Answer:
The value of k is 3.
Step-by-step explanation:
The function f(x) passes through the points (0,4) and (-6,-2)
So the equation of the function is
⇒ y = x + 4 ....... (1)
Again the function g(x) passes through the points (0,4) and (-2,-2).
Therefore, the equation of g(x) will be
⇒ y = 3x + 4
Therefore, g(x) = 3x + 4 = f(3x) {from equation (1).
So, the value of k is 3. (Answer)
answer is in image attached
Answer:
a) 0.7486; b) 0.6518; c) No
Step-by-step explanation:
We use z scores to answer these questions. The formula for a z score is
Our mean, μ, is 44; our standard deviation, σ, is 1.5.
For part a,
We want P(X > 43):
z = (43-44)/1.5 = -1/1.5 = -0.67
Using a z table, we see that the area under the curve to the left of this is 0.2514. However, we want the area to the right; this means we subtract from 1:
1 - 0.2514 = 0.7486
For part b,
We want P(42 ≤ X ≤ 45):
z = (42-44)/1.5 = -2/1.5 = -1.3
z = (45-44)/1.5 = 1/1.5 = 0.67
Using a z table, the area under the curve to the left of z = -1.3 is 0.0968. The area under the curve to the left of z = 0.67 is 0.7486.
The area between them is 0.7486 - 0.0968 = 0.6518.
For part c,
A response of 35 has a z score of
z = (35-44)/1.5 = -9/1.5 = -6
This is 6 standard deviations below the mean. This is more than the amount required to make this an outlier, or an unlikely response.
Answer:
The Mean is not equal to $31,129.
Step-by-step explanation:
Consider the provided information.
The mean is $31129
Thus, the null hypothesis
Alternative hypothesis
A random sample of 15 firstyear CMAs in Denver produces a mean salary of $32,279, with a standard deviation of $1,797.
Thus the value mean of sample is 32279, standard deviation is 1797 and number of samples are 15.
Now use the 2 sided t-test.
Now substitute the respective values in the above formula.
Test Value = 2.4785 approximately
Now, find the corresponding p-value in your t-table with DF(degree of freedom) 14.
p = 0.0265
as the value of p < 0.05, so you reject null hypothesis.
Thus, the Mean is not equal to $31,129.