Below are two parallel lines with a third line intersecting them. What is x
2 answers:
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Answer:
Step-by-step explanation:
Given data and notation
indicates the sample mean
refers to the sample standard deviation
is the sample size
represents the value we are testing.
indicates the significance level for the hypothesis test.
t refers to the statistic of interest.
is the p-value for the test (the variable we are interested in).
Formulate the null and alternative hypotheses.
I will set up the hypotheses to verify if the mean weight falls below 4 ounces, formalizing:
Null hypothesis:
Alternative hypothesis:
Since our sample size is < 30 and the population standard deviation is unknown, it’s advisable to utilize a t test to compare the actual mean against the reference value, with the statistic calculated as follows:
(1)
t-test: "This test compares group means and is commonly utilized to determine if the mean is (greater than, less than, or not equal to) a specific value."
Calculate the statistic
We can substitute the provided information into formula (1):
The question clearly seeks the highest values from both functions, meaning the vertices of each.
<span>The graph depicting the path of Ed’s football indicates the vertex's coordinates (the peak of the graph).
</span>
Specifically,
(h,k) = (1.5, 7.5)
Where (h,k) represents the vertex's location.
Conversely,<span>the trajectory of Steve's football is defined by the equation:
y = - 2x
²</span> + 5x + 4<span>To find the axis of symmetry, we use the formula:x = - b
÷ 2a
Where:
a = -2</span>
b = 5
Consequently,
x = - 5 ÷ - 4
x = 5 / 4
x = 1.25
Now substituting this x-value back into the main equation to determine y.
y = - 2x² + 5x + 4
y = - 2(1.25)² + 5(1.25) + 4
y = - 3.125 + 6.25 + 4
y = 7.125
Thus, the vertex (h,k) = (1.25, 7.125)
As observed from the calculations
Ed’s
<span>football attains a higher height.</span>
<span>The graph depicting the path of Ed’s football indicates the vertex's coordinates (the peak of the graph).
</span>
Specifically,
(h,k) = (1.5, 7.5)
Where (h,k) represents the vertex's location.
Conversely,<span>the trajectory of Steve's football is defined by the equation:
y = - 2x
²</span> + 5x + 4<span>To find the axis of symmetry, we use the formula:x = - b
÷ 2a
Where:
a = -2</span>
b = 5
Consequently,
x = - 5 ÷ - 4
x = 5 / 4
x = 1.25
Now substituting this x-value back into the main equation to determine y.
y = - 2x² + 5x + 4
y = - 2(1.25)² + 5(1.25) + 4
y = - 3.125 + 6.25 + 4
y = 7.125
Thus, the vertex (h,k) = (1.25, 7.125)
As observed from the calculations
Ed’s
<span>football attains a higher height.</span>