A car's wheel with a radius of 1.5 feet is spinning at a rate of 20 revolutions per minute. How fast is the car traveling?

8.23 A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators

Kitty [74]

Answer:

The 95% confidence interval estimate for the population mean force is (1691, 1755).

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally.

The sample selected here is <em>n</em> = 30.

Thus, the sampling distribution of the sample mean will be normal.

Compute the sample mean and standard deviation as follows:

$\bar x=\frac{1}{n}\sum x=\frac{1}{30}\times 51702=1723.4\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{30-1}\times 232561.2}=89.55$

Construct a 95% confidence interval estimate for the population mean force as follows:

$CI=\bar x\pm z_{\alpha /2}\times\frac{s}{\sqrt{n}}$

$=1723.4\pm 1.96\times\frac{89.55}{\sqrt{30}}\\\\=1723.4\pm 32.045\\\\=(1691.355, 1755.445)\\\\\approx (1691, 1755)$

Thus, the 95% confidence interval estimate for the population mean force is (1691, 1755).

3 0

3 years ago

How can you find 5% of any number using mental math?

Kryger [21]

Answer:

Step-by-step explanation:

I'm not sure my way is going to be any quicker or better. Let's take an example.

Suppose you start with 456

Put a decimal at the end of the 6. You get 456.

Shift the decimal to the left one place 45.6

Divide by 2

22.8 (done mentally)

Note: dividing by 2 is easier than dividing by 5. Or multiplying by 5 for that matter.

Check the result.

456 * 5/100 =2280 / 100.

Shift a decimal 2 places to the left.

22.80 which agrees with your result.

8 0

3 years ago

Read 2 more answers

Which equation correctly applies the distributive property?

ioda

From the word itself distribution, the distributive property of equality states that a number must be distributed to all the numbers inside the parenthesis. From the given choices, the only correct answer is:

C. −3 ⋅ (6.48)=(−3⋅6) + (−3⋅0.4) + (−3⋅0.08)

5 0

2 years ago

Read 2 more answers

Find f if f′(x)=2x−3/x^4, x>0 and f(1)=2.

slavikrds [6]

$f'(x)=2x-\dfrac3{x^4}$
$\displaystyle\int f'(x)\,\mathrm dx=\int\left(2x-\frac3{x^4}\right)\,\mathrm dx$
$f(x)=x^2+\dfrac1{x^3}+C$

Given that $f(1)=2$ , we get

$2=1^2+\dfrac1{1^3}+C$
$2=2+C$
$\implies C=2$

so that

$f(x)=x^2+\dfrac1{x^3}$