If there are 31 horses competing in a show, then the blue, red, and yellow ribbons can be awarded in 26970 different ways.
As per the question statement, 31 horses are competing in a show.
We are required to calculate the number of ways in which the blue, red and yellow ribbons can be awarded.
To solve this question, first, we need to know a basic rule of horse shows, which is the 1st place or the winner is awarded with a blue ribbon, the second place or the runners-up is awarded with a red ribbon and the third place or the second runners-up is awarded with a yellow ribbon.
That is, in simpler terms, we have to calculate the number of different ways, in which the first, second and third places can be achieved between 31 different horses, each having equal probability of winning.
To solve this question, we just need to know the formula of permutation which goes as [tex][(nPr)=\frac{n!}{(n-r)!} ][/tex], i.e., we are to select an ordered set or "r" from a set of "n".
As per our question, (n = 31) and (r = 3), and using these in the above mentioned formula of permutation, we get
[tex](31C)=\frac{31!}{(31-3)!}=\frac{31!}{28!} =\frac{28!*29*30*31}{28!}=(28*29*30)=26970.[/tex]
That is, the blue, red and yellow ribbons can be awarded in a show with 31 horses as contestants in 26970 different ways.
Probability: In mathematics, probability of an event is the extent to which it is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.Permutation: In mathematics, a permutation of a set is an arrangement of its members into a particular sequence, or if the set is already ordered, a rearrangement of its elements.To learn more about permutations, click on the link below.
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he mean life of a tire is 30,000 km. The standard deviation is 2000 km.
Then, 68% of all tires will have a life between ___________ km and __________ km.
The conclusion is that 68% of all tires will have a life between 28000 km and 32000 km.
How to use the Empirical Rule of statistics?
The empirical rule in statistics states that for a normal distribution,
68% of the distribution are within one standard deviation from the mean.95% are within two standard deviation from the mean.99.7% are within three standard deviations from the mean.We are given;
Mean (μ) = 30000 km
Standard deviation (σ) = 2000 km
Using the empirical rule of 68% which lies within one standard deviation from the mean, we have;
μ ± σ = 30000 ± 2000 = (28000, 32000)
Thus, we conclude that 68% of all tires will have a life between 28000 km and 32000 km.
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A water bottle holds 120oz. Each time Anna takes a sip she drinks 10oz.a) Write a function to represent the scenario
b) How many sips can Anna take before she needs to refill?
c) Create a graph to represent this situation.
d) What is the domain of the function?
From the situation described, we have that:
a) The linear function is: f(s) = 120 - 12s.
b) She can take 10 sips before she needs to refill.
c) The graph is given at the end of the answer.
d) The domain is: 0 ≤ s ≤ 10.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the parameters are given as follows:
m = -12, b = 120.
Hence the function is:
f(s) = 120 - 12s.
She can take sips until f(s) = 0, hence:
120 - 12s = 0
12s = 120
s = 10.
She can take 10 sips before she needs to refill, and hence the domain(set that contains the input values for the function) is 0 ≤ s ≤ 10.
The graph is given at the end of the answer.
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2.) A rectangular garden is 6 ft longer than it is wide. Its area is 352 ft2. What are its dimensions?
Answer:
Length = 22, Width = 16
Step-by-step explanation:
Let L be the length of the garden and W the width
The area, A = L x W = 352 ft²
It is given that L = W + 6
Substituting for L in the area equation we get
L x W
==> (W + 6) x W = 352
Expanding the brackets
==> W.W + 6.W = 352
==> W² + 6W = 352
Subtract 352 from both sides:
W² + 6W - 352 = 0
This is a quadratic equation which can be solved using the quadratic formula.
- 352 = - 16 x 22 and -16 + 22 = 6
So we can factor the quadratic equation as
(W - 16) (W + 22) = 0
==> W = 16 or W = -22
Since we can disregard negative values in this context,
W = 16 and L = W + 6 = 16 + 6 = 22
Dimensions are Length = 22, Width = 16
Alfonso and Cordell each bought one raffle ticket at the state fair. If 50 tickets were randomly sold, what is the probability that Alfonso got ticket 14 and Cordell got ticket 23? Express your answer as a fraction in simplest form.
The probability that Alphonso gets ticket 14 and Cordell gets ticket 23 is = 1/2450
Alphonso can pick a ticket from 50 tickets in 50 ways;
When Alphonso pick a ticket, then Cordell can pick a ticket in 49 ways;
Total number of ways = 50 × 49 = 2450;
Alphonso can get ticket 14 and Cordell can get ticket 23 in only one way;
So, the probability that Alphonso gets ticket 14 and Cordell gets ticket 23 is = 1/2450;
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A supermarket wants to send codes for $0.25 off a bag of chips to its rewards program members. Each coupon code will have one digit followed by four letters. The letters D and E and the digits 0, 5, and 8 will not be used. So, there are 24 letters and 7 digits that will be used. Assume that the letters can be repeated. How many such coupon codes can be generated?
Using the Fundamental Counting Theorem, it is found that 2,322,432 codes can be generated.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering that the ode will have one digit followed by four letters, the parameters are given as follows:
[tex]n_1 = 7, n_2 = n_3 = n_4 = n_5 = 24[/tex]
Hence the number of codes that can be generated is:
N = 7 x 24 x 24 x 24 x 24 = 2,322,432.
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Find the area of a parallelogram whose altitude is 17 inches and whose base is 12 inches.
Answer:
A= 204 in²
Step-by-step explanation:
The base is 12 in, and the height is 17 in.
A=b h=12·17=204 in²
it it right
Luis and Jasmine are making scale drawings of the front of their school for an art contest. Luis uses the scale 3 in. to 10 ft. Jasmine uses the scale 5 in. to 20 ft. The tree in front of the school in Luis's drawing is 7.5 inches tall. How tall is the tree in Jasmine's drawing?
The height of the tree in Jasmines drawing is; 6.25 inches tall
How to interpret Scale Drawing?The scale factor used by Louis is; 3in : 10 ft
The scale factor used by Jasmine is; 5in : 20ft
We are told that the tree in front of the school in Luis's drawing is 7.5 inches tall. Thus;
True height of tree in Louis drawing is; (7.5 * 10)/3 = 25 ft
Thus, height of tree in Jasmines drawing = (25 * 5)/20 = 6.25 inches tall
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Triangle XZ is translated 4 units up and 3 units left to yield urz. What is the distance between any two corresponding points on 2 and
DRYZ?
OA 7 units
OB √nts
OD. 25 units
The value of x is 5
Question is based on the Pythagorean theorem :
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple
Consider the triangle given above:
Where “a” is the perpendicular,
“b” is the base,
“c” is the hypotenuse.
According to the definition, the Pythagoras Theorem formula is given as:
X is the side opposite to the right angle, hence it is a hypotenuse.
Now, by the theorem we know;
Hypotenuse2 = Base2 + Perpendicular2
x2 =[tex]4^{2} +3^{2}[/tex]
x2 = 16+9
x = [tex]\sqrt{25}[/tex]
Therefore, the value of x is 5
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Find unit rate $602 for 20 hours of work
Can anybody please help me
Answer:
7x+2/x² +x +2
that's my answer
What is the value of f(2) when f(x)= 3x-7?
Helpp please I don’t understand :(
Answer:
s = 2 1/3 + 1/2
t = 2/3 + 3/2
We have to find the sum of both s and t.
2 1/3 + 1/2 = 2 2/6 + 3/6 = 2 5/6
2/3 + 3/2 = 4/6 + 9/6 = 13/6 = 2 1/6
If we look at the number lines, we can see that c matches with both points.
After the point Y (-4, -9) is translated along the vector <-6, 2>, the image will be located at point
The image of the coordinates of the resulting point are Y'(x, y) = (- 10, - 7).
How to find the coordinates of the image of a given point
In this problem we have the coordinates of a original point and a translation vector, the coordinates of the image is obtained by using the following formula:
Y'(x, y) = Y(x, y) + T(x, y)
Where:
Y(x, y) - Coordinates of the original pointY'(x, y) - Coordinates of the resulting pointT(x, y) - Translation vectorTo learn more on Y(x, y) = (- 4, - 9) and T(x, y) = (- 6, 2), then the coordinates of the resulting point are:
Y'(x, y) = (- 4, - 9) + (- 6, 2)
Y'(x, y) = (- 10, - 7)
The image of the coordinates of the resulting point are Y'(x, y) = (- 10, - 7).
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A party rental company has chairs and tables for rent. The total cost to rent 9 chairs and 7 tables is $86. The total cost to rent 3 chairs and 5 tables is $52. What is the cost to rent each chair and each table
Answer: ok here is ur answer The cost for 1 chair is $2.75 and the cost for 1 table is $8.75
Use the elimination method of linear equations to find your answer.
Our equations for this problem are:
3c+5t=52 and 9c+7t=86
1. Multiply the entire first equation by -3.
-3(3c+5t=52)
2. Simplify the equation from above:
-9c-15t=-156
3. Stack the two equations on top of each other and add/subtract:
-9c-15t=-156
9c+7t=86
4. You should be left with -8t=-70. Simplify this to find the value of t:
t=8.75
5. Plug the value of t into any of the original equations and solve for c.
3c+5(8.75)=52
6. Simplify the equation above:
3c+43.75=52
7. Subtract 43.75 from both sides of the equation:
3c=8.25
8. Divide both sides by 3 to get your c value:
c=2.75
Step-by-step explanation: i really hope this helps pls lmk if i am wrong (:
Evaluate fog and go f and use the results to determine if g is the inverse function of f.
If [tex]f,g[/tex] are inverses of one another, then
[tex]f\circ g(x) = g\circ f(x) = x[/tex]
Given [tex]f(x)=x^2-1[/tex] and [tex]g(x)=\sqrt{x-8}[/tex], then
[tex]f\circ g (x) = f(g(x)) = f(\sqrt{x-8}) = \left(\sqrt{x-8}\right)^2 - 1 = \boxed{x - 9} \neq x[/tex]
so right away we know [tex]f[/tex] and [tex]g[/tex] are not inverses.
In the other direction, we come to the same conclusion.
[tex]g\circ f(x) = g(f(x)) = g(x^2 - 1) = \sqrt{(x^2-1)-9} = \boxed{\sqrt{x^2 - 9}} \neq x[/tex]
Solve for x.
x³ = 1000
Enter your answer in the box.
X =
Answer:
10
Step-by-step explanation:
10*10*10=1000
10^3=1000
Earl Bean sells shoes for Target. Target pays Earl $10 per hour plus 4% commission on all sales. Assume Earl works 39 hours for the week and has $6,000 is sales. What is Earl's gross pay?
The kinetic energy T units of a moting body (of constant mass) varies as the square of its speed vm/s. If T = 800 units when v= 20m/s: Calculate V when T= 1800.
The kinetic energy T units of a motion body (of constant mass) varies as the square of its speed v m/s. If kinetic energy T = 800 units when speed v= 20m/s: Calculate V when T= 1800.
If T=1800 then V=30m/s.
kinetic energy is nothing but The energy an object has as a result of motion is known as kinetic energy.
Given that,
If T = 800 units when v= 20m/s
Kinetic energy formula is
[tex]T=\frac{1}{2}mv^{2}[/tex]
Here, T is kinetic energy , m is mass and v is speed
Now,
[tex]800=\frac{1}{2}m(20)^{2} \\800\times2=m(400)\\\frac{1600}{400}=m\\ m=4[/tex]
We got mass m as 4
Now, when T= 1800 find v=?
[tex]1800=\frac{1}{2}\times4\times v^{2} \\1800\times2= v^{2} \\ v^{2} =900\\v=30[/tex]
Therefore, we got speed v=30m/s when the kinetic energy T=1800.
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4. A lawn sprinkler shoots out a circle of water that goes
12 feet in all directions. What is the area of the part of the
lawn that the sprinkler waters?
The sum of 8 and three times a number is 41
Answer:
The number is 11
Step-by-step explanation:
First turn this into a mathematical equation
8+3x=41
subtract 8 from both sides
3x=33
divide both sides by 3
x=11
la la la, la la la, la la la la la~
sorry beinggreat I didnt know what to name it ;-;
[tex]31\% = \frac{31}{100} = 0.31 > 0.275 \\ 32.6\% = \frac{32.6}{100} = 0.326 > 0.310 \\ 0.325 = \frac{32.5}{100} = 32.5\% > 27.5\% \\ 0.310 = \frac{31}{100} = 31\% < 32.5\%[/tex]
only Option B is correctAnswer:
Letter B is the answer
Step-by-step explanation:
A. 31% < 0.275
31% < 27.5%
B. 32.6% > 0.310
32.6% > 31%
C. 0.325 < 27.5%
32.5% < 27.5%
D. 0.310 > 32.5%
31% > 32.5%
help please and explain why
Translate the image by (3x - 1, y + 5) D(1,2)→ D'_ E(-3,-5)→E'. F(4,-1)→→ F
The image of D (1, 2) is D' ( 2, 7).
The image of E (-3 -5) is E' ( -10, 0).
The image of F (4, -1) is F' ( 11, 4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given points are;
D (1, 2), E(-3, -5) and F(4, -1)
Now, The rule is to find the image of points is;
(x, y) → (3x - 1, y + 5)
Hence,
The image of D (1, 2) = (3 * 1 - 1, 2 + 5)
= (3-1, 7)
= (2, 7)
The image of E (-3 -5) = (3*-3 - 1, -5 + 5)
= (-9-1, 0)
= (-10, 0)
The image of F (4, -1) = (3*4 - 1, -1 + 5)
= (12-1, 4)
= ( 11, 4 )
Therefore, The image of D (1, 2) is D' ( 2, 7).
The image of E (-3 -5) is E' ( -10, 0).
The image of F (4, -1) is F' ( 11, 4).
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[tex]-\sqrt[4]{324}[/tex]
How do I solve this??
Answer:
Step-by-step explanation:
Answer: 144
Step-by-step explanation:
find the area of the circle
The area of the circle based on the information illustrated is C. 28.26ft².
What will the area be?It should be noted that the area of a circle is given as:
= πr²
In this case, the radius is 3ft.
Therefore, the area will be:
= πr²
= 3.14 × 3²
= 3.14 × 9
= 28.26 ft²
In conclusion, the area of the circle is 28.26ft².
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If ∠HJK is 35° and ∠FJI is 95°, what is the measure of ∠KJG?
Answer:
180-(35+95)=50
Step-by-step explanation:
Any triangle in the world sum of its angle equal 180
e At its highest
is 5,762 feet
At its lowest point, the elevati
15. Make Sense and Persevere At its bio
point, the elevation of a county is 5,762
above sea level. At its lowest point. th
of the county is 9 feet below sea level.
ow sea level.
a. What is the difference between the highest and lowest points of the country?
The difference between the highest and the lowest points of the country is 5771 feet.
What is subtraction?The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller.
The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).
Let the sea level be x.
The highest point of the country is 5,762 feet above the sea. So, we can write it as
x+5,762
Since the lowest point is 9 feet below sea level, we can write this expression:
x-9
The difference is the result of subtraction. Therefore, we can find the expression that represents the difference between the elevations by subtracting x+5,762 and x-9:
(x+5,762)-(x-9)
= x+5762-x+9
= 5762+9
=5771 feet
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A quadrilateral with one right angle must be a rectangle
Answer:
false
Step-by-step explanation:
Question 3 of 10
A triangle has two sides of lengths 6 and 9. What value could the length of
the third side be? Check all that apply.
A. 10
B. 12
C. 4
D. 15
E. 7
F. 2
SUBIT
The third side of the triangle have to greater than the difference of the two provided sides.
A triangle is polygon with 3 edges and 3 vertices.
x > (9-6) so x > 3x < (9+6) so x < 15So possible answers could be:
A. 10B. 12C. 4E. 7