Multiple Choice
A car travels 172 miles using 7 gallons of gas. At that rate, how far can the car travel using 42 gallons of gas?
A. 1,032 miles
B. 1,548 miles
C. 1,204 miles
D. 1,376 miles

Answer: b

Step-by-step explanation: When you rotate it around the axis (think of it as a pole) it will become a cylinder with radius 5

a. When evaluating a model, we use R2 as a parameter for performance assessment.

b. If model A has a higher MAPE but model B has a higher R2, we choose the model with the higher R2 for better overall performance.

c. For accuracy measures, we typically use MAPE (Mean Absolute Percentage Error) due to its interpretability and ability to capture relative errors.

When evaluating a model's performance, it is crucial to choose the appropriate parameters to assess its accuracy and reliability. In the case of MAPE (Mean Absolute Percentage Error) and R2 (Coefficient of Determination), the choice between them depends on the specific evaluation goals.

The R2 parameter is commonly used for evaluating models because it measures the proportion of the dependent variable's variance that can be explained by the independent variables. R2 provides insights into how well the model fits the data and captures the relationship between the input features and the target variable. Therefore, R2 is a suitable parameter to use when evaluating a model.

When comparing two models, if model A has a higher MAPE but model B has a higher R2, it is advisable to choose the model with the higher R2 value. This is because R2 indicates the proportion of variance explained, suggesting that model B performs better in capturing the underlying patterns and predicting the target variable.

Although model A may have a lower relative error (MAPE), it is crucial to prioritize the model's ability to explain and predict the target variable accurately.

Among MAPE, MAD (Mean Absolute Deviation), and MSD (Mean Squared Deviation), MAPE is commonly preferred as a parameter for accuracy measures. MAPE calculates the average percentage difference between the predicted and actual values, making it interpretable and easily understandable.

It captures relative errors and enables comparisons across different scales and datasets. MAD and MSD, on the other hand, measure absolute and squared errors, respectively, but they do not account for the relative magnitude of the errors. Hence, MAPE is a more suitable parameter for accuracy measures.

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To write a cosine function with an amplitude of 3 and a period of 2π, we can use the general form of the cosine function: f(x) = A * cos(Bx + C) + D

Here, A represents the amplitude, B determines the frequency (in this case, B = 2π/period), C represents any horizontal shift, and D represents any vertical shift. Given the amplitude of 3 and the period of 2π, we have:
A = 3
Period = 2π

Since the period is 2π, we can substitute this value into the formula for B:
B = 2π/period
B = 2π/(2π)
B = 1
Therefore, the cosine function with an amplitude of 3 and a period of 2π is: f(x) = 3 * cos(x) + D Since no vertical shift is mentioned in the description,  we can assume D = 0.

The cosine function with an amplitude of 3 and a period of 2π is f(x) = 3 * cos(x). To write a cosine function with an amplitude of 3 and a period of 2π, we can use the general form of the cosine function:

f(x) = A * cos(Bx + C) + D. In this case, the amplitude is given as 3 and the period is given as 2π. The amplitude, represented by A, determines the maximum value of the function.

Since the amplitude is 3, the maximum value of the cosine function will be 3 and the minimum value will be -3. The period, represented by B, determines the length of one complete cycle of the function. In this case, the period is 2π, which means that one complete cycle of the cosine function occurs over an interval of 2π. By substituting the given values into the general form of the cosine function, we can write the specific function as f(x) = 3 * cos(x). This function represents a cosine curve with an amplitude of 3 and a period of 2π.

The cosine function with an amplitude of 3 and a period of 2π is f(x) = 3 * cos(x).

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Answer:

It’s just -24 minus -18 so that’s $-6

Step-by-step explanation:

The maximum Number of  scholars in each row is 12. This means that the  scholars can be arranged in rows with an equal number of  scholars, and each row can have a  outside of 12  scholars.

To find the maximum number of  scholars in each row, we need to determine the  topmost common divisor( GCD) of the total number of  scholars in each section. The GCD represents the largest number that divides all the given  figures unevenly.  

Given that there are 24, 36, and 60  scholars in the three sections, we can calculate the GCD as follows    Step 1 List the  high factors of each number  24 =  23 * 31  36 =  22 * 32  60 =  22 * 31 * 51    

Step 2 Identify the common  high factors among the three  figures  Common  high factors 22 * 31    Step 3 Multiply the common  high factors to find the GCD  GCD =  22 * 31 =  4 * 3 =  12  

 thus, the maximum number of  scholars in each row is 12. This means that the  scholars can be arranged in rows with an equal number of  scholars, and each row can have a  outside of 12  scholars.

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The function represented in the graph attached is

The standard vertex form of quadratic equation is of the form,

y = a(x - h)² + k     where a = 1/4p

The vertex

v (h, k) = (-1, 2) (from the graph)

h = -1

k = 2

substitution of the values into the equation gives

y = a(x + 1)² + 2

solving for a using point (0, -1) on the graph

-1 = a(0 + 1)² + 2

-1 = a + 2

-1 - 2 = a

a = -3

substituting the value of "a" into the equation

y = a(x + 1)² + 2

y = -3(x + 1)² + 2  (standard vertex form)

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Answer:

Step-by-step explanation:

Well if that’s the whole answer than it’s fine but i’m sure you don’t want to write that out so just round it to 2

Answer:

Yes, a repeating decimal is considered a rational number because it can be written as a fraction, so it is rational.

Step-by-step explanation:

The value of a of the given cube root expression is: a = 1

The cube root of a number is defined as that number which when  multiplied 3 times gives us the original number. Whenever a number (x) is multiplied three times, then we can say that the resultant number is known as the cube of that number.

We are given the expression as:

∛(81x¹⁵y⁹)

Now, expressing this individually gives us the expression:

\(81^{\frac{1}{3} } * x^{\frac{15}{3}} * y^{\frac{9}{3}}\)

= 3¹x⁵y³

Thus, a = 1

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The solution to the equation F'(x) = x² is F(x) = (x³/³) - 2x.

To evaluate the integral ∫-1 to 4 f(x) dx, split the integral into two parts based on the given piecewise function:

∫-1 to 4 f(x) dx = ∫-1 to 0 (1 - e⁻ˣ) dx + ∫0 to 4 (x² - 2) dx

For the first part, integrate 1 - e⁻ˣ with respect to x from -1 to 0:

∫-1 to 0 (1 - e⁻ˣ) dx = [x + e⁻ˣ] from -1 to 0

= (0 + e⁰) - (-1 + e¹)

= 1 - e + e

= 1

For the second part, we integrate x² - 2 with respect to x from 0 to 4:

∫0 to 4 (x² - 2) dx = [(x³/³) - 2x] from 0 to 4

= (4³/³ - 2(4)) - (0³/³ - 2(0))

= (64/3 - 8) - (0 - 0)

= 64/3 - 8

= 40/3

Therefore, the integral ∫-1 to 4 f(x) dx is equal to 1 + 40/3, which simplifies to 43/3.

Now, solve the equation F'(x) = x² for x.

Given that F(x) = ∫0 to x (t² - 2) dt, differentiate F(x) with respect to x to find F'(x):

F'(x) = (d/dx) ∫0 to x (t² - 2) dt

To differentiate an integral with a variable limit, use the Leibniz rule, which states:

(d/dx) ∫a to b f(t,x) dt = (d/dx) F(b,x) - (d/dx) F(a,x)

Applying this rule to our integral, where a = 0 and b = x, we get:

F'(x) = (d/dx) F(x,x) - (d/dx) F(0,x)

The first term on the right-hand side, (d/dx) F(x,x), can be calculated by applying the Fundamental Theorem of Calculus:

(d/dx) F(x,x) = x² - 2

The second term, (d/dx) F(0,x), is zero because F(0,x) does not depend on x.

Therefore, we have:

F'(x) = x² - 2

To solve this equation, we can integrate both sides:

∫ F'(x) dx = ∫ (x² - 2) dx

F(x) = (x³/³) - 2x + C

Now we need to find the value of C. We know that F(0) = 0 since F(0,x) is zero, so we substitute x = 0 into the equation:

F(0) = (0³/³) - 2(0) + C

0 = 0 - 0 + C

C = 0

Therefore, the solution to the equation F'(x) = x² is F(x) = (x³/³) - 2x.

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Answer:

A on edge. -

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 1, 2, 3. Column 2 is labeled y with entries 0, 3, 4, 7.

y = 3x² – 6x + 4

{(3, 4), (6, 5),

(7, 9), (9, 15)}

Step-by-step explanation:

got it right

Answer:

it is A on edge the guy before me is wrong

Step-by-step explanation:

Answer:

y = 3x + 4

Step-by-step explanation:

Given:

Coordinates

(-3 , -5)

Slope m = 3

Find;

Equation of slope

Computation:

Given, x1 = -3 and y1 = -5

Equation of slope = y - y1 = m(x - x1)

Equation of slope = y - (-5) = 3(x + 3)

Equation of slope = y + 5 = 3x + 9

Equation of slope = y = 3x + 9 - 5

Equation of slope = y = 3x + 4

y = 3x + 4

Given equation g = x-1/k in terms of x would be x = 1 + gk

for given question,

we have been given an equation g = x-1/k

Dyani began solving the equation g = x-1/k for x by using the addition property of equality.

We solve given equation for x.

⇒ g = x-1/k                      ..........(Given)

⇒ gk = (x - 1/k)k               .........(Multiply both the sides by k)

⇒ gk = x - 1

⇒ gk + 1 = x - 1 + 1           .........(Add 1 to each side)

⇒ gk + 1 = x

⇒ x = 1 + gk

Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk

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Using the power series expansion of cos(x) to find the sum of this series. Recall that:

cos(x) = ∑[n=0, ∞] (-1)^n (x^(2n)) / (2n)!

Comparing the given series to the power series expansion of cos(x), we have:

(-1)^n 2^(2n) / (2n)! = (-1)^n 42^n (2n)! / (2n)!

Therefore, cos(x) = ∑[n=0, ∞] (-1)^n (x^(2n)) / (2n)! = ∑[n=0, ∞] (-1)^n 2^(2n) / (2n)! = ∑[n=0, ∞] (-1)^n 42^n (2n)! / (2n)!

Setting x = 4 in the power series expansion of cos(x), we get:

cos(4) = ∑[n=0, ∞] (-1)^n (4^(2n)) / (2n)! = ∑[n=0, ∞] (-1)^n 2^(2n) / (2n)!

Therefore, the sum of the given series is cos(4) / 42 = cos(4) / 1764.

Hence, the sum of the series is cos(4) / 1764.

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The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.

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

Given that −8 represents the depth of water in the swimming pool. Hence:

The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.

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Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

We have a linear function         \(\displaystyle\bf y=\underbrace{k}_{gradient}x+b\)       and we know that                                                                                         \(\displaystyle\bf \left \{ {{-2\cdot-3+b=2} \atop {-4\cdot -2+b=k}} \right. => \left \{ {{b=-4} \atop {b+8=k} \right. => k=8-4=4 \\\\Answer: \boxed{B) \quad k=4}\)                                                                                                                                              

Answer:just add if i am right?

Step-by-step explanation:

Answer:

With enough centrifugal force and outward thrust the rocket can exceed the pull of the vacuum no matter how strong it is.

Step-by-step explanation:

To find the probability density of Y, we will use the transformation method. First, we find the inverse function of Y = 1-2X, which gives X = (1-Y)/2.

a) The probability density of Y can be found by substituting X = (1-Y)/2 into the density function of X:

fY(y) = fX((1-y)/2) * |dx/dy|

= 2(1 - (1-y)/2) * 1/2

= (3/2)(1-y) for 0≤y≤1

= 0 elsewhere

b) The distribution function of Y can be found by integrating the probability density function of Y:

FY(y) = ∫[0, y] fY(t) dt

= ∫[0, y] (3/2)(1-t) dt

= (3/2)(y - y^2/2) for 0≤y≤1

= 0 for y<0, 1 for y≥1

c) The mean of Y can be found by integrating y * fY(y) over the range [0, 1]:

E(Y) = ∫[0, 1] y * (3/2)(1-y) dy

= 3/4

The variance of Y can be found by calculating E(Y^2) - [E(Y)]^2:

E(Y^2) = ∫[0, 1] y^2 * (3/2)(1-y) dy

= 1/4

Var(Y) = E(Y^2) - [E(Y)]^2

= 1/4 - (3/4)^2

= 3/16

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Answer:

0.8

Step-by-step explanation:

5 is divided by 5 to get to 1. Divide 4 by 5 to get 0.8.

In a ratio, whatever you do to one side you have to do to the others.

Answer:

it will be

4/5 : 1 or 0.8 : 1

in n : 1 form

Answer:

766,000

Step-by-step explanation:

The thousands place is the 5 in 765,903. Because the hundreds place is 5 or above, the thousands place should be rounded up.

Answer: CD≈3.47

Step-by-step explanation:

Let CD=x.

\(\displaystyle\\\left \{ {{AC^2=24^2-(17+x)^2} \atop {AC^2=13^2-x^2}} \right. \\24^2-(17+x)^2=13^2-x^2\\576-(17^2+2*17*x+x^2)=169-x^2\\576-289-34x-x^2=169-x^2\\576-289-169=34x\\118=34x\\\)

Divide both parts of the equation by 34:

\(x\approx3.47\)

Hence, CD≈3.47

Answer:

y=3÷9

Step-by-step explanation:

2x-9y=11

or,2×7-9y=11

or,14-11=9y

or,3÷9=y

Answer:

boys = 250

girls = 150

Step-by-step explanation:

5g = 3b       eq. 1

g + b = 400       eq. 2

g = girls

b = boys

From the eq. 2

g = 400 - b

Replacing this last eq. on eq. 1:

5(400-b) = 3b

5*400 + 5*-b = 3b

2000 - 5b = 3b

2000 = 3b + 5b

2000 = 8b

2000/8 = b

250 = b

From eq. 2

g + 250 = 400

g = 400 - 250

g = 150

Check:

from eq. 1

5*150 = 3*250  = 750

The total weight of Mrs. Portillo's cat and the dog is 34 kilograms.  

The mathematical operations known as operators focus on particular activities, such as adding, taking away, adding multiple times and dividing equally, etc.

The four fundamental operations in Maths are

1. Addition

2. Subtracting

3. Multiplications

4. Divisions

Here we use Addition to solve the problem

Here we have

Cat's weight = 6 kilograms

Her dog weighs 22 kilograms more than her cat

Weight of dog = Cat's weight + 22 kilograms

= 6 kilograms + 22 kilograms

= 28 kilograms

Total weight of Mrs. Portillo's cat and dog = 6 + 28 = 34 kilograms

Therefore,

The total weight of Mrs. Portillo's cat and the dog is 34 kilograms.  

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Complete Question:

What is the total weight of her cat and dog? Mrs. Portillo's cat weighs 6 kilograms her dog weighs 22 kilograms more than her cat.

In the picture, there is graph with a line. The equation of the line is

2x+y-1=0.

Given that,

In the picture, there is graph with a line.

We have to find the equation of the line in the graph.

The equation of a line can be constructed using the slope of the line and a point on the line.

The equation for a line traveling through a point (x₁,y₁) and having a slope of m is given as follows: y-y₁=m(x-x₁)

Additionally, this equation can be resolved and condensed into the equation of a line in its usual form.

Here, we have points (0,1) and (1,-1).

Slope of the line m=\(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

m=(-1-1)/(1-0)

m=-2/1

m=-2

We got Slope of the line m=-2

Take point (0,1)

y-1=-2(x-0)

y-1=-2x

2x+y-1=0

Therefore, the equation of the line from the given graph is 2x+y-1=0.

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Answer:

\(y = \frac{7}{4}x +14\)

Step-by-step explanation:

Given

\(y = \frac{7}{4}x + 4\)

Required

Determine the equation of line that passes through (-8,0) and parallel to \(y = \frac{7}{4}x + 4\)

Parallel lines have the same slope.

In \(y = \frac{7}{4}x + 4\)

The slope, m is

\(m = \frac{7}{4}\)

because the general form of a linear equation is:

\(y = mx + b\)

Where

\(m = slope\)

So, by comparison:

\(m = \frac{7}{4}\)

Next, is to determine the equation of line through (-8,0)

This is calculated using:

\(y - y_1 = m(x - x_1)\)

Where

\(m = \frac{7}{4}\)

\((x_1,y_1) = (-8,0)\)

So, we have:

\(y - 0 = \frac{7}{4}(x -(-8))\)

\(y - 0 = \frac{7}{4}(x +8)\)

\(y - 0 = \frac{7}{4}x +\frac{7}{4}*8\)

\(y - 0 = \frac{7}{4}x +7*2\)

\(y - 0 = \frac{7}{4}x +14\)

\(y = \frac{7}{4}x +14\)

The similar circles P and Q can be made equal by dilation and translation, the scale factor of dilation from circle P to Q is 2.5.

The dilation means the act or action of enlarging, expanding, or widening : that is, the state of being dilated: such as. :we can say that, the act or process of expanding (such as in extent or volume) is known as dilation.

here, we have,

The distance between the center of circles P and Q, which is horizontal distance, is 11.70 units

The scale factor from circle P to Q is 2.5 of dilation

The horizontal distance between their centers?

From the figure, we get that,

now, we have the centers as:

P = (-5,4)

Q = (6,8)

The distance is then calculated using:

d = √(x2 - x1)² + (y2 - y1)²

So, we have:

d = √(6 + 5)^2 + (8 - 4)^2

Evaluate the sum

d = √137

Evaluate the root

d = 11.70

Hence, the distance between the center of circles P and Q, which is horizontal distance, is 11.70 units.

The scale factor from circle P to Q, of dilation ,

We have their radius to be:

P = 2

Q = 5

now, we divide the radius of Q by the radius of P to determine the scale factor (k)

k = Q/P

k = 5/2

k = 2.5

Hence, the scale factor from circle P to Q is 2.5 of dilation.

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After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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The equation would be: ΔT = 2 - (-12) = 14 degrees Celsius, ΔT = T2 - T1, where ΔT is the change in temperature, T2 is the final temperature (-12 degrees Celsius)

A. d = rt, where d = 12 meters, r = 2 meters per second (rate), and t is the time it takes for the whale to get to an elevation of 12 meters. The equation would be:

12 = 2t

B. r = d/t, where r is the rate of diving, d = 12 meters (depth), and t = 2 minutes (time). The equation would be:

r = 12/(2 x 60) = 0.1 meters per second

C. ΔT = T2 - T1, where ΔT is the change in temperature, T2 is the final temperature (2 degrees Celsius), and T1 is the initial temperature (-12 degrees Celsius). The equation would be:

ΔT = 2 - (-12) = 14 degrees Celsius

D. ΔT = T2 - T1, where ΔT is the change in temperature, T2 is the final temperature (-12 degrees Celsius), and T1 is the initial temperature (2 degrees Celsius). The equation would be:

ΔT = -12 - 2 = -14 degrees Celsius

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