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frez [133]
3 years ago
14

Assume the parent function has been shifted up

Mathematics
2 answers:
mars1129 [50]3 years ago
6 0

Answer:

If y=(x-2)^2+4 is the transformed function, then the parent function y=x^2 has been shifted up vertically by 4 units and horizontally right by 2 units

Step-by-step explanation:

Assume the function is y=f(x) is the parent function.

A vertical shift,b units up  will transform the function to y=f(x)+b .

A horizontal shift a units.

y=f(x-a)+b

For instance, if y=x^2, b=4, and a=2 units.  

Then the transformed function becomes:

y=(x-2)^2+4

vlabodo [156]3 years ago
5 0

Answer:

Vertical shift is 1 unit up

Step-by-step explanation:

Horizontal shift is pi/4 units right

The period is pi/2

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In a random sample of 1066 U.S. adults, 580 think that the U.S. government
alexandr402 [8]

Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the adults who think that the U.S. government is doing too little to protect the environment presently and the adults who think that the U.S. government is doing too little to protect the environment 10 years ago. The population proportions would be p1 and p2 respectively.

p1 - p2 = difference in the proportion of adults who think that the U.S. government is doing too little to protect the environment presently and the adults who think that the U.S. government is doing too little to protect the environment 10 years ago.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 ≠ p2

p1 - p2 ≠ 0

it is a two tailed test

Sample proportion = x/n

Where

x represents number of success

n represents number of samples

For the present,

x1 = 580

n1 = 1066

p1 = 580/1066 = 0.54

For 10 years ago,

x2 = 514

n2 = 1038

P2 = 514/1038 = 0.5

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (580 + 514)/(1066 + 1038) = 0.52

1 - pc = 1 - 0.52 = 0.48

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.54 - 0.5)/√(0.52)(0.48)(1/1066 + 1/1038) = 0.04/0.02178551744

z = 1.84

Since it is a two tailed test, the curve is symmetrical. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above the test z score in the right tail 1 - 0.967 = 0.033

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p = 0.033 × 2 = 0.066

Alpha = 0.1

Since alpha, 0.1 > p value 0.066, we would reject the null hypothesis.

Therefore, at a = 0.10, we can reject the

claim that the proportion of U.S. adults who think that the U.S. government

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