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3 years ago

5

If f(x) =1/4x+14, then f^-1(x)=

1 answer:

Naddika [18.5K]3 years ago

8 0

Answer: f⁻¹(x)=4x-56

Step-by-step explanation:

f⁻¹(x) is the inverse of f(x). To find the inverse, we replace the y with x, and x with y. Once we do that, we solve for y.

$x=\frac{1}{4}y+14$ [subtract 14 on both sides]

$x-14=\frac{1}{4}y$ [multiply both sides by 4]

$4(x-14)=y$ [distribute 4]

$4x-56=y$

$f^-^1(x)=4x-56$

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Solve and check 8-(6-8x) =4x+4

navik [9.2K]

Greetings!

"Solve and check $8-(6-8x)=4x+4$ "...

Solve for x<span>:
</span> $8-(6-8x)=4x+4$
Remove the Parenthesis.
$8-6-8x=4x+4$
Simplify.
$2-8x=4x+4$
Add -4 to both sides.
$(2-8x)+(-4)=(4x+4)+(-4)$
Simplify.
$-2-8x=4x$
Add 8x to both sides.
$(-2-8x)+8x=(4x)+8x$
Simplify.
$-2=12x$
Divide both sides by 12.
$(-2)/12=(12x)/12$
Simplify.
$-0.166666667=x$

The answer is: <em>x=-0.166666667

</em>Hope this helps.
<em></em>-Benjamin

7 0

3 years ago

The following results come from two independent random samples taken of two populations.

photoshop1234 [79]

Answer:

$(a)\ \bar x_1 - \bar x_2 = 2.0$

$(b)\ CI =(1.0542,2.9458)$

$(c)\ CI = (0.8730,2.1270)$

Step-by-step explanation:

Given

$n_1 = 60$ $n_2 = 35$

$\bar x_1 = 13.6$ $\bar x_2 = 11.6$

$\sigma_1 = 2.1$ $\sigma_2 = 3$

Solving (a): Point estimate of difference of mean

This is calculated as: $\bar x_1 - \bar x_2$

$\bar x_1 - \bar x_2 = 13.6 - 11.6$

$\bar x_1 - \bar x_2 = 2.0$

Solving (b): 90% confidence interval

We have:

$c = 90\%$

$c = 0.90$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.90$

$\alpha = 0.10$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.10/2}$

$z_{\alpha/2} = z_{0.05}$

The z score is:

$z_{\alpha/2} = z_{0.05} =1.645$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.645 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.645 * \sqrt{0.3306}$

$2.0 \± 0.9458$

Split

$(2.0 - 0.9458) \to (2.0 + 0.9458)$

$(1.0542) \to (2.9458)$

Hence, the 90% confidence interval is:

$CI =(1.0542,2.9458)$

Solving (c): 95% confidence interval

We have:

$c = 95\%$

$c = 0.95$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.95$

$\alpha = 0.05$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.05/2}$

$z_{\alpha/2} = z_{0.025}$

The z score is:

$z_{\alpha/2} = z_{0.025} =1.96$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.96 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.96* \sqrt{0.3306}$

$2.0 \± 1.1270$

Split

$(2.0 - 1.1270) \to (2.0 + 1.1270)$

$(0.8730) \to (2.1270)$

Hence, the 95% confidence interval is:

$CI = (0.8730,2.1270)$

8 0

3 years ago

What is 40% of 206?<br><br> Enter your answer as a decimal in the box.

IRISSAK [1]

206 X .4 = 82.4

That's the answer.

5 0

3 years ago

Read 2 more answers

Kayson is looking at two buildings, building A and building B, at an angle of elevation of 59°. Building A is 40 feet away, and

Snezhnost [94]

Answer:

last one Building B; it is around 33.29 feet taller than building A Step-by-step explanation:

4 0

3 years ago

Find the distance between the points (3, 8) and (-1, 9).

xxMikexx [17]

Answer:

9,1

Step-by-step explanation:

6 0

3 years ago