The formula for the slope a of the regression line is:
a = r(sy/sx)
The reason for the connection between the value of r and the slope of the least squares line has to do with the formula that gives us the slope of this line. For paired data (x,y) we denote the standard deviation of the x data by sx and the standard deviation of the y data by sy.
The formula for the slope a of the regression line is:
a = r(sy/sx)
The calculation of a standard deviation involves taking the positive square root of a non-negative number. As a result, both standard deviations in the formula for the slope must be nonnegative. If we assume that there is some variation in our data, we will be able to disregard the possibility that either of these standard deviations is zero. Therefore the sign of the correlation coefficient will be the same as the sign of the slope of the regression line.
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Can someone explain how to solve this problem
Answer: [tex]\displaystyle 2x^4 + 9x^3-8x^2+9x -13[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle (2x^4 + 9x^3 -8)-(8x^2-9x+5)[/tex]
Subtract the second term:
[tex]\displaystyle (2x^4 + 9x^3 -8)-8x^2+9x-5[/tex]
Reorder by the power's degree:
[tex]\displaystyle 2x^4 + 9x^3-8x^2+9x -8-5[/tex]
Combine like terms:
[tex]\displaystyle 2x^4 + 9x^3-8x^2+9x -13[/tex]
Jimmy went on a tour to Europe with $5,000. He spent 4/25 of it on hotel accommodation, 3/20 of it on airfare 1/10 of it on shopping and 1/5 on the remainder How much more did he spend on hotel accommodation than on food?
Answer:
Jimmy spent 4/25 of his $5,000 budget on hotel accommodation, which is equal to $2,000. He spent 3/20 of his budget on airfare, which is equal to $1,500, 1/10 of his budget on shopping, which is equal to $500, and 1/5 of his budget on the remainder, which is equal to $1,000. This means that Jimmy spent $2,000 on hotel accommodation, which is $500 more than he spent on food.
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Use the Binomial Theorem to expand (a+b)^15. You can use your calculator to determine the coefficient. Write the step.
Binomials include formulas such as a + b, x - y, etc. For the expansion of a binomial raised to exponents 2 and 3, we have a set of algebraic identities. Examples are (a + b)2 = a2 + 2ab + b2.
What Are Binomial Expansion Formulas?Let us review the definition of a "binomial" before understanding the formulas for binomial expansion. An expression in algebra with two terms is called a binomial.
Binomials include formulas such as a + b, x - y, etc. For the expansion of a binomial raised to exponents 2 and 3, we have a set of algebraic identities. Examples are (a + b)2 = a2 + 2ab + b2.
However, what happens if the exponents are larger numbers? The expansion can be difficult to locate manually.
This procedure is made simpler using the binomial expansion formula. Learn the formula for the binomial expansion and a few examples with solutions.
The expansion of (a + b)3 can be found in Example 1.
Solution:
The sum of (a plus b)3
by applying the binomial expansion formula,
(x + y)n = nC 0 xn y0 + nC 1 xn-1 y1 + nC 2 xn-2 y2 + nC 3 xn-3 y3 +... + nC n 1 x yn-1 + nC n x0yn
(a + b)
3 = 3C
0 a3 + 3C
1 a(3 - 1) (3 - 1) b + 3C
2 a(3 - 2) (3 - 2) b2 + 3C
3 a(3 - 3) b3
= ( 3! / [(3-0)!0!] ) a3 + ( 3! / [(3-1)!1!] ) a(3 - 1) (3 - 1) b + ( 3! / [(3-2)!2!] ) a(3 - 2) (3 - 2) b2 + ( 3! / [(3-3)!3!] ) a(3 - 3) b3
= (a3 first) + (a2 second) + (a1 second) + (a0 third)
= a3 + 3 a2, b + 3 a b2, and b3
(A + B)3 = A3 + 3 A2 B + 3 A B 2 + B3.
The Complete Question.
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I NEED HELP ON THIS ASAP!
I need help on questions 2a and b
Answer:
a) Since the question is asking for a disjunction, involving an or, this means that the answer to the question can be either solution, not both.
b) Conjunction involves an "and" so it means both answers
Step-by-step explanation:
Consider the following parametric equations. Answer parts a through d. x=t?. y=t+4: -4 st 54 a. Make a brief table of values oft, x, and y t -4 -2 0 2 4 X(t) 16 4 0 16 y 0 2 26 B (Type integers or decimals.)
The table of x, y and t for the given parametric equations is
The Table is as follows:
t -4 -2 0 2 4
x 16 4 0 4 16
y 0 2 4 6 8
The parametric equations are given:
x = t², y = t + 4; -4 ≤ t ≤ 4
if t = -4
x = (-4)² = 16
y = -4 + 4 = 0
if t = -2
x = (-2)² = 4
y = -2 + 4 = 2
if t = 0
x = (0)² = 0
y = 0 + 4 = 4
if t = 2
x = (2)² = 2
y = 2 + 4 = 6
if t = 4
x = (4)² = 16
y = 4 + 4 = 8
The Table is as follows:
t -4 -2 0 2 4
x 16 4 0 4 16
y 0 2 4 6 8
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What is the measure of y
[tex]3 \sqrt{13} [/tex]
Absolute Value Functions:
Determine the value of y, if x is -7
Answer:
y = 17
Step-by-step explanation:
the absolute value always gives a positive value , that is
| - a | = | a | = a
given
y = | x | + 10 ( substitute x = - 7 into the equation )
y = | - 7 | + 10 = | 7 | + 10 = 7 + 10 = 17
What is the solution to the equation?
√2x+10 -6=2
Please show the steps! I will give brainliest!
The solution to the equation is x = 27
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
√2x+10 -6=2
Add 6 to both sides of the equation
This gives
√2x+10 = 8
Square both sides
So, we have the following representation
2x + 10 = 64
Subtract 10 from both sides
2x = 54
Divide by 2
x = 27
Hence, the solution is 27
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Identify the inital amount (a) and the rate of growth a a prevent y=100000(1. 09)^3
To identify the initial amount (a) and rate of growth in the equation y=100000(1.09)^3, you can use algebra to isolate the variables.
First, divide both sides of the equation by 100000 to get y/100000=(1.09)^3. Then, take the cube root of both sides of the equation to get y/100000=1.09.
Finally, multiply both sides of the equation by 100000 to get y=109000. Therefore, the initial amount (a) is 100000, and the rate of growth is 1.09.
The initial amount, also known as the starting point or the base value, is the value of a variable at the beginning of a given period.
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Drake ue 9/4 cup of ugar to make 9 mug of brownie. How much ugar i required to make one brownie?
Drake uses 9/4 cup of sugar to make 9 mug of brownie. Then the amount of sugar needed to make one brownie is 1/4 cup of sugar.
Determine how much sugar is needed
These are the specified parameters:
9/4 cup of sugar to make 9 mug of brownie.
Determine much sugar to make one brownie
Lots of sugar = cup of sugar : mug of brownie
= 9/4 : 9
= 9/4 × 1/9
= 1/4
So the amount of sugar needed to make one brownie is 1/4 cup of sugar.
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What is the quotient of (x4 − 3x3 + 6x2 − 12x + 8) ÷ (x − 1)?
The quotient of the division is x^3 - 2x^2 + 4x - 8
How to determine the quotientFrom the question, we have the following parameters that can be used in our computation:
quotient of (x4 − 3x3 + 6x2 − 12x + 8) ÷ (x − 1)?
Using the long division method of quotient, we have
x - 1 | x^4 - 3x^3 + 6x^2 - 12x + 8
The division steps are as follows
x^3 - 2x^2 + 4x - 8
x - 1 | x^4 - 3x^3 + 6x^2 - 12x + 8
x^4 - x^3
------------------------------------------------
-2x^3 + 6x^2 - 12x + 8
-2x^3 + 2x^2
------------------------------------------------
4x^2 - 12x + 8
4x^2 - 4x
------------------------------------------------
-8x + 8
-8x + 8
----------------------------------------------------
Hence, the quotient is x^3 - 2x^2 + 4x - 8
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Find the value of z.
15 cm
5 cm
82=
20 cm
Give your answer correct to 1
decimal place.
Z
Submit Answer
cm
Answer:
z=12.25
Step-by-step explanation:
first we are going to find the hypotenus x
of the first part of the tiangle as shown in my diagram, using the Pythagoras rule-
hyp= x
opp= 15
adj=5
thus hypothenus²=opposite²+adjacent²
x²=15²+5²
x²=225+25
x²=250
the you use √ to find x
√x²=√250
x=15.81
step 2= to find z
hyp=20
opp:z
adj:15.81
hyp²=opp²+adj²
20²=z²+15.81²
400=z²+250
z²+250=400
z²=400-250
z²=150
√z²=√150
z=12.25
Answer:
z ≈ 12.2 cm
Step-by-step explanation:
using Pythagoras' identity in the 2 right triangles.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
consider the right triangle on the left
let the third side, the hypotenuse be x , then
x² = 5² + 15² = 25 + 225 = 250
consider the right triangle on the right , then
x² + z² = 20²
250 + z² = 400 ( subtract 250 from both sides )
z² = 150 ( take square root of both sides )
z = [tex]\sqrt{150}[/tex] ≈ 12.2 cm ( to 1 decimal place )
An air traffic controller is tracking two planes. To start, Plane A was at an altitude of 800 meters, and Plane B was at an altitude of 360 meters. Plane A is gaining altitude at 15 meters per second, and Plane B gaining altitude at 25 meters per second . Let x be the number of seconds that have passed
a) The expressions are given as follows:
Plane A: A(t) = 800 + 15t.Plane B: B(t) = 360 + 25t.b) The will be at the same altitude at a time of: 44 seconds.
How to model the situation?The situation is modeled by linear functions in slope-intercept format, as follows:
y = mx + b.
In which:
The slope m represents the rate at which the planes are gaining altitude.The intercept b represents the initial altitude.Hence the functions are defined as follows:
Plane A: A(t) = 800 + 15t.Plane B: B(t) = 360 + 25t.The planes will have the same altitude when:
A(t) = B(t)
Hence:
800 + 15t = 360 + 25t
10t = 440
t = 44 seconds.
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5 1/3 + 7 1/4 = ?
Pls help
Answer:
13 7/12
Step-by-step explanation:
5+7+13
4/12+3/12+7/12
Consider a triangle ABC like the one below. Suppose that B=64°, C=72°, and c=19. (The figure is not drawn to scale.) Solve the triangle. Round your answers to the nearest tenth. I found angle A which is 44
Answer:
[tex]m\angle A = 44\textdegree, a = 13.9, b = 18.0[/tex]
Step-by-step explanation:
Step 1: Solve for the Missing Angle
The measures of all of the interior angles of a triangle will always add up to [tex]180\textdegree[/tex]. Therefore,
[tex]m\angle A = 180\textdegree - (m\angle B + m\angle C) = 180\textdegree - (64\textdegree + 72\textdegree) = 44\textdegree[/tex]
Step 2: Solve for the Missing Sides
When we are given the side lengths and angle measures of a triangle, we can use either the Law of Sines or the Law of Cosines to solve for the rest of the triangle.
The Law of Sines is as follows: [tex]\frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c}[/tex]
The Law of Cosines is as follows: [tex]c^{2} = a^{2} +b^{2} -2abcosC[/tex] (you can exchange c for a or b, respectively)
In this case, we are only given 1 side length and all 3 angle measures, so it would be more appropriate to use the Law of Sines as we need at least 2 side lengths to use the Law of Cosines.
Now that we know which formula to use, let's start by solving for [tex]a[/tex], using the given values of [tex]c=19[/tex], [tex]\angle A = 44\textdegree[/tex], and [tex]\angle C = 72\textdegree[/tex].
Substituting these values in, we get:
[tex]\frac{sinA}{a} = \frac{sinC}{c} \\ \frac{sin44\textdegree}{a} = \frac{sin72\textdegree}{19}\\a=\frac{19sin44\textdegree}{sin72\textdegree} \approx \bf 13.9[/tex]
Repeating this process for [tex]b[/tex], this time using [tex]\angle B = 64\textdegree[/tex], we get:
[tex]\frac{sinB}{b} = \frac{sinC}{c} \\ \frac{sin64\textdegree}{b} = \frac{sin72\textdegree}{19}\\b=\frac{19sin64\textdegree}{sin72\textdegree} \approx \bf 18.0[/tex]
Lowest common multiple for 1080, 1188, 1815
Answer:
To find the lowest common multiple (LCM) of 1080, 1188, and 1815, we need to find the smallest number that is a multiple of all three numbers.
One way to find the LCM is to use prime factorization. We can prime factorize each number and then multiply the highest exponent of each prime factor to get the LCM.
1080 = 2^4 * 3^3
1188 = 2^2 * 3 * 199
1815 = 5 * 11 * 163
The LCM is:
2^4 * 3^3 * 5 * 11 * 163 = 1080 * 11 * 163
So the LCM of 1080, 1188, 1815 is 207940.
the general form of a large-sample (1) 100onfidence interval for a population proportion p is where is the sample proportion of observations with the characteristic of interest.true or false
True, the general form of a large-sample 100% confidence interval for a population proportion p is where is the sample proportion of observations with the characteristic of interest.
The general form of a large-sample 100% confidence interval for a population proportion p is given by the formula:
p ± z(standard error of p)
where p is the sample proportion of observations with the characteristic of interest and z is the critical value from a standard normal distribution corresponding to the desired level of confidence (e.g. z = 1.96 for a 95% confidence interval). The standard error of p is calculated as the square root of (p(1-p)/n), where n is the sample size.
This formula is based on the central limit theorem and the assumption that the sample is random and large enough (n > 30). In this case, the distribution of p is approximately normal and the confidence interval provides a range of plausible values for the true population proportion.
Correct Question :
The general form of a large-sample 100% confidence interval for a population proportion p is where is the sample proportion of observations with the characteristic of interest. True or false.
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25.A fruit seller bought 600 bananas at Rs.16 a dozen. He sold 200 of
them at 4 for Rs.5 and the remaining at 2 for Rs.3. Find gain or loss
percent.
Which ordered pair represents point F?
Responses
(0, 5)
(0, -5)
(5, 0)
(-5, 0)
Answer:
(-5, 0)
Step-by-step explanation:
Answer:
D (-5,0)
Step-by-step explanation:
OOOOOOOOOOOOOOOOOOOOOOOO
The growth rate of Covid patient is 5% per hour. If the number of Covid patient in the morning 8:00 am is 44,100, what was the number before 2 hours?
Answer:
the answer to this question is 6:00
The number of patients before 2 hours is 40,000.
What is Percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.
As per the given data:
The growth rate of covid patients is given and number of patients at 8:00 am is 44,100.
We have to find out what was the number before 2 hours.
Growth rate (G) = 5% per hour.
Number of patients at 8 : 00 AM = 44,100
Let's assume the number of patients 2 hours before is P.
Patients after two hours:
P(1 + G/100)^2
= P(1 + 5/100)^2
= P(1.05)^2
= 1.1025P
From the given data:
1.1025P = 44,100
P = 40,000
The number of patients before 2 hours is 40,000.
Hence, The number of patients before 2 hours is 40,000.
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What is the slope of the line that contains the points (2, -8) and (-4, 4)?
O2
112
id
2
O-2
Answer:
-2
Step-by-step explanation:
Δy =4- (-8) =12
Δx = -4 -2 = -6
12/(-6) =-2
how to compute the mean median and mode of three sets of scores
To compute the median of three sets of scores, we need to arrange the scores in order from smallest to largest and then select the middle score.
Mean, median and mode are measures of central tendency and are used to describe the central value of a set of data. The mean is the average of all the values in the set, the median is the middle value and the mode is the most frequently occurring value.
To compute the mean of three sets of scores, we need to sum up all the scores and divide by the total number of scores. This can be represented by the formula:
Mean = (Score1 + Score2 + Score3) / 3
To compute the median of three sets of scores, we need to arrange the scores in order from smallest to largest and then select the middle score. This can be represented by the formula:
Median = (Score2 + Score3) / 2
To compute the mode of three sets of scores, we need to identify the score that occurs the most frequently. This can be represented by the formula:
Mode = Most Frequently Occurring Score
For example, if the three scores are 3, 7, and 4, then the mean is (3 + 7 + 4) / 3 = 4.67, the median is (3 + 4) / 2 = 3.
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find the ratios and reduce them in their lowest terms. 1m and 75 cm
Answer:
4:3
Step-by-step explanation:
1m = 100cm
75cm = 75cm
ratio of 1m:75cm
(100cm:75cm)÷25 = 4:3
so 1m:75cm = 4:3
Someone please Help. My brain is dead rn with this! (Btw can you put in a explanation with the answers, please and thank You)
1. The 08 08 bus takes 89 minutes to go from Birmingham to Coventry
2. The latest time Chris have to leave his house is 7:26
How to solve the problem?The bus time table shows that only two buses will leave can meet up with Chris resuming time. The bus 7:05 and the bus that leave by 7: 33
Calculating the latest time Chris could leave his home is by taking the second bus.
7 minutes to walk from his house to his bus stop. Therefore the 7minutes is deducted from the starting time of the second bus.
7:33-7minutes = 7: 26 am
Therefore the latest time he should leave home to meet up with 9:30 am resuming is 7:26 am
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Select the correct answer. The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation: 2n + 1 = 157. What is the first number? A. 77 B. 78 C. 79 D. 80
Answer:
The equation 2n + 1 = 157 represents the situation where the sum of two consecutive numbers is 157.
To find the first number, we can start by subtracting 1 from both sides of the equation:
2n = 156
Then we can divide both sides by 2:
n = 78
So the first number is 78, which corresponds to the answer choice B.
Step-by-step explanation:
a set of qualitative statistical techniques that are used to combine the results of multiple, independent research events to arrive at a summary statement about the data is the definition of .
Meta-analysis is a set of qualitative statistical techniques used to combine the results of multiple, independent research events to arrive at a summary statement about the data.
It is used to identify patterns across studies and to synthesize the results from different studies into a coherent and comprehensive interpretation of the research results. Meta-analysis is commonly used in medical research to identify treatments that are most effective, as well as in social sciences to determine the impact of a policy or program on a population.
Meta-analysis is also used to compare different theories and studies, to evaluate the strength of studies, and to identify any gaps in the existing research. By combining data from multiple studies, meta-analysis can provide a more robust and accurate summary of the effects of a particular intervention or program.
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how many micrograms are in 65.3 kg?
The total number of micrograms present in the 65.3 kilograms is equal to 65,300,000,000 micrograms.
Conversion of units from kilogram to grams is :
1 kilogram = 1,000 grams
Conversion of units from grams to micrograms is :
1 grams = 1,000,000 micrograms
⇒ 1 kilogram = ( 1,000 × 1,000,000 ) micrograms
⇒1 kilograms = 1,000,000,000 micrograms
Substitute the required value for the converting kilogram to micrograms we get,
⇒ 65.3 kilograms = ( 65.3 × 1,000,000,000 ) micrograms
⇒65.3 kilograms = 65,300,000,000 micrograms
Therefore, the total quantity of micrograms in 65.3 kilograms is equal to 65,300,000,000 micrograms.
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Question ID 111294, seed 6439
The graph illustrates a normal distribution for the prices paid for a particular model of HD television. The mean price paid is $1600 and the standard deviation is $95.
What is the approximate percentage of buyers who paid more than $1790?
__________________%
What is the approximate percentage of buyers who paid between $1505 and $1695?
__________________%
What is the approximate percentage of buyers who paid between $1600 and $1885?
__________________%
What is the approximate percentage of buyers who paid between $1410 and $1600?
__________________%
What is the approximate percentage of buyers who paid more than $1885?
__________________%
What is the approximate percentage of buyers who paid between $1600 and $1695?
__________________%
The percentage of buyers who paid more than $1790 is 2.275%.
The percentage of buyers who paid between $1505 and $1695 is 68.29%
The percentage of buyers who paid between $1600 and $1885 is 15.73%
What is z score?The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
Given:
Let X be a random variable representing the prices paid for a particular model of HD television.
It is provided that X follows a normal distribution with mean, μ = $1600 and standard deviation, σ = $95.
1. P(X> 1790)
= P( Z> (1790- 1600)/ 95)
= P(Z> 2)
= 1- P(z< 2)
= 1- 0.97725
= 0.02275
= 2.275%
2. P( 1505 < X < 1695)
= P( -1 < Z < 1)
= 0.68269
3. P( 1600 < X < 1885)
= P( 1 < Z < 3)
= P( Z< 3 ) - P(Z < 1)
= 0.99865 - 0.84134
= 0.15731
4. P( 1410 < X < 1600)
= P( - 2 < Z < 0)
= P( Z< 0 ) - P(Z < -2)
= 0.5 - 0.02275
= 0.47725
5. P (X> 1885)
= P( Z> 3)
= 1- P(Z<3)
= 0.0013
= 0.13%
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4. a rate constant is found to triple when the temperature is increased from 275 k to 300. k. at what temperature will the rate constant be five times greater than the rate constant at 275 k? report your answer in k.
The temperature at which the rate constant becomes five times greater than the rate constant at 275 K is 325 K.
Let's say that temperature is represented by t and the rate constant is represented by r.
Let' say r₁ = R, r₂ = 3R, t₁ = 275 K and t₂ = 300 K.
considering the relationship between rate constant and temperature is linear.
t - 300 = [(300 - 275)/(3R - R)](r - 3R)
t - 300 = (25/2R)(r - 3R)
We are asked to determine the temperature at which the rate constant becomes five times greater than the rate constant at 275 K.
t - 300 = (25/2R)(5R - 3R)
t - 300 = (25/2R)(2R)
t - 300 = 25
t = 325 K
Hence, the temperature at which the rate constant becomes five times greater than the rate constant at 275 K is 325 K.
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1. (2 points) your box of cereal may be a contest winner! it's rattling, which 100% of winning boxes do. of course, 1% of all boxes rattle and only one box in a million is a winner. what is the probability that your box is a winner? show details calculations 2. (3 points) someone rolls a fair six-sided die and you win points equal to the number shown. what is the expected number of points after one roll? after 2 rolls? after 100 rolls?
The probability that your box is a winner is 1/10,000,000.
The probability that your box is a winner can be calculated as the probability of a box rattling and being a winner, divided by the probability of a box rattling.
P(Winner | Rattle) = 1/1,000,000
P(Rattle) = 1/100
P(Winner) = P(Winner | Rattle) * P(Rattle)
= (1/1,000,000) * (1/100)
= 1/10,000,000
a. The expected number of points after one roll is the average of the possible outcomes, which are 1, 2, 3, 4, 5, and 6.
The average is (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5.
b. The expected number of points after two rolls is the average of the possible outcomes of the sum of two rolls.
For example, the possible outcome of 2 rolls could be (1,1), (1,2), (1,3), ..., (6,6).
The average of these 36 possible outcomes is 7.
c. The expected number of points after 100 rolls is the average of the possible outcomes of the sum of 100 rolls, which would be approximately 350.
This is because the expected value for each roll is 3.5, and for 100 rolls it would be 100 * 3.5 = 350.
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