Hybrid and electric cars have gained in popularity in the last decade as a consequence of high gas prices. But their great gas mileages often come with higher car prices. There may be savings, but how much and how long before those savings are realized? Suppose you are considering buying a Honda Accord Hybrid, which starts around $31,665 and gets 48 mpg. A similarly equipped Honda Accord will run closer to $26,100 but will get 31 mpg. How long would it take for the Prius to recoup the price difference with its lower fuel costs, assuming you drive 800 miles per month? First, use the following formula for gas savings, where GM stands for gas mileage, to determine how far you will need to drive to recoup the cost difference in the vehicles. Use the known values and the average price of gas in your area to write a specific equation. $Gas is $4.35 Determine the type of equation that results, and then solve it algebraically. $Saved = $Gas x (distance driven) x ( GM now GM improved) Choose a Tesla (electric car) that has NO gas cost and compare it in a similar way to a gas-powered cari, the Honda Accord. How long will it take to recoup the price difference for the miles you drive per month? Assume you still drive 800 miles a month. Be sure to consider TOTAL COST of each car. Explain what you thought TOTAL COST meant in the previous question. Because of these results, it is reasonable to be concerned that the benefits of a hybrid car might not outweigh the initial higher cost. How efficient would the hybrid need to be in order to recoup a $3,000 price difference within 10 years if the standard vehicle gets 25 mpg?

Answer:

x = 7.875

Step-by-step explanation:

Let the number = x

When a number is multiplied by 5 before subtracting from 78 the result obtained is the same as three times the sum of the number and 5 find the number

Hence,

78 -(x × 5) = 3(x + 5)

Expand the brackets

78 - 5x = 3x + 15

Collect like terms

78 -15 = 3x + 5x

63 = 8x

x = 63/8

x = 7.875

Answer:

y = 3x - 4

Step-by-step explanation

If the line is perpendicular, then it means that the slope will be opposite. So if it's -1/3 then it will become 3.

y = 3x + b

-1 = 3(1) + b

-1 = 3 + b

-4 = b

The equation is y = 3x - 4

The measure of the angle should be 170° as this angle looks like an obtuse angle.

Hope that helps!

Answer: x^2+5x-14

Step-by-step explanation:

2 and -7 are the roots of the polynomial then we have to write them as

 x=2 ,x=-7

To convert these as factors, we have to write them as

(  x-2) (x+7)

The product of those factors will give the polynomial. Because we have two factors, we will get a quadratic polynomial.

x^2+7x-2x-14

x^2+5x-14

Number of factors  =  Highest exponent of the polynomial

Answer:

y = x² + 5x - 14

Step-by-step explanation:

Given roots x = a, x = b, then the corresponding factors are

(x - a) and (x - b) and the polynomial is the product of the factors

y = (x - a)(x - b)

Here the roots are x = 2 and x = - 7, then the factors are

(x - 2) and (x - (- 7)) = (x + 7), so

y = (x - 2)(x + 7) ← expand using FOIL

y = x² + 5x - 14

Answer:

Rhombuses

Step-by-step explanation:

It has four vertical lines, then draw a Venn Diagram, opposite to opposite.

Order from Venn Diagrams:

Quadrilaterals

Rectangles

Squares

Rhombuses.

The required basis of the orthogonal complement is {(2, 1, 0), (3, 0, 1)}.

Given that the line spanned by (-1, 2, 3) in R3.

To find the basis of the orthogonal complement, we need to find the vector which is orthogonal to (-1, 2, 3).

Let x = (x1, x2, x3) be a vector in the orthogonal complement of the given line.

Then we have: (-1, 2, 3)·x = 0-1x1 + 2x2 + 3x3 = 0x1 = 2x2 + 3x3

Thus, every vector x in the orthogonal complement has the form x = (2x2 + 3x3, x2, x3) = x2(2, 1, 0) + x3(3, 0, 1)

Therefore, the set { (2, 1, 0), (3, 0, 1) } is a basis of the orthogonal complement of the line spanned by (-1, 2, 3) in R3.

This is because both these vectors are linearly independent, and every vector in the orthogonal complement of the given line can be written as a linear combination of these two vectors.

Hence, the required basis of the orthogonal complement is {(2, 1, 0), (3, 0, 1)}.

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Answer: 47.5 or just 47

Step-by-step explanation: Well, to start, set up a ratio.

x / 50 = 95 / 100

95 * 50 is 4750

4750 / 100 is 47.5.

Now, it's asking how many questions he got correct. You can't get 47.5 questions correct, it should be a whole number. Now, I don't know how the rules work with that question, but it is like 47.

Answer:

7. 0.50980392

9. 12

10. 50

A continuous function the graph of y = f(x) and the x-axis on the interval [a, b] evaluating the definite integral of f(x) over that interval, the changes of f(x) if applicable.

The area between the graph of y = f(x) and the x-axis on the interval [a, b]  by evaluating the definite integral of f(x) over that interval.

The definite integral of f(x) from a to b represents the signed area between the graph of f(x) and the x-axis. The sign of the area depends on the behavior of f(x) above and below the x-axis.

If f(x) is non-negative (greater than or equal to 0) on the interval [a, b], then the area between the graph of f(x) and the x-axis will be positive or zero.

If f(x) is non-positive (less than or equal to 0) on the interval [a, b], then the area between the graph of f(x) and the x-axis will be negative or zero.

If f(x) changes sign on the interval [a, b] (i.e., it is positive in some regions and negative in others), then the area between the graph of f(x) and the x-axis will be the sum of the positive areas minus the sum of the negative areas.

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Answer: 234 - 40 = 2x

              194 = 2x

              97 = x

x being the amount Trey had before mowing lawns

Answer:

surface area = 544 cm²

Step-by-step explanation:

surface area = (16)(8 + 6 + 8 + 6) + (2)(8)(6) = 448 + 96 = 544 cm²

Answer:

See attachment

Step-by-step explanation:

Given

[tex]Side\ 1 = 10cm[/tex]

[tex]Side\ 2 = 12cm[/tex]

[tex]\theta = 90^\circ[/tex]

Required [Missing from the question]

Draw the top of the cake

See attachment for reference.

From the attachment,

[tex]2cm = 1\ unit[/tex]

So:

[tex]Side\ 1 = 10cm[/tex]

[tex]Side\ 1 = 5 * 2cm[/tex]

Substitute [tex]2cm = 1\ unit[/tex]

[tex]Side\ 1 = 5 * 1unit[/tex]

[tex]Side\ 1 = 5\ units[/tex]

[tex]Side\ 2 = 12cm[/tex]

[tex]Side\ 2 = 6 * 2cm[/tex]

Substitute [tex]2cm = 1\ unit[/tex]

[tex]Side\ 2 = 6 * 1unit[/tex]

[tex]Side\ 2 = 6\ units[/tex]

This means that, the given side lengths will be represented by 5 units and 6 units on the grid, respectively.

See attachment for drawing

Answer:A. 3 inches

Step-by-step explanation: :)

Answer:

b and c

Step-by-step explanation:

Answer:

12 crew members I think hope this helps :)

Step-by-step explanation:

☁️ Answer ☁️

12.

(66 2/3)

---------- (x) = 8

100

Solve for x

(66 2/3)x = 800

x = 800/(66 2/3)

x = 800/(200/3)

x = 800(3/200)

x = 4(3)

x = 12

Here's the link: https://www.wyzant.com/resources/answers/286307/a_crew_is_made_up_of_8_men_the_rest_are_women_66_2_3_are_men_how_many_people_are_in_the_crew

Hope it helps.

Have a nice day noona/hyung.

The absolute maximum value of the function on the interval [-3, 1] is approximately 28.97, and the absolute minimum value is approximately 3.84.

To find the absolute maximum and minimum values of the function f(x) = 31/3 - 3x2/3 on the interval [-3, 1], we need to evaluate the function at its critical points and endpoints.

First, let's find the critical points by taking the derivative of the function:

f'(x) = (2/3)(31/3)(-3x^(-1/3)) = -2(31/3)(1/x^(1/3)) = -62/x^(1/3)

To find the critical points, we set f'(x) equal to zero and solve for x:

-62/x^(1/3) = 0

This equation has no solutions since the numerator is always non-zero.

Next, we evaluate the function at the endpoints of the interval:

f(-3) = 31/3 - 3(-3)^(2/3) ≈ 3.84

f(1) = 31/3 - 3(1)^(2/3) ≈ 28.97

Finally, we compare the values of the function at the critical points and endpoints to determine the absolute maximum and minimum:

Absolute maximum: f(1) ≈ 28.97

Absolute minimum: f(-3) ≈ 3.84

Therefore, the absolute maximum value of the function on the interval [-3, 1] is approximately 28.97, and the absolute minimum value is approximately 3.84.

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Answer:

x = 19.48 or 19 12/25

Step-by-step explanation:

cos 41° = 14.7/x

x = 19.48 or 19 12/25

Answer:

2. 95

3. 85

4. 95

Step-by-step explanation:

Mark me brainliest? :)

Answer:

hope this helps you out question 4 and 3 are the same

Answer:

...

Step-by-step explanation:

remeber that for every angle they give you, you need to subtract 90 from it to get the answer.

Answer:

Step-by-step explanation:

B i took that same quiz

The dimensions of the largest area that can be enclosed is 1590 × 795= 1264050 yd² when no fencing is required along the river.

Given the owner of the Rancho Los Feliz has 3180 yd of fencing to enclose a rectangular piece of grazing land along the straight portion of a river and then subdivide it by means of a fence running parallel to the sides. No fencing is required along the river.

We need to find the dimensions of the largest area that can be enclosed.

Therefore, the length of the land is the perimeter of the rectangle minus the river front.

We have; 2x + 3y = 3180 yd

Also, we can rewrite this equation in terms of x;

2x = 3180 - 3yy = (3180 - 2x) / 3

Substituting y in terms of x in the area equation;

Area A = x y= x(3180 - 2x) / 3

Taking the derivative of the area equation to find the maximum value of A;

A' = 1060 - 2x / 3 When A' = 0, x = 1590 / 2 = 795 yd.

Substitute x = 795 into the equation for y;

2(795) + 3y = 3180y = (3180 - 1590) / 3 = 530 yd

Therefore, the dimensions of the largest area that can be enclosed are; Length = 1590 yd Width = 795 yd

Hence, the area is given by; Area = Length × Width= 1590 × 795= 1264050 yd².

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Answer:

first one is 432

Step-by-step explanation:took the test and got it right

The height and depth of locker is 40 inch and 5 inch.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

As per the known fact, volume of rectangle is calculated by multiplying the entities width, height and depth. Let us assume the depth be d.

So, the height is 4d. Keep the values in formula to find the value of depth.

10800 = 12 × d × 4d

4d² = 10800 ÷ 12

Performing Division

4d² = 900

d² = 900 ÷ 4

Performing Division

d² = 225

d = ✓225

Taking square root

d = 15

The depth of locker is 15 inch.

So, the height = 4d

Height = 4 × 15

Performing multiplication

Height = 60 inch

Therefore, the depth and height of locker is 15 inch and 40 inch.

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complete question:

A locker in the shape of a rectangular prism has a width of 12 inches. Its height is four

times its depth. The volume of the locker is 10,800 cubic inches. Find the height and depth of the locker.

Height:

Answer:

Simplified : 1:3

Step-by-step explanation:

7:21 is equal to 1:3

Also, for algebra tips. Algebra is literally practice. There aren't too many complicated equations or anything until you get into a higher math class so practicing problems is best.

Answer:

7:21 = 1:3

Tips for algebra...

just know the basics and related rules or theorams and practice as much as u can

good day mate

According to the Capital Asset Pricing Model (CAPM), A) the expected rate of return on a security increases in direct proportion to a decrease in the risk-free rate is the false statement.

According to the Capital Asset Pricing Model (CAPM), the expected rate of return on a security increases in direct proportion to an increase in the risk-free rate. Therefore, the statement that "The expected rate of return on a security increases in direct proportion to a decrease in the risk-free rate" is false.

The Capital Asset Pricing Model (CAPM) is a model that shows the relationship between risk and expected return and is used to calculate the expected return on an investment.CAPM is based on several assumptions, one of which is that investors are rational and risk-averse.

Another assumption is that the market is in equilibrium, meaning that supply equals demand for all securities. The model also assumes that investors have homogeneous expectations of future returns and that there are no taxes or transaction costs.CAPM states that the expected rate of return on an asset is a function of the risk-free rate, the expected market return, and the asset's beta.

Beta is a measure of the asset's volatility compared to the market. If an asset has a beta of 1, it is as volatile as the market. If it has a beta of less than 1, it is less volatile than the market, and if it has a beta of more than 1, it is more volatile than the market.

Therefore, according to CAPM, the expected rate of return on a security increases as its beta increases.In equilibrium, all securities lie on the security market line, and a fairly priced security has an alpha of zero.

Therefore, options B, C, and D are true, and the answer is option A, "The expected rate of return on a security increases in direct proportion to a decrease in the risk-free rate."

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There exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

In order to answer the given question, we first need to understand the definition of subspaces of a vector space.A subspace of a vector space is a subset that meets three requirements:

i) It includes the zero element of the vector space.

ii) It is closed under addition (if u and v belong to the subspace, then u + v is also in the subspace).

iii) It is closed under scalar multiplication (if u is in the subspace and k is a scalar, then ku is also in the subspace).

there exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

The reason is simple because if T∩U = Ø, then either SIT or SIU will be the trivial subspace {0}.

However, this contradicts the fact that both SIT and SIU have to contain a non-zero vector as they are subspaces that are generated by S, T, and U.

Therefore, it is proven that there exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.

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Answer:

x=4

Step-by-step explanation:

so there are two triangles in that shape and they are similar to each other because their angles are equal and the ratio of their sides it 1:2

so the ratio of the side 5x & 40 is 1:2

5x/40=1/2

10x=40

x=4

Answer:

10 years

Step-by-step explanation:

Simple interest formula:

AV=PV(1+it)

13200=8000(1+.065t)

1.65=1+.065x

.65=.065x

10=x