The volume of a rectangular prism is 2,100 cm^3 , with length 25 cm and width 12 cm. What is the height, in cm?

Vika [28.1K]

If you're looking for the solution to the system of equations, here's how we solve using substitution
We know that y = x - 1, so we can plug that into the first equation giving
2x - 3(x-1) = -1
Now distribute the 3 giving 2x - 3x + 3 = -1. After combining like terms we get -x + 3 = -1. Now subtract 3 from both sides, -x = -4, and multiply both sides by -1 to make x positive. x = 4
Now we can plug that into the second equation to get y
y = x - 1, and we know that x = 4, so y = 4 - 1, y = 3. The solution is (4, 3)

8 0

3 years ago

Read 2 more answers

Approximately 5% of calculators coming out of the production lines have a defect. Fifty calculators are randomly selected from t

baherus [9]

Answer:

0.2611 = 26.11% probability that exactly 2 calculators are defective.

Step-by-step explanation:

For each calculator, there are only two possible outcomes. Either it is defective, or it is not. The probability of a calculator being defective is independent of any other calculator, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5% of calculators coming out of the production lines have a defect.

This means that $p = 0.05$

Fifty calculators are randomly selected from the production line and tested for defects.

This means that $n = 50$

What is the probability that exactly 2 calculators are defective?

This is P(X = 2). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{50,2}.(0.05)^{2}.(0.95)^{48} = 0.2611$

0.2611 = 26.11% probability that exactly 2 calculators are defective.

3 0

3 years ago

Jose and Maris work for different car dealerships. Jose earns a monthly salary of $3,500 plus a 6% commission on his sales, x. M

aev [14]

Answer: d.3,500 + 0.06x > 4,000 + 0.04x

Step-by-step explanation:

Hi, to answer this question we have to write each inequality:

Jose earns a monthly salary of $3,500 plus a 6% commission on his sales, x.

So, his monthly earnings must be equal to the sum of the fixed monthly salary ($3500) plus the product of the number of sales (x) and the commission percentage in decimal form (divided by 100):

So:

Jose’s earnings: 3,500 + x (6/100)

Jose’s earnings: 3,500 + 0.06x

Maris earns a monthly salary of $4,000 plus a 4% commission on her sales.

So, her monthly earnings must be equal to the sum of the fixed monthly salary ($4000) plus the product of the number of sales (x) and the commission percentage in decimal form (divided by 100):

Maris’ earnings: 4000+ x (4/100)

Maris’ earnings: 4000+ 0.04 x

Since Jose's earnings must be greater than Maris' earnings

3,500 + 0.06x >4000+ 0.04 x

4 0

3 years ago

Find a center of mass of a thin plate of density delta equals 5δ=5 bounded by the lines y equals xy=x and x equals 0x=0 and the

kow [346]

Answer:

center of mass

X = $\frac{my}{m} = \frac{28}{19}$