Answer:
Since the calculated value of z= -1.496 does not fall in the critical region z < -1.645 we conclude that the new program is effective. We fail to reject the null hypothesis .
Step-by-step explanation:
The sample proportion is p2= 7/27= 0.259
and q2= 0.74
The sample size = n= 27
The population proportion = p1= 0.4
q1= 0.6
We formulate the null and alternate hypotheses that the new program is effective
H0: p2> p1 vs Ha: p2 ≤ p1
The test statistic is
z= p2- p1/√ p1q1/n
z= 0.259-0.4/ √0.4*0.6/27
z= -0.141/0.09428
z= -1.496
The significance level ∝ is 0.05
The critical region for one tailed test is z ≤ ± 1.645
Since the calculated value of z= -1.496 does not fall in the critical region z < -1.645 we conclude that the new program is effective. We fail to reject the null hypothesis .
The formula is
A=p (1+rt)
A future value
P present value
R interest rate
T time in years
Rose investment
A=2,600×(1+0.041×9)
A=3,559.4
Dennis investment
A=2,200×(1+0.057×9)
A=3,328.6
So Rose investment is greater than Dennis investment by
3,559.4−3,328.6=230.8
Hope it helps!
The complete question is
Find the volume of each sphere for the given radius. <span>Round to the nearest tenth
we know that
[volume of a sphere]=(4/3)*pi*r</span>³
case 1) r=40 mm
[volume of a sphere]=(4/3)*pi*40³------> 267946.66 mm³-----> 267946.7 mm³
case 2) r=22 in
[volume of a sphere]=(4/3)*pi*22³------> 44579.63 in³----> 44579.6 in³
case 3) r=7 cm
[volume of a sphere]=(4/3)*pi*7³------> 1436.03 cm³----> 1436 cm³
case 4) r=34 mm
[volume of a sphere]=(4/3)*pi*34³------> 164552.74 mm³----> 164552.7 mm³
case 5) r=48 mm
[volume of a sphere]=(4/3)*pi*48³------> 463011.83 mm³----> 463011.8 mm³
case 6) r=9 in
[volume of a sphere]=(4/3)*pi*9³------> 3052.08 in³----> 3052 in³
case 7) r=6.7 ft
[volume of a sphere]=(4/3)*pi*6.7³------> 1259.19 ft³-----> 1259.2 ft³
case 8) r=12 mm
[volume of a sphere]=(4/3)*pi*12³------>7234.56 mm³-----> 7234.6 mm³
Answer:
There are 42 red colour socks and 44 green color socks
Step-by-step explanation:
Let there are r red socks and g green socks.
ATQ,
He has three times times as many red socks subtracted from four times as many green socks which he believes is 50 socks.
4g-3r=50 ....(1)
Half the number of green socks plus one-third of the number of red socks is 36.
Multiply equation (1) by 2 and equation (2) by 3.
8g-6r = 100 ....(3)
9g +6r = 648 ....(4)
Add equation (3) and (4)
8g-6r + 9g +6r = 100+648
17g = 748
g = 44
Put the value of g in equation (1).
4(44)-3r=50
176-3r = 50
176-50 = 3r
r = 42
Hence, there are 42 red colour socks and 44 green color socks.
