Answers
Answer:
56
Step-by-step explanation:
Here, n = 8, r = 3
[tex] \huge \orange{ \because \: ^nC_r = \frac{n!}{r!(n - r)!} } \\ \\ \huge \therefore \: ^8C_3 = \frac{8!}{3!(8 - 3)!} \\ \\ \huge \therefore \: ^8C_3 = \frac{8 \times 7 \times 6 \times 5!}{3 \times 2 \times 1 \times 5!} \\ \\ \huge \red{ \boxed{\therefore \:^8C_3 = \purple{56}}}[/tex]
Related Questions
1. If an equation contains decimals, what is the first step
you can perform to eliminate the decimals?
Answers
Answer:
Multiply by a power of 10
Step-by-step explanation:
By multiplying a power of ten, it will make the decimals whole numbers.
For example: 0.75*10=75
0.0075*10000
To eliminate the decimals, the first step we can perform is to multiply the decimal by a power of 10. If there are n numbers after the decimal point, then we will multiply the decimal by 10ⁿ.
What is decimal?In Algebra, a decimal is a type of number with a whole integer and a fractional part separated by a decimal point. The dot that appears between the entire number and the fractions part is the decimal point. 24.589, for example, is a decimal number. The whole number part is 24 and the fractional part is 589. The decimal point is ".".
How to solve this problem?If an equation contains decimals, then we have to check how many numbers are there in the fractions section. If there are 3 numbers like 24.589, to eliminate decimals we have to multiply 24.589 by 10³ to get a whole number [ Since 24.589×10³ = (24589/1000)× 1000 = 24589].
Therefore, to eliminate the decimals, the first step we can perform is to multiply the decimal by a power of 10. If there are n numbers after the decimal point, then we will multiply the decimal by 10ⁿ.
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5+1/5x=-1 plz find the answer
Answers
Answer:
X= -6/5
Step-by-step explanation:
Multiply to remove the variable from the denominator.
Hope this helps.
Answer:
Step-by-step explanation:
x/5 + 5 = -1
x/5 = -6
x= -30
Austin started with 26 video games and sold x video games. Caleb started with 40 video games and sold three times as many video games as Austin did. How many video games did Austin sell, given they had the same number of video games left?
Answers
Answer:
The answer is 7 video games
Step-by-step explanation:
The number of video games Austin sold will be 4.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Austin started with 26 video games and sold x video games. Caleb started with 40 video games and sold three times as many video games as Austin did.
Let x be the number of video games sold and y be the number of video games left. Then the equations will be
y = 26 - x
y = 40 - 3x
From equations 1 and 2, then we have
26 - x = 40 - 3x
3x - x = 40 - 26
2x = 14
x = 4
The number of video games Austin sold will be 4.
More about the solution of the equation link is given below.
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Suppose f(x)=4x-2 and g(x)=-2x+1. Find the value of f(5)/g(-3)
Answers
Answer:
17/7 (2 3/7 or 2. 428571...)
Step-by-step explanation:
f(x) = 4x-2
Find f(5)
f(5) = 4(5)-3f(5) = 20-3f(5) = 17g(x) = -2x+1
Find g(-3)
g(-3) = -2(-3)+1g(-3) = 6+1g(-3) = 7Find f(5)/g(-3)
f(5)/g(-3)17/7 (2 3/7 or 2. 428571...)The value of f(5)/g(-3) will be 18/7.
What is substitution method?To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The value of the function are,
⇒ f (x) = 4x - 2 and
⇒ g(x) = -2x + 1
Now,
Since, The value of the function are,
⇒ f (x) = 4x - 2 and
⇒ g(x) = -2x + 1
Hence, We get;
⇒ f (5) = 4 × 5 - 2
= 20 - 2
= 18
And, g (- 3) = - 2 × - 3 + 1
⇒ g (-3) = 6 + 1
= 7
Thus, The value of f(5)/g(-3) = 18/7
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The number 480 was changed to 4.8 times a
Answers
Answer:
100
Step-by-step explanation:
480/4.8=100
4.8x100=480
The diagram is not drawn to scale
14.
2x-9
Find the value of x.
Answers
Answer:Step-by-step explanation:
10
The value of the x is 8 if after using the property of a similar triangle.
What is the similarity law for triangles?
It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
We have a triangle shown in the picture.
By using the property of a similar triangle:
2/1 = 14/(2x-9)
2x - 9 = 7
2x = 7 + 9
2x = 16
x = 8
Thus, the value of the x is 8 if after using the property of a similar triangle.
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Caleb needs at least 30 cups for the party he already has 12 cups at least show many more cups does he need
A expression
B equation
C inequality
Answers
This is a Precal question.
Express the given geometric statement about numbers on the number line algebraically, using absolute values.
x is more than 2 units from c
Answers
Answer:
X= 4c The absolute value you can find witht the equation |4c|
resolve in factor x³-16x
Answers
Answer:
x (x + 4) (x - 4)
Find the midpoint of the segment with the given endpoints
(- 4.7) and (-1,-1)
The midpoint is?
Answers
——— , ——-
2 2
So -4= X1
7= Y1
-1= X2
-1= Y2
Plug those in
-4+-1 7+-1
———, ———-
2 2
Simplified
-5
( —, 3)
2
Mimi and Rita both plan to run for a spot on the school
board in their city. They must each collect a certain
number of signatures to get their name on the ballot. So
far, Mimi has 30 signatures, but Rita just started and
doesn't have any yet. Mimi is collecting signatures at an
average rate of 8 per hour, while Rita can get 14
signatures every hour. Assuming that their rate of
collection stays the same, eventually the two will have
collected the same number of signatures. How many
signatures will they both have?
Create two tables showing hours and signatures. Write,
graph, and solve a system of equations for this situation.
Explain what your solution means for the situation.
Answers
Answer:
The equal number of signatures Mimi and Rita eventually collects are 70 signatures
Step-by-step explanation:
1) The initial number of signatures Mimi has = 30 Signatures
The average rate at which Mimi can collect signatures = 8 signatures per hour
The average rate at which Rita can collect signatures = 14 signatures per hour
The table of values showing the number of signatures Mimi and Rita can have at a given hour is presented as follows;
For Mimi, we have;
Hour [tex]{}[/tex] Number of Signatures
0 [tex]{}[/tex] 30
1 [tex]{}[/tex] 38
2 [tex]{}[/tex] 46
3 [tex]{}[/tex] 54
4 [tex]{}[/tex] 62
5 [tex]{}[/tex] 70
For Rita, we have;
Hour [tex]{}[/tex] Number of Signatures
0 [tex]{}[/tex] 0
1 [tex]{}[/tex] 14
2 [tex]{}[/tex] 28
3 [tex]{}[/tex] 42
4 [tex]{}[/tex] 56
5 [tex]{}[/tex] 70
2) The equation representing the number of signatures Mimi has at a given time, t, is given as follows;
The number of signatures Mimi has = 30 + 8 × t
The equation representing the number of signatures Rita has at a given time, t, is given as follows;
The number of signatures Rita has = 14 × t
3) Please find attached the required graph of the number of signatures Mimi and Rita has
4) The solution if the system of equations is given as follows;
30 + 8 × t = 14 × t
From which we have;
30 = 14 × t - 8 × t = 6 × t
t = 30/6 = 5 Hours
By substituting t = 5 hours in the above equations, the equal number of signature of signatures Mimi and Rita can have is therefore;
30 + 8 × 5 = 70 signatures = (14 × 5) signatures
The equal number of signatures Mimi and Rita eventually collects are 70 signatures
5) The meaning of the solution is that is Mimi and Rita continue collecting signatures at their respective constant rate of 8 and 14 signatures per hour, given that Mimi already has 30 signatures, they will have the same number of 70 signatures after 5 hours
What is the volume of this rectangular prism?
Answers
Answer: V≈5.21 cm³
Step-by-step explanation:
To find the volume of a rectangular prism, you multiply the length, width and height.
[tex]V=wlh[/tex]
Since we were given the length, width and height, we can directly multiply them together.
[tex]V=\frac{5}{2} *\frac{5}{3} *\frac{5}{4}[/tex] [multiply]
[tex]V=\frac{125}{24} =5.21 cm^3[/tex]
Now, we know that the volume is approximately 5.21 cm³ or 125/24 cm³.
Write an explicit formula for the n^th term a n 13, 17, 21, 25, ...
Answers
The first term in our arithmetic sequence = 13
The common difference of our arithmetic sequence = 17 - 13 = 4
The formula for finding an equation for any arithmetic sequence is a(n) = A + B(n - 1)
A = the first term
B = the common difference.
Let's plug our numbers in.
a(n) = 13 + 4(n - 1)
Let's check to make sure we're correct.
a(1) = 13 + 4(1 - 1) = 13 + 4(0) = 13 + 0 = 13
a(2) = 13 + 4(2 - 1) = 13 + 4(1) = 13 + 4 = 17
That verifies that our formula is correct.
In conclusion,
a(n) = 13 + 4(n - 1)
3. A $1,250 deposit for 10 years at a simple interest rate of 5.25%
Answers
Step-by-step explanation:
I=(pxRxt)/100
I=(1250×5.25×10)/100
I=656.25
amount to be paid is $1906.25 pls give me brainliest
3. Find the solution set for this inequality:
-4(3x - 5) < 2(3x + 4)
Answers
Answer:
Step-by-step explanation:
x>2/3
Suppose triangle ABC is a right triangle. Side AB is 3 feet and side BC is 4 feet. Find the length of the hypotenuse, AC. Remember Pythagorean Theorem.
A. 25 feet
B. 5 feet
C. 16 feet
D. 4 feet
E. 9 feet
F. 3 feet
Answers
Answer:
5
Step-by-step explanation:
3 squared + 4 squared = c squared
3 squared= 9 4 squared= 16
9+16=c squared
25=c squared
5= c
.what is .02 divied by .30 please dont show the calculator answer
Answers
Answer:
1/15
Step-by-step explanation:
.02 = [tex]\frac{2}{100}[/tex] and .30 = [tex]\frac{3}{10}[/tex]
cross multiply
[tex]\frac{2}{100}[/tex] ÷ [tex]\frac{3}{10}[/tex] = 2(10) ÷ 300
[tex]\frac{20}{300} = \frac{1}{15}[/tex]
Fraction answer: 1/15
Decimal answer: 0.066666666666667
Help me please!!!!!!!!!!!!!!!
Answers
Answer:
The answer is D
Step-by-step explanation:
There are 6 black circles and 2 red circles which could be written as 6 + -2, the positive sign from will turn into a negative bc if the -2, so then it would be 6-2=4
enter in the number below that will make the right expression equivalent to the left expression:
1. 7+2+n=____+n
2. (3+7)+6=____+6
3. 2+(3+7)=2+___
4. 10+2+5=____
5. 7+(-4)+3=____+3
6. -11+8+n=____+n
Answers
2.10+6
3.2+10
4.17
5.3+3
6.-3+n
6- X=-12
Will mark brainlest if right!
Answers
Answer:
18
Step-by-step explanation:
6-18=-12
\(` u`)/
Answer:
X-18
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 6-x-(-12)=0
Solve : -x+18 = 0
Subtract 18 from both sides of the equation : -x=-18
Multiply both sides of the equation by (-1) : x = 18
Write an absolute value equation that has the given solution.
- 2 and 2
Answers
Answer:
|4| - 2 = 2
|4| - 6 = -2
Step-by-step explanation:
Plz help me I need help
Answers
Answer:
c has greatest ratio output with 0.6 compared to other
Step-by-step explanation:
How do you know if a whole number is a perfect square?
A. A whole number is a perfect square if it is divisible by 4.
B. A whole number is a perfect square if its square root is an irrational number.
C. A whole number is a perfect square if it is divisible by 2.
D. A whole number is a perfect square if its square root is a whole number.
Answers
whats the answer to this? A), B),C),D)
Answers
HELP PLZZZZ
What are the solutions to the system of equations graphed below? Select all
that apply.
Answers
Answer:
D(3,0) is correct answer
What is the product of (negative 6) (negative 7) (negative 1)?
–42
–14
14
42
Answers
Answer:
-42
Explanation:
(-6)(-7) = 42
(42)(-1) = -42
Get a calculator homie.
Answer:its negative 42
The length and width of a rectangle are ( 2x -5) and ( 3 x +4) What is the Perimeter?
Answers
Answer:
[tex] \fbox{ \sf{Perimeter \: of \: a \: rectangle = 10x - 2}}[/tex]
Step-by-step explanation:
[tex] \star{ \sf{ \: \: Length \: of \: a \: rectangle ( l ) = (2x - 5) }}[/tex]
[tex] \star{ \sf{ \: Width \: of \: a \: rectangle ( w ) = (3x + 4)}}[/tex]
[tex] \star{ \sf{ \: \: Perimeter \: of \: a \: rectangle = ?}}[/tex]
[tex] \boxed{ \bold{ \sf{Perimeter \: of \: a \: rectangle = 2(l + w)}}}[/tex]
[tex] \hookrightarrow{ \sf{Perimeter \: of \: a \: rectangle = 2(2x - 5 + 3x + 4)}}[/tex]
[tex] \text{Step \: 1 : \: Collect \: like \: term}[/tex]
[tex] \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base}[/tex]
[tex] \hookrightarrow{ \sf{2(2x + 3x - 5 + 4)}}[/tex]
[tex] \hookrightarrow{ \sf{2(5x - 5 + 4)}}[/tex]
[tex] \text{Step \: 2 \: : \: Subtract \: 4 \: from \: 5}[/tex]
[tex] \text{Remember !\: : the \: negative \: and \: positive \: integers \: are \: always \: subtracted \: but \: posses \: the \: sign \: of \: the \: bigger \: integer}[/tex]
[tex] \hookrightarrow{ \sf{2(5x - 1)}}[/tex]
[tex] \text{Step \: 3 \: : \: Distribute \: 2 \: through \: the \: parentheses}[/tex]
[tex] \hookrightarrow{ \sf{2 \times 5x - 2 \times 1}}[/tex]
[tex] \hookrightarrow{ \sf{10x - 2}}[/tex]
[tex] \sf{∴ \: The \: perimeter \: of \: a \: rectangle = 10x - 2}[/tex]
[tex] \text{Hope \: I \: helped !}[/tex]
[tex] \text{Best \: regards ! }[/tex]
~[tex] \text{TheAnimeGirl}[/tex]
PLEASE HELP! convert y=1/3x+9 to POINT SLOPE form
Answers
Answer:
y-10=1/3(x-3)
Step-by-step explanation:
I really don't want to explain, but tell me if you want an explanation and I will give it
Solve for x: 5 - (x + 5) > -2(x + 4) (1 point)
a
x>-8
Ob
X<-8
oc
x>-18
Od
X<-18
Answers
Answer:
x > - 8Step-by-step explanation:
5 - (x + 5) > -2(x + 4)
Expand the terms in the bracket
That's
5 - x - 5 > - 2x - 8
- x > - 2x - 8
Add 2x to both sides
That's
- x + 2x > 2x - 2x - 8
We have the final answer as
x > - 8Hope this helps you
Help me plz!!!!!!!!!!!!
Answers
explanation: it is given that the ratio is 5:3 (lillies to daisies). In order to get ten lillies, you would have had to multiply 5 by 10. Since it is a ratio, you have to do the same to the dasies, and you would get 6 dasies. 10+6=16, which is the total amount of flowers.