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mixer [17]
2 years ago
7

Can someone help me solv for x?

Mathematics
1 answer:
Alexxx [7]2 years ago
5 0

Answer:

AB=AC

X²+8 =33

X²=33-8

X²=25.

X=√25

X=5

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<span>There are 2 3/4 boxes and 1/2 pies in each box how many pies are there? </span>
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David is creating keychains out of colored beads. He has 18 red beads, 64 blue beads and 96 pink beads. If each keychain will ha
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sorry i cant help on that its tricky but try 8???

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2 years ago
919,827 to the nearest 1000, 100, and 100
OverLord2011 [107]

nearest 1000: 920,000

nearest 100: 919,800

nearest 10 (you said 100 but I think you mean 10): 919,830

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3 years ago
How Much Have I Saved? Portfolio
avanturin [10]

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;

\displaystyle FV_{A} = \mathbf{A \cdot \left (\frac{ \left(1 + \frac{r}{m} \right)^{m\cdot t} - 1}{\frac{r}{m} } \right)}

In option 1, m = 12 periods per year

Therefore;

\displaystyle FV_{A} = 25 \times \left (\frac{ \left(1 + \frac{0.0325}{12} \right)^{12 \times 30} - 1}{\frac{0.0325}{12} } \right) \approx  \mathbf{15,209.3}

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;

\displaystyle r_{eff} = \left(1 + \frac{0.04}{4} \right)^4 - 1 \approx \mathbf{0.04060401}

\displaystyle FV_{A} = 75 \times \left (\frac{ \left(1 + \frac{0.04060401}{4} \right)^{4 \times 30} - 1}{\frac{0.04060401}{4} } \right) \approx  17,437.7

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;

\displaystyle FV = \left (1 + \frac{0.0625}{12} \right)^{12 \times 30} \approx \mathbf{6,489.17}

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;

  • \begin{tabular}{|c|c|c|c|}Option \# &Contribution &Total Interest Earned&Final Balance\\1&\$9,000&\$6,209.3 & \$15,209.3\\2&\$9,000&\$8,467.04 &\$17,467.04\\3&\$1,000&\$5,489.17&\$6,489.17\end{array}\right]

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:

brainly.com/question/8243704

3 0
2 years ago
You have 480 grams of a radioactive kind of samarium. If its half-life is 90 years,
lisov135 [29]

Answer:

120 grams will be left after 180 years.

Step-by-step explanation:

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by

                                             N(t)=N_0(\frac{1}{2})^\frac{t}{t_{1/2}}

where,

N(t) = quantity of the substance remaining

N_0 = initial quantity of the substance

t = time elapsed

t_{1/2} = half life of the substance

From the information given we know that:

  • The initial quantity is 480 g,
  • The half-life is 90 years,
  • 180 years is the time elapsed.

And we want to find how much will be left. For this we use the above formula.

N(t)=480\left(\frac{1}{2}\right)^{\frac{180}{90}}\\\\N(t)=480\left(\frac{1}{2}\right)^2\\\\N(t)=480\cdot \frac{1}{2^2}=120

120 grams will be left after 180 years.

3 0
3 years ago
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