Answer:
Probability of selecting two songs from each category
= (22C2)*(14C2)*(7C2)*6!
Step-by-step explanation:
The total songs in the playlist will be 6
Two songs from each playlist
Number of ways of selecting playlist
= N(select 2 from each category and then arrange the selected 6)
Probability of selecting two songs from each category
= (22C2)*(14C2)*(7C2)*6!
How many divisors of 7! = 7:6:5.4.3.2.1 are divisible by 7 ? (Example: 14 has
two divisors, 7 and 14, that are divisible by 7.)
Answer:
30
Step-by-step explanation:
7! = 7*(2*3)*5*(2*2)*3*2*1 = [tex]7*5*3^{2}*2^{3}[/tex]
Ignoring the 7, there are 24 factors of this number as you will multily each of the factors of 6! by 7 to get each of the factors of 7! divisble by 7. But since you ignored the 7, you need to bring back the possible values of 7*6, 7*5, 7*4, 7*3, 7*2, 7*1.
24 + 6 = 30 divisors
There are 60 divisors of 7!.
What is factorial?The factorial function can be used to determine the ordered set of numbers or how many different ways things can be arranged. Daniel Bernoulli discovered the factorial function's well-known interpolating function. Numerous mathematical concepts, including probability, permutations and combinations, sequences and series, and so on, make use of the factorial idea.
Given 7!
We must first write 7! as the product of prime numbers, as shown below. The highest power of a prime number is typically divided by N! is given by [tex]s_{p}[/tex](N!)=N/p + N/p² + N/p³ +.......
Since you want to count the number of terms that are multiples of p and contribute one p to N!, the first term appears. However, when you have multiples of p², you are not simply multiplying one p; rather, you are multiplying two primes p to the product. Therefore, you now count and add the number of multiples of p² that are less than N.
let for p =2
[tex]s_{p}[/tex](7!) = 7/2 + 7/4 + 7/8 + ......... = 3 +1 = 4
we have to repeat this process for 3,5,7
we get 7!=2⁴ x 3² x5¹ x7¹
Now, the number of divisors of 7 is equivalent to number of ways of selecting zero or more objects from the group of identical objects
=(4 +1)(2 + 1)(1 + 1)(1 + 1) = 60 includes 1 and 7.
Hence the divisors of 7! is 60.
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Carpenters earn an average of $1120 less
per month than designers at a furniture
factory in Smithville. The factory employs
3 designers and 15 carpenters. Let x
represent the average monthly pay of a
designer
Which of the following functions correctly
shows the relationship between the
monthly payroll (P) and the wages of these
employees?
(1) P= 3x + 15(x - 1120)
(2) P= 3(x - 1120) + 15x
(3) P = 3(x - 1120) + 15(x -
1120)
(4) P= 3 + x + 15 + (x - 1120)
(5) P = 3(x)(15)(x - 1120)
Which polygon(s) below are similar (not congruent) to polygon A? Mark the similar polygon(s) with true
Hello guysssssss asap
Answer:
-9, -8, -4 , 6 then 9..
Step-by-step explanation:
Your welcome
When students are admitted to a particular university, they are given a six-digit identification number (NNNNNN). If the first digit must be either a 0 or 1, how many identification numbers are possible?
Answer:
200,000 identification numbers are possible
Step-by-step explanation:
For the first digit, there are only two possible outcomes, 0 or 1.
For the next five digits, there are 10 possible outcomes(0,1,2,3,4,5,6,7,8,9).
How many identification numbers are possible?
[tex]2 \times 10^5 = 200000[/tex]
200,000 identification numbers are possible
Learning Task 3: In your answer sheet, write the letter of the correct answe
1. Which is a polynomial function?
Plx) = 2x3 + 32 - 4x + 4
c. c. G(x) = 2x-3 +5
B. H2) = 4x1/2 - 3x 4
D. F lrl = 2x3-5x + 3
3x2
Answer:
a.) May or may not a polynomial function ( depends on c)
b.) Not a polynomial function.
c.) Not a polynomial function.
d.) It is a polynomial function.
Step-by-step explanation:
A polynomial function is of the form - [tex]a_{n}x^{n} + a_{n-1} x^{n-1} + a_{n-2} x^{n-2} + .....+ a_{1}x + a_{0}[/tex]
where n is positive integer and n[tex]\neq[/tex] 0
a.)
P(x) = 2x³ + 32 - 4x + 4c
It may or may not a polynomial function because we did not know about the constant c.
b.)
H(x) = 4[tex]x^{\frac{1}{2} }[/tex] - 3x⁴
It is not a polynomial function because [tex]\frac{1}{2}[/tex] is not integer.
c.)
G(x) = 2[tex]x^{-3}[/tex] + 5
It is not a polynomial function because -5 is not a positive integer.
d.)
F(x) = 2x³ - 5x + 33x²
It is a polynomial function.
The standard form of a polynomial is expressed as;
[tex]p(x)=a_nx^n+x_{n-1}x^{n-1}+x_{n-2}x^{n-2}+...[/tex]
The leading power of a polynomial must be greater than 2 and must be a positive integer.
a) For the polynomial [tex]P(x)=2x^3+3x^2-4x+4c[/tex]
This is a polynomial since the leading degree of the polynomial is greater than 2 and a positive integer.
b) For the function [tex]G(x)=2x^{-3}+5[/tex]
This is not a polynomial because the leading degree of the polynomial is a negative integer
c) For the function [tex]H(x) =4x^{\frac{1}{2} }-3x^4[/tex]
This is not a polynomial because the leading degree of the polynomial is a fraction.
d) For the polynomial [tex]P(x)=2x^3-5x+3+3x^2[/tex]
This is a polynomial since the leading degree of the polynomial is greater than 2 and a positive integer.
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Last season Sarah was up to bat 48 times,and got 16 hits.what is the simplified ratio of Sara's hits to Sara's hits to Sara's at-bats
Answer:
48:16 ---> 3:1
Step-by-step explanation:
48 and 16 can both be divided by 4 which makes it 12:4 but that can still be reduced which would make it 3:1
The store is selling lemons at $0.46 each. Each lemon yields about 2 tablespoons ofjuice. How much
will it cost to buy enough lemons to make three 9-inch lemon pies, each requiring half a cup of
lemon juice?
Answer:
12 lemons, $5.52
Step-by-step explanation:
Rectangle ABCD has m∠BAC=4x+5and m∠ACD=5x−4. Find m∠CAD m∠CAD =
Answer:
m∠CAD = 49degrees
Step-by-step explanation:
For a rectangle ABCD if m∠BAC=4x+5and m∠ACD=5x−4, then;
m∠BAC = m∠ACD (alternate angles)
4x+5 = 5x - 4
4x-5x = -4-5
-x = -9
x = 9
Also
m∠BAC+m∠CAD = 90
4x+5+m∠CAD = 90
4(9)+5+m∠CAD = 90
36+5+m∠CAD = 90
41+m∠CAD = 90
m∠CAD = 90-41
m∠CAD = 49degrees
Bryant had $450 in the bank yesterday. Then, Bryant bought a fancy new rug for $620, but didn't realize that he overdrew from his bank. His account balance was negative now and he was in debt! What is the absolute value of his new account balance?
sam's mother is twice as old as sam. in 12 years sam will be as old as his mother was 12 years ago, how old is sam and his mother now PLZ HELP NOW
Answer:
Sam will be 24 and his mom U can figure that out
Step-by-step explanation:
Math
Answer:
24
Step-by-step explanation:
`12
Maths in science
A student sampled a local playing field to estimate the total number of dandelion plants growing there
Answer:
Step-by-step explanation:
answer is that i dont know
Subtract. −5−(−9)−3
−17
−7
1
I don't know.
Answer:
-87
Step-by-step explanation:
Answer:
-87
Step-by-step explanation:
Need help with this question thanks :)
Answer:
Omar could invite 19 friends.
Step-by-step explanation:
the equation for this word problem would be
5x+30=125
subract 30 from both sides
5x=95
divide both sides by 5
x=19
Answer:
(125-30) divided by 5. Your answer is 19.
Step-by-step explanation:
subtract 30 from 125 and your left with 95. Divide 95 by 5 and you get 19.
round 256,733 to ten thousands
Answer:
260,000
Step-by-step explanation:
Answer:256.73 hope this helps!
Step-by-step explanation:
Jim invested $750 in a 3-year CD that earns 4.2% annual interest that is compounded monthly. How much will the CD be
worth at the end of the 3-year term? Include the dollar sign in your answer, and round to the nearest cent.
Provide your answer below:
Answer:
4.2% of 750 = 31.5
31.5 * 3 = 94.5
~Hope this helps~
The worth of CD after 3 years will be $853.07 at the given rate of interest.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
Given that,
Principle amount P = $750
Rate of interest R = 4.3%
Time period T = 3 years
Number of times interest compounded annually (n) = 12
The compound interest formula is given by;
A = P[1 + R/n]^nT
A = 750[ 1 + 4.3/1200]¹²⁽³⁾
A = $853.07
Hence "The worth of CD after 3 years will be $853.07 at the given rate of interest".
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Please help me answer this
whats the question? what does it want. ill edit this when you give me the question.
Step-by-step explanation:
40 employees in an office wear eyeglasses. 22 have single-vision correction, and 18 wear bifocals. If two employees are selected at random from this group, what is the probability that both wear bifocals? What is the probability that both have single-vision correction?
Round your answers to four decimal places
Step-by-step explanation:
The number of way to select 2 employees from 40 is 40C2.
The number of way to select 2 employees from 22 is 22C2.
So the probability of the two employees having single-vision correction is just the number of ways to select the 22 employees (22C2) divided by the total number of ways to select 2 employees (40C2).
22C2 / 40C2 = 77/260
We can use the same technique for the bifocal employees.
18C2 / 40C2 = 51/260
Please round this number to the second decimal:
113.097335529233
Answer:
113.1
Step-by-step explanation:
Answer:
Step-by-step explanation:
The 7 in the hundreths place would bring the 9 up. So your answer would then be 113.10
Ivan and Tanya share £150 in the ratio 4:1
Work out how much more Ivan gets compared to Tanya.
Answer:
Step-by-step explanation:
The £150 must be split 5 ways with Ivan getting 4 of those splits.
£150/5
----------------
£30
Ivan gets £30 times 4 (remember, Ivan gets a four split).
Tanya gets £30.
Ivan gets £120.
Tanya gets £30.
£120
- £30
----------------
£90
Ivan gets £90 more than Tanya.
Hope this helped!
Find the area of the circle. Use 3.14 for pi.
Question 1 options:
113.04 in2
56.52 in2
256.34 in2
1017.36 in2
Answer:
The answer is 254.34 in².
Step-by-step explanation:
Given that the diameter is 2 times the radius. So the radius will be 9 in. Next, you have to find the area of circle, A = π × r² :
A = π × r²
Let π = 3.14, r = 9,
A = 3.14 × 9²
A = 254.34 in²
Laura invests $2,000 in a bank account which pays a compound interest rate of 6.4%. To the nearest cent, what amount is in the account after 5 years and what amount of interest earned over 10 years?
Answer:
9,000
Step-by-step explanation:
it you count with time by ×it would be 9,000 because just add that up with money
Please help
look at picture
supplementary angles
Answer:
x=56
Step-by-step explanation:
(2x-3)degrees+71 degrees=180 degrees because they are supplementary angles
This simplifies to 2x+68=180 because -3+71 is 68.
2x+68=180
2x=180-68
2x=112
x=112/2
x=56
Graph the line 3y+x=3
What is the factors for x squared plus 5x - 6
Answer:
(x+6)(x-1)
Step-by-step explanation:
x^2+6x-x-6
x(x+6)-(x+6)
(x+6)(x-1)
Sarah is training for a bike race. she rides her bike 5 3/4 miles in 1/3 hour. what is Sarah's rate in miles per hour? Express your answer in a mixed number. show your work.
Answer:
17 1/4 miles per hour
Step-by-step explanation:
First let's convert the mixed number to a fraction so it is easier to work with:
5 3/4 = (5*4 + 3)/4 = 23/4 miles.
Because she travelled it in a third of an hour, she could do it 3 times in 1 hour.
Because of this to get speed we divide the distance by the time taken.
23/4 divided by 1/3 is the same as saying 23/4 times 3:
(3*23)/4 = 69/4 = 17 1/4 miles per hour
Answer:
17 1/4
Step-by-step explanation:
In which function table do all of the points (x, y) lie on the line that has a slope of 3 and a y-intercept of 2? A.-1, -1 . 2,8 . 5, 17 . 8, 26.
B. -1 , -1 . 2,7 . 5,17 . 8 , 26
C. -1 , -1 . 2-8 . 5,18 . 8,26
D . -1 , -1 . 2,8 . 5,17 . 8, 25
Answer:
D. -1, -1. 2,8. 5,17. 8, 25
Step-by-step explanation:
esa es
Jayne has 860 grams of caster sugar.
How much more caster sugar will she need to make 4 jars of jam?
A scientist was in a submarine below sea level, studying ocean life. Over the next ten minutes, she went up 22.1 feet. How many feet had she been below sea level, if she was 2.5 feet below sea level after she went up?
Answer:
24.6
Step-by-step explanation:
it's 24.6 because if you add 2.5 plus 22.1 equals 24.6
An antique store increases all of its prices by $40\%$, and then announces a $25\%$-off-everything sale. What percent of the original prices (before the increase) are the new prices? show work plz! It's not 5% by the way
Answer:
105%
Step-by-step explanation:
We'll analyse the question one step at a time
Let the original price be x.
Let y be the 40% increase
[tex]y =x + 40\% *x[/tex]
Express as decimal
[tex]y =x + 0.40 x[/tex]
[tex]y =1.40x[/tex]
Let z be the 25% off sale
[tex]z = (1 - 25\%) * y[/tex]
Express as decimal
[tex]z = (1 - 0.25) * y[/tex]
[tex]z = (0.75) * y[/tex]
[tex]z = 0.75y[/tex]
Substitute 1.40s for y
[tex]z = 0.75*1.40x[/tex]
[tex]z = 1.05x[/tex]
Express 1.05 as a fraction
[tex]z = 105\% * x[/tex]
The percentage is 105%