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Yanka [14]
3 years ago
8

The parent function of the function g(x) = (x - 5)2 + k is f(x) = x2. The vertex of the function g(x) is located at (9,-8).

Mathematics
1 answer:
likoan [24]3 years ago
6 0

Answer:

h = 5 and k = -8.

Step-by-step explanation:

The parent equation is f(x) = x², which is the equation of a parabola having the vertex at point (0,0).

The original equation is given by g(x) = (x - 5)² + k, ⇒ y = (x - 5)² + k

⇒ y - k = (x - 5)²

So, the vertex of the original equation is at (5, k) which is given to be (5, -8)

Therefore, h = 5 and k = -8. (Answer)

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A cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled. Each box of cereal is supposed to
Vaselesa [24]

Answer:

We conclude that the population average weight of a cereal box is equal to 13 ounces.

Step-by-step explanation:

We are given that a cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled.

A random sample of 36 boxes is tested. The sample average weight is 12.85 ounces and the sample standard deviation is 0.75 ounces.

<u><em /></u>

<u><em>Let </em></u>\mu<u><em> = population average weight of a cereal box</em></u>

So, Null Hypothesis, H_0 : \mu = 13 ounces    {means that the population average weight of a cereal box is equal to 13 ounces}

Alternate Hypothesis, H_A : \mu \neq 13 ounces    {means that the population average weight of a cereal box differs from 13 ounces}

The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about population standard deviation;

                                  T.S.  = \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample average weight = 12.85 ounces

            \sigma = sample standard deviation = 0.75 ounces

            n = sample of boxes = 36

So, <u><em>test statistics</em></u>  =  \frac{12.85-13}{\frac{0.75}{\sqrt{36} } }  ~ t_3_5

                               =  -1.20

The value of the test statistics is -1.20.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, <u>the t table gives critical values between -2.03 and 2.03 at 35 degree of freedom for two-tailed test</u>.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that the population average weight of a cereal box is equal to 13 ounces.

3 0
3 years ago
Which best describes how the graph of g(x) =1/9
Sauron [17]

Answer:

Step-by-step explanation:

4 0
3 years ago
Which equation represents a line which is parallel to the line 2x+y=-6?
joja [24]
The answer is:  [C]:  " y = -2x - 1 "  .
____________________________________________________
5 0
2 years ago
Given that P = (-4, 11) and Q = (-5, 8), find the component form and magnitude of vector QP
Svetach [21]
The given points are
P = (-4,11)
Q = (-5,8)

The x-component of vector QP is
-4 - (-5) = 1
The y-component of vector QP is
11 - 8 = 3

The vector QP is 
(1,3) or
\vec{QP} = \hat{i} + 3\hat{j}

The magnitude of the vector is
√(1² + 3²) = √(10)

Answer:
\vec{QP} = \hat{i}+3\hat{j} \,\, or \,\, (1,3)
The magnitude is √(10).

8 0
2 years ago
Which equation describes the same line asy- 3 =-1(x+ 5)?
aliya0001 [1]
The answer would be A
6 0
3 years ago
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