Answer:
117600
Step-by-step explanation:
50 x 49 x 48 = 117,600 ways
You have 50 possible for 1st, 49 for 2nd, 48 for 3rd
or
Permutations 50P3 = 117,600
There are total 59280 ways that can the runners finish first, second and third in a race.
What is permutation?
A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.
Formula for permutation[tex]nP_{r} =\frac{n!}{(n-r)!}[/tex]
Where,
[tex]nP_{r}[/tex] is permutation.
n is total number of objects.
r is number of objects selected.
According to the given question
Total number of runners, n = 40
Total number of runners to be selected for first, second and third position is 3 i.e. r = 3
Therefore,
The number of ways can the runners finish the first, second and third is given by
[tex]40P_{3} = \frac{40!}{((40-3)!} =(40)(39)(38)=59280[/tex]
Hence, there are total 59280 ways that can the runners finish first, second and third in a race.
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WILL GIVE BRAINLEST!!!
Answer:
18 12
6 22
Step-by-step explanation:
if u understand my handwriting lol
Factorise the following expression:
[tex] {a}^{2} + 10a + 24[/tex]
Step-by-step explanation:
[tex]a^{2} + 10a + 24[/tex]
= [tex]a^{2}[/tex] + 6a + 4a + 24
= a(a + 6) + 4(a + 6)
= (a + 6)(a + 4)
Answer:
solution:
[tex] {a}^{2} + 10a + 24[/tex]
a²+6a+4a+24
a(a+6)+4(a+6)
(a+6)(a+4) is your answer
Someone please please help me with this!!!
Answer:
[tex]4x {}^{2} - 36 \\ = (2x + 6)(2x - 6) \\ hence \: option \: b \: is \: correct[/tex]
Can Someone Help Me. ? Please
Answer:
the first answer maybe?
Step-by-step explanation:
1. Which equation represents the line that passes through the points (1,1) and (-2,7)?
a. y=-2x + 9
b. y=-2x + 3
c. y=-1/2x + 8
d. y=-1/2x + 6
Answer:
B
Step-by-step explanation:
find slope which is -2 then plug into equation y=mx+b to find constant of 3
Write two integers whose sum is 6 and difference is also 6.
Answer:
6,0
Step-by-step explanation:
QUESTION 1
1.1
The sequence 1 ; 5 ; 11 ; 19 ; .......is a quadratic sequence.
1.1.1 Determine an expression for the nth term of the sequence.
(4)
(4)
1.1.2 Which term of the sequence is 2 549?
1.2
The following sequence of numbers is given: -2;-3; -6;-11;
(4)
1.2.1 Determine an expression for the nth term of the sequence.
1.2.2 Explain why the sequence of numbers will never contain a positive term.
(1)
[13]
GESTION 2
The nth terms of sequence 1 ; 5 ; 11 ; 19 is n² + n + -1 and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3 .
What is quadratic sequence?The differences (referred to as first differences) between every two successive terms are the same, then it is called an arithmetic sequence (which is also known as a linear sequence). But if the first differences are NOT same, and instead, the second differences are the same, then the sequence is known as a quadratic sequence.
According to the question
The sequence 1 , 5 , 11 , 19
First difference : 4 6 8
Second difference: 2 2
1.1.1>
Now, expression for the nth term of the sequence.
Quadratic equation
ax² + bx + c
at n= 1
a + b + c = 1 -----------------(1)
At n = 2
4a + 2b + c = 5 ------------------(2)
At n = 3
9a + 3b + c = 11 -------------------(3)
solving equation
Subtracting equation (3) from (2)
9a + 3b + c = 11
-4a - 2b - c = -5
5a + b = 6 ----------------------(4)
Subtracting equation (2) from (1)
4a + 2b + c = 5
-a - b - c = -1
3a + b = 4 ---------------------------- (5)
Subtracting equation (5) from (4)
5a + b = 6
-3a - b = -4
2a = 2
a = 1
Putting value in equation (5)
3a + b = 4
3*1 + b = 4
b = 1
Substituting the value in equation (1)
a + b + c = 1
1 + 1 + c = 1
c = -1
Substituting the value in the quadratic equation
x² + x + -1
For nth term
n² + n + -1
1.1.2>
Term of the sequence is 2549
Now,
using the nth term
n² + n + -1 = 2549
n (n+1) = 2550
n (n+1) = 50 * 51
n = 50
1.2> sequence of numbers is given: -2 ,-3 ,-6 ,-11
First difference = -1 -3 -5
Second difference = -2 -2
1.2.1 >
Now , expression for the nth term of the sequence.
Quadratic equation
ax² + bx + c
at n= 1
a + b + c = -2 -----------------(1)
At n = 2
4a + 2b + c = -3 ------------------(2)
At n = 3
9a + 3b + c = -6 -------------------(3)
solving equations
Subtracting equation (3) and (2)
9a + 3b + c = -6
-4a - 2b - c = 3
5a +b = -3 ----------------(4)
Subtracting equation (2) and (1)
4a + 2b + c = -3
-a - b - c = 2
3a + b = -1 -------------------(5)
Now,
Subtracting equation (5) and (4)
5a +b = -3
-3a - b = 1
2a = -2
a = -1
Putting value of a in equation (5)
3*-1 + b = -1
b = 2
Substituting values in equation (1)
-1 + 2 + c = -2
c = -3
nth term
-n² + 2n -3
1.2.2>the sequence of numbers will never contain a positive term.
because its first term is -ve and difference between consecutive term is always -ve. or as per nth term n² is a -ve term .
Hence, the nth terms of sequence 1 ; 5 ; 11 ; 19 is n² + n + -1 and the nth terms of sequence -2;-3; -6;-11; is -n² + 2n -3 .
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I NEED HELP!!!!
SELECT ALL THAT APPLY
WHICH SHAPE(S) COULD THE FOLLOWING FORMULA BE USED FOR?
A=1/2bh
A. Trapezoid
B. Triangle
C. Rectangle
D. Square
E. Cube
Answer:
B
Step-by-step explanation:
Cand D: A= bh
A: A = (a+b)/2h
E: A= 6a^2
What is the volume of the prism? Enter your answer in the box as a mixed number in simplest form: 41 cm 22cm 6 cm cm
Answer:
V = 5412 cm^3
Step-by-step explanation:
[tex]v \: = 41 \times 22 \times 6 \\ \\ v = 5412 \: {cm}^{3} [/tex]
I hope that is useful for you :)
THIS IS DUE IN AN HOUR PLS HELP !
Answer:
27
Step-by-step explanation:
Answer:
22°
Step-by-step explanation:
<1 is a secant-secant angle (it lies outside the circle, created by two lines that cut through the circle). The measure of a secant-secant angle is half the difference of the measures of the intercepted arcs:
<1=(0.5)(98-54)
<1=(0.5)(44)
<1=22°
Find the value of x. Round to the nearest tenth
Meiling needed $5.35 to buy a ticket to a show. In her wallet, she found 2 dollar bills, 11 dimes, and 5 pennies. How much more money does Meiling need to buy the ticket?
Answer:
no she needs $2.20 more
Step-by-step explanation:
2+ 1.10+.05= $3.15
$5.35 - $3.15 = the answer
2) Determine whether 5 would be a solution to the inequality w+ 11 < 22.* 1 po Yes, it is a solution. No, it is not a solution.
Answer:
An equation or an inequality that contains at least one variable is called an open sentence. When you substitute a number for the variable in an open sentence, the resulting statement is either true or false. If the statement is true, the number is a solution to the equation or inequality.
Answer:
Yes, w=5 is a solution for this inequality.
Step-by-step explanation:
w+11<22
If w=5, this is:
5+11<22
16<22, which is true. So w=5 works as a solution
Can someone please help with this problem ASAP!!!
Answer:
Step-by-step explanation:
(1,5 ) indicates that for every 1 book they make 5 dollars so the point means that for every book they sell they make 5 dollars.
Plz help, I award brainliest!
Answer:
15 m E. B. C. D. that's why I will be there
An entry code into a building is a 5-digit number.
The number of different codes can be counted using
a. permutations
b. combinations
Answer:B
Step-by-step explanation:
On the Federal Job site it states that at a 90% confidence level that the true population mean salary of High School Mathematics teachers in Bergen County New Jersey is between $52,000 and $108,000 per year. 9) I am offered a job as a High School Mathematics teacher in Dale county Florida. The salary they offer is $48,000 a year. Can I make any conclusions based on the confidence interval
Answer:
Option c (I cannot........Florida) is the appropriate response.
Step-by-step explanation:
The given statement of query seems to be incomplete. Please find the attachment of the complete problem below.
Throughout New Jersey, the Federative Recruitment agency informs you of the average wage of mathematics in high schools.Unless you're in Florida and therefore don't know concerning Dale County Florida wages, this same work you've been given is well beyond the area whereby you know the compensation of teachers or instructors, you can't make any view.The other three given alternatives aren't related to the question. Thus option c is the correct one.
help please i need it asap! thank tou
Answer:
X = 3
Step-by-step explanation:
x= 6 x 1/2
please helppppppppppp...... 17 points
Answer:
x = 24.5
Step-by-step explanation:
the angles form a straight line, and a straight line equals to 180°
=> (5x + 8) + (3x - 24) = 180
=> 8x = 196
=> x = 24.5
Find the MEDIAN
48 28 43 87 15 65 73 82 7 33 90
Answer:
48
Step-by-step explanation:
The area of a pasture is 4200 m and the perimeter is 260 m. What are the length and width of the pasture?
Answer:
70 m and 60 m
Step-by-step explanation:
The formula for the area of a rectangle is length ⋅ width.
The area of the pasture of 4200 meters.
70 ⋅ 60 = 4200.
The formula for the perimeter of a rectangle is side + side + side + side.
The perimeter of the rectangle is 260 meters.
70 + 60 + 70 + 60 = 260.
Therefore, the length and width of this pasture are 70 meters and 60 meters.
Please help due in 2 and a half Min!
NO LINKS ALLOWED
What is the angle between any two windmills blades in the windmill
Michael has a pail that holds 5 gallons of
water. How many quarts of water does the
pail hold?
Answer:
20 quarts.
Step-by-step explanation:
Because there are 20 quarts in 5 gallons.
which expression is equivalent to 8^8x8^-5
Step-by-step explanation:
{(2)³}⁸×{(2)³}-⁵
2²⁴× 2-¹⁵
2²⁴-¹⁵. ( subtract 24 and 15)
2⁹= 512
So...
8×8×8= 512
hence
8³ Answer
Car A travels 18 miles every 20 minutes. Car B travels 13 miles every 12 minutes. Which statement best compares how far the two cars can travel in an hour?
Answer:
The answer is C) car b travels 11 more miles than car a in one hour
Step-by-step explanation:
Car A: 18/20(60)=54 mph
Car B: 13/12(60) = 65 mph
So car b travels 11 more miles than car a in one hour
PLS HELP: DETERMINE WHETHER THE PAIR OF RATIOS FORMS A PROPORTION
Answer:
No
Step-by-step explanation:
To form a proporion, both would need to be a multiple of the same thing, whcih they aren't
Daniel buys a DVD at an electronics store. The DVD costs $24.35. Daniel hands the cashier two $20 bills. How much change did Daniel get?
Answer:
$15.65
Step-by-step explanation:
$20 + $20 = $40
$40 - $24.35 = $15.65
Roseanne drew a circle with a radius of 20.2 cm. What was the approximate circumference of the circle if you use 3.14 for ?
A. 63.428 cm
B. 126.856 cm
C. 126.956 cm
D. 253.712 cm
Mackenzie thought that the basketball
team would win 16 games, but they
only won 12. What was his percent
error?
His percent error is 25% because 12 is 75% of 16. 100 - 75 = 25
Answer:
75% correct and 25%error
Step-by-step explanation:
As 12÷16×100=75%
The error =100-75=25%