Answer:
PV= $40,279.36
Step-by-step explanation:
Giving the following information:
Number of periods= 8*12= 96 months
Interest rate= 0.039/12= 0.00325
Future value (PV)= $55,000
<u>To calculate the initial investment, we need to use the following formula:</u>
PV= FV/(1+i)^n
PV= 55,000 / (1.00325^96)
PV= $40,279.36
Answer:
a= 17√3/ 2 or a≈14.72
Step-by-step explanation:
c = 17 and is the side opposite to the angle C
c=AB =17
a= BC because is the side opposite to angle A
sin 60° = opp./hyp = BC / AB = BC/17
sin 60° = BC /17 multiply both sides by 17
BC = 17* sin 60 = 17√3/2 ≈14.72
The value of n is 4 and yz is 1 if y is between x and z i.e. if y, x and z are collinear points.
According to the given question.
We have some linear equations.
xy = 4n + 3
yz = 2n - 7
and
xz = 20
Since, y is between x and z. Which means y, x and z are collinear points.
Therefore,
xy + yz = xz
⇒ 4n + 3 + 2n - 7 = 20
⇒ 6n -4 = 20
⇒ 6n = 20 + 4
⇒ 6n = 24
⇒ n = 24/6
⇒ n = 4
Therefore,
yz = 2n - 7 = 2(4) - 7 = 8- 7 = 1
Hence, the value of n is 4 and yz is 1 if y is between x and z i.e. if y, x and z are collinear points.
Find out more information about collinear points here:
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Answer:
6. No. See explanation below.
7. 18 months
8. 16
Step-by-step explanation:
6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.
Let's find the GCF of 85 and 99:
85 = 5 * 17
99 = 3^2 + 11
5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.
Answer: No because the GCF of 85 and 99 is 1.
7.
We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.
6 = 2 * 3
9 = 3^2
LCM = 2 * 3^2 = 2 * 9 = 18
Answer: 18 months
We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.
Month Charlie Dasha
1 home home
2 home home
3 home home
4 home home
5 home home
6 trip home
7 home home
8 home home
9 home trip
10 home home
11 home home
12 trip home
13 home home
14 home home
15 home home
16 home home
17 home home
18 trip trip
Answer: 18 months
8.
First, we find the prime factorizations of 96 an 80.
96 = 2^5 * 3
80 = 2^4 *5
GCF = 2^4 = 16
Answer: 16
