PLSSS.the function : ℝ → ℝ, () = 2^, : (0; +∞) → ℝ, () = √4 + 1 + 1.show
that the graphs of the functions and intersect at the abscissa point x=2
Answers
[tex]f(2) = g(2) = 4[/tex], which means that the graphs of the two functions intersect at x = 2.
What is the abscissa point?To show that the graphs of the functions [tex]f(x) = 2^x[/tex] and [tex]g(x) = \sqrt(4x + 1) + 1[/tex] intersect at the abscissa point x = 2, we need to show that both functions have the same value at [tex]x = 2.[/tex]
First, we evaluate f(2):
[tex]f(2) = 2^2 = 4[/tex]
Next, we evaluate g(2):
[tex]g(2) = \sqrt(4(2) + 1) + 1 = \sqrt9 + 1 = 4[/tex]
Therefore, [tex]f(2) = g(2) = 4[/tex] , which means that the graphs of the two functions intersect at [tex]x = 2[/tex] .
To visualize this, we can plot the two functions on the same set of axes:
As we can see from the graph, the two curves intersect at the point (2, 4).
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The complete question is: How can you show that the graphs of the functions f(x) = [tex]2^x[/tex] and g(x) = √(4x + 1) + 1 intersect?
Related Questions
Write an equation (any form) for the quadratic graphed below
Answers
Answer:
[tex]y = -2(x - 1)^2 + 3[/tex]
Step-by-step explanation:
The given figure which is a quadratic is the shape of a parabola
The general vertex form equation of a parabola is
[tex]y = a(x - h)^2 + k[/tex]
where,
( h, k ) is the vertex and a is a constant
Looking at the figure we see the vertex is at [tex](1, 3)[/tex]
So the equation of the parabola is
[tex]y = a(x - 1)^2 + 3[/tex]
To compute the constant [tex]a[/tex] take a point (x, y) through which the parabola passes, plug in these x, y values into the above equation and solve
The parabola passes through point [tex](3, -5)[/tex]
Plugging
[tex]x = 3, y = -5[/tex]
gives
[tex]- 5 = a(3-1)^2 + 3\\\\-5 = a\cdot 2^2 + 3\\\\-5 = 4a + 3\\\\-5-3=4a\\\\-8 = 4a\\\\a = -8/4 = -2\\\\[/tex]
Therefore the equation of the given quadratic(parabola) is
[tex]y = -2(x - 1)^2 + 3[/tex]
help please
the triangle above has the following measures. q = 7cm m
Answers
Answer:
Put your calculator in degree mode.
sin(35°) = 7/r
r sin(35°) = 7
r = 7/sin(35°) = 12.2 cm
-3 > 5 -b
Please help
Answers
Step-by-step explanation:
To solve the inequality:
-3 > 5 - b
We can start by isolating the variable b on one side of the inequality. We can do this by subtracting 5 from both sides of the inequality:
-3 - 5 > -b
Simplifying the left-hand side of the inequality, we get:
-8 > -b
To isolate b, we can multiply both sides of the inequality by -1. When we do this, we need to reverse the inequality sign:
8 < b
So the solution to the inequality is:
b > 8
This means that b must be greater than 8 for the inequality to be true.
The amount of money in a savings account increases by 0.2% every month.
Part A
Write a function for the amount of money in the account, B, after t months with an initial deposit of $100.
B(t) =
(
)t
Part B
By what factor does the amount in the account increase every month? Every year? Every 5 years? Round answers to the nearest thousandth.
each month:
each year:
every five years:
Answers
a) A function for the amount of money in the account, B, after t months with an initial deposit of $100 isB(t) = [tex]100(1 + 0.002)^t[/tex]
b) The amount in the account increases by a factor of approximately 1.002 every month, approximately 1.025 every year and approximately 1.099 every five years.
a) The function for the amount of money in the account after t months with an initial deposit of $100 and an increase of 0.2% per month can be written as:
B(t) = [tex]100(1 + 0.002)^t[/tex]
where t is the number of months.
b) To determine the factor by which the amount in the account increases every month, year, and five years, we can calculate the value of the function for t = 1, t = 12, and t = 60, respectively, and then divide each value by the previous one.
For each month:
B(1) = 100(1 + 0.002) = $100.20
B(2) = 100(1 + 0.002)² = $100.40
B(2)/B(1) = $100.40/$100.20 = 1.001993
The amount in the account increases by a factor of approximately 1.002 every month.
For each year:
B(12) = 100(1 + 0.002)¹² = $102.44
B(24) = 100(1 + 0.002)²⁴ = $105.01
B(24)/B(12) = $105.01/$102.44 = 1.0249
The amount in the account increases by a factor of approximately 1.025 every year.
For every five years:
B(60) = 100(1 + 0.002)⁶⁰ = $110.41
B(120) = 100(1 + 0.002)¹²⁰ = $121.20
B(120)/B(60) = $121.20/$110.41 = 1.0991
The amount in the account increases by a factor of approximately 1.099 every five years. Therefore, the amount in the account increases by a small factor every month, a moderate factor every year, and a larger factor every five years.
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What is the domain indicated on the graph for each portion of the piecewise function?
f(x) = StartLayout enlarged left-brace 1st Row 1st column negative 2, 2nd column Domain 1st piece 2nd row 1st column 2 x + 1, 2nd column Domain 2nd piece Third row 1st column negative one-half x, 2nd column Domain 3rd piece EndLayout
Answers
The domain of the 1st piece is -10 < x < 0, for 2nd piece is 0 < x < 4, and for 3rd piece is 4 < x < 8.
What is a function?A function is a particular kind of relationship where there is a set domain and range, and every input value in the domain is associated with a single output value in the range.
We have a piecewise function shown in the picture:
From the graph:
f(x) = -2, Domain: -10 < x < 0
f(x) = 2x + 1, Domain: 0 < x < 4
f(x) = (-1/2)x, Domaim: 4 < x < 8
Thus, the domain of the 1st piece is -10 < x < 0, for 2nd piece is 0 < x < 4, and for 3rd piece is 4 < x < 8.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
The half-life of the particular compound is approximately 9.4 days. (Correct choice: B)
How to find the half-life of a compound
The statement indicates the decay function of a particular compound, which is an exponential function of the form:
y = a · exp(- λ · t)
Where:
a - Initial mass of the compound.λ - Decay constant, in days⁻¹.t - Time, in days.The half-life of the particular compound is determined by the following expression:
t = ㏑ 2 / λ
Where t is the half-life.
If we know that λ = 0.0736, then the half-life of the particular compound is:
t = ㏑ 2 / 0.0736
t = 9.4 days
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Ayudenme a resolver esos 2 problemas, son inecuaciones, ya tengo la respuesta, falta solucion
Answers
The solution set for each rational inequality:
Case 1: - 9 ≤ x < - 5
Case 3: Every real number except x = 1.
How to solve a rational inequality
In this problem we find two cases of rational inequality, whose solution sets can be found by using algebra properties and sign laws. Now we proceed to solve on each case:
Case 1
(3 · x + 7) / (x + 5) ≥ 5
(3 · x + 7) / (x + 5) - 5 ≥ 0
[(3 · x + 7) - 5 · (x + 5)] / (x + 5) ≥ 0
(- 2 · x + 18) / (x + 5) ≥ 0
- 2 · (x - 9) / (x + 5) ≥ 0
The inequality is positive for - 9 ≤ x < - 5.
Case 3
(- x² - 1) / (- x² + 2 · x - 1) > 0
[(- 1) · (x² + 1)] / [(- 1) · (x² - 2 · x + 1)] > 0
(x² + 1) / (x² - 2 · x + 1) > 0
(x² + 1) / (x - 1)² > 0
The inequality is positive for all real number except x = 1.
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Use mathematical induction to prove 2^n>=2n is true for all positive integers.
Answers
By the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.
The given inequality is 2ⁿ≥2n.
Let n = 1
2^1 ≥ 2^1
2 ≥ 2 which is true
Inductive Step: Assume 2ⁿ≥2n is true for some arbitrary positive integer k.
We need to prove that 2^(k+1) ≥ 2^(k+1)
2^(k+1) ≥ 2*2^k (by the inductive hypothesis)
2^(k+1) ≥ 2*2^(k+1)
2^(k+1) ≥ 2^(k+1) which is true
Therefore, by the Principle of Mathematical Induction, 2ⁿ≥2n is true for all positive integers.
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Mrs. Hopkins gives her students a math quiz every 8 and a science quiz every 6 days. If she gives math and science quizzes today, how many days will it be before both quizzes are given on the same day again?
Answers
Therefore , the solution of the given problem of unitary method comes out to be once more administer maths and science quizzes on the same day.
Definition of a unitary method.The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.
Here,
List the multiples of each integer until we discover a common multiple as one method to determine the least common multiple:
=> 8, 16, 24, 32, 40, 48, 56, 64, 72, and 80 are all multiples of 8.
=> 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60 are multiples of 6.
As an alternative, we can use the prime factorization technique to identify the smallest common multiple:
=> 8's prime factors are 2 x 2 x 2
=> 6's prime factors are 2 x 3
=> 2 x 2 x 2 x 3 = 24
We can see that 24 is the smallest common multiple once more, and in 24 days,
Mrs Hopkins will once more administer maths and science quizzes on the same day.
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Select the correct answer.
Simplify the expression so there is only one positive power for each base.
2.7^(-3) * 3.8^(2) * 2.7^(4) * 3.8^(3)
A. 2.7^(7) * 3.8^(5)
B. 2.7^(-7) * 3.8^(5)
C. 2.7 * 3.8^(5)
D. 2.7 * 3.8
E. 2.7^(7) * 3.8
Answers
The expression can be simplified to get:
2.7^(1)*3.8^(5)
The correct option is C.
How to simplify the expression?Remember that if we have the product of two powers with the same base, we only need to add the exponents.
Then we will get:
2.7^(-3) * 3.8^(2) * 2.7^(4) * 3.8^(3)
= (2.7^(-3)*2.7^(4)*3.8^(2)*3.8^(3))
= (2.7^(-3 + 4)*3.8^(2 + 3))
= 2.7^(1)*3.8^(5)
That is the expression simplified, we can see that the correct option is C.
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A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 5 students' scores on the exam after completing the course:
2,14,1,2,−6
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal.
Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
The critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).
What is Critical value ?
In statistics, a critical value is a threshold value that is used to determine whether to reject or fail to reject the null hypothesis in a statistical test. It is typically based on the significance level of the test, which is the probability of rejecting the null hypothesis when it is actually true.
To find the critical value for a 90% confidence interval with n = 5, we need to use a t-distribution with (n-1) degrees of freedom.
Using a t-distribution table or a calculator, we can find the critical value with a 90% confidence level and 4 degrees of freedom (n-1 = 5-1 = 4) to be approximately 2.132.
Therefore, the critical value that should be used in constructing the confidence interval is 2.132 (rounded to three decimal places).
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A student wants to compare the amount of money that two local movie theaters make over a two-week period for the last nightly showing of a particular movie. The following box plots show the data for the amount of money each theater makes over the period. Compare the median of each box plot.
Answers
Answer:
mt1= 995
mt2=975
Step-by-step explanation:
the line inside the box plot shows where the median is.
Hey folks help me out for some points :)
Answers
Answer:
C
Step-by-step explanation:
Positive numbers represent a positive situation. And negative numbers coincide with a negative situation.
Ex: An increase in temperature corresponds to a positive number, and a decrease in temperature with a negative number.
Making an Informed Decision Using the Quantitative Reasoning Process
Step 1: Understand the Problem
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 190 miles per week to commute to work. With gas prices currently at $
2.9 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 18 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $
770 per year (as long as nothing serious goes wrong).
The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $
6,500 over a three-year loan process. This car gets 32 miles per gallon and would only require an average of $
10 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this.
Step 2: Identify variables and assumptions
Manny has identified some key variables for his situation. Select the two variables that should be removed from his list because they do not apply to the current situation.
Manny’s graduation date from elementary school.
The cost of repairs on the old car.
The cost of gas.
The number of miles Manny drives each week.
Manny’s wages.
The loan cost of the used car.
The year Manny was born.
The cost of the used car.
Manny has also made a list of key assumptions he will be using to make his decision. Check the boxes for the three assumptions from his list that are not useful in this scenario.
Manny assumes that nothing will go seriously wrong with either car during this three year period.
Manny assumes the loan period will be 3 years.
Manny assumes gas costs will remain about the same over the three years.
Manny assumes he will continue to go running in the mornings every weekday for the next three years.
Manny assumes there are 52 weeks in a year.
Manny assumes his lunches will continue to cost about the same for the next three years.
Manny assumes he will continue to drive about the same number of miles each week over this three year period.
Manny assumes he will still like spinach at the end of three years no matter which choice he makes.
Step 3: Apply Quantitative Tools
Use computational and algebraic tools to quantify the total costs (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Scenario
Total Cost for Three Years
Keep the old car
$
Number
Buy the fuel-efficient used car
$
Number
Step 4: Make an Informed Decision
Based on the information presented what do think Manny should decide?
Option #1: Keep the old car
Option #2: Buy the fuel-efficient used car
Option #
1
Step 5: Evaluate Your Reasoning
Manny plans to start looking at cars and will evaluate his reasoning before he makes a purchase.
( need help on the assignment)
Answers
What integer values of x make the statement -3/x lesser than -x/3 true?
x=0
x=2
x=3
Any interger greater than -3
Any integer less than -3
x=1
You need to choose more than 1 answer
Answers
The integer values that make the statement true are x = -3, -2, -1, 1, 2, 3
We have,
We can start by multiplying both sides of the inequality by -3x to get rid of the denominators:
-3/x < -x/3
Multiplying by -3x on both sides.
-9 < -x²
Rearranging.
x² < 9
Taking the square root of both sides.
|x| < 3
This means that x can take any integer value between -3 and 3, excluding 0.
Thus,
The integer values are x = -3, -2, -1, 1, 2, 3
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How much money should Be deposited today in an account that earns 10.5 percent compounded monthly so that it will accumulate to $22,000 in four years
Answers
Answer:
$12,276.24
Step-by-step explanation:
22000 / (1 + 0.105/12)^4*12
12276.24
A = P(1 + r/n)^(nt)
where A is the future value, P is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, we want to find the present value P that will accumulate to $22,000 in four years at an annual interest rate of 10.5% compounded monthly (i.e., n = 12). Therefore, we have:
A = $22,000
r = 0.105/12 (monthly interest rate)
n = 12
t = 4
Substituting these values into the formula and solving for P, we get:
P = A/(1 + r/n)^(nt) = $22,000/(1 + 0.105/12)^(12*4) ≈ $14,005.70
Therefore, the amount that should be deposited today in the account is approximately $14,005.70.
50 Points! Multiple choice algebra question. Photo attached. Which represents the correct synthetic division of (x^2-4x+7) divided by (x-2)? Thank you!
Answers
Option D is the correct synthetic division of (x^2-4x+7) divided by (x-2)
What is the synthetic division?Synthetic division is a shorthand procedure used to divide a polynomial by a linear factor of (x - a) form, in which "a" is constant. This method gives an expedient way to locate the quotient and remainder without carrying out long division.
x - 2 | x^2 - 4x + 7
x^2 - 2x
---------
-2x + 7
-2x + 4
-------
3
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surface area of a square prism 3ft 3ft 15ft
Answers
Answer:
198 ft^2
Step-by-step explanation:
l = 3
w = 3
h = 15
2(3*3) + 4(3*15) = 18 + 180
18 + 180 = 198 ft^2
Would like some help with this question, please.
Answers
Answer:
i believe 67 its somewhat hard to tell but the line seems to be in the middle between 150 and 140
Step-by-step explanation:
since it heats up to 212 then the person lets it cool down for 10 mins the temp goes to 145 (Answer is 67)
how much money does she make all together in one week
Answers
needs more explanation
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet. In how many ways can this be done?
Answers
Total number of ways = (Number of ways to select appetizers) x (Number of ways to select main courses) x (Number of ways to select desserts)
Number of ways to select appetizers = C(5,4) = 5
Number of ways to select main courses = C(11,9) = 330
Number of ways to select desserts = C(4,3) = 4
Therefore, the total number of ways the customer can select 4 appetizers, 9 main courses, and 3 desserts is:
Total number of ways = 5 x 330 x 4 = 6,600
So, there are 6,600 ways the customer can select the items for the banquet.
There are 1100 many ways can be done that is when catering service offers 5 appetizers, 11 main courses, and 4 desserts.
Given that,
A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet.
We have to find how many ways can this be done.
We know that,
Number of appetizers offered = 5
Number of appetizers customer is to select = 4
Number of main courses offered = 11
Number of main courses customer is to select = 9
Number of desserts offered = 4
Number of desserts the customer is to select = 3
So,
To determine the number of ways this can be selected,
By using the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]^nC_r = ^5C_4\times ^{11}C_9\times^4C_3[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!(5-4)!} \times \frac{11!}{9!(11-9)!}\times \frac{4!}{3!(4-3)!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!1!} \times \frac{11!}{9!2!}\times \frac{4!}{3!1!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!} \times \frac{11!}{9!(2)}\times \frac{4!}{3!}[/tex]
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 5 × 11 × 5 × 4
[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 1100
Therefore, There are 1100 many ways this can be done.
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4cos45°-2sin45°. Please let me know the answer with thorough steps.
Answers
We know that cos(45) = sin(45) = √2/2.
Substituting these values, we can simplify the expression as follows:
4cos(45) - 2sin(45)
= 4(√2/2) - 2(√2/2) (substituting cos(45) and sin(45) values)
= 2√2 - √2
= √2
Therefore, the answer is √2.
Which fraction is a multiple of 1/9?
Answers
Unit fractions are the fraction in which the value of numerator is 1. The multiple of the given fraction are,
1/9 = 2/9, 3/9, 4/9,5/9 ......so on.
Here, we have,
To find the multiple of the fraction 1/9 we need to know about the multiple of fraction.
We have,
Multiple of fraction is the number which is n times of the original function. Here can be any whole or fraction number.
The given number in the problem is the fraction number which is,
The above number is the unit fraction.
Unit fraction-
Unit fractions are the fraction in which the value of numerator is 1.
The multiple of unit fraction is in times the original function. For the given fraction the multiple fraction can be given as,
1/9 = 2/9, 3/9, 4/9,5/9 .......so on.
Hence the multiple of the given fraction are,
1/9 = 2/9, 3/9, 4/9,5/9 ......so on.
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In ΔFGH, g = 910 cm,
m∠G=98° and
m∠H=51°. Find the length of h, to the nearest 10th of a centimeter.
Answers
In ΔFGH, the length of h is 714.2 cm
Let us assume that in ΔFGH, f represents the opposite side to angle F, g represents the opposite side to angle G, and h represents the opposite side to angle H.
Consider the following figure.
Using sine rule for triangle FGH,
sin F/f = sin G/g = sin H/h
Consider equation sin G/g = sin H/h
sin(98°) / 910 = sin(51°) / h
We solve this equation for h.
h = (sin(51°) × 910)/ sin(98°)
h = (0.777 × 910)/ 0.99
h = 714.21
h = 714.2 cm
This is the required length of h.
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Who can help me with this?
Answers
The original price of this car is equal to $6,600.
What is a percentage?In Mathematics, a percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
Assuming the original price is represented by the variable x, we have the following:
12.5/100 × x = x - 5,775
0.125x = x - 5,775
5,775 = (x - 0.125x)
5,775 = 0.875x
x = 5,775/0.875
x = $6,600.
In conclusion, we can logically deduce that the percentage Pat Bain paid is 87.5%.
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Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two serving of blueberry pie provides 1290 calories
Answers
The caloric content for ice cream C is 250 calories while the caloric content for ice cream B is 270 calories.
How to determine the caloric contentTo determine the caloric content, we will assign algebraic notations to each of the dessert types.
1 Icecream + 2 Blueberry pie = 790 calories
3 icecream + 2 Blueberry pie = 1290 calories
Now the first equation will be subtracted from the second equation as follows:
2 icecream = 500 calories
So, 1 ice cream is 250 calories.
Also, since, 1 icecream serving equals 250 calories, 2 Blueberry pies = 790 - 250 = 540 calories, and 1 Blueberry pie equals 270 calories.
Complete question:
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories. Find the caloric content of each item.
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3^-1/2 x^1/2
express with radical signs instead of fractional exponents. rationalize the denominator.
please help
Answers
Answer:
[tex]\sqrt{x/3}[/tex]----------------------
Use the following identities:
[tex]a^{-b}=1/a^b[/tex][tex]a^{1/2}=\sqrt{a}[/tex][tex]a^bc^b=(ac)^b[/tex]Apply the identities to the given expression:
[tex]3^{-1/2}x^{1/2}=(3^{-1}x)^{1/2}=(x/3)^{1/2}=\sqrt{x/3}[/tex]What is the equation of the line that passes through the point ( 4 , 0 ) and has a slope of − 2?
Answers
Step-by-step explanation:
y=m(x-x1)+y1
y=-2(x-4)+0
y=2x-8+0
y=2x-8
On the axes below sketch the graph of y = 4x² + 8x +3
Label all points of intersection and the turning point in your sketch.
Answers
1. Find the vertex (turning point) of the parabola by using the formula x = -b/2a, where a = 4 and b = 8. This gives x = -1, which is the x-coordinate of the vertex. To find the y-coordinate, substitute x = -1 into the equation: y = 4(-1)² + 8(-1) + 3 = -1.
2. Plot the vertex at the point (-1, -1).
3. To find the x-intercepts, set y = 0 in the equation and solve for x. This gives x = (-8 ± √(8² - 4(4)(3)))/(2(4)) = (-8 ± √16)/8 = -1/2 or -3. Plot these points on the x-axis.
4. To find the y-intercept, set x = 0 in the equation and solve for y. This gives y = 3, so the y-intercept is at the point (0, 3).
5. Since the coefficient of x² is positive, the parabola opens upwards. Sketch the curve passing through the points found above.
6. Label the points of intersection and the turning point on the graph.
the diagram below shows all the possible totals from adding the results of rolling a two fair dice.
a) whats the probability of rolling a total of 5? give ur answer as a fraction in its simplest form.
b) if you rolled a pair of fair dice 180 times, how many times would you expect to roll a total of five?
Answers
Answer:
Expected number of times to roll a total of 5 = Probability of rolling a total of 5 x Total number of rolls
= (1/9) x 180
= 20
Step-by-step explanation:
The diagram is not visible in the question. However, I can provide a general method to solve the problem.
a) To find the probability of rolling a total of 5, we need to count the number of ways we can get a sum of 5 and divide it by the total number of possible outcomes. From the diagram, we can see that there are four ways to get a sum of 5: (1,4), (2,3), (3,2), and (4,1). Since each die has six equally likely outcomes, there are 6 x 6 = 36 possible outcomes in total. Therefore, the probability of rolling a total of 5 is:
Probability of rolling a total of 5 = Number of ways to get a total of 5 / Total number of possible outcomes
= 4/36
= 1/9 (in its simplest form)
b) If we rolled a pair of fair dice 180 times, the expected number of times we would roll a total of 5 can be calculated as follows:
Expected number of times to roll a total of 5 = Probability of rolling a total of 5 x Total number of rolls
= (1/9) x 180
= 20