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3 years ago

Find the length of molding needed for a 10'5" by 9'8" floor

1 answer:

4 0

Perimeter = 2(length + width)
p = 2(10'5" + 9'8")
p = 2(19'13")
p = 38'26"

26" = 2'4"

So...
38' + 2'4" = 40' 4" for the perim,eter

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Brian invests ?1900 into a savings account. The bank gives 3.5% compound interest for the first 2 years and 4.9% thereafter. How

Scorpion4ik [409]

let's check how much is it after 2 years firstly.

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &1900\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=1900\left(1+\frac{0.035}{1}\right)^{1\cdot 2}\implies A=1900(1.035)^2\implies A=2035.3275$

Brian invested the money for 6 years, so now let's check how much is that for the remaining 4 years.

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &2035.3275\\ r=rate\to 4.9\%\to \frac{4.9}{100}\dotfill &0.049\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}$

$\bf A=2035.3275\left(1+\frac{0.049}{1}\right)^{1\cdot 4}\implies A=2035.3275(1.049)^4 \\\\\\ A\approx 2464.54\implies \boxed{\stackrel{\textit{rounded up }}{A=2465}}$

4 0

3 years ago

Find all the square roots of x2 ≡ 53 (mod 77)

Nikolay [14]

Answer:

$x=\pm\sqrt{77n+53}$

Step-by-step explanation:

We have been given an equivalence equation $x^2\equiv 53\text{ (mod } 77)$ . We are asked to find all the square root of the given equivalence equation.

Upon converting our given equivalence equation into an equation, we will get:

$x^2-53=77n$

Add 53 on both sides:

$x^2-53+53=77n+53$

$x^2=77n+53$

Take square root of both sides:

$x=\pm\sqrt{77n+53}$

Therefore, the square root for our given equation would be $x=\pm\sqrt{77n+53}$ .

3 0

3 years ago

guys i need help with solving the system of equations and combining the equations. also show your work. the equations are x-4y=-

Firdavs [7]

X-4y=-12
4x-y=12

eliminate y's
multily 2nd equaiton by -4 and add to top one

x-4y=-12
<u>-16x+4y=-48 +
</u>-15x+0y=-60

-15x=-60
divide both sides by -15
x=4
sub back
x-4y=-12
4-4y=-12
minus 4 both sides
-4y=-16
divide both sides by -4
y=4

x=4
y=4
(x,y)
(4,4)<u>
</u>

5 0

3 years ago

A circle has radius 50 cm. Find the area of the circle to the nearest hundredth.

padilas [110]

Multiply by 2 which will get you a diameter and then multiply it by pi which is 3.14.

7 0

2 years ago

What is the chance of rolling a 4 with a single die four times in a row?

BlackZzzverrR [31]

Answer:

16.66

Step-by-step explanation:

5 0

3 years ago