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anygoal [31]
3 years ago
11

Round the product of 0.24 and 0.26 to the nearest hundredth. What is the answer?

Mathematics
1 answer:
Andreyy893 years ago
3 0
0.06 because the product is 0.0624
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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
Suppose that 35 people are divided in a random manner into two teams in such a way that one team contains 10 people and the othe
Effectus [21]

Answer:

0.5798 or 57.98%

Step-by-step explanation:

The total number of ways to form the two teams is the combination of choosing 10 people out of 35 (₃₅C₁₀). The number of possibilities that A and B are both on the 10-people team is given by the combination of choosing 8 people (since two are fixed) out of 33 (₃₃C₈).The number of possibilities that A and B are both on the 25-people team is given by the combination of choosing 10 people out of 33 (₃₃C₈).

Therefore, the probability that two particular people A and B will be on the same team is:

P = \frac{_{33}C_8+_{33}C_{10}}{_{35}C_{10}} \\\\P=\frac{\frac{33!}{(33-8)!8!}+\frac{33!}{(33-10)!10!} }{\frac{35!}{(35-10)!10!}} \\\\P=\frac{69}{119} = 0.5798

The probability is 0.5798 or 57.98%.

8 0
3 years ago
A 6-pound bag of chocolate candies costs $14.04. What is the unit price?
Ber [7]

Answer:

2.34 per pound is unit price

Step-by-step explanation:

14.04 divided by 6 is 2.34

3 0
3 years ago
PLS HELP I WILL MARK BRAINLIST
Likurg_2 [28]

Answer: B. 0 ≤ x ≤ 4

Step-by-step explanation: Have a nice day bro!✌️

8 0
3 years ago
What is the decimal equivalent of 61 3/9
Elden [556K]
The equivalent decimal is 61.(3)
7 0
3 years ago
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