Answer: L = 14
Concept:
Here, we need to understand the idea of evaluation.
When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.
Solve:
<u>Given information</u>
W = 7
P = 42
<u>Given expression</u>
P = 2L + 2W
<u>Substitute values into the expression</u>
42 = 2L + 2 (7)
<u>Simplify by multiplication</u>
42 = 2L + 14
<u>Subtract 14 on both sides</u>
42 - 14 = 2L + 14 - 14
28 = 2L
<u>Divide 2 on both sides</u>
28 / 2 = 2L / 2
Hope this helps!! :)
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Answer:
if ∠Q=∠R
draw an angular bisector from P to QR in which it intersect wit Qr at point S
now we have two triangle : QPS and RSP
in which angle : QPS=RPS ( PS is angular bisector)
and we have angle Q and angle R are equal
and PS is common side
this makes triangle QPS and RSP are congruent by AAS(angle angle side)
which also means that pQ=PR ( proved)
Answer:
a)
The null hypothesis is
The alternative hypothesis is
b-1) The value of the test statistic is t = 1.86.
b-2) The p-value is of 0.0348.
Step-by-step explanation:
Question a:
Test if the battery life is more than twice of 5 hours:
Twice of 5 hours = 5*2 = 10 hours.
At the null hypothesis, we test if the battery life is of 10 hours or less, than is:
At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:
b-1. Calculate the value of the test statistic.
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
In which X is the sample mean, is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
10 is tested at the null hypothesis:
This means that
In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
This means that
Then
The value of the test statistic is t = 1.86.
b-2. Find the p-value.
Testing if the mean is more than a value, so a right-tailed test.
Sample of 45, so 45 - 1 = 44 degrees of freedom.
Test statistic t = 1.86.
Using a t-distribution calculator, the p-value is of 0.0348.