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3 years ago

9

Cheryl mixed a 32 cup batch of orange juice and pineapple juice using a ratio of 3 cups of orange juice to 5 cups of pineapple j

uice. How many cups of orange juice did she use?

1 answer:

den301095 [7]3 years ago

4 0

12 cups.

If she made 4 batches then it would be 12 cups of orange, and 20 cups of pineapple which adds to 32.

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It takes 20 minutes for 5people to paint 5 walls. How many minutes does it take 9 people to paint 9walls?

juin [17]

Answer:

20 minutes.

Step-by-step explanation:

Since it takes 5 people to paint 5 walls 20 minutes, that means that it would take 1 person 20 minutes to paint 1 wall. That also means that 2 people would take 20 minutes to paint 2 walls. So, it would take 9 people 20 minutes to paint 9 walls.

Hope this helps!

8 0

3 years ago

You randomly select k integers between 1 and 100, inclusive. What is the smallest k that guarantees that at least one pair of th

vredina [299]

Answer:

51

Step-by-step explanation:

The possible components to sum up to 101 can only be divided into 2 groups, 1 is larger than 50 and the other is less than or equals to 50

For example

50 + 51 = 101

52 + 49 = 101

60 + 41 = 101

...

99 + 2 = 101

100 + 1 = 101

Therefore, the worst case scenario is to pick all numbers from only 1 group, either all number less than or equal to 50, which there are 50 of them from 1 to 50, or greater than 50, which there are 50 of them from 51 to 100.

So k has to be at least 51 to guarantee that at least one pair of the selected integers will sum to 101

6 0

4 years ago

What is the solution to the system of equations? Use the substitution method. {y=−2x+5 3x−4y=2

GaryK [48]

We have that
<span>y=−2x+5 --------> equation 1
3x−4y=2---------> equation 2
</span><span>substituting 1 in 2
</span>3x-4*(-2x+5)=2--------> 3x+8x-20=2--------> 11x=22-----> x=2
y=-2x+5-----> -2*2+5-----> y=1

the solution is
x=2
y=1

5 0

4 years ago

Read 2 more answers

A number cube with faces labeled from 1 to 6 was rolled 20 times. Each time the number

kari74 [83]

Answer:

0.4

Step-by-step explanation:

These are the relative frequencies of each face (data are missing in the text of the problem):

Number Showing on Top Face Frequency

1 0

2 3

3 3

4 6

5 3

6 5

The probability to obtain a certain number when throwing the dice is given by

$p(x_i)=\frac{f_i}{\sum f}$

where

$f_i$ is the relative frequency of the number $x_i$ to occur

$\sum f$ is the sum of the relative frequencies

Here the sum of the frequencies is:

$\sum f=0+3+3+6+3+5=20$

For number 5 here, we have:

$f_5 = 3$ (from the table)

So the probability of getting a 5 is

$p(5)=\frac{3}{20}$

For number 6 here, we have

$f_6=5$

So the probability of getting a 6 is

$p(6)=\frac{5}{20}$

So the probability to obtain either a 5 or a 6 in the next rolling is:

$p(5\cup 6)=p(5)+p(6)=\frac{3}{20}+\frac{5}{20}=\frac{8}{20}=0.4$

6 0

3 years ago

Find sin 0, where is the angle shown.<br> Give an exact value, not a decimal approximation.

Nata [24]

Answer:

$\displaystyle \sin\theta=\frac{12}{13}$

Step-by-step explanation:

Recall that in a right triangle, sine is the ratio of the opposite side to the hypotenuse:

$\displaystyle \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$

We are actually not given the opposite side in this case. However, since we know the hypotenuse and the adjacent side, we can use the Pythagorean Theorem to find the opposite side. So:

$a^2+b^2=c^2$

Let <em>a</em> be the adjacent side and <em>b</em> be the opposite side. <em>c</em> will be the hypotenuse.

Substitute:

$(5)^2+b^2=(13)^2$

Solve for <em>b: </em>

<em /> $b=\sqrt{169-25}=\sqrt{144}=12$ <em />

So, the opposite side measures 12.

Then sine will be:

$\displaystyle \sin\theta=\frac{12}{13}$

3 0

3 years ago