Expand the function f(x)=(2x+3)^4

allochka39001 [22]

Answer:

b. 82m³

Step-by-step explanation:

$V = \frac{1}{3}(\frac{1}{2} bh_1)h_2\\b = 8.2m\\h_1 = 4m\\h_2 = 15m\\\\V = \frac{1}{3}(\frac{1}{2}(8.2)(4))(15)\\V = 82m^{3}\\$

3 0

2 years ago

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Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.5

Fynjy0 [20]

Answer:

Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

Step-by-step explanation:

Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables a, b, and c, respectively.

Since a total of 14 cups of coffee was served:

$a+b+c=14$

A total of 204 ounces of coffee was served. Therefore:

$10a+14b+20c=204$

A total of $16.70 was collected. Hence:

$0.95a+1.15b+1.5c=16.7$

This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.

From the first equation, let's subtract a and b from both sides:

$c=14-a-b$

Substitute this into both the second and third equations:

$10a+14b+20(14-a-b)=204$

And:

$0.95a+1.15b+1.5(14-a-b)=16.7$

In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:

For the Second Equation:

$\displaystyle \begin{aligned} 10a+14b+280-20a-20b&=204\\ -10a-6b&=-76\\5a+3b&=38\end{aligned}$

And for the Third:

$\displaystyle \begin{aligned} 0.95a+1.15b+21-1.5a-1.5b&=16.7\\ -0.55a-0.35b&=-4.3\end{aligned}$

We can solve this using substitution. From the second equation, isolate a:

$\displaystyle a=\frac{1}{5}(38-3b)=7.6-0.6b$

Substitute into the third:

$-0.55(7.6-0.6b)-0.35b=-4.3$

Distribute and simplify:

$-4.18+0.33b-0.35b=-4.3$

Therefore:

$-0.02b=-0.12\Rightarrow b=6$

Using the equation for a:

$a=7.6-0.6(6)=4$

And using the equation for c:

$c=14-(4)-(6)=14-10=4$

Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.

7 0

2 years ago

Which of the following numbers is closest to 4? O A. V13 O B. V18 C. 15 D. 719

OverLord2011 [107]

Answer:

$\huge\boxed{B.\ \sqrt{18}}$

Step-by-step explanation:

$4=\sqrt{4^2}=\sqrt{16}$

3 0

2 years ago

vWhat is the probability of drawing either a king, a queen, or a jack from a deck of 52 playing cards

Bas_tet [7]

Answer:

20 por ciento de probabilidad de que elijas una de esas cartas

Step-by-step explanation:

20 por ciento de probabilidad de que elijas una de esas cartas

6 0

2 years ago

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A farmer can spend no more than $4,000 on fertilizer and seeds. The fertilizer costs $2 per pound and seeds cost $20 per pound.

lilavasa [31]

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

f -----> the number of pounds of fertilizer

s ----> the number of pounds of seeds

we know that

The inequality that represent the situation is

$2f+20s\leq 4,000$

using a graphing tool

see the attached figure

The solution is the triangular shaded area

7 0

3 years ago

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