Answer:
(n-2)×180=1080
180n -360=1080
180n = 1080+360
180n =1440
dividing by 180
n=8
hence it is a regular polygon with 8 sides .I.e it is an octagon
Step-by-step explanation:
we are given the total interior angles in the polygon and we know that the formula to find the total interior angles of a polygon is (n-2) ×180
where n is the number of sides
Answer:
b
Step-by-step explanation:
the anwser to this question is b i think
Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere which is shown below.

Here, we are given that our sphere has a radius of 4 units.
So plugging into the formula, we have
.
Start by simplifying the exponent.
(4 units)³ is equal to (4 units) (4 units) (4 units) or 64 units³.
So we have
.
Next, we multiply (4/3)(64) which can
be thought of as (4/3)(64/1)
So multiplying across the numerators and across the denominators,
we have
.
We need to work out the z-value of each question to work out the probability
Question a)
We have
X = 5 minutes
The mean, μ = 6.7 minutes
Standard deviation, σ = 2.2 minutes
z-score = (X - μ) / σ = (5 - 6.7) / 2.2 = -0.77
We want to find the probability of z < -0.77 so we read the z-table for the value of z on the left of -0.77 we have the probability P(z< -0.77) = 0.2206
The table is attached in picture 1 below
The probability of assembly time less than 5 minutes is 0.2206 = 22.06%
Question b)
z-score = (10-5) / 2.2 = 2.27
Reading the z-table for P(z<2.27) = 0.9884
The table reading is shown in the second picture below
The probability the assembly time will be less than 10 minutes is 0.9884
We can use this information to find the probability of the assembly time will be more than 10 minutes = 1 - 0.9884 = 0.0116 = 1.16%
Question c)
The value of z between 5 minutes and 10 minutes is
P(-0.77<z<2.27) = P(z<2.27) - P(z< -0.77)
P(-0.77<z<2.27) = 0.9884 - 0.2206 = 0.7678 = 76.78%
Step-by-step explanation:
1 Remove parentheses.
8{y}^{2}\times -3{x}^{2}{y}^{2}\times \frac{2}{3}x{y}^{4}
8y
2
×−3x
2
y
2
×
3
2
xy
4
2 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}
b
a
×
d
c
=
bd
ac
.
\frac{8{y}^{2}\times -3{x}^{2}{y}^{2}\times 2x{y}^{4}}{3}
3
8y
2
×−3x
2
y
2
×2xy
4
3 Take out the constants.
\frac{(8\times -3\times 2){y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
(8×−3×2)y
2
y
2
y
4
x
2
x
4 Simplify 8\times -38×−3 to -24−24.
\frac{(-24\times 2){y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
(−24×2)y
2
y
2
y
4
x
2
x
5 Simplify -24\times 2−24×2 to -48−48.
\frac{-48{y}^{2}{y}^{2}{y}^{4}{x}^{2}x}{3}
3
−48y
2
y
2
y
4
x
2
x
6 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
.
\frac{-48{y}^{2+2+4}{x}^{2+1}}{3}
3
−48y
2+2+4
x
2+1
7 Simplify 2+22+2 to 44.
\frac{-48{y}^{4+4}{x}^{2+1}}{3}
3
−48y
4+4
x
2+1
8 Simplify 4+44+4 to 88.
\frac{-48{y}^{8}{x}^{2+1}}{3}
3
−48y
8
x
2+1
9 Simplify 2+12+1 to 33.
\frac{-48{y}^{8}{x}^{3}}{3}
3
−48y
8
x
3
10 Move the negative sign to the left.
-\frac{48{y}^{8}{x}^{3}}{3}
−
3
48y
8
x
3
11 Simplify \frac{48{y}^{8}{x}^{3}}{3}
3
48y
8
x
3
to 16{y}^{8}{x}^{3}16y
8
x
3
.
-16{y}^{8}{x}^{3}
−16y
8
x
3
Done