The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other. The ar
1 answer:
Answer
Find out the original side length of the square .
To prove
Let us assume that the original length of the square be x.
Formula
As given
The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other.
Length becomes = x + 8
Breadth becomes = x -3
The area of the resulting rectangle is 126 in²
Put in the formula
(x + 8) × (x - 3) = 126
x² -3x + 8x -24 = 126
x ²+ 5x = 126 +24
x² + 5x - 150 = 0
x² + 15x - 10x - 150 = 0
x (x + 15) -10 (x +15) =0
(x + 15)(x -10) =0
Thus
x = -15 , 10
As x = -15 (Neglected this value because the side of the square cannot be negative.)
Therefore x = 10 inches be the original side of the square.
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Step-by-step explanation:
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We conclude that garbage collector's average picking is more than four tons of garbage per day.
Step-by-step explanation:
We are given the following information n the question:
First, we design the null and the alternate hypothesis
Significance level = 5% = 0.05
P-value = 0.04
- The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.
- P values evaluate how well the sample data support that the null hypothesis is true.
- P-value is a measure or indicator that helps us to know that whether the sample belongs to the population or not.
- Null hypothesis states that the sample belongs to the population.
- A high p-values states that the null hypothesis is true ad the sample belongs to the population.ll.
- A low p-value suggests that sample provides enough evidence that you the null hypothesis is not true and the sample does not belong to the population.
- We compare p-value to significance level to obtain our result.
Here,
p-value = 0.04 < Significance level = 0.05
Since the p-value is lower than the significance level, we fail to accept the null hypothesis and reject it. That is there were enough evidence to support the fact that sample does not belong to the population and we conclude that garbage collector's average picking is more than four tons of garbage per day.