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James has t toy cars and Paul has 13 more. How many cars will James have if Paul gives him half of his cars?
1 answer:
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Answer:
The final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.
Step-by-step explanation:
General Formula
<em>A way to solve this problem is as follows</em>:
The general formula for this is taking into account that:
The <em>starting point</em> is number 784.
The most important key is the solution for this answer is that:
Where <em>x</em> is a number that we need to find. Then
[1]
Is 784 increased or decreased after all?
We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.
Finding the result
If 784 increases by 3%, we have:
Which is equal to
Solving for <em>x</em>, we first multiply by 784 to both sides of the previous formula:
Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.
Subtracting 784 to both sides:
Multiplying by -1 to both sides:
We have to remember that:
Then
Therefore, using formula [1], an increase of 3% is
Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.
As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.
In a more <em>terse way</em> of solving this problem, we can say that:
Increase of 4% = 784 * 0.04 = 31.36.
Decrease of 1% = 784 * 0.01 = 7.84.
Difference = 31.36 - 7.84 = 23.52.
Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).
Answer:
a
The 95% confidence interval is
b
The sample proportion is
c
The critical value is
d
The standard error is
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is
The alternative hypothesis is
Generally the sample proportion is mathematically evaluated as
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
Next we obtain the critical value of from the normal distribution table, the value is
Generally the standard of error is mathematically represented as
substituting values
The margin of error is
=>
=>
The 95% confidence interval is mathematically represented as
=>
=>
The figure shown below illustrates the problem.
The volume of the empty cone is
V₁ = (1/3) π r²h
The volume of the sphere is
V₂ = (4/3) π r³
Because the melted ice cream completely fills the cone, therefore
V₁ = V₂
(1/3) π r² h = (4/3) π r³
Divide each side by (1/3) π r².
h = 4r
Answer:
The height of the cone is 4 times greater than the radius f the cone.
The volume of the empty cone is
V₁ = (1/3) π r²h
The volume of the sphere is
V₂ = (4/3) π r³
Because the melted ice cream completely fills the cone, therefore
V₁ = V₂
(1/3) π r² h = (4/3) π r³
Divide each side by (1/3) π r².
h = 4r
Answer:
The height of the cone is 4 times greater than the radius f the cone.