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4 years ago

What is -(7 - 5x) = -2x

1 answer:

3 0

Distribute the negative sign to (7-5x) and then you will get -7+5x=-2x. Then you subtract 5x from both sides and you will get -7=-7x. Next you will divide by -7 to get x alone so the answer is x=1

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(10 points) Ben, Max, and Yolanda are at the front of three separate lines in the cafeteria waiting to be served. The serving ti

Alex777 [14]

Answer:

1/2 ; 1/3 ; 1/6

Step-by-step explanation:

Given :

Ben ~ exp(1)

Max ~ exp (2)

Yolanda ~ exp(3)

Ben :

X ~ exp(1)

Max:

Y ~ exp(2)

Yolanda :

Z ~ exp(3)

Probability that Yolanda is served first :

P(Z < (X, Y)) = Z /(x + y + z) = 3 /(1 + 2 + 3) = 3/6 = 1/2

Probability that Ben is served before Yolanda :

P(X < Z) = 1/ (1 + 2) = 1/3

Expected waiting time for first person served :

First person served = 1

Total = (1 + 2 + 3) = 6

Expected waiting time; E(x) :

E(x) : 1 / 6

4 0

3 years ago

What’s 32% of ____=8

Zanzabum

Answer:

Step-by-step explanation:

32% = 32/100 = 0.32

Let the unknown number be x.

0.32 x = 8

x = 25

6 0

4 years ago

Please answer this question is it a b c d or what

OleMash [197]

Answer:

its a because it gives us

Step-by-step explanation:

n= 25 over 4

decimal form

n= 6.25

6 0

3 years ago

Which ratio is equal to 54 : 24<br> A. 27:12<br> B. 18:6<br> C. 8:3<br> D. 24:54

Romashka [77]

54:24
=27:12. As a result, the answer will be A. Hope it help!

5 0

4 years ago

A circle has the order pairs (-1, 2) (0, 1) (-2, -1) what is the equation . Show your work.

olga55 [171]

We know that:

$(x-a)^2+(y-b)^2=r^2$

is an equation of a circle.

When we substitute x and y (from the pairs we have), we'll get a system of equations:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}$

and all we have to do is solve it for a, b and r.

There will be:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}\\\\\\
\begin{cases}1+2a+a^2+4-4b+b^2=r^2\\a^2+1-2b+b^2=r^2\\4+4a+a^2+1+2b+b^2=r^2\end{cases}\\\\\\
\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\\\\\
$

From equations (II) and (III) we have:

$\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}$

and from (I) and (II):

$\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}$

Now we can easly calculate a and b:

$\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}$

Finally we calculate $r^2$ :

$a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}$

And the equation of the circle is:

$(x-a)^2+(y-b)^2=r^2\\\\\\\left(x-\left(-\dfrac{3}{2}\right)\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}\\\\\\\boxed{\left(x+\dfrac{3}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}}$

7 0

3 years ago