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2 years ago

No scams. Show your work. write answer as a percent and round the nearest whole number if needed.

Mathematics

1 answer:

Ierofanga [76]2 years ago

7 0

Answer:

Step-by-step explanation:

we will find the area of the inner circle and then the area of the outer circle and see what the ratio is between those 2

area of a circle = $\pi$ $r^{2}$ (where r is the radius, NOT the diameter, easy to confuse)

the radius of the inner circle is 2.5. which is half of the diameter of 5

inner circle = $\pi$ *(2.5)^2

inner circle = 19.6349...

outer circle = $\pi$ *(10^2)

outer circle = 314.1592...

the ratio is 19.6349... / 314.1592... = 0.0625

0.0625 = 6.25%

= 6% ( rounded to nearest whole number )

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manager needs to buy chairs for his office the price for 1 chair is 79.99 dollars. If the manager buys 2 or more chairs then he

artcher [175]

1 chair is 79.99
40% discount
79.99 ÷ 100 =0.7999
0.7999 × 60 = 47.994
47.994 rounded down is $47.99
79.99-47.99=30.00
he saved $30

3 0

2 years ago

Can a 3 foot-by-9 foot rectangle be a scaled copy of a 3 foot-by-1 foot rectangle? Explain

Bumek [7]

No,because 9 feet is way bigger than 1 foot.

7 0

3 years ago

Solve these linear equations by Cramer's Rules Xj=det Bj / det A:

timurjin [86]

Answer:

(a) $x_1=-2,x_2=1$

(b) $x_1=\frac{3}{4} ,x_2=-\frac{1}{2} ,x_3=\frac{1}{4}$

Step-by-step explanation:

(a) For using Cramer's rule you need to find matrix $A$ and the matrix $B_j$ for each variable. The matrix $A$ is formed with the coefficients of the variables in the system. The first step is to accommodate the equations, one under the other, to get $A$ more easily.

$2x_1+5x_2=1\\x_1+4x_2=2$

$\therefore A=\left[\begin{array}{cc}2&5\\1&4\end{array}\right]$

To get $B_1$ , replace in the matrix A the 1st column with the results of the equations:

$B_1=\left[\begin{array}{cc}1&5\\2&4\end{array}\right]$

To get $B_2$ , replace in the matrix A the 2nd column with the results of the equations:

$B_2=\left[\begin{array}{cc}2&1\\1&2\end{array}\right]$

Apply the rule to solve $x_1$ :

$x_1=\frac{det\left(\begin{array}{cc}1&5\\2&4\end{array}\right)}{det\left(\begin{array}{cc}2&5\\1&4\end{array}\right)} =\frac{(1)(4)-(2)(5)}{(2)(4)-(1)(5)} =\frac{4-10}{8-5}=\frac{-6}{3}=-2\\x_1=-2$

In the case of B2, the determinant is going to be zero. Instead of using the rule, substitute the values of the variable $x_1$ in one of the equations and solve for $x_2$ :

$2x_1+5x_2=1\\2(-2)+5x_2=1\\-4+5x_2=1\\5x_2=1+4\\ 5x_2=5\\x_2=1$

(b) In this system, follow the same steps,ust remember $B_3$ is formed by replacing the 3rd column of A with the results of the equations:

$2x_1+x_2 =1\\x_1+2x_2+x_3=0\\x_2+2x_3=0$

$\therefore A=\left[\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right]$

$B_1=\left[\begin{array}{ccc}1&1&0\\0&2&1\\0&1&2\end{array}\right]$

$B_2=\left[\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right]$

$B_3=\left[\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right]$

$x_1=\frac{det\left(\begin{array}{ccc}1&1&0\\0&2&1\\0&1&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{1(2)(2)+(0)(1)(0)+(0)(1)(1)-(1)(1)(1)-(0)(1)(2)-(0)(2)(0)}{(2)(2)(2)+(1)(1)(0)+(0)(1)(1)-(2)(1)(1)-(1)(1)(2)-(0)(2)(0)}\\ x_1=\frac{4+0+0-1-0-0}{8+0+0-2-2-0} =\frac{3}{4} \\x_1=\frac{3}{4}$

$x_2=\frac{det\left(\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{(2)(0)(2)+(1)(0)(0)+(0)(1)(1)-(2)(0)(1)-(1)(1)(2)-(0)(0)(0)}{4} \\x_2=\frac{0+0+0-0-2-0}{4}=\frac{-2}{4}=-\frac{1}{2}\\x_2=-\frac{1}{2}$

$x_3=\frac{det\left(\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)}=\frac{(2)(2)(0)+(1)(1)(1)+(0)(1)(0)-(2)(1)(0)-(1)(1)(0)-(0)(2)(1)}{4} \\x_3=\frac{0+1+0-0-0-0}{4}=\frac{1}{4}\\x_3=\frac{1}{4}$

6 0

3 years ago

I need help on this question

kherson [118]

Answer:

Step-by-step explanation:

Just put x = 80 and y = 210 into the equation...

or put x = 40, y = 90.

210 - 90 = 3(80-40)

120 = 120√

210 + 90 = 3(80+40)

300 = 360×

210 - 90 = 2.6(80-40)

120 = 104×

210 + 90 = 2.6(80+40)

300 = 312×

8 0

3 years ago

What is the sum of the seven terms of the geometric series 2- 8+32-...?

egoroff_w [7]

The first term is 2 and the common ratio = -8/2 = -4

S7 = 2 * (-4)^7 - 1
------------- = 6554 answer
-4-1

6 0

2 years ago

No scams. Show your work. write answer as a percent and round the nearest whole number if needed.​

No scams. Show your work. write answer as a percent and round the nearest whole number if needed.