The value of n in [tex]^nC_3=120[/tex] is 10 .
Combining is defined as "arrangement of objects in any order in which objects are selected", meaning "selection of objects" in any order. The number of combinations of n different things for each r is " n " and it is given by [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex] ....(1) where 0 ≤ r ≤ n. This forms a general combination formula. Prime factorization means that writing a number into its product of prime numbers .
It is given that [tex]^nC_3=120[/tex]
Using equation (1) , we get
[tex]\frac{n!}{3!(n-3)!} =120\\\ \\\frac{n(n-1)(n-2)(n-3)!}{3\times2(n-3)!} =120\\\\\n(n-1)(n-2)=720\\[/tex] ....(2)
Prime factorization of 720 is given by
[tex]720=2^4\times3^2\times5\\720=10\times9\times8[/tex]
720 can be written as [tex]10(10-1)(10-2)[/tex]
Putting above value in equation (2) , we get
[tex]n(n-1)(n-2)=10(10-1)(10-2)[/tex]
On comparing LHS = RHS we get
n = 10
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A dealer made a profit of 22.5% by selling a car for GH¢5,880. Find the percentage profit he would have realized if he had sold it for GH¢6,120.
The percentage of profit would be $1,377 if the dealer would have sold the car for $6,120.
What do we mean by percentages?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. It is frequently denoted by the percent sign, "%."One percent (symbolized 1%) is the one-hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given amount. For example, 1% of 1,000 chickens equals 1/100 of 1,000, or 10 chickens; 20% of the quantity equals 20/100 1,000, or 200 chickens.So, we need to obtain 22.5% of $6,120.
Then,
$6,120/100 × 22.561.2 × 22.51,377Therefore, the percentage of profit would be $1,377 if the dealer would have sold the car for $6,120.
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a. If a family has 5 children, in how many ways could the parents have 2 boys and 3 girls as children?
Answer: 10 ways
Step-by-step explanation:
5! / (3! * 2!)=
1*2*3*4*5/(1*2*3*1*2)=
4*5/(1*2)=
20/2=10 ways
Find the value of x.
28°
X
X
x = [?]°
Step-by-step explanation:
180-28=152
152÷2=76
x=76°
Suppose that a code (similar to a postal code) is of the form LDL DLD, where 'L' is an uppercase letter from A to N (i.e., 14 possible letters) and 'D' is a digit from 0 to 4. Suppose that such a code is randomly generated.
- Find the probability that the code either starts with an 'A' or ends with an even digit (note that 0 is even).
Answer: 47/70
Step-by-step explanation:
Starts with an A ==> 1 possibility out of 14 ==> 1/14
Ends with an even digit from 0-4:
Even digits: 0, 2, 4 ==> 3 possibilities out of 5 ==> 3/5
1/14 + 3/5=
(1/14 + 3/5)*70/70= ==> get rid of different denominators
(1*70/14 + 3*70/5)/70=
(70/14 + 210/5)/70=
(5+42)/70=47/70
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Which of the a values are solutions to the following equation?
a² = 6.4
Choose all answers that apply:
()
B
U
(D)
a = -0.8
a=0.8
a = -3.2
a=3.2
None of the above
Answer:
a= -0.8 and a= 0.8
Step-by-step explanation:
this questions wants u to find a perfect square for numbers if its difficult becuz of the decimals I suggest u move it and bring it back in your final answer
Josh buys 6 pencils at the bookstore. Each pencil costs $0.20. How can Josh use the number line to find the total cost of the pencils? A number line from 0 to 2.4 is divided with marks every two-tenths. fill in the blank Numbers may be used once or not at all. 4 1.2$ 1.20 0.66 0.20$1.00 1 $6.00 Start at ____ on the number line. Mark ____ parts that are each___ . Th product ____ represents the total cost, which is ____.
Josh start at 0 on the number line and mark 6 parts that are each 0.20.The product (6 *0.20) represents the total cost which is $1.20 .
What is a number line ?
A number line is a representation of numbers on a line with the marks placed at the line at equal intervals. This marks or scale of line can be chosen as per our requirement.
For example if we scale the number line such that each mark is placed at an interval of number 1 then number 4 will come at 4th mark as each mark is at 1 unit distance with each other .
Given that josh buys 6 pencils at the bookstore and each pencil is of $0.20
Thus, the total cost of pencils = 6 * 0.20 = 1.20
Now on the given number line the numbers starting from 0 and ending at 2.4 and each one is at 2/10=0.2 intervals
Total marks on the line = ( final - initial number )/(length of each interval)
= ( 2.4-0) /(0.2) =12
To find at how many marks total cost would be placed = total cost / interval length = 1.2 / 0.2 = 6
Therefore, when we start from 0 and at 6 marks at this number line our number value will 1.20 that is our total cost.
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Two trains leave the same station at the same time but are headed in opposite directions. One train travels at 80 mph and the other train travels at 65 mph. How much time passes until the trains are 580 miles apart?
a: 4 hours
b : 6.4 hours
c: 7.7 hours
d: 8 hours
e: 38.7 hours
38.7 hours would have passed until the trains are 580 miles apart
How much time passes until the trains are 580 miles apart?The given parameters are
Train 1 = 80 mph
Train 2 = 65 mph
The difference in the speeds of the trains is
d = 80mph - 65mph
Evaluate
d = 15mph
The distance moved is
Distance = 15 * t
At 580 miles apart, we have
15 * t = 580
Divide by 15
t = 38.7 hours
Hence, 38.7 hours would have passed until the trains are 580 miles apart
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What will the result be if you add two negative numbers?
Answer:
When you have two negative signs, one turns over, and they integrate together to make a positive. If you have a positive and a negative, there is one dash left over, and the answer is negative.
The prom committee is decorating the venue for prom and wants for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5, EF=39, and m angle GHF=128 degrees, find GE and m
The length of diagonal GE is 89 units
What is a quadrilateral?
quadrilateral is a plane mathematical closed figure consist of four side and four edges. There are 7 types of quadrilateral.
Trapezium, Parallelogram, Rectangle, Rhombus, Square, Kite.
It is given that :
length of side EF = 39 units
and, DH = 44.5 units
It is known that :
Diagonals of a Rectangle
A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other.
The diagonals of a rectangle bisects each other into equal segments.
The diagonals of the rectangular room are:
DF and GE
Thus:
DF = GE
DH = 1/2(DF)
44.5 = 1/2(DF)
DF = 2(44.5)
DF = 89
Therefore :
DF = GE = 89
GE = 89 units
Thus, The length of diagonal GE is 89 units.
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3(x-6)-8x=-2+5(2x+1)
Answer:
x=-21/15
Step-by-step explanation:
3x-18-8x=-2+10x+5
-5x-18=10x+3
15x=-21
x=-21/15
B. Do the following exercises.
Let A = {0, 1, 2, 3, 4, 5} ; B = {0, 1, 5, 6, 9} ; C = {0, 2, 6, 7, 8}
1.) A ∪ B
2.) A ∩ C
3.) A ∪ B ∪ C
4.) A ∩ B ∩ C
Answer:
1) A ∪ B = {0, 1, 2, 3, 4, 5 ,6 ,9}
2) A ∩ C = {0, 2}
3) A ∪ B ∪ C = {0, 1, 2, 3, 4, 5, 6 7. 8. 9}
4) A ∩ B ∩ C = {0}
Step-by-step explanation:
Definitions
Union of two or more sets is the set of elements in all of those sets with duplicates removed. The symbol used is ∪
Intersection of two or more sets is the set of elements common to those sets. Symbol ∩
1) A ∪ B = {0, 1, 2, 3, 4, 5} ∪ {0, 1, 5, 6, 9} = {0, 1, 2, 3, 4, 5 ,6 ,9}
2) A ∩ C = {0, 1, 2, 3, 4, 5} ∩ {0, 2, 6, 7, 8} = {0, 2}
3) A ∪ B U C = (AUB) ∪ C
= {0, 1, 2, 3, 4, 5 ,6 ,9} U {0, 2, 6, 7, 8} = {0, 1, 2, 3, 4, 5, 6 7. 8. 9}
4) A ∩ B ∩ C = {0, 1, 2, 3, 4, 5} ∩ {0, 1, 5, 6, 9} ∩ {0, 2, 6, 7, 8}
= {0}
Answer:
1) A ∪ B = {0, 1, 2, 3, 4, 5, 6, 9}
2) A ∩ C = {0, 2}
3) A ∪ B ∪ C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
4) A ∩ B ∩ C = {0}
Step-by-step explanation:
Set Notation
[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]
Given sets:
A = {0, 1, 2, 3, 4, 5}B = {0, 1, 5, 6, 9}C = {0, 2, 6, 7, 8}Question 1
[tex]\begin{aligned}\sf A \cup B & =\sf \{ 0, 1, 2, 3, 4, 5 \} \cup \{0, 1, 5, 6, 9 \}\\& =\sf \{ 0, 1, 2, 3, 4, 5, 6, 9 \}\end{aligned}[/tex]
Question 2
[tex]\begin{aligned}\sf A \cap C& =\sf \{0, 1, 2, 3, 4, 5 \} \cap \{ 0, 2, 6, 7, 8 \}\\& =\sf \{0, 2 \}\end{aligned}[/tex]
Question 3
[tex]\begin{aligned}\sf A \cup B \cup C& =\sf \{ 0, 1, 2, 3, 4, 5 \} \cup \{0, 1, 5, 6, 9 \} \cup \{0, 2, 6, 7, 8 \}\\& =\sf \{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 \}\end{aligned}[/tex]
Question 4
[tex]\begin{aligned}\sf A \cap B \cap C& =\sf \left(A \cap B\right) \cap \left(B \cap C\right) \\ & =\sf \left(\{ 0, 1, 2, 3, 4, 5 \} \cap \{0, 1, 5, 6, 9 \}\right) \cap \left(\{0, 1, 5, 6, 9 \} \cap \{0, 2, 6, 7, 8 \} \right)\\& =\sf \{ 0, 1, 5 \} \cap \{0, 6 \}\\ & = \sf \{ 0 \}\end{aligned}[/tex]
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-6
-4
-2
6
4
2
2
4 6
f(1) =
Answer:
f(1)= -4
Step-by-step explanation:
o_o. .............>|||✓✓✓✓✓
The point (7, 8) in the coordinate plane represents a ratio. Adela claims that you can find an equivalent ratio by adding the same number to both coordinates of the point. Is Adela correct? Explain. riculum Associates, LLC Copying is not permitted. Lesson 13 Find fo
The verdict on Adela's idea of retaining the same ratio by adding the same number to both coordinates of the point is that; Adela is incorrect.
What is the approach to retaining the same ratio as represented by the coordinate given?It follows from the task content that, Adela claims that you can find an equivalent ratio by adding the same number to both coordinates of the point.
Adela's claim as indicated above is false because, if for instance, 2 is added to both coordinates, then we have; (9, 10).
And, since 9 : 10 is not equivalent to; 7: 8. Adela's claim is incorrect.
On the other hand, to retain the ratio, the coordinates should be multiplied by the same number. For instance by 3; so that we have;
21 : 24 which is equivalent to the ratio, 7 : 8.
The verdict on Adela's idea of retaining the same ratio by adding the same number to both coordinates of the point is that; Adela is incorrect
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Can someone help me with this ??
The quotient of a number and -5 increased by 7 os at minimum 1
The quotient of a number and -5 increased by 7 os at minimum 1 is x ≤ 30.
Sometimes they will ask for a remainder or to find a quotient using the dividend and divisor values. Whatever they ask for, you can quickly discover the right answer if you know how to write it down or how to build the equation based on reading the question.
Here, we assume that the quotient of a number is x, and we first write the formula by deciphering the provided question.
The product of a number's ratio to -5 and 7 is
x/-5 + 7
This is at least one
x/-5 + 7 ≥ 1
Take 7 away from both sides.
x/-5 ≥ -6
Add -5 to both sides. Since this integer is negative, the inequality sign must be changed:
x ≤ 30
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VIEW IMAGE
9. The parent or basic absolute value function, f (x)= xl, is transformed to become
1
g(x)= -lal. Which of the following are true about f (x) and g(x)?
The domain of both f (x) and g (x) are all real numbers.
II The graphs of each function are vertical reflections of each other.
III The axis of symmetry of the graphs of both functions is x = 0.
The range of both f (x) and g (z) are all real numbers.
Both [tex]f(x)[/tex] and [tex]g(x)[/tex] have real domains.
What is domain?
The domain is all x-values or function inputs, and the range is all y-values or function outputs. When looking at a graph, the domain is all of the graph's values from left to right. The range includes all of the graph's values from bottom to top.
Here, the options
(I) The domain of both [tex]f(x)[/tex] and [tex]g(x)[/tex] are all real numbers,
(II) The axis of symmetry of the graphs of both functions is [tex]x=0[/tex]
are correct.
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40 mi/h to kilometers per hour
Answer:
64.3738 km/h
Step-by-step explanation:
50 POINTS!!!!
Answer the questions by drawing on the coordinate plane below.
(a) Draw the image of ∆ABC under the dilation with scale factor 3 and the origin as the center of dilation. Label the image ∆A'B'C'. Make sure to include the coordinates of A’, B’, and C’.
(b) Draw the image of ∆DEF under the dilation with scale factor -1/2 and the origin as the center of dilation. Label the image ∆D'E'F'. Make sure to include the coordinates of D’, E’, and F’.
Using dilation rules, the dilated triangle is given at the end of the answer. The coordinates of the vertices are as follows:
A'(-6,6), B'(-3,0), C'(3,6).
What is the rule for a dilation?To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:
(x,y) -> (ax, ay).
The coordinates of the vertices of ABC are given as follows:
A(-2,2), B(-1,0), C(1,2).
After a dilation with a scale factor of 3, the coordinates of the vertices of A'B'C' will be given as follows:
A'(-6,6), B'(-3,0), C'(3,6).
These coordinates are derived multiplying the coordinates of A, B and C by 3.
The image of the triangle is given at the graph at the end of the answer.
For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by -1/2 to generate the dilated triangle.
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☆
Problem Solving
27. Maura's dance team wants to buy costumes
that cost $56 each. They have $523 saved in a
fund. How much money will they have left in
the fund after they buy 9 costumes?
Answer:
$19
Step-by-step explanation:
56x9=504
523-504=19
The perimeter of a rectangle is 24 m. The length is 3 m more than two times the width. Find the
length and the width of the rectangle.
Answer: l=2w+3
Step-by-step explanation:
The circle graph on the right shows the uses of corn production. Use this graph to answer the question. What percent of corn production is used for ethanol or exports?
Answer:
37%
Step-by-step explanation
Reading the graph we see:
The percent of corn production is used for ethanol is 18%
The percent of corn production is used for exports is 19%
Answer the question:
The percent of corn production used for ethanol OR exports is the sum of the two 18%+19% = 37%
Please show step by step
Answer:
[tex]\begin{pmatrix}6&-5\\ 0&-2\end{pmatrix}[/tex]
Step-by-step explanation:
[tex]2\begin{pmatrix}2&-3\\ 1&-1\end{pmatrix}=\begin{pmatrix}4&-6\\ 2&-2\end{pmatrix}[/tex]
[tex]\begin{pmatrix}4&-6\\ 2&-2\end{pmatrix}+\begin{pmatrix}2&1\\ -2&0\end{pmatrix}[/tex]=
[tex]\begin{pmatrix}6&-5\\ 0&-2\end{pmatrix}[/tex]
A recipe calls for 20 fluid ounces of milk. If Nita buys a half gallon of milk, how many batches of that recipe can she make?
Show workk
Answer:
3 can be made.
Step-by-step explanation:
There are 64 fl. oz. in half gallon. Using 20 oz per recipe, 64 divided by 20 gives you 3.2.
(3x-2y). (6xy-³)
I WILL MARK BRAINLY FOR THE RIGHT ANSWER
[tex] \large \bf \implies{18 {x}^{ - 1} {y}^{ - 2}}[/tex]
Step-by-step explanation:[tex] \bf \longrightarrow(3 {x}^{ - 2}y)(6xy^{ - 3}) \\ \\ \bf \longrightarrow3 \times 6 \times {x}^{ - 2} \times {x}^{1} \times {y}^{1} \times {y}^{ - 3} \\ \\ \bf \longrightarrow18 {x}^{( - 2 + 1)}y^{(1 - 3)} \\ \\ \bf \longrightarrow \boxed{ 18 {x}^{ - 1}y^{ - 2}} \: ans.[/tex]
2. Erica Matthews is married and earns $54,730 per year as a grant writer. Her state's tax rate is 3.5% of
taxable income.
If the income is $54730 and state tax rate is 3.5% then the amount of tax that Erica Matthews needs to pay is $1915.55.
Given that the income is $54730 and state tax rate is 3.5%.
We are required to find the amount of tax that Erica Matthews need to pay.
State Government is basically tax that is levied by state government on the people living in that state.State governments basically use taxpayer dollars to fund road maintenance, law enforcement agencies and other public services.
Income=$54730
Tax rate=3.5%
Tax=54730*3.5/100 (We assumed that full amount is taxable.)
=$1915.55
Hence if the income is $54730 and state tax rate is 3.5% then the amount of tax that Erica Matthews needs to pay is $1915.55.
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ank, the owner of Hank's Hot Dog Hut, deposited $175 this morning from his late-night sales. This afternoon, he deposited another $280 from lunch sales.
Hank added 455.00 more to his bank account. The Total change in Hanks bank account is $455
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that Hank, the owner of Hank's Hot Dog Hut, deposited $175 this morning from his late-night sales. In afternoon, he deposited another $280 from lunch sales.
We need to Just add 175 and 280
175 + 280
455
Therefore, Hank added 455.00 more to his bank account.
Hence The Total change in Hanks bank account is $455
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The complete question is
Hank, the owner of Hank's Hot Dog Hut, deposited $175 this morning from his late-night sales. This afternoon, he deposited another $280 from lunch sales.
What was the total change in Hank's bank account relative to where it started?
can someone please help with this thank u
Answer:
y = {-1/4 for x < -3; +1/4 for x > -3}
see attached for a graph
Step-by-step explanation:
You want the function y = |x+3|/(4x+12) written as a piecewise function and graphed.
Absolute value functionThe absolute value function resolves into two pieces, each with its own domain. These let you write the function as a piecewise function.
(x+3) < 0When (x+3) < 0, the absolute value function negates this value:
y = -(x+3)/(4(x+3)) = -1/4 . . . . . for x < -3
(x+3) ≥ 0When (x+3) ≥ 0, the absolute value function does nothing. That means the equation becomes ...
y = (x +3)/(4(x +3))
When the denominator is zero, the function is undefined. When the denominator is not zero, the function becomes ...
y = 1/4 . . . . . for x > -3
Piecewise functionThen the definition of the piecewise function is ...
[tex]y=\begin{cases}-\dfrac{1}{4},&x < -3\\\dfrac{1}{4},&x > -3\end{cases}[/tex]
The graph is attached.
Help me understand this pls
The area of the polygon is equal to 10.006 square units.
How to determine the area of a polygon
In this case we find a polygon with four vertices, that is, a tetragon, also called quadrilateral. By geometry we know that quadrilaterals can be armed by uniting two triangles and the area of a quadrilateral is equal to the areas of the two triangles. Hence, the polygon NPQR is the result of combining the triangles NPQ and NQR.
First, determine the lengths of the sides of the two triangles:
NP = √[[3 - (- 2)]² + (1 - 1)²]
NP = 5
PQ = √[(3 - 3)² + [1 - (- 1)]²]
PQ = 2
NQ = √[[3 - (- 2)]² + (- 1 - 1)²]
NQ = √29
NR = √[[- 2 - (- 2)]² + [- 1 - (- 1)]²]
NR = 2
QR = √[(- 2 - 3)² + [(- 1) - (- 1)]²]
QR = 5
Second, calculate the areas of the two triangle:
s₁ = 0.5 · (NP + PQ + NQ)
s₁ = 0.5 · (5 + 2 + √29)
s₁ ≈ 6.193
A₁ = √[s₁ · (s₁ - NP) · (s₁ - PQ) · (s₁ - NQ)]
A₁ = √[6.193 · (6.193 - 5) · (6.193 - 2) · (6.193 - √29)]
A₁ ≈ 5.003
s₂ = 0.5 · (NQ + NR + QR)
s₂ = 0.5 · (√29 + 2 + 5)
s₂ ≈ 6.193
A₂ = √[s₂ · (s₂ - NQ) · (s₂ - PQ) · (s₂ - QR)]
A₂ = √[6.193 · (6.193 - √29) · (6.193 - 2) · (6.193 - 5)]
A₂ ≈ 5.003
A = 5.003 + 5.003
A = 10.006
The area of the polygon is equal to 10.006 square units.
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Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
The point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
In this question we have been given a graph of Skateboards vs. Bikes.
We need to find the point that represents an INEFFICIENT point of production.
Inefficient production means the economy can be producing more goods without using any additional resources.
In given production possibility curve, an INEFFICIENT point of production is point A.
Therefore, the point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
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14x-3y=-2
4x + 5y = 14
solve each system of equations by elimination
Answer:
x = [tex]\frac{16}{41}[/tex]
y =[tex]\frac{102}{41}[/tex]
Step-by-step explanation:
To use elimination I need either the x terms to be inverses of each other or the y terms to be inverses of each other. There are a number of ways to do this. I am going to focus on the y's. If I multiple the first equation through by 5 and the second equation through by 3. I will make equivalent equations that will allow the y terms to be eliminated.
14x - 3y = -2
5(14x - 3y) =5(-2)
70x - 15y = -10
4x + 5y = 14
3(4x + 5y) = 3(14)
12x +15y =42
Add together the 2 bold equations above
70x - 15y = -10
12x + 15y = 42
82x = 32 Divide both sides by 82
x = [tex]\frac{32}{82}[/tex] = [tex]\frac{16}{41}[/tex]
Plug this in either equation to solve for y
y = [tex]\frac{102}{41}[/tex]
