What is twenty divided by two plus ten

Use the addition method to solve the system of linear equations for x. (Enter an exact number.)

kirill [66]

Answer:

work is shown and pictured

6 0

3 years ago

120 inch board cut in 8 inch

Vikki [24]

Answer:

15, 8 inch boards

Step-by-step explanation:

120/8=15

4 0

3 years ago

3x+1/5y=7 solve for y

Vladimir79 [104]

Hello!

First, let's write the problem.
$3x+\frac{1}{5}y=7$
Subtract 3x from both sides.
$3x+\frac{1}{5}y-3x=7-3x$
$\frac{1}{5}y=7-3x$
The opposite of division is multiplication, so we are going to multiply in order to undo the fraction.
$5\cdot \frac{1}{5}y=5\cdot \:7-5\cdot \:3x$

Our final answer would be,
$y=35-15x$

Thanks!
-TetraFish

5 0

4 years ago

A machine is shut down for repairs if a random sample of 100 items selected from the daily output of the machine reveals at leas

Harlamova29_29 [7]

Answer:

0.7995 = 79.95% probability that the sample will contain at least three defectives.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Suppose that a random sample of 20 items is selected from the machine.

This means that $n = 20$

The machine produces 20% defectives

This means that $p = 0.2$

Mean and standard deviation:

$\mu = E(X) = np = 20*0.2 = 4$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.2*0.8} = 1.79$

Probability that the sample will contain at least three defectives

Using continuity correction, this is $P(X \geq 3 - 0.5) = P(X \geq 2.5)$ , which is 1 subtracted by the pvalue of Z when X = 2.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{2.5 - 4}{1.79}$

$Z = -0.84$

$Z = -0.84$ has a pvalue of 0.2005

1 - 0.2005 = 0.7995

0.7995 = 79.95% probability that the sample will contain at least three defectives.

4 0

3 years ago

The price of milk has been steadily increasing 5% per year. If the cost of a gallon is now $3.89: What will it cost in 10 years?

saw5 [17]

This is the concept of exponential growth; The rate of growth of the price milk is 0.05, current price=$ 3.89;
this information can be modeled by the exponential growth equation given by:
y=ae^(nr)
where;
a=initial value
r=rate of growth;
n=number of years
thus the function modeling our information will be:
y=3.89e^0.05n

the price after 10 years will be:
y=3.89e^(0.05*10)
y=3.89*1.649
y=6.41

the price after 10 years will be $ 6.41

The price 5 years ago will be:
y=3.89*e^(-5*0.05)
y=3.89 e^(-0.25)
y=3.03
thus we conclude that the price 5 years ago was $ 3.03

3 0

3 years ago