Answer:
71.6 degrees
Step-by-step explanation:
Given the vectors
u= <8,4> v = <9.-9> (5 points)
u*v = (8, 4)*(9, -9)
u*v = 8(9)+(4)(-9)
u*v = 72 - 36
u*v = 36
|u| = √8²+4²
|u| = √64+16
|u| = √80
|v| = √9²+9²
|v| = √81+81
|v| = √162
Using the formula
u*v = ||u||v| cos theta
36 = √80(√162)cos theta
36 = √12960 cos theta
cos theta = 36/√12960
cos theta = 36/113.8
cos theta = 0.3162
theta = arccos(0.3162)
theta = 71.56 degrees
Hence the angle between the given vectors to the nearest tenth of a
degree is 71.6 degrees
1 1/2 - 2 1/2 is 3/2:5/2 or a 3:5 ratio
2 2/5 - 4 is 12/5:20/5 or a 3:5 ratio
3 3/4 - 6 1/4 is 15/4:25/4 or a 3:5 ratio
4 - 6 2/3 is 12/3:20/3 or a 3:5 ratio
1.2- 2 if divided by .4 is a 3:5 ratio
1.8-3 if divided by .6 is a 3:5 ratio
the unit rate is 3:5
Since all units are 3:5 it is proportional
Answer: (15.47, 24.53)
Step-by-step explanation:
We know that the confidence interval for population mean is given by :_

, where n= sample size.
= standard deviation.
= sample mean.
z*= Critical value.
Given : n= 450


Critical value for 95% confidence = z*=1.96 [From z-value table]
Then, the 95% confidence interval will be :-




Hence, the 95% confidence interval for the mean change in score μ μ in the population of all high school seniors. : (15.47, 24.53)
Answer:
<h2>$ 22200 in higher yielding bank and $ 44400 in lower yielding bank</h2>
Step-by-step explanation:
Jolene invests in two bank accounts. The first account gives a 4% interest per year and the second bank gives a 10% interest rate per year.
She puts twice as much in the lower yielding bank account. Let us denote the amount put in high yielding bank account by
. Lower yielding bank account will have
.

Interest from lower yielding bank = 
Interest from higher yielding bank = 
Total Interest per year = $ 3996 = 

∴ Jolene invested $ 22200 in higher yielding bank and $ 44400 in lower yielding bank.