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3 years ago

What is negative nine plus five

Mathematics

1 answer:

melisa1 [442]3 years ago

8 0

negative nine plus five equals negative four

-9 + 5 = - 4

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Assignment: Compound Interest Investigation

sukhopar [10]

To help Tyler better understand how his money will increase in an account that uses simple interest and one that uses compound interest, we are going to use two formulas: a simple interest formula for the accounts that use simple interest, and a compound interest formula for the accounts that use compound interest.
- Simple interest formula: $A=P(1+rt)$
where:
$A$ is the final investment value
$P$ is the initial investment
$r$ is the interest rate in decimal form
$t$ is number of years
- Compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where:
$A$ is the final investment value
$P$ is the initial investment
$r$ is the interest rate in decimal form
$t$ is he number of years
$n$ is the number of times the interest is compounded per year

1.
a. This is a compound interest account, so we are going to use our compound interest formula. We now that $P=1500$ , $t=5$ , and since the interest is compounded annually (1 time a year), $n=1$ . To find the interest rate in decimal form, we are going to divide it by 100%: $r= \frac{4}{100} =0.04$ . Now that we have all the values lets replace them in our compound interest formula:
$A=1500(1+ \frac{0.04}{1}) ^{(1)(5)}$
$A=1824.98$
We can conclude that after 5 years he will have $1824.98 in this account.
b. Here we will use our simple interest formula. We know that $P=1500$ , $t=5$ , and $r= \frac{4}{100} =0.04$ . Lets replace those values in our simple interest formula:
$A=1500(1+(0.04)(5))$
$A=1800$
We can conclude that after 5 years he will have $1800 in this account.
c. The compound interest account from point a will yield more money than the simple account one from point b. The difference between the tow amounts is $1824.98-1800=24.98$

2.
a. Here we are going to use our compound interest formula. We know that $P=2000$ , $t=1$ and $r= \frac{8}{100} =0.08$ . We also know that the interest is compounded Quaternary (4 times per year), so $n=4$ . Now that we have all our values lets replace them into our formula:
$A=2000(1+ \frac{0.08}{4} )^{(4)(1)}$
$A=2164.86$
We can conclude that after 1 year he will have $2164.86 in this account.
b. Here we are going to use our simple interest formula. We know that $P=2000$ , $t=1$ , and $r= \frac{8}{100} =0.08$ . Once again, lets replace those values in our formula:
$A=2000(1+(0.08)(1))$
$A=2160$
We can conclude that after 1 year he will have $2160 in this account.
c. The compound interest account from point a will yield more money than the simple account one from point b. The difference between the tow amounts is $2164.86-2160=4.86$

3.
a. Since Bank A offers an account with a simple interest, we are going to use our simple interest formula. From the question we know that $P=3200$ , $t=3$ , and $r= \frac{3.5}{100} =0.035$ . Now we can replace those values into our formula to get:
$A=3200(1+(0.035)(3))$
$A=3536$
Now, to find the interest earned for Bank A we are going to subtract $P$ from $A$
$InterestEarned=3536-3200=336$
We can conclude that the interest earned for Bank A is $336
b. Since Bank B offers an account with a compound interest, we are going to use our compound interest formula. We know that $P=3200$ , $t=3$ , $r= \frac{3.4}{100} =0.034$ , and since the interest is compounded annually (1 time a year), $n=1$ . Now that we have all the values, lets replace them in our formula to get:
$A=3200(1+ \frac{0.034}{1} )^{(1)(3)}$
$A=3537.62$
Now, to find the interest earned for Bank A we are going to subtract $P$ from $A$ :
$InterestEarned=3537.62-3200=337.62$
We can conclude that the interest earned for Bank B is $337.62
c. Even tough the interest returns between the tow Banks are very similar, Bank B offers a slightly better interest over a period of time, which can make a big difference in the long run. If Tyler wants the earn more money, he definitively should deposit his money in Bank B.
d. The compound interest account from Bank B will yield more money than the simple account one from Bank A The difference between the tow amounts is $3537.62-3536=1.62$

6 0

3 years ago

Some people took part in a game. The frequency shows information about their scores.

Wittaler [7]

80
117
169
180
448
817
=
1811 / 91

19.901 and that rounded to 2 decimal places is 19.9

3 0

3 years ago

Uestion

Stella [2.4K]

Check the picture below, so the park looks more or less like so, with the paths in red, so let's find those midpoints.

$~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ J(\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad K(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 -3}{2}~~~ ,~~~ \cfrac{ 3 +1}{2} \right) \implies \left(\cfrac{ -2 }{2}~~~ ,~~~ \cfrac{ 4 }{2} \right)\implies JK=(-1~~,~~2) \\\\[-0.35em] ~\dotfill$

$~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ L(\stackrel{x_1}{5}~,~\stackrel{y_1}{-1})\qquad M(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 +5}{2}~~~ ,~~~ \cfrac{ -3 -1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ -4 }{2} \right)\implies LM=(2~~,~~-2) \\\\[-0.35em] ~\dotfill$

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ JK(\stackrel{x_1}{-1}~,~\stackrel{y_1}{2})\qquad LM(\stackrel{x_2}{2}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ JKLM=\sqrt{(~~2 - (-1)~~)^2 + (~~-2 - 2~~)^2} \\\\\\ JKLM=\sqrt{(2 +1)^2 + (-2 - 2)^2} \implies JKLM=\sqrt{( 3 )^2 + ( -4 )^2} \\\\\\ JKLM=\sqrt{ 9 + 16 } \implies JKLM=\sqrt{ 25 }\implies \boxed{JKLM=5}$

now, let's check the other path, JM and KL

$~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ J(\stackrel{x_1}{-3}~,~\stackrel{y_1}{1})\qquad M(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -1 -3}{2}~~~ ,~~~ \cfrac{ -3 +1}{2} \right) \implies \left(\cfrac{ -4 }{2}~~~ ,~~~ \cfrac{ -2 }{2} \right)\implies JM=(-2~~,~~-1) \\\\[-0.35em] ~\dotfill$

$~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ K(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad L(\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +1}{2}~~~ ,~~~ \cfrac{ -1 +3}{2} \right) \implies \left(\cfrac{ 6 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies KL=(3~~,~~1) \\\\[-0.35em] ~\dotfill$

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ JM(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad KL(\stackrel{x_2}{3}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ JMKL=\sqrt{(~~3 - (-2)~~)^2 + (~~1 - (-1)~~)^2} \\\\\\ JMKL=\sqrt{(3 +2)^2 + (1 +1)^2} \implies JMKL=\sqrt{( 5 )^2 + ( 2 )^2} \\\\\\ JMKL=\sqrt{ 25 + 4 } \implies \boxed{JMKL=\sqrt{ 29 }}$