This is a 2 Step process: answer to step 1: -1 , needing help with Step 2. Step 2: Find the restricted values of y, if any, for the given rational expression. Separate multiple answers with a comma.

Answer:

Step-by-step explanation:

Based on the information provided, the residual plot makes sense based on the scatter plot.

In the given scatter plot, the points are plotted with horsepower on the x-axis and observed MPG (miles per gallon) on the y-axis. The scatter plot shows the relationship between horsepower and MPG for the motorcycles.

The residual plot, on the other hand, shows the differences between the observed MPG values and the predicted MPG values based on the regression line or model. Residuals represent the vertical distances between the observed data points and the regression line.

Looking at the residual plot, we can see that the residuals are scattered randomly around the zero line. Some residuals are positive, while others are negative, indicating that the observed MPG values deviate both above and below the predicted MPG values.

Given this information, option A is the correct answer: "The random residual plot makes sense because the scatter plot appears to have a linear relationship." The scatter plot does not necessarily suggest a positive or negative relationship between horsepower and MPG. It simply shows the general trend or pattern. The random distribution of residuals in the residual plot indicates that the regression model is capturing the relationship adequately, and the variations or deviations from the regression line are random, which is expected in a good regression model.

The residual plot created by Jorge does make sense as it reflects the negative relationship between horsepower and miles per gallon present in the original scatter plot. As the horsepower increases, the miles per gallon decreases which is depicted accurately in the residual plot made.

The best answer for this is B. The random residual plot makes sense because the scatter plot appears to have a negative relationship. A residual plot is a graph that is used to examine the goodness of fit in regression and ANOVA analysis. It is the differences between the observed and predicted values of data. The points in a residual plot are randomly dispersed around a horizontal axis if the corresponding regression model is appropriate for the data.

In this case, the scatter plot demonstrates a negative relationship between the horsepower of motorcycles and miles per gallon. As the horsepower increases, the miles per gallon decrease. This negative relationship is reflected in the pattern of residuals, which fluctuates around the zero line on the y-axis of the residual plot. Consequently, the random distribution of residuals on Jorge's plot does make sense given the scatter plot data.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer: True

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Answer:

36.3636364%

or 36.36

Step-by-step explanation:

Answer: 0.75km per hour or 3/4km per hour.

Step-by-step explanation: 1/4 / 1/3 = 3/4.

We need to find the unit rate, that is kilometer per hour

The unit rate is 3/4 km/hr

kilometer, km

Hour, hr

unit rate

\( = \frac{number \: of \: kilometer}{number \: of \: hours} \)

\( = \frac{1 \div 4}{1 \div 3} \)

\( = 1 \div 4 \times 3 \div 1\)

= 3/4 km/hr

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The coordinates to which the portable irrigation system should be sent to water the area are:

(495.75, 672).

The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.

Hence the coordinates are given as follows:

Hence the x-coordinate of the point to which the system should be sent is:

x = (56 + 144 + 888 + 895)/4 = 495.75.

(the mean is given by the sum of the observations divided by the number of observations).

The y-coordinate of the point to which the system should be sent is:

y = (289 + 332 + 1012 + 1055)/4 = 672.

The area is given by the image at the end of the answer.

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The bags of chips sold are 111.

The percentage is the term use to tell the hundredth part of something.

Given that, The snack bar sold 75% of its inventory of bags of chips, and the snack bar still has 37 bags of chips,

Let the original number of bags of the chips be x,

Since, 75% is already sold, so left number of bags are = 100%-75% = 25%

Therefore,

25% of x = 37

x = 37x4

x = 148

The number of bags sold = 75% of 148

= 75x148/100

= 111

Hence, they sold 111 bags of chips.

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Answer:

x=25/3

Step-by-step explanation:

I'm not sure if it is correct but. . .

Answer: x=25/3

Step-by-step explanation:

By definition of conditional expectation,

\(\mathrm E\left[ X \mid Y = y \right] = \displaystyle \sum_x x\, p_{X\mid Y}(x \mid y) = \sum_x x \frac{p_{X,Y}(x,y)}{p_Y(y)}\)

where \(p_Y(y)\) is the marginal probability mass function (pmƒ) of Y. We find this by summing up all joint probabilities over the possible values of X :

\(p_Y(y) = \displaystyle \sum_x p_{X,Y}(x,y) = p_{X,Y}(1,y) + p_{X,Y}(2,y) + p_{X,Y}(3,y)\)

Consult the given values of the joint pmƒ. The values you actually list are unclear… if p(1, 1) = 1, then all other probabilities should be 0, so you must mean something else.

To get around this, I'll just make up a valid joint pmƒ of my own, and show you how to get what you need **using this pmƒ**.

\(\begin{array}{c|c|c|c} & A=1 & A=2 & A=3 \\ ---&---&---&--- \\ B=1 & 0.3 & 0.1 & 0.05 \\ B=2 & 0.02 & 0.02 & 0.01 \\B=3 & 0.25 & 0 & 0.25 \end{array}\)

The marginal pmƒ for B is

\(p_B(b) = \begin{cases} p_{A,B}(1,1)+p_{A,B}(2,1)+p_{A,B}(3,1) = 0.45 & \text{if }b = 1 \\ p_{A,B}(2,1)+p_{A,B}(2,2)+p_{A,B}(3,1) = 0.05 & \text{if }b = 2 \\ p_{A,B}(3,1)+p_{A,B}(3,2)+p_{A,B}(3,3)=0.5 & \text{if }b = 3\\0&\text{otherwise}\end{cases}\)

Now get the conditional expectation:

\(\mathrm E\left[A \mid B = b\right] = \begin{cases}\dfrac{1\cdot p_{A,B}(1,1)+2\cdot p_{A,B}(2,1)+3\cdot p_{A,B}(3,1)}{p_B(1)} \approx 1.44 & \text{if }b = 1 \\\\\dfrac{1\cdot p_{A,B}(1,2)+2\cdot p_{A,B}(2,2)+3\cdot p_{A,B}(3,2)}{p_B(2)} = 1.8 & \text{if }b = 2\\\\\dfrac{1\cdot p_{A,B}(1,3)+2\cdot p_{A,B}(2,3)+3\cdot p_{A,B}(3,3)}{p_B(3)} = 2 & \text{if }b = 3\end{cases}\)

If A and B are independent, then \(p_{A,B}(a,b)=p_A(a)p_B(b)\) and it follows that E[A | B] = E[A]. Compute the expectation of A :

\(\mathrm E\left[A\right] = \displaystyle \sum_a a \, p_{A,B}(a,b)\)

\(\mathrm E[A] = \begin{cases}1\cdot p_{A,B}(1,1)+2\cdot p_{A,B}(2,1)+3\cdot p_{A,B}(3,1) = 0.65 & \text{if }b = 1 \\ 1\cdot p_{A,B}(1,2)+2\cdot p_{A,B}(2,2)+3\cdot p_{A,B}(3,2) = 0.9 & \text{if }b = 2\\ 1\cdot p_{A,B}(1,3)+2\cdot p_{A,B}(2,3)+3\cdot p_{A,B}(3,3) = 1 & \text{if }b = 3\end{cases}\)

But E[A | B] ≠ E[A], so A and B are not independent.

The system of equations y =−7x + 8  and y = −7x − 8 ​ have no solution

From the question, we have the following parameters that can be used in our computation:

y =−7x + 8

y = −7x − 8 ​

Subtracting the two equations

We have

y - y = -7x + 7x + 8 + 8

When the like terms are evaluated, we have

0 = 16

The above equation is false

This means that the equation has no solution

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The slope of the line passing through given points is 5/7

We know that the slope is the ratio of the change in y-values to the change in x-values.

We use slope formula,

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

For pair of points (1, 3) and (8, 8),

m1 = (8 - 3)/(8 - 1)

m1 = 5/7

For pair of points (8, 8)  and (15, 13),

m2 = (13 - 8)/(15 - 8)

m2 = 5/7

For pair of points (22,18)  and (29, 23),

m3 = (23 - 18)/(29 - 22)

m3 = 5/7

For pair of points (15, 13)  and (22, 18),

m4 = (18 - 13)/(22 - 15)

m4 = 5/7

Since the rate of change of output values to the input values is constant i.e., 5/7, the slope of the line is 5/7

Therefore, the slope of the line passing through given points is 5/7

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Answer:

k = 77

Step-by-step explanation:

\(\frac{k}{11} =7\\\\\rightarrow 11 * 7 = 77\\\rightarrow 77 \div 11 = 7\)

Answer:

k = 77

Step-by-step explanation:

The question in equation form is :

\(\frac{k}{11} =7\)

Now we multiply both sides by 11 to solve for k :

k = 7×11

k = 77

Hope this helped and brainliest please

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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Answer: x-9

Step-by-step explanation: You can rewrite that to get 4/3x-1/3x-5-4

That simplifies to x-9

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer:

The function is growth with a growth rate of 7%

Step-by-step explanation:

The equation is in the form.

y = a * b^x

if b > 1 then it is growth.

If b < 1 it is decay.

Since b > 1 it is growth.  The growth rate is

b = 1+r

1.07 = 1+r

r= .07

7%

The function is growth with a growth rate of 7%

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

After solving the quadratic equation, the roots are (x - 2) and (x + 7).

To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.

The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.

As per the given equation in the question,

x² + 5x - 14 = 0

b² - 4ac

5² - 4(1)(-14)

25 + 56 = 81

Use the equation,

-b ± \(\sqrt{b^2-4ac}/2a\)

Substitute the values,

(-5 + 9)/2 = 2 and,

(-5 - 9)/2 = -7

Therefore, the root will be (x - 2) and (x + 7).

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Answer:

-20x^4y + 40x^3y^2.

Step-by-step explanation:

-5x^3y(4x-8y)

= -5x^3y * 4x + -5x^3y * -8y

= -20x^4y + 40x^3y^2

Answer:

AB = 41 cm

Step-by-step explanation:

If B is the midpoint of AC, then B splits AC into 2 equal halves: AB & BC.

Therefore, AB = ½ of AC.

Given, AC = 82 cm.

So,

AB = ½ × AC

AB = 82/2

AB = 41 cm

_____

Hope it helps ⚜

The area of the region is equal to the area of the septagon minus the area of the circumscribing circle. The area of the septagon = 7 x (5^2 x (1 + sqrt(3))/4). The area of the circumscribing circle = pi x (5^2/2).

The area of the region between the septagon and its circumscribing circle can be found by subtracting the area of the circumscribing circle from the area of the septagon. The side length of the septagon is 5 inches. The area of the septagon can be calculated using the formula A = 7 x (5^2 x (1 + sqrt(3))/4). This is equal to 58.82 inches squared. The area of the circumscribing circle can be calculated using the formula A = pi x (5^2/2). This is equal to 78.54 inches squared. Therefore, the area of the region between the septagon and its circumscribing circle is 58.82 inches squared minus 78.54 inches squared, which is equal to 19.72 inches squared.

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The ratio of the length of a tile in the model to the length of an actual tile is 1/8.

The ratio of the area of a tile in the model to the area of an actual tile is 1/64.

From the information, it should be noted that in the model, each tile has length 1/3in and width 1/4 in and the actual tiles have length 1/4 ft and width 3/16ft .

The ratio of the length of a tile in the model to the length of an actual tile will be:

= 1/4 ÷ 2

= 1/4 × 1/2

= 1/8

The ratio of the area of a tile in the model to the area of an actual tile is (1/4 × 1/6) / (2 × 4/3)

= 1/64

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Answer:

Step-by-step explanation:

Read simply, it is m + (r - 2). It is a very clear statement, so you can depend on the answer.

Answer:

\(P(Red) = \frac{3}{20}\)

Step-by-step explanation:

Given

\(Red = 3\)

\(Trials = 20\)

Required

Determine the experimental probability of next marble being red

This is calculated as:

\(P(Red) = \frac{n(Red)}{Trials}\)

Substitute values for n(Red) and Trials

\(P(Red) = \frac{3}{20}\)

Angle ADG, angle BEH and angle CFI, all have two curves in their angles. Same number of curves are used to represent that their measure are equal.

So, m angle CFI = m angle ADG

So, m angle CFI = m angle ADG=> m angle CFI = 92°