True or False? The following triangle has just one 90 degree angle. Any scaled copy of this triangle must also have one 90 degre
2 answers:
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Answer:
B
Step-by-step explanation:
Reflection is a transformation that preserves lengths.
Triangle XYZ, with side lengths XY = 7 in, YZ = 5 in, XZ = 4 in, is reflected across the x-axis to result in △X'Y'Z'.
This means that corresponding sides have the same lengths:
- XY = X'Y' = 7 in;
- XZ = X'Z' = 4 in;
- YZ = Y'Z' = 5 in.
Find the perimeters of both triangles:
Hence, only option B is true.
The time value of money calculation can be performed using formula equations or online calculators.
The correct responses are;
- 1) Option 3
- 2) Option 2
- 3) The difference in principal is approximately $8,000
- The difference in interest earned is approximately $2,977.87
- 4) It is better to invest more money at the beginning of the 30 years
Reasons:
Option 1: Present value = 0
Amount invested per month, A = $25/month
The Annual Percentage Rate, APR, r = 3.25%
Number of years = 30
The future value of an annuity is given by the formula;
In option 1, m = 12 periods per year
Therefore;
Contribution = $25 × 12 × 30 = $9,000
Total interest earned = $15,209.3 - $9,000 = $6,209.3
Final balance = $15,209.3
Option 2: Present value = 0
Amount, A = $75/quarter
m = 4 periods per year
The Annual Percentage Rate, APR = 4.00%
Therefore;
The effective interest rate is therefore;
Using an online calculator, FV = $17,467.04
Contribution = $75 × 4 × 30 = $9,000
Total interest earned = $17,467.04 - $9,000 = $8,467.04
Final balance = $17,467.04
Option 3: Present value = $1,000
APR = 6.25%
m = 12 period per year
Number of years, t = 30 years
Therefore;
Contribution = $1,000
Total interest earned = $6,489.17 - $1,000 = $5,489.17
Final balance = $6,489.17
The table of values is therefore;
1) The option that has the least amount invested are <u>option 3</u>
Option 3 investment plan is a present value of $1,000, invested for 30 years at 6.25% APR compounded monthly.
2) <u>Option 2</u> yielded the highest amount at the end of 30 years, given that the APR is higher than the APR for option 1, although the amount invested over the period are the same.
The basis of option 2 investment plan is $75 invested quarterly at 4.00% APR compounded monthly for 30 years.
3) The difference in the principal invested for the highest and lowest final balance is $9,000 - $1,000 = <u>$8,000</u>
The difference in the interest earned is; $8,467.04 - $5,489.17 = <u>$2,977.87</u>
4) In option 1 the present value is zero, therefore zero amount was invested at the beginning.
The interest to investment ration is 6,209.3:9,000 ≈ 0.7:1
In option 3, all the money was invested at the beginning.
The interest to investment ratio of option 3 is; 5,489.17:1,000 ≈ 5.5:1
Given that the interest to investment ratio, which is the return on investment is larger when more money is saved at the beginning as in option 3, <u>it is better to invest more money at the beginning</u>.
Learn more about future value of an annuity here:
the complete question in the attached figure
1) Find the probability that all nine victims would select the same person. You should enter your answer as a decimal, not as a percent. Do not round, as your answer should be a terminating decimal.
P=(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)=0.000000512
2) what is the probability that the first victim picks SOMEONE? ANYONE?
P=(1/5)=0.20 ---------------- > 20%
3) Now let’s look at victim #2. What is the probability that they pick the same person as victim #1?
P=(1/5)*(1/5)=0.04 --------------> 4%
4) Now let’s look at victim #3. What is the probability that they pick the same person as victim #1?
P=(1/5)*(1/5)*(1/5)=0.008 --------------> 0.8%
5) Now let's look at victim #9. What is the probability that they pick the same person as victim #1?
P=(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)*(1/5)=0.000000512
6) Once you find all those probabilities, what rule would apply?
the probability is given by (1/5)^n
n=number of victims that pick the same person---------> in this problem = 9
P=(1/5)^9= 0.000000512
