Answers
The number of ways 3 man and 3 woman line up at the counter in a store is 720 ways.
What are factorials?Factorials is defined as the mathematical expression that is the product of the given number down to 1. It is denoted with the symbol n! which means that is n is given as 4, then it's factorial would be = 4×3×2×1 = 24.
Given that, three men and three women line up at a checkout counter in a store.
a) Number of ways = 6!
= 6×5×4×3×2×1
= 720 ways
b) The first person in line is a woman, and then the line alternates by gender that is a woman, a man, a woman, a man, a woman, a man, and so on
There are 3 number of ways for woman standing in the odd position and for men standing in the even position.
So, number of ways = 3!×3!
= 3×2×1×3×2×1
= 36 ways
c) There are 3 men and 3 women.
Probability first is a woman is 3/6
Probability second is a man is 3/5
Probability third is a woman is 2/4
Probability fourth is a man is 2/3
Probability fifth is a woman is 1/2
Probability sixth is a man is 1/1
Multiply all these probabilities together and you get:
3/6 × 3/5 × 2/4 × 2/3 × 1/2 × 1/1 = 0.05
Therefore, the number of ways 3 man and 3 woman line up if the first person in line is a woman, and then the line alternates by gender that is a woman is 36 ways.
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Related Questions
Please help me with this question please
Answers
How many bundles of strip flooring are needed to cover a rectangular floor area 16 ft by 14 ft 6 in size if a bundle of strip flooring contains 25 sq ft, and if 30 % extra must be allowed for side and end matching?
Answers
If a bundle of strip flooring has 25 sq ft and 30% extra is provided for side and end matching, 12.2 bundles of strip flooring are required to cover a rectangle floor space 16 ft by 14 ft 6 in size.
How do you find the area of the rectangle?Once the length and breadth of a rectangle are determined, the area is computed. The area of a rectangle may be calculated by multiplying its length and width.
In this question, because the rectangular floor has an area of 16 ft by 14 ft 6 in, we can compute the total area of the floor by multiplying 16 ft by 14 ft 6 in, which is 234 [tex]ft^{2}[/tex]. We also know that a strip flooring bundle comprises 25 square feet. As a result, we must determine how many bundles of strip flooring are required to cover the floor.
We must account for side and end matching, which is computed by increasing the total floor area by 30%. To determine the extra space required for side and end matching, multiply 234 ft2 by 0.3. This equates to 70.2 [tex]ft^{2}[/tex].
We can now compute the total area required to cover the floor. This is 234 [tex]ft^{2}[/tex] + 70.2 [tex]ft^{2}[/tex] = 304.2 [tex]ft^{2}[/tex].
Because each strip flooring bundle includes 25 square feet, we can divide 304.2 [tex]ft^{2}[/tex] by 25 to determine the total number of bundles required to cover the floor.
This corresponds to 12.2 bundles.
Therefore, 12.2 bundles of strip flooring are needed to cover a rectangular floor area 16 ft by 14 ft 6 in size, with 30% extra for side and end matching.
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Suppose you bought 45 shares of a telecommunications company 4 years ago at a price of $63.00 per share. You just sold it at $71.50 per share. How much money did you make? OOOO $377.50 $382.50 $387.50 $392.50 I don't know One attempt
Answers
You made a profit of $382.50 from selling the 45 shares of the telecommunications company.
How to calculate the profit you made from selling the 45 shares of the telecommunications companyFirst we need to determine the total cost of purchasing those shares, and then subtract that from the total revenue from selling them.
The total cost of purchasing the 45 shares at a price of $63.00 per share is:
45 shares x $63.00 per share = $2,835.00
The total revenue from selling the 45 shares at a price of $71.50 per share is:
45 shares x $71.50 per share = $3,217.50
To calculate the profit, we subtract the cost from the revenue:
Profit = Revenue - Cost
Profit = $3,217.50 - $2,835.00
Profit = $382.50
Therefore, you made a profit of $382.50 from selling the 45 shares of the telecommunications company.
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Please help:)
Limits calc questions
Answers
======================================================
Explanation:
If we plugged x = 4 into the expression, then we'll have 0 in the denominator. This causes a division by zero error.
Luckily the numerator factors to (x-4)(x-2)^2. This is found by using the Rational Root Theorem, along with either synthetic division or polynomial long division. I'll skip these steps unless you need me to write them out.
Once we know the numerator factors this way, we can then write the following steps:
[tex]L = \displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}\frac{(\text{x}-4)(\text{x}-2)^2}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}(\text{x}-2)^2\\\\\\L = (4-2)^2\\\\\\L = 4\\\\\\[/tex]
Therefore,
[tex]\displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}=4\\\\\\[/tex]
You can use graphing software like Desmos or GeoGebra to confirm the answer is correct. WolframAlpha is another good choice.
One is looking to invest 10 thousand dollars among 5 opportunities. Each investment should be integral in units of 500 dollars ($10K = 20 units). A portfolio corresponds to an investment policy. For example, (5,6,3,2,4) is a portfolio that invests 5 units in the first opportunity, 6 units in the second, 3 units in the third, 2 units in the fourth, and 4 units in the fifth opportunity. The investor has to invest all $10K, and at least one unit in each opportunity. The total number of portfolios is:
Answers
There are a total of 13 different ornaments to choose from, with 3 types of ornaments.
What is total number?Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.
When Cherry chooses at least 1 of each type, she will have to select a total of 5 ornaments. This means that Cherry can make a total of 13C5 (13 choose 5) different selections. This is equal to 715 different selections.
This can also be calculated by first selecting 1 ornament from each of the 3 types, which gives 3 different selections. Then, for the 2 remaining ornaments, Cherry can select any of the 13 ornaments, giving a total of 3 x 13 = 39 different selections. In total, this gives 3 + 39 = 42 different selections.
To conclude, Cherry can make a total of 715 different selections when she chooses at least 1 of each type of ornament.
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. how much does 2.6 cubic feet of water weigh in pounds? in tons?
Answers
Answer: Weight of water in 1 cubic foot water (in pounds)
Weight of water in 1 cubic foot water (in ounces)=
Step-by-step explanation:
Given: One cubic foot holds 7.48 gallons of water.
One gallon of water weighs 8.33 pounds.
To find the weight of water in 1 cubic foot water in pounds we apply Unitary method.
Weight of water in 1 cubic foot water (in pounds)
⇒Weight of water in 1 cubic foot water (in pounds)
Since , 1 pound = 16 ounces .
Weight of water in 1 cubic foot water (in ounces)=
Step-by-step explanation:
If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a (normal, uniform, skewed, or bimodal) distribution?
If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a (normal, uniform, skewed, or bimodal) distribution?
Answers
Answer:
Step-by-step explanation:
If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a normal distribution.
If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a normal distribution. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution.
The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that, as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution. This means that even if the original population distribution is skewed, bimodal, or any other shape, the distribution of the sample means will tend towards a normal distribution as the sample size increases.
The reason for this is that the sample means are essentially an average of a number of independent random variables, and the normal distribution is the result of the combination of many independent random variables. When the sample size is large, the distribution of the sample means becomes very close to a normal distribution, even if the underlying population is far from normal.
In the case of a bimodal distribution, the sample means will still approach a normal distribution as the sample size increases, but the distribution may have a different mean and standard deviation than the original population.
In the case of a very skewed distribution, the sample means will also approach a normal distribution as the sample size increases, but the distribution may still be skewed, just less so than the original population.
In conclusion, the Central Limit Theorem states that the distribution of the sample means will tend towards a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.
If my answer has satisfied your requirements, I would appreciate it if you would give me a rating : Brainliest Answer!
Please answer quickly thanks
Answers
The meaning of 5 = f(I) is that the 5% have an income of $6000
The average rate is that %0.054 per thousand of dollars
How to determine the solution to the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The equation is given as
5 = f(I)
This means that:
We find x when f(I) = 5
Using the graph, we have
x = 6
This means that the income is $6000
The average rate of changeThis is calculated as
Rate = (f(x2) - f(x1))/(x2 - x1)
Substitute the known values in the above equation, so, we have the following representation
Rate = (1.8 - 4.5)/(10 - 60)
Evaluate
Rate = 0.054
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The profit a company makes decreases exponentially at a rate of 0.9% per year. In 2014, the profit was $9500. Calculate the profit in 2019.
Answers
Answer: $9080.13
Step-by-step explanation:
use the equation y=b(x)^t, where b is the original profit, x is the percent remaining after one year, and t is the amount of years.
SUBSTITUTE:
y=9500(0.991)^5
Use calculator, and y=9080.126 in 2019. Round off to $9080.13
hope this helps!
MM
Compare the rates to find which is greater.
45 points in 36 hours or 18 points in 15 hours
The unit rate for 45 points in 36 hours is
rate for 45 points in 36 hours is
Answers
18 points in 15 hour is greater than 45 points in 36 hours.
What is unit rate?The unit rate compares a certain number of units of one quantity to units of another quantity. In other words, the second quantity in the comparison is always 1.
45 points in 36 hours and 18 points in 15 hours.
Points per hour
45 points in 36 hours is given by,
[tex]\frac{45}{60} =1.25[/tex] points.
18 points in 15 hours is given by,
[tex]\frac{18}{15}[/tex] = 1.2 points.
On comparing these points 1.2 > 1.25.
Hence, 18 points in 15 hour is greater than 45 points in 36 hours.
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Find the equation of any line parallel to the line 2x-3y=6
Answers
Answer:
The equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6 is 2x + 3y - 5 = 0.
Step-by-step explanation:
High Tech Chip Company is expected to have EPS in the coming year of $2.50. The expected ROE is 12.5%. An appropriate required return on the stock is 11%. If the firm has a plowback ratio of 70%, the growth rate of dividends should be
Answers
Required return on the stock = 11% Expected return on equity = 12.5%
Growth rate = (Expected return on equity - Required return on the stock) * Plowback Ratio
Growth rate = (12.5% - 11%) * 0.7 Growth rate = 0.6875%
What is the distance from the origin to point A graphed on the complex plane below?
-5-4-3
O √5
O√13
O 9
-94
--
13
A
& 1 14.
543
2
1
+2+
Mark thin ond roturn
-3-
4
4
L
1 2 3 4 5 X
Save and Exit
57
Answers
The distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.
What is complex plane?The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.
Complex numbers can be geometrically interpreted using the complex plane. They add like vectors when addition is applied. Polar coordinates make it simpler to represent the product of two complex numbers, whose magnitude or modulus is the sum of their absolute values.
The coordinates of the point A are (-3, -2).
If we extend the line from the origin to the point A it forms a right angled triangle with base = 3 and height = 2.
Using the Pythagoras theorem:
c² = a² + b²
Substituting the values:
c² = (2)² + (3)²
c = √13
Hence, the distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Landon sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
28 visitors purchased no costume.
319 visitors purchased exactly one costume.
34 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase exactly one costume as a fraction in simplest form.
Answers
Answer:
319/381
Step-by-step explanation:
You want the probability that a customer will buy exactly one costume, given that the numbers buying 0, 1, or >1 costumes were 28, 319, and 34, respectively.
Exactly oneThe probability is the ratio of customers buying one to total customers:
P(n=1) = 319/(28 +319 +34) = 319/381
This fraction cannot be reduced, so ...
The probability the next person will purchase exactly one costume is 319/381.
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Solve basic applications of percent
Question
After 3 months of a new weightlifting program, Lisa has lost 12% of her original weight. She lost 24 lb.
original weight?
Provide your answer below:
Rent attribution
FEEDBACK
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Answers
Answer:
200 lb
Step-by-step explanation:
Let her original weight be [tex]x[/tex].
[tex]0.12x=24 \implies x=200[/tex]
Which of the following complexe numbers is equal to (4 + 3i)(5 - 2i)?
20 + i
20+6i
26 + i^2
26 + 7i
Answers
Answer:
The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:
(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i
= 20 - 8i + 15i - 6i^2
= 20 + 7i - 6(-1)
= 26 + 7i
So the answer is (4) 26 + 7i.
I believe the answer is (d) 26 + 7i.
What are the lengths of KL, LM, MN, and NK?
Answers
The length of
KL = 7.8units
LM = 7.1 units
MN = 8.5 units
NK = 7.8units
What is the distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).
KL = √1-(-4)²+3-(-3))²
KL = √5²+6²
KL = √ 25+36
KL = √ 61 = 7.8 units
To find the length KN
KN = √ 1-7)²+ 3(-2)²
KN = √ 6²+5²
KN = √ 36+ 25
KN = √ 61 = 7.8 units
to find LM
LM = √-4-1)²+-3(-8)²
LM = √25+25
LM = √50
LM = 7.1 units
to find MN
√ 7-1)²+ -2-(-8)²
MN= √ 6²+6²
MN = √ 36+36
MN=√ 72
MN = 8.5 units
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Choose the answer that is equal to the expression below.
5^2.5^0
Answers
Answer:
5
Step-by-step explanation:
The expression 5^2.5^0 is equal to 5^(2.5^0), which can be simplified as follows:
2.5^0 = 1 (because any number raised to the power of 0 is equal to 1)
So, 5^2.5^0 = 5^1 = 5
Therefore, the answer is 5.
Omg please someone help me
Answers
Answer:
Planes
Step-by-step explanation:
You can think of a plane as a sheet of paper that goes on in all directions.
Answer:
B. planes
Step-by-step explanation:
The grammer makes sense
Swimming Pool On a certain hot summer's day, 507 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $761.75. How many children and how many adults swam at the public pool that day?
Answers
Answer:384 children and 123 adults swam at the public school.
Step-by-step explanation:
A bee weighs 2.5 x 10-4 pounds. A
moose weighs 1.25 × 10³ pounds.
How many bees would equal the
weight of a moose? (Give your
answer in standard form.)
Answers
The number of bees that will equal the mass of a single moose is 5 × 10⁶.
How many bees would equal the weight of a moose?Given the data in the question;
Mass of one bee = 2.5 × 10⁻⁴ poundsMass of one moose = 1.25 × 10³ poundsTo determine the number of bees that will equal the mass of a single moose.
Let the number be represented by x.
Hence;
Number of bees × mass of bee = mass of moose
n × ( 2.5 × 10⁻⁴ ) = 1.25 × 10³
Divide both sides by ( 2.5 × 10⁻⁴ ).
n = ( 1.25 × 10³ ) / ( 2.5 × 10⁻⁴ )
n = 1250 / 0.00025
n = 5,000,000
Therefore, the number of bees is 5,000,000.
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Find the rate of change of the function on the interval specified for the real number h  f(x) = 7x+4 on [ x,x+h]
Answers
The rate of change of the function on the interval specified as in the task content is; 7.
What is the rate of change of the function on the given interval?It follows from the task content that the rate of change of the function on the interval specified for the real number h  f(x) = 7x+4 on [ x,x+h] is to be determined.
Since the function is a linear function, it follows that the rate of change is a constant and hence is given by;
f'(x) = 7.
Ultimately, the rate of change of the function on the given interval is; 7.
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A car purchased for $9,000 depreciates at a constant rate of 16.5%. What will be the value of the car in 6 years.
The value in 6 years is $_____.
round answer to 2 decimal places
Answers
The value in 6 years is $3050.43
What is depreciation?The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life.
Using the formula:
Value = P(1-r)^n
From the question, the original value is $9,000, the depreciation rate is 16.5% or 0.165, and the time is 6 years. Plugging in the values:
Putting the values into the formula
Value = 9000(1-0.165)^6
Value = 3050.43
Hence, the value of the car after 6 years will be $3050.43
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Examine the right triangle below, solve for x, round to two decimal places if
necessary.
Answers
The value of X in the right angle triangle that is given above would be = 28.89
How to calculate the missing side of a triangle?The given figure shows a right triangle with a hypotenuse with a length of 48. An indicated angle has a measure of
53∘.
To calculate the missing side the formula;
cos 0 = adj/hyp
where, adj = X
hyp = 48
0 = 53°
cos 53° = X/ 48
Make X the subject of formula;
X = 48 × cos 53°
X = 48 × 0.601815023
X = 28.887121104
X = 28.89 ( to two decimal places)
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let n be an integer. show that if a, b are relatively prime integers, each of which divides n, then ab divides n.
Answers
[tex]a*b[/tex] must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.
Let n be an integer and a, b be relatively prime integers, each of which divides n. This means that a and b have no common factors other than 1. According to the Fundamental Theorem of Arithmetic, the prime factorization of n can be written as n = p1^k1 * p2^k2 * ... * pn^kn. Since a and b divide n, each of their prime factorizations must contain all of the prime factors of n, and the exponents must be less than or equal to the exponents of n. Therefore, a*b must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.
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100 POINTSSS WILL VOTE MOST BRAINLIEST
The table lists several points on a polar graph.
θ 0 pi over 6 pi over 3 pi over 2 2 pi over 3 5 pi over 6 π
r 4 2 −2 −4 −2 2 4
Which of the following graphs is represented by the table?
Answers
Answer:
r = 4 cos(2θ)
See the attached image for a graph.
Step-by-step explanation:
The points given by the table are in the graph of a cosine rose with 4 petals whose amplitudes are 4.
For the equation r = a cos(nθ), a is the amplitude of the petals (4), and n is half the number of petals, as there are an even number of petals (4/2 = 2).
Hence,
r = 4 cos(2θ)
Mrs Chong paid for a frying pan that cost $64 with some $10, $5 and $2 notes .If she used a total of 15 notes,how many $5 notes did she use?
Required process!
Thank you
Answers
For every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.
What is Inequalities?
Inequalities are mathematical statements used to express the comparison between two values. Unlike equalities (e.g., 3 + 4 = 7), which use the "equals" sign (=), inequalities use symbols such as "greater than" (>), "less than" (<), "greater than or equal to" (>=), and "less than or equal to" (<=) to express a relationship between the values.
Let's call the number of $10 notes Mrs. Chong used as "x".
We know the total amount she paid was $64, and the number of notes used was 15, so we can set up an equation:
10x + 5y + 2z = 64
Where "y" is the number of $5 notes used and "z" is the number of $2 notes used. We know that x + y + z = 15 (because this is the total number of notes used).
We can substitute x = 15 - y - z into the first equation:
10(15 - y - z) + 5y + 2z = 64
Expanding the equation:
150 - 10y - 10z + 5y + 2z = 64
Combining like terms:
150 - 5y + 3z = 64
Subtracting 150 from both sides:
-5y + 3z = -86
Dividing both sides by -5:
y - (3/5)z = 17.2
So, for every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.
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Solve for x
.........
Answers
The solution for x in the trapezoid is x = 12
How to solve for x in the trapezoid?
The midsegment of a trapezoid is a line segment that connects the midpoints of the parallel sides of the trapezoid.
The midsegment of a trapezoid is parallel to the bases of the trapezoid and is equal in length to half the sum of the lengths of the two bases. That is:
DE = 1/2 * (KL + JM)
14 = 1/2 * (11 + 3x - 19)
14 = 1/2 * (3x - 8)
14 * 2 = 3x - 8
28 = 3x - 8
3x = 28 + 8
3x = 36
x = 36/3
x = 12
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100 points!!!!!
Using the information for West Coast Entertainment Inc. presented in the table below, determine the following:
1. The number of shares bought and sold on this trading day.
2. Amount of income per share paid to a stockholder in the last 12 months.
3. Percentage of change in the stock's price since the beginning of the year.
Answers
Percentage of change in the stock's price since the beginning of the year is: 12.32%
What is stock's price?The price at which a stock's share is currently trading on the market is referred to as the stock price. Every publicly listed company issues its shares at a price, which is an estimation of their value that, ideally, corresponds to the worth of the firm itself.
The market forces of supply and demand govern a company's share price once it becomes public and its shares begin trading on a stock exchange. Price increases will occur if there is a large demand for its shares. A stock's price might be reduced by sellers if the company's prospects for future growth appear uncertain.
Given that,
Closing price today = $21.20
Closing price on the previous trading day= $28.83
Difference between closing price today and closing price on the previous trading day= $21.20 - $28.83
= $7.63
Percentage of change in the stock price since the beginning of the year
= Year-to-date % change
= 12.32%
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Consider the following function.
f(x)= |x+5|, x>-5
Find the inverse function f-¹.
I
f-¹(x) =
State the domain and range of f. (Enter your answers using interval notation.)
domain
range
State the domain and range of f-1. (Enter your answers using interval notation.)
domain
range
Answers
Inverse function for the function f(x)= |x+5|, x>-5 is f⁻¹(x) = -5 ± x
What is inverse function?An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.
Given function,
f(x) = |x + 5| , x>-5
It can be written as
y = |x + 5|
Replacing x with y
x = |y + 5|
Solving for y
y + 5 = ± x
y = -5 ± x
Replacing y with f⁻¹(x)
f⁻¹(x) = -5 ± x
Hence, f⁻¹(x) = -5 ± x is the inverse function for function f(x)= |x+5|, x>-5
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