We use the z statistic:
z = (x – u) / s
But first let us calculate the standard deviation s,
sample x and mean u.
s = sqrt (n p q)
s = sqrt (112 * 0.77 * (1 – 0.77))
s = 4.45
x = 0.81 * 112 = 90.72
u = 0.77 * 112 = 86.24
So the z score is:
z = (90.72 – 86.24) / 4.45
z = 1.00
From the standard tables, the P value at z = 1.00 using
right tailed test is:
<span>P = 0.1587 = 15.87%</span>
Answer:
$35,000
Step-by-step explanation:
The amount that would be repaid = amount borrowed + interest earned on loan
interest earned on deposit can be determined by determining the simple interest
Simple interest = principal x time x interest rate
principal = the amount deposited = 20,000
Time = the duration of the deposit =5
interest rate = the percentage on deposit that would be earned = 15
20,000 x 5 x 0.15 = $15,000
total = 20,000 + 15,000 = $35,000
As usual, draw a diagram. You can easily see that if you are x away from the wall,
<span>the angle of elevation of the bottom of the screen (A) is </span>
<span>cotA = x/3 </span>
<span>A = arccot(x/3) </span>
<span>angle B to the top is </span>
<span>cotB = x/10 </span>
<span>B = arccot(x/10) </span>
<span>So, since θ = B-A </span>
<span>dθ/dt = dB/dt - dA/dt </span>
<span>= -3/(x^2+9) + 10/(x^2+100) </span>
<span>= 7(x^2-30)/((x^2+9)(x^2+100)) </span>
<span>so, at x=30 </span>
<span>dθ/dt = 203/30300</span>
Refer to the diagram shown below.
The given constraints are
(a) y ≥ 24 ft
(b ) x ≤ 10 ft
(c) y ≥ 3x
(d) y ≤ 33 ft
The acceptable region is shown shaded.
A (0, 33) satisfies all conditions
B (4, 36) fails condition (d)
C (4.8, 30.5) satisfies all conditions
D (9, 26) fails condition (c)
E (2, 22) fails condition (a)
Answer:
The acceptable points are A and C.