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Ugo [173]
2 years ago
7

Which expression represents the volume, in cubic units, of the shaded part of the sphere? four-thirdsπ(103) four-thirdsπ(43) fou

r-thirdsπ(103) – four-thirdsπ(43) four-thirdsπ(203) four-thirdsπ(43) four-thirdsπ(203) – four-thirdsπ(43)
Mathematics
1 answer:
oee [108]2 years ago
6 0

The volume of the shaded part in cubic units is  4/3π(20)³ -  4/3π(4)³

<h3>Volume of composite object</h3>

The sphere is a a solid 3-dimensional object. THe formula for calculating its volume is expressed as:

V = 4/3πr³

where:

r is the radius of the sphere

<u>For the outer sphere:</u>

V = 4/3π(20)³

<u>For the inner sphere:</u>

V = 4/3π(4)³

The volume of the shaded part in cubic units is  4/3π(20)³ -  4/3π(4)³

Learn more on volume of sphere here: brainly.com/question/10171109

#SPJ4

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Zachary completes a hypothesis test and finds that he rejects the null hypothesis. Which statement gives a reason for rejecting
padilas [110]

Answer:

The z-statistic lies in the critical region

Step-by-step explanation:

When a hypothesis test is performed, the decision to reject or not reject the null hypothesis is made on basis of following observations:

  • If the z-statistic falls in the critical or rejection region, there is enough evidence to reject the Null Hypothesis
  • If the z-statistic falls outside the critical or rejection region, there is not enough evidence to reject the Null Hypothesis.

In the given statement Zachary rejects the Null Hypothesis, this means the z-statistic she calculated must have been inside the critical or rejection region. Hence the correct answer would be:

The z-statistic lies in the critical region

4 0
3 years ago
Read 2 more answers
HELP PLSSS<br> The The coordinates of ​' R is
V125BC [204]

Answer:

The coordinate r is the length of the line segment from the point (x,y) to the origin and the coordinate θ is the angle between the line segment and the positive x-axis.

Step-by-step explanation:

=>

4 0
2 years ago
What is the equation of the line in the graph
iren [92.7K]

Always, ALWAYS remeber this format: y = mx + b

In this equation, 'm' is the slope, and 'b' is the y-intercept

When you're trying to find a slope, remember that the equation is \frac{rise}{run}

When finding the rise and run, look at two points that are on the graph AND on the line as well. Essentially, make sure the points you're using are integers.

In this, case, the rise is -3, and the run is 2. This means that the slope is  \frac{-3}{2}

Now we have the first part of our equation:

y = - \frac{3}{2} + b

But wait! How do we find b?

Sometimes you have to input x in order to find it, but only when you're not supplied with a graph. In this case, all you have to do is look!

The point of the line that is on the y-axis is called the y-intercept.

In this graph, the y-intercept is -1

Now we have our complete equation!

y = - \frac{3}{2} - 1

Good luck!

3 0
3 years ago
If one table and two lamps cost $88, and two
Paul [167]

Answer:

One lamp is equal to 23 dollars

One table is equal to 42 dollars.

Step-by-step explanation:

We can solve this by first organizing what we have.

1 table (t) + 2 lamps (l) = 88.

2 tables (t) + 3 lamps (l) = 153.

_____________

===============

1t + 2l = 88

2t + 3l = 153

===============

-------------------------

If we multiply both sides by 2 on the first equation of

1t + 2l = 88

we could get

2t + 4l = 176.

If that is true, we can subtract the second equation of

2t + 3l = 153 from the new equation to get the price of a lamp.

    2t + 4l = 176

-    2t + 3l = 153

____________

= 0t + l = 23

One lamp is equal to 23.

We can check this by plugging it into an equation.

1 + 2(23) = 88

1t + 46 = 88

1t + 46 - 46 = 88 - 46

1t = 42

If one table equals 42, we can put this back into the second equation to check.

2 (42) + 3 (23) = 153

84 + 69 = 153

That is correct.

Another way to solve is to put this like a system of equations in a graph, by replacing "t" by "x" for example, and "l" by y.

Then you could put it into a graphing calculator and solve by looking for the place where the two lines converge or meet.

Since we put "x" for "t", that means that whatever the x-value is on the solution point, that is the cost of a table, and the y-value is the cost of the lamps.

Another way to solve, is to find the unit rate first by subtracting the first equation from the second equation.

    2t + 3l = 153

 -  1t + 2l = 88

____________

= t + l = 65

If t + l = 65, we can rearrange that equation to be something like t = 65 - l.

That means "t" is equal to 65 bucks minus a lamp.

We put this back into the first equation of

1t + 2l = 88

and replace "t" with the previous expression.

1(65 - l) + 2l = 88

Simplify/distributive property

65 - l + 2l = 88

65 - 65 - l + 2l = 88 - 65

-l + 2l = 23

l = 23

One lamp is equal to 23 bucks.

Confirmed :)

5 0
3 years ago
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Investigate what happens with the “ninth” fractions.
Anestetic [448]

Given:

Fractions \dfrac{1}{9},\dfrac{2}{9},\dfrac{3}{9} etc.

To find:

What happens with the “ninth” fractions.

Solution:

We have, the values of \dfrac{1}{9},\dfrac{2}{9},\dfrac{3}{9} are

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\dfrac{2}{9}=0.22222...

\dfrac{3}{9}=0.33333...

Clearly we can spot a pattern, because after decimal the numerator digit of fraction is repeating.

Similarly,

\dfrac{9}{9}=0.99999...

Therefore, the decimal value of \dfrac{9}{9} is 0.99999..., which is approximately 1.

3 0
3 years ago
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