Step-by-step explanation:
a. The random variable is a binomial distribution.
b. the sample space, X = {0, 1, 2, 3, 4, 5}
the pmf
we solve for this using
nCx * P^x * (1-p)^n-x
n = 5
p = 0.3
for x = 0
5C0 * 0.3⁰(1-0.3)^5-0
= 1 * 1* 0.7⁵
= 0.16807
for x = 1
5C1*0.3¹(1-0.3)^5-1
= 5*0.3(0.7)⁴
= 5x0.3x0.2401
= 0.36015
for x = 2
5C2 * 0.3² * (1-0.3) ^5-2
= 0.30870
for x = 3
5C3 * 0.3³ * (1-0.3) ^ 5-3
= 10 * 0.027 * 0.7²
= 0.1323
for x = 4
5C4 * 0.3⁴ (1-0.3) ^ 5-4
= 5 * 0.0081 * 0.7
= 0.02835
for x = 5
5C5 *0.3⁵ (1- 0.3) ^5-5
= 1*0.00243*0,7⁰
= 0.00243
c. E[X] = N*p = 5*0.3 = 1.5
var[X] = np(1-p) = 5*0.3*0.7 = 1.05
d. 20/9 = 2.222
so we have that if x is greater than or equal to 3, cost will exceed 20
p(x=3) + p(x=4) + p(x=5)
= 0.1323 + 0.02835 + 0.00243
probability = 0.16308
E[C] = 1.5 * 9 = 13.5
VAR[C] = 1.05 * 9 = 9.45
Check the picture below.
surely you can solve for "v", right?
Keurig takes about 58 days 15 hours and 30 mins. So we have to turn this into hours
So 58 days = 1392
Now we add + 15
-------
1407
Answer:
The vertex form is y = (x + 4)² - 13
The minimum value of the function is -13
Step-by-step explanation:
∵ y = x² + 8x + 3
∵ 8x ÷ 2 = 4x ⇒ (x) × (4)
∴ We need ⇒ x² + 8x + 16 to be completed square
∴ y = (x² + 8x + 16) - 16 + 3 ⇒ we add 16 and subtract 16
∴ y = (x + 4)² - 13 ⇒ vertex form
∵ The vertex form is (x - a)² + b
Where a is the x-coordinate of the minimum point and b is y-coordinate of the minimum point (b is the minimum value of the function)
∴ The minimum value is -13
<u>The question looks to be incomplete (without the appropriate choices). But still answering related to the inequalities part:</u>
Inequalities are the relationships between two expressions which are not equal to one another. The symbols used for inequalities are <, >, ≤, ≥ and ≠.
reads as '7 is greater than x' (or ' x is less than 7', reading from right to left). Here above, Statements are equivalent when both sides are true or logically the inequality holds good here.
We have , -2.5<8/13 . which is equivalent to -2.5< 0.615 which holds true. We know that any negative number is always smaller than any positive number, also less than 0. And , -2.5 value is less than 0.615. ∴ Inequality holds good!