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2 years ago

Which of the following equations could be the trend line of variables that have a negative correlation?

Mathematics

1 answer:

fgiga [73]2 years ago

7 0

Answer:

We will now call regression with just one explanatory variable simple linear re- ... We now think that the relationship between longevity and thorax length has ... parallel lines is s = √. 1 n − 3. ∑ residual. 2 = √. 1 n − 3. ∑. (y − ^y)2 ... Comparing these estimated regression equations with the two separate regression lines ...

Step-by-step explanation:

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If 5/8 of the students in a school ar boys, what is the ratio of boys to girls<br><br>

babymother [125]

Answer:

5:3

Step-by-step explanation:

math

4 0

2 years ago

HELPPPPPPPPP i have the most trouble with math what’s the answer??

lakkis [162]

Answer:

Second Option

$\frac{5\sqrt{11} +5\sqrt{3}}{8}$

Step-by-step explanation:

To simplify the expression you must multiply the numerator and the denominator of the fraction by the conjugate of the denominator.

If you have an expression of the form

$a -b$ then its conjugate will be $a + b.$

The result of that multiplication will be

$a ^ 2 -b ^ 2$

Therefore we have the expression

$\frac{5}{\sqrt{11} -\sqrt{3}}$

By multiplying by the conjugate of the denominator we have

$\frac{5}{\sqrt{11} -\sqrt{3}}*\frac{\sqrt{11} +\sqrt{3}}{\sqrt{11} +\sqrt{3}}\\\\\\\frac{5(\sqrt{11} +\sqrt{3})}{(\sqrt{11})^2 -(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11} +5\sqrt{3}}{11 -3}\\\\\\\frac{5\sqrt{11} +5\sqrt{3}}{8}$

6 0

2 years ago

Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

$x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}$

By Fermat's little theorem, we have

$x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5$

$x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7$

5 and 7 are both prime, so $\varphi(5)=4$ and $\varphi(7)=6$ . By Euler's theorem, we get

$x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5$

$x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7$

Now we can use the Chinese remainder theorem to solve for $x$ . Start with

$x=2\cdot7+5\cdot6$

Taken mod 5, the second term vanishes and $14\equiv4\pmod5$ . Multiply by the inverse of 4 mod 5 (4), then by 2.

$x=2\cdot7\cdot4\cdot2+5\cdot6$

Taken mod 7, the first term vanishes and $30\equiv2\pmod7$ . Multiply by the inverse of 2 mod 7 (4), then by 6.

$x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6$

$\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}$

$x^5\equiv3\pmod{64}$

We have $\varphi(64)=32$ , so by Euler's theorem,

$x^{32}\equiv1\pmod{64}$

Now, raising both sides of the original congruence to the power of 6 gives

$x^{30}\equiv3^6\equiv729\equiv25\pmod{64}$

Then multiplying both sides by $x^2$ gives

$x^{32}\equiv25x^2\equiv1\pmod{64}$

so that $x^2$ is the inverse of 25 mod 64. To find this inverse, solve for $y$ in $25y\equiv1\pmod{64}$ . Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that $(-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}$ .

So we know

$25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}$

Squaring both sides of this gives

$x^4\equiv1681\equiv17\pmod{64}$

and multiplying both sides by $x$ tells us

$x^5\equiv17x\equiv3\pmod{64}$

Use the Euclidean algorithm to solve for $x$ .

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that $(-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}$ , and so $x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}$

5 0

2 years ago

Which is equal to 6^-8/6^-2 A. 616 B. 64 C. 6−6 D. 6−10

rjkz [21]

6-6.
6^-8/6^-2 becomes 6^-8(6^2) which is 6^-8+2=6^-6

4 0

3 years ago

Please tell me the steps to this problem. i will give brainliest

gayaneshka [121]

Option C: -3 is the average rate of change between $x=-1$ and $x=1$

Explanation:

The formula to determine the average rate of change is given by

Average rate of change = $\frac{y_2-y_1}{x_2-x_1}$

We need to find the average rate of change between $x=-1$ and $x=1$

Thus, from the table, we have,

$x_1=-1$ , $y_1=5$

$x_2=1$ , $y_2=-1$

Thus, substituting these values in the formula, we get,

Average rate of change = $\frac{-1-5}{1+1}$

$=\frac{-6}{2}$

$=-3$

Thus, the average rate of change between $x=-1$ and $x=1$ is -3.

Hence, Option C is the correct answer.

6 0

2 years ago