how many ways are there for eight men and five women to stand in a line so that no tow women stand right next to each other
There are therefore 609638400 different ways to arrange eight men and five women in a line so that no two women are positioned adjacent to one another.
What is fundamental counting principle?The basic counting principle is a method for keeping track of all the potential outcomes in a situation. It states that there are n*m ways to carry out both of these activities if there are n ways to carry out one action and m ways to carry out another action after that.
Here,
Number of ways men can stand,
=8!
=40320 ways
Number of ways women are standing,
=9P5
As shown in the image,
=15120 ways
For arranging both of them,
=40320*15120
=609638400 ways
So there is 609638400 ways of arranging eight men and five women to stand in a line so that no two women stand right next to each other.
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A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?.
The shortest length of fence that the rancher can use is 6000 ft.
What is meant by length?
The measuring of one thing from finish to finish or on its longest aspect, or a measuring of a selected a part of one thing is known as length.
Main Body:
x = width of rectangle
y = length of rectangle
A = area of rectangle = xy = 1500000 ft^2
L = length of fencing needed = 2(x + y) + x = 3x + 2y
L = 3x + 2(1500000/x) = 3x + 3(10^6)x^(-1)
As x –> 0+, L –> +inf.
As x –> +inf, L –> (3x)+.
Sketch and see that there will be a minimum in Quadrant I.
dL/dx = 3 - 3(10^6)x^(-2)
Extrema occur when dL/dx = 0:
3 - 3(10^6)x^(-2) = 0
(10^6)x^(-2) = 1
x^2 = 10^6
x > 0, so x = 1000 feet for shortest length.
Hence,Shortest L = 3000 + 3(10^6)(10^3)^(-1) = 6000 feet.
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Tom bought a bag full of coal. After one week the bag was 2 3 full. During the next week he used 1 4 of the remaining coal. What fraction was left in the bag?.
We conclude that there is zero (0) fraction of coal left in the bag with Tom.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
The number is represented mathematically as a quotient, where the numerator and denominator are split.
Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
The numerator of a proper fraction is less than the denominator.
So, a fraction of coal left in the bag:
After 1 week the was 2/3 full. So, we have:
1 - 2/3 = 1/3
Next week, he used the remaining 1/3 coal. Now, we have:
1/3 - 1/3 = 0/0
Therefore, we conclude that there is zero (0) fraction of coal left in the bag with Tom.
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Correct question:
Tom bought a bag full of coal. After one week the bag was 2/3 full. During the next week, he used 1/3 of the remaining coal. What fraction was left in the bag?
Factorise the following x^2+6x+8
Answer: (x+2) (x+4)
Hope this helps!
Which number is greatest? A. 3.4 × 10-2 B. 4.3 × 10-3 C. 5.2 × 10-4 D. 6.1 × 10-4
Mathwy is To solve this type of3.4 x 10-2 PEMDAS
hello! please help me with this, it’s due tomorrow (picture)
Answer:
[tex]\frac{8}{b^{30} }[/tex]
Step-by-step explanation:
Start within the parentheses
1. Divide coefficients
6/3 = 2
2. Divide variables
When dividing exponents with the same base, in this case b, you subtract.
b^20 - b^30 = b^-10
3. Exponent outside parentheses
When there's an exponent on an exponent, you multiply the exponents.
(2b^-10)^3
8 b^-30
4. Simplify?
This step isn't necessary, but when you have a negative exponent on a variable, the variable can be put in the denominator with a positive exponent.
8b^-30 can become 8/b^30
Leonardo put a $600 ring on layaway by making a 10% down payment and agreeing to pay $65 a week. How many weeks will it take leonardo to pay off the ring?.
It will take approx. 8.3 weeks to completely pay the remaining amount after the down payment.
Given, Leonardo put a $600 ring on layaway by making a 10% down payment and agreeing to pay $65 a week.
So, he made a down payment of 10% of $600 i.e. $60
remaining amount to pay be,
600 - 60 = 540
Let he will take x weeks to pay the remaining amount.
Now, if he pay $65 per week
then, 65x = 540
x = 540/65
x = 8.31
So, it will take approx. 8 - 9 weeks to completely pay the remaining amount after the down payment.
Hence, it will take approx. 8.3 weeks to completely pay the remaining amount after the down payment.
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Answer:
9 weeks
Step by step explanation:
It’s right.
14. Ronny is taking a jar with 50 dimes and
quarters to CoinMaster to redeem for dollar
bills. The total value of his jar is $8.
a. Write a system of equations to represent the
number of quarters, q, and the number of
dimes, d, in the jar.
b. Solve the system to determine the number of
quarters and dimes in the jar.
The system of equations to represent the
number of quarters, q, and the number of
dimes, d, in the jar is
d + q = 50
0.10d + 0.25q = 8
The number of quarters and dimes in the jar is 20 and 30 respectively.
How to determine the number of quarters and dimes?Let
number of quarters = qthe number of dimes = dd + q = 50
0.10d + 0.25q = 8
From (1)
d = 50 - q
Substitute into equation (2)
0.10d + 0.25q = 8
0.10(50 - q) + 0.25q = 8
5 - 0.10q + 0.25q = 8
- 0.10q + 0.25q = 8 - 5
0.15q = 3
divide both sides by 0.15
q = 3/0.15
q = 20
Substitute q = 20 into (1)
d + q = 50
d + 20 = 50
d = 50 - 20
d = 30
In conclusion, the given situation can be solved using simultaneous equation where number of dimes and quarters are 30 and 20 respectively.
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oh no i have a F+in math please help me
Answer: 2 1/4
Step-by-step explanation: If you add all those numbers like : 1/3+3/4+4/6+1/2 = and you will get 2 1/4
Answer:
[tex]2\frac{1}{4}[/tex]
Step-by-step explanation:
add them all and you'll get that answer
Joe ha eaten 4/5 of a pizza. Jane ha eaten 1/4 of a pizza how many time more pizza ha joe eaten then Jane
By conducting simple mathematical operations, we know that Joe eats 11/20 times more pizza than Jane.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.
The quantity of operands affects the operation's arity.
The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.
We can recall the PEMDAS steps in the following order: parentheses, exponents, multiplication, and division (from Left to right), addition, and subtraction (from left to right).
So, we know that:
Jow eats 4/5 of the pizza.
Jane eats 1/4 of the pizza.
Times Joe eats more pizza than Jane:
4/5 - 1/4
4(4) - 5(1)/20
16 - 5/20
11/20
Therefore, by conducting simple mathematical operations, we know that Joe eats 11/20 times more pizza than Jane.
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Find the nth term of this number sequence
15, 12, 9, 6, ...
Answer:
[tex]a_{n}[/tex] = 18 - 3n
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence, that is
12 - 15 = 9 - 12 = 6 - 9 = - 3
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 15 and d = - 3 , then
[tex]a_{n}[/tex] = 15 - 3(n - 1) = 15 - 3n + 3 = 18 - 3n
in a natural deduction problem if your conclusion is a conditional statement that does not appear in any of the premises, then the basic strateguy tells you to do what
In a natural deduction problem, if your conclusion is a conditional statement that does not appear in any of the premises, then it is not a valid argument.
Natural deduction is a process/theory that we use to derive the conclusion of any argument from the premises by using the rules of inference. Now, as the definition itself has established, in natural deduction problems we solve arguments from the premise. But in the argument, we have been told that the conclusion isn't from the premises.
Any argument or conclusion becomes valid if the premise is valid as well. This means that if the conclusion is not in the premise, then it is not valid.
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2. Stella's aunt donates 42 red roses, 70 pink carnations, and 56 yellow daisies for the party. The flowers will need to be arranged and placed on the tables. Stella wants each arrangement to have the same number of each color of flower. There are 12 tables at the party. Can she make an arrangement for each table and have no flowers left?
Answer:
no she will have 24 flowers left
Step-by-step explanation:
,Lm
In a 30°-60°-90° triangle, what is the length of the longer leg when the length of the hypotenuse is 44 inches?
Answer:
22√3 inches
Step-by-step explanation:
You want to know the length of the longer leg of a 30°-60°-90° triangle when the hypotenuse is 44 inches.
Side lengthsThe ratios of side lengths in a 30°-60°-90° triangle are ...
1 : √3 : 2
This means the longer leg is (√3)/2 times the length of the hypotenuse.
ApplicationIn the given triangle, the longer leg is ...
(44 in)(√3)/2 = 22√3 in
Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is a. much larger than one b. zero c. infinity d. None of these alternatives is correct.
Since the sun must rise tomorrow, then the probability of the sun rising tomorrow is much larger than one.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
Firstly, it is important to clarify that when people say ‘‘The Sun Will Rise Tomorrow’ they are implying only how It only appears to an observer on earth that the sun rises and sets. In reality the sun neither rises nor sets it only appears to do so because the earth takes one day (24 hours to rotate on its axis). It has appeared to do this for as long as the earth has existed (approx. 4.5 billion years). Although for the purpose of this short reflection, the idiom will signify part of the day-night process -being able to see the sun rise from the perspective of a human on earth.
Although the chances might be extremely high, they are not certain. Even thought it may be very improbably unless an infinite amount of days in which the sun has risen has occurred, the probability will not exactly be one. Ludwig Wittgenstein, Austrian-British philosopher who worked primarily in logic and philosophy of mathematics, said, “It is an hypothesis that the sun will rise tomorrow: and this means that we do not know whether it will rise.” Although we may reasonably argue that the earth while rise tomorrow to a 99.99999999% chance, there still is that 0.000000001 which states that it would not in fact rise.
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Select the reason why these triangles are similar. If they are not, select "Not similar."
Numbers selected in the triangle 2.5, 2.25,0.5,2,1, and 1
Answer choices: A. AA, B. Not similar, C. SAS, D. SSS
Answer: B
Step-by-step explanation: One is a triangle and one is not. The bigger one has four sides therefore it is not a triangle
Answer:
B. Not similar
Step-by-step explanation:
You want an appropriate choice of similarity reason for the triangles shown in the figure.
Side ratiosThe side ratios in the smaller triangle are ...
0.5 : 1 : 1 = 1 : 2 : 2
The side ratios in the larger triangle are ...
2.25 : 3 : 3.5 = 9 : 12 : 14
The side ratios are not the same, so the triangles are not similar.
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Of the 52 plays attributed to a playwright, 19 are comedies, 10 are tragedies, and 14 are histories. If one play is selected at random, find the odds against selecting a tragedy
The answer is 3/5, or 60%
11 (comedies) + 19 (tragedies) = 30
30/50 = 3/5, or 60%
2 Determine whether the table represents a linear relationship. If so, state the slope of
the line.
X
2
3
4
5
сл
y
14
21
28
35
X
-2
-1
0
1
y
10
5
0
-5
x
2
3
4
5
y
48
72
90
114
Answer:
Tables A and B represent linear relationship-------------------------
Table Ax = 2, 3, 4, 5 Difference is 1y = 14, 21, 28, 35 Difference is 7This is linear and the slope is 7Table Bx = -2, -1, 0, 1 Difference is 1y = 10, 5, 0, -5 Difference is - 5This is linear and the slope is - 5Table Cx = 2, 3, 4, 5 Difference is 1y = 48, 72, 90, 114 Difference is inconsistentThis is not linearLinear Equations w/ Distribution 2
(5y−1)=28
Answer:
29/5 or 5.8
Step-by-step explanation
First, we put the 1 on the other side which turns it positive 5y=29
Then, we divide 29 by 5 which gives us 29/5 which is equal to 5.8
There is a new ride share service that charges a rate of $5 for the
first 5 miles, then charges $0.50 per mile after that.
If you want to spend $12 or less, what is the maximum number of
miles you could go using the ride share service?
The maximum number of miles you could go using the ride share service for $12 or less is 14 miles
How to find the miles to go with $12The problem is solved by generating the equations
assuming x represents the number of extra miles
$5 is charged for the first 5 miles and $0.50 per mile after that
This can be represented using the equation
total cost, y = $5 + $0.5x
$0.50 for the extra miles
Having $12 the number of miles is calculated as below
$12 = $5 + $0.5x
0.5x = 12 - 5
0.5x = 7
x = 7 / 0.5
x = 14 miles
The number of miles that can be paid for using $12 is 14 miles and this is the maximum number since the amount will result to lesser miles
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Lin runs 5 laps in 6 minutes
How many minutes per lap is that.
Answer:
0.83 laps per minute
Answer: 0.83 laps per minute.
Step-by-step explanation:
While hiking, Mr. Fury burns 808 calories in 8 hours. At this rate, how many calories does he burn in 60 minutes?
(1): 6,464 calories
(2): 110 calories
(3): 101 calories
(4): 250 calories
While hiking, Mr. Fury burns 808 calories in 8 hours. At this rate, how many calories does he burn in 60 minutes?
(1): 6,464 calories
(2): 110 calories
(3): 101 calories
(4): 250 calories
808/8 = 101 per hour
60 minutes = 1 hour so:
101 * 1 = 101
you're ordered to attempt to memorize a series of images. there are 15 images in the series. when you are asked to state the order of the images you remember the first 3 and then it starts to get fuzzy. this is an example of the .
you're ordered to attempt to memorize a series of images. there are 15 images in the series. when you are asked to state the order of the images you remember the first 3 and then it starts to get fuzzy. This is an example of memory retrieval.
What do you mean by series?
The total of a particular sequence of terms is known as a series in mathematics. These phrases often refer to real or complex numbers, though considerably more generality is possible.
In calculus and its generalization, mathematical analysis, the study of series plays a significant role. Most mathematical disciplines employ series, including combinatorics, where generating functions are employed to explore finite structures.
Along with being widely utilized in mathematics, infinite series are also frequently employed in other quantitative fields like physics, computer science, statistics, and finance.
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Adriel buys 7 bottles of apple juice at the corner store for a total cost of $5.25. If each bottle costs the same amount, how much is each bottle of juice?
Answer:
$5.25 = 525 cents
525/7=75
each bottle is 75 cents or $0.75
sean wants to test a hypothesis according to which the mean amount of sales dollars per employee will vary between three store locations: the oak ridge, oak wood, and oak park shopping malls. the most appropriate statistical test/analysis would be the .
The most appropriate statistical test/analysis for Sean who wants to test a hypothesis according to which the mean amount of sales dollars per employee will vary between 3 store locations would be the T-test.
What is the T-test?A T-test is a statistical test which compares the means of two samples. It is used in hypothesis testing, with a null hypothesis which the difference in group means is zero and an alternate hypothesis which the difference in group means is different from zero.
The choice of T-test depends on whether we are studying one group or two groups, and whether we care about the direction of the difference in group means.
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c8 q8 v1: a random sample of 100 students is taken from a larger population of students in a multi-lecture course and the sample mean (average) of their final grades is found to be 62.25. suppose that the population standard deviation is known to be 4.5. which of the following is correct? (note that you can answer these questions from understanding gleaned in lecture and lab, but may find r helpful.)
99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
Given, the mean of the final grades of the sample be 62.25 and the standard deviation be 4.5
On Subtracting 1 from your sample size, we get
100 – 1 = 99.
On Subtracting confidence level from 1, and then divide by two.
(1 – .997) / 2 = 0.0015
Now, df = 99 and α = 0.0015
from the table at df = 99 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(100) = 2.8
Now, 2.262 × 2.8 = 6.33
So, the confidence interval be,
(100 - 6.33 , 100 + 6.33) = (44.67 , 56.33)
Hence, 99.7% of the students scored between (44.67 , 56.33) i.e.
between 44 and 56.
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The enrollment at Grove
Middle School is expected to increase
by 40 students each year for the next
5
years.
If their current enrollment is
600 students, find their enrollment
after each of the next 5 years.
Answer:
After one year, the enrollment will be 600 + 40 = 640. After two years, the enrollment will be 640 + 40 = 680. After three years, the enrollment will be 680 + 40 = 720. After four years, the enrollment will be 720 + 40 = 760. After five years, the enrollment will be 760 + 40 = 800.
Step-by-step explanation:
A runner is 7/8 miles away from the finish line. If she can travel 3/8 miles per minute, how long will it take her to finish the race?
The time that runner takes to finish the race is 2.133 minutes.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The speed of the runner is given as 3/8 miles per minute.
The remaining distance to be travelled is 7/8 miles.
Then, the time taken by the runner is the ratio of distance to be travelled to the speed. It can be written as follows,
Time taken by runner = (7/8)/(3/8)
= 7/3
= 2.133
Hence,the time taken by the runner to finish the race is 2.133 minute.
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a study of 26 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.87. a. state the decision rule for 0.025 significance level: h0: rho ≤ 0; h1: rho > 0. (round your answer to 3 decimal places.) b. compute the value of the test statistic. (round your answer to 3 decimal places.) c. can we conclude that the correlation in the population is greater than zero? use the 0.025 significance level.
The value of the test statistic using correlation coefficient and sample size is equal to 8.776 ( round up to 3 decimal places.)
As given in the question,
Sample size 'n' = 26
Correlation coefficient 'r' = 0.87
Significance level 'α' = 0.025
a. Decision rule for the system of hypothesis are:
Null hypothesis : H₀ : ρ ≤0
Alternative hypothesis: H₁ : ρ > 0
Value of the test statistic 't'
= r√n-2 / √1 - r²
= (0.87√ 26 - 2) / √1- 0.87²
= 4.3 / √0.2431
= 4.3 / 0.49
= 8.776
Therefore, value of the test statistic using the given values is equal to 8.776.
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When selecting from unbiased estimators, an estimator with small bias may be preferred over the minimum variance unbiased estimator when the variance of the estimator with bias is less than for the MVUE
yess it is true because of unbiased estimator
what is variance?
Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in respect to the mean when the data are more dispersed
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