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3 years ago

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A manufacturer of new light bulbs claims the average lifetime of its long-life bulb is more than 4000 hours. To test this claim,

a reputable testing firm took a random sample of 100 bulbs and life tested them. The testing firm found the average life of the sample to be 4500 hours with a sample standard deviation, s = 400 hours. The value of the test statistic for this problem isA 1.25B -1.25C 12.5D -12.5E None of the values listed

1 answer:

natka813 [3]3 years ago

5 0

Answer: C. 12.5

Step-by-step explanation:

Given : A manufacturer of new light bulbs claims the average lifetime of its long-life bulb is more than 4000 hours.

Population mean : $\mu=4000$

Sample size : n= 100

Sample mean : $\overline[x}=4500$

Standard deviation: $s=400$

The value of test-statistic is given by :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}\\\\\Rightarrow\ z=\dfrac{4500-4000}{\dfrac{400}{\sqrt{100}}}\\\\\Rightarrow\ z= 12.5$

Hence, the value of the test statistic for this problem is 12.5.

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Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same poi

skelet666 [1.2K]

Answer:

Alan: 200 m/min

Brian: 150 m/min

Step-by-step explanation:

Given : Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes.

To find : What are their rates, in meters per minute?

Solution :

Let n represent the number of laps that Alan completes in 9 minutes.

Then n-1 is the number of laps Brian completes.

45 seconds = 3/4 minutes.

The difference in their lap times in minutes per lap is

$\frac{9}{(n -1)}-\frac{9}{n} =\frac{3}{4}$

Solving the equation we get,

$\frac{9n-9n+9}{n(n -1)} =\frac{3}{4}$

$9\times 4=3\times n(n -1)$

$36=3\times n(n -1)$

$n^2-n-12=0$

$n^2-4n+3n-12=0$

$n(n-4)+3(n-4)=0$

$(n-4)(n+3)=0$

$n=4,-3$

Neglecting n=-3

So, n=4

Then Alan's speed in m/min is

$S=\frac{D}{T}$

$S_a=\frac{4\times 450}{9}$

$S_a=200 m/min$

Brian completes 3 laps in that 9-minute time, so his rate is

$S_b=\frac{3\times 450}{9}$

$S_b=150 m/min$

Therefore, Alan: 200 m/min

Brian: 150 m/min

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3 years ago

What are solutions for |x+4|=3x-5

Furkat [3]

Answer:

Step-by-step explanation:

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3 years ago

Not too sure how to do this equation its on the attached file

Akimi4 [234]

Answer:

The answer is 72

Step-by-step explanation:

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3 years ago

The number of subscribers to a streaming video service doubles each week.

Ilya [14]

Answer:

Step-by-step explanation:

This is an exponential equation that is solved by taking the natural log of both sides. The equation is

$f(x)=2^x$

If we are looking for x when f(x) = 64, then

$64=2^x$

Take the natural log of both sides:

$ln(64)=ln(2^x)$

The rules of logs allows us to bring the x down in front:

$ln(64)=xln(2)$

Divide both sides by ln(2) to get:

$\frac{ln(64)}{ln(2)}=x$

Do this on your calculator to get that x = 6.

You could also have just gone right to your calculator and started raising 2 to consecutive powers starting at like 3 or 4 to eventually get that 2 to the 6th power is equal to 64, but for the basics of solving log equations, you need to know how to do this.

5 0

3 years ago

Read 2 more answers

FRÉD AND ETHEL WACHED TV FOR SEVERAL HOURS ONE AFTERNOON. THEY BEGAN AT 1:30 P.M AND CONTINUED WACHING TV FOR 3 HOURS AND 45 MIN

QveST [7]

$30 + 45 =75$
$3 + 1 = 4$
There are 60 minutes in one hour, so 75 minutes is equal to 1 hour and 15 minutes.

$4 + 1 = 5$
Their mom turned the TV off at 5:15.

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3 years ago