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mariarad [96]
3 years ago
10

Someone please help -4x ≤ 28

Mathematics
2 answers:
Allisa [31]3 years ago
7 0

-4x≤28

Divide 4 both sides

-x≤7

x≥-7

A

liq [111]3 years ago
6 0

Answer:

A

Step-by-step explanation:

-4x<28

divide by -4 since it is a negative you have to flip the sign

so x>-7

option A

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15x+50=500(divide by 45)
Dmitry_Shevchenko [17]
15x = 500-50
15x = 450
x = 450/15
x =30
Thus, x is equal to 30.

7 0
3 years ago
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The points (4,- 4) and (4,- 6) lie on a circle with a radius of 1. Find the center point of the circle.
Katyanochek1 [597]

If we intersect the circle of radius 1 around (4,-4) and the circle of radius 1 around (4,-6) they'll intersect at the center of circle radius 1 that has both those points.  

Here we don't really have to do any math.  It's clear that the midpoint (4,-5) is 1 away from both (4,-4) and (4,-6) so that's our answer:

Answer: (4,-5)

6 0
3 years ago
A study of long-distance phone calls made from General Electric's corporate headquarters in Fairfield, Connecticut, revealed the
Jet001 [13]

Answer:

a) 0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

b) 0.0668 = 6.68% of the calls last more than 4.2 minutes

c) 0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

d) 0.9330 = 93.30% of the calls last between 3 and 5 minutes

e) They last at least 4.3 minutes

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 = 3.6, \sigma = 0.4

(a) What fraction of the calls last between 3.6 and 4.2 minutes?

This is the pvalue of Z when X = 4.2 subtracted by the pvalue of Z when X = 3.6.

X = 4.2

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

Z = \frac{4.2 - 3.6}{0.4}

Z = 1.5

Z = 1.5 has a pvalue of 0.9332

X = 3.6

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

Z = \frac{3.6 - 3.6}{0.4}

Z = 0

Z = 0 has a pvalue of 0.5

0.9332 - 0.5 = 0.4332

0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

(b) What fraction of the calls last more than 4.2 minutes?

This is 1 subtracted by the pvalue of Z when X = 4.2. So

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

Z = \frac{4.2 - 3.6}{0.4}

Z = 1.5

Z = 1.5 has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% of the calls last more than 4.2 minutes

(c) What fraction of the calls last between 4.2 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 4.2. So

X = 5

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

Z = \frac{5 - 3.6}{0.4}

Z = 3.5

Z = 3.5 has a pvalue of 0.9998

X = 4.2

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

Z = \frac{4.2 - 3.6}{0.4}

Z = 1.5

Z = 1.5 has a pvalue of 0.9332

0.9998 - 0.9332 = 0.0666

0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

(d) What fraction of the calls last between 3 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 3.

X = 5

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

Z = \frac{5 - 3.6}{0.4}

Z = 3.5

Z = 3.5 has a pvalue of 0.9998

X = 3

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

Z = \frac{3 - 3.6}{0.4}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

0.9998 - 0.0668 = 0.9330

0.9330 = 93.30% of the calls last between 3 and 5 minutes

(e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4% of the calls. What is this time?

At least X minutes

X is the 100-4 = 96th percentile, which is found when Z has a pvalue of 0.96. So X when Z = 1.75.

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

1.75 = \frac{X - 3.6}{0.4}

X - 3.6 = 0.4*1.75

X = 4.3

They last at least 4.3 minutes

7 0
3 years ago
If arc SQ = 84° and ∠RPS = 26°, what is the measure of arc RS? need answer asap thank you
Lera25 [3.4K]

Answer:

arc\ RS=136\°

Step-by-step explanation:

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

In this problem

m∠RPS=26\° ------> external angle

so

m∠RPS=\frac{1}{2}(arc\ RS-arc\ SQ)

we have

m∠RPS=26\°

arc\ SQ=84\°

substitute the values

26\°=\frac{1}{2}(arc\ RS-84\°)

Solve for arc RS

52\°=(arc\ RS-84\°)

arc\ RS=52\°+84\°=136\°

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3 years ago
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stiv31 [10]
Well, if u=12 and you are dividing you would do 144/5 which equals 12. I hope this helps and have a blessed day!

8 0
3 years ago
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