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3 years ago

2 It takes Aisha 84 seconds to run one lap of an athletics track.

Mathematics

1 answer:

DochEvi [55]3 years ago

3 0

Answer:

672

Step-by-step explanation:

the factors of 84 are 3 2 2 7

the factors of 96 are 2 2 2 2 2 3

the factors of the lowest common multiple will be 2 2 2 2 2 3 7

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Jack is a college athlete who has been weighing himself weekly on the same scale in the athletic center for the past few years.

Radda [10]

Answer:

a) Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

b) $\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

c) $\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

$200+1.64 = 201.64$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X= 200$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=3$ represent the population standard deviation

n=9 represent the sample size

Part a

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

Part b

The distribution for the sample mean is given by:

$\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

Part c

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

$200+1.64 = 201.64$

8 0

3 years ago

Find the volume of the rectangular prism<br><br> Due by 12:00 am!!

Roman55 [17]

Answer:

length x width x height

1.5 yards x 4.5 yards x 7 yards

Step-by-step explanation:

47.25 cubic yards

5 0

3 years ago

Read 2 more answers

Multiply (x + 2y)(x2 − xy + 3y).

erma4kov [3.2K]

Answer:

${x}^{3} + {x}^{2} y + 3xy - 2x {y}^{2} + 6 {y}^{2}$

4 0

3 years ago

Which function describes the arithmetic sequence shown?<br> 1,-2, -5, -8, -11, ...

antiseptic1488 [7]

Answer:

a(n)=1+(n-1)(-3)

Step-by-step explanation:

Notice there's a common difference of d=-3.

If we use the formula a(n)=a1+(n-1)d to find the nth term given the first term and the common difference, we will see that the function that describes the arithmetic sequence as a(n)=1+(n-1)(-3)

6 0

3 years ago

Please help me!! Thanks!

nikdorinn [45]

Answer: $30 and 1 cent more

$60.50 - $30.50 = $30

0.12 - 0.11 = 0.01

I hope this helps.

5 0

3 years ago