F(x) = x2. What is g(x)?

Ameer uses \dfrac14 4 1 start fraction, 1, divided by, 4, end fraction of a bottle of shampoo to give each of his dogs a bath.

svet-max [94.6K]

Answer:

138 3/8

Step-by-step explanation:

total shampoo used for 555 dogs = 1/4 x 555 = 138 3/8 bottles

7 0

2 years ago

Five-sixths of the thirty students passed their test. How many student did not pass

vlada-n [284]

Answer:

5 as 5/6 of 30= 25 and 25+5 =30

Step-by-step explanation:

5 0

3 years ago

Two cars travel at the same speed to different destinations. Car A reaches its destination in 17 minutes. Car B reaches its dest

Goryan [66]

Answer:

speed of car A =Speed of car B=0.8 miles/minutes.

Step-by-step explanation:

We are given that speed of car A is equal to speed of car B.

Also let car A travels x miles.

and car B travels y miles.

Car A reaches its destination in 17 minutes.

this means that speed of car A is given by: $\dfrac{x}{17}$ miles/minutes ( since speed is defined as the ratio of distance and time).

Car B reaches its destination in 32 minutes.

This means that the speed of car B is given by: $\dfrac{y}{32}$ miles/minutes

as speed of both cars are equal this means:

$\dfrac{x}{17}=\dfrac{y}{32}$ ------(1)

Also we are given Car B travels 12 miles farther than Car A.

this means $y-x=12$

$y=12+x$ ------(2)

on using equation (1) and (2) we have:

$\dfrac{x}{17}=\dfrac{12+x}{32}\\ \\32x=17(12+x)\\\\32x=17\times12+17x\\\\32x-17x=17\times12\\\\15x=122\times17\\\\x=13.6$

Hence the speed of car A is 0.8 miles/minutes ( since x/17 is the speed of car A)

Speed of car B=0.8 miles/minutes.

8 0

3 years ago

A giraffe can travel 800 feet in 20 seconds. Write a direct variation equation for the distance traveled any time | Please expla

Diano4ka-milaya [45]

The direct variation equation is:
d=kt
where d is the distance that the giraffe travels
k is the constant of variation
and t is time
Now we are told that the giraffe can travel 800 ft in 20 seconds, so we can solve for the constant of variation (k)
800=k(20) divide both sides by 20
k=40-------------and the units are ft per sec
So now we can write
d=40t
ck
d=40t
800ft=40*20 ft
800 ft= 800 ft

Hope this helps!

8 0

3 years ago

I really need help please answer

belka [17]

Answer: Choice B) between 6:48 AM and 5:12 PM

=========================================================

Explanation:

I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.

We want to find values of t that satisfy f(t) > 25

This is the same as trying to solve f(t) - 25 > 0

So we have,

$f(t) = 24 - 5\cos\left(\frac{\pi}{12}t\right)\\\\ f(t)-25 = 24 - 5\cos\left(\frac{\pi}{12}t\right)-25\\\\ f(t)-25 = -1 - 5\cos\left(\frac{\pi}{12}t\right)\\\\ f(t)-25 > 0\\\\ -1 - 5\cos\left(\frac{\pi}{12}t\right) > 0\\\\$

To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.

Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.

Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)

Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.

When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.

Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.

Then focusing on the point (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours

1700 hours in military time = 17-12 = 5 pm

The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.

We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).

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

In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.

Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.

8 0

3 years ago