Given:
There are 15 players on a soccer team.
Only 11 players can be on the field for a game.
We will find the number of groups of players of 11 players can the coach make.
Note: the position does not matter, so, we will use the combinations
We will use the following formula:
\(^nC_r=\frac{n!}{(n-r)!*r!}\)substitute n = 15, and r = 11
\(^{15}C_{11}=\frac{15!}{(15-11)!*11!}=\frac{15*14*13*12*11!}{4*3*2*1*11!}=\frac{32760}{24}=1365\)So, the answer will be:
The number of different groups = 1365
Answer:
1,365
Step-by-step explanation:
I got it right on the test.
Leo dug up 6 4/5 pounds of
treasure on his first dig. Anne dug
up 4 1/2 pounds of treasure. How
much more treasure did Leo dig
up than Anne?
what is the formula to find time from distance
The formula to find time from distance is time = distance/speed
How to determine the formula of time?As a general rule, the formula of speed is
Speed = Distance/Time
Multiply both sides by Time
Time * Speed = Distance
Divide both sides by Speed
he formula to find time from distance
Hence, the formula to find time from distance is time = distance/speed
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John is 23 years old and rents a car for 4 days, from Thursday through Sunday. The cost of the car rental is 27.99 with unlimited miles, but the cost of the rental is 42% higher on Saturday and Sunday. The company charges a $40 fee for renters younger than 25 . How much will it cost John to rent the car?
Answer:
109.99 $
Step-by-step explanation:
add or maybe multiply the numbers that have to do with money: 27.99 + 42 + 40
It will cost $107.74 for John to rent a car.
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
John is 23 years old and rents a car for 4 days, from Thursday through Sunday.
The cost of the car rental is 27.99 with unlimited miles,
but the cost of the rental is 42% higher on Saturday and Sunday.
The company charges a $40 fee for renters younger than 25.
The total cost,
= 27.99 + 40 + 27.99 x 1.42
= $107.74
Therefore, the cost is $107.74.
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A dilation maps (6, 10) to (3, 5) and the center of dilation is the origin. Given A(12, 4), determine
under the same dilation.
Analyzing the coordinates being provided, the scale factor is found to be 0.5, hence the image of point A(12,4) under the same dilation and the center of dilation as origin is A'(6,2).
What is dilation?A dilation is a transformation in Euclidean space that enlarges or reduces all the points in a figure by a scale factor. In the example given, the dilation maps (6, 10) to (3, 5) with a scale factor of 0.5, and the center of dilation is the origin (0,0). The image of a point A(x,y) under this dilation would be A'(x*0.5, y*0.5). It means the point is scaled down by 0.5 in both x and y coordinate.
How can the dilation described above be used in real-world applications?The dilation described above can be used in real-world applications such as image processing, where it can be used to reduce the size of an image without losing important details, or to enlarge an image without introducing distortion. It can also be used in architectural design to create smaller or larger versions of floor plans and blueprints. Additionally, it can be used in cartography to change the scale of maps without altering the shape of the features on the map.
Analyzing the given dilation map , mapped from (6,10) to (3,5) ,the center of the dilation being origin. We can see that the scaling factor is 0.5.
So , using the same dilation for point A(12,4), The image of A will be,
A'(12*0.5,4*0.5) = A'(6,2)
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‼️‼️‼️PLEASE HELP ME OUT IM BEGGINGGGGGG‼️‼️‼️
Answer:
1) m = 9/2, n = 9
3) x = y = (3√2)/2
Step-by-step explanation:
1) We have a 30°-60°-90° right triangle, so the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is (9√3)/2, so m, the length of the shorter leg, is 9/2, and n, the length of the hypotenuse, is 18/2, or 9.
3) We have an isosceles right triangle, so the length of the hypotenuse is √2 times the length of each leg. The length of the hypotenuse is 3, so x and y, the lengths of the two congruent legs, are 3/√2, or (3√2)/2.
Need help in this mathquestion. The function h(x)=(x+2)^2 can be expressed in the form f(g(x)) where f(x)=x^2 , and g(x) is defined below:
Answer:
In a nutshell, \(g(x) = x+2\).
Step-by-step explanation:
A composition is operation between function that consist in replacing the independent variable of the first function, \(f(x)\) in this case, for \(g(x)\). Common notations for composition between functions are \(f(g(x))\) and \(f\circ g (x)\). If we know that \(h(x) = f\circ g (x) = (x+2)^{2}\) and \(f(x) = x^{2}\), then \(g(x) = x+2\).
In a nutshell, \(g(x) = x+2\).
Answer:
So, just like f(3) means that we replace x with 3 in our equation, f°g(x), aka f(g(x)), means that we replace x with g(x).
Since f(g(x)) = (x - 8)4 and f(x) = x4, you'll notice the difference is that x has been replaced with x - 8, so g(x) = x - 8.
Step-by-step explanation:
The manager of the school bookstore ordered 180 boxes of pencils. Based on the average daily use, she knows that the pencils will last about 30 days. Which linear equation represents the situation?
How many boxes of pencils should the manager expect to have after 20 days?
A. y = - 6x + 180; 120 boxes
B. y = - 6x + 180; 60 boxes
C. y = 6x + 180; 120 boxes
D. y = 6x - 180; 60 boxes
Will give 26 points!!
Which equation represents a line that passes through (5, 1) and has a slope of StartFraction one-half EndFraction?
y – 5 = y minus 5 equals StartFraction one-half EndFraction left-parenthesis x minus 1 right-parenthesis.(x –1)
y – y minus StartFraction one-half EndFraction equals 5 left-parenthesis x minus 1 right-parenthesis. = 5(x –1)
y – 1 = y minus 1 equals StartFraction one-half EndFraction left-parenthesis x minus 5 right-parenthesis.(x –5)
y – 1 = 5y minus 1 equals 5 left-parenthesis x minus StartFraction one-half EndFraction right-parenthesis.
Step-by-step explanation:
Slope 1/2 point 5,1
in point slope form would be
(y-1) = 1/2 (x-5)
I need help on this question
Answer:
it is 74389
Step-by-step explanation:
you do 74 + 094904
-12<-3x+9<24solve this
Let's solve the inequality:
\(\begin{gathered} -12<-3x+9<24 \\ -12-9<-3x<24-9 \\ -21<-3x<15 \\ -15<3x<21 \\ -\frac{15}{3}Therefore, the solution of the inequality is:\(\begin{gathered} -5(-3,5) (3,7)
What is the slope of AB ?
The table shows the amount of cake 333 friends ate. 3/10 5/10 1/10 How much cake did all three friends eat combined?
Answer:
9/10
Step-by-step explanation:
Combined usually means to add. You only add the top.
Answer:
9/10 okqkwlqlakwlwlaka
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a) Factorise x² + 5x-14
b) Solve x² + 5x-14= 0
After solving the quadratic equation, the roots are (x - 2) and (x + 7).
What is a Quadratic function?To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.
The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.
As per the given equation in the question,
x² + 5x - 14 = 0
b² - 4ac
5² - 4(1)(-14)
25 + 56 = 81
Use the equation,
-b ± \(\sqrt{b^2-4ac}/2a\)
Substitute the values,
(-5 + 9)/2 = 2 and,
(-5 - 9)/2 = -7
Therefore, the root will be (x - 2) and (x + 7).
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I need this by to night somebody help pls
Answer:
0° < x < 83.76°
Step-by-step explanation:
Assuming a pyramid with a square base, and the height of the pyramid varies from almost zero to almost infinity.
The largest value for the angle x+2 is when the height of the pyramid is almost zero.
Then the face is an isosceles triangle with base 13 and height 14.
The angle opposite the base is then
x+2 = 2*atan(6.5/7) = 2* 42.879 = 85.76°
when the height is almost infinite, the angle is almost zero.
Therefore the range of the value of x
0° < x < 83.76°
PLEASE HELP WILL GIVE BRAINLIEST
The number of automobiles in a certain town was 1,890 in 2015, and it was 2,420 in 2020. If we were to make a linear model that gives the number of automobiles in this town as a function of the number of years since 2015, what would be the y-intercept?
The y-intercept of the linear model is 211,400, which represents the estimated number of automobiles in the town in the year 2015 (when the independent variable is zero).
To find the y-intercept of the linear model, we need to determine the value of the dependent variable (the number of automobiles) when the independent variable (the number of years since 2015) is equal to zero.
Let's first find the slope of the line, which represents the rate of change of the number of automobiles per year:
slope = (change in number of automobiles) / (change in number of years)
slope = (2420 - 1890) / (2020 - 2015) = 106 automobiles per year
Now we can use the point-slope form of a linear equation to find the y-intercept:
y - y1 = m(x - x1)
where y1 is the value of the dependent variable when the independent variable is x1. In this case, x1 = 2015, y1 = 1890, and m = 106 (the slope we just calculated).
y - 1890 = 106(x - 2015)
To find the y-intercept, we can set x = 0:
y - 1890 = 106(0 - 2015)
y - 1890 = -213,290
y = 211,400
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Need help with number 9
9514 1404 393
Answer:
(b) diagonals bisect each other
Step-by-step explanation:
It is helpful to understand the definitions of the various plane figures we study in geometry.
A parallelogram is a quadrilateral with both pairs of opposite sides parallel. It has the characteristics that ...
opposite angles are congruentopposite sides are congruentthe diagonals bisect each other.A trapezoid has only one pair of parallel sides.
Subtract the product of 5 and 8 from 50.
HOW DO I WRITE THIS IN A NUMERICAL EXPRESSION?
Answer:
50-(5×8)
Step-by-step explanation:
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A movie theatre's daily revenue follows a normal distribution, with an average daily revenue of $3,152. The standard deviation for the distribution is $1281. What is the probability that the theatre generates more than $4,000 in revenue on a randomly selected day?
ANSWER
0.2546
EXPLANATION
The movie theatre's daily revenue, X, is normally distributed with a mean of $3152 and a standard deviation of $1281.
We have to find the probability that the theatre generates more than $4000 in revenue on a randomly selected day,
\(P(X>4000)\)To find this probability, we have to standardize X using the formula,
\(Z=\frac{X-\mu}{\sigma}\)So the probability is,
\(P\left(\frac{X-\mu}{\sigma}\gt\frac{4000-3152}{1281}\right)=P(Z\gt0.66)\)Now, we have to look up this z-value in a z-score table. These tables usually show the area to the left of the z-score - this means that they show the probability for a z less than the z-score, so we have to find the complement,
\(P(Z\gt0.66)=1-P(Z\lt0.66)\)In a z-score table,
So the probability is,
\(P(X>4000)=1-P(Z\lt0.66)=1-0.7454=0.2546\)Hence, the probability that the theatre generates more than $4000 in revenue on a randomly selected day is 0.2546.
A new computer graphics company employs 10 programmers. The company decides to expand into digital animation and needs to transfer 3 of the programmers into the new department. How many different combinations of 3 programmers can be chosen to transfer to the new department?
A. 3
B. 30
C. 120
D. 840
There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department
How to determine the ways of selection?From the question, we have
Total number of programmers, n = 10
Numbers to programmers to select, r = 3
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 10 and r = 3
Substitute the known values in the above equation
Total = ¹⁰C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 10!/(7! * 3!)
Evaluate
Total = 120
Hence, the number of ways is 120
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you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?
Answer:
The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.
Step-by-step explanation:
Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing
In this case:
Probability of Winning = 0.05
Payout for Win = $5
Cost of Playing = $1
Expected Value = (0.05 * $5) - $1
Expected Value = $0.25 - $1
Expected Value = -$0.75
According to a poll, 80% of Americans report being afflicted by stress. Suppose a random sample of 1,200 Americans is selected. Complete parts (a) through (d) below.
a. What percentage of the sample would we expect to report being afflicted by stress?
The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%
How to calculate the percentage afflicted by stress?The percentage of a data set is when part of the data is represented per 100 with a symbol of %.
It was stated in the question that 80% of Americans report being afflicted by stress.
Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.
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What are the most important differences between the distributions for owner-occupied and rented housing units
Answer:
The answer is "Renters typically have much fewer rooms, as well as their distribution, becomes less skewed than that of the home allocation which is inhabited by one's owner".
Step-by-step explanation:
Please find the complete question and its solution in the attachment file:
Pls answer this quickly. I need at atleast 70%
The equation of the line with yellow point in slope intercept form is y = 7 / 6 x + 2.
How to find the equation of a line?The equation of a straight line can be represented in different form such as slope intercept form, point slope form, etc.
Therefore, let's represent the line with yellow point in slope intercept form.
Hence,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (0, 2) and (6, 9).
m = 9 - 2 / 6 - 0
m = 7 / 6
Hence, let's find the y-intercept
y = 7 / 6 x + b
2 = 7 / 6(0) + b
b = 2
Therefore,
y = 7 / 6 x + 2.
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Estimate 147+14+85 by first rounding each number to the nearest ten.
Answer:
250
Step-by-step explanation:
because 147 rounded is 150 14 is 10 and 85 is 90 these added together are 250
Given the function f(x) = -5x + 2, find the range ofly for x = -1, 0, 1.
O 7, 2, -3
O 7, 2, 3
O-7, -2, 3
0-7, -2, -3
Answer:
A
Step-by-step explanation:
f(-1)=7, f(0)=2, f(1)=-3
what is the value of x when h(x) x-3
Answer:
-1
Step-by-step explanation:
I did it in my review
Find the product 8 1/3 × 3/5 then write in simplest form
Answer:
the answer is 5
Step-by-step explanation:
8 1/3 x 3/5
1. First, you convert the mixed number to an improper fraction
25/3 x 3/5
2. Then, reduce the numbers with the greatest common factor 3
25 x 1/5
3. Then reduce the numbers with the greatest common factor 5
5
Find what minimum population size you need to have if you have a 99% confidence, 100 standard deviation and want a size 3 margin of error
A minimum population size of approximately 7373 to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100.
How to calculate the minimum population size?To calculate the minimum population size required to achieve a 99% confidence interval with a margin of error of 3 and a known standard deviation of 100, we can use the following formula:
n = [(z-value × SD) / ME]²
Where:
n = the minimum sample size required
z-value = the critical value for the desired confidence level (99% in this case)
SD = the known standard deviation (100 in this case)
ME = the desired margin of error (3 in this case)
First, we need to determine the z-value for a 99% confidence level. Using a standard normal distribution table, we find that the z-value for a 99% confidence level is approximately 2.576.
Substituting the values into the formula, we get:
n = [(2.576 × 100) / 3]²
Simplifying this expression, we get:
n = 7373.08
Therefore, we would need a minimum population size of approximately 7373.
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There are 36 people in a fitness studio. What fraction represents the number of people running? • 3 8 of the people lifted weight • 1 3 of the people did cross training •the remaining people were running
Answer:
7/24
Step-by-step explanation:
3/8 is changed to 9/24 people lifting weights
1/3 is changed to 8/24 people cross training
17/24 people are not running
7/24 people are running
7/24 cannot be reduced
Hello everyone-SOLVING nonlinear system of equations- ALGEBRA 1
The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.
To solve the nonlinear system of equations:
Equation 1: \(y = -x^2 + 7\)
Equation 2: y = 2x + 4
We can equate the right sides of both equations since they both represent y.
\(-x^2 + 7 = 2x + 4\)
To simplify the equation, we can rearrange it to be in the standard quadratic form:
\(x^2 + 2x - 3 = 0\)
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
(x + 3)(x - 1) = 0
From this equation, we get two possible solutions:
x + 3 = 0 => x = -3
x - 1 = 0 => x = 1
Now, we substitute these x-values back into either equation to find the corresponding y-values.
For x = -3:
y = 2(-3) + 4
y = -6 + 4
y = -2
For x = 1:
y = 2(1) + 4
y = 2 + 4
y = 6
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