The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. what is the value of k?

a: 3
b: 7
c: 10
d: 13

B: 7

Step-by-step explanation:

If you think about it, we have the function f(x), right?  Now just imagine a marker on the 3, because we know the function is there, hence the 3 added to the exponent of x.  But the equation f(x) = 2^(x-k) took away the 3.  so with the function down to 0 instead of 3, how far do we have to go down to get to 10 below the 3 marker? If we move 10 units below the 3 mark, we are at -7 on the y line, right?

So, now we know the ending y value is going to be -7, so how much do we need to subtract from 0 to get there? 7!

Here's a drawing if it helps simplify it:

Note: sorry if the number line is confusing!  it's only purpose is to show the value of x, sorry if that does seem very clear! My bad -v-'

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;