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3 years ago

Determine the center for: x^2 + y^2 − 8x + 6y + 12 = 0

Mathematics

2 answers:

Anit [1.1K]3 years ago

7 0

Answer:

1/3

Step-by-step explanation:

Just divide

levacccp [35]3 years ago

3 0

your answer should be (4,-3)

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Ken makes 75 cookies. He gives 35 of them to his classmates and 13 of them to his teachers. He brings the rest home. He brings h

IrinaVladis [17]

27 cookies because 75 - 35=40. 40 - 13=27

3 0

3 years ago

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Simplify<br> x^2(y^3)^4/xy^5=x^a•y^b

givi [52]

Answer: a = 1 b = 7

Step-by-step explanation:

x^2(y^3)^4/x.y^5 = x^a.y^b

x^2(y^12) = x^a.y^b

(x^2).(y^12)/x^y^5 = x.y^7

x.y^7= x^a . y^b -> <u>x^1.y^7</u>

7 0

3 years ago

How many rational numbers lie between-2/3 and 7/3

tiny-mole [99]

Answer:

infinite

Step-by-step explanation:

name two, and then find a third in between them.

you can repeat that as often as you want.

3 0

3 years ago

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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the gi

STatiana [176]

Answer:

To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and $f^{-1}(x)= \frac{ln\ x+4}{2}$

Step-by-step explanation:

Data provided in the question

f(x) = e^2x - 4

Now

to find the inverse let

So,

y = e^2x - 4

Now

Replace x and y

Therefore

x = e^2y - 4

Now compute the value of y

So,

x + 4 = e^2y

Now take ln on both sides:

The equation is

ln(x+4) = ln(e^2y)

ln(x+4) = 2y

y = ln(x+4) ÷ 2

$f^{-1}(x)= \frac{ln\ x+4}{2}$

Therefore, To determine the inverse of the given function, change f(x) to y, switch x and y and solve for y and $f^{-1}(x)= \frac{ln\ x+4}{2}$

5 0

3 years ago

Suppose we roll a fair die and let X represent the number on the die. (a) Find the moment generating function of X. (b) Use the

Likurg_2 [28]

Answer:

(a) moment generating function for X is $\frac{1}{6}\left(e^{t}+e^{2 t}+e^{2 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$

(b) $\mathrm{E}(\mathrm{X})=\frac{21}{6} \text { and } E\left(X^{2}\right)=\frac{91}{6}$

Step-by step explanation:

Given X represents the number on die.

The possible outcomes of X are 1, 2, 3, 4, 5, 6.

For a fair die, $P(X)=\frac{1}{6}$

(a) Moment generating function can be written as $M_{x}(t)$ .

$M_x(t)=\sum_{x=1}^{6} P(X=x)$

$M_{x}(t)=\frac{1}{6} e^{t}+\frac{1}{6} e^{2 t}+\frac{1}{6} e^{3 t}+\frac{1}{6} e^{4 t}+\frac{1}{6} e^{5 t}+\frac{1}{6} e^{6 t}$

$M_x(t)=\frac{1}{6}\left(e^{t}+e^{2 t}+e^{3 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$

(b) Now, find $E(X) \text { and } E\((X^{2})$ using moment generating function

$M^{\prime}(t)=\frac{1}{6}\left(e^{t}+2 e^{2 t}+3 e^{3 t}+4 e^{4 t}+5 e^{5 t}+6 e^{6 t}\right)$

$M^{\prime}(0)=E(X)=\frac{1}{6}(1+2+3+4+5+6)$

$\Rightarrow E(X)=\frac{21}{6}$

$M^{\prime \prime}(t)=\frac{1}{6}\left(e^{t}+4 e^{2 t}+9 e^{3 t}+16 e^{4 t}+25 e^{5 t}+36 e^{6 t}\right)$

$M^{\prime \prime}(0)=E(X)=\frac{1}{6}(1+4+9+16+25+36)$

$\Rightarrow E\left(X^{2}\right)=\frac{91}{6}$

Hence, (a) moment generating function for X is $\frac{1}{6}\left(e^{t}+e^{2 t}+e^{3 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)$ .

(b) $\mathrm{E}(\mathrm{X})=\frac{21}{6} \text { and } E\left(X^{2}\right)=\frac{91}{6}$

6 0

4 years ago