Desmos here is a rectangular prism made from a stack of cubes. Determine the volume of the stack.​

Solving a system of equations we can see that the washer costs $750, and the dryer costs $250.

Let's define the variables:

x = cost of the washer.

y = cost of the dryer.

We know that the cost combined is $1000, then:

x  + y = 1000

And the washer cost 3 times the cost of the dryer, then we will get:

x = 3y

So we have a system of equations, we can replace the second equation into the first one, so we will get:

3y + y = 1000

4y = 1000

y = 1000/4

y = 250

The cost of the washer is:

x = 3*250 = 750

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Answer: The athletes would need to run a total of 3 laps around the track to run 3 miles.

Step-by-step explanation: 3x1=3 tada

The equation representing this relationship is y = 1.5x and the constant of proportionality is 1.5.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Suppose we have two ratio p : q and r : s. If both these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Given that, the amount of flour needed for a recipe is proportional to the number of servings planned.

If a variable x is proportional to the other variable y, then the equation representing the relation is y = kx.

Here y is the amount of flour required and x is the number of servings planned.

When y = 4.5, x = 3.

4.5 = 3k

k = 4.5 / 3 = 1.5

The equation is y = 1.5 x, which represents the relationship between the amount of flour required and the number of servings planned.

Constant of proportionality is 1.5.

This means that the ratio of the y to x is a constant and is equal to 1.5.

Hence the equation representing the situation is y = 1.5x.

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Answer:

5x ^2 + 5x + 4

Step-by-step explanation:

Combining like terms we have

(1+4)x^2 + (3+2)x + (-1+5)

= 5x^2 + 5x + 4

A, percentages

You would see percentages on a circle graph, because it's how many parts of the whole that they take up.

Happy to help, have a great day! :)

Answer:

1.2

Step-by-step explanation:

{2.8, 0.75, +1.2}

Median: 1.2

Answer:  4.75

Step-by-step Explanation

Answer:

6) x=5

7)x=6

8)x=10

9)x=12

Step-by-step explanation:

6) 3x-5=10. 7) 36=4x+12. 8) 3(x+2)=36

+5 +5. - 12. - 12. 3x + 6=36

3x = 15. 24 = 4x. - 6. -6

÷3. ÷3. ÷4. ÷4. 3x=30

x=5. 6 = x. x = 10

9) 7(2x-15)=63

14x - 105=63

+105. +105

14x = 168

÷14. ÷14

x=12

Answer:

82991 employees

Step-by-step explanation:

One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that

28300 = 34.1%

If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get

829.912 = 1%

Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get

100% = 82991

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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The misleading about the data shown on the figure is the clas width

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

The histogram

On the histogram, we have the following readings

From the above, we can see that

The above readings are not consistent i.e. the class widths are not equal

Hence, the misleading about the data shown on the figure is the clas width

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Answer: C = $37.5

Step-by-step explanation:

Given information

Price of one ticket = $8.50

Convenience fee = $3.50

Number of tickets = 4

Given expression

C = 8.50t + 3.50

Substitute the value of the ticket into the expression

C = 8.50 (4) + 3.50

Simplify by multiplication

C = 34 + 3.5

Simplify by addition

C = $37.5

Hope this helps!! :)

Please let me know if you have any questions

Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer:

11.93 ml

rounded to two significant figures: 12ml

Step-by-step explanation:

65/5.45=11.93 ml

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Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer:

$67.5

Step-by-step explanation:

50+25=75. Then, it's 1/10 of 75 which is $7.5. Then, 75-7.5 which is $67.5

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The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs.

We have,

The Pythagorean theorem that relates to the sides of a triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (known as the legs). Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the legs, and "c" is the length of the hypotenuse.

Now,

In a right triangle, the legs are the two sides that form the right angle, and the hypotenuse is the side that is opposite to the right angle. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse = sum of the squares of the legs. So, the relationship between the legs and the hypotenuse can be described by this theorem. In other words, if we know the length of the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse, and vice versa. The hypotenuse is always the longest side of the right triangle, and it is also the side that connects the two legs.

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complete question:

Applying the Pythagorean Theorem In this activity, you will explain your understanding of mathematical relationships and use the Pythagorean theorem to solve real-world problems. Question 1 In your own words, explain the relationship between the legs and the hypotenuse of a right triangle.

Answer:

y=2.9

Step-by-step explanation:

The constant proportion of y = 2.9x is 2.9.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

y = 2.9x

This can be written as,

y ∝ x

y = kx

Where k is the constant of proportionality.

Now,

Comparing y = kx and y = 2.9x

k = 2.9

Thus,

The constant proportion is 2.9.

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Answer:

12/13

Step-by-step explanation:

P(card is not an Ace) =

(# of ways to not pick an ace) / (# of ways to pick a card from the deck) =

(52 - 4)/(52) =

48/52 =

12/13

Percentages can be expressed as decimals. Percentage of something can be found by multiplying the number by the decimal.

20% = 0.20

20%(18.5)
0.20(18.5)
3.7

Since this is a 20% increase, we will add this to the original value.

18.5 + 3.7 = 22.2

Answer:

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(3, −7) and (−1, 1)

The slope is

\(m = \frac{1 - - 7}{ - 1 - 3} = \frac{1 + 7}{ - 4} = - \frac{8}{4} = - 2 \\ \)

We have the final answer as

Hope this helps you

Answer:

slope = difference_in_y/difference_in_x

= (-1 - -7)/(3 - 1)

= 6/2

= 3

Step-by-step explanation:

Answer:

Units of hair products = 2634 units

Step-by-step explanation:

Given that:

Worth of products in the inventory = $6400

Average cost per unit = $2.43

Number of units = \(\frac{Total\ worth}{Per\ unit\ cost}\)

Number of units = \(\frac{6400}{2.43}\)

Number of units = 2633.73

Rounding off to nearest whole number = 2634 units

Hence,

Units of hair products = 2634 units

Answer:

37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

945 accidents.

In 64 of them, the pedestian was intoxicated.

In 292 of them, the driver was intoxicated.

Probability that the pedestrian was intoxicated or the driver was intoxicated.

(64+292)/945 = 0.3767

37.67% probability that the pedestrian was intoxicated or the driver was intoxicated.

a) The value of x is 42.6 when k =16/3 is directly proportional to y.

b) The value of x is -56 when k is -7  is directly proportional to y.

What kind of variation is one where x and y are directly proportional?

x varies directly as y

x α y

x = ky

a) x=6 ; y = 32

x = ky

6 = k(32)

k = 16/3

if y = 8

then,

x = (16/3) * 8

= 128/3

x = 42.6

Hence, the value of x is 42.6 when k =16/3 is directly proportional to y.

b) x= 14 and y = -2

x = ky

14 = k(-2)

k = -7

if y = 8

then,

x = ky

x= (-7) 8

x = -56

Hence, the value of x is -56 when k is -7  is directly proportional to y.

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Answer:

16 is natural, whole, and an integer. Since it can also be written as the ratio 16:1 or the fraction 16/1

Step-by-step explanation:

Answer:

0/33

Step-by-step explanation:

There are 12 people who play tennis, but all of those 12 people also play football, so nobody only plays tennis.

Answer:

Option B

Step-by-step explanation:

The figures are made out of squares.

\(\text {Formula for area of a square: } A =s^2\\s-\text {Length of side.}\)

Square 1 (the gray square):

The side measure is 4 cm.

\(A = 4^2 = 16cm^2\)

Square 2 (white square):

The side measure is 2 cm.

\(A=2^2=4cm^2\)

Subtract the area of the white square from the gray square to get the area of the shaded region:

\(16 - 4 =12\)

The shaded region is \(12cm^2\).

Option B should be the correct answer.

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The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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Answer: B and C

Step-by-step explanation:

Answer:

x<-6

Step-by-step explanation:

-2x-4>8

(move the constant to the right)

-2x > 8+ 4

(calculate)

-2x>12

(divide both sides)

x<-6

(your answer)