A segway travels 12.5 miles every 1/2 hour. What is the unit rate of miles per hour?
1 answer:
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Answer:
A
Step-by-step explanation:
Given
y - 2x - 8 = 0 ( add 2x + 8 to both sides )
y = 2x + 8 → (1)
y² + 8x = 0 → (2)
Substitute y = 2x + 8 into (2)
(2x + 8)² + 8x = 0 ← expand left side using FOIL and simplify
4x² + 32x + 64 + 8x = 0
4x² + 40x + 64 = 0 ( divide through by 4 )
x² + 10x + 16 = 0 ← in standard form
(x + 8)(x + 2) = 0 ← in factored form
x + 8 = 0 ⇒ x = - 8
x + 2 = 0 ⇒ x = - 2
Substitute these values into (1) for corresponding values of y
x = - 8 : y = 2(- 8) + 8 = - 16 + 8 = - 8 ⇒ P (- 8, - 8)
x = - 2 : y = 2(- 2) + 8 = - 4 + 8 = 4 ⇒ Q (- 2, 4 )
Calculate the length of PQ using the distance formula
PQ =
with (x₁, y₁ ) = P (- 8, - 8) and (x₂, y₂ ) = Q (- 2, 4 )
PQ =
=
=
=
=
=
= ×
= 6 → A
Answer:
We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.
Step-by-step explanation:
Jenna claims that the average time of texting at her larger high school is greater than 94 minutes per day.
From here we can see that we have to perform a hypothesis test about a sample mean. The null and alternate hypothesis will be:
Null Hypothesis:
Alternate Hypothesis:
Jenna collected data from a sample of 32 students. So, sample size will be:
Sample Size = n = 32
Sample Mean = x = 96.5
Sample Standard Deviation = s = 6.3
We have to perform a hypothesis test, to test Jenna's claim. Since, the value of Population Standard Deviation is unknown and the value of Sample Standard Deviation is known, we will use One Sample t-test in this case.
The formula to calculate the test statistic is:
Using the values, we get:
The degrees of freedom will be:
df = n - 1 = 32 - 1 = 31
We have to convert the t-score 2.245 with 31 degrees of freedom to its equivalent p-value. From t-table this value comes out to be:
p-value = 0.0160
The significance level is:
Since, the p-value is lesser than the level of significance, we reject the Null Hypothesis.
Conclusion:
We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.
