Find the Correlation of the following two variables X: 2, 3, 5, 6 Y: 1, 2, 4, 5

Answer:

[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]

Step-by-step explanation:

First find the radius

Which is the distance between the 2 points.

Radius =5

The answer in the standad form is above.

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

The standard equation of a circle is given as:

(x - a)² + (y - b)² = r²

where (a, b) is the center of the circle and r is the radius of the circle.

Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:

[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]

hence:

(x - 3)² + (y - (-5))² = 5²

(x - 3)² + (y + 5)² = 25

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

Find out more at: https://brainly.com/question/13658927

Answer:

300 SF

Step-by-step explanation:

just took the test

Answer:

We conclude that there is no difference in potential mean sales per market in Region 1 and 2.

Step-by-step explanation:

We are given that a random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6.

A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5.

Let [tex]\mu_1[/tex] = mean sales per market in Region 1.

[tex]\mu_2[/tex]  = mean sales per market in Region 2.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1-\mu_2[/tex] = 0      {means that there is no difference in potential mean sales per market in Region 1 and 2}

Alternate Hypothesis, [tex]H_A[/tex] : > [tex]\mu_1-\mu_2\neq[/tex] 0      {means that there is a difference in potential mean sales per market in Region 1 and 2}

The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;

                            T.S.  =  [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+ {\frac{1}{n_2}}} }[/tex]   ~  [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean sales in Region 1 = 84

[tex]\bar X_2[/tex] = sample mean sales in Region 2 = 78.3

[tex]s_1[/tex]  = sample standard deviation of sales in Region 1 = 6.6

[tex]s_2[/tex]  = sample standard deviation of sales in Region 2 = 8.5

[tex]n_1[/tex] = sample of supermarkets from Region 1 = 12

[tex]n_2[/tex] = sample of supermarkets from Region 2 = 17

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]s_p=\sqrt{\frac{(12-1)\times 6.6^{2}+(17-1)\times 8.5^{2} }{12+17-2} }[/tex] = 7.782

So, the test statistics =  [tex]\frac{(84-78.3)-(0)}{7.782 \times \sqrt{\frac{1}{12}+ {\frac{1}{17}}} }[/tex]  ~   [tex]t_2_7[/tex]

                                   =  1.943  

The value of t-test statistics is 1.943.

Now, at a 0.02 level of significance, the t table  gives a critical value of -2.472 and 2.473 at 27 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that there is no difference in potential mean sales per market in Region 1 and 2.

Answer:

Step-by-step explanation:

Given

Garden: [tex]x^2+18x+81[/tex]

One Bag: [tex]x^2 - 81[/tex]

Requires

Determine the number of bags to cover the whole garden

This is calculated as thus;

[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]

Expand the numerator

[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]

[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]

[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]

Express 81 as 9²

[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]

Evaluate as difference of two squares

[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]

[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]

Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]

Answer:

25 CAN be written as a fraction.

=> 250/10 = 25

Square root of 14 is 3.74165738677

It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION,  but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION

=> 374/100

-1.25 CAN be written as a fraction.

=> -5/4 = -1.25

Square root of 16 CAN also be written as a fraction.

=> sqr root of 16 = 4.

4 can be written as a fraction.

=> 4 = 8/2

Pi = 3.14.........

It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION

=> 314/100

.6 CAN be written as a fraction.

=> 6/10 = .6

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are there for the interviewer to create the list?

Since the question deals with selection, we will apply the combination rule. Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

According to the question, if the the interviewer is to select 6 applicants from a pool of 20 applicants that are interviewed for a job, this can be done in 20C6 number of ways.

20C6 = 20!/(20-6)!6!

20C6 = 20!/14!6!

20C6 = 20*19*18*17*16*15*14!/14!*6*5*4*3*2

20C6 =  20*19*18*1716*15/6*5*4*3*2

20C6 = 27,907,200/720

20C6 = 38,760 different ways.

Hence, the interviewer can create the list in 38,760 different ways.

Answer:

how did not orderstan that

Answer:

5:8

Step-by-step explanation:

If I understand your question correctly, we have 1500/2400=15/24=5/8, so we have Lynn:Bo is 5:8, however, in the future please be more clear.

What is "estimates roof jon"? And, instead of saying "ratio to lynn to bo" say "What is the ratio of the estimates?" or whatever you're asking. If this answer is wrong, you only have yourself to blame.

We have

[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]

(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)

Recall for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

So we have

[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]

Answer:

If we have an integer number N, the opposite of N will be:

-1*N = -N.

Then, the opposite of 0°C is:

-1*0°C = 0°C.

The number 0 is it's own opposite.

And for 32F, the opposite is:

-1*32F = -32F

So, while the numbers 0°C and 32F physically represent the same thing (the same temperature), mathematically, they behave differently.

Step-by-step explanation:

Total catalysts = 10

Probability of 2 lower acidic catalysts = 2/10 = 1/5

Answer:

y= -(4x)

Step-by-step explanation:

Answer:

30 31 64 59 58 33 54 77 56 41 (arrange it)

30 31 33 41 54 56 58 59 64 77 (done!)

Mean: Find the number in the middle (54+56)/2= 110/2 = 55

Mode: None

Mean: (30+31+33+41+54+56+58+59+64+77)/10=503/10= 50,3

Answer:

(a) 658,008 different samples can be chosen.

(b) 222,111 samples will contain at least one defective board.

(c) The probability that a randomly chosen sample of five contains at least one defective board is 0.34.

Step-by-step explanation:

We are given that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects.

(a) To find how many different samples can be chosen, we will use a combination formula here because the order of selecting a sample of 5 from the production run of 40 doesn't matter.

Here, n = total sample = 40 and r = selected sample = 5

So, the combination formula is; [tex]^{n}C_r= \frac{n!}{r! \times (n-r)!}[/tex]

             [tex]^{40}C_5= \frac{40!}{5! \times (40-5)!}[/tex]

              [tex]^{40}C_5= \frac{40!}{5! \times 35!}[/tex]

              [tex]^{40}C_5[/tex] = 658,008 ways

So, 658,008 different samples can be chosen.

(b) To find how many samples will contain at least one defective board, we will first find how many samples will contain no or 0 defective board.

For this also, we will use a combination where n = 40 - 3 = 37 non-defective computer board and a sample of r = 5 computer boards.

So,          [tex]^{n}C_r= \frac{n!}{r! \times (n-r)!}[/tex]

             [tex]^{37}C_5= \frac{37!}{5! \times (37-5)!}[/tex]

              [tex]^{37}C_5= \frac{37!}{5! \times 32!}[/tex]

              [tex]^{37}C_5[/tex] = 435,897 ways

This means that 435,897 of the 658,008 samples will contain no defective board.

Now, the samples that will contain at least one defective board = Total samples - Samples that contain no defective board

           = 658,008- 435, 897

           = 222,111

(c) The probability that a randomly chosen sample of five contains at least one defective board is given by;

      Required Probability =  [tex]\frac{222,111}{658,008}[/tex]

                                         =  0.34 or 34%

Answer:

The equation is [tex]x(t) = -13 cos (8 \pi t )[/tex]

Step-by-step explanation:

From the question we are told that

      The  amplitude is  [tex]A = 13 \ in[/tex]

       The period is  [tex]T = 0.25[/tex]

Generally the displacement function for a simple harmonic motion is mathematically represented as

        [tex]x(t) = A cos (wt )[/tex]

Here  [tex]w[/tex] is the angular frequency which is mathematically represented as

          [tex]w = \frac{2 \pi }{T}[/tex]

substituting values

          [tex]w = \frac{2 \pi }{ 0.25}[/tex]

          [tex]w = 8\pi[/tex]

Given that at t =  0  the displacement is equal to 0 it means that there is no phase shift and also  we are told that it is initially moving downward which implies that its Amplitude is  [tex]A = -13\ in[/tex]

So the equation modeling the displacement d as a function of time t is mathematically represented as

          [tex]x(t) = -13 cos (8 \pi t )[/tex]

Answer:

a) The company sold 93 Chicken dinners, 76 Beef dinners and 31 Fish dinners.

b) [tex]y=3x^{2}-4x+2[/tex]

Step-by-step explanation:

a)

In order to solve part a of the problem, we must start by setting our variables up:

C=# of Chicken dinners

B=# of Beef dinners

F=# of Fish dinners

Next we can use these variables to build our equations. We start by taking the fact that they sold a total of 200 dinners. The sum of all the variables should add up to that so we get:

C+B+F=200

Then the problem tells us the price of each dinner and the total amount of money they made from selling the dinners that day:

"A TV Dinner Company Sells Three Types Of Dinners: A Chicken Dinner For $10, A Beef Dinner For $11, Or A Fish Dinner For $12. For A Grand Total Of $2138"

So we can use this information to build our second equation:

10C+11B+12F=2138

We have two equations now but three variables, so we need an additional equation so we can finish solving this. The problem tells us that:

"they sold three times as many chicken dinners as they did fish"

which translates to:

C=3F

so now we have enough information to finish solving the problem. We can start by substituting the last equation into the previous two equations so we get:

C+B+F=200

3F+B+F=200

4F+B=200

and

10C+11B+12F=2138

10(3F)+11B+12F=2138

30F+11B+12F=2138

42F+11B=2138

So now we can take the two bolded equations and solve them simultaneously. We can solve them by using any method we wish. Let's solve it by substitution.

We start by solving the first equation for B so we get:

B=200-4F

and now we substitute it into the second equation:

42F+11(200-4F)=2138

and now we solve for F

42F+11(200-4F)=2138

42F+2200-44F=2138

-2F=2138-2200

[tex]F=\frac{-62}{-2}[/tex]

F=31

So now that we know the value of F, we can find the values of the rest of the variables so we can take the previous equations to figure this out:

B=200-4F

B=200-4(31)

B=200-124

B=76

and finally:

C=3F

C=3(31)

C=93

So

The company sold 93 Chicken dinners, 76 Beef dinners and 31 Fish dinners.

b) For the second part of the problem we need to build a system of equations to find the equation we are looking for. We were given three points:

(-1,9), (2,6) and (3,17)

so we need to substitute each of the points on the given quadratic equation so we get:

[tex]9=a(-1)^{2}+b(-1)+c[/tex]

eq.1:  [tex]9=a-b+c[/tex]

[tex]6=a(2)^{2}+b(2)+c[/tex]

eq. 2:  [tex]6=4a+2b+c[/tex]

[tex]17=a(3)^{2}+b(3)+c[/tex]

eq. 3:  [tex]17=9a+3b+c[/tex]

So now that we have our three equations we can solve them simultaneously to get the values of a, b and c by using the method you feel more comfortable with. Let's solve it by elimination:

So let's take the first equations and let's subtract them:

[tex]9=a-b+c[/tex]

[tex]-6=-4a-2b-c[/tex]

-------------------------------

3=-3a-3b

And now we repeat the process with the first and third equations:

[tex]9=a-b+c[/tex]

[tex]-17=-9a-3b-c[/tex]

-------------------------------

-8=-8a-4b

So now we have two new equations we can solve simultaneously, but they can be simplified by dividing the first one into -3 and the second one into -4 so they become:

a+b=-1

2a+b=2

We can now solve them by substitution. Let's solve the first one for a and then let's substitute it into the second equation:

a=-1-b

let's substitute

2(-1-b)+b=2

and solve for b

-2-2b+b=2

-b=4

b=-4

Now we can find a:

a=-1-b

a=-1+4

a=3

and now we can find c:

c=9-a+b

c=9-3-4

c=2

So we can use these answers to build our equation:

[tex]y=ax^{2}+bx+c[/tex]

[tex]y=3x^{2}-4x+2[/tex]

[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto m\approx0.5[/tex]

Answer:

[tex]m=\frac{1}{2}[/tex]

Step-by-step explanation:

The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-4}{10-4}[/tex]

[tex]m=\frac{3}{6}[/tex]

[tex]m=\frac{1}{2}[/tex]

[tex]m=0.5[/tex]

a. y = 2.5x + 2000

b. The variable x represents the domain because the domain is the range of the possible x values.

c. x ≥ 0

d. The variable y represents the range because the range is the range of the possible y values.

e. y ≥ 2000

f. y = 2.5(25) + 2000

  y = 62.5 + 2000

  y = $2062.50

g. 2500 = 2.5x + 2000

   2.5x = 500

   x = 200

h. I am sorry I cannot make the graph but hopefully you can figure out how to make it using the info I have given in the above parts of the problem :)

A certain​ animal's body temperature has a mean of 94.72° F and a standard deviation of 0.57°F. Convert the given temperatures to z scores.

a. 93.52 °F  b. 95.22 °F      c. 94.72 °F

Answer:

a. z = - 2.1053

b. z = 0.87719

c. z = 0

Step-by-step explanation:

Given that :

The population mean μ = 94.72

The standard deviation σ = 0.57

the formula for calculating the standard normal z score, which can be represented as:

[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]

For  a.

The sample mean [tex]\bar x[/tex] = 93.52

The z score can be computed as follows:

[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]

[tex]z= \dfrac{93.52 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{-1.2}{0.57}[/tex]

z = - 2.1053

For  b.

The sample mean [tex]\bar x[/tex]  =  95.22    

[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]

[tex]z= \dfrac{95.22 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{0.5}{0.57}[/tex]

z = 0.87719

For  c.

The sample mean [tex]\bar x[/tex]  = 94.72

[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]

[tex]z= \dfrac{94.72 - 94.72}{0.57}[/tex]

[tex]z= \dfrac{0}{0.57}[/tex]

z = 0

Answer:

Step-by-step explanation:

we call the number X

x/5 is the fifth part of that number

I propose equality:

x + x/5 = 17

we add the fractions on the left side:

6x/5 = 17

We pass 5 to multiply to the other side:

6x = 5 * 17

6x = 85

we clear x

x = 85/6

x = 14.17

test

14.17 + 2.83 = 17

okay

Answer:

14.1666666667

Step-by-step explanation:

We can write the equation as:

x + x/5 = 17

=> 5/5x + 1/5x = 17

=> 6/5x = 17

=> 6x = 17 * 5

=> 6x = 85

=> x = 85/6

=> x = 14.1666666667

Let's check whether our answer is correct

=> 14.1666666667 + 14.1666666667 / 5 = 17

=> 14.1666666667 +  2.83333333333 = 17

=> 17 = 17

So, the answer is 14.1666666667

Answer:

Step-by-step explanation:

3\4 bc on a nuberline it would be 3 3\4

                                                        I--I----(etc)

so yeah hope i helped

Answer:

Final population after 10 years

= 288911718

Step-by-step explanation:

Present population p = 258,316,051

Rate of growth R%= 1.12%

Number of years t= 10 years

Number of times calculated n = 10

Final population A

= P(1+r/n)^(nt)

A= 258,316,051(1+0.0112/10)^(10*10)

A= 258,316,051(1+0.00112)^(100)

A= 258,316,051(1.00112)^100

A= 258,316,051(1.118442762)

A= 288911717.6

Approximately A= 288911718

Final population after 10 years

= 288911718

Answer:

136 cm²

Step-by-step explanation:

Surface area = 2(lw+wh+hl)

l = 7

w = 2

h = 6

so,

2(7×2+2×6+7×6)

= 136 cm²

Answer:

136 cm^2

Step-by-step explanation:

L 7cm

W 6cm

D 2cm

7 x 6 + 6 x 2 + 2 x 7 (x 2) = 68 x 2 = 136cm^2

━━━━━━━☆☆━━━━━━━

▹ Answer

80

▹ Step-by-Step Explanation

(2²)³ + (2³)² ÷ 4

Rewrite:

2⁶ + 2⁶ ÷ 2²

Divide:

2⁶ + 2⁴

Factor:

(2² + 1) * 2⁴

Evaluate:

(4 + 1) * 2⁴

Calculate:

5 * 16

= 80

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

y = 2.98x

Step-by-step explanation:

x = number of sketchbooks

y = total cost

Answer: .0228

Step-by-step explanation:  z = (6 − 10)/√4 = −2

P(X < 6) = .0228

Answer:

13.85

Step-by-step explanation:

U use the pythagorean theorem

So 2^2 + x^2 = 14^2

Simplify the equation: 4+x^2=196

--> x^2=192

--> x=13.85

-Hope this helps :)

9514 1404 393

Answer:

  c.  8√3

Step-by-step explanation:

The Pythagorean theorem applies.

  14² = s² + 2²

  s = √(14² -2²) = √192 = 8√3

The length of the remaining side is 8√3.

Answer:

1006

Step-by-step explanation:

Take proportion, p = 62%

n = (Z² * pq) / M.E²

Margin error = 0.03

p = 62% = 0.62

q = 1 - p = 1 - 0.62 = 0.38

Zcritical at 95% = 1.96

n = (1.96² * (0.62*0.38)) / 0.03²

n = 0.90508096 / 0.0009

n = 1005.6455

n = 1006

Sample size = 1006

Work Shown:

A = P*(1+r)^t

A = 21450*(1+(-0.08))^5

A = 21450*(1-0.08)^5

A = 21450*(0.92)^5

A = 21450*0.6590815232

A = 14137.29867264

A = 14,137.30

Notice how I used a negative r value to indicate depreciation rather than growth.

Answer:

Step-by-step explanation:

Given that v(x) = g(x)×(3/2*x^4+4x-1)

Let's find V'(2)

V(x) is a product of two functions

● V'(x) = g'(x)×(3/2*x^4+4x-1)+ g(x) ×(3/2*x^4+4x-1)

We are interested in V'(2) so we will replace x by 2 in the expression above.

g'(2) can be deduced from the graph.

● g'(2) is equal to the slope of the tangent line in 2.

● let m be that slope .

● g'(2) = m =>g'(2) = rise /run

● g'(2) = 2/1 =2

We've run 1 square to the right and rised 2 squares up to reach g(2)

g(2) is -1 as shown in the graph.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's derivate the second function.

Let h(x) be that function

● h(x) = 3/2*x^4 +4x-1

● h'(x) = 3/2*4*x^3 + 4

● h'(x) = 6x^3 +4

Let's calculate h'(2)

● h'(2) = 6 × 2^3 + 4

● h'(2) = 52

Let's calculate h(2)

●h(2) = 3/2*2^4 + 4×2 -1

●h(2)= 31

■■■■■■■■■■■■■■■■■■■■■■■■■■

Replace now everything with its value to find V'(2)

● V'(2) = g'(2)×h(2) + g(2)× h'(2)

● V'(2)= 2×31 + (-1)×52

●V'(2) = 61 -52

●V'(2)= 9