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Mekhanik [1.2K]
3 years ago
12

Tiffany is filling her daughter's pool with water from a hose. She can fill the pool at a rate of LaTeX: \frac{1}{5}1 5gallons/s

econd. a. At this rate, how long will it take her to fill the pool with 5 gallons of water?
Mathematics
1 answer:
Hitman42 [59]3 years ago
6 0

Answer:

25 seconds

Step-by-step explanation:

You have a rate of:

\dfrac{1}{5}gal/s

And you want to find how many seconds it would take to fill in 5 gallons of water. Using the rate, we use it as a conversion factor from rate to seconds:

5gal\times\dfrac{1sec}{\frac{1}{5}gal}=\dfrac{5sec}{\frac{1}{5}}=25sec

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UDD Question 6 10 pts Solve for x. Round to the nearest tenth (one decimal place). Just type the number, no unit of measurement.
NISA [10]

Answer:

The answer is;

54.4

Step-by-step explanation:

The given parameter are;

Triangle ΔFGH = Right triangle

The length of segment \overline {FH} = 48

The measure of ∠HFG = 28°

The measurement required = The measure of segment \overline {FG} = x

The measure of ∠FHG = 90° angle opposite hypotenuse side of a right triangle

Therefore, ∠FGH = 180° - ∠HFG - ∠FHG = 180° - 90° - 28° = 62°

∠FGH = 62°

By sine rule, we have;

\overline {FH}/(sin ∠FGH) = \overline {FG}/(sin(∠FHG)

By substituting the known values, we have;

48/(sin 62°) = x/(sin(90°)

sin(90°) = 1, therefore, we have;

x/1 = x = 48/(sin 62°) = 54.4 (by rounding the answer to the nearest tenth)

x = 54.4

8 0
2 years ago
What is the number if 50% of 25% of the number is 96
tamaranim1 [39]

Answer:

12

Step-by-step explanation:

the number is 96

hence,

25% of 96=

25/100*96/1

=24

50% of 24=

50/100*24/1=

12

it also possible that you're to sum them,but since you were not asked for the sum of the number the answer is 12.

3 0
3 years ago
Read 2 more answers
Write an equation to show that Y is directly proportional to x using the constant of proportionality given. Then solve for the u
olga55 [171]

Answer:

y = 2\frac{5}{11}

Step-by-step explanation:

y ∝ kx

y = \frac{3}{11} × 9 = 2\frac{5}{11}

8 0
3 years ago
A bus travels on an east-west highway connecting two cities A and B that are 100 miles apart. There are 2 services stations alon
melamori03 [73]

Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.  

X~ Uniform(0,100)

Then the probability mass function is given as follows.

f(x) = P(X=x) = 1/100  \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0  \,\,\,\, \text{otherwise}

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located  70 meters away from city A then the mid point between 20 and 70  is (70+20)/2 = 45 then we can represent D as follows

D(x) =\left\{ \begin{array}{ll}  x  & \mbox{if } 0\leq x \leq 20 \\  x-20 & \mbox{if } 20\leq x < 45\\                70-x & \mbox{if } 45 \leq x \leq 70\\                x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable Y = D(X), Y is a random variable as well, remember that there is a theorem that says that

E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx

Where f(x) is the probability mass function of X. Using the information of our problem

E[Y] = \int\limits_{-\infty}^{\infty}  D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx  \bigg]\\= \frac{51}{4} = 12.75

3 0
3 years ago
0.5=0.4y - 0.25x Solve for y<br>​
Ad libitum [116K]

Answer:

y=0.625x+1.25

Step-by-step explanation:

5 0
2 years ago
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