7. how many ways are there to select three unordered el- ements from a set with five elements when repetition is allowed?
Answers
There are 35 ways to select three unordered elements from a set with five elements when repetition is allowed.
Explanation:
To find the number of ways to select three unordered elements from a set with five elements when repetition is allowed, we can use the combination formula, which is:
nCr = n! / r!(n-r)!
where n is the total number of elements in the set, r is the number of elements we want to select, and ! denotes the factorial function (i.e., the product of all positive integers up to and including the given number).
In this case, we have n = 5 and r = 3, so we can plug these values into the formula:
5C3 = 5! / 3!(5-3)!
= (5 x 4 x 3 x 2 x 1) / [(3 x 2 x 1) x (2 x 1)]
= (120) / (6 x 2)
= 20 x 1
= 20
However, this formula assumes that repetition is not allowed (i.e., once an element is selected, it cannot be selected again). Since repetition is allowed in this case, we need to account for the fact that each element can be selected multiple times.
To do this, we can use a "stars and bars" approach. Imagine that we have three stars (representing the three elements we want to select) and four bars (representing the four "gaps" between the five elements in the set). We can place the stars and bars in any order to represent different selections of elements. For example:
* | * * | * represents selecting the first element twice and the third element once.
| * * * | represents selecting the second element three times.
* * * | | represents selecting the first three elements once each.
There are a total of 7 objects (3 stars and 4 bars), and we need to choose where to place the 3 stars. This is equivalent to choosing 3 out of the 7 objects to be stars (and the rest are bars). So the number of ways to select three unordered elements from a set with five elements when repetition is allowed is:
7C3 = 7! / 3!(7-3)!
= (7 x 6 x 5 x 4 x 3 x 2 x 1) / [(3 x 2 x 1) x (4 x 3 x 2 x 1)]
= (7 x 2 x 5)
= 70 / 2
= 35
Therefore, there are 35 ways to select three unordered elements from a set with five elements when repetition is allowed.
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Related Questions
a. If the pediatrician wants to use height to predict head circumference dete variable is the explanatory variable and which is response variable. b. Draw a scatter diagram of the data. Draw the best fit line on the scatter diagram . d. Does this scatter diagram show a positive negative, or no relationship between a child's height and the head circumference ?
Answers
If the best fit line is nearly horizontal, it suggests no significant relationship between height and head circumference.
What is the equation to calculate the area of a circle?In this scenario, the explanatory variable is the child's height, as it is being used to predict the head circumference.
The response variable is the head circumference itself, as it is the variable being predicted or explained by the height.
To draw a scatter diagram of the data, you would plot the child's height on the x-axis and the corresponding head circumference on the y-axis. Each data point would represent a child's measurement pair.
Once all the data points are plotted, you can then draw the best fit line, also known as the regression line, that represents the overall trend or relationship between height and head circumference.
By observing the scatter diagram and the best fit line, you can determine the relationship between a child's height and head circumference.
If the best fit line has a positive slope, it indicates a positive relationship, meaning that as height increases, head circumference tends to increase as well.
If the best fit line has a negative slope, it indicates a negative relationship, meaning that as height increases, head circumference tends to decrease.
By assessing the slope of the best fit line in the scatter diagram, you can determine whether the relationship between height and head circumference is positive, negative, or nonexistent.
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how many different ways can 11 player soccer team be selected if there are 16 players trying out for tthe team?
Answers
There are 4,368 different ways to select an 11-player soccer team from a group of 16 players.
What is combination formula?The combination formula is used to determine the number of ways to select items from a collection where the order of selection is irrelevant.
We can use the combination formula to determine the number of ways to select an 11-player soccer team from a group of 16 players. The combination formula is:
n choose k = n! / (k! * (n - k)!)
where n is the total number of items, k is the number of items to choose, and ! denotes the factorial function (i.e., the product of all positive integers up to and including the argument).
In this case, we want to choose k = 11 players from a group of n = 16 players. Therefore, the number of ways to select an 11-player soccer team from a group of 16 players is:
16 choose 11 = 16! / (11! * (16 - 11)!) = 4368
Therefore, there are 4,368 different ways to select an 11-player soccer team from a group of 16 players.
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solve the equation -9v-9=-27 for v.
Answers
Answer:
v=2
Step-by-step explanation:
-9v-9=-27
add nine to both sides
-9v-9+9=-27+9
simplify
-9v=-18
divide both sides by -9
-9v/-9 -18/-9
simplify y=2
hope this helps :) have a nice day !!
Answer:
v=2
Step-by-step explanation:
-9v-9=-27
add nine to both sides
-9v-9+9=-27+9
simplify
-9v=-18
divide both sides by -9
-9v/-9 -18/-9
simplify y=2
Find the equation of the line shown
Answers
Step-by-step explanation:
at 3=3
at 0=9
at 4=1
\(y = ax + b\)
\(1 = 4a + b \\ 3 = 3a + b \\ 2 = - a \\ a = - 2 \\ 1 = - 4 \times 2 + b \\ b = 1 + 8 = 9 \\ y = - 2x + 9\)
Answer:
y=-2x+9
Step-by-step explanation:
From looking at the line you can already tell that the slope is going to be negative, and the y-intercept is going to be 9, since that's where y is when x is 0. You can see that when x is one, y is 7. When x is 2, y is 5. And when x is 3, y is 3.
So:
0: 9
1:7
2:5
3:3
And the difference of y over the difference of x is the slope
-2/1=-2
So the slope is -2
Therefore, putting the equation together makes:
y=-2x+9
Hope this helps!
Can somebody help me find this missing angle please.
Answers
Answer:
x = 96 degrees
Step-by-step explanation:
49 + 35 + x = 180
84 + x = 180
x = 180 - 84
x = 96 degrees
3. What percent of 150 is 15?
unknown:
Known:.
Answers
Answer:
Step-by-step explanation:
Can someone help with these and please show work
Answers
Step-by-step explanation:
3.)
34 + 3√(4 • 6 ÷ 2)^2 + 5^2
34 + 3√(12)^2 + 25
34 + 3√144 + 25
34 + 3√169
34 + 3 × 13
34 + 39 = 73
4.)
|9 - 12 • 3| - 2 + 10/2^2 + 10 - 7
|9 - 36| + 8/4 + 10 - 7
9 + 36 + 8/7 = 53/7
you own 16 cds. you want to randomly arrange 9 of them in a cd rack. what is the probability that the rack ends up in alphabetical order? the probability that the cds are in alphabetical order is
Answers
The probability that the rack ends up in alphabetical order is 1/9! or approximately 1.46 x 10⁻⁷.
The problem involves arranging 9 CDs out of 16 in alphabetical order in a CD rack. The total number of possible ways to arrange 9 CDs out of 16 is 16 choose 9, which equals 11440. Only one of these arrangements is in alphabetical order. Therefore, the probability of randomly selecting an alphabetical order is 1/11440, which is approximately 0.0000874 or 0.00874%. This is a very small probability, indicating that it is highly unlikely that the CDs will end up in alphabetical order by chance.
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13. What is the mean of the data set in the box below? −8, −6, −2, 0, −6, −8, 4, −7, −8, 1 A. −8 C. −6 B. −7 D. −4
Answers
To find the mean you sum up all the numbers then divide by the number of numbers there are
For example there are 10 numbers in this list so you would divide the sum of all of them by 10
-40/10=-4
Answer: D. -4
Step-by-step explanation:
-8 + -6 + -2 + 0 + -6 + -8 + 4 + -7 + -8 + 1= - 40
-40 divided by 10= -4
(You're dividing by 10 because there are 10 numbers that you added up)
The mean is -4.
6 Kay sees a jacket in New York costing $170. She knows the same jacket costs £132 in London.Using the exchange rate £1 = $1.30, work out in which place the jacket is cheaper and by how much. Show all stages of your working out.
Answers
A swear
Is
Uk beacause it’s cheap
i need help it is due today
Answers
Answer:
8
Step-by-step explanation:
Using the Heron's formula we can find that the total area of the triangle is 84 inches.
Then, to find the height of the triangle, you have to multiply the area by 2 since the formula for the area of a triangle is (h*b)/2
Now, when we multiply 84 and 2 we get 168, so you have to divide 168 by 21 to find 8.
Tyra buys 14 gallons of gas for 35$ how could she figure out how much 1 gallon of gas cost her
Answers
Answer: 2.50
Step-by-step explanation: you would divide the cost by the amount so 35 divided by 14.
an education can be the key to higher earnings. in a u.s. census bureau study, high school graduates earned $30,400 per year. associate’s degree graduates averaged $38,200 per year. bachelor’s degree graduates averaged $52,200 per year
Answers
The given statement "an education can be the key to higher earnings" is true, as a U.S. Census Bureau study shows that earnings increase with the level of education.
The study shows that high school graduates earned $30,400 per year, associate’s degree graduates averaged $38,200 per year, and bachelor’s degree graduates averaged $52,200 per year. This indicates that an individual's earnings will increase with their level of education.
As an individual's level of education increases, their earnings also increase. The U.S. Census Bureau study demonstrates that a high school graduate earns less than an associate's degree graduate, and an associate's degree graduate earns less than a bachelor's degree graduate.
This is because education enables an individual to obtain better job opportunities and more specialized skills in their area of interest, which are valued in the job market. As a result, higher education has a significant impact on an individual's income.
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Five times the sum of a number and 3 is the same as 3 times the difference of twice the number and 1.
What is the number?
Answers
Answer:
12
Step-by-step explanation:
5(x+3) = 3(2x-1)
5x+15 = 6x-3
15-3 = 6x-5x
12 = x
x = 12
The number should be 12.
Given that,
Let us assume the number be x.Five times the sum of the number & 3 should be the same because 3 times is the difference of the twice of the number and 1.Based on the above information, the following equation should be made:
5(x+3) = 3(2x-1)
5x+15 = 6x-3
15-3 = 6x-5x
12 = x
x = 12
Therefore we can conclude that the number is 12.
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Use Pythagorean theorem
Answers
Answer:
15
Step-by-step explanation:
a^2+b^2=c^2
y^2+8^2=17^2
Step 1: Simplify both sides of the equation.
y^2+64=289
Step 2: Subtract 64 from both sides.
y^2+64−64=289−64
y^2=225
Step 3: Take square root.
y=15
Answer:
15
Step-by-step explanation:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Let the demand function for a product be q = 100 - 2p. the inverse demand function of this demand function is:_______
Answers
The inverse demand function of the given demand function is p = 50 - q/2.
A graph that depicts the relationship between a product's price and demand is called a demand curve. On a demand graph, the horizontal axis represents the amount desired, while the vertical axis represents the product's price.
The price is a function of the quantity required when there is an inverse demand curve. The inverse of a demand curve indicates that variations in the amount required cause changes in price levels. The formula for calculating the demand curve for a product yields the graph of an inverse demand curve.
Given demand function: q = 100 - 2p.
To find the inverse demand function, we find the inverse of the equation, by isolating p, to get:
q = 100 - 2p,
or, 2p = 100 - q,
or, p = 100/2 - q/2,
or, p = 50 - q/2.
Thus, the inverse demand function of the given demand function is p = 50 - q/2.
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To calculate the linear demand function, we need to determine the values of "a" and "b" in the equation Q(P) = a - bP, where Q(P) represents the quantity demanded at a given price.
First, let's find the value of "a." We know that when the price was $17, the average quantity sold was 2,108 mugs. Substituting these values into the equation, we have:
2,108 = a - b(17)
Next, let's find the value of "b." We now have a second data point: when the price increased to $24, the average quantity sold dropped to 1,632 mugs. Substituting these values into the equation, we have:
1,632 = a - b(24)
Now, we have a system of two equations:
2,108 = a - 17b
1,632 = a - 24b
We can solve this system of equations to find the values of "a" and "b." Subtracting the second equation from the first, we get:
476 = 7b
Dividing both sides by 7, we find:
b = 68
Now, we can substitute the value of "b" into either equation to solve for "a." Let's use the first equation:
2,108 = a - 17(68)
2,108 = a - 1,156
Adding 1,156 to both sides, we find:
a = 3,264
Therefore, the linear demand function for the pumpkin shaped coffee mugs is:
Q(P) = 3,264 - 68P
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In 2011, the moose population in a park was measured to be 5,800. By 2017, the population was measured again to be 8,000. If the population continues to change exponentially, find an equation for the moose population, P, as a function of t, the years since 2011.What does your model from above predict the moose population to be in 2022?
Answers
This problem asks to:
a) Find a model to predict the population P as a function of t (years since 2011).
b) Predict the population in 2022.
To find this information, follow the steps below.
Step 1: Write a general equation for populational growth.
The population growth can be represented as:
\(P=P_0\cdot e^{r\cdot t}\)Where:
P is the population in time t;
Po is the initial population;
r is the rate of growth;
t is the time.
Step 2: Write the equation that represents the moose population.
Since the problems aks to evaluate the population from 2011. Use the population in 2011 as the initial population.
Then, P0 = 5,800.
\(P=5,800\cdot e^{r\cdot t}\)Now, to find r, use the information for 2017.
In 2017,
P = 8,000
t = 6 (2017 - 2011)
Then,
\(\begin{gathered} 8,000=5,800\cdot e^{r\cdot6} \\ \end{gathered}\)To isolate r, first divide both sides by 5,800:
\(\begin{gathered} \frac{8,000}{5,800}=e^{r\cdot t} \\ \frac{80}{58}=e^{r\cdot t} \\ \end{gathered}\)Take the ln from both sides.
\(\begin{gathered} \ln (\frac{40}{29})=\ln e^{6r} \\ \text{ Using the properties of ln:} \\ \ln (\frac{40}{29})=6r\cdot\ln e \\ \ln (\frac{40}{29})=6r\cdot1 \\ \ln (\frac{40}{29})=6r \end{gathered}\)Divide both sides by 6:
\(\begin{gathered} \frac{6r}{6}=\frac{\ln (\frac{40}{29})}{6} \\ r=\frac{\ln(\frac{40}{29})}{6} \\ or \\ r=\frac{0.3216}{6}=0.0536 \end{gathered}\)So,
(a) The equation that represents the moose population over the years is:
\(P=5,800\cdot e^{0.0536\cdot t}\)Step 3: Predict the population in 2022.
In 2022,
t = 11 (2022 - 2011).
Then,
\(\begin{gathered} P=5,800\cdot e^{0.0536\cdot t} \\ P=5,800\cdot e^{0.0536\cdot11} \\ P=5,800\cdot e^{0.5895} \\ P=5,800\cdot1.8032 \\ P=10,458.6 \\ P=10,459 \end{gathered}\)(b) The moose population in 2022 will be 10,459.
Answer:
(a)
\(P=5,800\cdot e^{0.0536\cdot t}\)(b) 10,459.
describe the similarities and differences between a frequency table and a frequency distribution. be sure to include which requires qualitative data and which requires quantitative data.
Answers
A frequency table is a simple tabular representation of the number of times a particular value or range of values appears in a data set.
It lists the values in one column and the corresponding frequencies in another column. For example, if we have data on the heights of a group of people, a frequency table could list the heights (in cm) in one column and the number of people with that height in the other column.
A frequency distribution is a graphical representation of the same information as a frequency table. It shows the number of occurrences of values in a data set by grouping the values into classes or intervals, and then plotting the frequency of each class or interval. For example, a histogram is a type of frequency distribution where the data is divided into equal-width intervals and the height of each bar represents the frequency of the data that falls within that interval.
A frequency table can be used for both qualitative and quantitative data, whereas a frequency distribution can only be used for quantitative data. This is because the classes or intervals used in a frequency distribution require a numerical representation of the data, which is not possible for qualitative data.
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Classify the following polynomial by its degree value.
2x5 + xy5 – 5z3
Answers
Answer:
this equation has the degree value of 6
Step-by-step explanation:
cm(72, x) = 360 and gcd(72, x) = 12 then the smallest possible value for
Answers
Given gcd(72, x) = 12 and cm(72, x) = 360, the smallest possible value is 3.
What is GCD?The original number is divided equally by its factors. If 8 is a factor of 64, for instance, then 8 can split 64 into 8 equal parts.
A factor is said to be a common factor for two numbers if it also factors another number. Since 2 is a factor of both 4 and 8, for instance, it is a common factor.
There are numerous ways to determine the biggest common divisor of a pair of numbers.
Long division method, the Euclid algorithm for division, and the prime factorization method.
There are numerous ways to determine the biggest common divisor of a pair of numbers.
The highest common factor (hcf), greatest common divisor (gcd/GCD), or common factor (gcf) of two or more.
According to our question-
21 = 3×7
72 = 23×32
GCD = 3
21 / 3 = 7
72 / 3 = 24
Hence, Given gcd(72, x) = 12 and cm(72, x) = 360, the smallest possible value is 3.
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Please answer this question I need to answer please answer HURRY!!!!
Answers
Answer:
52
Step-by-step explanation:
\(r^{2} -14+8p\)
Substitute values given:
\((8)^{2} -14+8(\frac{1}{4} )\)
Simplify:
64-14+2
50+2
52
Therefore 52 is our answer
Answer:
56
Step-by-step explanation:
if r = 8 than r to the second power is 8 to the second power (or 8x8) which equals 64
64 - 14 + 8p
If p + 1/4 = 2
64 - 14 + 2
54 + 2
56
I need help plz!!!!!!!
Answers
Answer:
Lorena will have more money in six weeks.
She will have $8 more
Step-by-step explanation:
Please give brainliest
Help me solve this problem please
Answers
Answer: (2, -2)
x=2, y=-2
Answer:
(2, -2)
Step-by-step explanation:
4x + y = 6
x - 2y = 6
x = 2y + 6
4(2y + 6) + y = 6
8y + 24 + y = 6
9y + 24 = 6
9y = 6 - 24
9y = -18
y = -18 ÷ 9
y = -2
4x + (-2) = 6
4x - 2 = 6
4x = 6 + 2
4x = 8
x = 8 ÷ 4
x = 2
Confirm:
4x + y = 6
4(2) - 2 = 6
8 - 2 = 6
6 = 6 (Correct)
(2, -2)
what is the length and width of a basketball court
Answers
The length of a standard basketball court is 94 feet (28.65 meters), and the width is 50 feet (15.24 meters).
A standard basketball court is rectangular in shape and follows certain dimensions specified by the International Basketball Federation (FIBA) and the National Basketball Association (NBA). The length and width of a basketball court may vary slightly depending on the governing body and the level of play, but the most commonly used dimensions are as follows:
The length of a basketball court is typically 94 feet (28.65 meters) in professional settings. This length is measured from baseline to baseline, parallel to the sidelines.
The width of a basketball court is usually 50 feet (15.24 meters). This width is measured from sideline to sideline, perpendicular to the baselines.
These dimensions provide a standardized playing area for basketball games, ensuring consistency across different courts and facilitating fair play. It's important to note that while these measurements represent the standard dimensions, there can be slight variations in court size depending on factors such as the venue, league, or specific regulations in different countries.
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what is 1 1/3 divided by 3/5
Answers
Answer:
55/9
Step-by-step explanation:
Answer:
20/9 or 2 2/9
Step 1: convert mixed number into improper fraction
4/3
Step 2: copy dot flip
4/3 × 5/3
Step 3: solve
20/9
Step 4 (if your hw requires it): convert to mixed number
2 2/9
What is 2+2.2*46-13(41+3 x)-16x
Answers
Answer:
7912.8x
Step-by-step explanation:
First do what in the parenthesis (41+3x)=44x
Then what to the left of the ()
2+2.2*46-13=180.2
then multiply what you got in the () to what we just got
180.2*44x=7928.8x
finally we subtract it to the -16x
7928.8x-16x=7912.8x
Mr. Quesada took out a loan for $12,000. To pay it back, he will make 24 monthly payments of $629. How much will he pay in interest?
Answers
Answer:
$3,096
Step-by-step explanation:
To find the total interest Mr. Quesada will pay, we need to first calculate the total amount he will pay back, and then subtract the original amount borrowed.
The total amount Mr. Quesada will pay back over 24 months is:
$629 x 24 = $15,096
Subtracting the original loan amount, we get:
$15,096 - $12,000 = $3,096
So Mr. Quesada will pay a total of $3,096 in interest over the course of the loan.
a telephone pole is 90 feet tall. it casts a shadow that is 24 feet long. a tree that is next to the telephone pole is 15 feet tall. how long is the shadow of the tree?
Answers
The shadow of the tree is 9 feet long.
The length of the shadow is determined by the height of the object casting the shadow and the angle of the sun. The angle of the sun is indirectly proportional to the length of the shadow. The taller the object, the longer the shadow. The angle of the sun also affects the length of the shadow. When the sun is high in the sky, the shadows are shorter. When the sun is lower on the horizon, the shadows are longer.
Assuming that the tree is standing next to the telephone pole, the shadow of the tree would be 15 feet long. The shadow of the telephone pole is 24 feet long, so the difference between the two shadows is 9 feet. The tree is 9 feet shorter than the telephone pole, so the tree's shadow is 9 feet shorter than the telephone pole's shadow.
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Solve the given differential equation by separation of variables.
y ln x * (dx/dy) = [(y+1)/x]^2
Answers
The general solution to the differential equation. If initial conditions are given, we can solve for the constants C1 and C2.
The given differential equation is:
y ln x * (dx/dy) = [(y+1)/x]^2
We can solve this equation by separation of variables, which means we can rearrange the equation so that all the x terms are on one side and all the y terms are on the other side. Then, we can integrate both sides with respect to their respective variables.
First, we rewrite the equation in a form suitable for separation of variables:
y ln x dx = [(y+1)/x]^2 dy
Next, we separate the variables and integrate both sides:
∫y ln x dx = ∫[(y+1)/x]^2 dy
Integrating the left-hand side by parts, we have:
u = ln x dv = y dx
du/dx = 1/x v = (1/2) y^2
∫y ln x dx = (1/2) y^2 ln x - ∫(1/2) y dx
= (1/2) y^2 ln x - (1/4) y^2 + C1
where C1 is the constant of integration.
Integrating the right-hand side, we use the substitution u = y+1:
u = y+1 du = dy
∫[(y+1)/x]^2 dy = ∫(u/x)^2 du
= (1/x^2) ∫u^2 du
= (1/3x^2) u^3 + C2
where C2 is the constant of integration.
Substituting this back into the original equation, we have:
(1/2) y^2 ln x - (1/4) y^2 + C1 = (1/3x^2) (y+1)^3 + C2
This is the general solution to the differential equation. If initial conditions are given, we can solve for the constants C1 and C2.
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Which of the following will cause a logical error if you are attempting to compare x to 5?
Answers:
a. if (x >= 5)
b. if (x = 5)
c. if (x == 5)
d. if (x <= 5)
Answers
Logical Error: In computer programming language, a logic error is a bug or in a program or code that causes it to operate incorrectly, but not to terminate abnormally (or crash).
A logic error developed unintended or undesired output or other behavior, although it may not immediately be recognized as such.
For example, assigning a value to the wrong variable may cause a many of unexpected program errors.
These errors can be programmer mistakes or sometimes machine less memory to load the code.
if(x>=5) {
// program
}
else if(x==5) {
//program
}
else(x<=5) {
//program
}
they all do not give any error.
x=5 gave an error because it is value assigning to 5.
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