A family has two cars. During one particular week, the first car consumed 15 gallons of gas and the second consumed 25 gallons of gas. The two cars drove a combined total of 1525miles, and the sum of their fuel efficiencies was 75 miles per gallon. What were the fuel efficiencies of each of the cars that week?

Answer:

i do not see a graph... :/

Step-by-step explanation:

sorry-

Answer:

graph?

Step-by-step explanation:

The graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed

The function is given as:

f(x) = x^2

When the coefficient of x^2 changes to 1/3, we have:

f(x) = 1/3x^2

The above represents a stretch of the function

This means that the graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed

Read more about transformation at:

https://brainly.com/question/24850937

#SPJ1

Answer:

B) in the modern art section of an art museum

Step-by-step explanation:

Hope it helps! =D

The probabilities for this problem, considering that the first two balls chosen are red, are given as follows:

a) Both are red: 1/3.

b) The next is red: 2/3.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When two balls are selected, either with two colors, red or blue, the possible outcomes are given as follows:

We know that the two balls chosen were red, meaning that the possible outcomes are given as follows:

Hence the probability that both are red is of 1/3, which is one of the three outcomes (Red - Red).

Then, considering that each of the three outcomes is equally as likely, the probability that the next is red is calculated as follows:

p = 1/3 + 2/3 x 1/2 = 1/3 + 1/3 = 2/3.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The answer is:

g(x + 1) = 6x + 1

g(4x) = 24x -5

Work/explanation:

To evaluate, I plug in x + 1 into the function:

\(\sf{g(x)=6x-5}\)

\(\sf{g(x+1)=6(x+1)-5}\)

Simplify

\(\sf{g(x+1)=6x+6-5}\)

\(\sf{g(x+1)=6x+1}\)

------------------

Do the same thing with g(4x)

\(\sf{g(4x)=6(4x)-5}\)

\(\sf{g(4x)=24x-5}\)

Hence, these are the answers.

Answer:

C.

Step-by-step:

The measure of angle A is congruent to the measure of angle P.

A sample size of at least 44 is required to estimate the population mean with 90% confidence and a margin of error of 5, assuming the population standard deviation is approximately .

To find the sample size required to estimate a population mean with a certain level of confidence and margin of error, we can use the formula:

n = (z * σ / E)^2

where:

n = sample size

z = z-score corresponding to the desired level of confidence (in this case, 90% confidence corresponds to a z-score of 1.645)

σ = population standard deviation

E = margin of error

Plugging in the given values, we get:

n = (1.645 * / 5)^2

Simplifying this expression, we get:

n = 43.56

Rounding up to the nearest whole number, we get:

n = 44

Therefore, a sample size of at least 44 is required to estimate the population mean with 90% confidence and a margin of error of 5, assuming the population standard deviation is approximately .

Learn more about sample size at https://brainly.com/question/28583871

#SPJ1

Answer:

Hey there!

Step-by-step explanation:

This is ur answer...

The calculus of variations is a field of mathematics about solving optimization problems. This is done by minimizing and maximizing functionals. The methods of calculus of variations to solve optimization problems are very useful in mathematics, physics and engineering.

Hope it helps!

Brainliest pls!

Follow me <3

Answer:

9514 1404 393

Answer:

 $67,200

Step-by-step explanation:

The amount if interest is given by the formula ...

I = Prt

where P is the amount invested, r is the annual rate, and t is the number of years. Here, we want to find P when r = 0.05 and t = 1/2 such that I = 1680.

 P = I/(rt) = $1680/(0.05·0.5) = $1680/0.025

 P = $67,200

The amount invested was $67,200.

Step-by-step explanation:

Thegreatest common factor of the expression 3x^3-9x^2-30x is 3x.

Here we want to get the greatest common factor of the expression:

3x^3-9x^2-30x

We can se that all the terms have some multiple of 3 and some power of x, then the greatest common factor of the given expression is just 3x.

3x^3-9x^2-30x = 3x*(x^2 - 3x - 10)

If you expand the thing in the right you will get the original expression.

LEarn more about greatest common factor at

https://brainly.com/question/219464

#SPJ1

Answer:

Step-by-step explanation:

This problem is a composition of function defined by C(V(r)), now we have the functions \(V(r)= \pi r^{3}\) and \(C(V)=3.2V\), where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,

\(C(V(r))=3.2(\pi r^{3} )\)

Therefore, the right answer is the last choice.

Answer:

Step-by-step explanation:

Answer:

The equation that can be used to solve for m∠1 is:

m∠1 = One-half(a – b)

This is because angle 1 intercepts arc a, which has a measure of a. By the same token, angle 2 intercepts arc b, which has a measure of b. The sum of the measures of angles 1 and 2 is equal to the measure of the angle formed by the two intersecting chords, which is one-half the sum of the measures of arcs a and b. Therefore, we have:

m∠1 + m∠2 = One-half(a + b)

Since m∠2 is not given, we cannot solve for m∠1 using this equation. However, we can use the fact that the sum of the measures of the angles in a triangle is 180 degrees to get:

m∠1 + m∠2 + m∠3 = 180

where m∠3 is the measure of the angle formed by the two chords outside the circle. Since this angle is supplementary to angle 1, we have:

m∠1 + m∠3 = 180

Substituting the equation for the sum of the measures of angles 1 and 2, we get:

m∠1 + One-half(a + b) = 180

Solving for m∠1, we get:

m∠1 = 180 - One-half(a + b) = One-half(360 - a - b) = One-half(a - b)

An equation for the function graphed above include the following: g(x) = -1/4|x + 1| - 2.

By critically observing the graph of this absolute value function, we can reasonably infer and logically deduce that the parent absolute value function f(x) = |x| was vertically compressed by a factor of 1/4, reflected over the x-axis, followed by a vertical translation 2 units down, and then a horizontal translation to the left by 1 unit, in order to produce the transformed absolute value function as follows;

f(x) = |x|

y = A|x + B| + C

g(x) = -1/4|x + 1| - 2

In conclusion, the value of the variables A, B, and C are -1/4, 1, and 2 respectively.

Read more on absolute value function here: brainly.com/question/28308900

#SPJ1

Answer:

2340 mm

Step-by-step explanation:

We know that since the rectangular prism has a square base, the length and width are equal

So we have V = 10 * 10 * 15

For the small rectangular slab we can subtract 10 from 40 to get 30 for the length

Thus we have V = 30 * 4 * 7

Hope this helps

Answer:

2450

Step-by-step explanation:

Answer:

dV ≈ 927.4 cm³

Step-by-step explanation:

Formula for volume of a cylinder is;

V = πr²h

Using differentials, we have;

dV = (dV/dr)dr + (dV/dh)dh

Now, dV/dr = 2πrh

dV/dh = πr²

Thus, at r = 24/2 = 12 cm

And at h = 60 cm, we have;

dV/dr = 2π(12 × 60)

dV/dr = 4523.89 cm²

Also;

dV/dh = π(12)²

dV/dh = 452.39 cm²

the metal in the top and bottom is 0.1 cm thick. Thus, dr = 2 × 0.1 = 0.2

the metal in the sides is 0.05 cm thick. Thus; dh = 0.05

Thus;

dV = (4523.89 × 0.2) + (452.39 × 0.05)

dV ≈ 927.4 cm³

Answer:

880

Step-by-step explanation:

I hope this answer helps!

Let "x" represent the number of dozens sold, if each dozen is sold for $3, then "3x" represents the amount earned after selling "x" dozens of cookies.

You need to raise $1000 by selling cookies, then:

Divide both sides by 3

You need to sell approximately 334 dozens of cookies to raise $1000.

Multiply the result by 12 to calculate the number of cookies:

You have to sell 4000 cookies.

Problem 13, part A

Recall that the term "circumference" is a special name for the distance or perimeter around a circle. Think "circle fence" which sounds a bit like "circumference", at least if you say it fast enough. That's how I remember it.

We're given 100 feet of fencing and we need to find the diameter of the circle that can be formed with this amount of fencing. We'll plug C = 100 into the circumference formula below and solve for d.

C = pi*d

100 = 3.14d

3.14d = 100

d = 100/(3.14)

d = 31.84713

The diameter of this circle is roughly 31.84713 feet

=========================================================

Problem 13, part B

Cut the diameter we just found in half to get

r = d/2

r = (31.84713)/2

r = 15.923565

Now use this radius value to find the area of this circle

A = pi*r^2

A = 3.14*(15.923565)^2

A = 796.178156

The area of the circle is roughly 796.178156 square feet

=========================================================

Problem 14

(1 inch)/(25 miles) = (6.5 inches)/(x miles)

1/25 = (6.5)/x

1*x = 25*6.5

x = 162.5

Therefore, 6.5 inches on the map correspond to 162.5 miles

The percentage decrease of the depth of the lake from January to August is 20%.

The difference between the initial and final numbers is shown as a percentage reduction. It displays a percentage loss of value compared to the original regardless of the units. The decrease is equal to the initial amount less the final amount.

Given,

The depth of lake in January = 943 feet

The depth of lake in August = 754.4 feet

The difference is = (943-754.4) feet

                             = 186.6 feet

So, the percentage decrease of the depth of the lake from January to August will be =  (186.6 ÷ 943) × 100

                        = 20%

Therefore, the answer is 20%.

To know more about percentage decrease refer to:

https://brainly.com/question/13631568

#SPJ1

Entering the values obtained from the data in the table based on the

given functions of y = a·x + b, and y = a·|x| + b, we have;

(1) y = -0.0614·x + 1.58772

(2) y = 0.3824·x + 0.91168

The least squares regression formula is presented as follows;

\(a = \mathbf{\dfrac{\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right) }{\sum \left(x_i - \bar x\right )^2 }}\)

(1) From the data in the table, and by using MS Excel, we have;

\(\overline x\) = -0.2

\(\overline y\) = 1.6

\(\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right)\) = -1.4

\(\sum \left(x_i - \bar x\right )^2\) = 22.8

Which gives;

\(a = \dfrac{-1.4}{22.8 } \approx \mathbf{-0.0614}\)

1.6 ≈ b - 0.0614 × (-0.2)

b = 1.6 -  0.0614 × (0.2) = 1.58772

The equation of best fit for the function, y = a·x + b, is therefore;

(2) For the function, y = a·|x| + b, we have;

\(\overline x\) = 1.8

\(\overline y\) = 1.6

\(\sum \left(x_i - \bar x\right) \times \left(y_i - \bar y\right)\) = 2.6

\(\sum \left(x_i - \bar x\right )^2\) = 6.8

Which gives;

\(a = \dfrac{2.6}{6.8} \approx \mathbf{0.3824}\)

1.6 ≈ b + 0.3824 × (1.8)

b = 1.6 -  0.3824 × (1.8) = 0.91168

The equation of best fit for the function, y = a·|x| + b, is therefore;

Learn more about the least squares regression line here:

https://brainly.com/question/15882801

Answer:

A = 20%

B = 80%

Step-by-step explanation:

200/1000 people said Lombardi's, or:

since 1,000 = 100

and 200 = 20

then we can simplify this to

20/100 0r 20%

and if 100 people to the survey and 20/100 said Lombardi's,

that means 80% must have said Patsy's, because,

100 - 20 is the 80 percent of people who didn't vote for Lombardi's, and since Patsy's is the only other option, that means the other 80% voted for Patsy's.

So

20% said Lombardi's

and

80% said Patsy's!

to be honest, I think I like Patsy's more as well.

Mark Brainliest if this helped, and have a good day! :D

With the calculations carried out, we came to the conclusion that 63 women work in this factory.

Percentage or percentage rate is a way of denoting a denominator ratio of 100 or any representation equivalent to it.

Examples:

\(● \: 70\% = \frac{70}{100} = \frac{7}{10} = 0.7 \\ \\ ● \: 0.15 = \frac{15}{100} = \frac{3}{20} = 15\%\)

Data provided by the statement:

Solution:

Therefore, 63 women work in this factory.

Answer:

A: 12.5

B: 36

C: 40

D: 88

Step-by-step explanation:

those are the answers

Answer:

4(x - 5)(x + 3) = 0

Step-by-step explanation:

To factor a quadratic equation in standard form, we need to find two binomials that multiply together to give us the quadratic equation.

The quadratic equation in standard form with a=4, b=-8, and c=-60 is:

Copy code

4x^2 - 8x - 60 = 0

To factor it completely, we need to find two binomials that multiply together to give us this quadratic equation. The first term of each binomial must be 2x since 2x times 2x gives us 4x^2. The last term of each binomial must be negative since -6 times 10 is -60.

So, we need to find two factors of -60 that add up to -4 (which is -b/a).

The two factors of -60 that add up to -4 are -10 and 6.

Therefore, we can factor the quadratic equation as:

4x^2 - 8x - 60 = 0

4(x^2 - 2x - 15) = 0

4(x - 5)(x + 3) = 0

So the factored form of the quadratic equation is 4(x - 5)(x + 3) = 0