There are 154,440 different ways for the names of the top 5 participants to be listed on the leaderboard.
To determine the number of ways the names can be listed for the top 5 participants on the leader board, you can use the concept of permutations. The formula for permutations is:
[tex]\[ P(n, r) = \frac{n!}{(n - r)!} \][/tex]
where [tex]\( n \)[/tex] is the total number of items and [tex]\( r \)[/tex] is the number of items to be selected.
In this case, you have 13 participants, and you want to select and order the top 5 participants. So, the formula becomes:
[tex]\[ P(13, 5) = \frac{13!}{(13 - 5)!} \][/tex]
Now, calculate the permutations:
[tex]\[ P(13, 5) = \frac{13!}{8!} \][/tex]
[tex]\[ P(13, 5) = \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8!}{8!} \][/tex]
[tex]\[ P(13, 5) = 13 \times 12 \times 11 \times 10 \times 9 \][/tex]
Now, calculate the result:
[tex]\[ P(13, 5) = 154,440 \][/tex]
So, there are 154,440 different ways for the names of the top 5 participants to be listed on the leader board.
30 POINTS!!!
The height of a cable in a suspension bridge changes based on the horizontal distance from the tower supporting the cable. The graph shows the relationship between horizontal distance and height.
For what horizontal distance is the height the smallest?
250 feet * this is what I think*
300 feet
500 feet
900 feet
Answer:
250 feet
Step-by-step explanation:
Vertex: (250,300)
Minimum height is 300 when the horizontal distance is 250
Step-by-step explanation:
Step 1: Find the smallest height
If you look at the graph, you can tell that at 250 feet, the height in feet is the lowest and it is at 250. Therefore, the vertex is also (250, 250). But, we are just looking for the x-value which will be 250.
Answer: Option A, 250 feet... you were correct :) Good Job
Isaiah creates 5 music playlists for a party. Each playlist has 10 songs. How many songs did Isaiah include in all of
his playlists?
Answer:
Isaiah included 50 songs in all of
his playlists.
Step-by-step explanation:
Each playlist has 10 songs. So if you have 2 playlists then you have 10 songs for the first playlist and 10 songs for other playlist.
In this question there are 5 playlists, so 10 + 10 + 10 + 10 + 10 =50 songs.
In mathematics you can multiply to get the answer quickly:
5 * 10 = 50
That is a lot faster and you still get the same result!
Construct the indicated confidence interval for the difference between population proportions Assume that the samples are independent and that they have been randomly selected. Be sure to provide the (1) Null & Alternative Hypotheses, (2) Test Statistic, (3) P-value (or critical value), and (4) concluding statements.
x1 = 15, n1 = 50 and x2 = 23, n2 = 60;
Construct a 90% confidence interval for the difference between population proportions p1 - p2.
Null Hypothesis (H0): p1 - p2 = 0. Alternative Hypothesis (H1): p1 - p2 ≠ 0. Test Statistic: Z-score. 90% confidence interval: (-0.191, 0.291). Conclusion: Fail to reject H0, indicating no significant difference in population proportions.
1) Null Hypothesis (H0): There is no difference between the population proportions (p1 - p2 = 0).
Alternative Hypothesis (H1): There is a difference between the population proportions (p1 - p2 ≠ 0).
2) Test Statistic: Z-score for two independent proportions.
3) P-value or Critical Value: Z-value for a 90% confidence interval.
4) Concluding Statement: With a 90% confidence interval, we find the difference in population proportions to be between -0.191 and 0.291. Thus, we fail to reject the null hypothesis.
The complete question is:
Construct the indicated confidence interval for the difference between population proportions Assume that the samples are independent and that they have been randomly selected. Be sure to provide the (1) Null & Alternative Hypotheses, (2) Test Statistic, (3) P-value (or critical value), and (4) concluding statements. x1 = 15, n1 = 50 and x2 = 23, n2 = 60; Construct a 90% confidence interval for the difference between population proportions p1 - p2.
If you had a penny today, that doubled everyday for a month How much will you have in each account at the end of the month?
Write your explanation
Today: 1 cent.
Since there are 30 days which you double, multiply it by [tex]2^{30} .[/tex]
You get ABOUT 1 billion, or 1,000,000,000
Convert that to dollars (divide by 100), and you get...
Answer:
A Penny Doubled Everyday. Quite a big difference once you look at it as you would be getting over 5 million dollars with the penny doubled everyday for 30 days route.
Step-by-step explanation:
Which expressions are equivalent to q+p+q+p+qq+p+q+p+qq, plus, p, plus, q, plus, p, plus, q?
Answer:
A&B
Step-by-step explanation:
3q + 2p is our correct answer.
Given,
q + p + q + p + q
We need to find the final expression.
Since the options are not given here we will assume the answers.
What is expression?An expression is a sentence with more than one numbers or variables and at least one math operation.
We have,
q + p + q + p + q
There are 3 q and 2 q
Now add the like terms
3q + 2p
Thus the expression we got is 3q + 2p.
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Super urgent!
Solve the equation for all real values of x. 3tan^2 = sqrt3 tanx
To solve the equation 3tan^2 = sqrt3 tanx for all real values of x, divide both sides of the equation by tan(x) and then take the inverse tangent of both sides. The solutions for x are 30°, 210°, 390°, ...
Explanation:To solve the equation 3tan^2 = sqrt3 tanx for all real values of x, we can start by rearranging the equation. Divide both sides of the equation by tan(x) to get:
3tan(x) = sqrt3
Next, divide both sides of the equation by 3 to get:
tan(x) = sqrt3/3
Now, we need to find the values of x where the tangent function equals sqrt3/3. We can use the inverse tangent function to find the angles. Taking the inverse tangent of both sides gives:
x = arctan(sqrt3/3)
Then, we can simplify the expression:
x = 30° + n * 180°
where n is an integer. Therefore, the solutions for x are 30°, 210°, 390°, ...
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Samuel has a hamster cage that is a rectangular prism. It is 20 inches
long, 12 inches deep, and 10 inches tall. What is the volume, in cubic
inches, of Samuel's hamster cage?
2,400 1/8 cubic inches
2,521 1/2 cubic inches
5791 1/9 cubic inches
1,158 1/4 cubic inches
Answer:
well im not sure but that's what i got
Step-by-step explanation:
(20)(12)(10)=2400
2400/4= 800
The volume of the given rectangular prism is 2400 cubic inches.
Given that, a rectangular prism dimensions are length = 20 inches, width = 12 inches and height = 10 inches.
What is a rectangular prism?A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
Volume of a rectangular prism = Area of a base × Height.
Here, Area of a base = length × width
= 20 × 12
= 240 square inches
So, volume = 240 × 10
= 2400 cubic inches
Therefore, the volume of the given rectangular prism is 2400 cubic inches.
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Which of the following is the equation of a line in slope-intercept form for a
line with slope = 4 and y-intercept at (0, 2)?
O A. y = 2x+4
B. y = 4x-2
c. y = 4x + 2
D. x = -2x-4
Answer:
C features a slope of +4 and a y-intercept of +2
Step-by-step explanation:
Only the middle two answers feature a slope of +4, so eliminate answers A and D. Answer C features a slope of +4 and a y-intercept of +2
The equation of a line in slope-intercept form for a line with slope 4 and y-intercept at (0, 2) is C. y = 4x + 2.
Explanation:In the slope-intercept form of a linear equation, y = mx + b, 'm' represents the slope and 'b' represents the y-intercept. If we substitute the given values into this equation, with m = 4 (the slope) and b = 2 (the y-coordinate of the y-intercept), we get y = 4x + 2. So, the correct answer is C. y = 4x + 2.
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Aidan has $65 in his bank account. His brother Michael also has a bank account. They want to calculate the amount of money in both accounts combined. What variable is needed to calculate their combined total?
A.
m, the amount of money in Michael's bank account
B.
d, the difference between the amounts in Aidan's and Michael's account
C.
l, the amount of money in Michael's account last month
D.
a, the amount of money in Aidan's bank account
Answer:
the answer was A m the amount of money in Michael's account
Step-by-step explanation:
Answer: a, the amount of money in Michaels bank account
Step-by-step explanation:
Question 2 of 10
2 Points
Which of the following describes a rigid motion transformation?
O
A. Enlarging the size of a parking spot
O
B. Dilating a picture
O
C. Slicing a sandwich into 4 pieces
O
D. Hitting a tennis ball over a net
Option (D) Hitting a tennis ball over a net describes the rigid motion transformation option (D) is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have a statement:
Which of the following describes a rigid motion transformation?
As we know, geometric transformation also known as rigid transformation is a change in geometry.
Thus, option (D) Hitting a tennis ball over a net describes the rigid motion transformation option (D) is correct.
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If a math test has questions on spelling, the test does not
have this type of validity.
Answer:
True
Step-by-step explanation:
It's a math test so it should be math questions not spelling.
The area of a square can be found using the equation A = s, where A is the area and s is the measure of one side of the square
Match the equation for how to solve for the side length of a square to its description.
A square has an area of 60 in?
8=V602 in.
s=760 in.
S = 602 in
S = 60 in
Plz help
Answer:
7880
Step-by-step explanation:
If A is S then S is A so using Trin's method...you can find 18x*760+y
A local hamburger shop sold a combined total of 768 hamburgers and cheeseburgers on Saturday. There were 68 more cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?
The area of a kite ABCD is 900cm2 and one diagonal is 25cm long. Find the length of the other diagonal. Please answer!!!
Answer:
72 cm
Step-by-step explanation:
The area (A) of a kite is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ( d₁ and d₂ are the diagonals )
Here A = 900 and d₁ = 25, thus
[tex]\frac{1}{2}[/tex] × 25 × d₂ = 900 ( multiply both sides by 2 )
25d₂ = 1800 ( divide both sides by 25 )
d₂ = 72 cm
evaluate the expression for f=6
15+f
Answer:
21
Step-by-step explanation:
15+f
Let f = 6
15+6 = 21
If m∠X = 55° and m∠Y = 75°, then m∠W =
The correct answer is C) 105°.
The sum of the angles in a triangle is 180 degrees. Since we know the measures of two of the angles, we can find the measure of the third angle by subtracting the sum of the first two angles from 180 degrees.
In this case, m∠X + m∠Y = 55° + 75° = 130°.
Therefore, m∠W = 180° - 130° = 50°.
However, the diagram shows angle W as an exterior angle of the triangle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this case, the remote interior angles are ∠X and ∠Y.
Therefore, m∠W = m∠X + m∠Y = 55° + 75° = 130°.
Answer Choice Explanation:
A) 20° is too small.
B) 35° is too small.
C) 105° is correct.
D) 130° is too large.
Therefore, the correct answer is C) 105°.
A soccer ball is at rest and is then kicked giving it a final velocity of 6.0 m/s. The ball has a mass of
0.28 kg. If the time of contact between the soccer player's foot and the ball is 0.020 s, what was the
average force applied to the ball?
Answer:
The average force applied to the ball is 84N
Step-by-step explanation:
This problem bothers on the impulse of a force
Given data
Mass of ball m= 0.28kg
Initial speed u= 0m/s
Final speed v= 6m/s
Time of impact t= 0.02s
We know that the impulse of a force
Ft= mv-mu
Hence the force is
F= (mv-mu)/t
F=m(v-u)/t
F= 0.28(6-0)0.02
F= 1.68/0.02
F= 84N
Dolce the equation below for x 1/2(x+256)=180? I need help
Answer:
x=104
Step-by-step explanation:
x+256=360
x=360-256
x=104
Answer:
Step-by-step explanation:
104
Boomtown completes a census every ten years. The table shows the population of the town for each census taken.
What will be the population in 2100?
A. 119,574,225
B. 39,858,075
C. 367
D. 4,782,969
Answer: b 39,858,075
Answer:
Answer: b 39,858,075
Step-by-step explanation:
Mia has $1,000 in savings and wants to deposit her money in the savings account that will pay the most annual
interest. She is choosing between two accounts: Account A pays 5 percent and Account B pays 4 percent. Which
account will pay more interest? How much more will it pay each year?
Answer: Account A pays more interest. It pays $10 more.
Step-by-step explanation:
The following information can be derived from the question:
Principal= $1000
Account A rate= 5%
Time = 1 year
Interest= (Principal × Rate × Time)/100
= ($1000 × 5 × 1)/100
= $5000/100
= $50
Account A pays interest of $50
Principal= $1000
Account B rate= 4%
Time = 1 year
Interest= (Principal × Rate × Time)/100
= ($1000 × 4× 1)/100
= $4000/100
= $40
Account B pays interest of $40
From the solutions provided, Account A pays more interest. This is calculated as: $50 - $40 = $10
21. Is the histogram uniform, symmetric, or skewed? (1 point)
uniform
symmetric
skewed
Answer:
Symmetric
Step-by-step explanation:
The data is spread out symmetrically. It isn't uniform because the values aren't around each others values. It isn't skewed because the data isn't 'closer' to one side.
Answer:
symmetric
Step-by-step explanation:
if you put a line down the middle you’ll notice both sides are symmetric, kind of like looking into a mirror
Find the area of the triangle with a = 3 feet, b = 4 feet, and c = 6 feet. Round to the nearest tenth.
Answer:
12 feet squared.
Step-by-step explanation:
The formula is (A*B)/2. (Remember, multiply first, then divide.)
Explain how to complete the square for an expression of the form x2+bx
.
Add [tex]\left(\dfrac{b}{2}\right)^2[/tex] in the expression to make it perfect square.
Important information:
The given expression is [tex]x^2+bx[/tex].Completing the square:We know that,
[tex](x+y)^2=x^2+2xy+y^2[/tex]
[tex](x+y)^2=a^2+(2y)a+\left(\dfrac{2y}{2}\right)^2[/tex]
It means, we need to add the square of half of the coefficient of x in [tex]x^2+bx[/tex] to make it perfect square, i.e., [tex]\left(\dfrac{b}{2}\right)^2[/tex].
[tex]x^2+bx+\left(\dfrac{b}{2}\right)^2=\left(x+\dfrac{b}{2}\right)^2[/tex]
Therefore, add [tex]\left(\dfrac{b}{2}\right)^2[/tex] in the expression to make it perfect square.
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To complete the square for an expression [tex]x^2+bx[/tex] you divide the coefficient of 'x' by 2, square it, and add and subtract that within the square, which can then be factored to a perfect square trinomial.
Explanation:Completing the square for an expression of the form [tex]x^2+bx[/tex] involves a process to rewrite the quadratic expression into a form that can be factored as a perfect square trinomial. Here are the steps to do so:
Divide the coefficient of x (which is 'b' in your equation) by 2 and square the result. This will be the value added and subtracted within the square to complete it. Add and subtract the calculated number from step 1 inside the parenthesis to maintain the balance of the equation. Simplify the equation, factoring out the perfect square trinomial formed.
In other words, x^2+bx can be rewritten as [tex][x+(b/2)]^2 - (b/2)^2[/tex]. Here, [tex][x+(b/2)]^2[/tex] is the perfect square trinomial.
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A circle has a radius of 18 and a center at (10,-9). Find the equation of the circle.
Answer:
(x-10)²+(y+9)²= 324.
Step-by-step explanation:
For this question, you will need to substitute these values into the equation of a circle:
(x-h)²+(y-k)²= r²
'h and k' represent the center points, and 'r' represents the radius.
This will result in:
(x-10)²+(y+9)²=324.
The equation ___ has no solution.
A. 13y+2-2y=10y+3-y
B. 9(3y+7)-2=3(-9y+9)
C. 32.1y +3.1+2.4y-8.2=34.5y-5.1
D. 5(2.2y+3.4_=5(y-2)+6y
Answer:
c) 32.1y +3.1+2.4y-8.2=34.5y-5.1
Solve for x 5(x + 1)= 4x +7
Answer:
x = 2
Step-by-step explanation:
5(x + 1) = 4x + 7
5x + 5 = 4x + 7
x + 5 = 7
x = 2
Answer:
x=2
Step-by-step explanation:
Let's solve your equation step-by-step.
5(x+1)=4x+7
Step 1: Simplify both sides of the equation.
5(x+1)=4x+7
(5)(x)+(5)(1)=4x+7(Distribute)
5x+5=4x+7
Step 2: Subtract 4x from both sides.
5x+5−4x=4x+7−4x
x+5=7
Step 3: Subtract 5 from both sides.
x+5−5=7−5
x=2
Consider Carmen’s new set of plans. Parallel lines k and l are crossed by transversal t. Line m crosses lines t, k, and l. The angles formed by lines k, t, and m, clockwise from top left are 2, 1, blank, blank, blank (6 x + 5) degrees; formed by lines l and t are blank, (7x minus 4) degrees, blank, blank; formed by lines l and m are 48 degrees, blank, blank, blank. Examine the lines that are cut by transversals to determine the measure of angle 1. What is the measure of angle 1? m <1= ° Why?
Based on the vertical angles theorem, the measure of angle 1 is: 48°.
What are Vertical AnglesVertical angles are always directly opposite each other and are formed when two straight lines crosses each other.
In the diagram given, the angle that is directly opposite angle is 48°, since it is an alternate angle to 48° formed on lines m and n (lines k and l are parallel lines).
Therefore:
m∠1 = 48° (vertical angles)
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Answer:
The Answer it's 48 And It corresponds to the 48-degree anglee.
Step-by-step explanation:
On EDGE 2022!
4. If f(x) = 4x - 9, what is the equation for f1(x)?
ºf-'(x) == -9
X+9
© f*(x) = **
© F"(x) = + 9
f"(x) = x -9
0
Answer:
F1(x) = 4x-9 Thats the answer
PLEASE HELP!!!
Which expression can be used to find the surface area of the following square pyramid?
Choose 1 answer:
O 36+30+30+30+30
O 36+15
O 36+15+15+15
O 36+15+15+15+15
Answer:
36+15+15+15+15
Step-by-step explanation:
the base is 36, 6x6, and then you do the triangles, 6x5(1/2) which is 15, but there are 4 of them.
Answer:
its A) 36+15+15+15+15
Step-by-step explanation:
Toniqua opens a savings account and deposits $43 in the account. Each week, she deposits $16 to the account.
Which equation gives the amount of money in Toniqua's bank account, y, after x weeks?
A. y = 16x
B. y = 43x
C. y = 16 + 43x
D. y = 43 + 16x
Please hurry!!
Answer:
D
Step-by-step explanation:
Because of the fact that she opened a savings account and deposited $43 you are going to add that to 16x. Why? Because x represents the number of weeks she deposits $16 in her savings account. The y represents the money in her bank account, which is what we are trying to find.
I hope I've helped! Please leave a Thanks and Vote/Rate.
The correct equation representing the amount of money in Toniqua's bank account after x weeks is y = 43 + 16x. It combines the initial deposit of $43 with the $16 added each week multiplied by the number of weeks.
Explanation:The question asks for an equation that represents the amount of money in Toniqua's bank account, y, after x weeks. Considering that Toniqua starts with a deposit of $43 and then adds $16 each week, the total amount of money after x weeks would be the initial deposit plus the weekly deposit amount times the number of weeks. Therefore, the correct equation would be:
y = 43 + 16x
The initial deposit is a one-time amount, so it does not multiply by the number of weeks, hence the 43 is not multiplied by x. However, the weekly deposit of $16 does multiply by the number of weeks, which gives us the 16x term in the linear equation.