Answer:
The scores are between 50 and 90
Step-by-step explanation:
When we say middle 95%, we means that this value falls between 2 standard deviations of the mean i.e
μ ± 2σ
Hence,
mean of 70 and a standard deviation of 10
μ ± 2σ
μ - 2σ
70 - (2 × 10)
= 70 - 20
= 50
μ + 2σ
= 70 + (2 × 10)
= 70 + 20
= 90
66
Step-by-step explanation:
pretty sure it's 66 because the two lengths added together is 66
Answer:
4
Step-by-step explanation:
Let y be the width of the rectangle
The length of the rectangle is 5 unit more than the width. This is written as:
Length = y + 5
Area = 36
Recall:
Area of rectangle = length x width
36 = (y + 5) x y
36 = y^2 + 5y
Rearrange the expression
y^2 + 5y — 36 = 0
To solve this problem by factorization, multiply the first term (i.e y^2) and last term ( i.e — 36) together. This gives — 36y^2
Next, find two factors of —36y^2 such that when we add them together it will result to the second term (5y). These factors are —4y and 9y. Now we substitute —4y and 9y in place of 5y in the equation. This is illustrated below:
y^2 + 5y — 36 = 0
y^2 —4y + 9y — 36 = 0
We factorize as follows:
y(y — 4) + 9(y —4) = 0
(y + 9) (y — 4) =0
y + 9 = 0 or y — 4 = 0
y = —9 or y = 4
Since the measurement can not be negative, therefore y (i.e the width) is 4
Answer:
x = 8
Step-by-step explanation:
When cutting the wire we will get two pieces
x and 12 - x
If we build a circle whith x , the lenght of the circle will be x, and if we look at the equation for a lenght of a cicle 2*π*r = x
then r = x/2π
and consequentely A₁ = area of a circle = πr² A₁ = π*x/2π
A₁ = x/2
With the other piece 12 - x we have to make an square so wehave to divide that piece in four equal length
side of the square = s
s = 1/4 ( 12 - x ) and the area is A₂ = [1/4 ( 12 - x)]²
A₂ = ( 12 - x )²/16
Then A₁ + A₂ = A(t) and this area as fuction of x
A (x) = x/2 + 1/16 ( 144 + x² -24x) A (x) =[ (8x + 144 + x² -24x)]/16
Taken derivatives in both sides
A´(x) = 8 + 2x - 24 = 0
2x -16 = 0 x = 8 and s = 12 - 8 s = 4
