Four points are labeled on the number line which point represents the value of -1/2

Express as a trinomial (3x+8) (x+10)

docker41 [41]

Answer:

$3x^{2} +38x+80$

Step-by-step explanation:

Hello!

A trinomial is a expression consisting of three different terms

To turn this into a trinomial we multiply everything to each other

3x

3x * x = $3x^{2}$

3x * 10 = 30x

8

8 * x = 8x

8 * 10 = 80

Now we put them all together in an equation

$3x^{2} +30x+8x+80$

Combine like terms

$3x^{2} +38x+80$

The answer is $3x^{2} +38x+80$

Hope this helps!

7 0

3 years ago

Jillian measured the distance around a small fish pond as 27 yards. Which would be a good estimate for the distance across the p

DochEvi [55]

Assuming the fish pond is round, what you're given is the circumference.
So you know that 2πr = 27.
We want to solve for the diameter, or d = 2r. We should isolate that.
2r = 27/π
2r = 8.59 yards, or ~9 yards.

3 0

3 years ago

What is the solution to the following system of equations? x+2y=2 x-2y=-2

Tcecarenko [31]

All in all you would get the answer x+y=1.

7 0

3 years ago

The mean life of a television set is 119 months with a standard deviation of 14 months. If a sample of 74 televisions is randoml

irina [24]

Answer:

50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 119, \sigma = 14, n = 74, s = \frac{14}{\sqrt{74}} = 1.63$

If a sample of 74 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.1 months

This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So

X = 120.1

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

By the Central Limit Theorem

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