There are 6840 ways to choose a president, a vice-president, and a secretary from a committee of 20 members.
To choose a president, a vice-president, and a secretary from a committee of 20 members,
We will use the formula for combinations,
which is: C(n, k) = n! / (k! (n - k)!)
where n is the total number of members and k is the number of members being chosen.
So, for n = 20 and k = 1, we have:
C(20, 1) = 20! / (1! (20 - 1)!) = 20
This gives us 20 choices for the president.
For the vice president,
We need to choose 1 member from the remaining 19 members.
So, for n = 19 and k = 1,
we have:
C(19, 1) = 19! / (1! (19 - 1)!) = 19
This gives us 19 choices for the vice president.
Finally, for the secretary,
We need to choose 1 member from the remaining 18 members.
So, for n = 18 and k = 1,
we have:
C(18, 1) = 18! / (1! (18 - 1)!) = 18
This gives us 18 choices for the secretary.
Now for finding the total number of ways to choose the three positions, we multiply the number of choices for each position:
So, the required number of ways will be 20 * 19 * 18 = 6840
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twelve lights are tested to see if they last as long as the manufacturer claims to they do. three light bulbs fail the test. two light bulbs are selected at random with replacement. find the probability that both bulbs fail the test.
The probability that both bulbs fail the test is 1/9. This is because out of the twelve lights, three of them have already failed the test, leaving nine lights that passed.
This is because out of the 12 lights tested, 3 have already failed and there is a 1 in 4 chance that the two bulbs selected at random will be the same two failed bulbs.
Since the bulbs are selected at random with replacement, the probability that both bulbs fail the test is 1/9, or 11.11%.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
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You are buying an old "go to work" pickup with a price tag of $1,600. You apply a down payment of $200. 0. Sales tax is 6. 5%. You will have to borrow $1,504 at 8% interest for one year to complete the purchase. What will your full purchase price be with principal, tax and interest
For the given case the full purchase price will be $1,628.92,Principal will be $1,600, Tax will be $101.60,Interest will be $27.32 and Total is $1,728.92.
To calculate the full purchase price, first, you must calculate the sales tax. To do this, multiply the price of the pickup ($1,600) by the sales tax rate (6.5%), which equals $101.60. Next, you must calculate the interest. To do this, multiply the amount borrowed ($1,504) by the interest rate (8%) and the number of years (1), which equals $27.32.
Finally, you must add the principal ($1,600), the sales tax ($101.60), and the interest ($27.32) to get the full purchase price of $1,728.92. Once you subtract the down payment of $200, the total purchase price is $1,628.92.
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The average tuition for a full-time under-
graduate student in a public college in 2002 was $4,790. In
2012 it was $8,240. Using the linear function model, estimate
the cost of tuition in 2018.
The estimated cost of tuition in 2018 using this linear function model is $726,430
What is the linear function?
A linear function is a mathematical function that describes a straight line. The general form of a linear function is:
y = f(x) = mx + b
To estimate the cost of tuition in 2018 using a linear function model, we can use the two given data points to find the slope and y-intercept of the line.
First, we can find the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) is the data point for 2002 and (x2, y2) is the data point for 2012.
Substituting the values, we get:
m = (8,240 - 4,790) / (2012 - 2002) = 3,450 / 10 = 345
Next, we can use one of the data points and the slope to find the y-intercept of the line. Let's use the data point for 2002:
y = mx + b
4,790 = 345 * 2002 + b
b = 4,790 - 345 * 2002 = -1,015,290
So, the equation of the line is y = 345x - 1,015,290
To estimate the cost of tuition in 2018, we can substitute x = 2018 into the equation:
y = 345(2018) - 1,015,290 = 726,430
Hence, the estimated cost of tuition in 2018 using this linear function model is $726,430
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Please help you will get 25 points!
Explore Part 2
Here is a number pyramid puzzle.
Each number is the product of the two numbers directly below it.
Complete the pyramid.
Answer:
Check image :D
Step-by-step explanation:
The image is the answer. I hope this helps you out :D
Which of the inequalities are equivalent?
3x+6≤8+ 2x
5x-527x-9
12-3x <=18
-2-3x≥-3-x
The inequalities that are equivalent are 3x+6≤8+ 2x and 12-3x ≤18
What are inequalities?
Inequalities are simply defined as relations that makes a non-equal comparison between two mathematical expressions, equations or numbers.
It is mostly used to compare two numbers or expressions based on the magnitude on the number line.
Inequality signs in mathematic include;
< represents less than> represents greater than≤ represents less than or equal to≥ represents greater than or equal toGiven the inequalities;
3x + 6 ≤ 8 + 2x
collect like terms
3x - 2x≤ 8 - 6
subtract like terms
x ≤ 2
12-3x ≤18
collect like terms
3x≤ 18 - 12
3x ≤ 6
Divide both sides by 3
x ≤ 2
Hence, the inequalities are 3x+6≤8+ 2x and 12-3x ≤18
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HURRY 60 POINTS Question Consider the two-way table. Group 1 Group 2 Category A 36 20 Category B 12 35 Complete the table below to show the relative frequencies of the data in the first column. Enter numbers in the boxes as decimals to the hundredth place. Group 1 Category A Category B
Answer:
Category A 0.75
Category B 0.25
Hope it helps !!
Please help me i have a horrible grade in this class
If the triangles ABC and DEF are similar, then the measurement of line segment DE = 108.72 units.
What are triangles?
Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.
It is given that triangle ABC is similar to triangle DEF.
It can be seen in the image that ΔDEF is a dilated version of ΔABC.
In ΔABC the measurement of side AB = 23 units
In ΔABC the measurement of side BC = 11 units
In ΔDEF the measurement of side EF = 52 units
In ΔDEF the measurement of side DE = x units
Apply the formula for indirect measurement to find the measurement of side DE.
AB/DE = BC/EF
Substitute the values in the equation -
23/x = 11/52
23 × 52 = 11x
x = (23 × 52)/11
x = 1196/11
x = 108.72
Therefore, the measurement of DE is 108.72 units.
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Benita buys 2 shirts for the same price, s. The sales tax rate is 6. 5%.
Write an expression to represent the total cost of the shirts in two different ways.
Enter the correct answers in the boxes
The required total cost of the two shirts after 6.5% of the tax is given as 2.13s.
Now, According to the question:
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Benita buys 2 shirts for the same price, s.
The sales tax rate is 6. 5%.
Write an expression to represent the total cost of the shirts.
1 way, paid the cost of 2 shirts jointly
The total cost of the two shirts becomes,
Total cost = 2[ s + 0.065s]
Total cost = 2.13s
2nd way, paid the cost of two shirts individually,
total cost = s + 0.065s + s + 0.065s
= 2.13s
Thus, the required total cost of the two shirts after 6.5% of the tax is given as 2.13s.
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8 of the tables at Joy's Italian Restaurant are full and the other 13 tables are empty. What is the ratio of the number of empty tables to the total number of tables?
The ratio of the number of empty tables to the total number of tables is 13:21
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, 8 of the tables at Joy's Italian Restaurant are full, and the other 13 tables are empty, we are asked to find the ratio of the number of empty tables to the total number of tables,
Number of empty table = 13
Total number of tables = 13 + 8 = 21
Ratio of the number of empty tables to the total number of tables = 13 / 21
Hence, the ratio of the number of empty tables to the total number of tables is 13:21
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The side view of a bookend is shown. The perimeter of the bookend is 58
centimeters.
A four-sided closed figure is shown. The lengths of the sides are five times m minus fourteen, two times m minus seven, three halves times m plus two, and three times m plus eight.
Part A. Write an equation in simplest form that represents the perimeter of the bookend in centimeters.
Part B. What is the value of m
?
Enter the correct answers in the boxes.
The equation in the simplest form that represents the perimeter of the bookend in centimeters is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Part A :
Perimeter of a closed figure is the sum of the lengths of it's boundary.
Given the lengths of the sides of the bookend as,
5m - 14, 2m - 7, 3/2 m + 2 and 3m + 8.
Perimeter is given as 58 centimeters.
(5m - 14) + (2m - 7) + (3/2 m + 2) + (3m + 8) = 58
(5m + 2m + 3/2 m + 3m) + (-14 - 7 + 2 + 8) = 58
23/2 m - 11 = 58
11 [tex]\frac{1}{2}[/tex] m - 11 = 58
Part B :
We have,
11 [tex]\frac{1}{2}[/tex] m - 11 = 58
11 [tex]\frac{1}{2}[/tex] m = 58 + 11
11 [tex]\frac{1}{2}[/tex] m = 69
23/2 m = 69
m = 6
Hence the required equation is 11 [tex]\frac{1}{2}[/tex] m - 11 = 58 and the value of m is 6.
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I need help solving
Answer: 189 degrees
Step-by-step explanation:
Since 17x + 2 = 16x + 9, we can solve for x:
17x + 2 = 16x + 9
Subtract 16x from both sides:
x + 2 = 9
Subtract 2 from both sides:
x = 11
The angle indicated in bold is 17x + 2, so we just substitute 11 into x and get 17 * 11 + 2, = 187 + 2 = 189 degrees :>
A line has a slope of 7 and passes through the point (-1, -8). Write its equation in slope-
intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
Step-by-step explanation:
we know the slope and we have a point , so
y = 7x + b
sub in the point ...
-8 = 7(-1) + b
-8 + 7 = b
b = -1
y = 7x - 1
His former car was able to travel 20. 28 miles per gallon. Is Xavier getting better gas
mileage in his new car? Explain.
Xavier is not getting better mileage with his new car.
it is given that
distance traveled by Xavier's new car in 20.28 gallons = 472miles
the mileage can be calculated using the formula = (distance traveled)/( gallons of fuel used).
So, the mileage of the new car = 472/20 = 23.06 miles per gallon, and the mileage of Xavier's former car = 20.28 miles per gallon.
From the above data, we can see that the mileage of the former car is greater than the new car.
Therefore, Xavier is not getting better mileage with his new car.
The given question is incomplete, the complete question is
Xavier's new car uses 25 gallons for 472 miles, His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?
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a hotel chain, with 3 locations, wants to survey customers who stayed at their facilities over the last year to determine customer satisfaction profiles. they plan to use a sample of customers who visited the hotel chain over the last year. which of the below sampling methods describes a stratified sampling method?
It describes the Cluster Sampling method.
It is a cluster sampling method because customers are divided into clusters at random and no personal judgment is involved. Thus, each cluster has an equal probability of selection, and sampling is done randomly.
Cluster sampling involves splitting the population into subgroups, but each subgroup should have similar properties to the whole sample.
Cluster sampling is a probability sampling method in which we divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as our sample.
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How many groups of 1/8 are in 15/4
Answer:
30 groups
Step-by-step explanation:
We can first set 15/4 to have the same denominator as 1/8, which will be 30/8.
Since the question asks for the number of groups of 1/8, 30/8 will consist of 30 groups of 1/8.
I am building a kite. The short crosspiece (short diagonal) is 24". I have 2 rods that are 37" and 2 rods that are 13". Those rods can be used for the outside edges of the kite. How long does the longer cross piece (long diagonal) need to be to make a kite?
The longer crosspiece needs to be about 18 inches long.
To find the length of the longer crosspiece, you need to use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (the hypotenuse).
Let's call the length of the longer crosspiece x. Then, we have two right triangles:
x^2 = (37-24)^2 + (13)^2
x^2 = 13^2 + 13^2
Solving for x:
x = sqrt(13^2 + 13^2) = sqrt(2 * 13^2) = 13 * sqrt(2) = 18.03 inches
So, the longer crosspiece needs to be about 18 inches long.
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an engine with a 12- gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour. the tank was full when the engine began running, and there are now 9.3 gallons left in the tank. create and solve an equation to find the number of hours x the engine has been running.
If the engine with 12 gallon fuel tank uses fuel at a constant rate of 0.6 gallons per hour , then the equation to find number hours the engine has been running is "12 - 0.6x = 9.3" .
the total capacity of the tank is = 12 gallon ;
the constant use rate of engine is = 0.6 gallons per hour ;
the amount of fuel left in the tank is = 9.3 gallons ;
let the number of hours the engine is running is = x hours ;
the above situation can be represented as ⇒ 12 - 0.6x = 9.3 ;
⇒ 12 - 0.6x = 9.3 ;
⇒ 12 - 9.3 = 0.6x ;
⇒ 0.6x = 2.7 ;
⇒ x = 2.7/0.6 ;
⇒ x = 4.5 hours
Therefore , the engine has been running for 4.5 hours .
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Frank owes $212 on his credit card. Then, he charges $105 more. What is the new balance on Frank's credit card? Write your answer as an integer.
Answer:
Step-by-step explanation:
212+105
We make this the equation because it says he charges 105 and he owes 212, so 212+105=317
Frank owes: $317
Nicole is buying dog nuts for the bus ride to cheer competition. Plain glazed donuts are $4 per box and chocolate cake donuts cost $5 per box. She spends a total of $91 for 20 boxes. How many boxes of each kind of donut did she buy?
Answer: We can start solving this problem by using a system of equations. Let x be the number of plain glazed donuts Nicole buys, and y be the number of chocolate cake donuts she buys. We know that:
x + y = 20 (The total number of boxes of donuts she buys is 20)
4x + 5y = 91 (The total amount of money she spends is $91)
We can use the first equation to solve for one variable in terms of the other. For example, we can substitute x = 20 - y into the second equation:
4(20 - y) + 5y = 91
80 - 4y + 5y = 91
-4y + 5y = 91 - 80
y = 11
So Nicole bought 11 boxes of chocolate cake donuts. We can substitute that back into the first equation to find the number of plain glazed donuts she bought:
x + 11 = 20
x = 9
So Nicole bought 9 boxes of plain glazed donuts.
We can check our answer by substituting our values of x and y back into the original equations:
x + y = 9 + 11 = 20 (This is the total number of boxes of donuts she bought, which is 20)
4x + 5y = 4(9) + 5(11) = 91 (This is the total amount of money she spent, which is $91)
Both equations are true, so our solution is correct.
Step-by-step explanation:
What is the length of line segment AB?
B
ty
A
units
The length of line segment AB is 8 cm in the above-mentioned diagram.
What is the length in units of line segment?A line segment is hence a section or component of a line with two endpoints. A line segment, unlike a line, has a set length. Measuring the length of a line segment can be done using either metric measurements, such as millimetres or centimetres, or conventional measurements, such as feet or inches.Let's now examine how to calculate the length of a line segment given the coordinates of its two ends. The distance formula, D = [(x2x1 x 2 x 1)2 + (y2y1 y 2 y 1)2], is used in this situation.Place the ruler's zero marking along the line's starting point to determine the length of a line segment AB.To learn more about segment refer to:
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Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
The axis of symmetry of the graphed function is:
x = -2
How to find the axis of symmetry?Here we want to find the axis of symmetry of the graphed function, which is a quadratic one.
The axis of symmetry is a line of the form:
x = a
Where a is a real number
Such that it divides the graph of the function in two equal parts.
Notice that the parabola is perfectly divided by the line x = -2, so that is the axis of symmetry of the graphed function.
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which property justifies that 3(x-2) is equivalent to 3x-6?
The distributive property of multiplication justifies that 3(x-2) is equivalent to 3x-6.
What is distributive property of multiplication?When a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then the two products added together to produce the same result as multiplying the first number by the sum. When you multiply a value by a sum, the distributive property of multiplication over addition is used. For instance, suppose you want to multiply 5 by the sum of 10 + 3. When we have similar terms, we usually add the numbers and then multiply by 5. However, the property states that you must first multiply each addend by 5.
Here,
3(x-2) is equivalent to 3x-6 due to the distributive property of multiplication.
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Translate 6 units right and 3 units up.
Answer:
Step-by-step explanation:
Move each point up by 3 points. you should have the same shape moved up on the graph. then move each point to the right by 6 squares. This should be your final square D''E''G''F''
is y=2.2x proportional
Answer:
yes
Step-by-step explanation:
A proportional relation has an equation of the form
y = kx,
where k is a real number.
y = 2.2x is an equation of the form y = kx with k = 2.2, so y = 2.2x is proportional.
Answer: yes
a) what is the probability that the company will make less than $2m? b) what is the probability that the company will make less than $1m or at least $2m?
The probability that the company will make less than $2m is 0.8 and b) the probability that the company will make less than $1m or at least $2m is 0.7
Here we are given respective probabilities of the revenue a company could make in a year.
a) Here we need to find the probability that it makes a revenue less than $ 2 million
This means that we need t find the probability that it makes revenue
less than $1M + greater than $1 M but less than $2M
= P(A₁) + P(A₂)
= 0.5 + 0.3
= 0.8
b)
The probability that the company will make less than $1M or at least $2M is
P(A₁ U A₃)
= P(A₁) + P(A₃) - P(A₁ ∩ A₃)
Since A₁ and A₃ are clearly mutually exclusive events, P(A₁ ∩ A₃) will be 0.
Hence we get
P(A₁ U A₃) = 0.5 + 0.2
= 0.7
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Complete Question
Assume the following in regard to a company’s annual revenue:
A₁ : Revenue < $1M; P(A₁) = 0.5
A₂ : Revenue > $1M but < $2M; P(A₂) = 0.3
A₃ : Revenue > $2M; P(A₃) = 0.2
a)What is the probability that the company will make less than $2M?
b)What is the probability that the company will make less than $1M or at least $2M
a certain family has 6 children, consisting of 3 boys and 3 girls. assuming that all birth orders are equally likely, what is the probability that the 3 eldest children are the 3 girls?
The probability that the 3 eldest children are the 3 girls is 0.05.
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To determine the probability, we can use the permutation.
A permutation is an arrangement of a set of objects in a particular order. It is a way of counting the number of ways that a group of items can be arranged in a specific order.
There are a total of 6! ways in which the 6 children can be ordered. If the first 3 children are girls, there are 3! ways to arrange the 3 girls, and 3! ways to arrange the 3 boys. Therefore, the probability that the 3 eldest children are the 3 girls is
(3! x 3!) / 6! = (6 x 6) / 720 = 0.05
Therefore, there is a 0.05 chance or probability that the 3 eldest children are the 3 girls.
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Amelia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.60 plus $0.50 per mile. The total fare was $13.60, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
Answer:
18 miles
Step-by-step explanation:
m = # of miles
$4.60 + ($0.50/mi)m = $13.60
($0.50/mi)m = $13.60 - $4.60 = $9.00
m = ($9.00) / ($0.50/mi) = 18 miles
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=880(1. 958)^xy=880(1. 958)x
The change represents growth and percentage rate of increase is 95.8%.
The exponential function y = 880(1.958)^x is a function that models growth.
The base of the exponential function, 1.958, is greater than 1. This means that the function is increasing with respect to x, which is the independent variable.
For every unit increase in x, the function increases by a factor of 1.958. This is evident from the fact that 1.958 is raised to the power of x.
The percentage rate of increase is calculated by taking the difference between the base of the exponential function and 1, and then multiplying that difference by 100%.
In this case, the base of the exponential function is 1.958, so the percentage rate of increase is
(1.958- 1)*100 = 95.8%.
This means that for every unit increase in x, the value of y increases by 95.8% of its previous value.
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A sphere has a radius of 2 mm. What is the difference between the volume of the sphere and an approximation using a left sum with 16 intervals? Round to the nearest hundredth
The difference between the volume of the sphere and an approximation using a left sum with 16 intervals is 17.51 mm.
The term called volume in math is known as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
Here we know that the sphere has a radius of 2 mm.
Then the volume of the sphere is calculated by using the formula,
=> V = 4/3πr³
Here we know that the value of r = 2.
Then the volume is calculated as,
=> V = 4/3 x π x 2³
When we simplify this one then we get,
=> V = 10.67π = 33.51
Here we need to find the difference between the volume of the sphere and an approximation using a left sum with 16 intervals is
=> 33.51 - 16
=> 17.51
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Please help me with this geometry question