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3 years ago

What is the least common multiple of 8, 7, and 2?

Mathematics

2 answers:

Talja [164]3 years ago

7 0

Step-by-step explanation:

List all prime factors for each number.

Prime Factorization of 2 shows:

2 is prime => 21

Prime Factorization of 7 shows:

7 is prime => 71

Prime Factorization of 8 is:

2 x 2 x 2 => 23

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 2, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 7 = 56

In exponential form:

LCM = 2^3 x 7^1 = 56

LCM = 56

Therefore,

LCM(2, 7, 8) = 56

fiasKO [112]3 years ago

4 0

Answer:

1 i know its one hope it help

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The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a la

lara31 [8.8K]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 7463

For the alternative hypothesis,

µ ≠ 7463

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 7463 hours

x = 7163 hours

σ = 1080 hours

n = 81

b) z = (7163 - 7463)/(1080/√81) = - 2.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.02

Recall, population mean is 7463

The difference between sample sample mean and population mean is 7463 - 7163 = 300

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 7463 - 300 = 7163

the x value for the right tail is 7463 + 300 = 7763

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area below z as 0.02

We would double this area to include the area in the right tail of z = 2.5. Thus

p = 0.02 × 2 = 0.04

It means that in a sample of size 81 light bulbs, we would observe a sample mean of 300 hours or more away from 7463 about 4% of the time by chance alone.

c) Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × σ/√n

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, z score for 95% confidence level is 1.96

Margin of error = 1.96 × 1080/√81

= 235.2

Confidence interval = 7163 ± 23.2

a) Since alpha, 0.05 > than the p value, 0.04, then we would reject the null hypothesis. Therefore, at a 5% level of significance, there is evidence that the mean life is different from 7463 hours

Comparing the results of a and c, it is true that the population mean life is not 7463 hours.

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3 years ago

An air conditioning repair company has a flat

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Answer:

Step-by-step explanation:

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4 years ago

Convert each fraction to a decimal. Classify the decimal as terminating, non-terminating, repeating, or nonrepeating. If the dec

mixas84 [53]

Answer:

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Step-by-step explanation:

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3 years ago

What is the horizontal asymptote of f(x) =-2x/x+1 y=-2 y=-1 y=0 y=1

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Answer:

Y=0

Step-by-step explanation:

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3 years ago

Read 2 more answers

10 COINS TO BEST ANSWER

podryga [215]

For quadratic
.. ax^2 +bx +c = 0
the discriminant is
.. d = b^2 -4ac

You have
.. a = 2
.. b = -5
.. c = 7
so the value of the discriminant for your equation is
.. (-5)^2 -4(2)(7)
.. = 25 -56
.. = -31

Because the discriminant is negative, the roots of the quadratic are complex.

Reasoning: this is the usual interpretation of the sign of the discriminant. It derives from the fact that the square root of the discriminant is part of the roots of the quadratic. That part will be imaginary when the discriminant is negative.

_____
The graph shows there are no real roots.

6 0

3 years ago