Answer: True.
Because the trapezoid is isosceles, the base angles are congruent by default.
Given isosceles trapezoid ABCD
Sides AB and DC are congruent
By the SAS postulate, triangles ABC and DCB are congruent
Therefore, segment AC is congruent to segment DB
In a recent year, companies spent a total of $87.5 billion on newspaper, television, and radio ads. The total amount spent on television and
radio ads was only $2.9 billion more than the amount spent on newspaper ads alone. The amount spent on newspaper ads was $5.4 billion
more than what was spent on television ads. How much was spent on each form of advertising? (Hint: Let the variables represent numbers of
billions of dollars.)
How much was spent on newspaper ads? $
How much was spent on television ads? $
How much was spent on radio ads? $ billion
billion
billion
Answer:
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billionStep-by-step explanation:
You want the amount spent on ads in each medium given the total and relations between amounts spent for newspaper, television, and radio ads.
SetupLet n, t, r represent the amounts spent on ads in newspapers, television, and radio, respectively. The given relations tell you ....
n +t +r = 87.5
-n +t +r = 2.9
n -t = 5.4
SolutionThe augmented coefficient matrix can be reduced to row-echelon form using a suitable calculator or spreadsheet. This tells you the amounts spent in each medium. The attachment shows this.
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billion__
Additional comment
The value of n can be found by subtracting the second equation from the first. That can be used in the third equation to find t, and both of those values can be used in either of the first two equations to find r.
Which of the following is a polygon answer? give reason
POLYGON
A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit.
TYPES OF POLYGON
Triangle- Has 3 sidesQuadrilateral- Has 4 sidesPentagon-Has 5 sidesHexagon- Has 6 sidesHeptagon-Has 7 sidesOctagon-Has 8 sidesNonagon-Has 9 sidesDecagon-Has 10 sides8Learn more about Polygons at :
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Order the following numbers from least to greatest: 3√2 , √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.
Answer:-2.3, -1/3, square root of 3, square root of 7, 5.1
What is the probability of getting a queen if a card is drawn out from a pack of 52 cards?; What is the probability of getting a 9 from a deck of 52 cards?; Which explains the most likely reason for the discrepancy between Josh's predicted and actual results?; What is the probability of getting 8 from the of card?
The probability of getting a queen if a card is drawn out from a pack of 52 cards is 1/13
Probability is the chance of an event to occur with respect to the given conditions.
Probability of an event P(E) = number of favorable outcomes (n)/total number of outcomes(N)
P(E) = n/N
Total cards in a pack (N) = 52
Number of queens (n) = 4
P(getting a queen from pack of cards) = Number of queens/Total cards in a pack
P(E) = n/N
P(E) = 4/52
P(E) = 1/13
Hence, the probability of the given event is 1/13.
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What is ASA congruence rule Class 7?
The ASA (angle-side-angle) congruence rule states that two triangles are congruent if two angles and the side between them are equal in both triangles.
What is ASA congruence rule Class 7?The ASA congruence rule is a fundamental rule of geometry that states that two triangles are congruent when two angles and the side between them are equal in both triangles. This rule is especially important when solving geometry problems, as it can help determine the size and shape of a triangle.
The ASA congruence rule is applicable to all triangles, regardless of their size or shape, and can be used to find the missing angles or sides of a triangle. By applying the ASA congruence rule, students can gain a better understanding of the properties of triangles and other geometric shapes.
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The weights of bags of raisins are normally distributed with a mean of 175 grams and a standard deviation of 11 grams. Bags in the upper 4.5% are too heavy and must be repackaged. Also, bags in the lower 5% do not meet the minimum weight requirement and must be repackaged. What are the ranges of weights for raisin bags that need to be repackaged? Use Excel, and round your answers to the nearest integer. Provide your answer below Repackaging has to be done if the weights are less than lI grams and more than grams
The solution is 194, rounded to the closest whole number. Thus, x2≈194. In light of this, the weight ranges for raisin bags that require new packaging are less than 157 grams and also more than 194 grams.
What is standard deviation ?A statistic called the standard deviation describes how much variation or dispersion there is in a set of statistics .In contrast to a high standard deviation, which shows that the values are spread out, a low standard deviation suggests that the values tend to be close to the mean of the collection. out over a wider range.
Here,
In this instance, the standard deviation is 11 and the mean is 175. Assume that x1 is the heaviest weight at which the bags fall into the lower 5% and x2 is the lightest weight at which they fall into the upper 4.5%. 5% of the time, and 4.5% of the time, the likelihood is below x1 and above x2. The raisin bags should fall below x1 and above x2 if they need to be repackaged. The points x1 and x2 are illustrated in the image below.
1 x 0.045 x 0.05 = 0.905 is the probability between x1 and x2. Below is a picture of the normal distribution curve for raisins bag weights.
To calculate x1 and x2, locate x1 first. To the left of x1, there is a 0.05 probability. To find x1, use Excel. 1. Start Excel. Toggle a cell that is empty. Press ENTER after typing =NORM.INV(0.05,175,11).
The answer is 157, rounded to the nearest whole number. Thus, x1≈157. To compute x2, use the formula 0.05+0.905=0.955 for the probability to the left of x2. To determine x2, use Excel. Start Excel. Toggle a cell that is empty. Enter the command =NORM.INV(0.955,175,11).
The solution is 194, rounded to the closest whole number. Thus, x2≈194. In light of this, the weight ranges for raisin bags that require new packaging are less than 157 grams and also more than 194 grams.
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Pls help me with this. I don’t understand it
Answer:
it is using the Pythagorean theorem its basically a^2 + b^2 = c^2 watch videos on it, it will explain better
The base of the following pyramid is a square. what is the surface area of the pyramid?
1164 [tex]inch^{3}[/tex] is the surface area of a pyramid with a side of 4 inches and a slant height of 6 inches.
what is surface area of pyramid ?The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The sum of the exterior surfaces of a three-dimensional object, or the item's faces, is what determines an object's surface area. The units used for measurement are square.
n order to calculate a pyramid's surface area, we use the formula SA=B+12ps, where B denotes the base's size, p its perimeter, and s its slant height. Since the base is a triangle, we will use the triangle's area formula to determine B.
so area of triangle = 1/2 * base* height = 1/2* 4 *6
area of triangle= 12 [tex]inch^{2}[/tex]
and perimeter of pyramid = 4a = 16 [tex]inch^{2}[/tex]
and surface area of pyramid = base + 12 * perimeter * slant height
= 12 + 12*16*6
= 1164 [tex]inch^{3}[/tex] is the area of a pyramid with a side of 4 inches and a slant height of 6 inches.
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Answer:64
Step-by-step explanation:
Given A(-9,-12), B(-2,2), C(x,6) and D(-5,-2) find the value of x so that ab parallel to cd
The value of x will be equal to -1 so that ab and cd are parallel to each other.
What is the slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given information provided by the question,
(a)
Let's determine their slopes based on these line segments.
The first one is AB.
[tex]m=\frac{2-(-12)}{-2-(-9)}[/tex]
m = 14/7
m = 2
(b)
The slope of two parallel lines is the same, thus let's set this slope formula to provide the value of m=2. In consideration of CD :
[tex]2=\frac{-2-6}{-5-x}[/tex]
2(-5 -x) = -8
-10 -2x = -8
-2x = -8 + 10
x = -2/2
x = -1
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Harrison deposits $345 in a savings account that earns 4.2% simple interest paid annually. How long will it take for the total amount in the account to reach $410?
PLEASE ASAP I HAVE THIS QUESTION ON A TEST HELLPP
The time required for the total amount in Harrison's account to reach $410 is 4.49 years.
What is time required to reached an accrued amount of $410?The simple interest formula is expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $345Interest rate r = 4.2% = 4.2/100 = 0.042Accrued amount A = $410Time t = ?Plug the given values into the above formula and solve for time t.
A = P( 1 + rt )
A/P = 1 + rt
A/P - 1 = rt
t = ( A/P - 1 ) / r
t = ( $410/$345 - 1 ) / 0.042
t = ( 13/69 ) / 0.042
t = 4.49 years
Therefore, the time needed to reach accrued amount is 4.49 years.
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state the null and alternative hypotheses siegel was testing. be careful to distinguish between a population and a sample. null hypothesis g
A hypothesis is a tested statement regarding the relationship between two or more variables or a proposed explanation for some observable occurrence.
An complete group is referred to as a population when making inferences about it.
Your chosen group for data collection is referred to as a sample. Always, a sample's size is smaller than the population as a whole.
Using a statistical test, researchers compare the evidence supporting the null and alternative hypotheses, which are two conflicting claims:
There is no population impact, or null hypothesis (H0).
There is a population effect, or alternative hypothesis (Ha or H1).
No effect, no difference, or no association are all examples of null hypotheses. They always have an equivalence when expressed in mathematical terms.
The complement of the null hypothesis is the alternative hypothesis. The extensive nature of null and alternative hypotheses ensures that they account for all potential outcomes.
The question is incomplete so, I've answered in general
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Write the following expression using the fewest possible terms.
(−3x − 12) + (16 + 8x)
5x + 4
5x + (−4)
11x + 28
11x + (−4)
Therefore option a) 5x+4 is the simplified form of the equation.
What is equation?Equations in mathematics are logical statements with two algebraic expressions on either side of the equals (=) symbol. The equality of the expressions on the left and right in relation to one another is shown. LHS = RHS (left hand side = right hand side) is the first step in any mathematical equation. You can solve equations to determine a variable's or quantity's value. It is not an equation if the statement lacks the "equal to" sign. It will be thought of as a phrase. Later on in this essay, there will be an explanation of the distinctions between an expression and an equation.
Here,
Given:
=>(−3x − 12) + (16 + 8x)
=> -3x-12+16+8x
=> 5x+4
So 5x+4 is the simplified form of the equation
Therefore option a) 5x+4 is the simplified form of the equation
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I need help with this 1 question. Please help
Answer: x = 56
Step-by-step explanation:
The angle horizontally adjacent from 73 is also equal to 73 due to the triangle being isosceles (the legs are given as equal). Therefore the other angle in that triangle has to be 180 - (73*2) = 34. This angle is a part of the 90 degree angle that is noted in the figure. The other part of that angle must be 90 - 34 = 56. Since this angle is in another isosceles triangle, the angle horizontally adjacent to it must also be 56. x is equal to this angle by definition of vertical angles, so x = 56.
what was the mistake that was made?
Answer:
In step 2 you would multiply both sides by 2 not divide by 2
Step-by-step explanation:
1/2w=30
*2 *2
w=60
Answer:
The mistake is between Step 1 and Step 2.
Step-by-step explanation:
Leon is isolating the variable, w. In this case, he should have multiplied 2 to both sides of the equation to isolate the variable, w.
[tex]2 * (\frac{1}{2})w = 3 * 2\\ w = 3 * 2\\w = 6[/tex]
For the whole question
1) Add 12 to both sides of the equation:
[tex]\frac{1}{2} w - 12 = 18\\\frac{1}{2} w - 12 (+12) = 18 (+12)\\\frac{1}{2} w = 18 + 12\\\frac{1}{2} w = 30[/tex]
2) Multiply 2 to both sides of the equation:
[tex](2 *) (\frac{1}{2}w) = 30 (* 2)\\w = 30 * 2\\w = 60[/tex]
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seven teams play a soccer tournament in which each team plays every other team exactly once. no ties occur, each team has a 50% chance of winning each game it plays, and the outcomes of the games are independent. in each game, the winner is awarded 1 point and the loser gets 0 points. the total points are accumulated to decide the ranks of the teams. in the first game of the tournament, team a beats team b. the probability that team a finishes with more points than team $B$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$
The team a finishes with more points than team b with a probability of 319/512
seven teams play a soccer tournament in which each team plays every other team exactly once
in the first game of the tournament, team a beats team b
We need to find the probability that team a finishes with more points than team b
Both teams, a and b play 6 matches each
In the first match, a wins. Now they can play 5 matches each
Of the remaining 5 games
a win 0 and b win zero
P(a > b) = 5C1/2^5 x 5C1 / 2^5 = 1/1024
a win 1 and b win 1 or zero
P(a > b) = 5C1/2^5 x(5C0 + 5C1) / 2^5 = 30/1024
a win 2 and b win 2 or 1 or zero
P(a > b) = 5C2/2^5 x(5C0 + 5C1 + 5C2) / 2^5 = 160/1024
a win 3 and b win 3 or 2 or 1 or zero
P(a > b) = 5C3/2^5 x(5C0 + 5C1 + 5C2 + 5C3) / 2^5 = 260/1024
a win 4 and b win 4 or less
P(a > b) = 5C4/2^5 x(5C0 + 5C1 + 5C2 + 5C 3 + 5C4) / 2^5 = 155/1024
a win 5 and b win 5 or less
P(a > b) = 5C1/2^5 x(5C0 + 5C1+ 5C2 + 5C3 + 5C4 + 5C5) / 2^5 = 32/1024
P(a> b) = (1 + 30 + 160 + 260 + 155 + 32)/1024 = 638/1025 = 319/512
Therefore, the the probability that team a finishes with more points than team is 319/512
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What ratio, a:b, is represented in the table?
a b
1.5 2.5
51 85
99 165
Answers
A 4:54:5
B 2:32:3
C 3:5
The ratio a : b represented in the table of values is (c) 3 : 5
How to determine the ratio a : b represented in the table of values?From the question, we have the following table of values that can be used in our computation:
a b
1.5 2.5
51 85
99 165
Remove the last two entries in the table
So, we have the following representation
a b
1.5 2.5
Express the remaining entries as a ratio
So, we have the following representation
Ratio = a : b
Substitute the known values in the above equation, so, we have the following representation
Ratio = 1.5 : 2.5
Divide the ratio by 0.5
So, we have the following representation
Ratio = 1.5/0.5 : 2.5/0,5
Evaluate the quotients
So, we have the following representation
Ratio = 3 : 5
Hence, the ratio is (c) 3 : 5
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If cabbage costs $0.39 per pound, then how many pounds of cabbage can you buy for $5.00? Explain why you can use division to solve this problem.
The amount of cabbage 12.82 pounds will be to buy for $5.00.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The cabbage costs $0.39 per pound.
Now,
Since, The cabbage costs $0.39 per pound.
Hence, The amount of cabbage to buy for $5.00 = 1/0.39 × 5
= 12.82 pounds
Thus, The amount of cabbage 12.82 pounds will be to buy for $5.00.
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What is the value of the expression 6\ times10+4^36×10+4
3
The value of the expression; 6 × 10 + 4³ as given in the task content is; 124.
What is the value of the expression 6 × 10 + 4³?It follows from the task content that the value of the expression given in the task content; 6 × 10 + 4³ is to be determined.
Hence, the value of the expression can be evaluated using PEMDAS guidelines as follows;
Since the given expression is;
6 × 10 + 4³
Since the exponent, so that we have;
6 × 10 + 64
Next, solve the multiplication, so that we have;
60 + 64
= 124.
On this note, the value of the expression is; 124.
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Last summer, five randomly selected students took a math aptitude test before they began their statistics course in the fall. The data on (i) math aptitude test scores and (ii) performance on statistics course are given below: Student 1 2 3 4 5Math aptitude test score 95 85 80 70 60Statistic Grade 85 95 70 65 70a. What regression equation best predicts statistics performance, based on math aptitude scores? b. What significance is there to a ? Explain briefly. What significance is there to b ? Explain briefly. c. If a student scored an 80 on the aptitude test, what would be the estimated statistics grade? d. Determine the standard error of the estimate? What does it indicate? e. Calculate and interpret the coefficient of correlation and the coefficient of determination.
The regression equation y=0.37x+62.5 predicts statistics performance based on math aptitude scores, with a strong positive correlation and 65.1% of the variation explained.
a. The regression equation that best predicts statistics performance, based on math aptitude scores is y = 0.37x + 62.5, where y is the statistics grade and x is the math aptitude test score.
b. The significance of a is the intercept of the regression line, which is the predicted value of the statistics grade when the math aptitude score is 0. The significance of b is the slope of the regression line, which indicates the amount of change in the statistics grade for a unit change in the math aptitude score.
c. If a student scored an 80 on the aptitude test, the estimated statistics grade would be 79.5.
d. The standard error of the estimate is 6.36. This indicates the average amount of error between the observed values and the predicted values.
e. The coefficient of correlation is 0.807 and the coefficient of determination is 0.651. The coefficient of correlation indicates a strong positive linear relationship between the math aptitude scores and statistics grades. The coefficient of determination indicates that 65.1% of the variation in statistics grades is explained by the math aptitude scores.
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19 ÷ 359 with remainder
Answer: 18 with a remainder of 17
Step-by-step explanation:
Which system of linear inequalities has the point (3, -2) in its solution set?
y < -3; y ≤ 2/3x - 4
y > -3; y ≥ 2/3x - 4
y < -3; y ≥ 2/3x - 4
y > -2; y ≤ 2/3x - 4
The system that has linear inequalities has the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.
We know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
In option B, we have
y > -3 ----> inequality A
y ≥ 2/3x - 4 ----> inequality B
In both inequality, change the values of x and y at the point (3, -2) and then compare the outcomes.
Inequality A
y > -3 ----> is true
Inequality B
y ≥ 2/3x - 4 ----> is true
Therefore
The ordered pair is a solution of the system B
As a result, the point (3, -2) in the solution set of the system with linear inequalities is y > -3; y 2/3x - 4.
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Suppose a math class contains 40 students, 23 females (five of whom speak French) and 17 males (six of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.
6/11 is the probability that a randomly selected student speaks French, given that the student is male
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
There are 11 members who speak french and 5 are females in 11 members
5/11
p(a given b) = p(a and b) / p(b).
6 of the people in the group are men that speak french, then the probability of (a and b) becomes 6/40
probability that a person speaks french is 11/40
p(a given b)=6/40/11/40
=6/40×40/11=6/11
Hence, 6/11 is the probability that a randomly selected student speaks French, given that the student is male.
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Maya said farewell to her favorite uncle as he boarded a plane for Paris. That night she dreamed about an airplane that ran into a thunderstorm and crashed into a mountain, killing everyone onboard. When she woke up, she learned that her uncle’s plane had encountered violent turbulence on the way to Paris and that several passengers had been injured on the flight. She concluded that this series of events (E) is very strong evidence that she has the ability to see distant things using only her mind (H).
Maya thinks that E is strong evidence for H. Assuming she has updated properly given her probability assignments, what does this mean about her assignments to P( E | ~H ) and P( E | H )? For each of these values, how might you challenge her assignment? (Don’t focus on P( H ) and P( ~H ).)
The likelihood of this question will be determined as P( E | ~H)=1 - P(E|H).
For independent events the probability P( E | H ) is calculated as:
P( E | H ) = P( E ) * P( E and H)
P( E and H) = P(E) * P(H).
Since the event E has already happened and is obvious, if P(E | H)>P(E | H) then the event E is dependent on the mind of maya, but if P(E | H)>P(E | H) then the event E is not dependent on the mind of maya.
In our situation, P(E | H), which means that the plane crushing is independent of Maya's thoughts, is the probability that will suit this argument.
Since it is illogical to claim that Maya can perceive far-off objects with her mind, the likelihood of this question will be determined as P( E | ~H ) = 1 - P( E | H ).
For independent events the probability P( E | H ) is calculated as
P( E | H ) = P( E ) * P( E and H)
P( E and H) = P(E) * P(H).
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A 224-inch pipe is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.
Given that,
Cut into two halves is a 224-inch pipe. The length of one component is three times that of the other.
We have to determine the shorter piece's length.
We know that,
Let's use the variable L to represent the longer pipe and the variable S to represent the shorter pipe.
Since the pipe will be the sum of L and S, we can create the following equation:
L+S=224
The longer piece is three times the shorter piece, which is another thing we know.
L=3S
Substituting the second equation for the first equation
L+S=224
3S+S=224
4S=224
S=224/4
S=56
The shorter piece is 56 inches.
The lengthier component should be used to replace the following:
L=3S
L=3(56)
L=168
The longer piece is 180 inches.
Therefore, The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.
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find the slope and y intercept
5y - 2x = 1
Slope is: 2/5.
The y-intercept of this equation is located at point (0, 1/5).
Step-by-step explanation:1. Write the expression.[tex]5y - 2x = 1[/tex]
2. Solve the equation for y.[tex]5y=1+2x\\ \\\frac{5y}{5}=\frac{1+2x}{5} \\ \\y=\frac{1}{5}+\frac{2x}{5} \\ \\y=\frac{2}{5} x+\frac{1}{5}[/tex]
3. Identifying the slope.The slope of a linear equation will always be the coefficient of the variable "x" when the equation is solved for "y". Therefore, the slope of this linear equation is [tex]\frac{2}{5}[/tex] .
4. Y intercept.The Y incercept is the value of "y" where the line of the equation touches the y axis. In other words, the y-intercept is the value when x= 0. Hence, we may substitute x by 0 in the equation and calculate a value for y:
[tex]y=\frac{2}{5} (0)+\frac{1}{5}\\ \\y= \frac{1}{5}[/tex]
The y-intercept of this equation is located at point (0, 1/5).
In Bill the Boring's dryer there are 11 black shirts, 8 gray shirts, 12 black sweaters, and 10 gray sweaters. Bill is going to take one of these pieces of clothing
out of the dryer at random to check if his clothes are completely dry. What is the probability that the piece of clothing Bill takes out is gray or is a shirt?
Do not round intermediate computations, and round your answer to the nearest hundredth.
(If necessary, consult a list of formulas.)
Answer:
70.73%
29/41 = 0.7073...
Move the decimal over 2 places and get: 70.73
Britney is buying a shirt and a hat at the mall. The shirt costs $31.18, and the hat costs $18.32. If Britney gives the sales clerk $100.00, how much change should she receive? (Ignore sales tax.)
The change she should receive is $50.50 and we can find it by using simple cost and price calculations.
What is selling price?
Selling price is the amount of money that a seller charges for a product or service. It is the amount of money that a buyer pays for a product or service. The selling price is determined by a variety of factors, such as the cost of production, the perceived value of the product or service, the market demand for the product or service, competitive pricing in the market, and the profit desired by the seller. The selling price may also be affected by the availability of financing options for buyers, taxes, and other applicable fees. The selling price is an important factor in marketing and promoting a product or service. It must be set at the right level to attract buyers and ensure that the seller can make a profit.
Selling price for a shirt = $31.18
Selling price for a hat = $18.32
Total amount she have = $100
Total selling price (for both) = $49.50
So, the remaining amount = $100 - $49.50
= $50.50
So, the change she should receive = $50.50
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Graph triangle ABC with vertices
A( − 4, − 3), B(0, – 2),
and C(2, 2) and and its
image after a 90° clockwise
rotation about point C.
Check the picture below.
If g(t) varies inversely with t and g(t)=9 when t=4. Find the value of g(t) when t=2
The value of g(t) is 18 when x is 2.
What is proportionality?Proportionality is defined as, the fact or quality of being in proper balance or relation as to size or quantity, degree, severity, etc
Given that, g(t) varies inversely with t and g(t)=9 when t=4.
According to question,
g(t) ∝ 1/t
Let k be constant of proportionality, then,
g(t) = k/t
Solving for k, we get,
9 = k/4
k = 36
When, t = 2, then
g(t) = 36/2
g(t) = 18
Hence, The value of g(t) is 18 when x is 2.
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(See Example 12) A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. In how many ways can the executive committee be formed?
Since , A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. The executive committee can be formed in 850668 ways.
a. The number is ⁴²P₅ = 42!/37!
=42×41×40×39× 38 ×37!/37!
=102080160 ways.
b. The number is ⁴²C₅ = 42!/ 5! × 37!
=42× 41× 40× 39 ×38×37!/ 5×4×3×2×1 ×37!
= 850668 ways.
If you have trouble applying concepts, consider pure mathematics. Select 4 objects out of 24 to replace the first problem. Since there is a replacement, it is a permutation. So the answer is ⁴²P₅= 102080160 possibilities. Obviously there can't be a substitute for the next, so it's a combo. So the answer is ⁴²C₅= 850668 ways.
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