Graph the following function on the axes provided.

Answer with step-by-step explanation:

The distance between Rockville and San Jose is 2407.2. Since there are 63360 inches in a mile, we divide it by 2, which is 31680. We multiply 2407.2 by 31680, and get 76260096.

Answer: 1,488,000

Please tell me if I’m wrong.

Answer:

11

Step-by-step explanation:

You have an equation \(f(x)\) and you set \(x=5\), and the result is 2.

You have another equation \(g(x)\) and you set \(x=5\), and the result is 9.

Therefore, if you add both equations, represented by \((f+g)(x)\), and you set \(x=5\), the result is simply 2 + 9 = 11.

Answer: 1

Step-by-step explanation:

If \(x > -7\), then \(x+7 > 0 \implies |x+7|=x+7\)

So, we have the original fraction is equal to

\(\frac{x+7}{x+7}=\boxed{1}\)

Answer:

y=7(6)^x

xStep-by-step explanation:

Answer:

58 members of the House of Representatives, and 28 members of the senate.

Step-by-step explanation:

We can find the answer to this by simply subtracting:

86 - 58 = 28

So, there are 58 members of the House of Representatives, and 28 members of the senate.

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With what?

Where is the picture

Answer:

b

Step-by-step explanation:

i just answered the same thing earlier

For the graphed function, we have:

Domain:  (-1, 1) U (3, 5)

Range: (5, 2)

For any function y = h(x) we define the domain as the set of the inputs while we define the range as the set of the outputs.

To find the domain we need to look at the horizontal axis, we can see that the function is graphed on the intervals (-1, 1) and (3, 5), so the domain is:

D: (-1, 1) U (3, 5)

For the range we need to look at the vertical axis, the two intervals are (-4, 2) and (-5, 0), the union of these intervals gives:

(-4, 2) U (-5, 0) = (5, 2)

Then the range is R: (5, 2)

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In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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In cylindrical coordinates, a point (r, θ, z) in space corresponds to the point (rcosθ, rsinθ, z) in Cartesian coordinates. The region E in cylindrical coordinates is defined by the equations x2 + y2 = 9 and -2 ≤ z ≤ 2, which can be rewritten in terms of r and θ as follows:

r2cos2θ + r2sin2θ = 9

-2 ≤ z ≤ 2

The first equation can be simplified to r2 = 9, which means that r = 3 for all points in the region E. The region E is therefore the region inside the cylinder with radius 3 and height 4, centered at the origin.

To evaluate the triple integral, we can use cylindrical coordinates to express the volume element dV as follows:

dV = rdrdθdz = 3rdrdθdz

The integral we want to evaluate is then:

∫∫∫_E (x^2 + y^2) dV = ∫∫∫_E (r^2cos^2θ + r^2sin^2θ) dV

= ∫∫∫_E r^2(cos^2θ + sin^2θ) dV

= ∫∫∫_E r^2 dV

= ∫∫∫_E 3^2 rdrdθdz

= 3^2 ∫∫∫_E rdrdθdz

We can now use the limits of integration for r, θ, and z to evaluate the triple integral:

= 3^2 ∫_0^2π ∫_0^3 ∫_-2^2 rdrdθdz

= 3^2 ∫_0^2π ∫_0^3 (2 - (-2))rdrdθ

= 3^2 ∫_0^2π ∫_0^3 4rdrdθ

= 3^2 ∫_0^2π 4 * (r^2/2)dθ

= 3^2 ∫_0^2π (3^2/2)dθ

= 3^2 * (3^2/2) * (2π - 0)

= 3^2 * 3^2 * π

= 81π

Therefore, the value of the integral is 81π.

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The perimeter is a measure of the distance around the shape. This means that to find the perimeter we usually are going to add the lenghts of the sides of the figure (the circle is an exception to that rule since this is a curve figure).

The are is a measure of the space inside the figure. This means that to find the area we usually are going to multiply the lenghts of the sides of the figure to get the area.

Now the area of a triangle is given as:

whereas the area of a paralelogram is given by:

From this we notice that the area of the triangle is half the area of a parallelogram.

The length of line having mid point B ⇒  7x - 2.

Given that,

B is the mid point of AC

And also given that

length of segment AB = 2x+5

And length of segment BC = 5x - 7

A straight path established by linking a group of points in a plane is known as a line. It is a one-dimensional form with only a length and no width or height. A line can extend indefinitely in both ends in opposite directions. To indicate a line, we can use upper case characters.

Now since B is the mid point of AC,

So, The line AC is sum of the line segment AB and line segment BC.

Therefore,

AC = AB+BC

     = (2x+5)+(5x - 7)

     = 7x - 2

Hence,

The length of AC is 7x - 2

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

x = 41.81°, 138.19°, 210°, 330°

Explanation:

3cos(2x) + sin(x) = 1

subtract one from both sides

→ 3cos(2x) + sin(x) − 1 = 0

rewrite using trigonometry identities

→ 2 + sin(x) − 6sin²(x) = 0

solve x by substitution

f(x) = 2 + sin(x) − 6sin²(x)

= 2 + 4sin(x) - 3sin(x) − 6sin²(x)

= −2sinx(3sinx −2) − (3sinx−2)

= (3sinx −2)(−2sinx−1)

= −(3sinx −2)(2sinx+1)

f(x) = 2 + sin(x) − 6sin²(x) = 0

= −(3sinx −2)(2sinx+1) = 0

(3sinx −2) = 0 (2sinx+1) = 0

→sinx = 2/3 →sinx = −1/2

x = 41.81°, 138.19° x = 210°, 330°

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Answer:

1. y = 0.437798+0.829539X

2. there is a significant effect

3. 7.523

4. 41.914

5. no

6. 0.8777

Step-by-step explanation:

1.

from the regression output we have

intercept = 0.437798

slope = 0.829539

the regression line would therefore be =

y = 0.437798 + 0.829539X

2.

h0 = regression is not significant

h1: regression is significant

alpha = 0.05

p value = 0.0001

we compare p-value with alpha

0.0001<0.05

we therefore reject H0 and conclude that hours spent studying have significant effect on total points.

3.

To get standard error of estimate:

mean sum of squared error = MSE

MSE = 56.5974

= √56.5974

= 7.523

4.

points of a student who spent 50 hours studying. we calculate this from the regression line

y = 0.437798 + 0.829539X

x = 50

y = 0.437798 + 0.829539(50)

y = 41.914

5.

no I would not be comfortable using estimate regression equation to predict his point of a student spent 120 hours studying. this value is out of range of the predictor values (independent variables)

6. to get r² (r squared)

r² = SSR/SST

SSR = 3249.72

SST = 3702.5

r² = 3249.72/3702.5

= 0.8777

7.

we are supposed to solve question 7 from question 8. but no question 8 was given. hence no solution

Answer:

The change in revenue from the sale of one more doghouse if 110 doghouses have already been sold is dR/dx=66.67 $/doghouse.

Step-by-step explanation:

We have a revenue function that is:

\(R(x)=14,000\cdot \text{ln}(0.01x+1)\)

We have to approximate the change in revenue from the sale of one more doghouse, if 110 doghouses have already been sold.

That is the marginal revenue at x=110.

The marginal revenue is expressed as the first derivative of the revenue.

Then, we calculate the derivative of R:

\(\dfrac{dR}{dx}=\dfrac{d}{dx}[14,000\cdot \text{ln}(0.01x+1)]\\\\\\\dfrac{dR}{dx}=14,000\dfrac{d}{dx}[\text{ln}(0.01x+1)]\\\\\\\dfrac{dR}{dx}=14,000\cdot\dfrac{1}{0.01x+1}\cdot \dfrac{d}{dx}(0.01x+1)\\\\\\\dfrac{dR}{dx}=14,000\cdot\dfrac{1}{0.01x+1}\cdot 0.01\\\\\\\dfrac{dR}{dx}=\dfrac{14,000}{x+100}\)

We then evaluate this marginal revenue at point x=110:

\(\dfrac{dR}{dx}_{|x=110}=\dfrac{14,000}{110+100}=\dfrac{14,000}{210}=66.67\)

Answer:

Step-by-step explanation:

i hope is this help you

The probability that both marbles are red is 1/8.

When we pull out the first marble, there are six red marbles and sixteen total marbles remaining in the jar. Therefore, the probability of getting a red marble on the first draw is 6/16, which simplifies to 3/8.

After the first marble is removed, there are five red marbles and fifteen total marbles remaining in the jar. Therefore, the probability of getting a red marble on the second draw, given that the first marble was red, is 5/15, which simplifies to 1/3.

To find the probability that both marbles are red, we multiply the probability of getting a red marble on the first draw by the probability of getting a red marble on the second draw, given that the first marble was red:

(3/8) x (1/3) = 1/8

So, the probability of getting two red marbles in a row is 1/8.

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Answer:

x=10

Step-by-step explanation:

Answer:

x = - 5/3

Step-by-step explanation:

Calculate the product

4x/5 = 2x + 4/2

Reduce the faction with 2

4x/5 = 2x + 2

Multiply both sides of the equation by 5

4x = 10x + 10

Move variable to the left-hand side and change its sign

4x - 10x = 10

Collect like terms

-6x = 10

Divide both sides of the equation by -6

x = - 5/3

Solution

x = -5/3

Alternate form

x = -1 2/3, x = -1.6

1 foot= 12 inches.

To convert you must have "2 fractions" to multiply.

Your first fraction must be 100in/1min. (100 inches per 1 minute).

The second should serve to convert inches to feet. It should be 1 foot/ 12 inches. (1 foot per 12 inches).

Your product should be 100ft/12 which equals 8.3 repeating or 25/3 (8 1/3) feet.

-8(x+1)=-5(x+10)

-8x-8=-5x-50

+50           +50

-8x+42=-5x

+8x        +8x

42=3x

/3     /3

14=x

The row of tiles would be 24 1/2 inches long.

B:The  row of 10 tiles would be 35 inches long.

A 1. To be able to know the length of the row of tiles, one need to multiply the length of one tile by the number of tiles in the said  row.

So, all tile measures 3 1/2 inches on each side, Hence  the length of one tile is 3 1/2 inches.

Based on the fact that there are 7 tiles in a row, we have to multiply the length of one tile by 7:

Length of the row = 3 1/2 inches/tile x 7 tiles

                              = 24 1/2 inches

So, the row of tiles is 24 1/2 inches long.

B 2. Also, to find the length of a row of 10 tiles, we need to multiply the length of one tile by 10.

Note that:

Length of one tile = 3 1/2 inches

Number of tiles in the row = 10

Hence:

Length of the row = 3 1/2 inches/tile x 10 tiles

                               = 35 inches

So, the row of 10 tiles is 35 inches long.

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Answer: The equation of a line perpendicular to 2x + 2y = - 10 that passes through the point (6, 2) is y = x - 4

Answer:

Yes

Step-by-step explanation:

This is a function because each input has an output