Solve for r. This is for combinations and permutations.
Answer:
○ D) A and C
Step-by-step explanation:
[tex]\displaystyle \frac{n!}{r![-r + n]!} = {}_nC_r[/tex]
All you need to do is plug each choice into the formula:
[tex]\displaystyle \frac{10!}{2![-2 + 10]!} \Longrightarrow \frac{[2][3][4][5][6][7][8][9][10]}{2[-2 + 10]!} \longrightarrow \frac{[2][3][4][5][6][7][8][9][10]}{2[(2)(3)(4)(5)(6)(7)(8)]} \\ \\ \boxed{45} = \frac{90}{2}[/tex]
OR
[tex]\displaystyle \frac{10!}{8![-8 + 10]!} \Longrightarrow \frac{[2][3][4][5][6][7][8][9][10]}{[(2)(3)(4)(5)(6)(7)(8)][-8 + 10]!} \\ \\ \boxed{45} = \frac{90}{2}[/tex]
So, from what you see, both values of [tex]\displaystyle r[/tex] work. In fact, when using the formula pertaining to combinations, you will see that each result has a “repetitive pattern”. This is something you must look out for when using this formula.
I am joyous to assist you at any time.
Justin is considering two websites for downloading music. The costs are detailed here.
Website 1: a yearly fee of $30 and $1.50 for each download
Website 2: $2 for each download
What is a system of equations to represent the costs for one year?
Express your equations in the form of y=mx+b where x is the number of downloads for the year and y is the total cost for the year.
Enter your equations in the boxes.
Website 1:
Website 2:
Answer:
website 2 hope this helps
33-(2c + 4) = 2(c + 7) +C
Answer:
c=3
Step-by-step explanation:
Colton is about to ride a straight water slide. The launching platform is at the top of a tower that is 8 meters tall. The splash pool at the end of the slide is 15 meters from the base of the tower. How long is the water slide itself? Show your work.
Answer:
The length of the water slide itself is 17 meters
Step-by-step explanation:
Here, we want to calculate the length of the water slide
from the description given in the question;
we have a right angled triangle where the height of the tower, the distance from the base of the tower and the length of the slide itself represents the sides of the triangle
From the description given in the question, the water slide length represents the slope of the right triangle formed
thus, mathematically by using Pythagoras’ theorem;
The square of the hypotenuse equals the sum of the squares of the two other sides
Let us call the length of the water slide y
y^2 = 8^2 + 15^2
y^2 = 64 + 225
y^2 = 289
y = √289
y = 17 meters
Which number is divisible by both 5 and 6?
A. 132,359
B. 142,645
C. 164,780
D. 193,560
Answer:
D
Step-by-step explanation:
HELP ASAPP PLEASE OR ELSE I WILL FAIL CLASS
Work out the equation of the line which has a gradient of 3 and
passes through the point (-2, 4).
Answer:
y=3x+10
Step-by-step explanation:
We can use standard form to write the equation of this line.
y=mx+b
where m=the slope (or gradient) of the line
and where b= the y-intercept
now to solve...
we know the slope (gradient) or m=3
so we can put this in the equation.
y=3x+b
now we must solve for b.
in order to this we can subsitute the coordinate (-2,4) into x and y since
a coordinates values/variable representation is (x,y) -> (-2,4)
So subsituting the coordinate in...
y=3x+b
4=3(-2)+b
simplify.
4=-6+b
b=10
This means the y-intercept=10
so...
y=3x+10
is the equation of the line.
35 = 2b + 5b pls help
Step-by-step explanation:
2b+5b=7b
35=7b
35/7=5
b=5
Answer:
b=5
Step-by-step explanation:
2b+5b=35
7b=35
b=35/7
b=5
Josie took a long multiple-choice, end-of-year vocabulary test. The ratio of the number of problems Josie got incorrect to the number of problems she got correct is : . If Josie missed questions, how many did she get correct? *---------- If josie missed 20 questions how many did she get correct--- PLEASE HELP ME
Answer:
36 correct answers
Step-by-step explanation:
Given that,
The ratio of the number of problems Josie got incorrect to the number of problems she got correct is 2:9.
Josie missed 8 questions
Let incorrect answers be 2x and that of correct answers be 9x.
ATQ,
2x = 8
x = 4
Correct answers = 9x
= 9(4)
= 36
Hence, she will get 36 correct answers.
find The equation pleaseeeeee
Answer:
y=2x+4
Step-by-step explanation:
the slop is 2 hense 2x, and the y intercept is 4
mark got 14 problems wrong on the test. his score was 72% correct.how many problems were on the test
9514 1404 393
Answer:
50 problems
Step-by-step explanation:
The percentage wrong was 100% -72% = 28%. Then the number n of problems on the test was ...
14 = 0.28·n
n = 14/0.28 = 50
There were 50 problems on the test.
Jiangsu divided 751.6 by 10 to the second power and obtained a quotient of 0.7516. Yessenia thinks the quotient. Who has the reason? Explain your answer.
Answer:
Yessenia is correct.
Step-by-step explanation:
Supose Yessenia thinks the quotient is 7.516, then Yessenia is correct.
The reason why Yessenia is correct is that, if we interpret the question mathematically, we have:
[tex]= \dfrac{751.6}{10^2}[/tex]
[tex]= \dfrac{751.6}{100}[/tex]
From above the decimal point will shift to the left twice since we are dividing 751.6 by 100, which is:
= 7.516 and not 0.7516
A paper cup is tossed 50 times. It lands right side up 11 times, upside down 14 times, and on its side 25 times. What percent of time did it land upside down?
Answer
28 percent
Step-by-step explanation:
divide 14/50
Can someone please help? I need by 2:45 PM
Answer:
dilated coordinates are A(-18,-3) and B(-6,-12)
Step-by-step explanation:
distance of new segment is 15 units
distance formula = [tex]\sqrt){y-y_{1})^{2} +( x - x_{1})^{2} }[/tex]
Tell whether the relation is a function. {(-5, -3), (-1, 3), (4, 3), (8, 8)}
Given:
The relation is {(-5, -3), (-1, 3), (4,3), (8, 8)}.
To find:
Whether the given relation is a function or not.
Solution:
A relation is called a function, if there exist a unique output for each input.
We have, a relation given as
{(-5, -3), (-1, 3), (4,3), (8, 8)}
Here, all x-values are different. So, each x-value has a unique y-value.
Thus, there exist a unique output for each input.
Therefore, the given relation is a function.
Solve the following systems of equations for x:
2x + 3y = 5
4x – 3y = 1
Answer:
b
Step-by-step explanation:
2x+3y=5 rearrange 2x=5-3y times all by 2 4x=10-6y
4x-3y=1 4x=1+3y
1+3y=10-6y 6y+3y=10-1 9y=9 y=1
4x-3(1)=1 4x=1+3 4x=4 x=1
Answer:
B
Step-by-step explanation:
2x+3y=5
(2×1)+(3×1)==5
2+3=5
(4×1)-(3×1)=1
4-3=1
Create a sample division problem with a 2-digit divisor and give an incorrect answer, showing the steps taken to get the incorrect answer.
Answer:
Incorrect Answer Below
Step-by-step explanation:
Problem: We have a total of 28 candies that need to be divided evenly between 4 students.
(Incorrect) Solution: In order to solve this problem we can seperate the total number of candies into single digits and then divide each digit by 4 like so...
2 / 4 = 0.5
8 / 4 = 2
Now that we have the answer of both of these divisions we can simply add these values together to get the number of candies each student will get
0.5 + 2 = 2.5 candies
Question 8 (4 points) Find the values of x and y if NO = x + 2y, MO = 3x, PQ = 6x + 4, and OQ = 2y + 4.
Answer:
x = 12 and y = 16
Step-by-step explanation:
Given the following lengths;
NO = x + 2y,
MO = 3x,
PQ = 6x + 4, and
OQ = 2y + 4.
The following postulates are true;
MN = PQ
Since MO + ON = MN
MN = 3x + x+2y
MN = 4x + 2y
Recall that PQ = 6x+4
Equating both expressions;
4x + 2y= 6x+4
Collect like terms;
4x-6x + 2y = 4
-2x + 2y = 4
x - y = -4 ...... 1
Also MO = OQ
3x = 2y + 4
3x-2y= 4 ....2
from 1; x = -4 + y
Substitute into 2:
3x-2y= 4
3(-4+y)-2y = 4
-12+3y-2y = 4
-12+y = 4
y = 4 + 12
y = 16
Since x = -4+y
x = -4 + 16
x = 12
Hence x = 12 and y = 16
find the slope PLEASE HELP
Answer:
-1/4
1
-1/4
1
Step-by-step explanation:
Slope is obtained thus :
(y2 - y1) / (x2 - x1)
Slope ST :
S(1, 4) ; T(5, 3) ;
x1 = 1, y1 = 4 ; x2 = 5 ; y2 = 3
Slope ST = (3 - 4) / (5 - 1) = - 1 / 4
Slope TU :
T(5, 3) ; U(3, 1)
x1 = 5, y1 = 3 ; x2 = 3 ; y2 = 1
Slope TU = (1 - 3) / (3 - 5) = - 2/ - 2 = 1
Slope UV :
U(3, 1) ; V(-1, 2)
x1 = 3, y1 = 1 ; x2 = - 1 ; y2 = 2
Slope UV = (2 - 1) / (-1 - 3) = 1 /-4 = - 1/4
Slope SV:
S(1, 4) ; V(-1, 2)
x1 = 1, y1 = 4 ; x2 = - 1, y2 = 2
Slope SV = (2 - 4) / (-1 - 1) = - 2 / - 2 = 1
Roger spent 22 minutes on his math homework and 25.08 minutes on his spelling
homework. He spent percent more time on his spelling homework.
Answer:
114%
Step-by-step explanation:
okay, so we know he spent 22 minutes on math and 25.08 on spelling.
m=22
s=25.08
so to find a percent, you have to divide s/m
s/m= 25.08/22
s/m= 1.14
because this is a decimal, we have to convert it to a percent
114%
to check the answer, multiply 22 times 114%
the answer is 25.08, so we know we got the right answer.
PLS HELP MEEE ILLL GIVE BRAINLEST
Answer:40
Step-by-step explanation:
Smaller than 60 and 80.
Answer:
B
Step-by-step explanation:
Because I did this test before and I got this right :)
Aisha is a cyclist. She rode 3 ¾ miles in ⅓ hours. A. How fast was she going in miles per hour?
Answer:
11 1/4 miles per hour
Step-by-step explanation:
Put the mixed number in improper form to make it easier. You get 15/4 miles in 1/3 hours. You want the miles for 1 hour. So you multiply 15/4 miles by 3 to get 45/4 miles, or 11 1/4 miles per hour
The relationship between the number of
$4 lunches you buy with a $100 school
lunch card and the money remaining on
the card
Which ordered pair is a solution of the equation y+1=3(x-4)
Step-by-step explanation:
When x = 4 and y = -1,
(-1) + 1 = 3(4 - 4) = 0.
Hence (4, -1) is an ordered pair.
When x = 5 and y = 2,
(2) + 1 = 3(5 - 4) = 3.
Hence (5, 2) is an ordered pair.
Therefore the answer is C.
NEED ANSWERS ASAP!!( no need for explanation just final answers)
Answer
x, y
0, -4
1, -1
2, 2
3, 5
please click heart to give thanks :)
Answer:
Answer
x, y
0, -4
1, -1
2, 2
3, 5
Step-by-step explanation:
there's the math
PLz help I need help
Answer:
Missing statements:
R2. Definition of corresponding anglesR3. Corresponding angles postulateR5. Supplement PostulateS7. m∠2 + m∠3 = m∠1 + m∠3S8. m∠1 + m∠3 = 180°Which quadrilaterals always have congruent diagonals? Select all that apply.
[tex]\huge {\colorbox {black}{\color{magenta}{✿Aиѕωє༉}}} [/tex]
RectanglesSquares[tex]\huge\sf\underline{\underline{\red{❥︎ Thanks}}}[/tex]
Which quadrilaterals always have congruent diagonals?
[tex]\hookrightarrow[/tex] [tex]\bold{rectangle }[/tex]
[tex]\rightsquigarrow[/tex] [tex]\bold{ square }[/tex]
On a coordinate plane, 2 lines with negative slopes are shown. Line M N goes through points (negative 2, 0) and (negative 6, 8). Line M prime N prime goes through (6, negative 4) and (2, 4). Use the graph of the lines to determine if the two lines are parallel. Line MN was translated down units and right
units to create line M'N'.
The slope of Line M N .
The slope of Line M prime N prime .
Answer:
Line MN was translated down
✔ 4
units and right
✔ 8
units to create line M'N'.
The slope of Line M N
✔ −2
. The slope of Line M prime N prime
✔ −2
.
Step-by-step explanation:
On edge 2021 Hope this helps :)
Answer: is in picture
Step-by-step explanation:
Is a function or not a function?
Answer:
yes this is
Step-by-step explanation:
Find the slope between:
(-1,-5)
(0, -1)
Answer: sry dunno
Step-by-step explanation: