Simple linear regression methods can be used for studying relationship among maximum five variables. True False

Answers

Answer 1

Answer:

False.

Step-by-step explanation:

In a data where two variables are observed simultaneously, such data is termed to be Bivariate Data. When this data are represented graphically, such a diagrammatic representation is called scatter diagram. In a scatter diagram, all the points lie on or near one particular line. This line is called the regression line.

Recall that the equation for a straight line in the gradient intercept form is y = ax+b .

As an approximation , one can fit the regression line by first computing x and y. The regression line should pass through (x,y) in such a way that the remaining scatter points are evenly distributed on both sides of the line. Therefore, Simple linear regression methods can be used for studying relationship among maximum five variables is a false statement.


Related Questions

If f(x)=4x-6 and g(x) vx+2 what is (f*g)(7)

Answers

Answer: The value of (f*g)(7) is 66.

Step-by-step explanation:

Given functions: [tex]f(x)= 4x-6\text{ and } g(x)=\sqrt{x+2}[/tex]

Since, product of two functions: [tex](u*v)(x)=u(x)\times v(x)[/tex]

[tex](f*g)(x)=f(x)\times g(x)\\\\=4x-6\times \sqrt{x+2}\\\\\Rightarrow\ (f*g)(x)=(4x-6) \sqrt{x+2}[/tex]

[tex](f*g)(7)=(4(7)-6)\sqrt{7+2}\\\\=(28-6)\sqrt{9}\\\\=22\times 3=66[/tex]

Hence, the value of (f*g)(7) is 66.

How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 147 153 170 172 185 181 182 185 181 170 181 167 153 145

Answers

Answer:

Mean: 169.4

Median: 171

Mode: 181

Step-by-step explanation:

I first sorted the numbers by value, least to greatest.

145 147 153 153 167 170 170 172 181 181 181 182 185 185

We can see that 181 occurs the most, 3 times, so it's the mode.

The median of this set will be the middle number(s).

When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.

We can add all the numbers and divide by 14 to get the mean.

[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]

Hope this helped!

A researcher measures daily driving distance from college and weekly cost of gas for a group of commuting college students. What kind of correlation is likely to be obtained for these two variables?

Answers

Answer:

There is a positive correlation between these two variables.

Step-by-step explanation:

Positive correlation is an association amid two variables in which both variables change in the same direction.  

A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

As the distance covered by the vehicle increases the amount of gas consumed also increases. Thus, the weekly cost of gas will also increase.

Thus, there is a positive correlation between these two variables.

Consider a bag of jelly beans that has 30 red, 30 blue, and 30 green jelly beans. a) How many color combinations of 15 beans have at least 6 green beans

Answers

Answer:

680

Step-by-step explanation:

Number of red beans = 30

Number of Blue beans = 30

Number of green beans = 30

How many color combinations of 15 beans have at least 6 green beans?

Since at least 6 of the beans must be green,

Then (15 - 6) = 9

Then, the remaining 9 could be either red, blue or green.

Therefore, C(9 + (9 - 1), 3)

C(17, 3) = 17C3

nCr = n! ÷ (n-r)! r!

17C3 = 17! ÷ (17 - 3)! 3!

17C3 = 17! ÷ 14!3!

17C3 = (17 * 16 * 15) / (3 * 2)

17C3 = 4080 / 6

17C3 = 680 ways

Using the combination formula, it is found that there are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

The order in which the beans are chosen is not important, hence, the combination formula is used to solve this question.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Th total number of combinations of 15 beans from a set of 30 + 30 + 30 = 90 is:

[tex]C_{90,15} = \frac{90!}{15!75!} = 45795674000000000[/tex]

With less than 6 green, we have:

0 green:

[tex]C_{30,0}C_{60,15} = \frac{60!}{15!45!} = 53194089000000[/tex]

1 green:

[tex]C_{30,1}C_{60,14} = \frac{30!}{1!29!} \times \frac{60!}{14!46!} = 520376960000000[/tex]

2 green:

[tex]C_{30,2}C_{60,13} = \frac{30!}{2!28!} \times \frac{60!}{13!47!} = 2247585600000000[/tex]

3 green:

[tex]C_{30,3}C_{60,12} = \frac{30!}{3!27!} \times \frac{60!}{12!48!} = 5681396900000000[/tex]

4 green:

[tex]C_{30,4}C_{60,11} = \frac{30!}{4!26!} \times \frac{60!}{11!49!} = 9391696900000000[/tex]

5 green:

[tex]C_{30,5}C_{60,10} = \frac{30!}{5!25!} \times \frac{60!}{10!50!} = 10744101000000000[/tex]

Hence, the total for the number of combinations with less than 5 green is:

[tex]53194089000000 + 520376960000000 + 2247585600000000 + 5681396900000000 + 9391696900000000 + 10744101000000000 = 28638351000000000[/tex]

Subtracting the total amount of combinations from the number with less than 5 green, the number of combinations with at least 6 green is:

[tex]T = 45795674000000000 - 28638351000000000 = 17157323000000000[/tex]

There are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

A similar problem is given at https://brainly.com/question/24437717

if P(x)=1+6x-5x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit?

Answers

Answer:

600

Step-by-step explanation:

[tex]p(x) = 1 + 6x - 5x^2[/tex]

x max = [tex]-b/2a[/tex]

a = -5

b = 6

-6/2(-5) = 6/10 = 3/5 = .6

.6 thousand = 600

600 speakers should be sold.

Alternatively, you can check the vertex of the parabola formed.

4 solid cubes were made out of the same material. All four have different side lengths: 6cm, 8cm, 10cm, and 12cm. How to distribute the cubes onto two plates of a scale so the scale is balanced? Answer: A= the cube with side length 6 cm, B= the cube with side length 8 cm, C= the cube with side length 10 cm, D= the cube with side length 12 cm. On one side of the scale : , on the other side of the scale

Answers

Answer: The cube with side length of 12cm is alone in one plate, the other 3 cubes are in the other plate.

Step-by-step explanation:

We have 4 cubes with side lengths of:

6cm, 8cm, 10cm and 12cm.

Now, some things you need to know:

If we want a scale to be balanced, then the mass in both plates must be the same.

The volume of a cube of side length L is:

V = L^3

And the mass of an object of density D, and volume V is:

M = D*V.

As all the cubes are of the same material, all of them have the same density, so the fact that we do not know the value of D actually does not matter here.

Then we want to forms two groups of cubes in such a way that the total volume in each plate is the same (or about the same), the volumes of the cubes are:

Cube of 6cm:

V = (6cm)^3 = 216cm^3

Cube of 8cm:

V = (8cm)^3 = 512cm^3

Cube of 10cm:

V = (10cm)^3 = 1000cm^3

cube of 12cm

V = (12cm)^3 =  1728cm^3

First, if we add the volumes of the first two cubes, we have:

V1 = 216cm^3 + 512cm^3 = 728cm^3

Now we can see that we add 1000cm^3 the volume will be equal to the volume of the larger cube, so here we can also add the cube with side length of 10cm

Then the volume of the 3 smaller cubes together is:

V1 = 216cm^3 + 512cm^3 + 1000cm^3 = 1728cm^3.

Then, if we want to have the same volume in each plate, then we need to have the 3 smaller cubes in one plate, and the larger cube in the other plate.

In a recent​ year, the scores for the reading portion of a test were normally​ distributed, with a mean of and a standard deviation of . Complete parts​ (a) through​ (d) below. ​(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than . The probability of a student scoring less than is nothing. ​(Round to four decimal places as​ needed.) ​(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between and . The probability of a student scoring between and is nothing. ​(Round to four decimal places as​ needed.) ​(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than . The probability of a student scoring more than is nothing. ​(Round to four decimal places as​ needed.) ​(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. than 0.05. B. than 0.05. C. The event in part is unusual because its probability is less than 0.05. D. The events in parts are unusual because its probabilities are less than 0.05.

Answers

The question is incomplete. Here is the complete question.

In a recent year, the socres for the reading portion of a test were normally distributed, with a mean of 23.3 and a standard deviation of 6.4. Complete parts (a) through (d) below.

(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 18. (Round to 4 decimal places as needed.)

(b) Find a probability that a random selected high school student who took the reading portion of the test has a score that is between 19.9 and 26.7.

(c) Find a probability that a random selected high school student who took the reading portion of the test ahs a score that is more than 36.4.

(d) Identify any unusual events. Explain your reasoning.

Answer: (a) P(X<18) = 0.2033

              (b) P(19.9<X<26.7) = 0.4505

              (c) P(X>36.4) = 0.0202

               (d) Unusual event: P(X>36.4)

Step-by-step explanation: First, determine the z-score by calculating:

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

Then, use z-score table to determine the values.

(a) x = 18

[tex]z = \frac{18-23.3}{6.4}[/tex]

z = -0.83

P(X<18) = P(z< -0.83)

P(X<18) = 0.2033

(b) x=19.9 and x=26.7

[tex]z = \frac{19.9-23.3}{6.4}[/tex]

z = -0.67

[tex]z = \frac{26.7-23.3}{6.4}[/tex]

z = 0.53

P(19.9<X<26.7) = P(z<0.53) - P(z< -0.67)

P(19.9<X<26.7) = 0.7019 - 0.2514

P(19.9<X<26.7) = 0.4505

(c) x=36.4

[tex]z = \frac{36.4-23.3}{6.4}[/tex]

z = 2.05

P(X>36.4) = P(z>2.05) = 1 - P(z<2.05)

P(X>36.4) = 1 - 0.9798

P(X>36.4) = 0.0202

(d) Events are unusual if probability is less than 5% or 0.05. So, part (c) has an unusual event.

The probability will be:

(a) 0.2038

(b) 0.4046

(c) 0.0203

(d) Event in part (c) is unusual.

According to the question,

[tex]\mu = 23.2[/tex][tex]\sigma = 6.4[/tex]

Let,

"X" shows the test scores.

(a)

The z-score for X=18 will be:

→ [tex]z = \frac{X- \mu}{\sigma}[/tex]

      [tex]= \frac{18-23.3}{6.4}[/tex]

      [tex]= -0.828[/tex]

So,

The probability will be:

→ [tex]P(X<18) = P(z < -0.828)[/tex]

                     [tex]= 0.2038[/tex]

(b)

The z-score for X=19.9 will be:

→ [tex]z = \frac{X -\mu}{\sigma}[/tex]

     [tex]= \frac{19.9-23.3}{6.4}[/tex]

     [tex]= -0.531[/tex]

The z-score for X=26.7 will be:

→ [tex]z = \frac{X -\mu}{\sigma}[/tex]

      [tex]= \frac{26.7-23.3}{6.4}[/tex]

      [tex]= 0.531[/tex]

So,

The probability will be:

→ [tex]P(19.9 < X< 23.3) = P(-0.531 < z< 0.531)[/tex]

                                   [tex]= 0.4046[/tex]

(c)

The z-score for X=36.4 will be:

→ [tex]z = \frac{X -\mu}{\sigma}[/tex]

     [tex]= \frac{36.4-23.3}{6.4}[/tex]

     [tex]= 2.047[/tex]

So,

The probability will be:

→ [tex]P(X > 36.4 )= P(z > 2.047)[/tex]

                       [tex]= 0.0203[/tex]

(d)

Just because it's probability value is less than 0.05, so that the events is "part c" is unusual.

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algebra and trigonometry difference

Answers

Answer:

Algebra deals with knowing the value of unknown variables and functional relationships, while trigonometry touches on triangles, sides and angles and the relationship between them.

Algebra is more on polynomial equations, x and y while trigonometry more on sine, cosine, tangent, and degrees.

Trigonometry is much more complicated than algebra but algebra has its uses in our daily lives, be it calculating distance from point to another or determining the volume of milk in a milk container.

Step-by-step explanation:

Answer:

Although both Algebra II and Trigonometry involve solving mathematical problems, Algebra II focuses on solving equations and inequalities while Trigonometry is the study of triangles and how sides are connected to angles.

hope this answer helps u

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Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7

Answers

Rewrite 3 3/4 as an improper fraction

3 3/4 = 15/4

Now you have

15/5 / 5/7

When you divide fractions, change the division to multiplication and flip the second fraction over:

15/4 x 7/5

Now multiply the top numbers together and the bottom numbers together:

( 15 x 7) / (4 x 5) = 105/20

Write as a proper fraction:

105/20 = 5 1/4

Answer: 21/4 or 5 1/4

Explanation:
3 3/4 divide by 5/7
= 15/4 x 7/5
= 105/20
= 21/4 or 5 1/4

Twelve apples cost $2.00. How much will 50 apples cost?

Answers

Answer:

$8.33

Step-by-step explanation:

[tex]Solve \:using \: proportion\\\\12\:apples = \$ 2\\50\:apples = \$ x\\Cross \: Multiply\\\\12x = 100\\\\\\\frac{12x}{12} = \frac{100}{12} \\\\x = \$ 8.333[/tex]

Answer:

About $8.33.

Step-by-step explanation:

Write a proportion. Make sure the values line up horizontally:

[tex]\frac{12\text{ apples}}{\$2} =\frac{50\text{ apples}}{\$x}[/tex]

Cross multiply:

[tex]100=12x\\x=25/3\approx\$8.33[/tex]

6. If x + 2 is the only factor of the polynomial P(x),then P(2) is:
Options:
A. Cannot be determined
B. Not Zero
C. R(2)
D. Zero

Answers

Answer:

P(x) = x + 2p(2) = 2 + 2 p(2) = 4

So option B is the answer.

If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) is Not Zero. Therefore, the option B is the correct answer.

What is standard form of a polynomial?

Suppose the considered polynomial is of only one variable.

Then, the standard form of that polynomial is the one in which all the terms with higher exponents are written on left side to those which have lower exponents.

Given information;

If x + 2 is the only factor of the polynomial P(x) then we need to find the P(2) :

P(x) = x + 2

p(2) = 2 + 2

p(2) = 4

The P(2) is Not Zero.

Therefore, the option B is the correct answer.

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The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Answers

Answer:

The Width = 65.44 inches

The Height = 36.81 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Using Pythagoras Theorem we known that:

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 75²

We are given ratio: 16:9 as aspect ratio

Width = 16x

Height = 9x

(16x)² +(9x)² = 75²

= 256x² + 81x² = 75²

337x² = 5625

x² = 5625/337

x² = 16.691394659

x = √16.691394659

x = 4.0855103303

Approximately x = 4.09

For the newer 75 inch tv set

The Height = 9x

= 9 × 4.09

= 36.81 inches

The Width = 16x

= 16 × 4.09

= 65.44 inches.

Find the distance between the points. Give an exact answer and an approximation to three decimal places.
(3.1,0.3) and (2.7. - 4.9)
The exact distance is
(Simplify your answer. Type an exact ans

Answers

Answer:  sqrt(27.2) =approx 5.215

Step-by-step explanation:

The distance between 2 points can be calculated using Phitagor theorem

L= sqrt( (x1-x2)²+(y1-y2)²)

Where x1, y1 are the coordinates of the first point and  x2, y2 are the coordinates of the 2-nd point.

L=sqrt((3.1-2.7)²+(0.3-(-4.9))²)= sqrt(0.4²+5.2²)=sqrt(27.2) - this is exact answer.

sqrt(27.2)=5.21536...=approx 5.215

a sheet metal worker earns $26.80 per hour after receiving a 4.5% raise. what was the sheet metal worker's hourly pay before raise? Round your answer to the nearest cent

Answers

Answer

$25.59

Step-by-step explanation:

subtract by percentage or you can also do:

100% - 4.5% = 95.5%

95.5% x $26.80 = $25.594

IF ROUNDED: $25.59

Answer:

$25.65

Step-by-step explanation:

Let the original hourly rate be r.  

Then 1.045r + $26.80/hr.

Dividing both sides by 1.045, we get:

      $26.80/hr

r = ------------------ = $25.65  This was the before-raise pay rate.

         1.045

Solve for x: 3(x + 1)= -2(x - 1) + 6.

Answers

Answer:

x=1

Step-by-step explanation:

3(x + 1)= -2(x - 1) + 6.

Distribute

3x+3 = -2x+2+6

Combine like terms

3x+3 = -2x+8

Add 2x to each side

3x+3+2x = 8

5x+3 = 8

Subtract 3 from each side

5x =5

Divide by 5

x =1

A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.

(a) If the initial distribution for states A, B, and C is P0 = ( 1/3 , 1/3 , 1/3 ), find the distribution of X2

(b) Find the steady state distribution by solving πP = π.

Answers

Answer:

A) distribution of x2 = ( 0.4167 0.25 0.3333 )

B) steady state distribution = [tex]\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}[/tex]

Step-by-step explanation:

Hello attached is the detailed solution for problems A and B

A) distribution states for A ,B, C:

Po = ( 1/3, 1/3, 1/3 )  we have to find the distribution of x2 as attached below

after solving the distribution

x 2 = ( 0.4167, 0.25, 0.3333 )

B ) finding the steady state distribution solving

[tex]\pi p = \pi[/tex]

below is the detailed solution and answers

Find the distance between points P(5, 1) and Q(3, 4) to the nearest tenth.
3.6
5
9.4
13

Answers

Answer:

≈ 3.6

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)

d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]

   = [tex]\sqrt{(-2)^2+3^2}[/tex]

   = [tex]\sqrt{4+9}[/tex]

    = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )

Answer:

3.6

Step-by-step explanation:

Look above bru

Algebra Review

Write an algebraic expression for each verbal expression.

1. the sum of one-third of a number and 27

2. the product of a number squared and 4

3. Write a verbal expression for 5n^3 +9.

Answers

Answer:

Step-by-step explanation:

1. The sum of one-third of a number and 27

= [tex]\frac{1}{3}\times x +27\\= 1/3x +27[/tex]

2. The product of a number squared and 4

[tex]Let\:the\:unknown\: number\: be \:x\\\\x^2\times4\\\\= 4x^2[/tex]

3.Write a verbal expression for 5n^3 +9.

The sum of the product and of 5 and a cubed number and 9

About how many feet are in 3.6 kilometers? 1 m = 39.37 in

Answers

Answer:

11811 feet

Step-by-step explanation:

Hope it helps!

There are about 11,812 feet in 3.6 kilometers.

To convert kilometers to feet, we need to use the conversion factor:

1 kilometer = 3,280.84 feet.

Now, to find how many feet are in 3.6 kilometers,

we can multiply 3.6 by the conversion factor:

So, 3.6 kilometers x 3,280.84 feet/kilometer

= 11,811.504 feet.

Thus, Rounded to a whole number, there are about 11,812 feet in 3.6 kilometers.

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Suppose we want to choose 6 colors, without replacement, from 14 distinct colors. (a) How many ways can this be done, if the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?

Answers

Answer:

(a) 2,162,160

(b) 3,003

Step-by-step explanation:

(a) order matters

You can choose from 14 for the first pick. Then you have 13 left for the second pick. Then you have 12 left for the third pick. Keep going until you have 9 left for the 6th pick. The number when order matters is:

total = 14 * 13 * 12 * 11 * 10 * 9 = 2,162,160

(b) Order does not matter

Start with the same number as above for picking 6 out of 14. Since order does not matter, we divide by the number of ways you can arrange 6 items.

Since there are 6! ways of arranging 6 items,

total = 2,162,160/6! = 3,003

The number of ways when the order matters are 121080960.

The number of ways when order does not matters are 3003.

Given,

Choose 6 colors, without replacement, from 14 distinct colors.

We have to find:

- How many ways can this be done, if the order of the choices matters.

- How many ways can this be done if the order of the choices does not matter.

What are permutation and combination?

We use permutation when the order of the arrangements matters.

It is given by:

[tex]^ nP_r[/tex] = n! / r!

We use combination when order does not matter.

It is given by:

[tex]^nC_{r}[/tex] = n! / r! (n-r)!

Find the number of ways when order matters.

We have,

n = 14 and r = 6

[tex]^{14}P_{6}[/tex]

= 14! / 6!

= (14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6!) / 6!

= 4 x 13 x 12 x 11 x 10 x 9 x 8 x 7

= 121080960

Find the number of ways when order does not matter.

We have,

n = 14 and r = 6

[tex]^{14}C_{6}[/tex]

= 14! / 6! 8!

= 14 x 13 x 12 x 11 x 10 x 9 / 6 x 5 x 4 x 3 x 2

= 7 x 13 x 11  x 3  

= 3003

Thus,

The number of ways when the order matters are 121080960.

The number of ways when order does not matters are 3003.

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Use the model to show to help find the sum 0.34 plus 0.49

Answers

Answer/Step-by-step explanation:

The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.

Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.

The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].

Using the model, we can solve 0.34 + 0.49.

Add both fractions together.

[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]

[tex] \frac{83}{100} = 0.83 [/tex]

(3) In a group of 60 seldiers have enough food for
20 days - How many soldiers should leave the group
so that the food is enough for 100 days ? Find it.​

Answers

Answer:

48 soldiers

Step-by-step explanation:

60 soldiers                    20 days

x soldiers                       100 days

60 x 20 = 1200 = 100x

Therefore x = 1200/100 = 12

60 - 12 = 48

Hope that helped!!! k

Answer:

30 Soldiers

Step-by-step explanation:

Given:

1) No of soldiers=60

No of days=20

2) No of days=100

No of soldiers=?

No of soldiers to leave=?

Solution:

Let us use the cross multiplication method.

Let x be the no of soldiers.

No of days                                     No of  soldiers

1) 20                                                     60

2) 100                                                    x

by cross multiplying,

20x=100 x 60

20x=600

x=600/20

x=30 soldiers

Therefore, No of soldiers to leave =60-30=30 soldiers

State the correct polar coordinate for the graph shown:

Answers

Answer:

Solution : ( - 5, 5π / 4 )

Step-by-step explanation:

There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. Let's start by listing coordinates when r is positive. r here is 5 units from the positive x - axis.

( 5, θ ) theta here is between 30 and 60 degrees, so we can say it's about 45 degrees.

( 5, θ ) theta here is the remaining negative side of 360 - 45 = 315. That would make it - 315.

And when r is negative ( r < 0 ),

( - 5, θ ) now the point is going to lie on the ray pointing in the opposite direction of the terminal side of theta. This will be 45 degrees more than 180, or 180 + 45 = 225 degrees.

Right away we know that ( - 5, 225° ) is our solution, we don't have to consider the second case. Converting 225 to radians in terms of π will be 5π / 4 radians, giving us a solution of ( - 5, 5π / 4 ) or option b.

What is the rise over run for the slope -11/9

Answers

Answer:  11 down and 9 right

Step-by-step explanation:

Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down

and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.

Given slope = -11/9

the numerator is -11 so the "rise" is  DOWN 11 units

the denominator is 9 so the "run" is RIGHT 9 units

A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?

Answers

Answer:

b = - 3.7

Step-by-step explanation:

here are the data values:

x   y          XY        X²

14 46         644       196

15 49         735       225

16 37          592      256

17 42          714        289

18 37          666      324

19 31           589      361

20 25         500      400

21 23          483       441

22 20         440       484

23 15          345       529

24 12         288       576

now we are required to find the summation (total) of all values of X, Y, XY and X².

∑X = 209

∑Y = 337

∑XY = 5996

∑X² = 4081

The formular for finding b is given as:

b = n∑XY - (X)(Y) / n∑X² - (∑X)²

= 11(5996) - (209)(337) / 11(4081) - (209)²

= 65956 - 70433 / 44891 - 43681

= -4477/ 1210

= -3.7

The question asked us to find the value of b but we can  go further to find the equation of the regression line:

a = ∑Y - b∑X / n

= 337 - (-3.7)(209)/  11

=1110.3/11

= 100.94

the equation is:

Y = 100.94 - 3.7X

I hope you find my solution useful!

=

An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

418 421 421 422 425 428 431 435 437
438 445 447 448 453 458 462 465
(c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.) Note that it is plausible that the given sample observations were selected from a normal distribution and there are no outliers.

(___ , ___)



Does the interval suggest that 441 is a plausible value for true average degree of polymerization?

Yes or No


Does the interval suggest that 451 is a plausible value?

Yes or No

Answers

Answer:

Step-by-step explanation:

Form a set of values we get

n = 17

And with the help of a calculator

μ₀ = 438,47

σ  = 14,79

Normal Distribution is :  N ( 438,47 ; 14,79 )

c)

CI = 95 % means  α = 5 %    α/2 = 2,5 %    α/2 = 0,025

and as n < 30  we should use t-student distribution with n -1 degree of freedom  df = 16.  t score for 0,025 and 16 s from t-table 2,120

By definition:

CI = [  μ₀  ±  t α/2 ; n-1 * σ/√n ]

CI = [  μ₀  ± 2,120* 14,79/√17 ]

CI = [  μ₀  ±  7,60 ]

CI = [ 438,47 ± 7,60 ]

CI = [  430,87 ; 446,07 ]

95% confidence interval for true average degree of polymerization is  [430.87 ; 446.07] and this interval suggest that 441 is a plausible value for true average degree of polymerization and also this interval does not suggest that 451 is a plausible value.

Given :

Sample = [ 418, 421, 421, 422, 425, 428, 431, 435, 437,  438, 445, 447, 448, 453, 458, 462, 465 ]95% confidence interval.

The total number of values given is, n = 17

Mean, [tex]\mu_0=438.47[/tex]

Standard Deviation, [tex]\sigma = 14.79[/tex]

The normal distribution is given by: N (438.47 ; 14.79)

If Cl  is 95% then [tex]\alpha[/tex] is 5% and [tex]\alpha /2[/tex] is 2.5%

[tex]\alpha /2 = 0.025[/tex]

Now, use t-statistics distribution with (n-1) degree of freedom df = 16

So, the t score for 0.025 and 16 s from t-table 2.120.

[tex]\rm Cl = [\mu_0 \pm t_{\alpha /2};(n-1)\times \dfrac{\sigma}{\sqrt{n} }][/tex]

[tex]\rm Cl = [\mu_0 \pm 2.120\times \dfrac{14.79}{\sqrt{17} }][/tex]

[tex]\rm Cl = [\mu_0 \pm 7.60][/tex]

Cl = [430.87 ; 446.07]

Yes, the interval suggests that 441 is a plausible value for true average degree of polymerization.

No, the interval does not suggest that 451 is a plausible value.

For more information, refer to the link given below;

https://brainly.com/question/2561151

If AD=2/3AB, the ratio of the length of BC to the length of DE is A. 1/6 B. 1/4 C. 3/2 D. 3/4

Answers

Answer:

The correct answer is c

Step-by-step explanation:

Answer:

C.) 3/2

Explanation:

PLATO

The cost in dollars y of producing x computer
desks is given by y = 40x + 4000
X
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $6200. (Hint: Find x when y = 6200.)
a. Complete the table.
х
100
200
300
y
b. For $6200,_ computer desks can be produced

Answers

Answer:

a.

y= 40x +4000

x= 100 --> y= 40(100)+4000= 4000+4000=8000

x=200 --> y= 40(200)+4000= 6000+4000= 10000

x=300 --> y= 40(300)+4000= 12000+4000= 16000

(in $)

b.

y= 40x+4000

6200= 40x+4000

6200-4000= 40x

2200= 40x

2200/40= x

55= x

(in unit)

Step-by-step explanation:

I hope this helps

if u have question let me know in comments ^_^

(-1, 4) and (-2, 2).

Answers

Answer:

Slope : 2

slope-intercept: y = 2x + 6

Point-slope (as asked): y - 4 = 2 (times) (x + 1)

standered: 2x - y = -6

Step-by-step explanation:

Find the product of the roots of the equation
xl-5x - 36 = 0

Answers

Answer:

Step-by-step explanation:

Hello, I assume that you mean

[tex]x^2-5x-36[/tex]

The product is -36.

[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]

So in this example, it means that the sum is 5 and the product is -36.

Thank you

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