The solution of the equation is x = 71 / 36.
<h3>How to solve an equation with one variable</h3>
Herein we have an equation with several rational constants and only one variable, x, which has to be cleared by using algebra procedures. The procedure is shown below:
2 · x + 1 / 3 + x - 1 / 4 = 13 / 2 Given
2 · x + x = 13 / 2 - 1 / 3 - 1 / 4 Compatibility with addition / Existence of additive inverse / Modulative property
3 · x = 71 / 12 Definitions of addition and subtraction / Distributive property
x = 71 / 36 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / Result
The solution of the equation is x = 71 / 36.
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Answer: 11 months
Step-by-step explanation:
Let the number of months that it will take him to reach his goal be represented by x.
Based on the information given in the question, this can be formed into an equation as:
8 + 4x = 52
4x = 52 - 8
4x = 44
x = 44/4
x = 11
It will take 11 months to reach the goal
A all squares have the sides
-- He must have at least one of each color in the case, so the first 3 of the 5 marbles in the case are blue-green-black.
Now the rest of the collection consists of
4 blue
4 green
2 black
and there's space for 2 more marbles in the case.
So the question really asks: "In how many ways can 2 marbles
be selected from 4 blue ones, 4 green ones, and 2 black ones ?"
-- Well, there are 10 marbles all together.
So the first one chosen can be any one of the 10,
and for each of those,
the second one can be any one of the remaining 9 .
Total number of ways to pick 2 out of the 10 = (10 x 9) = 90 ways.
-- BUT ... there are not nearly that many different combinations
to wind up with in the case.
The first of the two picks can be any one of the 3 colors,
and for each of those,
the second pick can also be any one of the 3 colors.
So there are actually only 9 distinguishable ways (ways that
you can tell apart) to pick the last two marbles.
Given:
p = 7.6% = 0.076, the percentage of people who stay overnight at the hospital.
E = 1.5% = 0.015, margin of error
95% confidence interval.
The standard error is
Es =
where
n = the sample size.
The margin of error is
where
z* = 1.96 at the 95% confidence level.
Because the margin of error is given, there is no need to calculate it.
The 95% confidence interval is
p +/- E = 0.076 +/- 0.015 = (0.061, 0.091) = (6.1%, 9.1%)
Answer:
The 95% confidence interval is between 6.1% and 9.1%.
