The
<u>correct answers</u> are:
1/6πd³;
3; and
9 cm.
Explanation:
For the <u>first question</u>:
The formula for the volume of a sphere is:

We have the diameter, not the radius. The diameter is twice as much as the radius; this means to find the radius using the diameter, we divide by 2. This gives us:

When we raise a fraction to a power, we raise both the numerator and the denominator to that power. This gives us:

We start multiplying this:

For the <u>second question</u>:
The planes of symmetry are the planes through which we can fold the figure in half. These are in the middle horizontally through the figure; in the middle vertically (through the width) through the figure; and in the middle vertically (through the length) through the figure. This makes 3.
For the <u>third question</u>:
The formula for the volume of a triangular prism is:

,
where b is the base of the triangular base of the pyramid, h is the height of the triangular base of the pyramid, and H is the height of the pyramid.
We know the volume is 90; the base of the triangle is 12 and the height is 5:

We divide both sides by 10:
90/10 = 10H/10
9 = H
Answer:
Evelyn monthly allowance is $187.
Step-by-step explanation:
Let the monthly allowance be 'x'.
Given:
Money taken with for shopping = 
Money spent of dress = $39.95
Also Given:
3/7 of the remainder on some accessories.
Money spent on accessories is equal to
times Difference of monthly allowance and Money spent of dress.
framing in equation form we get;
Money spent on accessories = 
Also Given:
Money left after shopping = $30.60
Now we know that;
Money taken with for shopping is equal to sum of Money spent of dress and Money spent on accessories and Money left after shopping.
framing in equation form we get;

Combining like terms we get;

Now we will make denominator common using L.C.M

Hence Evelyn monthly allowance is $187.
5x<50-20
x<10-4
x<6
x= the cost of the shirts
50= cost limit
-20= discount
5= number of shirts
Answer:
(x, y) = (1, 1/3)
Step-by-step explanation:
The x-coefficient in the first equation is -2 times that in the second equation, so adding twice the second equation to the first will eliminate x:
(4x -9y) +2(-2x +3y) = (1) +2(-1)
-3y = -1 . . . . simplify
y = 1/3 . . . . . divide by -3
The y-coefficient in the first equation is -3 times the y-coefficient in the second equation, so adding 3 times the second equation to the first will eliminate y:
(4x -9y) +3(-2x +3y) = (1) +3(-1)
-2x = -2 . . . . . . simplify
x = 1 . . . . . . . . . divide by -3
The solution is (x, y) = (1, 1/3).