Answer:
see below
Step-by-step explanation:
12.5x − 10.2 = 3(2.5x + 4.2) - 6
Use the distributive property to distribute the 3
12.5x − 10.2 = 7.5x + 12.6 − 6
Combine like terms
12.5x − 10.2 = 7.5x + 6.6
Add 10.2 to each side of the equation by using the addition property of equality
12.5x = 7.5x + 16.8
Subtraction 7.5x from each side of the equation by using the subtraction property of equality
5x = 16.8
Divide by 5 on each side by using the division property of equality
x = 3.36
Answer:


Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
For this case we select a sample of n =100
From the central limit theorem we know that the distribution for the sample mean
is given by:
So then the sample mean would be:

And the standard deviation would be:

(a) 0.059582148 probability of exactly 3 defective out of 20
(b) 0.98598125 probability that at least 5 need to be tested to find 2 defective.
(a) For exactly 3 defective computers, we need to find the calculate the probability of 3 defective computers with 17 good computers, and then multiply by the number of ways we could arrange those computers. So
0.05^3 * (1 - 0.05)^(20-3) * 20! / (3!(20-3)!)
= 0.05^3 * 0.95^17 * 20! / (3!17!)
= 0.05^3 * 0.95^17 * 20*19*18*17! / (3!17!)
= 0.05^3 * 0.95^17 * 20*19*18 / (1*2*3)
= 0.05^3 * 0.95^17 * 20*19*(2*3*3) / (2*3)
= 0.05^3 * 0.95^17 * 20*19*3
= 0.000125* 0.418120335 * 1140
= 0.059582148
(b) For this problem, let's recast the problem into "What's the probability of having only 0 or 1 defective computers out of 4?" After all, if at most 1 defective computers have been found, then a fifth computer would need to be tested in order to attempt to find another defective computer. So the probability of getting 0 defective computers out of 4 is (1-0.05)^4 = 0.95^4 = 0.81450625.
The probability of getting exactly 1 defective computer out of 4 is 0.05*(1-0.05)^3*4!/(1!(4-1)!)
= 0.05*0.95^3*24/(1!3!)
= 0.05*0.857375*24/6
= 0.171475
So the probability of getting only 0 or 1 defective computers out of the 1st 4 is 0.81450625 + 0.171475 = 0.98598125 which is also the probability that at least 5 computers need to be tested.
<u>Solution-</u>
The atmospheric pressure at sea level = 14.7 lb/in²
Pressure gets reduced by half for each 3.6 miles we move up.
Taking,
x = miles above the sea-level
y = pressure in lb/in²
0 14.7
3.6 7.35
7.2 3.675
10.8 1.8375
It can be observed that both the variables are in inverse proportion as the distance from sea-level increase the pressure decreases.
As only the second graph satisfies the points and inverse proportional condition, so that is the correct graph.
By plotting the graph in excel taking these data set, the following plot was obtained.
Answer:
The total number of bugs in the collection is 36
Step-by-step explanation:
Let
x -----> the number of bugs that you find out
y ----> the number of bugs that the classmate find out
we know that
-----> equation A
----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (20,16)
The total number of bugs in the collection is
