Answer:
A) f(x) = |x|
B) f(x) = -|x+3| + 3
Step-by-step explanation:
Absolute value functions
The general form of an absolute value function is f(x) = a|x-b| +c
a indicates the 'amplitude' or multiplier
b indicates horizontal shift
c indicates vertical shift
The turning point of f(x) = |x| is (0, 0)
a = y/x when b = 0 and c = 0
A) f(x) = |x|
Since the turning point is still (0, 0) there is no horizontal nor vertical shift, meaning b = 0 and c = 0
We have the point (2, 2), thus a = 2/2 = 1
f(x) = a|x-b| + c
f(x) = |x|
B) f(x) = -|x+3| + 3
The turning point is at (-3, 3) b = -3 and c = +3
We have the point (3, -3), thus a = y/x = -3/3 = -1
f(x) = a|x-b| + c
f(x) = (-1) (|x-(-3)|) + (+3)
f(x) = -|x+3| + 3
Answer: No, It does not indicates that the population proportion of consumers loyal to Chevrolet is more than 47%.
Step-by-step explanation:
Let p denotes the proportion of consumers loyal to Chevrolet.
As per given , we have
![H_0: p=0.47\\\\ H_a: p>0.47](https://tex.z-dn.net/?f=H_0%3A%20p%3D0.47%5C%5C%5C%5C%20H_a%3A%20p%3E0.47)
Since the alternative hypothesis
is right-tailed so the test would be a right-tailed test.
Also , it is given that ,Chevrolet did a study of a random sample of 1006 Chevrolet owners and found that 490 said they would buy another Chevrolet.
i.e. n = 1006
x= 490
![\hat{p}=\dfrac{490}{1006}=0.487](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%5Cdfrac%7B490%7D%7B1006%7D%3D0.487)
Test statistic :
![z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Chat%7Bp%7D-p%7D%7B%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D)
, where p=population proportion.
= sample proportion
n= sample size.
i.e. ![z=\dfrac{0.487-0.47}{\sqrt{\dfrac{0.47(1-0.47)}{1006}}}=1.08](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B0.487-0.47%7D%7B%5Csqrt%7B%5Cdfrac%7B0.47%281-0.47%29%7D%7B1006%7D%7D%7D%3D1.08)
P-value (for right-tailed test)= P(z>1.08)=1-P(z≤1.08) [∵P(Z>z)=1-P(Z≤z)]
=1- 0.8599=0.1401 [By z-value table.]
Decision : Since p-value (0.14) is greater than the significance level (
) , it means we are failed to reject the null hypothesis.
Conclusion : We have sufficient evidence to support the claim that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice.
Hence, it does not indicates that the population proportion of consumers loyal to Chevrolet is more than 47%.
Answer:
c = 3.45 * p
Step-by-step explanation:
Since the total cost of Cheddar Cheese is dependant on the number of pounds that are being purchased then to calculate the total cost we would need to multiply the price per pound by the number of pounds being purchased. Therefore, the following equation would best represent the total cost of the cheddar cheese...
c = 3.45 * p
Answer:
2 intersections
Step-by-step explanation:
The greatest possible number of intersections of these graphs is 2 intersections. This is because a quadratic equation always appears on a graph as a parabola, either facing up or down. a Linear expression is a straight line, when placed in the same graph as a parabola only three things can happen. It can completely miss the parabola. It can pass through only one half of the parabola (thus intersecting at one point only), or lastly it can go through both halves of the parabola (intersecting at 2 points) as shown in the picture below.