(n-1) x (n-2)! ways of seating arrangements are possible if Fred (a boy) and Carrie (a girl) must be seated next to each other.
A permutation is the act of putting things or numbers in a certain order. Combinations are a method of picking things or numbers from a set of objects or collections without regard for their order.
Let's say there are n seats in total.
Then, there are (n-1) gaps between the seats that Fred and Carrie can be placed in.
If we place Fred and Carrie in one of these gaps, there will be (n-2)! possible arrangements for the rest of the seats.
Therefore, there will be (n-1) x (n-2)! total possible seating arrangements for Fred and Carrie if they must be seated next to each other.
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how to subtract a whole number from a mixed fraction?
Solve the following system of equations graphically on the set of axes below.
y= \frac{1}{6}x+7
y=
6
1
x+7
y= -2x-6
y=−2x−6
Plot two lines by clicking the graph.
Click a line to delete it.
The system of equations graphically on the set of axes is given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
y = (1/6)x + 7
y = -2x - 6
The graph of each equation is given below.
The point of intersection is (-6, 6).
i.e,
(1/6)x + 7 = -2x - 6
(1/6)x + 2x = -6 - 7
13x/6 = -13
x/6 = -1
x = -6
So,
y = -2x - 6
y = -2 x -6 - 6
y = 12 - 6
y = 6
Thus,
The system of equations graphically is given above.
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at a large university, the division of computing services surveyed a random sample of 45 biology majors and 55 business majors from populations of over 1,000 biology and 1,000 business majors. the sampled students were asked how many hours they spend per week using any university computer lab. let x¯1 represent the average hours per week spent in any university computer lab by the 45 biology majors, and let x¯2 represent the average hours per week spent in any university computer lab by the 55 business majors.
According to the central limit theorem, difference of sample mean of two normal populations will also fill normal distribution if the sample size is at least 30 .
What does a statistical sample distribution mean?
An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population. It describes a variety of potential possibilities for a statistic, such the mean or mode of some variable in a population.
What are the different forms of sample distribution?
This idea, which is a sort of probability distribution, is frequently used to gather precise data from a huge population that has been divided into a number of samples that have been chosen at random.
This idea is further broken down into three categories: sampling Distribution of the mean, percentage, and T-Sampling.
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The complete question is -
Ata large university, the division of computing services surveyed random sample of 45 biologv majors and 55 business majors from populations of over 1,000 biology and O00 business majors. The sampled students were asked how many hours they spend per week using any university computer lab. Let represent the average hours per week spent in any university computer lab by the 45 biology majors, and let 1, represent the average hours per week spent in any university computer lab by the 55 business majors. Which of the following Is the best explanation for why the sampling distribution of can be modeled with a normal distrlbution? A) The two sample standard deviations are assumed to be equal_
an arithmetic sequence $2,5,8, 11, 14,\ldots$ is written in order in a book, one hundred numbers per page, beginning on page one. on which page will the number $11{,}111$ appear?
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is always the same. In this case, the common difference is 3, so every term is 3 more than the previous term.
The [tex]$n^{th}$[/tex] term in the arithmetic sequence can be found using
[tex]$a_n = a_1 + (n - 1)d$[/tex]
where $a_1$ is the first term (2 in this case), $d$ is the common difference (3 in this case), and $n$ is the term number.
To find the page number that $11{,}111$ appears on, we need to find the term number that corresponds to this value:
[tex]$11{,}111 = 2 + (n - 1) \cdot 3$[/tex]
Solving for $n$, we have:
$11{,}109 = 3n - 1$
$3n = 11{,}110$
$n = 37{,}037$
Since each page contains 100 numbers, the number 11,111 appears on page $\left\lceil \frac{37{,}037}{100} \right\rceil = 371$.
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at a seaport, the depth of the water during the day can be found using the equation where is the depth of water in feet and is the number of hours after midnight. at 8:30pm what will be the water's height?
The water's height at 8:30 PM is approximately 0.69 feet.
As per the data given in the question,
We have the equation,
depth = 4 * sin (0.5 * t)
where t is the number of hours after midnight.
As we need to find the depth of the water at 8:30 PM,
For finding the value of the depth at 8:30 PM we need to first convert 8:30 PM to the number of hours after midnight.
8:30 PM = 20.5 hours after midnight
So, substituting t = 20.5 into the equation,
we will get it as:
depth = 4 * sin (0.5 * 20.5)
depth = 4 * sin (10.25)
depth = 4 * 0.1736481776669303
depth = 0.6945971520676809
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16. diagonal the perimeter of a rectangle is 32 feet. the length is three times as long as the width. find the length of the diagonal. round to the nearest tenth.
The length of the diagonal is 12.6 feet.
"Information available from the question"
The perimeter of a rectangle is 32 feet.
The length is three times as long as the width.
We have to find the length of the diagonal.
Let w = width
then
3w = length.
Because we know the perimeter:
Perimeter of the rectangle is : 2(l + w)
32 = 2(w + 3w)
32 = 2(4w)
16 = 4w
4 feet = w (width)
Length:
3w = 3(4) = 12 feet
Diagonal, we use the Pythagorean theorem:
Let d = diagonal
then,
[tex]d^2 = 4^2 + 12^2[/tex]
[tex]d^2[/tex] = 16 + 144
[tex]d^2[/tex] = 160
d = 12.6 feet
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Elena wants to create a scale drawing of her bedroom. Her bedroom is a rectangle with length 5 m and width 3 m. She decides on a scale of 1 to 50.
Draw and label the dimensions of a scale drawing of Elena’s bedroom, using
a scale of 1 to 50.
To create a scale illustration of her bedroom, Elena must draw a 10cm by 6cm rectangle.
How to draw a scale illustration of the bedroom?To create a scale illustration of her bedroom she must take into account the scale she will be using. In this case it would be 1:50, that is, each original unit must be divided into 50 parts. Therefore, we must divide the lengths into 50 as shown below. Additionally we must take the values in cm.
500cm / 50 = 10cm300cm / 50 = 6cmAccording to the above, a scale model would be 10cm by 6cm.
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HELP DUE IN 20 MINNNNNN WILL GIVE CORRECT ANSWER BRAINLIEST
The simplified expression for this problem is given as follows:
9 - 13j/7.
How to simplify the expression?The expression for this problem is defined as follows:
16 + (-4) - 5j/7 - 6j/7 + 7.
The plus sign means that the sign is maintained, hence:
16 + (-4) - 5j/7 - 6j/7 + 7 = 12 - 5j/7 - 6j/7 + 7.
Then we combine the like terms, as follows:
12 + 7 = 9.-5j/7 - 6j/7 = -13j/7.Hence the simplified expression is given as follows:
9 - 13j/7.
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Please help I don't know how to do it
The value of x is obtained as follows:
128º.
The measure of angle A is given as follows:
m < A = 132º.
How to obtain the measures?For a parallelogram, the opposite angles are congruent, meaning that they have the same measure, hence the value of x is obtained as follows:
5x - 508 = x + 4.
4x = 512
x = 512/4
x = 128.
Then the measure of angle A is given as follows:
m < A = 5(128) - 508
m < A = 132º.
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Richard and Teo have a combined age of 27. Richard is 3 years older than twice Teo's age. How old are Richard and Teo?
Answer: Richard is 22 and Teo is 9
Step-by-step explanation:
a graph titled residuals versus launch angle has launch angle (degrees) on the x-axis, and residual on the y-axis. points decrease, and then curve up. based on the residual plot shown, is a linear model appropriate for using launch angle to predict height? a linear model is appropriate because the residual plot is curved. a linear model is appropriate because many of the residuals are close to zero. a linear model is not appropriate because the residual plot shows a clear pattern. a linear model is not appropriate because the y-intercept of the regression equation is negative.
In a residual plot, the residuals are plotted against the predictor variable. Ideally, the residuals should be randomly scattered around zero, without any patterns or trends.
If there is a pattern, it suggests that the linear model is not an adequate representation of the data and a more complex model may be necessary.
In this case, the residual scatter plot shows that the residuals are randomly scattered around zero, which suggests that a linear model is appropriate for summarizing the relationship between the predictor and response variables. This means that a straight line can be used to approximate the relationship and make predictions based on the data.
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A cone has a volume of 1024π cubic inches. If the radius is 16 feet, what is the height of the cone?
The height of the cone is 0.083 inches
How to determine the height of the cone?From the question, we have the following parameters that can be used in our computation:
Volume = 1024π cubic inches
Radius = 16 feet
Convert the radius to inches
So, we have the following representation
Radius = 192 inches
The volume of a cone is
Volume = 1/3πr^2h
Substitute the known values in the above equation, so, we have the following representation
1/3πr^2h = 1024π
So, we have
r^2h = 3072
This gives
h = 3072/(192^2)
Evaluate
h = 0.083
Hence, the heightt is 0.083 inches
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determine whether the first is a subset of the second, the second is a subset of the first, or neither is a subset of the other. a. the set of people who were born in the u.s., the set of people who are u.s. citizens. b. the set of students studying a programming language, the set of students studying java. c. the set of animals living in the ocean, the set of fish.
Given the following subset phrases are neither is a subset of the other. A set whose elements are all members of another set is simply referred to as a subset.
Because U.S. citizenship can also be acquired through other means, the group of people born in the country is a subset of the group of people who are citizens of the country. The group of Java learners all belong to the group of learners of a programming language, so Because Java is simply one of the many distinct kinds of programming languages, the group of students studying Java is a subset of the group of students studying a programming language. Since fish are just one of the many different marine species that dwell in the ocean, fish are a subset of the animals that live in the ocean.
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60 suitcase marked down 20%
1.20×60=12001200/100=12
12suitcase
the tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2000 miles. what is the probability a particular tire of this brand will last longer than 58,000 miles?
The probability that a tire of this brand will last longer than 58,000 miles is 0.8413 or 84.13%.
Given in the question that the tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2000 miles.
We have to calculate the probability that a particular tire of this brand which will last longer than 58,000 miles.
The standard normal variable corresponding to the given tire's tread life being longer than 58,000 miles can be calculated using the z-score formula:
The formula for computing a z-score is =(DataValue-Mean)/StDev
Therefore , we can write z = (58,000 - 60,000) / 2000
Hence, z = -1
Next, we can use a standard normal table to find the probability that a standard normal variable will be less than -1:
P(Z < -1) = 0.1587
Hence P = 1 - 0.1587
P = 0.8413
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Not sure how to do this need it asap thanks <3
The value of the exponential function is g ( x ) = ( 1/4 )ˣ and the graph is plotted
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the equation will be
Substituting the values in the equation , we get
g ( x ) = ( 1/4 )ˣ
when x = 0
g ( 0 ) = ( 1/4 )⁰
g ( 0 ) = 1
Now , when x = 1
Substitute the value of x = 1 in the equation , we get
g ( 1 ) = ( 1/4 )¹
g ( 1 ) = ( 1/4 )
Now , when x = 2
Substitute the value of x = 2 in the equation , we get
g ( 2 ) = ( 1/4 )²
g ( 2 ) = ( 1/16 )
Now , when x = 3
Substitute the value of x = 3 in the equation , we get
g ( 3 ) = ( 1/4 )³
g ( 3 ) = ( 1/64 )
Now , when x = 4
Substitute the value of x = 1 in the equation , we get
g ( 4 ) = ( 1/4 )⁴
g ( 4 ) = ( 1/256 )
Hence , the equation is g ( x ) = ( 1/4 )ˣ and the graph is plotted
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an election is coming up between four candidates. in your opinion, candidate a is half as likely to win as candidate c. candidate b is twice as likely to win as candidate d. candidate d is three times more likely than c. for the candidate most likely to win the election, what is the probability that they are going to win?
The probability that candidate B is going to win the election is 2.
The probability of candidate A winning the election is 0.5, the probability of candidate B winning the election is 2, the probability of candidate C winning the election is 1/3 and the probability of candidate D winning the election is 2/3.
Therefore, the candidate most likely to win the election is candidate B, and the probability that they are going to win is 2. This can be calculated using the formula for probability, which states that the probability of an event occurring is the number of favourable outcomes divided by the total number of outcomes. In this case, the number of favourable outcomes is 1 and the total number of outcomes is 3, so the probability of candidate B winning is 1/3.
Therefore, the probability that candidate B is going to win the election is 2.
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The formula for the area of a triangle is , where b is the base and h is the height. rearrange the formula to solve for the height (h).
The formula to solve for the height of a given triangle is =h=2A/b
Given the area of a triangle formula = A=1/2×b×h
where , A=area of the triangle.
b=base of the triangle.
h=height of the triangle.
To find the height of the triangle using this formula=
A=1/2×b×h
2A=b×h
h=2A/b
thus,h=2A/b is the formula to solve for the height of a given triangle.
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Please answer the question in this picture I need help!! 50 points!
I need to know who to do these two problems
The value of the trigonometric function is -
sin(θ) = 21 / 29,
cos(θ) = 20/29,
csc(θ) = 29/21,
sec(θ) = 29/20,
cot(θ) = 20/21.
Given that,What is the trigonometric function?In a nutshell, trigonometric functions, also referred to as circular functions, are the functions of a triangle's angle. This suggests that these trig functions provide the relationship between a triangle's angles and sides. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given that,
tan (θ) = - 21 / 20
We can infer from the value that the triangle's two legs are 21 and 20, respectively.
Using the Pythagorean theorem, we can:
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex](21)^{2} + (20)^{2} = c^{2}[/tex]
441 + 400 =[tex]c^{2}[/tex]
c = 29
The value of :
sin(θ) = 21 / 29
cos(θ) = 20/29
csc(θ) = 29/21
sec(θ) = 29/20
cot(θ) = 20/21
Hence, the value of the trigonometric function is
sin(θ) = 21 / 29,
cos(θ) = 20/29,
csc(θ) = 29/21,
sec(θ) = 29/20,
cot(θ) = 20/21.
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What is
−5f + 6 > 10f − 10
Please answer!
The solution to the given inequality [tex]-5f + 6 > 10f - 10[/tex] is [tex]f < 16/15[/tex].
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
The inequality is given in the question, as follows:
[tex]-5f + 6 > 10f - 10[/tex]
To solve the inequality [tex]-5f + 6 > 10f - 10[/tex], we need to isolate the variable [tex]f[/tex] on one side of the inequality.
We will first subtract 6 from both sides to isolate the [tex]-5f[/tex] term:
[tex]-5f + 6 - 6 > 10f - 10 - 6[/tex]
Simplifying the left side:
[tex]-5f > 10f - 16[/tex]
Next, we will subtract [tex]4f[/tex] from both sides to isolate the [tex]-5f[/tex] term on the left side:
[tex]-5f - 10f > 10f - 10f - 16\\-15f > -16[/tex]
Finally, we will divide both sides by -9,
[tex]-( 15 f )/9 > -16/15[/tex]
Dividing both sides by -15:
[tex]f < 16/15[/tex]
This is the required solution to the given inequality.
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Which equations have no real solution but have two complex solutions? please thanks
Answer3rd one and 1st
Step-by-step explanation:
The price of an item has been reduced by 80%. The original price was $70. What is the price of the item now?
Please help me it's timed, plus you'll get 100 points.
!!!If correct, Brainliest, Thanks, and 5 stars!!!
Simplify the expression:
[tex]\frac{\frac{x-1}{x+1} -\frac{x+1}{x-1} }{\frac{x-1}{x+1} +\frac{x+1}{x-1} }[/tex]
PLEASE HELP!!!
For the figure below, what is the total sum degrees of the interior angles? Use the correct formula and show all work!
Answer: 900
Step-by-step explanation:
The Interior Angle formula is (n-2)x180. So you take 7 minus 2 times 180 and that gives you 900
All students in the six grade either purchased their lunch or brought their lunch from home on Monday 24% of the students purchased their lunch 190 students brought their lunch from home how many students are in the six grade
Answer:
250
Step-by-step explanation:
190 students = 76%
190/76=2.5
2.5 x 100 =250
Eric's freezer has a volume of 20,000 cubic inches. He freezes 30 cartons of strawberries in the freezer. Each carton is 10 inches long, 4 inches wide, and 5 inches high.
What is the volume of one carton of strawberries?
Enter your answer in the box.
in³
Check Answer
Question 2
What is the volume of all of the cartons of strawberries?
Enter your answer in the box.
in³
The volume of one carton of strawberries is 200 in³.
The volume of all of the cartons of strawberries is 6,000 in³.
What is the volume?The volume of each carton can be determined by multiplying the length, width and height together.
Volume = length x width x height
10 x 4 x 5 = 200 in³
The volume of all the boxes of strawberries can be determined by multiplying the number of cartons by the volume of one carton.
Volume of the 30 cartons of strawberries = 200 in³ x 30 = 6,000 in³
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I don’t Understand this question
According to this information, investments with 4.2, 1.3 and 2.8 interest have a profit of more than $100. On the other hand, investments with interest of 0.75 and 5.2 have a profit of less than $100.
How to calculate the profit of these investments?To calculate the profit of these investments we must carry out the following procedure:
1. We must divide the interest in 100
2. We must multiply the interest by the total value of the investment ($1500).
3. We must multiply the result by the number of years of the investment.
4. We must classify the result as less than or greater than $100.
According to the above, investments with 4.2, 1.3 and 2.8 interest have a profit of more than $100. On the other hand, investments with interest of 0.75 and 5.2 have a profit of less than $100.
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Priya and Han plan a fundraiser for the running club. They begin with a balance of -80 because of expenses. In the first hour of the fundraiser they collect equal donations from 9 parents, which brings their balance to -44 .
How much did each parent give?
Answer: 4
Step-by-step explanation:
(-88) - (-44) = -36
remove the (-) = 36
36 ÷ 9 = 4
3(4w+2)+13 this was for hw and i need to get my grade up pls help
Answer:
12w+19
Step-by-step explanation:
[tex]3(4w + 2) + 13[/tex]
You multiply everything in the brackets with 3[tex]3(4w) + 3(2) + 13[/tex]
[tex]12w + 6 + 13[/tex]
combine the like terms[tex]12w + 19[/tex]