Would someone help me understand this type of math

What value of x is in the solution set of –5x – 15 > 10 + 20x?

Sunny_sXe [5.5K]

-5x - 15 > 10 + 20x...subtract 10 from both sides, add 5x to both sides
-10 - 15 > 20x + 5x ...simplify
-25 > 25x...divide both sides by 25
-25/25 > x ....reduce
-1 > x or x < -1 <===

6 0

3 years ago

My Notes A large manufacturing plant uses lightbulbs with lifetimes that are normally distributed with a mean of 1600 hours and

Evgen [1.6K]

Answer:

The bulbs should be replaced each 1436.9 hours.

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 1600, \sigma = 70$

How often should the bulbs be replaced so that no more than 1% burn out between replacement periods?

This is the first percentile of hours. So it is X when Z has a pvalue of 0.01.

So it is X when Z = -2.33.

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

$-2.33 = \frac{X - 1600}{70}$

$X - 1600 = -2.33*70$

$X = 1436.9$

The bulbs should be replaced each 1436.9 hours.

6 0

3 years ago

How many handshakes are possible at a party of 65 people if everyone shakes hands once?

riadik2000 [5.3K]

You must calculate how many ways can 2 people be selected from 65.
The formula is:
n! / r! * (n-r)! =
65! / 2! * 63! =
65*64*63! / 2 * 63! =
65*64 / 2 =
2,080 handshakes

Source:
http://www.1728.org/combinat.htm

7 0

3 years ago

What is a possible value of sin(theta) when cos2(theta)=0.73?

Sindrei [870]

We use the following trigonometric identity to answer the question:
sin^ 2 (theta) + cos^ 2 (theta) = 1
We substitute the values:
sin ^ 2 (theta) + 0.73 = 1
We cleared:
sin ^ 2 (theta) = 1-0.73
sin ^ 2 (theta) = 0.27
Answer:
a possible value of sin ^ 2 (theta) is:
c.0.26 (nearest option)

8 0

3 years ago

Pls answer clearly thank you will be marking smartest correct answer!

balandron [24]

Number 9 is no because if you were to divide that it be a decimal and a decimal is an irrational number.

Number 10 is yes. When divide 2 by 5 you get 0.4 which is a terminating number because it never ends

3 0

3 years ago