100 pointer and will mark brainliest thank you. Hi! I ask that you provide a digital scatter plot image of this graph and predict the line of best fit and make sure to sketch it on the graph aswell. Thank you. Arm Span (inches) Height (inches) 58 60 49 47 51 55 19 25 37 39 44 45 47 49 36 35 41 40 46 50 58 61 And then provide the answers to these questions about the scatter plot which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined. What does the slope of the line represent within the context of your graph? What does the y-intercept represent Test the residuals of two other points to determine how well the line of best fit models the data. Use the line of best fit to help you to describe the data correlation. Using the line of best fit that you found, approximate how tall is a person whose arm span is 66 inches According to your line of best fit, what is the arm span of a 74-inch-tall person

100 Pointer And Will Mark Brainliest Thank You. Hi! I Ask That You Provide A Digital Scatter Plot Image

Answers

Answer 1

I used arm span as the x-axis and height as the y-axis; arm span is the independent variable because height is typically dependent on arm span. Although the opposite could be argued for.

The equation of the line of best fit is y= 12+(7/9)x. To get the slope I used the points (37,39) and (19,25). The slope is therefore 14/18=7/9. The slope represents that height increases by 7/9 inches when arm span increases by 1 inch. The y-intercept 12 represents roughly the height when arm size is very small. I tested the residuals of the points (47,49) and (58,61). The respective predictions are 48.556 and 57.111. The respective residuals are then (49-48.556)=0.444 and (61-57.111)=3.889. It seems that the line models the data well until the x values get larger, where the performance decreases. The line of best fit with its positive slope indicates that there is a positive correlation with arm span and height.

Using the model, a person with arm span 66 inches has a height of 12+(7/9)*66= 63.333 inches. A person with 74 inches height has an estimated arm span of 62*9/7= 79.714 inches.

100 Pointer And Will Mark Brainliest Thank You. Hi! I Ask That You Provide A Digital Scatter Plot Image
Answer 2

The equation of best  fitted line is given as follows

[tex]\rm y = 0.955x+ 3.787 \\with \; R^2 = 0.951[/tex]

The y  intercept 3.787 represents the  height of that is independent of Arm span.

The height of the person whose arm span is 66 inches is 66.817 inch.

The arm span of a person whose height is 74 inches is 73.52 inch

According to the given data the arm span  and heights are given in inches

Using Microsoft excel we can draw the scatter plot of both the variables such that arm span is on X axis and Height is on Y axis

The  image for the excel work done showing calculations and scatter plot  is attached.

Now we can fit the linear tread line and  to find out the equation of fitted line just tick on the " show equation" line option of trend line fitting

The equation of best  fitted line is given as follows

[tex]\rm y = 0.955x+ 3.787 .....(1) \\with \; R^2 = 0.951[/tex]

Slope of line of best fit = 0.955

So we can conclude that height (Y) is related to Arm span according to equation (1)

Equation (1) shows the equation of line of best fit for the given data

The y  intercept 3.787 represents the  height of that is independent of Arm span.

So the height of the person whose arm span is 66 inches is given following

[tex]\rm y = 0.955 \times 66+ 3.787 \\y = 66.817 \; inch[/tex]

Similarly the arm span of a person whose height is 74 inches

[tex]\rm 74 = 0.955x +3.787 \\x = 73.52 \; inches[/tex]

For more information please refer to the link given below

https://brainly.com/question/2659237

100 Pointer And Will Mark Brainliest Thank You. Hi! I Ask That You Provide A Digital Scatter Plot Image

Related Questions

Find the P​-value in a test of the claim that the mean IQ score of acupuncturists is equal to​ 100, given that the test statistic is z2.00.

Answers

Answer:

P-value = 0.0455

Step-by-step explanation:

In this question, we are concerned with calculating the P- value in a test.

Mathematically we know that;

P-value = 2 * P(Z > |z|)

Please check attachment for complete solution and by step explanation

Line l has a slope of −6/13. The line through which of the following pair of points is perpendicular to l? A. (13,−4),(−7,2) B. (6,−4),(−7,2) C. (2,6),(−4,−7) D. (6,9),(−4,−4)

Answers

Answer: Choice C.  (2,6) and (-4,-7)

=========================================================

Explanation:

The original line has a given slope of -6/13. The opposite reciprocal is 13/6. We flip the fraction and the sign from negative to positive.

With any two perpendicular slopes, they always multiply to -1

(-6/13)*(13/6) = (-6*13)/(13*6) = -78/78 = -1

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

Since the perpendicular slope is 13/6, we need to see which of the four answer choices produces a slope of 13/6. Use the slope formula.

This is something you do through trial and error. You could start with A and work your way to D, or just pick at random. I'll go through each one by one starting at choice A.

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

Let's try choice A

m = (y2 - y1)/(x2 - x1)

m = (2 - (-4))/(-7 - 13)

m = (2 + 4)/(-7 - 13)

m = 6/(-20)

m = -3/10, we can see that choice A is not the answer, since we want m = 13/6 instead.

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

Let's try choice B

m = (y2 - y1)/(x2 - x1)

m = (2 - (-4))/(-7 - 6)

m = (2 + 4)/(-7 - 6)

m = 6/(-13)

m = -6/13, that doesn't work either

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

Let's try choice C

m = (y2 - y1)/(x2 - x1)

m = (-7 - 6)/(-4 - 2)

m = -13/(-6)

m = 13/6, we found the answer

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

For the sake of completeness, here is what choice D would look like

m = (y2 - y1)/(x2 - x1)

m = (-4 - 9)/(-4 - 6)

m = -13/(-10)

m = 13/10, which isn't the slope we want

name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)

Answers

Answer:

Step-by-step explanation:

Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.

- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.

∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]

- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.

∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]

- Angles having the same relative positions at the point of intersection are the corresponding angles.

∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]

- Co interior angles are the angles between the parallel lines located on the same side of the transversal.

∠4 and ∠5, ∠3 and ∠6 [Co interior angles]

- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.

∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]

1+3^2⋅2−5 order of operations

Answers

The order for operations:

()
^
* /
+ -

So,
1+3^2*2-5 =
1+((3^2)*2)-5 =
1+(9*2)-5 =
1+18-5 =
14

Answer:

Below

Step-by-step explanation:

● 1 + 3^2 × 2 -5

Start by calculating 3^2 wich is 9

● 1 + 9 × 2 -5

Multiply 2 by 9 (9×2=18)

● 1 + 18 -5

Add 1 to 18 (1+18 = 19)

● 19 -5

Substract 5 from 19 (19-5 = 14 )

● 14

Which expression is equivalent to 73 ⋅ 7−5? 72 77 1 over 7 to the 2nd power 1 over 7 to the 7th power

Answers

Answer:

  1/7^2

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  a^-b = 1/a^b

__

Then your expression simplifies to ...

  [tex]7^3\cdot 7^{-5}=7^{3-5}=7^{-2}=\boxed{\dfrac{1}{7^2}}[/tex]

Answer:

The answer is 1/7^2

Step-by-step explanation:

I took the test lol

36 minus 20 minus 32 times 1/4

Answers

Answer:

6

Step-by-step explanation:

36 - 20 - 32 x 1/4

=> 36 - 20 - 32/4

=> 36 - 20 - 8

=> 36 - 28

=> 6

find x, if sq.root(x) +2y^2 = 15 and sq.root(4x) - 4y^2=6

Answers

Answer:

Example: solve √(2x−5) − √(x−1) = 1

isolate one of the square roots:√(2x−5) = 1 + √(x−1) square both sides:2x−5 = (1 + √(x−1))2 ...

expand right hand side:2x−5 = 1 + 2√(x−1) + (x−1) ...

isolate the square root:√(x−1) = (x−5)/2. ...

Expand right hand side:x−1 = (x2 − 10x + 25)/4. ...

Multiply by 4 to remove division:4x−4 = x2 − 10x + 25.

Answer:

Step-by-step explanation:

ewrerewrwrwerrwer

Using the constant of proportionality, determine how much water will be in the bathtub after 2.5 minutes.

Answers

Answer:

[tex]\boxed{41.25}[/tex]

Step-by-step explanation:

Hey there!

Well we know the constant of proportionality is 16.5 because on the table it states 1 minute is 16.5 gallons.

So we can set up the following,

W = 2.5*16.5

W = 41.25

Hope this helps :)

Answer:

The amount of water in the bathtub after 1 minute is 16.5 gallons. So, the amount of water in the tub after 2.5 minutes of filling will be

2.5 minutes × 16.5 gallons per minute = 41.25 gallons.

There will be 41.25 gallons of water in the bathtub after 2.5 minutes.

Step-by-step explanation:

7.19 We are given the following probability distribution. x P(x) b. c. d. 0 1 2 3 .1 .4 .3 .2 a. Calculate the mean, variance, and standard deviation.

Answers

Answer:

Mean = 1.6

Variance = 0.84

Standard deviation = 0.916

Step-by-step explanation:

We are given the following probability distribution below;

            X                         P(X)              [tex]X \times P(X)[/tex]         [tex]X^{2} \times P(X)[/tex]

            0                          0.1                     0                        0

            1                           0.4                   0.4                     0.4

            2                          0.3                   0.6                     1.2

            3                          0.2                  0.6                    1.8      

         Total                                               1.6                    3.4    

Now, the mean of the probability distribution is given by;

         Mean, E(X) =  [tex]\sum X \times P(X)[/tex]  = 1.6

Also, the variance of the probability distribution is given by;

        Variance, V(X) =  [tex]\sum X^{2} \times P(X) - (\sum X \times P(X))^{2}[/tex]

                                 =  [tex]3.4 - (1.6)^{2}[/tex]

                                 =  3.4 - 2.56 = 0.84

And the standard deviation of the probability distribution is given by;

          Standard deviation, S.D. (X) =  [tex]\sqrt{Variance}[/tex]

                                                         =  [tex]\sqrt{0.84}[/tex]  = 0.916.

When ________ angles made by two lines and a transversal are supplementary, the lines are parallel. Question 20 options: A) corresponding B) same side interior C) alternate exterior D) alternate interior

Answers

Answer:

B) same side interior

Step-by-step explanation:

Supplementary angles are angles that can add up to the sum of angles on a straight line, [tex]180^{0}[/tex]. While a transversal in a line that passes through two parallel lines at two points.

If two lines are parallel to each other and a transversal through the lines, the sum of either same side interior angles would be supplementary.

The correct option for the given question is B, same side interior.

Answer:

B

Step-by-step explanation:

Write the polar form of a complex number in standard form for [tex]8[cos(\frac{\pi}{2}) + isin(\frac{\pi}{2})][/tex]

Answers

Answer:

Solution : 8i

Step-by-step explanation:

We can use the trivial identities cos(π / 2) = 0, and sin(π / 2) = 1 to solve this problem. Let's substitute,

[tex]8\left[cos\left(\frac{\pi }{2}\right)+isin\left(\frac{\pi \:}{2}\right)\right][/tex] = [tex]8\left(0+1i\right)[/tex]

And of course 1i = i, so we have the expression 8(0 + i ). Distributing the " 8, " 8( 0 ) = 0, and 8(i) = 8i, making the fourth answer the correct solution.

I will mark u brainleiest if u help me and 5 stars

Answers

Answer:

[tex]\boxed{50}[/tex]

Step-by-step explanation:

Because the initial temperature is 40 degrees and it increases by 10, add the two values together to get the final temperature.

40 + 10 = 50

Therefore, the final answer is 50 degrees.

Answer:

50

Step-by-step explanation:

If it starts at 40 degrees and increases 10 degrees, it is going to be 50 degrees.  Increases means adding, so it is asking you to add 10 to 40 which is 50.  If it asks decreases in the future you will have to subtract.

Which angle of rotation is determined by the matrix below?{1/2 -sqrt3/2 sqrt3/2 1/2] 30° 60° 120° 300°

Answers

Answer:

  60°

Step-by-step explanation:

You have the rotation matrix ...

  [tex]\left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]=\left[\begin{array}{cc}\dfrac{1}{2}&-\dfrac{\sqrt{3}}{2}\\\dfrac{\sqrt{3}}{2}&\dfrac{1}{2}\end{array}\right][/tex]

This tells you the angle of rotation is ...

  [tex]\tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(\dfrac{\sqrt{3}}{2}\right)}{\left(\dfrac{1}{2}\right)}=\sqrt{3}\\\\\theta=\arctan{\sqrt{3}}=60^{\circ}[/tex]

The angle of rotation is 60°.

Answer:

B----- 60

Step-by-step explanation:

PLEASE I NEED HELP 30 POINTS AND BRAINLYEST Order from least greatest 3.5, -2.1, square root of 9, -7/2, and square root of 5

Answers

Answer:

-7/1, -2.1, square root of 5, square root of 9, and last 3.5

Step-by-step explanation:

Square root of 9 is 3.

Square root of 5 is 2.24

-7/2 as a decimal is -3.5

So, from least to greatest order is:

-7/2 > -2.1 > Square root of 5 > Square root of 9 > 3.5

A survey of undergraduates revealed the follwoing information: WOMEN MENsample mean weight 124.7 183.3sample standard deviation of weight 23.32 25.41sample proportion Roman Catholic 0.40 0.32Sample mean GPA 3.34 3.24Sample standard deviation of GPA 0.35 0.44Sample size 20 25Assume the populations are normally distributed. Suppose you want to determine whether the proportion of SCU women who are Roman Catholic is greater than the proportion of SCU men that are Roman Catholic.a. What are the null and alternative hypothesis to run this test?b. What is the calculated value of the test statistic?c. What is the p-value of the calculated test statistic?d. What is the conclusion of the hypothesis test, at 5% the significance level?

Answers

Answer:

the answers are below:

Step-by-step explanation:

a. null hypothesis:

H0: Pw - Pm = 0 (so Pw = Pm)

alternate hypothesis:

H1: Pw - Pm > 0 (so Pw > Pm)

where Pw is the proportion of women

Pm is the proportion of men

b.) proportion of women = o.40

proportion of men =  0.32

sample size of women = 20

sample size of men = 25

[tex]z = 0.4 - 0.32/ \sqrt{((0.4 *0.6)/20) * (0.32 * 0.68)/25)}[/tex]

[tex]z = 0.56[/tex]

c.) p value =

p(z>0.56)

= 0.7123

= 1 - 0.7123

= o.2877 which can be approximated to be 0.288

d. alpha value was set at 0.05

the p value is greater than alpha.

therefore it is not statistically significant.

we conclude that the proportion of roman catholic women is not greater than men.

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's.
a. What is the minimum score needed to make an A?
b. What is the maximum score among those who received an F?
c. If there were 5 students who did not pass the course, how many students took the course?

Answers

Answer:

a)  z (score) 1,53

b)  z ( score) - 1,96

c) 200 students

Step-by-step explanation:

Normal Distribution N ( 74;10)

a) From z-table, and for 6,3 %  ( 0,063 ) we find the z (score) 1,53

Note : 6,3 % or 0,063 is the area under the curve, the minimum score neded to get A

b) To fail   2,5 %  ( 0,025 ) from z-table  get - 1,96

c) If the group of  student who did not pass the course (5) correspond to 2,5 % then by simple rule of three

5                 2,5

x ?               100

x = 500/2,5

x = 200

How do I solve? Show with steps.

Answers

Step-by-step explanation:

or,[(√-x-1)+(√x+9)]^2=4^2

or,(√-x-1)^2+2√(-x-1)(x+9)+(√x+9)^2=16

or,-x-1+2√-x^2-10x-9 +x+9=16

or,2√-x^2-10x-9=8

or,√-x^2-10x-9=4

squaring on both sides

or,-x^2-10x-9=16

or,-x^2-10x=25

or,-x(x+10)=25

Either,

x=-25 or, x=15.

1. Transform the polar equation to a Cartesian (rectangular) equation: 2. Transform the Cartesian (rectangular) equation to a polar equation: y^2 = 4x

Answers

Answer:

Attachment 1 : 5x + 6y = 5, Attachment 2 : 4cotθcscθ

Step-by-step explanation:

Remember that we have three key points in solving these types of problems,

• x = r cos(θ)

• y = r sin(θ)

• x² + y² = r²

a ) For this first problem we need not apply the third equation.

( Multiply either side by 5 cos(θ) + 6 sin(θ) )

r [tex]*[/tex] ( 5 cos(θ) + 6 sin(θ) ) = 5,

( Distribute r )

5r cos(θ) + 6r sin(θ) = 5

( Substitute )

5x + 6y = 5 - the correct solution is option c

b ) We know that y² = 4x ⇒

r²sin²(θ) = 4r cos(θ),

r = 4cos(θ) / sin²(θ) = 4 cot(θ) csc(θ) = 4cotθcscθ - again the correct solution is option c

write a letter to your friend in Ghana stating your experience in your presentation school in nigeria​

Answers

Answer:

hi Ghana how are you doing I am fine here. I really miss u and my friends in the old.U know what in Nigeria this school is really awesome and fantastic we have a swimming pool here and we can go to trip and we can have many things here I really loved this school.

at starting I was not have any friends and know I have many friends. But I really miss u this is what about our . Come to my house I can show you my school it is very near to my house .

Ur friend

writ ur name

I need help on this question :(​

Answers

Answer: 40 degree

Explanation:

FT bisect angle EFD dividing it into 2 equal angles (EFT and DFT)

And EFD = 80

We get :
EFT = 80/2
EFT = 40

And EFT + DFT = EFD = 80 degree

Therefore EFT = 40 degrees

Twice one number added to another number is 18. if the 2nd number is equaled to 12 less than 4 times the 1st number, find the two numbers

2x + y= ? ; y= ?x - ?​

Answers

Answer:

8

Step-by-step explanation:

Math Word Problem: Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the number.?

Let the two numbers be x and y

As per statement twice one number added to another number is 18.

2x + y = 18

y = 18 - 2x…Eq..1

Four times the first number minus the other number is 12.

4x - y = 12…Eq..2

Now substituting the value of y from Eq..1 to Eq..2

4x - y = 12

4x - (18 - 2x) = 12

4x - 18 + 2x = 12

4x + 2x = 12 + 18

6x = 30

x = 30 / 6

x = 5

Thus one number is 5. Now calculating the other number by putting the value of x in Eq. 1

y = 18 - 2x

y = 18 - 2×5

y = 18 - 10

y = 8

Other number is 8

Answer the two numbers are 5 and 8

Let us check the correctness of answer by putting the value of x and y in Eq. 1

y = 18 - 2x

8 = 18 - 2 × 5

8 = 18 - 10

8 = 8

Means answer is correct

2x + y = 18
y = 4x - 12

2x + y = 18
2x + (4x - 12) = 18
6x - 12 = 18
6x = 30
x = 5

y = 4x - 12
y = 4(5) - 12
y = 20 - 12
y = 8

Therefore the first number is 5 and the second number is 8.

If the occurrence of one event does not influence the outcome of another event, then two events are:
A. conditional
B. disjoint
C. independent
D. interdependent

Answers

Answer:

C. Independent

Step-by-step explanation:

Independent events are events that have no impact on each other.

So, if the occurrence of an event doesn't influence the outcome of another, this means that they are independent because they do not impact each other.

This must mean C is correct because the two events have to be independent.

If In (x) = 3.53, what is the value of x ?

Answers

I need more information please ?

what are the next terms in the number pattern -11, -8, -5, -2, 1

Answers

Answer:

4, 7, 10, 13

Step-by-step explanation:

Hey there!

Well in the given pattern,

-11, -8, -5, -2, 1

we can conclude that the pattern is +3 every time.

-11 + 3 = -8

-8 + 3 = -5

-5 + 3 = -2

-2 + 3 = 1

And so on

4, 7, 10, 13

Hope this helps :)

120 meals to 52 meals what is the percentage change?

Answers

Answer: The percentage change is 56.67%.

Step-by-step explanation:

From 120 meals to 52 meals, change in meals = ( 120- 52) meals

= 68 meals

The percentage change = [tex]\dfrac{\text{change in meals}}{\text{Original quantity of meals}}\times100[/tex]

[tex]=\dfrac{68}{120}\times100\\\\=56.67\%[/tex]

Hence, the percentage change is 56.67%.

4(x/2-2) > 2y-11 which of the following inequalities is equivalent to the inequality above?
1) 4x+2y-3 > 0
2) 4x-2y+3 > 0
3) 2x+2y-3 > 0
4) 2x-26+3 > 0

Answers

4) 2x-2y+3 > 0

although it is spelt "26" on the choices

what is the least common denominator of 1/8, 2/9, and 3/12

A. 864

B. 108

C. 72

D. 48

Answers

Answer:

c. 72

Step-by-step explanation:

you just have to see what is the lowest number the three denominators: 8, 9, 12, all go into

8 times 9=72 and 12 times 6=72, which makes answer choice C. &2 the least common denominator for the fractions 1/8, 2/9, and 3/12.

Answer:

c.72 he's right love you guys byeee you all welcome

Step-by-step explanation:

A linear regression analysis uses two distinct types of data. The first are variables that are at least nominal level.
a) true
b) false

Answers

Answer:

The answer is

A. True

Step-by-step explanation:

In linear regression, Linear models make a prediction using a linear function of the input features, with one being

For regression, the general prediction formula for a linear model looks as follows:

ŷ = w[0] * x[0] + w[1] * x[1] + ... + w[p] * x[p] + b

Here, x[0] to x[p] denotes the features (in this example, the number of features is p)

of a single data point, w and b are parameters of the model that are learned, and ŷ is

the prediction the model makes. For a dataset with a single feature, this is

ŷ = w[0] * x[0] + b

which you might remember from high school mathematics as the equation for a line.

Here, w[0] is the slope and b is the y-axis offset. For more features, w contains the

slopes along each feature axis. Alternatively, you can think of the predicted response

as being a weighted sum of the input features, with weights (which can be negative)

given by the entries of w.

1. Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The sum is 6, given that the green one is either 4 or 1.
2. Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The red one is 6, given that the sum is 11.

Answers

Answer:

1. 1/6

2. 1/6

Step-by-step explanation:

Let A be the event that the sum of the two die is 6 and B be an event that the green die is either 4 or 1.

The conditional probability will be given by P (A/B) = P (A∩B)/ P (B).

Now the total sample space consists of 36 outcomes .

And to find (A∩B) we need to find the outcomes in which green die is either 4 or 1 and the sum of the two die is 6.

So when green is 1 red must be 5

So when green is 4 red must be 2

So there are two ways in which green die is either 4 or 1 and the sum of the two die is 6.

Therefore the probability of (A∩B)= P (A∩B)= 2/36= 1/18

Now we find the probability of green die having 4 or 1

So when green is 4 red can have all the numbers from 1- 6

And when green is 1 red can have all the numbers from 1- 6

The total number would be 12 .

So probability of green die having 1 or 4 is given by = P (B)= 12/36

Now the conditional probability = P (A/B) = P (A∩B)/ P (B)=1/18/ 1/3

= 3/18= 1/6

2. Similarly we find the conditional probability of the two die when the red one is 6, given that the sum is 11.

When red is 6 the green must be 5 to get 11. So the probability

=P (A∩B)=  1/36

Now we find the probability of red die having 6 =P(B)= 6/36

Now the conditional probability = P (A∩B)/P(B) =  1/36/ 6/36= 1/6

Answer 1:

Let A be the event that the sum of the two die is 6 Let B be an event that the green die is either 4 or 1.

Conditional probability Formula :

P (A/B) = P (A∩B)/ P (B).

Total sample space=36 outcomes

Conditions are :

So when green is 1 red must be 5 So when green is 4 red must be 2 So there are two ways in which green die is either 4 or 1 and the sum of the two die is 6.

The probability of (A∩B)= P (A∩B)= 2/36= 1/18

Now we find the probability of green die having 4 or 1

When green is 4 red can have all the numbers from 1- 6

And when green is 1 red can have all the numbers from 1- 6

Total number = 12

 P (B)= 12/36

Therefore, conditional probability = P (A/B)

P (A/B) = P (A∩B)/ P (B) P (A/B)=1/18/ 1/3  P (A/B)= 3/18 P (A/B)= 1/6

The conditional probability of the indicated event when two fair dice  are rolled will be 1/6.

Answer 2:

Let A be the event that the sum of the two die is 6 Let B be an event that the green die is either 4 or 1. The sum is 11.

Condition :

When red is 6 the green must be 5 to get 11.

P (A∩B)=  1/36

The probability of red die having 6 =P(B)= 6/36

The conditional probability= P (A∩B)/P(B)

P (A∩B)/P(B) =  1/36/ 6/36P (A∩B)/P(B)= 1/6

The conditional probability of the indicated event when two fair dice are 1/6.

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Solve the following equations
x-1=6/x​

Answers

[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]

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