(sec 12A - 1)/(sec 6A -1) = tan 12A / tan 3A

Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate.

tiny-mole [99]

Answer:

The system of equation that models the situation is:

w = 4c

w + c = 100

And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.

Step-by-step explanation:

1. Let's review the information given to us to answer the problem correctly:

Owen wants to make 100 quarts of lemonade

Number of quarts of water 4 times the number of quarts of concentrate

2. Which of the following systems of equations models this situation?

c = number of quarts of concentrate

w = number of quarts of water

Like the alternatives of systems of equations that model the situation were not given, let's write them by ourselves, this way:

w = 4c (Number of quarts of water 4 times the number of quarts of concentrate)

w + c = 100 (Owen wants to make 100 quarts of lemonade)

Now, let's solve for c and w, this way:

w = 100 - c

Substituting w in the first equation, we have:

100 - c = 4c

100 = 5c

c = 20 ⇒ 4c = 20 * 4 = 80

w = 4 * 20

w = 80

The system of equation that models the situation is:

w = 4c

w + c = 100

And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.

4 0

2 years ago

A population consists of the following five values: 1, 3, 4, 4, and 6. List all samples of size 2 from left to right without rep

aniked [119]

Answer:

The sample of sizes 2 and their mean are given below.

Step-by-step explanation:

The population consist of 5 values, S = {1, 3, 4, 4, 6}.

The number of samples of size 2 (without replacement) that can be formed from these 5 values is:

${5\choose 2}=\frac{5!}{2!(5-2)!} =10$

Th formula to compute the mean is:

$\bar x=\frac{1}{n}\sum x_{i}$

List the 10 samples and their mean as follows:

Sample Mean

(1, 3) $\bar x=\frac{1}{2}[1+3]=\frac{4}{2}=2.0$

(1, 4) $\bar x=\frac{1}{2}[1+4]=\frac{5}{2}=2.5$

(1, 6) $\bar x=\frac{1}{2}[1+6]=\frac{7}{2}=3.5$

(3, 4) $\bar x=\frac{1}{2}[3+4]=\frac{7}{2}=3.5$

(3, 6) $\bar x=\frac{1}{2}[3+6]=\frac{9}{2}=4.5$

(4, 4) $\bar x=\frac{1}{2}[4+4]=\frac{8}{2}=4.0$

(4, 6) $\bar x=\frac{1}{2}[4+6]=\frac{10}{2}=5.0$

8 0

2 years ago

Emily wants to hang a painting in a gallery. The painting and frame must have an area of 31 square feet. The painting is 5 feet

seropon [69]

Area=legnth times width=31
the frame must go around the frame with equal legnth, x
so
the total area (meaning the frame +picture) is 5+x by 6+x
31=(5+x)(6+x)
expand
31=30+11x+x^2
minus 31 both sides
0=-1+11x+x^2
x^2+11x-1=0

answer is third one

6 0

2 years ago

Read 2 more answers

U Get 73 pts !!CAN I PLS GET HELP !!!!Cassandra calculated the total volume of the figure below. A rectangular prism has a lengt

Arlecino [84]

Answer:

1.She used square units instead of cubic units.

2.In calculating the volume of the pyramid, she did not multiply by 1/3.

4.She subtracted the pyramid volume instead of adding it.

Step-by-step explanation:

because i got it right on my test.

8 0

2 years ago

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Using the standard normal table, the probability that Seth’s light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is abo

lana66690 [7]

Answer:

How many standard deviations above the mean is 14,500 hours? 1.25 1.5 2.5 Using the standard normal table, the probability that Seth's light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is about ✔ 89% .

5 0

1 year ago

Read 2 more answers