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4 years ago

5

WILL MARK BRAINLIST ! Carissa also has a sink that is shaped like a half sphere. The sink has a volume of 20003π in3. One day th

e sink clogged, so she had to use a cup to scoop the water out of the sink. The sink is completely full when Carissa begins scooping.
The cup is a cone with a diameter of 4 inches and a height of 8 inches. How many cups of water must Carissa scoop out of the sink with this cup to empty it? Round to the nearest whole number.

BE SURE TO SHOW YOUR WORK or THINKING for full credit

1 answer:

faltersainse [42]4 years ago

7 0

Answer:

63 cups of water.

Step-by-step explanation:

The volume of a cone is V = 1/3πr²h. The diameter of the cup is 4, the radius of the cup is 2, so the volume is:

1/3π×8×2²

8/3π×4 = 32π/3.

Divide the volume of the sink by the volume of the cup:

2000π/3 ÷ 32π/3 = 6000π/96π = 62.5.

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In many cases the Law of Sines works perfectly well and returns the correct missing values in a non-right triangle. However, in

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$\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \sin B=\frac{b \sin A}{a} \\ \\ \sin B=\frac{13 \sin 29^{\circ}}{7.2} \\ \\ \boxed{m\angle B =\arcsin \left(\frac{65\sin 29^{\circ}{36} \right), 180^{\circ}-\arcsin \left(\frac{65\sin 29^{\circ}}{36} \right)}$

Considering the diagram. $\angle B$ is shown to be acute, so $\boxed{m\angle B=\arcsin \left(\frac{65\sin 29^{\circ}}{36} \right)}$ .

Angles in a triangle add to 180°, so $m\angle C= 151^{\circ}-\arcsin \left(\frac{65\sin 29^{\circ}}{36} \right)$ .

Using the law of cosines,

$AB=\sqrt{13^2 + 7.2^2-2(13)(7.2)\cos \left(\arcsin \left(\frac{65\sin 29^{\circ}}{36} \right) \right)} \\ \\ \boxed{AB=\sqrt{220.84-187.2\cos \left(\arcsin \left(\frac{65\sin 29^{\circ}}{36} \right) \right)}}$

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1 year ago

Which operation would you do second in the following problem?

sleet_krkn [62]

Answer:

C. Multiplication

Step-by-Step Explanation:

This problem is testing your knowledge of the Order of Operations. Here is the correct order:

Exponents (inside parenthesis)- There are no exponents for you to solve in this expression, so just ignore this step for now. (example: (4 + 2²) --> (4 + 4))

Parenthesis (from left to right)- In this case, you would solve the expressions inside the parenthesis <em>first</em> because there are no exponents.

Multiplication and Division (from left to right outside of parenthesis)- After solving the expressions inside the parenthesis, there will be one multiplication you need to solve next.

Addition and Subtraction (from left to right outside of parenthesis)- The only operation left for you to do now is addition. You can either do this in one whole step, or you can divide it into two steps. I've done it in two to keep it simple.

Here is the problem worked out in steps in case you are confused:

Step 1: Parenthesis

(-8 ÷ 4) + 5 + 4(3 - 6)

(-2) + 5 + 4(-3)

Step 2: Multiplication

-2 + 5 + 4(-3)

-2 + 5 + (-12)

Step 3: Addition

-2 + 5 + (-12)

3 + (-12)

-9

(Note: '3 + (-12)' could also be written as '3 - 12', making it a subtraction instead of an addition)

Hope this helps!

5 0

3 years ago

Read 2 more answers

The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.94. T

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Answer:

a) 25

b) 67

c) 97

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample. In this problem, $\sigma = 0.25$

(a) The desired margin of error is $0.10.

This is n when M = 0.1. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.1 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.1\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.1}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.1})^{2}$

$n = 24.01$

Rounding up to the nearest whole number, 25.

(b) The desired margin of error is $0.06.

This is n when M = 0.06. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.06 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.06\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.06}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.06})^{2}$

$n = 66.7$

Rounding up, 67

(c) The desired margin of error is $0.05.

This is n when M = 0.05. So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.05 = 1.96*\frac{0.25}{\sqrt{n}}$

$0.05\sqrt{n} = 1.96*0.25$

$\sqrt{n} = \frac{19.6*0.25}{0.05}$

$(\sqrt{n})^{2} = (\frac{19.6*0.25}{0.05})^{2}$

$n = 96.04$

Rounding up, 97

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3 years ago

A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students state

Lorico [155]

Answer:

$a=502 +1.28*81=605.68$

So the value of height that separates the bottom 90% of data from the top 10% is 605.68.

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(502,81)$

Where $\mu=502$ and $\sigma=81$

We want to find a value a, such that we satisfy this condition:

$P(X>a)=0.1$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.28$

And if we solve for a we got

$a=502 +1.28*81=605.68$

So the value of height that separates the bottom 90% of data from the top 10% is 605.68.

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4 years ago

One reading at an Arctic research station showed that the temperature was -35 Celsius.what is this temperature in degrees Fahreh

dem82 [27]

-31F because of the formula.
-35°C multiplied by 9/5 +32 = -31°F
~JZ
Hope it helps

8 0

4 years ago