Is y = 24x proportional

Answer:

Part A: 32 square yards per gallon

Part B: 13 square feet per gallon difference

Step-by-step explanation:

Part A:

To find how many square yards each gallon covers, you have to divide 42 2/3 by 1 1/3, which equals 32. That means each gallon of paint covers 32 square yards.

Part B:

First, you have to convert how much Angela covered in square yards to square feet. Since one square yard is equal to 9 square feet, we have to multiply 32 by 9, which equals 288. To find the difference, you have to subtract 288 - 275, which equals 13.

Final answer:

Angela's rate of paint coverage in square yards per gallon is 32, and the difference in square feet per gallon between Angela’s rate and the average rate on the paint label is 13 square feet per gallon.

Explanation:

Part A: Calculating Paint Coverage

To find Angela’s rate of paint coverage in square yards per gallon, we would divide the total area painted by the amount of paint used. We have 42 2/3 square yards painted using 1 1/3 gallons of paint. First, it's easier to work with improper fractions, so we convert 42 2/3 to (126/3 + 2/3) = 128/3 square yards, and 1 1/3 to (3/3 + 1/3) = 4/3 gallons. Now, we calculate the rate by dividing the square yards by the gallons:

Rate = ​(128/3) / (4/3) = (128/3) × (3/4) = 128/4 = 32 square yards per gallon.

Part B: Difference in Square Feet per Gallon

To find the difference in square feet per gallon, we need to compare Angela's rate to the average rate given on the label. Angela's rate is 32 square yards per gallon, and there are 9 square feet in a square yard. So, Angela's rate in square feet would be 32 × 9 = 288 square feet per gallon. The label states an average coverage rate of 275 square feet per gallon. Thus, the difference is:

Difference = Angela’s rate - Label’s rate = 288 - 275 = 13 square feet per gallon difference.

Answer:

The length of the base edge is 3 cm

Step-by-step explanation:

Volume of square pyramid =[tex]\frac{1}{3}BH[/tex]

Where B = area of square base

H = Height

Let the length of base edge be x

Area of base = [tex]Side^2 = x^2[/tex]

Height of pyramid = 5 cm

So,Volume of square pyramid =[tex]\frac{1}{3}BH=\frac{1}{3} \times x^2 \times 5[/tex]

We are given that The volume of a square pyramid is 15 cubic centimeters.

So,[tex]\frac{1}{3} \times x^2 \times 5=15[/tex]

[tex]x^2 = \frac{15 \times 3}{5}[/tex]

[tex]x=\sqrt[2]{\frac{15 \times 3}{5}}[/tex]

x=3

Hence the length of the base edge is 3 cm

Answer: $7.19

Step-by-step explanation:

28.76/4=7.19

Answer:

32.5% off

Step-by-step explanation:

Answer:

Using the combination formula, the number of different committees with 4 members that can be formed from a group of 9 students and order is not important, would be: 9C4 = 126

Hope this helps!

:)

Answer:

1% of 800 is 8, while 2% of 800 is 16

Step-by-step explanation:

Please mark brainliest :)

Answer:

1% of 800 is 8

2% of 800 is 16

Step-by-step explanation:

Answer:

Point D

Step-by-step explanation:

Answer:

The sandcastle B has the greatest volume

Step-by-step explanation:

The volume of a pyramid is given by the following formula:

V = (1/3) * A * h

Where A is the base area and h is the height.

Now we can calculate the volume of both pyramids:

V1 = (1/3) * 30 * 6 = 60 in3

V2 = (1/3) * 24 * 8 = 64 in3

So the volume of the pyramid B is bigger than the volume of the pyramid A.

Answer:

C. -11 x 6

Step-by-step explanation:

When you multiply a negative number with a positive, your answer will always be negative. In this case:

-11 x 6 = -66.

~

Answer:

C. -11 × 6

Step-by-step explanation:

A. -12×(-8)  =96

B. -72÷(-9) =8

C. -11×6 =-66

D. -14+24=10

Only option C gives a negative answer.

Step-by-step explanation:

X + x + x + x = 4x

4x = 4x

It is true

There are a total of 24 different combinations of exterior color, interior color, and engine that the car company can offer.

The multiplication principle states that if there are a number of choices for one aspect of a problem, and a number of choices for another aspect of the problem, and the choices for each aspect are mutually exclusive (i.e., they do not overlap), then the total number of choices is the product of the number of choices for each aspect.

As per the question, there are 4 choices for the exterior color of the car, 3 choices for the interior color of the car, and 2 choices for the engine of the car.

Using the multiplication principle, we can determine that the total number of different variations of the car is :

4 x 3 x 2 = 24.

This means that the car company may provide a total of 24 distinct exterior colors, interior colors, and engine combinations.

To learn more about the multiplication principle click here:

https://brainly.com/question/29117304

#SPJ5

Using the multiplication principle, by simply multiplying together the number of options for each feature (4 exterior colors, 3 interior colors, 2 engines), we find that there are 24 possible variations of the car that the company can make.

The multiplication principle in mathematics is a tool used in combinatorics that suggests that if you have multiple groups of items, and you want to know how many different combinations there are of one item from each group, you can simply multiply the amount of items in each group. In the context of your car company question, with 4 exterior colors, 3 interior colors, and 2 types of engines, the multiplication principle suggests you can calculate the total combinations by multiplying these numbers together. So, you would have:

4 (exterior colors) * 3 (interior colors) * 2 (engine types) = 24 total variations

Therefore, according to the multiplication principle, there would be 24 different variations of the car the company could produce.

https://brainly.com/question/17758398

#SPJ12

-2x means -2*x or "-2 times x" where x is a placeholder for any number you want.

To graph y = -2x, you just need two points. Each point is of the form (x,y)

Let's plug in zero as it is often the easiest to work with.

If x = 0, then -2*x = -2*0 = 0. Notice how I replaced x with 0 and simplified.

Therefore, if x = 0, then y = 0. We have (x,y) = (0,0) as one point on this line. I have marked it as point A in the graph.

Point B is (1, -2) and it is found by plugging x = 1 into the equation to get...

y = -2x

y = -2*1

y = -2

You could find other points, but two points is enough to draw a straight line through them. The slope of this line is -2 = -2/1. The y intercept is 0.

Answer:

About 90%

Step-by-step explanation:

If the cup was filled at a constant rate, then the cup fills at 70/2=35 cubic centimeters per second. The formula for the volume of a cone is [tex]\frac{1}{3} \pi r^2 h[/tex], or in this case [tex]\frac{112}{3}\pi[/tex] cubic centimeters. After 3 seconds, the cup would have 35*3=105 cubic centimeters of water inside of it, or about 89.52% which rounds to 90%. Hope this helps!

Answer:

(a) 55080 m³

(b) 1312 truckloads

(c) 11 days

Step-by-step explanation:

(a) We have a rectangular prism with the dimensions 12 by 85 by 54, so the volume is just the product of these numbers:

V = 12 * 85 * 54 = 55080 m³

(b) The truck can hold 42 m³ of earth, so divide 55080 by 42 to get the number of truckloads required:

55080 / 42 = 1311.4

Since we will still need a truckload to hold that little bit of earth that involves 0.4 of a truck, we round up to 1312 truckloads.

(c) In one day, 4 trucks work for 6 hours and since each truck can remove 42 m³ with 5 loads per hour, we have:

42 * 5 * 6 * 4 = 5040 m³ earth removed a day

Divide 55080 by 5040 to get the number of days:

55080 / 5040 = 10.9 ≈ 11 days

Part A:

The volume can be found by multiplying all the dimensions of the earth being evacuated.

12 * 85 * 54 = 55,080m³

Part B:

Divide the number of capacity that each truck carries of earth.

55,080 / 42 = 1,311.4285

I would assume we round up since that little bit that's left over is another load.

So, 1,311.4285 → 1,312 truckloads

Part C:

4 trucks work non-stop for a 6 hour day, each truck can transport 5 loads per hour, and each truck can carry 42m³ of earth. We can multiply all these numbers and divide by the total earth capacity.

42 * 6 * 5 * 4 = 5,040

55,080 / 5,040 = 10.9285...

Round up.

10.9285... → 11 days

Best of Luck!

Answer:

a=8

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2 +15^2 = 17^2

a^2 +225 = 289

Subtract 225 from each side

a^2 +225-225=289-225

a^2 = 64

Take the square root of each side

sqrt(a^2) = sqrt(64)

a = 8

Answer:

8

Step-by-step explanation:

Using the Pythagorean theorem, you can find that the missing side length is [tex]\sqrt{17^2-15^2}=8[/tex] units. Hope this helps!

Answer:

[tex]v=3[/tex]

Step-by-step explanation:

[tex]-2v+2=-7v+17[/tex]

[tex]-2v+2-2=-7v+17-2\\-2v=-7v+15\\-2v+7v=-7v+15+7v\\5v=15\\v=3[/tex]

Answer:

what is it over?

Step-by-step explanation:

you have to be more specific

The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius.

The circumference of a circle can be found using the formula C = 2πr, where C represents the circumference and r is the radius of the circle.

For example, if the radius of the circle is 5cm, the circumference would be C = 2π(5) = 10π cm. It is important to note that the circumference is always given in terms of π, which represents the mathematical constant.

Therefore, the circumference of a circle can be calculated by multiplying the radius by 2π.

https://brainly.com/question/26605972

#SPJ2

Answer:

x = (y - b)/m

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First subtract b from both sides:

y = mx + b

y (-b) = mx + b (-b)

y - b = mx

Next, divide m from both sides:

(y - b)/m = (mx)/m

x = (y - b)/m

x = (y - b)/m is your answer.

~

Answer:

  9 3/4 . . . . (for the numbers shown)

Step-by-step explanation:

Each number in the table is the product of the number in the left margin and the number in the top margin:

  9 = 3·3

  3/4 = 3·1/4

The total of these numbers in the table is the Area value being asked for.

  9 + 3/4 = 9 3/4

_____

If there is more to the question that isn't shown, you will need to add those partial products to the total, too. We presume you know how to add fractions and mixed numbers.

Answer:

1st Problem: 6m + n - 10p

Step-by-step explanation:

5m - {2n + [3p - (m + 3n - 7p)]}

5m - {2n + [ 3p - m - 3n + 7p]}

5m - {2n + 10p - m - 3n}

5m - {-n + 10p - m}

5m + n - 10p + m

6m + n - 10p

** I don't understand what you are trying to say in the 2nd problem **

Answer:

6, 8, 10, 12, 18, 20

Mean: 6 + 8 + 10 + 12 + 18 + 20 = 74/6 = 12.3

Median: 11

Mode: there are no mode in the following listed numbers or data set.

~hope this helps~

would highly appreciate it if you would mark me the brainliest

9514 1404 393

Answer:

  P = 8

Step-by-step explanation:

The "varies inversely" relation can be expressed by the equation ...

  P = k/x

For the given values, we can find k to be ...

  k = Px = (7)(8) = 56

Then for the new value of x, we have ...

  P = 56/x = 56/7

  P = 8

Final answer:

P varies inversely with x and given P=7 when x=8, the constant of variation k is determined to be 56. Using this constant, the value of P when x=7 is calculated to be 8.

Explanation:

The student's question relates to the concept of inverse variation in mathematics. The relationship between two variables is described as inversely proportional if their product is constant. In the given scenario, P varies inversely with x and the student provided a specific condition where P = 7 when x = 8. Therefore, using the constant of variation k, the equation can be written as P = k/x. To find the constant of variation, we use the provided values:

Now with the constant k found, to calculate the value of P when x = 7, we set up the equation:

Therefore, the value of P when x = 7 is 8.

Greetings :)

To find slope of two points we will need to use this equation:   [tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

 [tex]x^1[/tex]     [tex]x^2[/tex]     [tex]y^1[/tex]    [tex]y^2[/tex]  

( 6 , -12 ) ( 15 , -3 )

Now let's replace the equation with the numbers. (it will be a fraction).

[tex]\frac{-3-(-12)}{15-12}[/tex]         =         [tex]\frac{9}{9}[/tex]

The equation equals 9 over 9, which also equals 1.

The slope of the line is 1.

Answer:

The box has a total volume of 36 cubic inches.

Step-by-step explanation:

The total volume of the box is given by the volume that is filled with books plus the volume that doesn't have any books in it. Therefore, in order to solve this problem we must sum the two volumes. We have:

total volume = volume with books + volume without books

total volume = 24 + 12

total volume = 36 cubic inches

The box has a total volume of 36 cubic inches.

Answer:

96

Step-by-step explanation:

12x8=96

Answer:

15 people

Step-by-step explanation:

if each person eats 8 pieces of pizza, 12 people can be served because 8 slices are in 1 pizza and he ordered 12 pizzas.

Answer:

-3 and 12 are the answer

Step-by-step explanation:

-3 times 12 is - 36 and

-3 plus 12 is 9

Hope this helps ;)

The two unknown numbers are x=-3 and y=12.

Let the two unknown numbers be x and y.

Two numbers that multiply to -36 and add to 9.

xy=-36 -------(i)

x+y=9 -------(ii)

x=9-y -------(iii)

Substitute x=9-y in equation (i), we get

(9-y)y=-36

9y-y²=-36

y²-9y-36=0

y²-12y+3y-36=0

y(y-12)+3(y-12)=0

(y-12)(y+3)=0

y-12=0

y=12

Substitute y=12 in equation (ii), we get

x=-3

Therefore, the two unknown numbers are x=-3 and y=12.

To learn more about the linear system of an equations visit:

https://brainly.com/question/27664510.

#SPJ2

Answer:

1,2,5

Step-by-step explanation:

Answer:

1,2,5

Step-by-step explanation:

Answer:

x= 71, y= 19.

Step-by-step explanation:

To solve this, we will need to set up an algebraic equation. Since y is the smaller number, we can think of x in terms of y:

x= 3y+14

We can substitute this in the equation to get:

90= y+3y+14.

Simplifying this will give us:

76= 4y.

When solved, we get the value of y (the smaller number) to be 19.

To solve for x, we must plug this into the equation giving us:

x= 3(19)+14

x= 71.

Answer: x+y=90;x=14+3y

71, 19

Step-by-step explanation:

Answer:

X = -2

Y = 5

Step-by-step explanation:

Look at attachment:

Hope this helps! :)