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ella [17]
3 years ago
8

One fifth of a number is at most 30

Mathematics
2 answers:
Mamont248 [21]3 years ago
7 0
One fifth of a number is at most 30.
\sf\frac{1}{5}x \leq 30\\Multiply\ by\ 5\ on\ both\ sides.\\x \leq 30\times5\\x \leq 150
Arada [10]3 years ago
6 0
1/5x < = 30
x < = 30 * 5
x < = 150
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Simplify this expression: 13 + (–12) – (–5) = ?<br> A. 6<br> B. –6<br> C. –30<br> D. 30
Anuta_ua [19.1K]
13 + (-12) - (-5)

13 - 12 + 5

1 + 5

= 6.

Answer is A)
3 0
3 years ago
Read 2 more answers
fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed w
EastWind [94]

Answer:

The p-value obtained is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours

Step-by-step explanation:

Complete Question

fluorescent light factory that manufactures fluorescent lights that have a lifetime that is approximately normally distributed with a mean of 700 hours and a standard deviation of 45 hours. Test the hypothesis that mean is 700 hours against the alternative hypothesis that the mean is not equal to 700 hours, if a random sample of 30 bulbs has an average life of 688 hours. Use a P-value in your answer.

Solution

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, the null hypothesis is that the mean life of the fluorescent lights is 700 hours.

The alternative hypothesis will now be that the mean life of the fluorescent lights is significantly different from 700 hours.

Mathematically,

The null hypothesis is represented as

H₀: μ = 700

The alternative hypothesis is represented as

Hₐ: μ ≠ 700

To do this test, we will use the z-distribution because no information on the population standard deviation is known

So, we compute the z-test statistic

z = (x - μ₀)/σₓ

x = sample mean = 688 hours

μ₀ = 700 hours

σₓ = standard error = (σ/√n)

σ = standard deviation = 45 hours

n = Sample size = 30

σₓ = (45/√30) = 8.2158383626 = 8.216

z = (688 - 700) ÷ 8.216

z = 1.46

checking the tables for the p-value of this z-statistic

Significance level = 0.05 (This is used when significance level isn't given)

The hypothesis test uses a two-tailed condition because we're testing in two directions.

p-value (for z = 1.46, at 0.05 significance level, with a two tailed condition) = 0.14429

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.14429

0.14429 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there is enough evidence to conclude that the mean life of the fluorescent lights is 700 hours.

Hope this Helps!!

6 0
3 years ago
Rich deposited money into a bank account that earned 2.5% simple interest each year. After 2 years, he had earned $14.65 in inte
photoshop1234 [79]

we know that


The simple interest formula is equal to


I=Prt


where


P is the Principal amount of money to be invested


I is the amount of money in interest

r is the rate of interest  

t is Number of Time Periods


in this problem we have


t=2\ years\\ I=\$14.65\\r=0.025


substitute in the formula above  and solve for P

14.65=P(0.025)(2)

P=14.65/[(0.025)(2)]

P=\$293


therefore

<u>the answer is</u>

\$293




5 0
3 years ago
Read 2 more answers
100 POINTS IF U GET THIS RIGHT!
iVinArrow [24]

Answer:

That is the answer

Hope this helps!

3 0
2 years ago
Read 2 more answers
Solve the proportional equation 3/r = 5/r+3
romanna [79]

Answer:

r=9/2 or 4.5

Step-by-step explanation:

First of all our goal is to get R by itself

by cross multiplying we get,

(r+3)*3=5r

by distributive property we get

3r+9=5r

substracting 3r from both sides we get

9=2r

by dividing by 2 in both sides we get

r=9/2 or 4.5

6 0
2 years ago
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