Sandy can fold 6 towels in 3 minutes. If she continues at this rate, how many minutes will it take her to fold 36 towels?

In a group of Explore students, 38 enjoy video games, 12 enjoy going to the movies and 24 enjoy solving mathematical problems. O

Elodia [21]

Answer:

The number of students that like only two of the activities are 34

Step-by-step explanation:

Number of students that enjoy video games, A = 38

Number of students that enjoy going to the movies, B = 12

Number of students that enjoy solving mathematical problems, C = 24

A∩B∩C = 8

Here we have;

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) -n(A∩C) + n(A∩B∩C)

= 38 + 12 + 24 - n(A∩B) - n(B∩C) -n(A∩C) + 8

Also the number of student that like only one activity is found from the following equation;

n(A) - n(A∩B) - n(A∩C) + n(A∩B∩C) + n(B) - n(A∩B) - n(B∩C) + n(A∩B∩C) + n(C) - n(C∩B) - n(A∩C) + n(A∩B∩C) = 30

n(A) + n(B) + n(C) - 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) + 3·n(A∩B∩C) = 30

38 + 12 + 24 - 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) + 24 = 30

- 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) = -68

n(A∩B) + n(B∩C) + n(A∩C) = 34

Therefore, the number of students that like only two of the activities = 34.

8 0

3 years ago

The length of a rectangle is four times its width. If the area of the rectangle is 324m^2, find its perimeter.

Anuta_ua [19.1K]

Answer:

$perimeter=90$

Step-by-step explanation:

We know that the length is four times the width, so:

$l=4w$

We also know the area, which is 324 m². The formula for area:

$A=l*w$

Insert the known values:

$324=(4w)*w$

Solve for w. Simplify by removing parentheses:

$324=4w*w\\324=4w^2$

Divide 4 from both sides to isolate the variable:

$\frac{324}{4}=\frac{4w^2}{4} \\\\81=w^2$

Find the square root of both sides:

$\sqrt{81} =\sqrt{w^2} \\\\w=9$

The width is 9 m.

We know the width. Now find the length by using the area formula and inserting known values:

$324=l*9$

Solve for l. Divide both sides by 9:

$\frac{324}{9}=\frac{l*9}{9}\\\\ l=36$

The length of the rectangle is 36. (You can check: 4 times 9 is 36)

Now find the perimeter:

$P=2l+2w$

Insert values:

$P=2(36)+2(9)\\\\P=72+18\\\\P=90$

The perimeter is 90 m.

5 0

3 years ago

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

Scrat [10]

Answer:

4√(xy³)

Step-by-step explanation:

8√(x²y⁶)

The above expression can be simplified as follow:

8√(x²y⁶)

Recall:

m√a = a^1/m

Therefore,

8√(x²y⁶) = (x²y⁶)^1/8

Recall:

(aⁿ)^1/m = a^(n/m)

Therefore,

(x²y⁶)^1/8 = x^(2/8)•y^(6/8)

= x^1/4•y^3/4

= (xy³)^1/4

Recall :

a^1/m = m√a

Therefore,

(xy³)^1/4 = 4√(xy³)

Therefore,

8√(x²y⁶) = 4√(xy³)

6 0

3 years ago

Read 2 more answers

A conveyor belt carries supplies from the first floor to the second floor, which is 26 feet higher. The belt makes a 60° angle w

tamaranim1 [39]

<h3>Answer:</h3>

30 ft; 0.4 min

<h3>Step-by-step explanation:</h3>

The mnemonic SOH CAH TOA reminds you ...

... Sin = Opposite/Hypotenuse

Here, the angle of elevation is opposite the triangle side representing the distance between floors. The hypotenuse is the length of the conveyor belt. Rearranging the formula (by muliplying by Hypotenuse/Sin), we get ...

... Hypotenuse = Opposite/Sin

Filling in the values from this problem, we have ...

... length of conveyor = (26 ft)/sin(60°) ≈ 30 ft

The time it takes to travel that distance is given by ...

... time = distance/speed

... time = (30 ft)/(75 ft/min) = 2/5 min = 0.4 min

3 0

3 years ago

Jacob works as a mechanic at an hourly rate of $36 and earns time and a half for for any overtime. Last week he worked 37 hours

Korvikt [17]

Answer:

1620 which isn't there so I'm probably wrong but maybe c or a

Step-by-step explanation:

all we do is 36(37+8) and first we do 37 plus 8 that's 45 so 45×36

4 0

3 years ago