If sarah starts her chores at 10:15

What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi

Sphinxa [80]

Answer:

$15,000\:\mathrm{mm^3}$

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by $V=s^2\cdot h$ , where $s$ is the base length and $h$ is the height. Substituting given values, we have: $V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}$

The volume of a trapezoidal prism is given by $V=\frac{b_1+b_2}{2}\cdot l\cdot h$ , where $b_1$ and $b_2$ are bases of the trapezoid, $l$ is the length of the height of the trapezoid and $h$ is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ( $\frac{b_1+b_2}{2}$ ) multiplied by the trapezoid's height ( $l$ ).

Substituting given values, we get:

$V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}$

Therefore, the total volume of the composite figure is $5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}$ (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

$V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark$

8 0

3 years ago

Explain how you can find the center of dilation of a triangle and its dilation.

Naddika [18.5K]

In mathematics, the term "center of dilation" refers to a constant point on a surface from which all other points are either enlarged or compressed. The center of dilation and the scale factor comprise the two properties of a dilation.

4 0

3 years ago

Captain Jessica has a ship, the H.M.S Crimson Lynx. The ship is two furlongs from the dread pirate Ishaan and his merciless band

OLga [1]

Answer:

9/40

Step-by-step explanation:

Captain Jessica shoots first. This means her ship has not already been hit, which means she has a 2/5 chance of hitting the pirate ship. This also means she has a 1-2/5 = 3/5 chance of missing the pirate ship.

Since Captain Jessica misses, dread pirate Ishaan has a 3/8 chance of hitting the captain's ship. This means he has a

3/5(3/8) = 9/40 chance of the captain missing the pirate and the pirate hitting the captain.

6 0

4 years ago

Helppppp my brain just doesn’t work today. I’ll brainlist.

s344n2d4d5 [400]

Answer:

Number 6 is 1/6

Number 7 is 5/6

Number 8 is 3/6 or 1/2

Step-by-step explanation:

6. $\frac{1}{6}$ chance of landing on a 2 because there are 6 sides and the probability is equal.

There is a 1/6 chance it will land on 1, 2, 3, 4, 5, and 6. So 1/6 is the answer.

7. $\frac{5}{6}$ chance of not landing on 5. There are 5 "non-5" numbers. So 5/6 is the answer.

8. Let's see the odd numbers: 1, 2, 3, 4, 5, 6.

1, 3, and 5 are odd. So that's half of the numbers so the answer would be $\frac{3}{6}$ or simplified to $\frac{1}{2}$ .

6 0

3 years ago

If 33 laptops cost 30,000, what proportion could be used to determine the cost of 11 laptops?

andre [41]

Answer:

30,00 divided by 33= 909.09 times 11=9,999.99 hope it helps you

Step-by-step explanation:

6 0

3 years ago