Answer:
1/82.
Step-by-step explanation:
In a cross country race with 40 athletes, 10 of them are on the same team. The probability that the top four finishers are all from that same team is given by the expression 10P4/40P4.
The expression 10P4 represents the number of ways that the top four finishers can be chosen from the team of 10 athletes. Since the order in which the athletes finish does not matter, this is equivalent to choosing 4 athletes from a group of 10 without regard for order, which can be done in 10!/(4!6!) = 210 ways.
The expression 40P4 represents the number of ways that the top four finishers can be chosen from the entire group of 40 athletes. Since the order in which the athletes finish does not matter, this is equivalent to choosing 4 athletes from a group of 40 without regard for order, which can be done in 40!/(4!36!) = 34,650 ways.
Therefore, the probability that the top four finishers are all from the same team is given by the expression 10P4/40P4 = 210/34,650 = 1/164. This can be simplified to 1/82 by dividing the numerator and denominator by 2, so the final answer is 1/82.
A soccer training camp charges $9.50 per hour for training, plus a flat fee for equipment rental. The total fee for 12 hours of training was $128.
A) Write and solve a linear equation to find the equipment rental fee.
B) How much would it cost for 6 hours of training?
(High school)
a) The linear function used to find the equipment rental fee is of: y = 9x + 20.
b) The cost for 6 hours of training is of: $74.
How to define the linear function?The linear function is defined considering it's slope-intercept format, given as follows:
y = mx + b.
The coefficients of the function are given as follows:
m is the slope, representing the cost per hour.b is the intercept, representing the flat fee.A soccer training camp charges $9.50 per hour for training, hence the slope is of:
m = 9.
The total fee for 12 hours of training was $128, hence the intercept b is obtained as follows:
128 = 9(12) + b
b = 128 - 108
b = 20.
Hence the function is defined as follows:
y = 9x + 20.
The cost for six hours of training is obtained as follows:
y = 9(6) + 20 = $54.
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pls help me i’ll give you brainlist
Answer: it is 8 and if you need me to explain tell me.
−36+x<8 whats is the x
Answer:
Therefore, the possible values of x are all numbers less than 8.
Step-by-step explanation:
To find the value of x, we need to isolate the variable on one side of the inequality.
To do this, we can subtract 36 from both sides of the inequality to get -36 + x < 8 - 36.
This simplifies to -36 + x < -28.
Next, we can add 36 to both sides to get x < -28 + 36, which simplifies to x < 8.
Therefore, the possible values of x are all numbers less than 8.
Answer:
Inequality Form:
x<44
Interval Notation:
(−∞,44)
Step-by-step explanation:
Move all terms not containing x to the right side of the inequality.
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $6,000, annual interest: 6%, interest periods: 6, number of years: 18
The investment compounded annually has a higher final value than the investment you described because the annual compound interest rate is higher.
What is compound interest?
Compound interest is a type of interest that is calculated on the initial principal of an investment as well as any accumulated interest. In other words, compound interest is interest that is earned on both the original principal and on the accumulated interest from previous periods.
To compare the investment you described to an investment of the same principal at the same rate compounded annually, we need to calculate the final value of each investment after 18 years.
For the investment you described, the final value can be calculated using the formula:
FV = P(1 + r/n)^(nt)
Where FV is the final value, P is the principal, r is the annual interest rate, n is the number of interest periods per year, and t is the number of years.
Plugging in the values given in the problem, we get:
FV = $6,000(1 + 0.06/6)^(6*18) = $6,000(1.01)^108 = $12,688.80
For the investment compounded annually, the final value can be calculated using the same formula, but with n = 1:
FV = $6,000(1 + 0.06/1)^(1*18) = $6,000(1.06)^18 = $15,848.75
Hence, the investment compounded annually has a higher final value than the investment you described because the annual compound interest rate is higher. The difference in final value between the two investments is $15,848.75 - $12,688.80 = $3,159.95.
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Find all solutions of the equation
|x^2 - 30x - 1| + |x^2 - 30x + 29| = 30
Answer:
[15-√226, 1] ∪ [29, 15+√226]
Step-by-step explanation:
You want all solutions to |x^2 - 30x - 1| + |x^2 - 30x + 29| = 30.
DomainsThe equation resolves to a piecewise equation whose domains are delimited by the points where the absolute value arguments are zero.
Left argumentThe argument of the left absolute value function will be zero where ...
x^2 - 30x - 1 = 0
x = (-(-30) ±√((-30)² -4(1)(-1)))/(2(1) = 15 ± √226 ≈ {-0.0332964, 30.0332964}
Right argumentThe argument of the right absolute value function will be zero where ...
x^2 -30x +29 = 0
(x -29)(x -1) = 0
x = {1, 29}
Piece-wise equations-∞ < x < 15-√226In this domain, both absolute value arguments are positive, so the equation is ...
x^2 -30x -1 +x^2 -30x +29 = 30
2x^2 -60x +28 = 30 . . . . . collect terms
x^2 -30x -1 = 0 . . . . . . . . . write in standard form
x = {15 -√226, 15 +√226} . . . . solutions to the equation
These solutions are not in the domain we have defined for this equation.
15-√226 ≤ x ≤ 1In this domain, the left absolute value argument is negative, and the right argument is positive, so the equation is ...
-(x^2 -30x -1) +(x^2 -30x +29) = 30
30 = 30
All values of x in this domain (15-√226 ≤ x ≤ 1) are in the solution set.
1 < x < 29In this domain, both absolute value arguments are negative, so the equation is ...
-(x^2 -30x -1) -(x^2 -30x +29) = 30
-2x^2 +60x -58 = 0 . . . . . . write in standard form
x^2 -30x +29 = 0 . . . . . . . divide by -2
The solutions to this are x={1, 29}, neither of which is in the domain we have defined for this equation.
29 ≤ x ≤ 15+√226In this domain, the left absolute value argument is negative and the right argument is positive. The equation resolves to the same one as for the domain 15-√226 ≤ x ≤ 1: 30 = 30. Hence, all x-values in this domain (29 ≤ x ≤ 15+√226) are part of the solution set.
15+√226 < xIn this domain, both absolute value arguments are positive, so the equation is ...
x^2 -30x -1 = 0 . . . . . . . . . write in standard form
x = {15 -√226, 15 +√226} . . . . solutions to the equation
These solutions are not in the domain we have defined for this equation.
SolutionsIn interval notation, the solution set for the equation is ...
[15-√226, 1] ∪ [29, 15+√226]
Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent
Elyse can select from one of 960 cities or a combination of them. if Elyse decides to purchase a round-the-world ticket. From each of the continents she will travel, she will only get to view one city.
Define combinations and permutations.In mathematics, there are two additional methods for dividing a set of components into subsets: combination and permutation. The elements of the subset may be mixed in any order. The subset's elements are listed in a permutation in a certain order.
Given,
Elyse is planning to purchase a round-the-world flight. From each of the continents she will travel, she will only get to view one city. The continents she will visit and the number of cities she can visit are displayed in the table below. There are options for every continent.
We utilize permutations and combinations to calculate the number of alternatives Elyse will have.
For every 10 cities in Europe, she can choose from any of the eight cities in Asia. For every eight cities in Asia, she can choose any of the four in Africa. Africa and Australia share a similar situation.
Elyse can select one of these total:
10×8×4×3
960
Elyse can choose one of 960 cities or a combination of them.
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Find the coordinates of the circumcenter of the triangle with the given vertices.
H(-10,7), J(-6,3), K(-2,3)
find the circumvented
The coordinates of the circumcenter of the triangle with the vertices H(-10, 7), J(-6, 3) and K(-2, 3) is (-4, 9).
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
The given points are H(-10, 7), J(-6, 3) and K(-2, 3)
Since, Circumcenter of triangle is equidistant from vertices,
Therefore, H(-10, 7), J(-6, 3) and K(-2, 3) are equidistant from circumcenter O,
Let the coordinate of O be (x,y).
OH = OJ
(x + 10)² + (y - 7)² = (x + 6)² + (y - 3)²
x² + 100 + 20x + y² + 49 - 14y = x² + 36 + 12x + y² + 9 -6y
8x - 8y + 104 = 0
x - y + 13 = 0 (1)
Also, OH = OK
(x + 10)² + (y - 7)² = (x + 2)² + (y - 3)²
x² + 100 + 20x + y² + 49 - 14y = x² + 4 + 4x + y² + 9 - 6y
16x - 8y + 136 = 0
2x - y + 17 = 0 (2)
By solving equation (1) and (2),
x = -4
y = 9
The coordinate of the circumcenter is (-4, 9).
Hence, this is the required answer.
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plot the image of triangle ABC under a reflection across line l
The image of the triangle ΔABC under a reflection across the line l can be obtained my making use of the laws of reflection, and the rules of a reflection transformation, to obtain the triangle ΔA'B'C', with vertices at A'(10, -5), B'(13, -6), and C'(12, -3)
Please find attached the plot of the image of the triangle ΔABC, created with MS Excel
What is a reflection transformation?A reflection transformation is one that forms a mirror image of the object across the line of reflection, such that lines joining corresponding points on the pre-image and the image are perpendicular to the line of reflection, and the corresponding points on the pre-image and the image are equidistant from the line of reflection.
Taking the coordinate of the vertices of the triangle ΔABC as A(10, 5), B(13, 6), C(12, 3), and the line l as coinciding with the x-axis, we get:
The coordinates of the image of a point (x, y) following a reflection about the x-axis is the point (x, -y)
Therefor, the coordinates of the vertices of the image of the triangle under a reflection across the line l are;
A'(10, -5), B(13, -6), C'(12, -3)Please find attached the plot of the image of the triangle ABC under a reflection, across line l, created with MS Excel.
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At a charity fund-raiser, adult tickets were sold for $8 each and children's tickets were sold for $2 each. Write an algebraic expression for the total amount of money raised from the
sale of tickets. How much money was raised if the fundraiser sold 249 adult tickets and 388 children's tickets?
vGiven: Line segment N M is parallel to line segment P O. and Angle 1 is-congruent-to angle 3 Prove: Line segment N M is parallel to line segment N O. 4 lines are connected. Line segment L M connects to line segment M N to form angle 1. Line segment M N connects to line segment N O to form angle 2. Line segment N O connects to line segment O P to form angle 3. A 2-column table has 5 rows. Column 1 is labeled statements with the entries line segment N M is parallel to line segment P O, angle 2 is-congruent-to angle 3, angle 1 is-congruent-to angle 3, angle 1 is-congruent-to angle 2, line segment L M is parallel to line segment N O. What is the missing reason in the proof? given transitive property alternate interior angles theorem converse alternate interior angles theorem
Answer:r4r
Step-by-step explanation:
The Green Goober, a wildly unpopular superhero, mixes
3 liters of yellow paint with
5 liters of blue paint to make
8 liters of special green paint for his costume.
Write an equation that relates
y the amount of yellow paint in liters, and
b the amount of blue paint in liters, needed to make the Green Goober's special green paint.
Select each equation which is equivalent to 60% of 25.
0.6 • 25 = x
x • 1.6 = 25
610=x25
60100=25x
x25=60100
6.0 • 25 = x
Given expression 60% of 25 is equivalent to 0.6 × 25.
What do you mean by percentage?
a % is a quantity or ratio that can be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Given expression:
60% of 25
⇒ [tex]\frac{60}{100} \times[/tex] 25
⇒ 0.6 × 25
⇒ 15
Therefore, given expression 60% of 25 is equivalent to 0.6 × 25.
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Select the correct answer from each drop-down menu.
Consider the end behavior of this function, and then complete the statements.
h(x) = -x - 3| +4
As x approaches negative infinity, h (x) approaches
As x approaches positive infinity, h (x) approaches
Answer:Select the correct answer from each drop-down menu.
Consider the end behavior of this function, and then complete the statements.
h(x) = -x - 3| +4
As x approaches negative infinity, h (x) approaches
As x approaches positive infinity, h (x) approaches
Step-by-step explanation:
h(x) = -x - 3| +4 x311
A rectangle has a length 10 meters more than twice the width.
The area of the rectangle is less than 100 meters squared.
Write an expression that represents all possible widths (use the
variable x) of the rectangle. Write your answer as an inequality,
a
We only need to multiply by 10 to determine the length because we know the length is 10 meters longer than our width is 38.75 meters for L.
What is the explanation?The formula for a rectangle's perimeter is
2w + 2L = P where w stands for width and l for length.
The length is 10 meters longer than the breadth, according to this dilemma. So:
L = 10 + w
In our perimeter equation, we may replace L with 10 + w and also 80 in place of P, our perimeter, to solve:
2W + 2(10 + W) = 100
2W + 20 + 2W = 100
4W + 20 = 100
-25. -20
4W = 75
75 /4 =
18.75 meters in W
We only need to multiply by 10 to determine the length because we know the length is 10 meters longer than our width:
18.75 + 10 = 38.75 meters for L.
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Solve (x-2)^2- 40 = 0, where x is a real number
The required solution is given as x = -4.32 and x = 8.32.
Given that,
To Solve (x-2)²- 40 = 0, where x is a real number.
The process in mathematics to operate and the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
(x-2)²- 40 = 0
(x - 2) = √40
x - 2 = ± 6.32
Taking plus,
x = 6.32 + 2
x = 8.32
Taking minus
x = -6.32 + 2
x = -4.32
Thus, the required solution is given as x = -4.32 and x = 8.32.
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The following is a graph of the function f(x) = 2^x. The graph was transformation to h(x) = 1/7×2^x. How does this change the graph?
Answer:
The graph of h(x) = 1/7×2^x will be shifted to the left and compressed compared to the graph of f(x). The y-intercept of h(x) will be 1/7, whereas the y-intercept of f(x) is 1. The graph of h(x) will also have a much smaller range than the graph of f(x).
Step-by-step explanation:
The equation of a graph is given by y=f(x). After transformation, the equation changes to y=h(x).
h(x) = 1/7×2^x
h(x) = 1/7 × (2^x)
h(x) = 1/7 * 2^x
h(x) = (1/7)2^x
=> y = (1/7)2^x
=> y = 1/7 (2^x)
Therefore, the graph of h(x) = 1/7×2^x will be shifted to the left and compressed compared to the graph of f(x). The y-intercept of h(x) will be 1/7, whereas the y-intercept of f(x) is 1. The graph of h(x) will also have a much smaller range than the graph of f(x).
Answer:
The graph of h(x) = 1/7×2^x would be the same as the graph of f(x) = 2^x, but it would be vertically scaled down by a factor of 1/7. This means that all the points on the graph of h(x) would have the same x-coordinates as the corresponding points on the graph of f(x), but their y-coordinates would be 1/7 times smaller. For example, the point (1,2) on the graph of f(x) would be located at (1,1/7) on the graph of h(x).
Which decimal is equivalent to
22/7?
Answer:
3.1429
Step-by-step explanation
`(22)/(7)=3.1429` correct to four decimal places.
whats 10 x 34? please tell me
Answer:
340=10*340 calculated
Answer:
340
Step-by-step explanation:
i know math alot
Does the following system have a unique solution? Why?
The display summarizes grades on a World History exam.
100
95
90
85
80
75
70
65
60
55
50
World History Exams
Which of the following describes the data set?
The data is univariate and categorical.
O The data is univariate and numerical.
O The data is bivariate and categorical.
O The data is bivariate and numerical.
The data set is the data is univariate and numerical.
What is set ?
A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.
A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.
The display summarizes grades on a World History exam.
100,95,90,85,80,75,70,65,60,55, 50
The data is univariate and numerical.
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What’s
1.7a + 0.3a = 0.8
Please explain step by step to get picked brainliest!
1.7a+0.3a=0.8
2a=0.8
a=0.4
Part B
Find the slope of the following graph and enter your result in the empty box.
100
90
80
70
60
50
40
30
20
10
0
Slope =
10 20 30 40
1
50 60 70 80 90 100
Step-by-step explanation:
Using the points [tex](40,20)[/tex] and [tex](50,50)[/tex], [tex]m=\frac{50-20}{50-40}=3[/tex]
Complete the two-column proof. Given: 3x+7=X-5 Prove: -6 = X
Answer:
Refer to the photo taken.
Step-by-step explanation:
(Answer both please will give a brainlest )
To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across the lake using this information. (Assume points A and B are exactly along the
shoreline, and that a-2.92 miles and b-3.91 miles. Round your answer to two decimal places)
A parallelogram has sides of lengths 5 and 4, and one angle is 60°. Find the lengths of the diagonals. (Round your answers to two decimal places. Enter your answers as a comma-separated list
Answer:
Dang this is hard
Step-by-step explanation:
latus rectum is equal to hald of its mojor axis and which passes through the point (√6,1)
Answer:
The latus rectum of an ellipse is a line segment that is perpendicular to the major axis of the ellipse and passes through one of its foci. If the ellipse has a major axis of length 2a, then the latus rectum will have a length of a. Therefore, if the latus rectum is equal to half of the major axis, then the major axis must have a length of 2a, and the latus rectum will have a length of a.
The point (√6, 1) can be the end point of the latus rectum if it lies on the ellipse. To determine if this is the case, you can substitute the coordinates of the point into the standard equation of an ellipse. If the point satisfies the equation, then it lies on the ellipse and can be the end point of the latus rectum.
The standard equation of an ellipse with major axis of length 2a and minor axis of length 2b is:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
Where (h, k) is the center of the ellipse. In this case, we don't know the values of a, b, h, and k, so we can't determine if the point (√6, 1) lies on the ellipse. However, we can use the fact that the latus rectum has a length of a to find the center of the ellipse.
Since the latus rectum is perpendicular to the major axis and passes through the focus, it must also pass through the center of the ellipse. Therefore, the midpoint of the line segment defined by the coordinates (√6, 1) and the center of the ellipse must be the center of the ellipse. The coordinates of the center can be found by taking the average of the x-coordinates and the average of the y-coordinates. In this case, the center of the ellipse will have coordinates:
(x, y) = ((√6 + h) / 2, (1 + k) / 2)
Once you know the center of the ellipse, you can use the standard equation of an ellipse to find the values of a, b, h, and k. Once you have those values, you can determine if the point (√6, 1) lies on the ellipse and can be the end point of the latus rectum.
I hope this helps. Let me know if you have any other questions.
Caitlin is painting her bedroom. She paints 42 square feet in 2/3 hour. At this rate, how many square feet can she paint in one hour?
how do you get the answer for 412.3 divided by 35
Answer:
The answer will be 11.78
Step-by-step explanation:
The first step to dividing fractions of 412.3 and 35. Next to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed. You will get the answer in no time!
Find the value of x and show work please !!!
Answer:
E
Step-by-step explanation:
Solve for y.
6=2(y+2)
y=
Answer:
1
Step-by-step explanation:
6=2y+4
2=2y
y=1
45°25'11"+6°31′18". Give your answer in both degree-
minute-second and decimal forms.
the answer to the equation is x2=4 or 2-2