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3 years ago

15

If pump A can fill a water tank in 6 hours and Pump B can fill the water tank in 8 hours, how long will it take to fill the wate

r tank if the pumps work together

1 answer:

trasher [3.6K]3 years ago

5 0

Answer:

2 hours

Step-by-step explanation:

You might be interested in

Two arcs of a circle are congruent if and only if their associated radii are

Drupady [299]

Answer:

False

Step-by-step explanation:

Two arcs are congruent if they have the same length and belong to the same circle or two congruent circles. if two central angles of a circle are congruent then they form congruent arcs.

6 0

3 years ago

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it

lubasha [3.4K]

Answer:

a. 10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.

b. 0.2457 = 24.57% probability 10 of the problems can be resolved today

c. 0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today

d. 0.5017 = 50.17% probability more than 10 of the problems can be resolved today

Step-by-step explanation:

For each case, there are only two possible outcomes. Either they are solved, or they are not. Cases are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

It can resolve customer problems the same day they are reported in 80% of the cases.

This means that $p = 0.8$

Sample of 13 cases:

This means that $n = 13$

a. How many of the problems would you expect to be resolved today? What is the standard deviation?

Expected:

$E(X) = np = 13*0.8 = 10.4$

Standard deviation:

$\sqrt{V(X)} = \sqrt{13*0.8*0.2} = 1.44$

10.4 problems are expected to be resolved today, with a standard deviation of 1.44 problems.

b. What is the probability 10 of the problems can be resolved today?

This is $P(X = 10)$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457$

0.2457 = 24.57% probability 10 of the problems can be resolved today.

c. What is the probability 10 or 11 of the problems can be resolved today?

This is $p = P(X = 10) + P(X = 11)$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{13,10}.(0.8)^{10}.(0.2)^{3} = 0.2457$

$P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680$

$p = P(X = 10) + P(X = 11) = 0.2457 + 0.2680 = 0.5137$

0.5137 = 51.37% probability 10 or 11 of the problems can be resolved today.

d. What is the probability more than 10 of the problems can be resolved today?

This is

$P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13)$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 11) = C_{13,11}.(0.8)^{11}.(0.2)^{2} = 0.2680$

$P(X = 12) = C_{13,12}.(0.8)^{12}.(0.2)^{1} = 0.1787$

$P(X = 13) = C_{13,13}.(0.8)^{13}.(0.2)^{0} = 0.0550$

$P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) = 0.2680 + 0.1787 + 0.0550 = 0.5017$

0.5017 = 50.17% probability more than 10 of the problems can be resolved today

6 0

3 years ago

the total cost of water heater not including a 7% sales tax is 490.00$ what is the cost of the water heater with the tax

Angelina_Jolie [31]

7% = 0.07 -> Percent to decimal

$490.00 (0.07) = 34.3 ->7% of total price

$490.00 + $34.3 = $ 524.3 -> Added tax to total price

Your final answer is $524.30.

Hope that helps!

3 0

4 years ago

Write the inverse function for the function, ƒ(x) =x + 4. Then, find the value of ƒ -1(4). Type your answers in the box.

Contact [7]

Answer:

f-1(x)=x-4

f-1(4)=0

Step-by-step explanation:

to get an inverse function, replace x with y, and y with x.

y=x+4 ---> x=y+4

solve for y: x=y+4 --> y=x-4 --> f-1(x)=x-4

f-1(4)=(4)-4=0

5 0

3 years ago

Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.

arlik [135]

Answer:

$\sqrt[4]{2}$

Step-by-step explanation:

We start with the original problem:

$\frac{2^{3/4}}{2^{1/2}}$

So first we start by applying the quotient rule for powers, which tells you that whenever you are dividing two powers that have the same base and different power, you can copy the base and subtract the powers:

$\frac{b^{a}}{b^{c}}=b^{a-c}$

so:

$\frac{2^{3/4}}{2^{1/2}}=2^{\frac{3}{4}-\frac{1}{2}}$

which yields:

$2^{\frac{1}{4}}$

since we are talking about a rational exponent, we can next turn it into a radical by using the following rule:

$b^{\frac{1}{a}}=\sqrt[a]{b}$

so:

$2^{\frac{1}{4}}=\sqrt[4]{2}$

6 0

3 years ago

Read 2 more answers