What fraction of the first twenty counting numbers (1,2,3,...,18,19,20) are composite numbers

Given y = 2x + 4, what is the new y-intercept if the y-intercept is decreased by 5? A) −1 B) −3 C) −4 D) −5

The new y-intercept would be A)-1 because of the 4-5 = -1

3 0

3 years ago

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

B Christian installed an electric pump to pump water from a borehole into a 30 000 litre cement dam. If the water is pumped at a

skelet666 [1.2K]

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

Given that;

Amount of water needed to fill the dam A = 30000 litres
Pump rate r = 75 litres per minute
Time needed to fill the dam T = ?

To determine how long it take to fill the dam, we say;

Time need = Amount of water needed ÷ Pump rate

T = A ÷ r

T = 30000 litres ÷ 75 litres/minute

T = 400 minutes

Note that; 60min = 1hrs

Hence,

T = 6hours 40minutes

Given the amount of water needed to fill the cement dam and the water pump rate, the time needed to fill the dam is 400 minutes or 6hours 40minutes.

Option B)6h 40min is the correct answer.

Learn more word problems here: brainly.com/question/2610134

#SPJ1

8 0

2 years ago

Solve for a please show all your work

o-na [289]

Z = -b - a + 1

subtract 1
1z - 1 = -1b - 1a ( 1z is the same as z, same goes for b and a)

add -1b
1b - 1z - 1 = -1a

then we remove -1 by dividing it.
-1b -(-1z) + 1

Answer: -1b -(-1z) + 1 = A

A negative minus a negative is a positive, so the answer might as well be....
-1b + 1z + 1 = A

6 0

3 years ago

The population of a small town in the Midwest has been loosing 4% of its

yKpoI14uk [10]

Answer:

337.406388 or 337 people

Step-by-step explanation:

To figure this out, use the compound interest (compounding number?) equation which is Amount = People(1 + rate)^time

So if you fill that out you get

A = 20,000(.96)^100

A = 20,000(0.0168703194)

A = 337.406388

8 0

3 years ago

What fraction of the first twenty counting numbers (1,2,3,...,18,19,20) are composite numbers​

What fraction of the first twenty counting numbers (1,2,3,...,18,19,20) are composite numbers