we have
Convert to vertex form
we know that
the equation of a vertical parabola in vertex form is equal to
where
(h,k) is the vertex
Group terms that contain the same variable, and move the constant to the opposite side of the equation
Complete the square. Remember to balance the equation by adding the same constants to each side
Rewrite as perfect squares
the vertex is the point
therefore
<u>the answer is </u>
The y-value of the vertex is
Answer:
Step-by-step explanation:
Let p be the population proportion for the graduates from private nonprofit colleges in the region had at least one outstanding student loan at the time of graduation.
Given : Tristan is an administrator for a private nonprofit college and read a surprising statistic that 74% of graduates from private nonprofit colleges in the region had at least one outstanding student loan at the time of graduation.
i.e.
He believes that percentage is high and claims that the proportion of graduates at his college is less than the regional rate.
i.e.
Since, the null hypothesis is a statement which always takes equal sign or generally shows " no difference " where as alternative hypothesis takes unequal signs.
Then, the null and alternative hypotheses for this hypothesis test :-
The side MK measures 3.3 feet.
Step-by-step explanation:
Step 1:
In the triangle, the angle is 25°, the adjacent side has a length of x feet while the hypotenuse of the triangle measures 3.6 feet. The opposite side of the triangle is not given.
To determine the value of x, we determine the value of the cos of the given triangle.
To calculate the cos of an angle we divide the adjacent side by the hypotenuse of the same triangle.
Step 2:
The length of the adjacent side = x feet.
The length of the hypotenuse = 3.6 feet.
So the adjacent side of the triangle measures 3.2626 feet. Rounding this off to the nearest tenth, we get that MK measures 3.3 feet.