Rewrite as a simplified fraction. 1.6 repeating

Blake and James are planning to go on a trip. Blake already has some money saved. She earns $96 more by working overtime. James

rosijanka [135]

Blake saved $\bold{\$ 433.80}$

Option - A

<u>SOLUTION: </u>

Given, Blake and James are planning to go on a trip.

Blake already has some money saved.

Let the amount saved by Blake be $\$ n$ .

She earns $\$96$ more by working overtime.

Then, total amount by Blake $=\$(n+96)$

James has $\$ 53$ more than 4 times the amount of money that Blake has saved.

Then, total amount by James will be $\$ 53+4 \times \$ n=\$(4 n+53)$

If they have $\$2,318$ in all, we have to find how much money had Blake originally saved

Now, total amount = $\$2318$

$\begin{array}{l}{\rightarrow \text { Amount by Blake }+\text { amount by James }=2318} \\\\ {\rightarrow \mathrm{n}+96+4 \mathrm{n}+53=2318 \rightarrow 5 \mathrm{n}+149=2318 \rightarrow 5 \mathrm{n}=2318-149 \rightarrow 5 \mathrm{n}=2169 \rightarrow \mathrm{n}=433.8}\end{array}$

7 0

3 years ago

cynthia invests some money in a bank which pays 5% compound interest per year. She wants it to be worth over £8000 at the end of

exis [7]

Answer:

The smallest amount is $\£6,911$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=3\ years\\ A=\£8,000\\ r=5\%=5/100=0.05\\n=1$

substitute in the formula above

$8,000=P(1+\frac{0.05}{1})^{1*3}$

solve for P

$8,000=P(1.05)^{3}$

$P=8,000/(1.05)^{3}$

$P=\£6,910.70$

Round to the nearest pound she can invest

The smallest amount is $\£6,911$

6 0

3 years ago

Question: The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Which equation can be use

kramer

Answer:

The hypotenuse is the longest side in a triangle.

a^2=b^2+c^2.

14^2=9^2+c^2.

c^2=196-81.

c^2=115.

c=√115.

c=10.72~11cm

5 0

3 years ago

From the top of a tower, an object which is 97 m away from the base of the tower, is at a 37° angle of depression.

mario62 [17]

<h3>Answer: 73</h3>

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Work Shown:

Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.

tan(angle) = opposite/adjacent

tan(A) = BC/AB

tan(37) = x/97

97*tan(37) = x

x = 97*tan(37)

x = 73.094742859971

For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.