1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tekilochka [14]
3 years ago
7

5. If the covariance between the variables x and y is 18 and the variance

Mathematics
1 answer:
klasskru [66]3 years ago
5 0

Answer:

The coefficient of  correlation=0.5

Step-by-step explanation:

We are given that

Covariance between the variable  x and y=18

Variance of x=16

Variance of y=81

We have to find the coefficient of correlation

We know that

Coefficient of correlation

r=\frac{covariance(x,y)}{\sqrt{variance(x)}\times \sqrt{variance(y)}}

Using the formula

r=\frac{18}{\sqrt{16}\times \sqrt{81}}

r=\frac{18}{4\times 9}

r=0.5

Hence, the coefficient of  correlation=0.5

You might be interested in
There are 12 marbles in a box. 8 are purple, and 4 are green. What is the probability of picking a purple marble and then a gree
Bad White [126]

Answer: 8/33

Step-by-step explanation:

So the probability of picking a purple marble is 8/12, after that there are 11 marbles left in the box

Now the probability of picking a green marble without placing the first marble back is 4/11

So the probability of doing both is 8/12 x 4/11 = 8/33

8 0
1 year ago
twice the sum of a number and 2 is equal to three times the difference of the number and 8. Find the number.
Leto [7]

Answer: x = -22


Step-by-step explanation:

Look at picture!

4 0
3 years ago
What values for q (0 ≤q≤2π)<br> satisfy the equation?<br><br> 22√sin q + 2 = 0
Vesna [10]
Answer:
\frac{3 \pi }{4} , \frac{7 \pi }{4}

Explanation:
2√2 sin(q) + 2 = 0
2√2 sin(q) = -2
sin(q) = \frac{-2}{2 \sqrt{2} }
sin(q) = \frac{- \sqrt{2} }{2}

Now, we know that:
sin (45) = \frac{ \sqrt{2} }{2}

From the ASTC rule, we know that the sine function is negative in the third and fourth quadrant.
This means that:
either q = 90 + 45 = 135° which is equivalent to \frac{3 \pi }{4}
or q = 270 + 45 = 315° which is equivalent to \frac{7 \pi }{4}

Hope this helps :)
6 0
3 years ago
Read 2 more answers
Please help
alexandr402 [8]
\bf 3\sqrt[3]{2a} -6\sqrt[3]{2a}\qquad \stackrel{add ing~like-terms}{\implies }\qquad -3\sqrt[3]{2a}
3 0
2 years ago
Read 2 more answers
can someone show me how to find the general solution of the differential equations? really need to know how to do it for the upc
mariarad [96]
The first equation is linear:

x\dfrac{\mathrm dy}{\mathrm dx}-y=x^2\sin x

Divide through by x^2 to get

\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x

and notice that the left hand side can be consolidated as a derivative of a product. After doing so, you can integrate both sides and solve for y.

\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1xy\right]=\sin x
\implies\dfrac1xy=\displaystyle\int\sin x\,\mathrm dx=-\cos x+C
\implies y=-x\cos x+Cx

- - -

The second equation is also linear:

x^2y'+x(x+2)y=e^x

Multiply both sides by e^x to get

x^2e^xy'+x(x+2)e^xy=e^{2x}

and recall that (x^2e^x)'=2xe^x+x^2e^x=x(x+2)e^x, so we can write

(x^2e^xy)'=e^{2x}
\implies x^2e^xy=\displaystyle\int e^{2x}\,\mathrm dx=\frac12e^{2x}+C
\implies y=\dfrac{e^x}{2x^2}+\dfrac C{x^2e^x}

- - -

Yet another linear ODE:

\cos x\dfrac{\mathrm dy}{\mathrm dx}+\sin x\,y=1

Divide through by \cos^2x, giving

\dfrac1{\cos x}\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\sin x}{\cos^2x}y=\dfrac1{\cos^2x}
\sec x\dfrac{\mathrm dy}{\mathrm dx}+\sec x\tan x\,y=\sec^2x
\dfrac{\mathrm d}{\mathrm dx}[\sec x\,y]=\sec^2x
\implies\sec x\,y=\displaystyle\int\sec^2x\,\mathrm dx=\tan x+C
\implies y=\cos x\tan x+C\cos x
y=\sin x+C\cos x

- - -

In case the steps where we multiply or divide through by a certain factor weren't clear enough, those steps follow from the procedure for finding an integrating factor. We start with the linear equation

a(x)y'(x)+b(x)y(x)=c(x)

then rewrite it as

y'(x)=\dfrac{b(x)}{a(x)}y(x)=\dfrac{c(x)}{a(x)}\iff y'(x)+P(x)y(x)=Q(x)

The integrating factor is a function \mu(x) such that

\mu(x)y'(x)+\mu(x)P(x)y(x)=(\mu(x)y(x))'

which requires that

\mu(x)P(x)=\mu'(x)

This is a separable ODE, so solving for \mu we have

\mu(x)P(x)=\dfrac{\mathrm d\mu(x)}{\mathrm dx}\iff\dfrac{\mathrm d\mu(x)}{\mu(x)}=P(x)\,\mathrm dx
\implies\ln|\mu(x)|=\displaystyle\int P(x)\,\mathrm dx
\implies\mu(x)=\exp\left(\displaystyle\int P(x)\,\mathrm dx\right)

and so on.
6 0
3 years ago
Other questions:
  • Which of the following expressions are equivalent to (x + 0) + y + 0
    15·1 answer
  • Assume employees' weekly gross earnings are $80,000, federal income tax withholding is $22,634.50, and FICA taxes are $11,920 in
    6·1 answer
  • How to find and solve this ? <br><br>Shape A = ______ units<br><br>Shape B = _______ units​
    5·1 answer
  • Plz, help ASAP!!!!!!<br> WILL MARK BRAINLIEST IF YOUR ANSWER IS CORRECT!!!!!!
    9·1 answer
  • Plz help me i really need it
    14·1 answer
  • Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late deliv
    14·1 answer
  • Just put the answer A B C D please
    10·2 answers
  • Which ordered pair is generated from the equation shown below? y = 3x + 2 A. (3, 11) B. (3, 9) C. (5, 15) D. (2, 4)
    13·1 answer
  • This is the function that models a boulder being pushed of a cliff. Find the height after 1.5 seconds.
    10·1 answer
  • Graph the function f(x) = -42-4+ 5 on the axes below. You must plot the
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!