A set S has four members if there are six subsets of it, each with two members.
The combination formula, which is given by: can be used to determine the total amount of subsets with two members each.
[tex]^nC_k= \dfrac{n!}{(k!(n-k)!)}[/tex]
There are 6 subsets in this situation, each with 2 members.
So, [tex]^nC_2[/tex] = 6
Simplifying the equation:
n! / (2!(n-2)!) = 6
n(n-1) / (2 x 1) = 6
n(n-1) / 2 = 6
n(n-1) = 12
Expanding the equation:
[tex]n^2 - n = 12[/tex]
[tex]n^2 - n - 12 = 0[/tex]
Factoring the quadratic equation:
(n - 4)(n + 3) = 0
When all factors are set to zero and n is calculated:
n - 4 = 0 or n + 3 = 0
n = 4 or n = -3
Since n must be a positive integer.
So, n = 4 is the valid solution.
Thus, set S consists of 4 members.
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can i use a cash counter as a cashier. As in a website on my phone that tells me the exact change to give out to a person
Hence, find the values of y that satisfy the equation 2y-1)2 – 7(y – 1) + 4 = 0.
Answer:
y=3
Step-by-step explanation:
(2y-1)2-7(y-1)+4=0
4y-2-7y+7+4=0
9-3y=0
9=0+3y
9=3y
9/3=y
y=3
jane bought two new skirts for school. one cost 15 less than twice the cost of the total cost for both skirts was 75, what was the cost of each skirt?
Answer all questions olve the following logarithmic ec 2 log10 x + log103 = log10 75
[tex]2 log_{10}x + log_{10}(3) = log_{10}(75) [/tex]
Step-by-step explanation:
We can rewrite the left-hand side as
[tex]2\log{x} + \log{3} = \log{3x^2}[/tex]
Here, we used the following properties of logarithms:
[tex]\log{x^a} = a\log{x}[/tex]
[tex]\log{ab} = \log{a} + \log{b}[/tex]
We can then write
[tex] \log{3x^2} = \log{75} \Rightarrow 3x^2 = 75[/tex]
or
[tex]x = 5[/tex]
Use a commutative property to write an equivalent expression.
7x + y
9514 1404 393
Answer:
y +7x
Step-by-step explanation:
The commutative property of addition lets you swap the order of the two terms:
7x +y = y +7x
The commutative property of multiplication lets you swap the order of the factors.
7x +y = x·7 +y
How many cubes of side 2cm can be fitted into a box 12 cm long, 8cm wide and 4cm high?
Answer:
there are 48cubes fetted into a box
A shop in the mall is 6 yards by 11 yards. How much would it cost to recarpet the shop with carpet that costs $5.00 per square yard?
Answer:
$330
Step-by-step explanation:
To find the total area of the shop do 6 times 11
6*11 = 66 sq. yards
Now, do 5 * 66 because one yard is $5
5 * 66 = 330
It costs $330
Question is in the picture
9514 1404 393
Answer:
x = 3y = 9Step-by-step explanation:
Congruent sides are the same length.
AB = DF
3(2x +10) = 12x +12
6x +30 = 12x +12 . . . . eliminate parentheses
18 = 6x . . . . . . . . . . . . subtract 6x+12
3 = x . . . . . . . . . . . . . divide by 6
__
BC = FG
2y +12 = 2(2y -3)
y +6 = 2y -3 . . . . . . . divide by 2
9 = y . . . . . . . . . . . . subtract y-3
E is the mid point of DF. If DE= 7x. What is the length of DE
Answer:
I think you're missing information and don't you mean "what's the length of DF?"
Write 7 hundred as a decimal
Answer:
Step-by-step explanation:
7/100 as a decimal is 0.07.
Answer:
7.00
Step-by-step explanation:
To get a decimal, you move the decimal point to the left twice. If you move the decimal point two times to the left on 700, you would get 7.00.
Been stuck on this one. Sos
Answer:
B. 50%
Step-by-step explanation:
7/20 = 35%
35% + 15% = 50%
100% - 50% = 50%
i need to know whether it is the minimum or maximum function and what that number is as well as where x axis intercepts the quadratic graph . i need to know if there are any roots in the quadratic graph, and i need to know when y=1 , the value of x could be x= or x=
Answer:
The minimum value of this quadratic function is -4.
At the point (-4, 0), the x-axis intercepts with the quadratic graph.
There is 1 root of this quadratic equation.
Approximately, when y=1, the x value could be -5 or -3.
Determine the equation of the perpendicular bisector of the segment with endpoints (–5, 3) and (5, 5).
Answer:
y = –5x + 4
Step-by-step explanation:
i had this question
Plane P is a cross-section of the solid below. What shape is the cross section?
A. not enough information
B. rectangle
C. hexagon
D. pentagon
A rectangle exists as a quadrilateral with four right angles Option B. rectangles the cross section.
What is rectangle?
In Euclidean plane geometry, a rectangle exists as a quadrilateral with four right angles. It can also be described as an equiangular quadrilateral since equiangular compromises that all of its angles exist equal, or a parallelogram including a right angle. A rectangle with four sides of equivalent length exists as a square.
In mathematics, solid geometry or stereometry exists the traditional name for the geometry of three-dimensional, Euclidean spaces. Stereometry accords with the dimensions of volumes of different solid figures, including pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones; and balls bordered by spheres.
Hence,Option B. rectangles the cross section.
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Write an absolute value equation with-1 and 5 as the solution.
Answer:
it is detailed solution. please mark brainlest.
Thank you have a nice day
The equation of the absolute function that has the solutions of -1 and 5 will be |x - 2| = 3.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x |
The solutions of the absolute function are -1 and 5. Then the equation of the absolute function will be
x = -1, 5
Subtract -2 from both sides, then we have
x - 2 = -3, 3
Then apply Mode on both sides, then the equation will be
|x - 2| = 3
The equation of the absolute function that has the solutions of -1 and 5 will be |x - 2| = 3.
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write 0.8 as a fraction in simplest form.
The answer would be 8/10, but the simplified answer would be 4/5. I hope this helped answer your question for you. Enjoy your day, and take care!
Where do you graph 0, -1 and -1, 0 on a the coordinate plane? Please help asap
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\vector(1,0){4}}\put(0,0){\vector(-1,0){4}}\put(0,0){\vector(0,-1){4}}\put(0,0){\vector(0,1){4}}\put(0,-1){\circle*{0.5}}\put(-1,0){\circle*{0.5}}\end{picture}[/tex]
View it from web .
If a set contains 15 proper subsets then number of elements in that set
Answer
32,768
Step-by-step explanation:
Root 12 of Rood 12, see attached document
Lindsay prepared 9 containers of fruit punch for a party. After the party, there were still 4 4/9 containers of fruit punch left. How many containers were consumed in the party?
Turn 9 into [tex]\frac{81}{9}[/tex]. Then, convert 4 [tex]\frac{4}{9}[/tex] into a improper faction ( [tex]\frac{40}{9}[/tex] ). Then, subtract
[tex]\frac{81}{9} - \frac{40}{9} = \frac{41}{9}[/tex]. Lastly, convert [tex]\frac{41}{9}[/tex] to a mixed fraction ( [tex]4\frac{4}{9}[/tex] ).
Your answer is [tex]4\frac{4}{9}[/tex].
HELPPPP FASTTTT PLEASEEE!!!!!!!
Answer:
35 mph
Step-by-step explanation:
70/2 = 35
The sum of 7/4 and pi i
Hi! I'm happy to help!
To first of all write this expression, we need to know what sum means. Sum means addition, so we are adding. From there, we write it like this:
[tex]\frac{7}{4}[/tex]+[tex]\pi[/tex]
This is how you write it.
If you want to solve it, you need to know what pi is. pi is 3.14159...
It goes on forever, but we cane round to the nearest ten thousandth.
From here, you need to turn [tex]\frac{7}{4}[/tex] into a decimal. 4/4 is equal to 1, and 3/4 is equal to 0.75. Together, equal 1.75, or 7/4
Now, we solve our equation:
[tex]\frac{7}{4}[/tex]+[tex]\pi[/tex]
[tex]\frac{7}{4}[/tex]+3.14159
1.75+3.14159
4.89159
This is what the answer to the expression is.
I hope this was helpful, keep learning! :D
Find the quotient.
154 divided by 14
Answer:
11
Step-by-step explanation:
[tex]\frac{154}{14} =11\\\\check: 11*14=154[/tex]
154 divided by 14 equals 11.
To find the quotient of 154 divided by 14, we perform long division as follows:
11
14 | 154
First, we consider how many times 14 can be divided into 15, which is 1. We write the quotient, 1, above the line.
Next, we multiply 14 by 1, which equals 14. We subtract 14 from 15, resulting in 1. We bring down the next digit, which is 4.
We now consider how many times 14 can be divided into 14, which is 1. We write the quotient, 1, next to the 1 above the line.
Multiplying 14 by 1 gives us 14. Subtracting 14 from 14 gives us 0.
Since there are no more digits to bring down, we can conclude that the quotient is 11.
Therefore, 154 divided by 14 equals 11.
Long division is a method used to find the quotient and remainder when dividing two numbers. It involves dividing, multiplying, subtracting, and bringing down digits until there are no more digits to bring down. In this case, the quotient is 11, indicating that 154 can be divided by 14 precisely 11 times without any remainder.
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2. A doctor treated 2000 patients over a period of time. If he worked for 5 hours a day and spent 15 minutes on each patient how many days did the doctor spend to treat all patients?
Answer:
The answer is 6000 days.
6. In the triangle ABC, AB = 7 cm, BC = 8 cm and ABC = 90°. Point P lies inside the triangle such that BP = PC = 5 cm. Find:
a) the perpendicular distance from P to BC
b) the length AP.
GUYS HELP!
Answer:
Step-by-step explanation:
List the domain and range of the relation {(1, -9), (8,8), (0, -9), (8, 1), (1,9)}
Answer:
D={1, 8,0}
R={-9, 8,1,9}
Step-by-step explanation:
Here,
we, know, domain(D) =set of all first elements
thus, D={1,8,0}
again, range(R) =set of all second elements
thus R={-9,8,1,9}
What is the cube of the cube root of 27?
Answer:
[tex] { \sqrt[3]{27} }^{3} \\ we \: can \: solve \: this \: in \: two \: ways \\ 1)cube \: root \: means \: power \frac{1}{3} \\ so \: { \sqrt[3]{27} }^{3} = { {27}^{ \frac{1}{3} } }^{3} = {27}^{ \frac{3}{3} } = 27 \\ 2) { \sqrt[3]{27} }^{3} \\ \sqrt[3]{27} = 3 \\ so \: {3}^{3} = 27 \\ thank \: you[/tex]
Help please ASAP!!!!!
Answer:
answer is c because you gota tranlate it left
Step-by-step explanation:
A statement that consistently and correctly describes a natural phenomenon is a scientific.
A. Control
B. Theory
C. Hypothesis
D. Observation
Ryan, a consumer electronics salesperson, earns a base salary of $1100 per month and a commission of 8% on the amount of sales he makes. One month Ryan received a $1492 paycheck. Find the amount of his sales for the month.