Point A is at (-3,-5) and point M is at (-1,-7)

explain what does the constant rate of change means in the context, (basically what is the meaning of a constant rate change.).

LUCKY_DIMON [66]

Here the topic is "functions." Roughly speaking, we have a box. Input enters at one end and output exists at the other. Now, if every input value x (such as 2) is doubled by the box, every output value is 2x: (0,0), (1,2), (2,4), etc.

We call this "doubling" a "constant rate of change.

If you plot the points given, you'll see that they all are on a straight line. That straight line has the slope 2: y = 2x. Again, 2 is the "constant rate of change" here.

If you drive at a steady 55 mph, you are covering 55 miles during every hour behind the wheel. Again, 55 is a "constant rate of change."

4 0

3 years ago

Read 2 more answers

In ΔKLM, m = 18 inches, ∠M=124° and ∠K=29°. Find the length of k, to the nearest 10th of an inch

Anastaziya [24]

Answer:

10.5

Step-by-step explanation:

sin29

k

=

sin124

18

Plug in. Opposite sides go together.

k=\frac{18\sin 29}{\sin 124} \approx 10.526 \approx 10.5

k=

sin124

18sin29

≈10.526≈10.5

7 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

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

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