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andrezito [222]
3 years ago
7

(03.04) For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.

Mathematics
1 answer:
aleksklad [387]3 years ago
8 0
Vertex: (2,4)
domain: all real numbers
range: y is greater than or equal to 4
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Verdich [7]

Answer: Counter, 0, 0.

Step-by-step explanation:

Think about a clock. The hand of a clock goes clockwise. When you tighten something (righty tighty) you spin it clockwise. You can rotate an object, lets say a square, clockwise. You can also rotate it counterclockwise, in the other direction. Therefore, you can rotate an object clockwise and <u>counter</u>clockwise.

You can rotate a figure around any point, such as the center of the figure, the origin, or anywhere else. One common place to rotate a figure around, such as a square, is the origin. This is the center of the coordinate plane. This point is not up, down, left, or right at all from the center. This coordinate is (0, 0). Therefore, the next two blank spaces should both be filled with 0.

The blank spaces should look like this:

One direction is clockwise and the other is <u>counter</u>clockwise.

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This can be any coordinate point such as the origin which is at (<u> </u><u>0</u><u> </u>, <u>0</u><u> </u>)

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Emissions of sulfur dioxide by industry sett off chemical changes in the atmosphere that result in "acid rain". The acidity of l
horsena [70]

Answer:

Case n =5

z=\frac{4.8-5}{\frac{0.5}{\sqrt{5}}}=-0.894  

Case n =15

z=\frac{4.8-5}{\frac{0.5}{\sqrt{15}}}=-1.549  

Case n = 40

z=\frac{4.8-5}{\frac{0.5}{\sqrt{40}}}=-2.530  

P value

Case n =5

p_v =P(z  

Case n =15

p_v =P(z  

Case n =40

p_v =P(z  

Step-by-step explanation:

Data given and notation  

\bar X=4.8 represent the sample mean

\sigma=0.5 represent the population standard deviation

n sample size  

\mu_o =5 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is lower than 5, the system of hypothesis would be:  

Null hypothesis:\mu \geq 5  

Alternative hypothesis:\mu < 5  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

Case n =5

z=\frac{4.8-5}{\frac{0.5}{\sqrt{5}}}=-0.894  

Case n =15

z=\frac{4.8-5}{\frac{0.5}{\sqrt{15}}}=-1.549  

Case n = 40

z=\frac{4.8-5}{\frac{0.5}{\sqrt{40}}}=-2.530  

P-value  

Since is a left tailed test the p value would be:  

Case n =5

p_v =P(z  

Case n =15

p_v =P(z  

Case n =40

p_v =P(z  

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Answer:

D

Step-by-step explanation:

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Answer:

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