Answer: 0.0241
Step-by-step explanation:
This is solved using the probability distribution formula for random variables where the combination formula for selection is used to determine the probability of these random variables occurring. This formula is denoted by:
P(X=r) = nCr × p^r × q^n-r
Where:
n = number of sampled variable which in this case = 21
r = variable outcome being determined which in this case = 5
p = probability of success of the variable which in this case = 0.31
q= 1- p = 1 - 0.31 = 0.69
P(X=5) = 21C5 × 0.31^5 × 0.69^16
P(X=5) = 0.0241
Answer:
The number is 12
Step-by-step explanation:
Let x = number
2x+16 = 40
Subtract 16 from each side
2x+16-16 =40-16
2x = 24
Divide by 2
2x/2 =24/2
x = 12
Answer:
remainder = 6
Step-by-step explanation:
Hope it helps.....
Answer:
(1, 8.5 ) and ( - 17, 80.5 )
Step-by-step explanation:
Given the 2 equations
y = 
x² + 4x + 4 → (1)
y = - 4x + 12 → (2)
Substitute (1) into (2), that is
x² + 4x + 4 = - 4x + 12 ( multiply through by 2 to clear the fractions )
x² + 8x + 8 = - 8x + 25 ( add 8x to both sides )
x² + 16x + 8 = 25 ( subtract 25 from both sides )
x² + 16x - 17 = 0 ← in standard form
(x + 17)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 17 = 0 ⇒ x = - 17
x - 1 = 0 ⇒ x = 1
Substitute these values into either of the 2 equations and evaluate for y
Substituting into (2 )
x = 1 : y = - 4(1) + 12.5 = - 4 + 12.5 = 8.5 ⇒ (1, 8.5 )
x = - 17 : y = - 4(- 17) + 12.5 = 68 + 12.5 = 80.5 ⇒ (- 17, 80.5 )
For this question you need to use what's called point-slope form. It's named this way because you can use it if you have both the slope and a point at which the line passes through. That said, the equation is as follows:
y - y1 = m(x - x1)
Both y1 and x1 represent the y and x coordinates you are given in the question. Also, m represents the slope of the line that you are given. Knowing this, our equation now looks like this:
y - 4 = -0.5(x - (-5))
And now simplify:
y - 4 = -0.5(x + 5)
y - 4 = -0.5x - 2.5
y = -0.5x + 1.5
