) = g(f(x)) = g(x² + 1)

Replace x in g(x) with (x² + 1):
gof(x) = (x² + 1) + 2

Simplify the expression:
gof(x) = x² + 1 + 2 = x² + 3

So, gof(x) = x² + 3.

In conclusion, fog(x) = x² + 4x + 5 and gof(x) = x² + 3.

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To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.

First, we need to find r'(t):

r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i

The magnitude of r'(t) is ||r'(t)|| = sqrt(2).

So, the length of the curve is:

L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)

Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).

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Based on the given quadratic equation, the student's work is correct?

The correct answer choice is option C

10x² + 31x - 14 = 0

Using factorization method

(10 × -14) = -140

31

Find two numbers whose product is -140 and sum is 31

So,

35 × -4 = -140

35 + (-4) = 31

Then,

10x² + 35x - 4x - 14 = 0

5x(2x + 7) -2(2x + 7) = 0

(5x - 2) (2x + 7) = 0

5x - 2 = 0. 2x + 7 = 0

5x = 2. 2x = -7

x = 2/5. x = -7/2

Hence, the value of x is ⅖ or -7/2

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Katie runs the fastest at 14.469 ft/s

To compare the speeds of each runner, we need to convert all the measurements to the same units. Let's convert them all to feet per second:

Therefore, in order of fastest to slowest runner:

Katie (14.469 ft/s)

Noah (12.133 ft/s)

Stephanie (8 ft/s)

Jessica (9.514 ft/s)

Hence, Katie runs the fastest

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