M + 20 = 9
u need to subtract 20 from both sides because u want to isolate m
m + 20 = 9
m + 20 - 20 = 9 - 20
m = - 11
Present value = 2200
interest rates =5% for 3 years, and 4% afterwards
no. of periods = 7
Future value=2200*(1.05)^3(1.04)^(7-3)
=<span>£</span>2979.367 (please round to appropriate number of decimals)
<span>Answer:
The two events are independent. In the given scenario, P(M and N) =0.25
Explanation:
1) Independent events are those that do not affect each other. In this case the number that you roll does not change the flip of the coin. So, whatever number you get with the die, the probabilities of landing tail or head when tossing the coin are the same.
2) The probability of the two simultaneous events: getting an odd number and landing a tail, since they are independent, is equal to the product of the two independent events:
P(M and N) = P(M) x P (N) (only because they are independent)
3) The probability of getting and odd number is 0.5 (half of the numbers are odd and half are even => probability = 1/2)
4) The probability of the coin lands tail is 0.5 (1/2).
5) Then the joint probability is 0.5 x 0.5 = 0.25</span>
Answer:
$125,000.12 last year
$375,000.36 this year
Step-by-step explanation:
Last year, her profits were x.
This year, the profits are three times greater, so they are 3x.
Altogether for both years, the profits are x + 3x = 4x.
The profits for both years combined are $500,000.48
4x = 500,000.48
Divide both sides by 4.
x = 500,000.48/4
x = 125,000.12
The profits last year were $125,000.12
This year, the profits were 3x = 3(125,000.12) = 375,000.36, or $375,000.36
Answer: The length of segments between this point and the vertices of greater base are 
and 18.
Step-by-step explanation:
Let ABCD is the trapezoid, ( shown in below diagram)
In which AB is the greater base and AB = 18 DC= 11, AD= 3 and BC = 7
Let P is the point where The extended legs meet,
So, according to the question, we have to find out : AP and BP
In Δ APB and Δ DPC,
∠ DPC ≅ ∠APB ( reflexive)
∠ PDC ≅ ∠ PAB ( By alternative interior angle theorem)
And, ∠ PCD ≅ ∠ PBA ( By alternative interior angle theorem)
Therefore, By AAA similarity postulate,
Let, DP =x
⇒ 
⇒ 33 +11x = 18x
⇒ x = 33/7= 
Thus, PD=
But, AP= PD + DA
AP= 
Now, let PC =y,
⇒ 
⇒ 77 + 11y = 18y
⇒ y = 77/7 = 11
Thus, PC= 11
But, PB= PC + CB
PB= 11+7 = 18
