F(x) = 3√2x<br>g(x) = 3x + 1

Monica bought 12 gallons of paint. She used 2/3 of the paint to paint her house. How many gallons of the paint did she use?

BaLLatris [955]

12 / 3 = 4
4 x 2 = 8

Answer: She used 8 gallons of paint

8 0

3 years ago

Read 2 more answers

Find the value of each variable.<br>

V125BC [204]

Answer:

see explanation

Step-by-step explanation:

Using the exact values of the trigonometric ratios

sin60° = $\frac{\sqrt{3} }{2}$ , cos60° = $\frac{1}{2}$

sin45° = cos45° = $\frac{1}{\sqrt{2} }$

Using the sine ratio on the right triangle on the left

sin60° = $\frac{opposite}{hypotenuse}$ = $\frac{a}{4\sqrt{3} }$ = $\frac{\sqrt{3} }{2}$

Cross- multiply

2a = 4 $\sqrt{3}$ × $\sqrt{3}$ = 12 ( divide both sides by 2 )

a = 6

Using the cosine ratio on the same right triangle

cos60° = $\frac{adjacent}{hypotenuse}$ = $\frac{c}{4\sqrt{3} }$ = $\frac{1}{2}$

Cross- multiply

2c = 4 $\sqrt{3}$ ( divide both sides by 2 )

c = 2 $\sqrt{3}$

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Using the sine/cosine ratios on the right triangle on the right

sin45° = $\frac{a}{b}$ = $\frac{6}{b}$ = $\frac{1}{\sqrt{2} }$

Cross- multiply

b = 6 $\sqrt{2}$

cos45° = $\frac{d}{b}$ = $\frac{d}{6\sqrt{2} }$ = $\frac{1}{\sqrt{2} }$

Cross- multiply

$\sqrt{2}$ d = 6 $\sqrt{2}$ ( divide both sides by $\sqrt{2}$ )

d = 6

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a = 6, b = 6 $\sqrt{2}$ , c = 2 $\sqrt{3}$ , d = 6

3 0

3 years ago

8. Write an algebraic expression to represent each

skelet666 [1.2K]

3x-14 = n

Hope this helps

4 0

3 years ago

Find the partial derivatives of the function w=4r2+6s2+

lyudmila [28]

I'm taking the liberty of editing your function as follows: <span>w=4r^2+6s^2, where I use " ^ " to indicate exponentiation.

The partial of w with respect to r is 8r. That with respect to s is 12s.</span>

8 0

3 years ago

The centers for disease control and prevention reports 25% baby boys 6 to 8 months in the US weigh more than 20 pounds a sample

Vesna [10]

Answer:

P(x < 3) = 0.1971

Explanation:

To calculate the probability that x babies weigh more than 20 pounds, we will use the binomial distribution, so it can be calculated as:

$\begin{gathered} P(x)=nCx\cdot p^x\cdot(1-p)^{n-x} \\ Where\text{ nCx=}\frac{n!}{x!(n-x)!} \\ \\ With\text{ n = size of sample} \\ p=\text{ probability of success \lparen the baby weight more than 20 pounds\rparen} \end{gathered}$

So, replacing n = 16 and p = 0.25, we get that the probability is equal to

P(x) = 16Cx (0.25)^x (1 - 0.25)^(16 - x)

$P(x)=16Cx\cdot0.25^x\cdot(1-0.25)^{16-x}$

Now, the probability that fewer than three weights more than 20 pounds are equal to

$\begin{gathered} P(x$

Then

P(x < 3) = 0.01 + 0.0535 + 0.1336

P(x < 3) = 0.1971

Therefore, the answer is

P(x < 3) = 0.1971

3 0

1 year ago

F(x) = 3√2xg(x) = 3x + 1​

F(x) = 3√2xg(x) = 3x + 1