If a square-shaped pool with side lengths are 3a^5 then find the area of the pool
solution:
A = (3a^5) x (3a^5)
= 9a^5+5
= 9a^10
The area of the square-shaped pool are 9a^10 based on the given side length which is 3a^5
Factorise 18a³b³- 27a²b³ +36a³b²
1 answer:
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slope = - 2, midpoint = (2, - 2 )
the slope m is calculated using the ' gradient formula '
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (4, - 6 ) and (x₂, y₂ ) = (0, 2 )
m = =
= - 2
calculate midpoint using midpoint formula
{ (4 + 0 ),
(- 6 + 2 )] = (2, - 2 )
gradient of perpendicular bisector = - =
equation in slope-intercept form is
y = mx + c ( m is slope and c the y-intercept )
partial equation is y = x + c
to find c substitute ( 2, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 3
y = x - 3 in slope-intercept form
Answer:
4 miles
Step-by-step explanation:
<u>Walking:</u>
Distance = d miles
Rate = 4 mph
Time = t hours
<u>Biking:</u>
Distance = d miles
Rate = 10 mph
Time hours (convert minutes to hours)
Hence,
Therefore, the distance to friend's house is
and the total distance of the round trip is
Standard deviation(σ
) = √V(X) = 10
Therefore, variance of X. V(X) = 10² = 100
Variance of aX is given by,
V(aX) = a²V(X)
Therefore, variance of 3X will be,
V(3X) = 3²V(X) = 9(100) = 900
Therefore, standard deviation of 3X is,
σ
= √V(3X) = √900 = 30
Therefore, variance of X. V(X) = 10² = 100
Variance of aX is given by,
V(aX) = a²V(X)
Therefore, variance of 3X will be,
V(3X) = 3²V(X) = 9(100) = 900
Therefore, standard deviation of 3X is,
σ
Answer:
We conclude that the sonnets were written by by a certain Elizabethan poet.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 8.9
Sample mean, =10.2
Sample size, n = 6
Alpha, α = 0.05
Population standard deviation, σ = 2.5
First, we design the null and the alternate hypothesis
We use One-tailed z test to perform this hypothesis.
a) Formula:
Putting all the values, we have
Now,
b) We calculate the p value with the help of z-table.
P-value = 0.1003
The p-value is greater than the significance level which is 0.05
c) Since the p-value is greater than the significance level, there is not enough evidence to reject the null hypothesis and accept the null hypothesis.
Thus, we conclude that the sonnets were written by by a certain Elizabethan poet.