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krek1111 [17]
3 years ago
15

Find the size of each of 66 payments made at the end of each year into a 88​% rate sinking fund which produces ​$36000 at the en

d of 66 years.
The payment size is $
Mathematics
1 answer:
Assoli18 [71]3 years ago
8 0

Answer: $7787.99

Step-by-step explanation:

We know that the formula to find the periodic payment on an annuity is given by :-

P=\dfrac{r(PV)}{1-(1+r)^{-n}}, where PV is the present value , r is the rate of interest ( in decimal ) and n is the number of payments.

Given : Present value : $36000

Rate of interest = 8%=0.08

Time period = 6 years

Then , the periodic payment will be :-

P=\dfrac{(0.08)(36000)}{1-(1+0.08)^{-6}}\\\\\Rightarrow\ P=\dfrac{2880}{0.3698}\\\\\Rightarrow\ P=\$7787.99

Hence, the payment size is $7787.99.

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Value of x in 2x-7=35 is​
Reika [66]

Answer:

x=21

Step-by-step explanation:

2x - 7 = 35

    +7    +7

-----------------

2x = 42

-----   -----

 2      2

  x = 21

The answer is 21, hope this helps.

4 0
3 years ago
Read 2 more answers
A cash box contains $74 made up of quarters, half-dollars, and one-dollar
Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

0.25q+0.50h+1.00d=74

\displaystyle{h=\frac{3}{5}d+1}

q=4(d+h)

Then, substitute <em>q</em> in the first equation with the expression from the third equation:

0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74

Next, substitute <em>h</em> in that equation with the expression from the second equation:

\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}

2d+0.9d+1.5=74\\2.9d+1.5=74

Solve for <em>d</em>, the number of one-dollar coins:

2.9d+1.5=74\\2.9d=72.5\\d=25

Substitute 25 for <em>d</em> in the second equation to find <em>h</em>, the number of half-dollar coins:

\displaystyle{h=\frac{3}{5}d+1}

\displaystyle{h=\frac{3}{5}(25)+1}

h=15+1\\h=16

Substitute 25 for <em>d</em> and 16 for <em>h</em> in the third equation to find <em>q</em>, the number of quarters:

q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164

Then, verify that the coins total $74:

0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

\displaystyle{h=\frac{3}{5}d+1}

\displaystyle{16=\frac{3}{5}(25)+1}

16 = 15 + 1\\16 = 16\\\text{Check.}

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}

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3 years ago
A 50 foot ladder is set against the side of a house so that it reaches up 30 feet. If
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Answer:

21.8

Step-by-step explanation:

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Complete the square to the problem X^2+6x-16=0
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Answer:

<h2>x = -8 or x = 2</h2>

Step-by-step explanation:

(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\-------------------------------\\\\x^2+6x-16=0\qquad\text{add 16 to both sides}\\\\x^2+6x=16\\\\x^2+2(x)(3)=16\qquad\text{add}\ 3^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=16+3^2\\\\(x+3)^2=16+9\\\\(x+3)^2=25\Rightarrow x+3=\pm\sqrt{25}\\\\x+3=-5\ \vee\ x+3=5\qquad\text{subtract 3 from both sides}\\\\\boxed{x=-8\ \vee\ x=2}

3 0
3 years ago
You have a solid Rectangle of dough. Consider the cross sections that are formed when you slice into the cube as described. Draw
Phantasy [73]
B is the answer I think trying it tho
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