A. My sister is a graduate of Polytechnic University and a border services officer who lives in North Delta.
B. Yesterday, Jasmine left to visit her friend in Alberta.
A. They listened to relaxing music while they did their homework, which helped them concentrate.
B. To help them focus on their homework, they listened to relaxing music.
Combining sentences is a useful writing technique that helps make sentences concise and easy to read. Combining two or more sentences into one sentence can also help to create smoother transitions between ideas. When combining sentences, it is important to make sure the sentence remains grammatically correct, and to retain important information from the original sentences.
Another way to combine sentences is to delete certain words or phrases. For example, in the sentence “Yesterday, Jasmine left to visit her friend in Alberta”, the phrase “yesterday” can be removed without changing the meaning of the sentence.
You can also combine sentences by changing the order of the words. For example, in the sentence “They listened to relaxing music while they did their homework, which helped them concentrate”, the order of the words can be changed to “They did their homework while they listened to relaxing music, which helped them concentrate”.
Finally, it is important to make sure that the sentence remains grammatically correct. When combining sentences, it is important to make sure that the sentence still has a subject and verb, and that the verb is still in the correct tense.
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How long does it take for a deposit of $800 to double at 8% compounded continuously?
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ doubled }{\$ 1600}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases}[/tex]
[tex]1600 = 800e^{0.08\cdot t} \implies \cfrac{1600}{800}=e^{0.08t}\implies 2=e^{0.08t} \\\\\\ \log_e(2)=\log_e(e^{0.08t})\implies \log_e(2)=0.08t\implies \ln(2)=0.08t \\\\\\ \cfrac{\ln(2)}{0.08}=t\implies 8.66\approx t\qquad \textit{about 8 years and 241 days}[/tex]
Suppose that 30% of the applicants for a certain industrial job possess advanced training in
computer programming. Applicants are interviewed sequentially and are selected at random from
the pool. A) Find the probability that the first applicant with advanced training in programming is
found on the fifth interview. B) What is the expected number of applicants who need to be interviewed in order to find
the first one with advanced training
After calculating the probability we get, there is a 7.20 percent chance that the first candidate will be identified during the fifth interview and it should take 3.33 interviews to discover the first candidate.
The quantity X of repeated trials needed to obtain r successes with p probability in a binomial experiment is known as the negative binomial distribution.
When x succeeds after n tries, the probability is given by:
P(X-x) = Cn-1, x-1*p(power x) * (1 - p)power (n-x)
The number of unique combinations of x items from a set of n elements, Cn,x, is determined by the formula below.
Cn,x = n! / x! ( n! - x! )
This problem involves that:
Let's say that 30 percent of those who apply for a certain industrial position have advanced expertise in computer programming. That follows that.
(a) We need to determine the probability that the first applicant with advanced programming training will be discovered during the fifth interview.
This is the likelihood that it will take 5 attempts to get 1 success.
So, n=5, x=1
P(X-x) = Cn-1, x-1*p(power x) * (1 - p)power (n-x)
P(X-5) = C 4,0* (0.30)(power 1) * (0.70)power (4)
= 0.0720.
During the sixth interview, there is a 7.20% chance that the first candidate with advanced programming training will be discovered.
(b) To find how many applicants should be expected to be interviewed in order to select the first candidate with advanced training, calculate
It is stated by how many trials are anticipated to result in r success:
E = r/p
Thus with the value r=1
E = r/p
= 1/0.3
= 3.33.
For the first candidate with advanced training, it will take an average of 3.33 interviews.
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Math141 Spring 22 Do Home-Secling Di Uren Pit 01/01 12A Homework Section 7.2: Sampling Distributions Question 2.7.2.30 Part 2 of 2 1.3.6.7 and 9 ott 0.2.4.6, and even. Consider 24-tietoa random number table Compute porta and below HW Scon 1001N, 1.17 of 11 ports Points: 5 of 1 Save How many of the 24 digits would you expect to be even on average? 12. (Type an integer or a decimal. Do not round) b. If you actually courted, would you got exactly the number predicted in part ay? Explan OA Yes, because the sample is sufficiently large that the sample proportion will be the same as the population proportion OB. No, because samples will never have exactly the number predicted due to variation from sample to sample OC. No, beteuse while a sample might have exactly the number predicted, a sample could who have male or larger unbendus to variation from a OD, Yos, because samples will always match the population proportion
a) On average, 0.5 * 24 = 12 of the digits would be even. b) No, you would not necessarily get exactly the number predicted in part a. This is because there is always variation from sample to sample. While the expected value is 12
a. On average, you would expect 12 of the 24 digits to be even. This is because there are an equal number of even and odd digits (0, 2, 4, 6, 8 are even and 1, 3, 5, 7, 9 are odd), so the probability of a digit being even is 0.5. Therefore, on average, 0.5 * 24 = 12 of the digits would be even.
b. No, you would not necessarily get exactly the number predicted in part a. This is because there is always variation from sample to sample. While the expected value is 12, it is possible to get more or less than 12 even digits in a sample of 24.
This is due to the randomness of the random number table and the fact that samples do not always perfectly match the population proportion.
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Solve the system of equations and choose the correct answer from the list of options. d + e = 1 −d + e = −5 Label the ordered pair as (d, e). (4 points) a (0, 0) b (3, −2) c (−2, 3) d (−3, 0)
Answer:
b (3, −2)
Step-by-step explanation:
You want the solution to the system of equations ...
d +e = 1-d +e = -5EliminationWe see the coefficients of d are opposites, so we can add the equations together to eliminate the d variable:
(d +e) +(-d +e) = (1) +(-5)
2e = -4 . . . . . . . . simplify
e = -2
Substituting into the first equation, we have ...
d +(-2) = 1
d = 3 . . . . . . add 2
The solution is (d, e) = (3, -2).
__
Additional comment
We also note that the coefficients of 'e' are identical, so we can eliminate 'e' as a variable by subtracting one equation from the other. We choose to subtract the equation with the lower value coefficient of 'd'.
(d +e) -(-d +e) = (1) -(-5)
2d = 6 . . . . . . . simplify
d = 3 . . . . . . . . divide by 2; matches the solution above.
The attached graph uses x and y, because those are the built-in independent and dependent variables. Your graphing calculator may let you define the variables as you wish.
Solve the equation to: x/4 - 16 = (-32)
Thaink you all who answered this!!
dhgxjdbvsjsjjeve..nndbd
HELP PLS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
-3/2
Step-by-step explanation:
To find:-
Slope of the line.Answer:-
We are interested in finding out the slope of the given line . We can see that the line passes through the points (1,0) and (-1,3) . For finding out the slope we can use the formula,
[tex]:\implies \sf m =\dfrac{y_2-y_1}{x_2-x_1} \\[/tex]
Now on substituting the respective values, we have;
[tex]:\implies \sf m = \dfrac{0-3}{1-(-1)} \\[/tex]
[tex]:\implies \sf m = \dfrac{-3}{1+1}\\[/tex]
[tex]:\implies \sf \pink{m=\dfrac{-3}{2}}\\[/tex]
Hence the slope of the line is -3/2.
PLEASE ANSWER THIS QUICK
-12
WHAT COULD THE INTEGER BE??????
Answer: its all 3
Step-by-step explanation: https://socratic.org/questions/is-12-an-integer-rational-or-real-number#:~:text=Reals%3A%20any%20number%20that%20is%20rational%20or%20irrational,be%20found%20on%20the%20number%20line.%20Answer%20link
The volume of a right rectangular prism is 2.76 cubic centimeters. The length of the prism is 2.3 centimeters. The width of the prism is 0.8 centimeters. What is the
height of the of the prism?
The height of this prism is equal to 1.5 centimeters.
How to calculate the volume of a rectangular prism?Mathematically, the volume of a rectangular prism can be calculated by using this formula:
Volume = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.Substituting the given parameters into the formula for the volume of a rectangular prism, we have;
2.76 = 2.3 × 0.8 × H
Height, H = 2.76/1.84
Height, H = 1.5 centimeters.
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rewrite the expression in the form y^n y^6*y^3
The expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].
What is expression?
In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a particular way. Expressions can represent various mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and can be used to calculate a value or to represent a relationship between quantities.
The given expression is:
[tex]y^6 * y^3[/tex]
We can simplify this expression by adding the exponents of y:
[tex]y^6 * y^3 = y^(6+3) = y^9[/tex]
Therefore, the expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].
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PLEAAAASEEEE HELPP!!!!!!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!!!
The median of class A is equal to 40.
The median of class B is equal to 8.
The difference between the median of the two classes is 32.
What is a dot plot?In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.
Based on the dot plot, the median of class A can be determined by sorting the data set in ascending order;
10, 10, 10, 20, 20, 30, 40, 40, 40, 40, 50, 50, 50, 70, 70
Median of class A = 40.
Based on the dot plot, the median of class B can be determined by sorting the data set in ascending order;
4, 6, 6, 6, 6, 8, 8, 8, 8, 10, 10, 10, 12, 12, 16
Median of class B = 8.
For the difference, we have:
Difference = 40 - 8
Difference = 32.
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For a given rational function, n < m. what does this mean about the graph of the function?
There are both horizontal and oblique asymptotes.
There is no horizontal asymptote.
There is a horizontal asymptote at y=a/b
There is a horizontal asymptote at y=0 .
For rational function, n < m. There is a horizontal asymptote at y = 0.
Explain about the rational function?A rational function is one whose denominator is not zero and which can be expressed as the ratio between two polynomials.
f(x) = p(x) / q(x)
A horizontal line is only an asymptote to the graph's extreme left and right. Anything beyond the vertical asymptotes as well as x-intercepts is considered to be "far" left or "far" right. The midpoint of horizontal asymptotes is not asymptotic. A horizontal asymptote can be crossed in the middle.By examining the degrees of a numerator (n) and denominator, we can locate the horizontal asymptote (m).
The horizontal asymptote is at y=0 if nm, the x-axis, is true.Y=an/bm is the horizontal asymptote if n=m. The ratio of the main coefficients, in other words.There isn't a horizontal asymptote if n>m. It has an oblique or slant asymptote, though, if n=m+1.Thus, For rational function, n < m. There is a horizontal asymptote at y = 0.
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Shea runs a carpet cleaning business. The average cost to shea per cleaning is $30. Shea charges $60 per cleaning. Shea’s fixed plus variable costs per month total $1,500. How many carpet cleaning does shea need to do per year to break even?
Shea needs to do 600 carpet cleaning per year to break even.
What is revenue?
Total revenue is the total amount of money earned by a business from the sale of its products or services during a particular period of time.
To break even, the total revenue Shea generates from the carpet cleaning business must be equal to the total cost of running the business.
Let's first calculate the total cost of running the business per year:
Total Cost = Fixed Costs + Variable Costs
Since the fixed plus variable costs per month total $1,500, the total cost per year would be:
Total Cost = $1,500 x 12
Total Cost = $18,000
Now, let's calculate the profit that Shea makes per cleaning:
Profit per Cleaning = Price per Cleaning - Cost per Cleaning
Profit per Cleaning = $60 - $30
Profit per Cleaning = $30
So, Shea makes a profit of $30 per cleaning.
To break even, the total profit generated by the number of cleanings Shea does per year should be equal to the total cost of running the business per year:
Total Profit = Total Revenue - Total Cost
If x is the number of carpet cleaning Shea needs to do per year to break even, then:
Total Revenue = Price per Cleaning x Number of Cleanings per Year = $60x
Total Profit = Profit per Cleaning x Number of Cleanings per Year = $30x
Setting Total Profit equal to Total Cost:
$30x = $18,000
x = $18,000 / $30
x = 600
Therefore, Shea needs to do 600 carpet cleaning per year to break even.
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Classify the following variables.
discrete quantitative
quantitative continuous
qualitative nominal
qualitative ordinal
a. Number of newspapers sold in a day. b.Qualification of a newly elected politician (excellent, good, fair bad)
c. Gender of a student (male, female)
d. Number of students in a first-year classroom.
e. Number of a student (A000000000)
f. Olympic medal type (gold, silver, pronce)
The classification of the variables in the question above is as follows:
a. Number of newspapers sold in a day - discrete quantitative, as it is a countable number.b. Qualification of a newly elected politician (excellent, good, fair, bad) - qualitative ordinal, as it ranks or orders categories.c. Gender of a student (male, female) - qualitative nominal, as it is a categorical variable without a specific order.d. Number of students in a first-year classroom - discrete quantitative, as it is a countable number.e. Number of a student (A000000000) - qualitative nominal, as it is a categorical variable without a specific order.f. Olympic medal type (gold, silver, bronze) - qualitative ordinal, as it is a ranking or ordering of categories.Discrete quantitative data refers to data that can be counted in whole numbers and is often used to describe things that can be categorized into groups. like the number of people in a room or the number of cars in a parking lot.
Quantitative continuous data refers to data that can be measured on a continuous scale, such as time, temperature, or weight, like the temperature of a room or the weight of a person.
Qualitative nominal data refers to data that can be categorized into groups but cannot be measured or ranked, like the type of car someone drives or the color of someone's eyes.
Qualitative ordinal data refers to data that can be categorized into groups and can be ranked or ordered, like the level of education someone has achieved or the ranking of a sports team.
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What is the estimated quotient for 2 1/2 divided by 1 7/9
The estimated quotient of the given dividend 2 1 / 2 divided by the divisor 1 7/9 is equal to 1.41 ( round off up to the two decimals ).
Divisor = 1 7/9
Convert the divisor (mixed fraction ) into improper fraction,
1 7 /9
= [( 9× 1 ) + 7]/ 9
= 16/9
Dividend = 2 1 / 2
Convert the dividend (mixed fraction ) into improper fraction,
2 1 / 2
=[ ( 2 ×2 ) + 1] /2
= 5 /2
Divide the 5 / 2 by 16 /9 to get the estimated quotient ,
( 5 / 2 ) ÷ ( 16 / 9)
= ( 5 / 2 ) × ( 9 / 16 )
= ( 5 × 9 ) / ( 2 × 16 )
= 45 / 32
= 1.40625
= 1.41 ( round off up to the two decimals )
Therefore, the estimated quotient of the division is equal to 1.41( round off up to the two decimals ).
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Intense trig problem.
The answer is [5sqrt(6)] / (12).
How do I get there?
Using the definition of the tangent function, we will get that:
5√(6)/12 = sin(θ)
How to find the sine of theta?Here you need to remember how the tangent function is defined, we know that:
tan(θ) = sin(θ)/cos(θ)
Here we know that:
tan(θ) = √15/3
cos(θ) = √10/4
Replacing that we can write:
√15/3 = sin(θ)*(4/√10)
Solving for the sine, we will get:
(√15/3)*(√10/4) = sin(θ)
(√15*√10)/(3*4) = sin(θ)
(√150)/(12) = sin(θ)
(√(25*6))/(12) = sin(θ)
5√(6)/12 = sin(θ)
That is the answer.
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2566 concert tickets were sold for a total of $10,348.
if students paid $3 and nonstudents paid $5, how many student
tickets were sold?
1241 student tickets were sold. Below, you will learn how to solve the problem.
2566 concert tickets were sold for a total of $10,348, and if students paid $3 and nonstudents paid $5, then the number of student tickets sold can be calculated.
To solve this problem, we can set up an equation using the given information.
X + Y = 2566
3X + 5Y = 10348
Find the value of X:
Y = 2566 - X
3X + 5(2566 - X) = 10348
3X + 12830 - 5X = 10348
2X = 12830 - 10348
2X = 2482
X = 1241
Therefore, 1241 student tickets were sold.
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(p ↔ r) → (∼q → (p ∧ r))
simply this by propostional algebra
answer must be verifiable by truth table
Truth Table
This statement can be simplified using proportional algebra as follows: (p ∨ ∼r) ∧ (q ∨ (p ∧ r)). This can be verified using a truth table.
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Given the recursive formula for a geometric sequence find the common ratio, the first five terms, the term named in the problem, and the explicit formula.
Show work
Find f(9)
11) f(n) = f(n - 1) x 4
f(1) = 4
Answer:
No solution
Step-by-step explanation:
Use the given functions to set up and simplify f(9)
Your friend asks you for help to check a geometry exercise. Below is vour friend's paper.
What error did your friend make? Explain.
The error is made because two or more shapes are said to be similar if they have common corresponding properties of sides and/ angles. The Option D is correct.
What is the explanation of the Geometric error?All similar shapes are two or more given shapes that share some properties in terms of their corresponding sides or angles. As a result, if the corresponding sides or angles are related, they are similar. It is important to note that similarity does not imply congruency.
When the sides and angles of the given triangles LMN and QRS are compared, it is clear that: angle Side Angle (ASA) similarity implies that the included side between two pairs of congruent angles is similar. As a result, the Option D explains the error in the diagram.
Missing options "a.Your friend's paper does not name the triangles correctly for them to be congruent. b. Your friend's paper shows that the SAS Postulate should be used to show congruence because a pair of congruent angles is included between two pairs of congruent sides. c. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the triangles do not have two pairs of congruent angles. d. The ASA Postulate cannot be used to prove the congruence of the two triangles as shown because the included sides between the two pairs of congruent angles are not marked as congruent in both triangles.
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2. Write an equation with the given characteristics: a. Goes through: \( (2,13) \) and \( (2,-11) \)
An equation passing through the points (2, 13) and (2, -11) is x = 2.
The equation of a line can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the line that goes through the given points, we first need to find the slope. The slope can be calculated using the formula:
[tex]\[m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\][/tex]
Plugging in the given points, we get:
[tex]\[m = \frac{-11 - 13}{2 - 2} = \frac{-24}{0}\][/tex]
Since the denominator is 0, the slope is undefined. This means that the line is vertical. A vertical line has the equation x = a, where a is the x-coordinate of any point on the line. Since both of the given points have the same x-coordinate of 2, the equation of the line is x = 2.
Therefore, the equation with the given characteristics is x = 2.
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find (gof)(x) if f(x)=X^2-3, and g(x)=2x-1,
The composite result function ( g o f )(x) in the functions f(x) = x² - 3 and g(x) = 2x - 1 is 2x² - 7.
What is the function operation ( g o f )(x) in the given functions?A function is simply a relationship that maps one input to one output.
Given the data in the question;
f(x) = x² - 3g(x) = 2x - 1(g o f)(x) = ?First, set up the composite result function (g o f)(x).
(g o f)(x) = g( f(x) )
g( x ) = 2x - 1
g( f(x) ) = 2( f(x) ) - 1
g( f(x) ) = 2( x² - 3 ) - 1
Now, simplify the function by applying distributive property.
g( f(x) ) = 2( x² - 3 ) - 1
g( f(x) ) = 2 × x² - 2 × 3 - 1
g( f(x) ) = 2x² - 6 - 1
Add -6 and -1
g( f(x) ) = 2x² - 7
Therefore, the function operation ( g o f ) is 2x² - 7.
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Pls help!
In a video game each player earns 5 pts for reaching the next level and 15 pts for each coin collected. Make a table to show the relationship between the num of coins collected c and total pts p graph the ordered pairs and analyze the graph.
Answer:
Here is a table showing the relationship between the number of coins collected and the total points earned:
Number of coins (c) Total points (p)
0 0
1 20
2 35
3 50
4 65
5 80
6 95
7 110
8 125
9 140
10 155
To graph these ordered pairs, we can plot the number of coins collected (c) on the x-axis and the total points earned (p) on the y-axis. Then we can plot each ordered pair as a point on the graph and connect the points with a line. The resulting graph should show a linear relationship between c and p, with a slope of 15 and a y-intercept of 0.
Analyzing the graph, we can see that as the number of coins collected increases, the total points earned also increases at a constant rate. This suggests that collecting coins is an important part of the game, as it significantly increases the player's total score. Additionally, the slope of the line (15) tells us that each additional coin collected is worth 15 points, while reaching the next level is worth only 5 points.
help what is this 8y to the second power - 3y to the second power
Answer: 5y²
Step-by-step explanation:
Since 8y² and 3y² are similar terms, we can subtract the coefficients and keep the degree and variable the same.
8 - 3 = 5, so 8y² - 3y² = 5y²
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The volume of the given shapes are listed below with their options:
11.) 12 in³ = C
12.) 108 in³ = D
13.) 293.33 cm³ = C
14.) 287 mi³ = B
15.) 3801.33 cm³ = D
16.) 452.39 yd³ = C
17.) 3619.11 in³= B
18.) 16 ft³ = C
19.) 64 m³ = A
20.) 769.69 cm³ = C
How to calculate the volume of a pyramid, cylinder and a cone?The formula used to calculate the volume of a cylinder= πr²h
The formula used to calculate the volume of triangular prism = 1/3Bh
For a square based pyramid = 1/3b²h
For a rectangular pyramid = 1/3 lwh
Volume of a cone = 1/3πr²h
For question 11;
Volume of the triangular pyramid =1/3Bh= 1/3×6×6 = 12 in³
For question 12;
Volume of square pyramid =1/3b²h = 1/3 ×6×6×9 = 108 in³
For question 13.)
Volume of a rectangular pyramid = 1/3 lwh= 1/3×11*8*10=293.33 cm³
For question 14.)
Volume of square pyramid =1/3b²h = 1/3*9*9*11= 287 mi³
For question 15.)
Volume of a cylinder = πr²h = 3.14×11*11*10 = 3801.33 cm³
For question 16.)
Volume of a cone= 1/3πr²h= 1/3*3.14*6*6*12= 452.39 yd³
For question 17.)
Volume of a cone= 1/3πr²h= 1/3*3.14*12*12*24= 3619.11 in³.
For question 18.)
Volume of the triangular pyramid =1/3Bh = 1/3*6*8= 16 ft³
For question 19.)
Volume of the triangular pyramid =1/3Bh = 1/3*24*8= 64 m³
For question 20.)
Volume of a cylinder = πr²h = 3.14×7*7*5 = 769.69 cm³
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ill give brainlyist Please someone help me asap :(
The value of probabilities are,
P (1, 1) = 1 / 36 = 0.027
P (both odd) = 0.166
P (even, odd) = 0.25
P (2 anywhere) = 0.3055
P (sum 8) = 0.1389
P (sum 1) = 0
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Given that;
Two dice are rolled at the same time.
Hence, There are total number of possibilities = 36
Thus, The value of P (1, 1) is,
P (1, 1) = 1 / 36
Since, There are 6 possibilities when both dice have rolled to get odd.
Hence, The value of P (both odd) is,
P (both odd) = 6 / 36
= 1/ 6
Since, There are 9 possibilities to get first dice even and second odd.
Hence, The value of P (even, odd) is,
P (even, odd) = 9/36
= 1/4
Since, There are 11 possibilities when 2 is in anywhere.
Hence, The value of P (2 anywhere) is,
P (2 anywhere) = 11/36
Since, There are 5 possibilities to get sum 8.
Hence, Value of P (sum 8) is,
P (sum 8) = 5/36
Since, There are no possibilities to get sum 1.
Hence, P (sum 1) = 0
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In Exercises 1 through 4, show that AX = B is equivalent to the upper-triangular system UX = Y and find the solution.
2x1 - 2x2 + 5x3 = 6
2x1 + 3x2 + x3 = 13
- X1 + 4x2 - 4x3 = 3
2x - 2x2 + 5x3 = 6 5x2 - 4x3 = 7 0.9x3 = 1.8
To show that the system AX = B is equivalent to the upper-triangular system UX = Y and find the solution, we need to use the Gaussian elimination method. The Gaussian elimination method is a process of reducing a system of linear equations to an equivalent upper-triangular system.
Step 1: Write the given system of equations in matrix form:
```
| 2 -2 5 | | x1 | | 6 |
| 2 3 1 | * | x2 | = | 13 |
|-1 4 -4 | | x3 | | 3 |
```
Step 2: Use the Gaussian elimination method to reduce the matrix to an upper-triangular form:
```
| 2 -2 5 | | 6 |
| 0 7 -9 | = | 7 |
| 0 0 9/7| | 18/7|
```
Step 3: Write the upper-triangular system in equation form:
```
2x1 - 2x2 + 5x3 = 6
0x1 + 7x2 - 9x3 = 7
0x1 + 0x2 + 9/7x3 = 18/7
```
Step 4: Solve the system using back substitution:
```
x3 = 18/7 * 7/9 = 2
x2 = (7 + 9*2)/7 = 4
x1 = (6 + 2*2 - 5*2)/2 = 1
```
Step 5: Write the solution in vector form:
```
| x1 | | 1 |
| x2 | = | 4 |
| x3 | | 2 |
```
Therefore, the solution to the system AX = B is x1 = 1, x2 = 4, and x3 = 2.
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olve the following linear programming problem. Restrict x ≥ 0 and y ≥ 0. Maximize f = 2x + 4y subject to x + y ≤ 7; 2x + y ≤ 12; y ≤ 4.
(x,y)=
f=
The solution to this linear programming problem is (x,y) = (3,4) and f = 22.
To solve this linear programming problem, we need to find the feasible region by graphing the constraints and then use the objective function to find the maximum value of f.
1. Graph the constraints:
x + y ≤ 7 can be rewritten as y ≤ -x + 7
2x + y ≤ 12 can be rewritten as y ≤ -2x + 12
y ≤ 4
2. Find the feasible region:
The feasible region is the area that satisfies all of the constraints. In this case, it is the area bounded by the three lines and the x and y axes.
3. Use the objective function to find the maximum value of f:
f = 2x + 4y
To find the maximum value of f, we need to find the corner points of the feasible region and plug them into the objective function. The corner points are (0,4), (3,4), and (4,3).
f(0,4) = 2(0) + 4(4) = 16
f(3,4) = 2(3) + 4(4) = 22
f(4,3) = 2(4) + 4(3) = 20
The maximum value of f is 22 at the point (3,4).
Therefore, the solution to this linear programming problem is (x,y) = (3,4) and f = 22.
Answer:
(x,y) = (3,4)
f = 22
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For ab+ay-b^(2)-by, (a) Factor out the GCF from the polynomial and identify the category in which the remaining poly
The final factored form of the polynomial is b(a-b) and the category of the remaining polynomial is a binomial.
The first step in factoring out the GCF from the polynomial ab+ay-b^(2)-by is to identify the greatest common factor of all the terms. In this case, the GCF is b. Once we have identified the GCF, we can factor it out from each term by dividing each term by the GCF. This gives us:
ab+ay-b^(2)-by = b(a+y)-b(b+y) = b(a+y-b-y)
Next, we can simplify the remaining polynomial by combining like terms:
b(a+y-b-y) = b(a-b)
Finally, we can identify the category of the remaining polynomial. Since it has two terms and each term has a degree of 1, the remaining polynomial is a binomial.
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−2x−8y=10
2x−6y=18
−2x+9y=−4
2x+3y=−20
2x+5y=0
x + 5y = −10
−4x+y=9
−4x+9y=17
−5x−4y=−11
−4x + 4y = 20
−5x − 4y =
−15 −x + 4y = −3
3x + 2y =
−12 4x − 2y = −2
7x + 8y = 20
7x − y = 29
−3x − y = 8
−8x − y = 23
−6x − y =
−1 6x + 6y = −24
Please I need help like now I’m going to fail
The solution of the system of equation is
1) The solution to the system of equations is x = -7 and y = -2.
2) The solution to the system of equations is x = -7 and y = -2.
3) The solution to the system of equations is any point on the line 2x + 5y = 0
4) The solution to the system of equations is x = -2 and y = 1.
5) The solution to the system of equations is x = 1 and y = -16.
In mathematics, a system of equations refers to a set of two or more equations that must be solved simultaneously. Solving a system of equations involves finding the values of the variables that satisfy all the given equations. In this response, we will go through the process of solving five different systems of equations.
−2x−8y=10 and 2x−6y=18, in order to solve this system of equations, we need to eliminate one of the variables, x or y. One way to do this is to add the two equations together. When we add them, the x term cancels out, leaving us with -14y = 28. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.
And then the equations, −2x+9y=−4 and 2x+3y=−20, to solve this system of equations, we can use the method of elimination again. If we add the two equations, the x term cancels out, leaving us with 12y = -24. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.
Then the third one 2x+5y=0 and x + 5y = −10 is in this system of equations, we notice that the second equation is just the first equation with a constant term added. Therefore, these equations are dependent, meaning that they represent the same line. Any point that satisfies one equation will also satisfy the other equation.
And the fourth one has −4x+y=9 and −4x+9y=17, to solve this system of equations, we can use the method of substitution. We can solve the first equation for y, getting y = 4x + 9. Substituting this expression for y into the second equation, we get -4x + 9(4x + 9) = 17. Simplifying, we get 25x + 72 = 17. Solving for x, we get x = -2. Substituting this value of x into the first equation, we get y = 1.
−6x − y = 10 and −16x + 6y = −24, To solve this system of equations, we can use the method of elimination. If we multiply the first equation by -6 and the second equation by -1, we can add the two equations to eliminate y. Doing so, we get 80x = 80. Solving for x, we get x = 1. Substituting this value of x into either equation, we get y = -16.
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Complete Question:
Solve the system of equations
1) −2x−8y=10 and 2x−6y=18
2) −2x+9y=−4 and 2x+3y=−20
3) 2x+5y=0 and x + 5y = −10
4) −4x+y=9 and −4x+9y=17
5) −6x − y = 10 and −16x + 6y = −24
x=1/2 and y= -5
4(1/2) (4) -3 (-5)
The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.
What is an equation?An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷. They can be used to find unknown values, such as the area of a circle or the speed of a moving object.
The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.
Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.
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The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.
What is an equation?An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷. They can be used to find unknown values, such as the area of a circle or the speed of a moving object.
The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.
Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.
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Complete question -
Find the value of 4x - 3y when x=1/2 and y=-5.