(06.02 LC) Simplify (3x - 5) - (5x + 1). 0-2x + 6 0-2x - 6 O 2x

Dr. Black is standing 15 feet from a streetlamp. The lamp is making his shadow 8 feet long. He estimates that the angle of evela

lina2011 [118]

The base of the triangle is 15 + 8 = 23 feet
and the angle is 50 degrees
to find the height of the street lamp
multiply the base ( 23) by the Tan(50)
tan(50) x 23 = 27.41 feet rounded to nearest foot would be 27 fee

4 0

4 years ago

Ball bearings are manufactured with a mean diameter of 5 millimeters(mm). Because of variability in the manufacturing process, t

dexar [7]

Answer:

a) 0.0668 of ball bearings have a diameter more than 5.03 mm

b) 0.0124 of ball bearings will be discarded

c) The plant manager should expect to discard 372 balls.

d) 57,710 ball bearings should be manufactured.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

$\mu = 5, \sigma = 0.02$

(a) What proportion of ball bearings has a diameter more than 5.03 mm?

This is 1 subtracted by the pvalue of Z when X = 5.03. So

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

$Z = \frac{5.03 - 5}{0.02}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 of ball bearings have a diameter more than 5.03 mm

(b) Any ball bearings that have a diameter less than 4.95 mm or greater than 5.05 mm are discarded. What proportion of ball bearings will be discarded?

Lower than 4.95 or greater than 5.05. Both these proportions are the same, so we find one of them, and multiply by 2.

Less than 4.95:

pvalue of Z when X = 4.95. So

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

$Z = \frac{4.95 - 5}{0.02}$

$Z = -2.5$

$Z = -2.5$ has a pvalue of 0.0062

2*0.0062 = 0.0124

0.0124 of ball bearings will be discarded.

(c) Using the results of part (b), if 30,000 ball bearings are manufactured in a day, how many should the plant manager expect to discard?

0.0124 of 30,000. So

0.0124*30000 = 372

The plant manager should expect to discard 372 balls.

(d) If an order comes in for 50,000 ball bearings, how many bearings should the plant manager manufacture if the order states that all ball bearings must be between 4.97 mm and 5.03 mm?

Proportion of bearings between 4.97 mm and 5.03 mm:

pvalue of Z when X = 5.03 subtracted by the pvalue of Z when X = 4.97. So

X = 5.03

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

$Z = \frac{5.03 - 5}{0.02}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

X = 4.97

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

$Z = \frac{4.97 - 5}{0.02}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.9332 - 0.0668 = 0.8664 of ball bearings will have adequate proportions. So 0.8664 of x should be 50,000. then

$0.8664x = 50000$

$x = \frac{50000}{0.8664}$

$x = 57 710$

57,710 ball bearings should be manufactured.

3 0

3 years ago

Let's say that 1/3 of the eggs become cracked. What is the ratio of the number of eggs that have cracked to the number of eggs t

vladimir2022 [97]

We can say we have 2 cracked egss and 4 uncracked eggs for a 6 egg total.

The ratio of cracked to uncracked eggs is 2:4 which reduces to 1 to 2.

6 0

3 years ago

-2/5 x -1 1/4 A) -1 1/10 B) -1/2 C) 1 1/10 D) 1/2

Harrizon [31]

The answer would be C b/c negative 2 times 11 is positive 22 and 2negatives equal a positive and then negative 5 times 4 equal 20 it would be 22/20 divide be top and bottom by 2 and you get your answer .

4 0

3 years ago

The slope of a line can be stated many ways if not put into simplest form.

algol13

Answer:

slope is -3 or, so false

Step-by-step explanation:

5 0

3 years ago

(06.02 LC) Simplify (3x - 5) - (5x + 1). 0-2x + 6 0-2x - 6 O 2x - 6 O 2x + 6