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alex41 [277]
2 years ago
12

A table is on sale for 72% off. the price is $246.40. What is the regular price

Mathematics
1 answer:
ankoles [38]2 years ago
6 0

Answer:

$68.99

Step-by-step explanation:

This is called percentage decrease:

(100 - 72)% = 28%

246.40 × 28/100

= $68.99

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What decimal number is halfway between 16 and 17?
mote1985 [20]

Answer:

16.5?

Step-by-step explanation:

It's halfway between 16 and 17?

3 0
2 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
Researchers wanted to see which species of lizard (A, B, or C) is most likely to survive a bacterial infection. So they infected
Slav-nsk [51]

Answer:

A) attached below

B) 0.61

C) 0.47

Step-by-step explanation:

Given data:

Total number of lizards infected = 38

Of the 15 species B lizards 40% survived

For specie C one more survived than died

Out of the 24 lizards that died 1/3 were species A

<u>A) contingency table </u>

attached below

<u>B) Determine the proportion of these lizards in this study that were either specie A or Specie B </u>

P ( A or B ) = ( 8 + 15 ) / 38 = 0.605 ≈ 0.61

<u>C) determine the probability that specie C lizard did not study </u>

P ( not surviving  | C ) = 7 / 15 = 0.466 ≈ 0.47

7 0
2 years ago
What is the inverse of p(m) = m/5 + 8
zvonat [6]
The inverse is just switching y and x your answer should be . p^-1 (m)=5m-40

4 0
1 year ago
An object that weighs 1 pound on earth weighs only 0.17 pounds on the moon. Zach's dog weighs 17 1/2 pounds on earth. How much m
PtichkaEL [24]
 its actually .16 not .17
 284.192
3 0
2 years ago
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