What is 7 x 7 x 7 written using an exponent?

Solar-heat installations successfully reduce the utility bill 60% of the time. What is the probability that at least 9/10 solar-

Wittaler [7]

Answer:

4.23% probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill.

Step-by-step explanation:

For each installation, there are only two possible outcomes. Either it reduces the utility bill, or it does not. The probabilities for each installation reducing the utility bill are independent. 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.

In this problem we have that:

Solar-heat installations successfully reduce the utility bill 60% of the time, which means that $p = 0.6$

What is the probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill?

This is $P(X \geq 9)$ when $n = 10$ . So

$P(X \geq 9) = P(X = 9) + P(X = 10)$

In which

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

$P(X = 9) = C_{10,9}.(0.6)^{9}.(0.4)^{1} = 0.0363$

$P(X = 10) = C_{10,10}.(0.6)^{10}.(0.4)^{0} = 0.0060$

So

$P(X \geq 9) = P(X = 9) + P(X = 10) = 0.0363 + 0.0060 = 0.0423$

4.23% probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill.

3 0

3 years ago

How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … (

prohojiy [21]

Answer:

The equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … Will have:

(a) 6 solutions where there are no other restrictions.

(b) 4 Solutions for xi ≥ 3 for i = 1, 2, 3, 4, 5, 6(x3 + x4 +x5 + x6 = 25)

(c) 4 Solutions for 3 ≤ x1 ≤ 10

( x3 + x4 + x5 + x6 = 25)

(d) 5 Solutions for 2 ≤ x2 ≤ 7

Step-by-step explanation:

The equation have 6 unknown variables . This means it will have 6 solutions when no condition is imposed as in (a) above. The number of unknown variables in the equation will give the numbers of solutions

When the conditions are imposed, the numbers of unknown variables will give the number of solutions.

In (b) and (c), the equation will reduce to x3 + x4 +x5 + x6 = 25) and the unknown variables are 4, giving 4 solutions

In (d), the equation will reduce be 5 unknown variables(x2 + x3 + x4 +x5 + x6 = 25) and the solution is 5

8 0

3 years ago

A rectangle prism is11 3/5 meters long, 9 meters wide, and 121/2 meters high. What is the volume , in cubic meters, of the prism

lora16 [44]

Volume = Length * Height * Width

Volume = 11 3/5 * 121/2 * 9

V = 11.6 * 60.5 * 9

V = 701.8 * 9

V = 6316.2 m³

5 0

3 years ago

In 2.5 hours, 0.64 inch of rain fell. At about what rate did the rain fall? A 0.18 inch per hour 8 0.26 inch per hour 0 0.32 inc

julia-pushkina [17]

Answer:

0.26 per Hour

Step-by-step explanation:

0.26x2=0.52

0.26/2=0.13

0.52+0.13=0.65

0.65 is the closest to your question

5 0

3 years ago

Using the following preference list, which candidate is the winner using Plurality Voting?

jonny [76]

Answer:

c

Step-by-step explanation:

c

6 0

3 years ago