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Find the volume of the prisms. Show work!

Fed [463]

1. Answer = About 1451.42 m³

First, we need to find the volume of the cube:
Formula: πr²h

Volume = π * 3² * 50 = 1413.72 m³
Second, we need to find the volume of the cone:
Formula: (πr²h)/3
Volume = π * 3² * 4 = 37.69 m³
Third, we need to add these two volumes to find the total volume of the figure.

1413.72 m³ + 37.69 m³ = 1451.42 m³.

2. Answer = 960 m³

Formula: (1/2(b*l)) * 20
First, we need to find the area of the base (1/2 * b* l).
1/2 * 8 * 12 = 48.
Second, we need to multiply the area of the base by the height to get the volume.
B * h = 48 * 20 = 960 m³.

6 0

3 years ago

A woodworking artist makes two types of carvings: type X and type Y. He

ivolga24 [154]

Answer:

part C. 3x + 2y < 30, 5x + 7y < 105

Step-by-step explanation:

Part 1:

spends 3 hours making each type X (3x)-each type x will take 3 hours so as the number of type x increases, the hours will increase by 3.

spends 2 hours making each type Y (2y)-each type y will take 2 hours so as the number of type y increases, the hours will increase by 2.

Part 2:

he can spend up to 30 hours each week making carvings. (<30)-because he cannot spend more than 30 hours

Therefore, He has to spend 30 hours or less to make type X and type Y.

3x + 2y < 30

Part 3:

His materials cost him $5 for each type X carving. (5x)-each type x will take $5 so as the number of type x increases, the cost will increase by 5.

His materials cost him $7 for each type Y carving, (7y)-each type y will take $7 so as the number of type y increases, the cost will increase by 7.

Part 4:

he must keep his weekly cost for materials to $105 or less (<105)-total cost cannot be more than $105.

Therefore, the total cost of making x and y should be $105 or less.

5x + 7y < 105

!!

6 0

3 years ago

3 letters without replacement 4 letters A B C D how many ways can this be done if the order of the choices matters

Veseljchak [2.6K]

Answer:

Since the order of choice matters, we will permute the values. a bit more explanation for this:

If the order of choice did NOT matter, ABC and BCA will be counted as one since order of choice does NOT matter

Since order of choice does matter, ABC , BCA and CAB are all different possibilities for the arrangement of the same 3 letters

Since we have 3 slots:

___ ___ ___

Now, for the first slot. You can out either one if the 4 alphabets in the first slot since no slot has been used as of now

So:

_4_ ___ ___

**Keep in mind that the 4 is the possible number of values this slot can have**

Now that one slot has been used, one of the 4 alphabets has been used and since we are not allowed to repeat the same alphabets, we are left with 3 more alphabets

we can put any one of the 3 alphabets in this second slot, Hence:

_4_ _3_ ___

Now that 2 of the 4 alphabets have been used, we are left with only 2 alphabets, so there are only 2 possible alphabets for slot 3

Therefore:

_4_ _3_ _2_

Now that we know the possible alphabets for all 3 slots, we will multiply them with each other to get the total possible number of 3 - alphabet words we can make with 4 alphabets

Total possible words = 4 * 3 * 2

Total possible words = 24

We could've used the formula for Permutation as well

8 0

3 years ago

8. Combine the like terms in this expression: –3x + 2xy + 4y – xy + 2x – 11y

luda_lava [24]

Answer:

D. –X+XY–7y

Step-by-step explanation:

We just have to combine (add) the similar terms... so all terms that have an x in them for example.

–3x + 2xy + 4y – xy + 2x – 11y

Let's first re-write it placing similar terms next to each other

(-3x + 2x) + (2xy - xy) + (4y - 11y)

Then we sum them up, for each similar terms

1x + 1xy -7y

so, x + xy -7y

Answer D.

6 0

3 years ago

Write the number and the nature of the roots of the quadratic equation whose discriminant is -12

Orlov [11]

Hello
D. 2 imaginary roots (complex conjugates)

7 0

4 years ago