Answer:
Mean and Variance of the number of defective bulbs are 0.5 and 0.475 respectively.
Step-by-step explanation:
Consider the provided information,
Let X is the number of defective bulbs.
Ten light bulbs are randomly selected.
The likelihood that a light bulb is defective is 5%.
Therefore sample size is = n = 10
Probability of a defective bulb = p = 0.05.
Therefore, q = 1 - p = 1 - 0.05 = 0.95
Mean of binomial random variable: 
Therefore, 
Variance of binomial random variable: 
Therefore, 
Mean and Variance of the number of defective bulbs are 0.5 and 0.475 respectively.
Answer:
Step-by-step explanation:
The rate if increase of side of square is 7cm/s
dL/dt=7
At what area is the area increasing
dA/dt=?
Areas of square is give to be 36cm²
Analysis
Let L be the length of each side of the square, a square has equal side.
Area of square is give as L²
Area=L²
L²=36
i.e L=√36
L=6cm
Therefore at t=0 L=6cm and A=36cm²
A=L²
dA/dL=2L
Given that, dL/dt=7
Multiply the two differential together
dA/dt= dA/dL × dL/dt
dA/dt= 2L × 7
dA/dt= 2×6×7
dA/dt= 84cm²/s
The rate of increase of the square is 84cm²/s
Answer:
x^2 + 5x - 84 = 0
x = 7
Step-by-step explanation:
let the sister's age = y
sister's age (y) = 5 + x equation 1
xy = 84 equation 2
Make y the subject of the formula in equation 2
y = 84/x
equate equation 1 and 2
84/x = 5 + x equation 3
Multiply equation 3 by x
84 = 5x + x^2
x^2 + 5x - 84 = 0
tjis can be solved using quadratic equation
x^2 -7x + 12x -84 = 0
x(x + 12) -7(x + 12)
x = 7 or - 12
age cant be negative so his age is 7
Answer:
<u>The ordered pair of the solution is (0.022, -0.55). None of the alternatives given we can consider as the best estimate because there isn't at least one positive value for x, when it's actually positive. Picking (0, -2) as the best estimate is also far from the best estimate.</u>
Step-by-step explanation:
Let's solve the system of equations:
y = −25x
−2y = 5x+1
***********************
Substituting y in the 2nd equation:
-2 (-25x) = 5x + 1
50x = 5x + 1
45x = 1
x = 1/45
x = 0.022
**********************
Solving for y in the 1st equation:
y = -25 (0.022)
y = - 0.55
<u>The ordered pair of the solution is (0.022, -0.55). None of the alternatives given we can consider as the best estimate because there isn't at least one positive value for x, when it's actually positive. Picking (0, -2) as the best estimate is also far from the best estimate.</u>
