This is pretty easy but I don't have the brainpower to do it

Anastaziya [24]

Let,
f(x) = -2x+34
g(x) = (-x/3) - 10
h(x) = -|3x|
k(x) = (x-2)^2

This is a trial and error type of problem (aka "guess and check"). There are 24 combinations to try out for each problem, so it might take a while. It turns out that

g(h(k(f(15)))) = -6
f(k(g(h(8)))) = 2

So the order for part A should be: f, k, h, g
The order for part B should be: h, g, k f
note how I'm working from the right and moving left (working inside and moving out).

Here's proof of both claims

-----------------------------------------

Proof of Claim 1:

f(x) = -2x+34
f(15) = -2(15)+34
f(15) = 4
-----------------
k(x) = (x-2)^2
k(f(15)) = (f(15)-2)^2
k(f(15)) = (4-2)^2
k(f(15)) = 4
-----------------
h(x) = -|3x|
h(k(f(15))) = -|3*k(f(15))|
h(k(f(15))) = -|3*4|
h(k(f(15))) = -12
-----------------
g(x) = (-x/3) - 10
g(h(k(f(15))) ) = (-h(k(f(15))) /3) - 10
g(h(k(f(15))) ) = (-(-12) /3) - 10
g(h(k(f(15))) ) = -6

-----------------------------------------

Proof of Claim 2:

h(x) = -|3x|
h(8) = -|3*8|
h(8) = -24
---------------
g(x) = (-x/3) - 10
g(h(8)) = (-h(8)/3) - 10
g(h(8)) = (-(-24)/3) - 10
g(h(8)) = -2
---------------
k(x) = (x-2)^2
k(g(h(8))) = (g(h(8))-2)^2
k(g(h(8))) = (-2-2)^2
k(g(h(8))) = 16
---------------
f(x) = -2x+34
f(k(g(h(8))) ) = -2*(k(g(h(8))) )+34
f(k(g(h(8))) ) = -2*(16)+34
f(k(g(h(8))) ) = 2

5 0

4 years ago

Which of the following would be an appropriate alternative hypothesis?

Dennis_Churaev [7]

Answer:

a. The population proportion is less than 0.65

True, we ar interested in see if the population proportion is (less, higher, not equal) to a specified value.

Step-by-step explanation:

1) Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

2) Solution to the problem

a. The population proportion is less than 0.65

True, we ar interested in see if the population proportion is (less, higher, not equal) to a specified value.

b. The sample proportion is less than 0.65

FALSE, we are interesed on parameters, not in statistics like the sample proportion when we conduct a hypothesis test.

c. The population proportion is equal to 0.65

FALSE, the alternative hypothesis can never have an equal sign.

d. The sample proportion is equal to 0.65

FALSE, the alternative hypothesis can never have an equal sign. And we are interesed on parameters, not in statistics like the sample proportion when we conduct a hypothesis test.

e. both (a) and (d)

FALSE, a its correct but option d no.

5 0

3 years ago

Problem PageQuestion Working together, two pumps can drain a certain pool in hours. If it takes the older pump hours to drain th

gizmo_the_mogwai [7]

Answer:

10.5 hours.

Step-by-step explanation:

Please consider the complete question.

Working together, two pumps can drain a certain pool in 6 hours. If it takes the older pump 14 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?

Let t represent time taken by newer pump in hours to drain the pool on its own.

So part of pool drained by newer pump in one hour would be $\frac{1}{t}$ .

We have been given that it takes the older pump 14 hours to drain the pool by itself, so part of pool drained by older pump in one hour would be $\frac{1}{14}$ .

Part of pool drained by both pumps working together in one hour would be $\frac{1}{6}$ .

Now, we will equate the sum of part of pool emptied by both pumps with $\frac{1}{6}$ and solve for t as:

$\frac{1}{14}+\frac{1}{t}=\frac{1}{6}$

$\frac{1}{14}\times 42t+\frac{1}{t}\times 42t=\frac{1}{6}\times 42t$

$3t+42=7t$

$7t=3t+42$

$7t-3t=3t-3t+42$

$4t=42$

$\frac{4t}{4}=\frac{42}{4}$

$t=10.5$

Therefore, it will take 10.5 hours for the newer pump to drain the pool on its own.

6 0

3 years ago

Can someone help me with this ???

Aliun [14]

1) a. Socratics, chegg, khan academy
1) b. They all learning apps that help you understand problems if any subject. It also has online tutors to help you.

2. To insert a square root, just type \sqrt and then the Enter or Tab key to insert the square root symbol.

6 0

3 years ago

Can someone please solve this ASAP?

olga2289 [7]

The ladder and the wall form a right triangle.
The length is the hypotenuse = 15.
The base = 2*(15/5) = 2*3 = 6

Use pythagorean theorem to find other side of triangle:
$a^2 + b^2 = c^2 \\ \\ a^2 + 6^2 = 15^2 \\ \\ a^2 + 36 = 225 \\ \\ a^2 = 189 \\ \\ a = \sqrt{189} = 3 \sqrt{21}$

8 0

3 years ago