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1 year ago

CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already

Mathematics

1 answer:

Ratling [72]1 year ago

6 0

Answer:

15.7 in

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

$\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}$

It checks.

You might be interested in

The sum of the interior angles of a convex polygon is the same as the sum of its exterior angles. What type of polygon is it?

RideAnS [48]

A parallelogram.

All the angles in a parallelogram must add up to 360° as well as the exterior angles.

Hope that helps!

:D®

7 0

1 year ago

In 1998 the average income for middle class families in the US was $37,100 with a population standard deviation of $6362. We wan

sammy [17]

Answer:

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

The best answer would be:

A. Z test

Step-by-step explanation:

Data given and notation

$\bar X=36670$ represent the mean average

$\sigma=6362$ represent the population standard deviation for the sample

$n=1225$ sample size

$\mu_o =37100$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal or not to 37100, the system of hypothesis would be:

Null hypothesis: $\mu =37100$

Alternative hypothesis: $\mu \neq 37100$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

The best answer would be:

A. Z test

5 0

2 years ago

a traveling salesman drives his car 30000 miles a year. His car travels 16 miles to the gallon of gas. How many gallons of gas d

DENIUS [597]

Answer:

187.5 gallons

Step-by-step explanation:

Make a proportion

$\frac{16 miles}{1 gallon}$ = $\frac{3000 miles}{x}$

3000/16 = 187.5, so multiply 1 by 187.5 to find the gallons used in a year

This gets you 187.5 gallons used in a year

4 0

1 year ago

Read 2 more answers

Which two statements describe domestic stocks? They are directly affected by exchange rate fluctuations. They are always traded

kondaur [170]

Answer:

They are based in the investor’s country of residence

They are always traded in local currency.

Step-by-step explanation:

Stocks, in general, indicate ownership shares of a company and domestic stocks as the name suggests are stocks that are based in the investor's home country.

These domestic stocks are almost always traded in local currency and they are a great help to local investors because it eliminates the currency risk because of exchange rates which can change at any time.

6 0

1 year ago

A train is leaving in 11 minutes and you are one mile from the station. Assuming you can walk at 4mph and run at 8mph, how much

ddd [48]

7 minutes is the time can you afford to walk

Solution:

Given that, train is leaving in 11 minutes and you are one mile from the station

Let "x" represent how much time can you afford to walk

Then, (11 - x) is the time you run

You can walk at 4mph and run at 8mph

Convert to miles per minute

1 hour = 60 minutes

$4\ mph = 4 \times \frac{1}{60} \text{ miles per minute } = \frac{1}{15} \text{ miles per minute }\\\\8\ mph = 8 \times \frac{1}{60}\ \text{ miles per minute } = \frac{2}{15} \text{ miles per minute }$

We know that,

$Distance = speed \times time$

Given that, you are one mile from the station

Therefore,

1 mile = distance walk + distance run

$1 = x \times \frac{1}{15} + (11-x) \times \frac{2}{15}\\\\1 = \frac{1}{15}(x + 2(11-x))\\\\1 = \frac{1}{15}(x + 22 - 2x)\\\\x + 22 - 2x = 15\\\\x = 22 - 15\\\\x = 7$

Thus, 7 minutes is the time can you afford to walk

6 0

2 years ago