Answer:
30 degrees
Step-by-step explanation:
u dot v=1*4+1*4+1*4+0*4=4+4+4+0=12
|u|=sqrt(1^2+1^2+1^2+0^2)=sqrt(3)
|v|=sqrt(4^2+4^2+4^2+4^2)=sqrt(4*4^2)=2*4=8
cos(theta)=u dot v/(|u||v|)
cos(theta)=12/(sqrt(3)*8)
cos(theta)=3/(sqrt(3)*2)
cos(theta)=sqrt(3)/2
theta=30 degrees
Answer:
2a^4 / b^5
Step-by-step explanation:
(2a^2 / b) x ( a / b^2) ^2
= (2a^2 / b) x (a^2 / b^4)
= 2a^4 / b^5
(p.s if you are not gonna do it don't say "no thanks" and leech off this poor man's points)
Answer:
Option A. 4, 4.5, 5, 5.5
Step-by-step explanation:
Left point: a=x=4
Right point: b=x=6
Range: r=b-a→r=6-4→r=2
Width of each of the four equal intervals: w=2/4→w=0.5
The first left endpoint is x1=a→x1=4
The second left endpoint is x2=x1+w→x2=4+0.5→x2=4.5
The third left endpoint is x3=x2+w→x3=4.5+0.5→x3=5
The fourth left endpoint is x4=x3+w→x4=5+0.5→x4=5.5
Then, the list is: x1, x2, x3, x4 = 4, 4.5, 5, 5.5
Answer:
73.5 pounds of dog food in 7 days
Step-by-step explanation:
10 1/2 x 7
10x 7 =70
1/2 x 7 = 3.5
70 + 3.5 =73.5 pounds of dog food in 7 days
Answer:
a)0.6192
b)0.7422
c)0.8904
d)at least 151 sample is needed for 95% probability that sample mean falls within 8$ of the population mean.
Step-by-step explanation:
Let z(p) be the z-statistic of the probability that the mean price for a sample is within the margin of error. Then
z(p)= where
- Me is the margin of error from the mean
- s is the standard deviation of the population
a.
z(p)= ≈ 0.8764
by looking z-table corresponding p value is 1-0.3808=0.6192
b.
z(p)= ≈ 1.1314
by looking z-table corresponding p value is 1-0.2578=0.7422
c.
z(p)= ≈ 1.6
by looking z-table corresponding p value is 1-0.1096=0.8904
d.
Minimum required sample size for 0.95 probability is
N≥ where
- z is the corresponding z-score in 95% probability (1.96)
- s is the standard deviation (50)
- ME is the margin of error (8)
then N≥ ≈150.6
Thus at least 151 sample is needed for 95% probability that sample mean falls within 8$ of the population mean.