A certain car has a fuel efficiency of 55 miles per gallon when travelling at 70 miles per hour. How many miles will the car travel using 3 gallons?

analyze problem

2/5 are girls

35 students

working on first problem

1-2/5=3/5

ANSWER TO FIRST: 3/5

second

35 * 3/5

simplify denominator

7*3

21

21 boys

If 2/5 of the students in the class are girls, what fraction are the boys?

[] Let's say the whole class is equal to 5/5.

[] If there are only girls and boys in the class, then we can do the math 5/5 - 2/5 = 3/5 to find 3/5 of the class is boys

-> 3/5 of the class is boys

If the class has 35 students, how many boys are in the class?

[] With the second part of this problem, we are given more information.

[] Our whole, 5/5 before, is equal to 35. We can multiply 3/5 (boys in the class) by our whole, 35, for our answer. \(\frac{3}{5} *\frac{35}{1} =\frac{105}{5} =21\)

[] This gives us 21 boys in the class. We can test this by seeing that 3/5 = 21/35, so this solution makes sense.

-> There are 21 boys in the class

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

\(\tt x = 16\)

Step-by-step explanation:

\(\tt 4x-64=0\)

Add 64 to both sides.

\(\tt 4x - 64 + 64 = 0+ 64\)

Simplify.

\(\tt 4x = 64\)

Divide both sides by 4.

\( \tt \cfrac{4x}{4} = \cfrac{64}{4} \)

Simplify.

\(\tt x = 16\)

Done!!!

\(\Large\maltese\star\underline{\textbf{What is Asked}}\star\maltese\)

\(\Large\maltese\star\underline{\textbf{The required answer is below -:}}\star\maltese\)

First we need to add 64 to both sides. That way, we will be one step closer to solving this in terms of x.

\(\bf{4x-64+64=0+64}\) | on the left side the 64's sum to zero

\(\bf{4x=0+64}\) | the right side is now 64

\(\bf{4x=64}\) | divide the equation by 4

\(\bf{x=16}\)

\(\cline{1-2}\)

\(\gray\star\bf{Result / Required\;Answer:}\)

                  \(\star\blacksquare\Large\boxed{\boxed{\bf{X=16.}}}\blacksquare\star\)

When you're solving an equation in terms of x, or any other variable, use inverse operations to solve it. For instance, if something is added to x, use subtraction. If something is subtracted to x, use addition.

If x is multiplied by something, use division. If x is divided by something, use multiplication.

\(\infty\LARGE\boxed{\bf{\brace aesthetic\not1\theta\ell}}\infty\)

The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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So, in this case, the length of each of the equal sides is: 17 / \(\sqrt{2}\) ≈ 12.02

An isosceles triangle is a triangle in which two sides have the same length. This means that two of the three angles in the triangle are also equal in measure. The side that is not congruent to the other two sides is called the base of the triangle, and the angles opposite the congruent sides are called the base angles. In an isosceles triangle, the base angles are always equal in measure.

Isosceles triangles are a common shape in geometry and can be found in many real-world applications. They have special properties that make them useful in various fields of mathematics, such as trigonometry and geometry. For example, the base angles of an isosceles triangle are always equal, so if you know the measure of one of the base angles, you can determine the measure of the other base angle using the fact that the sum of the angles in a triangle is 180 degrees.

given by the question.

In an isosceles triangle with two equal angles of 45 degrees and a third angle of 90 degrees, the two equal sides are opposite the 45 degree angles, and the third side is opposite the 90 degree angle. Let's call the length of the missing side "x".

Using the Pythagorean theorem, we know that in a right triangle with legs of equal length (which is the case for the two 45-degree angles), the length of the hypotenuse is. \(\sqrt{2}\) times the length of the legs.

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Answer:

Step-by-step explanation:

185miles / 75mph =  2.5 hours

Answer:

Part A

The expression for the total amount of money Liz and Andy makes selling necklaces at the fair is

The total amount they both make from selling necklaces = 8·L + 8·A

Part B

The total amount they both make from selling jewelries = 35 + 8·L + 8·A

Step-by-step explanation:

The amount at which Liz and Andy sells necklaces = $8

The amount Andy makes selling bracelets = $35

Part A

The total amount of necklaces Liz sells = L

The total amount of necklaces Andy sells = A

The expression for the total amount of money Liz and Andy makes selling necklaces at the fair, 'N', is given as follows;

N = 8·L + 8·A

Part B

The expression for the total amount of money Liz and Andy makes selling jewelries at the fair, 'J', is given as follows;

J = 35 + 8·L + 8·A

The maximum distance between the earth and the satellite orbit with an elliptical orbit is 520 km.

In the question, we are given that a satellite orbits the Earth with an elliptical orbit modeled by x squared over 47 million four hundred seventy two thousand one hundred plus y squared over forty four million two hundred twenty two thousand five hundred equals 1, where the distances are measured in km. The Earth shares the same center as the orbit.

We are asked to find the maximum distance between the satellite and the Earth if the radius of the Earth is 6,370 km.

Given elliptical form is:

x²/47,472,100 + y²/44,222,500 = 1,

or, x²/6,890² + y²/6,650² = 1.

The radius of the Earth, R = 6,370 km.

We know that the standard elliptical form is:

(x - h)²/a² + (y - k)²/b² = 1, Where, in a horizontal ellipse;

a = The major axis (the longer axis), which gives the maximum distance between the satellite and Earth.

b = The minor axis (the shorter axis).

On comparing the given elliptical form to the standard elliptical form, we get a = 6,890.

The distance between the satellite and the surface of the Earth, d, is given as follows:

d = a - R

Which gives;

d = 6,890 km - 6,370 km = 520 km.

Thus, the maximum distance between the earth and the satellite orbit with an elliptical orbit is 520 km.

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Answer:

I have no idea how to do that.

Answer:

9576

Step-by-step explanation:

Area of the triangle × height

(1/2×28×19)×36

Answer:The sum-of-divisors function σ is multiplicative, with σ(pm)=1+p+…+pm for a prime p. In particular, σ(2m) is always odd, while for an odd prime .

Step-by-step explanation:

The number is 64

What are Factors of a Number?

Numbers that divide an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal parts. A factor is a number that divides another number, leaving no remainder

Given data ,

The number is less than 100

The number is even and sum of the digits is 10

So , the most probable numbers in the set S that would satisfy the given conditions are S = { 28 , 46 , 64 , 82 }

Now ,

The factors of 28 = 1,2,4,7,14 and 28

The factors of 46 = 1, 2, 23, and 46

The factors of 64 = 1, 2, 4, 8, 16, 32 and 64

The factors of 82 = 1, 2, 41 and 82

So , the number 64 is the only number with odd number of factors

Hence , the number is 64

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The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)

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

log₃(x²∛y²)

The product law of logarithms states that

log(ab) = log(a) + log(b)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  log₃(x²) + log₃(∛y²)

The power law of logarithms states that

log(aᵇ) =  blog(a)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  2log₃(x) + 2/3log₃(y)

This means that the values of A and B are A = 2 and B = 2/3

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Answer:

1, 0, -1, -2, -3, -4, -5, 3, 4, 5, 6, 7, 8, 9

Step-by-step explanation:

The algebraic expression for the sentence in this problem is given as follows:

n - (x + 8).

The sentence in this problem is given as follows:

"A number n minus the sum of the number and eight".

The sum of an unknown number x and eight is given as follows:

x + 8.

The subtraction of the number n by the expression is given as follows:

n - (x + 8).

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Answer:

Slope = \(\frac{7}{-3}\)

Step-by-step explanation:

(-5,18) (1,4)

\(\frac{18 - 4}{-5 - 1}\) = \(\frac{14}{-6}\) = \(\frac{7}{-3}\)

Answer:

Step-by-step explanation:

step 1:

determining the values for standard form for the equation of a line,

y = mx + c

Step 2:

calculation of m, where m is the gradient or slope which determines how steep the line is.

step 3:

calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept

The general solution to the given differential equation is:

y = (x/12) - (1/288)

How to solve the Differential Equation?

We want to solve the differential equation given as: y' - 24xy = -2x

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).

Multiplying the entire equation by the integrating factor, we get:

e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)

The left side of the equation is the derivative of (e^(-24x)y) with respect to x:

(d/dx)(e^(-24x)y) = -2xe^(-24x)

Integrating both sides with respect to x, we have:

e^(-24x)y = ∫(-2xe^(-24x))dx

Integrating the right side, we get:

e^(-24x)y = -∫(2xe^(-24x))dx

To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):

u = -2x (differential of u = -2dx)

dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)

Using the integration by parts formula:

∫uv dx = uv - ∫v du

We can compute the integral as follows:

-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]

= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]

= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]

= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]

= -[x/12e^(-24x) - 1/(288e^(-24x))]

= -[x/12 - 1/288]e^(-24x)

Substituting this back into the previous equation, we have:

e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]

Simplifying further:

e^(-24x)y = (x/12 - 1/288)e^(-24x)

Canceling out e^(-24x) on both sides:

y = x/12 - 1/288

Therefore, the general solution to the given differential equation is:

y = x/12 - 1/288

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Answer:

The third one.

Step-by-step explanation:

8x(5+2) is also 7x8 so you'd get 56. The 8x5 is 40 then you can do 40+(8x2) which is 40+16 which is = to 56. So the third one is equivalent to each other.

Answer:

The 3 is in the tens place

Step-by-step explanation:

Thousands, hundreds, tens, and ones

The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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Only the following two conclusions can be made:

This conclusion can be made by calculating the volume of water in Carmen's flask at time 6 seconds and at time 8 seconds, and comparing it to the volume of water in Matt's flask at the same times.

At time 6 seconds, the volume of water in Carmen's flask is 30 + 8.5(6) = 84 milliliters. At time 8 seconds, the volume of water in Carmen's flask is 30 + 8.5(8) = 94 milliliters. At time 6 seconds, the volume of water in Matt's flask is 10(1 + 0.28)^6 = 45.57 milliliters. At time 8 seconds, the volume of water in Matt's flask is 10(1 + 0.28)^8 = 64.15 milliliters.

Therefore, the volume of water in Carmen's flask is increasing at a faster rate than the volume of water in Matt's flask over the interval [6, 8].

This conclusion can be made because Matt's flask is increasing in volume by 28% each second, while Carmen's flask is increasing in volume by a fixed amount of 8.5 milliliters per second.

As time goes on, the percentage increase in Matt's flask will result in a faster rate of increase in volume compared to Carmen's flask.

Therefore, at some point, the volume of water in Matt's flask will be greater than the volume of water in Carmen's flask.

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Answer:

≈ 50°

Step-by-step explanation:

arc length is calculated as

arc = circumference × fraction of circle

let x be the angle subtending the arc, then

arc = 2πr × \(\frac{x}{360}\) , that is

7 = 2π × 8 × \(\frac{x}{360}\)

7 = 16π × \(\frac{x}{360}\) ( multiply both sides by 360 to clear the fraction )

2520 = 16π × x ( divide both sides by 16π )

\(\frac{2520}{16\pi }\) = x , then

x ≈ 50° ( to the nearest whole degree )

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

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

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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Answer:

Step-by-step explanation:

-4x-3=y

Here's link to the answer:

tinyurl.com/wpazsebu

Answer:

2.05

Step-by-step explanation:

The price of the stove in American dollars would be $407.72.

The exchange rate refers to the value of one currency in relation to another currency. It represents the rate at which one currency can be exchanged for another.

To convert the price of the stove from Canadian dollars to American dollars, we need to multiply the price in Canadian dollars by the exchange rate.

Price in American dollars = Price in Canadian dollars x Exchange rate

Price in American dollars = $529.50 x 0.77

= $407.72

Therefore, the price of the stove in American dollars would be $407.72.

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Answer:

7/10 = .70

3/5 = .60

9/11 = .81

1/2 = .50

9/11 is the most