Answer:
2(3x+y=4)
1(x+2y=-2)
6x+2y=8
(-) x+2y=-2
5x=10
5
x=2
x+2y=-1
2+2y=-1
-2 -2
2y=-3
2
y=-3/2
Step-by-step explanation:
have $500 at the end of the year?
A. $507.89
B. $480.40
C. $518.92
D. $492.31
To have $500 at the end of the year with a 4% APR compounded monthly, you would need to invest approximately $480.40 as a lump sum.
To find the amount of money needed to invest as a lump sum in order to have $500 at the end of the year with an approximate 4% APR compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)nt
Where:
A = final amount ($500)
P = initial investment (unknown)
r = annual interest rate (4% or 0.04)
n = number of times interest is compounded per year (12)
t = number of years (1)
Plugging the given values into the formula, we can solve for P:
P = A / ((1 + r/n)nt)
P = $500 / ((1 + 0.04/12)12*1)
P ≈ $480.40
Therefore, you would need to invest approximately $480.40 as a lump sum to have $500 at the end of the year.
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Answer: 480.40
Step-by-step explanation:
We can use the formula for compound interest to calculate how much money we will need to invest as a lump sum to have $500 at the end of the year.
FV = PV x (1 + r/n)^(nt)
FV = future value
PV = present value
r = interest rate
n = number of times compounded per year
t = time in years
We know that FV = $500, r = 4% or 0.04, n = 12 (since it is compounded monthly), and t = 1. We can plug in these values to solve for PV.
$500 = PV x (1 + 0.04/12)^(12 x 1)
$500 = PV x (1.003333)^12
$500 = PV x 1.0406
PV = $500 / 1.0406
PV = $480.40
Therefore, we will need to invest $480.40 as a lump sum to have $500 at the end of the year. So, the correct option is B. $480.40.
Answer:
B) Probability of number less than 8 OR a divisor of 15 = 1
Step-by-step explanation:
Given that the spinner number 1-10, therefore sample space = 10.
Each number is equally likely to be spun = 1/10 for each number.
A) probability of having an odd number OR a power of three?
Probability of odd number = number of odd number from 1-10 / sample space
Number of odd number = 5 {1,3,5,7,9}
Probability of odd number = 5/10 = 1/2
Probability of power of three = number of power of three from 1-10 / sample space
power of three from 1-10 = 1 (1x1x1) and 8 (2x2x2)
number of power of three from 1-10 = 2 {1,8}
Probability of power of three = 2/10
probability of having an odd number OR a power of three = probability of having an odd number + a power of three
probability of having an odd number OR a power of three = 5/10 + 2/10 = 7/10
B) probability of number less than 8 OR a divisor of 15
Number less than 8 = 7 {1,2,3,4,5,6,7}
Probability of number less than 8 = 7/10
Divisor of 15 from 1-10 = 3 {1,3,5}
Probability of divisor of 15 = 3/10
Probability of number less than 8 OR a divisor of 15 = probability of number less than 8 + a divisor of 15
Probability of number less than 8 OR a divisor of 15 = 7/10 + 3/10 = 10/10 = 1
The Probability of having an odd number OR a power of three is 7/10
The probability of a number less than 8 OR a divisor of 15 is 1.
Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorableoutcomes / total number of outcomes
It is given that the spinner number 1-10, So sample space = 10.
Each number is equally likely to be spun
A) probability of having an odd number OR a power of three
Probability of odd number = number of odd numbers / sample space
Number of odd number = {1,3,5,7,9}
Probability of odd number = 5/10
= 1/2
Probability of power of three = number of power of three / sample space
power of three from 1-10 = 1 and 8
number of power of three = 2
Probability of power of three = 2/10
Probability of having an odd number OR a power of three = probability of having an odd number + a power of three
= 5/10 + 2/10
= 7/10
Therefore, the probability of having an odd number OR a power of three is 7/10
B) Probability of number less than 8 OR a divisor of 15
Number less than 8 = {1,2,3,4,5,6,7}
Probability of number less than 8 = 7/10
Divisor of 15 from 1-10 = {1,3,5}
Probability of divisor of 15 = 3/10
Probability of number less than 8 OR a divisor of 15 = probability of number less than 8 + a divisor of 15
= 7/10 + 3/10
= 10/10
= 1
Therefore, the Probability of a number less than 8 OR a divisor of 15 is 1.
Learn more about probability :
The interest earned at $350 at 3% for 10 years is $105
Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Given;
P = $350
r = 0.03
t = 10 years
The interest earned;
I =I = P × r × t
I =350 × 0.03 ×10
I = $105
Therefore, the interest earned will be $105
Learn more about simple interest here;
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