Hello i need with this plz see attachmentss below

Problem 1

Choice C) sample is appropriately large; margin of error is plus/minus 0.187

Explanation:

At 90% confidence, the z critical value is roughly z = 1.645 (this is found using a table in the back of your textbook)

n = 250 is the sample size, which is appropriately large (it's over n = 30)

s = 1.8 is the standard deviation

The margin of error E is found by the formula below

E = z*s/sqrt(n)

E = 1.645*1.8/sqrt(250)

E = 0.18727008303518

E = 0.187

note: the sample mean is not used at all in the computation of the margin of error.

Problem 2

Choice D) both are effective; however, Intensity program is more effective compare to Q30X program

Explanation:

There's not much to say here other than your teacher really wrote a lot to set up this problem. There's a lot of extra filler that you need to toss out and ignore. Basically the short of it is that Brant wants to run faster so he tests two programs. He finds that both are effective (since they both yield roughly the same percent decrease in run times) but the Intensity program is better by two percentage points. It's not much, but it's something. So this is why the answer is choice D.

Problem 3

Choice A) appropriately large; margin of error is plus/minus 0.079

Explanation:

n = 150 is the sample size. It is appropriately large as it is over n = 30

At 95% confidence, using a stats table (in the back of your book) you should find the critical value is z = 1.960

p = 0.56 is the decimal version of 56%, this is the proportion of those who use public transportation

We'll use a slightly different margin of error formula. This time it's to measure the error for proportions (rather than means)

E = z*sqrt(p*(1-p)/n)

E = 1.960*sqrt(0.56*(1-0.56)/150)

E = 0.07943845584267

E = 0.079

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12