If you buy a burger and fries at your favorite fast food restaurant:___________
A. then GDP will be higher, but consumption spending will be unchanged.
B. then both GDP and consumption spending will be higher.
C. then neither GDP nor consumption will be affected because you would have eaten at home had you not bought the meal at the restaurant.
D. then GDP will be unchanged, but consumption spending will be higher.
Answers
Answer:
A. then GDP will be higher, but consumption spending will be unchanged.
Step-by-step explanation:
GDP is the monetary value of all the finished goods and services produced within a country in a specific time period by the country's citizens and foreigners.
It is primarily used to assess the health of a country's economy and it is calculated by adding the following figures together:
personal consumption private investment government spending; and exports
The burger and fries are services provided by the restaurant, which added value to the economy by increasing the GDP.
However, the consumption spending will not be affected because you would have eaten at home had you not bought the meal at the restaurant.
Therefore, the correct option is A " then GDP will be higher, but consumption spending will be unchanged".
Related Questions
7÷5=2. Prove It
Based on Critical Thinking and Reasoning. Not normal mathematics.
Answers
PLEASE HELP FAST!!! IT IS URGENT!!!!!
The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 30 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. Do the data provide convincing evidence at the Alpha level that the mean salary for the baseball players on the East Coast is different from $3.2 million?
What are the test statistic and P-value for this significance test?
Find the t-table here and the z-table here.
A. t = 1.83 and 0.025 < P-value < 0.05
B. z = 1.83 and 0.025 < P-value < 0.05
C. t = 1.83 and 0.05 < P-value < 0.1
D. z = 1.83 and 0.05 < P-value < 0.1
Answers
If the distribution of professional baseball player salaries has a mean of $3.2 million. the test statistic and P-value for this significance test is :A. t = 1.83 and 0.025 < P-value < 0.05.
What are the test statistic and P-value for this significance test?We will use a t-test to determine whether the sample mean salary of baseball players on the East Coast is significantly different from the population mean salary of $3.2 million, given a sample of 30 players with a sample mean of $3.9 million and a standard deviation of $2.1 million.
The null hypothesis is that the mean salary for baseball players on the East Coast is $3.2 million, while the alternative hypothesis is that it is different from $3.2 million.
The test statistic for this hypothesis test is:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
t = (3.9 - 3.2) / (2.1 / sqrt(30)) = 1.83
To find the P-value for this test, we need to determine the degrees of freedom (df) for the t-distribution. Since the sample size is 30, df = 30 - 1 = 29. Using the t-table with 29 degrees of freedom and a two-tailed test at the alpha level of 0.05, we find that the critical values are ±2.045.
The P-value for the test is the probability of getting a t-value as extreme as 1.83 or more extreme, given the null hypothesis. We can find this probability using the t-table or a statistical software program. Using the t-table with 29 degrees of freedom, we find that the area to the right of 1.83 (corresponding to the alternative hypothesis of a greater mean salary) is between 0.025 and 0.05.
Therefore, the correct answer is A. t = 1.83 and 0.025 < P-value < 0.05. This indicates that there is some evidence to suggest that the mean salary for baseball players on the East Coast is different from $3.2 million.
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Fats, sugars, and proteins are important food molecules. What do these types of molecules have in common?
Answers
The fact that Fats, sugars, and proteins molecules have in common is that all of these are macronutrients.
What are macronutrients?The many categories of macronutrients include proteins, lipids—also known as fats—carbohydrates, or sugars. These are the three primary nutrients that the body uses to function. This indicates that they are chemical substances that your cells use as a source of chemical energy and that you require in quite significant quantities. These nutrients also produce energy or calories. They are broken down into smaller components during digestion. Energy is derived from carbohydrates (glucose). After being broken down into fatty acids, fats are used for energy. Although it can be used as fuel, protein's primary function is in the synthesis of hormones, muscle, and other proteins.To know more about macronutrients visit:
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Answer:
They all have carbon atoms.
Step-by-step explanation:
A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour flight is .02. a) What is the probability that both will fail?b) Neither will fail?c) One or the other will fail? Show all steps carefully.
Answers
Answer:
a) 0.0004
b) 0.9604
c) 0.02
Step-by-step explanation:
When trying to find the probability of a sequence occurring you would simply need to multiply the probability of both of those things occurring together. Since the probability of an alternator failing is 0.02 then the probability of both failing would be...
0.02 * 0.02 = 0.0004
Now the probability of an alternator not failing is 0.98 (100% or 1 minus 0.02) therefore, the probability of both failing would be...
0.98 * 0.98 = 0.9604
Finally, the probability of one or the other failing would simply be the same as the probability of a single alternator failing which is 0.02
2. 50 vehicles belong to an enterprise that has three departments, A, B and C. 6 vehicles are available for the use of all three departments, while 2 vehicles give service to neither of the departments. 24 vehicles are administrated by department B, although 16 of them are also used by the others departments. There are twice as many vehicles in department A as there are in department C. If equal numbers of vehicles are allocated when used by any two departments, find the number of vehicles administrated by each department.
Answers
The number of vehicle administered by department A only = 18
The number of vehicle administered by department B only = 8
The number of vehicle administered by department C only = 1
Given data
50 vehicles belong to an enterprise that has three departments, A, B and C
6 vehicles are available for the use of all three departments
2 vehicles give service to neither of the departments
24 vehicles are administrated by department B
16 of the 24 used by B are also used by the others departments
There are twice as many vehicles in department A as there are in department C.
equal numbers of vehicles are allocated when used by any two departments
How to find the number of vehicles administrated by each departmentnumber of vehicles on department A = 2 * number of vehicles in department C.
say A = 2C
B = 24
let x represent the number of vehicles used by any two departments
16 of the 24 used by B are also used by the others departments and equal numbers of vehicles are allocated when used by any two departments hence
16 = 2x + 6
2x = 16 - 6
2x = 10
x = 5
B only = 24 - 2x - 6 = 18 - 2x = 18 - 10 = 8
A only = A - 2x - 6 = 2C - 10 - 6 = 2C - 16
C only = C - 2x - 6 = C - 10 - 6 = C - 16
adding up all the vehicles as allocated to get to the sum of 50
24 - 2x - 6 + A - 2x - 6 + C - 2x - 6 + x + x + x + 6 + 2 = 50
24 - 6 - 6 - 6 + 6 + 2 - 2x - 2x - 2x + x + x + x + A + C = 50
24 - 10 - 6x + 3x + 2C + C = 50
14 - 3x + 3C = 50
3C - 3X = 50 - 14
3C - 3(5) = 36
3C - 15 = 36
3C = 36 + 15 = 51
C = 17
C only
C only = C - 16
C only = 17 - 16
C only = 1
A only
A only = 2C - 16
A only = 2 * 17 - 16 = 34 - 16 = 18
The number of vehicle administered by department A only = 18
The number of vehicle administered by department B only = 8
The number of vehicle administered by department C only = 1
The number of vehicle administered by department A = 2C = 34
The number of vehicle administered by department B = 24
The number of vehicle administered by department C = 17
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solve for x, -6x > 72
Answers
Answer:
x < -12
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesStep-by-step explanation:
Step 1: Define
-6x > 72
Step 2: Solve for x
Divide -6 on both sides: x < -12Here we see that any value x smaller than -12 would work as a solution to the inequality.
-22 + (-10) + 15 I don’t know how to solve this problem
Answers
The answer is - 17
here, we have to apply BODMAS rule
given ,- 22 + (10) = 15
= - 22 - 10 + 15
= -32 + 15
= - 17
BODMAS is an acronym for the sequence of operations to be performed while simplifying the mathematical expressions.
B=Brackets
O=Off
D=Division
M=Multiplication
A=Addition
S=Subtraction
Achilles is a mathematician who invented BODMAS. It is a mnemonic that helps us remember how to evaluate mathematical operators in a mathematical statement involving more than one mathematical operation.The four basic Mathematical rules are addition, subtraction, multiplication, and division.
Basic math skills are those that involve making calculations of amounts, sizes or other measurements. Core concepts like addition, subtraction, multiplication and division provide a foundation for learning and using more advanced math concepts.
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2(a) Another 'think of a number' problem is represented by the equation below.
2w-1
5
Complete the steps below to show the mental calculations that were made.
I think of a number (call it w)
Step 1: Multiply it by 2
Step 2: multiply it by 1
-+w+2=2w
Step 3:multiply it by 5
Step 4:multiply it by 1
Step 5:multiply it by 8
The result is double the number I started with
Answers
The solution of the equation (2w - 1) / 5 + w + 2 = 2w will be 3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
(2w - 1) / 5 + w + 2 = 2w
Simplify the equation, then we have
(2w - 1) / 5 + w + 2 = 2w
(2w - 1) / 5 = w - 2
2w - 1 = 5w - 10
3w = 9
w = 3
The solution of the equation (2w - 1) / 5 + w + 2 = 2w will be 3.
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The complete question is given below.
Your team decides to change the rules of the game. Now, if a student ties with
the envelope, the student gets to have a second chance to play. The student gets
to choose whether he or she wants to keep all 24 envelopes to choose from or
eliminate the envelope he or she just opened. If the student decides to keep all
24 envelopes, your team will rearrange the slips of paper in the envelopes first.
If the student happens to tie again, the student’s dollar is donated to the fundraiser
and his or her turn is over. Which would be a better choice for the student if he
or she wants the dollar back? Which would be a better choice for your team if
you want to raise more money? Justify your answers using probabilities.
Answers
from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar.
While from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.
Step by step explanationAssuming that the slips of paper are randomly distributed and the student does not have any information about the distribution, let's analyze the probabilities for each choice:
Keeping all 24 envelopes: If the student decides to keep all 24 envelopes, the slips of paper in the envelopes will be rearranged, and the probability of choosing the envelope with the dollar will be 1/24, as there is only one envelope with the dollar. If the student ties again, the game ends and the dollar is donated to the fundraiser. The probability of tying again is (1/24) * (23/24) = 0.048, which is relatively low.Eliminating the opened envelope: If the student eliminates the opened envelope, the slips of paper in the remaining 23 envelopes remain in the same order, and the probability of choosing the envelope with the dollar will be 1/23. If the student ties again, the probability of choosing the envelope with the dollar will be 1/23 again, and the game ends with the donation of the dollar. The overall probability of winning the dollar in this scenario is (1/23) + (1/23) * (22/23) * (1/23) = 0.088.Thus, from the student's perspective, eliminating the opened envelope would be a better choice as it doubles their chances of winning the dollar. On the other hand, from the team's perspective, keeping all 24 envelopes would be better as it reduces the probability of the student winning the dollar to 1/24. Therefore, the team would likely raise more money if they encourage the students to keep all 24 envelopes.
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If the zeros of a quadratic functions are -2 and 4, which graph could represent the function? A. A parabola declines from (negative 3 point 1, 10) through (negative 3, 8), (negative 2, 0), (negative 1, negative 4), (1, negative) and rises through (2, negative 8), (3, negative 4), (4, 0), (5, negative 6), and (5 point 5, 10). B. A parabola declines from (negative 5 point 8, 10), (negative 5, 7), (negative 4, 0), (negative 8, negative 2), (negative 1, negative 8 point 4) and rises through (2, 0), (3, negative 6) and (3 point 9, 10). C. A downward open parabola rises from (negative 6 point 2, negative 10), (negative 5 point 2, negative 6), (negative 4, 0), (negative 3, 1) and declines through (negative 1 point 4, negative 2), (1, negative 4), (0, negative 8), and (0 point 5, 10). D. A downward open parabola rises from (negative 0 point 5, negative 10), (0, negative 8), (1, negative 4), (2, 0), (3, 1), and declines through (5, negative 4), (6, negative 8), and (6 point 5, negative 10) on the x y coordinate plane.
Answers
Option A. The only graph that could represent the function with the zeros of -2 and 4 is the graph is : A parabola declines from (negative 3 point 1, 10) through (negative 3, 8), (negative 2, 0), (negative 1, negative 4), (1, negative) and rises through (2, negative 8), (3, negative 4), (4, 0), (5, negative 6), and (5 point 5, 10).
How to determine the graphThe zeros of a quadratic function are the x-values where the function equals zero (where it crosses the x-axis). In this case, you mentioned that the zeros of the function are -2 and 4.
Looking at the provided options:
A. This graph crosses the x-axis at (-2, 0) and (4, 0), which are indeed the zeros of the function. Therefore, this could be a possible representation of the function.
B. This graph crosses the x-axis at (-4, 0) and (2, 0). These are not the zeros given for the function (-2 and 4), so this graph is not a possible representation of the function.
C. This graph crosses the x-axis at (-4, 0), but it never crosses at x=4. Instead, it crosses at x=2. Therefore, this is not a possible representation of the function.
D. This graph crosses the x-axis at (2, 0), but does not cross the x-axis at x=-2. Therefore, this is not a possible representation of the function.
So, the only graph that could represent the function with the zeros of -2 and 4 is the graph provided in Option A.
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Which has a greater effect on the volume-changing the radius by a given amount or changing the height by the same amount? Why?
Answers
Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.
Find g(x), where g(x) is the translation 2 units left and 4 units down of f(x)=x^2.
Write your answer in the form a(x–h)^2+k, where a, h, and k are integers.
g(x) =
Answers
The function g(x) in the form a(x-h)^2 + k is: \(g(x) = (x + 2)^2 - 4\)
Starting with\(f(x) = x^2\), the translation 2 units left and 4 units down would result in the following transformation:
g(x) = f(x + 2) - 4
Substituting\(f(x) = x^2:\)
\(g(x) = (x + 2)^2 - 4\)
Expanding the square:
\(g(x) = x^2 + 4x + 4 - 4\)
Simplifying:
\(g(x) = x^2 + 4x\)
Now we need to rewrite this expression in the form \(a(x-h)^2 + k.\) To do this, we will complete the square:
\(g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4\)
Therefore, the function g(x) in the form a(x-h)^2 + k is:
\(g(x) = (x + 2)^2 - 4\)
Where a = 1, h = -2, and k = -4.
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Alicia is writing the program for a video game. For one part of the game she uses the rule (, ) → ( − 2, + 5) to move points on the screen. (a) What output does the rule give when the input is ( 6,0) − ? Show your work. (b) What output does the rule give when the input is (3, 4) − ? Show your work. (c) Is the rule a function? Explain why it is or why it is not.
Answers
Answer:
As the mapping suggests, the first (x) coordinate is decreased by 3, and the second (y) coordinate is increased by 2. So, given the inputs, you have
And yes, this rule is a function: it has a starting set (the domain), which is all possible couples , and a landing set (the codomain), which is again composed by the couples . Since for every point in the domain you have one and only one output, this rule is a function
Step-by-step explanation:
What is the equivalent ratio for 4
Answers
The equivalent ratios are 8: 6 and 12:9.
Equivalent ratios:Two ratios are equivalent if they represent the same proportion or relative size. To find an equivalent ratio, we can multiply both terms of the ratio by the same non-zero number. This doesn't change the condition between the two terms.
Here we have 4:3
To find equivalent ratios, we can multiply both terms by the same number.
Multiplying by 2
=> 4 × 2 : 3 × 2
=> 8 : 6
Multiplying by 3
=> 4 × 3 : 3 × 3
=> 12: 9
Therefore,
The equivalent ratios are 8: 6 and 12:9.
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Complete Question
What is the equivalent ratio for 4: 3
I need some help with this
Answers
Consider the quadratic function:
f(x) = x2 – 8x – 9
Vertex: ( negative b Over 2a, f ( negative b Over 2 a))
What is the vertex of the function? ( , )
Answers
Answer:
(4, -25)
Step-by-step explanation:
The function is put into this form: f(x)= Ax^2 + Bx + C
In the equation x^2 - 8x - 9, A is 1, B is -8 and C is -9
The negatives cancel for negative B so 8 is positive.
8/ 2(1) = 4
Now we plug 4 into the function as x to find the y value
4^2 - 8(4) - 9
-25
whats the median of (20, 15, 14, 16, 17, 12, 20, 22)
ANSWER CHOICES 16 17 18 or 19
PLS HELPP
Answers
Answer:
16.5
Step-by-step explanation:
Given data to us is ,
20, 15, 14, 16, 17, 12, 20, 22 .Arrange it in ascending order .
= 12 , 14 , 15 , 16 , 17 , 20 , 20 , 22
The middle most observation will be median in case n is odd and average of middlemost observations if n is even , that is n = 8 .
=> Middlemost observations = 16 , 17
=> Mean = 16 + 17 /2 = 33/2 = 16.5
What is the volume of this cylinder? 40yd 11yd
Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
Volume of the cylinder is 15197.60(to the nearest hundredth).
What is cylinder?
In mathematics, Cylinder is the basic 3d shapes, which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center which is called height of the cylinder.
Given that the radius of the cylinder is 11yd.
and the height of the cylinder is 40yd.
Formula for the volume of cylinder is π × r² × h where π=3.14, r= radius and h= height.
Putting the values we get,
Volume of the cylinder is = 3.14 × (11)² × 40 cubic yd.
= 15197.6
Hence, Volume of the cylinder is 15197.60(to the nearest hundredth).
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evaluate f(-x)=x/x2+1
Answers
To evaluate f(-x) when f(x) = x/(x^2 + 1), we need to substitute -x for x in the function.
So f(-x) = (-x)/((-x)^2 + 1)
Simplifying the denominator we get:
f(-x) = (-x)/(x^2 + 1)
The function f(-x) is equivalent to the function f(x) with the x-value negated. The value of the function f(-x) is the same as the value of the function f(x) but with the x-value negated.
It's important to note that we can also express this as f(-x) = -f(x)
So the value of f(-x) is x/(x^2 + 1) with the x-value negated.
OK for real this is a hard only verified experts can do this!!!!
Answers
The numeric value of the exponential expression in this problem is given by the following option:
A. 2^12.
How to obtain the numeric value of the exponential expression?The exponential expression for this problem is defined as follows:
8^x/2^y.
8 is the third power of 2, hence:
8 = 2^3.
When a term is elevated to two of it's powers, the powers are multiplied, hence:
(2^3)^x = 2^(3x).
Meaning that the exponential expression is then written as follows:
8^x/2^y = 2^(3x)/2^y.
When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:
2^(3x)/2^y = 2^(3x - y).
As stated in the problem, the numeric value of the expression 3x - y is given as follows:
3x - y = 12.
Hence the entire expression is simplified as follows:
2^(3x - y) = 2^12.
Meaning that the correct option is given by option A.
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Answer:A. 2^12.
Step-by-step explanation:i did it and got it right
The Variance Inflationary Factor (VIF) measures the: a. correlation of the X variables with the Y variable. b. correlation of the X variables with each other. c. standard deviation of the slope. d. contribution of each X variable with the Y variable after all other X variables are included in the model. e. both a and b.
Answers
The X variables have an overall correlation of 0. VIF, or Variance Inflationary Factor, measures the
How much of an inflation variance factor is there?Regression analysis's level of multicollinearity is gauged by a variance inflation factor, or VIF. When several independent variables in some kind of a model with multiple regression correlate with one another, this is known as multicollinearity. The regression findings may be significantly impacted by this.
How high of a VIF is that?Greater correlation between the variable and other variables is indicated by a higher value. With values of Ten or more being considered very high, values greater than 4 or 5 are occasionally considered to be moderate to high.
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25 rays to4 ÷ 5 rays to3
Answers
Answer:
\( \frac{ {25}^{4} }{ {5}^{3} } \\ = \frac{ { {5}^{2} }^{4} }{ {5}^{3} } \\ = \frac{ {5}^{8} }{ {5}^{3} } = {5}^{5} \\ thank \: you\)
Solve (x+1)2 =13/4 using the square root property
Answers
Answer:
Starting with the equation:
(x + 1)^2 = 13/4
We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.
Taking the square root of both sides, we get:
x + 1 = ±√(13/4)
Simplifying under the radical:
x + 1 = ±(√13)/2
Now we can solve for x by subtracting 1 from both sides:
x = -1 ± (√13)/2
Therefore, the solutions to the equation are:
x = -1 + (√13)/2 or x = -1 - (√13)/2
Step-by-step explanation:
The students in mr aizawa’s history class are required to read 3 books from a list of 8 books. How many different combinations of books are possible?
Answers
Answer:
I just need points I have ro freaking clue
x-2y=-3
4x+y=6
does this system have one solution, no solution or infinite soltions- solve
Answers
Answer
One Solution
Step-by-step explanation:
x - 2•(-4x+6) = -3
9x = 9
x = 1
y = -4x+6
y = -4(1)+6 = 2
{x,y} = {1,2}
add.
(-5x^4+6x^3-43)+(6x^5-x^2+12x-12)
Answers
5
x
4
+
6
x
3
+
6
x
5
−
x
2
+
12
x
−
31
What’s the answer to the picture I took?
Answers
Answer:
y = - x
Step-by-step explanation:
From the given table:-
( x_1,x_2): (5,-5)
( y_1,y_2): (6,-6)
1) Let's find the slope (m):-
\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{ - 6( - 5)}{6 - 5} = \frac{ - 6 + 5}{1} = \frac{ - 1}{1} = - 1\)
2) Substitute x_1= 5, y_1=-5 and m=-1 into y-y_1=m(x-x_1)
\(y - ( - 5) = - 1(x - 5)\)
\(y + 5 = - x + 5\)
\(y = - x + 5 - 5\)
\(y = - x\)
Which function will cross the y-axis at (0, 7)?
Oy=x+7
Oy=x-7
0y=x+5
Oy=7x
Answers
The value of function which cross the y-axis at point (0, 7) will be;
⇒ y = x + 7
What is substitution method?To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The point which cross the function = (0, 7)
Now,
Since, The point which cross the function = (0, 7)
Hence, The point must be satisfy the function.
By option (1);
⇒ y = x + 7
Put (x, y) = (0, 7)
⇒ 7 = 0 + 7
⇒ 7 = 7
Thus, The correct function which passes through the point (0, 7) is,
⇒ y = x + 7
Option (i) is true.
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what is 8.45 = 2.16x - 2.35
Answers
The given equation is \(8.45 = 2.16x - 2.35\) . To solve for x, we need to isolate x on one side of the equation. the solution to the given equation is \(x = 5\) .
What is the algebraic operations?The equation \(8.45 = 2.16x - 2.35\) can be solved for x using basic algebraic operations as follows:
Add 2.35 to both sides of the equation:
\(8.45 + 2.35 = 2.16x\)
Simplify the left side:
\(10.8 = 2.16x\)
Divide both sides of the equation by 2.16:
\(x = 10.8 / 2.16\)
Simplify the right side:
\(x = 5\)
Therefore, the solution to the equation \(8.45 = 2.16x - 2.35 is x = 5\) .
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I put the question in the photo but it’s basically a contingency table I just can’t find which like formula to us
Answers
a) The probability that exactly one of them will be a girl = 0.3407
b) The probability that at least one of them will like the football = 0.7672
a) If we select three students then the probability that exactly one of them will be a girl
From the attached two way table we can observe that the total number of girls = 22
the total number of boys = 18
and the total number of students = 40
The possible outcomes for selecting 3 students from 40 would be,
⁴⁰C₃
Using combination formula,
⁴⁰C₃ = 40! / (3! × (40 - 3)!)
= 9880
If there is exactly one girl then other two must be boys in the set of 3 selected students.
So, the required probability would be,
P = (²²C₁ × ¹⁸C₂) / ⁴⁰C₃
P = (22 × 153)/9880
P = 0.3407
b) The number of students like the football = 15
and the number of students who don't like the football are 40 - 15 = 25
The probability that at least one of them will like the football would be,
P = (¹⁵C₃ × ²⁵C₀ + ¹⁵C₂ × ²⁵C₁ + ¹⁵C₁ × ²⁵C₂) / ⁴⁰C₃
P = ((455 × 1) + (105 × 25) + (15 × 300)) / 9880
P = 0.7672
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