Show that nC6 = nC4, find n
Answer:
n = 10
Step-by-step explanation:
From the question,
nC6 = nC4
n!/6!(n-6)! = n!/4!(n-4)!
Simplifying n! out of the equation
⇒ 1/6!(n-6)! = 1/4!(n-4)!
Crossmultiplying
4!(n-4)! = 6!(n-6)!
4!(n-4)! = 6×5×4!(n-6)!
(n-4)! = 30(n-6)!
(n-4)(n-5)(n-6)! = 30(n-6)!
⇒ (n-4)(n-5) = 30
n²-4n-5n+20 = 30
n²-9n+20-30
n²-9n-10 = 0
Solving the quadratic equation,
n-10n+n-10 = 0
(n-10n)+(n-10) = 0
n(n-10)+1(n-10) = 0
(n+1)(n-10) = 0
Either
n+1 = 0
n = -1
or
n-10 = 0
n = 10
n canot be a negative value,
Therefore, n = 10
A woman borrows $ 6,000 at 12% compounded monthly, which is to be amortized over 3 years in equal monthly payments. For tax purposes, she needs to know the amount of interest paid during each year of the loan. Find the interest paid during the first year, the second year, and the third year of the loan. [Hint: Find the unpaid balance after 12 payments and after 24 payments.]
Answer:
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Help me pls I need a good grade
Answer: 226
Step-by-step explanation:
arc ZW is 180 (it is a semi Circle) and arc WX is 46 (the angle opposite the arc)
so arc ZWX is 180+46=226
Please help me
10 + 963 = ?
Answer:
hi
Step-by-step explanation:
10+963=973
have a nice day
Answer:
10+963= 973
Step-by-step explanation:
Answer 973
i hope this help
Answer fast thank you
Answer:
D. 91 1/8
Step-by-step explanation:
The small square box has a width of 1 1/2. Since it’s a SQUARE box all sides are the same sides. to find volume we have to do length * width * height. the bigger square box is three times the small box size. So we would have to do 1 1/2 times three. Which is 4 1/2. Since all sides are the same and we have to do L*W*H, we have to multiply 4 1/2 by 4 1/2 by 4 1/2. Which equals 91 1/8. I find it easier to turn the fractions into decimals, so 1 1/2 is 1.5.
1.5 times 3= 4.5 4.5 times 4.5 times 4.5 = 91.125 convert to a fraction and its 91 1/8
Name the marked angle in 2 different ways.
V
U
S
T
Answer:
VUS, UST
Step-by-step explanation:
Use GCF and the distributive property to write equivalent
expressions.
A) 6x + 9y
B)3c +11c
Answer:
Step-by-step explanation:
Greatest common factor of 6x and 9y is 3.
6x + 9y = 3(2x + 3y)
:::::
Greatest common factor of 3c and 11c is c.
3c + 11c = (3+11)c
someone please help me answer this
Answer:
a = 6.7m is the answer.
Step-by-step explanation:
a = ?
b = 6m
c = 9m
According to the Pythagorean theorem,
a² + b² = c²
a² + 6² = 9²
a² + 36 = 81
a² = 81 - 36
a² = 45
a = 6.708
round to the nearest tenth,
a = 6.7m
∴ Janice is 6.7m high up in the air.
Solve for the area of the smaller
shape.
Round to the nearest TENTH.
A taxi driver wrote a formula to represent the mileage and fee for his last customer. He wrote the equation 3.00 + 0.50 m = 9.50, where m represents the number of miles traveled.
Which statement shows the meaning of the driver’s equation? Select two options.
Three dollars added to $0.50 is the same as $9.50.
Three dollars plus $0.50 times the number of miles is equal to nine dollars and fifty cents.
Three dollars more than the quotient of $0.50 and the number of miles is nine dollars and fifty cents.
The product of the number of miles and the sum of $3 and $0.50 is equal to $9.50.
The sum of three dollars and the product of 50 cents times the number of miles is nine dollars and fifty cents.
the last option i believe. sorry if it's wrong
Answer:
It’s B and E
Step-by-step explanation:
Three dollars plus $0.50 times the number of miles is equal to nine dollars and fifty cents.
The sum of three dollars and the product of 50 cents times the number of miles is nine dollars and fifty cents.
Solve this question for brainlest
1ч (х – 2) =36 times-Ч2
Answer:
x = -7
Step-by-step explanation:
14(x - 2) = 3(-42)
14x - 28 = -126
14x = -126 + 28
14x = -98
x = -7
tiffany spent 2 1/8 hours studying 1 3/8 hours talking on the phone 100 percent of an hour on chores and 1.75 hours walking which of the following lists her activities in order of greatest to least amount of time F. Chores, phone, walk, study G. Chores, study, walk, phone H. Study, phone, walk, chores J. Study, walk, phone, chores
Answer: J - Study. walk. phone, chores
Does anyone know this, scammers keep answering it
Answer:
Blank 1: 50
Blank 2: 95
Blank 3: is not
Blank 4: is not
Step-by-step explanation:
A right angle is 90 degrees, and a rectangle is a plane figure that has four straight sides and four right angles.
Solve the following percentage problem 85%of 40
Answer:34
85% of 40 = 34
Step-by-step explanation:85 percent of 40? = 34.
Answer:
34
Step-by-step explanation:
What is the domain of the function on the graph?
Answer:
x is greater than or equal to -3
[-3, infinity)
{x| -3 less than or equal to x les than infinity}
Solve the following radical equation , Show work also please !
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{-12=6\sqrt{x+4}}[/tex]
[tex]\mathsf{6 \sqrt{x + 4}=-12}[/tex]
[tex]\textsf{DIVIDE your BOTH SIDES by 6}[/tex]
[tex]\mathsf{\dfrac{6\sqrt{x + 4}}{6}= \dfrac{-12}{6}}[/tex]
[tex]\textsf{Introduce the new temporary equation}[/tex]
[tex]\mathsf{\sqrt{x + 4}=-2}[/tex]
[tex]\textsf{SOLVE for your SQUARE ROOT }[/tex]
[tex]\mathsf{\sqrt{{x + 4}}=-2}[/tex]
[tex]\mathsf{Like: x + 4 = (-2)^2}[/tex]
[tex]\textsf{SQUARE EACH of your SIDES}[/tex]
[tex]\mathsf{x + 4 = 4}[/tex]
[tex]\textsf{SUBTRACT your BOTH SIDES by 4 }[/tex]
[tex]\mathsf{x + 4 -4= 4-4}[/tex]
[tex]\mathsf{Cancel\ out\ 7-7 \ because\ it\ gives\ you\ 0}[/tex]
[tex]\textsf{Solving for your last temporary question}[/tex]
[tex]\mathsf{x = 4-4}[/tex]
[tex]\mathsf{4-4 = \bf 0}[/tex]
[tex]\mathsf{\bf x = 0}[/tex]
[tex]\textsf{Plug your x-value (x = 0) to make sure it works for your original equation}[/tex]
[tex]\textsf{You will see that it doesn’t work for the original problem so this means that the}\\\textsf{original equation \bf does NOT have any solutions.}[/tex]
[tex]\boxed{\boxed{\large\text{Answer: \huge\bf No solutions}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
prove that the electric field is negative of the gradient of electric potential
Answer:
Electric field points out the direction in which potential energy function is decreasing so it's the negative gradient vector of the potential energy function.
Step-by-step explanation:
^^
HELP PLSS I HAVE 10 minutes
Answer:
h≈1.43
Step-by-step explanation:
Simply ,Square the radius, and then divide the radius squared into the tripled volume. For this example, the radius is 2. The square of 2 is 4, and 300 divided by 4 is 75. Divide the amount calculated in Step 2 by pi, which is an unending math constant that begins 3.14, to calculate the cone's height.
please please please help me :(((
Answer:
In the last diagram the object is being acted upon by forces not adding up to zero.
Step-by-step explanation:
(Assuming force 1=force 2 in terms of magnitude)
Let forces acting towards the left = -1
Let forces acting toward the right = +1
In the first diagram, force1 is acting towards the left and force2 is acting towards the right:
Total force = force1+force2=-1+1=0
In the second diagram, force1 is acting towards the left and force2 is acting towards the right:
Total force = force1+force2=-1+1=0
In the third diagram, force1 is acting towards the right and force2 is acting towards the left:
Total force = force1+force2=+1-1=0
In the fourth diagram, force1 is acting towards the left and force2 is acting towards the left:
Total force = force1+force2=-1-1=-2. Here, the forces do not add up to zero.
A chemist mixed two samples together: a gray liquid that boils at 103°C and a colorless gas that boils at 19°C. She analyzed the results and found two ending substances. One of the ending substances was a pink liquid. This ending substance is made up of the repeating group of atoms shown above. Which of the diagrams to the left shows the repeating groups of atoms that make up the samples the chemist mixed together?
Answer:
Its C
Step-by-step explanation:
Diagram c to the left shows the repeating groups of atoms that make up the samples the chemist mixed together.
What is atoms?Atoms are the smallest unit of matter that make up all physical objects. Atoms are composed of three main components: protons, neutrons, and electrons. Protons and neutrons are found in the nucleus of the atom and have a positive charge, while electrons orbit the nucleus and have a negative charge.
here, we have,
we know that,
Atoms can join together to form molecules, which are the building blocks of all matter. Atoms of different elements can join together in different ways to form compounds and these compounds are the basis of all substances. Atoms are also the basis of all chemical reactions and can exist in different physical states, such as solid, liquid, or gas. Atoms can also be combined to form isotopes, which are atoms of the same element with different numbers of neutrons.
To learn more about atoms
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complete question:
11. A chemist mixed two samples together: a brown solid that melts at about 1,300°C and a colorless liquid that melts at about 20°C. She analyzed the results and found two ending substances. One of the ending substances melts at about 250°C. This ending substance is made up of the repeating group of atoms shown above. Which of the diagrams to the left shows the repeating groups of atoms that make up the samples the chemist mixed together?
please help me .....
What is the average speed (rate) if you traveled 83.6miles in 3.8 hours?
Answer:
22 mph
Step-by-step explanation:
83.6 miles
3.8 hours
83.6/3.8 = 22 mph
What is the domain of the following parabola? (5 points)
u-shaped graph that opens down with a vertex of 1, 2
Group of answer choices
y ≤ 2
x ≥ 1
All real numbers
x ≤ 1
Answer:
the domain for this parabola is all real numbers
the length of rectangular park is 15 m longer than that of the park is 114m find it's length and breadth
Answer: Length: ≈20.5 Breadth: ≈5.5
Step-by-step explanation: x(x+15)=114, solving for x we get 5.547 and 20.547.
Please Help me Due in 2 Mins
URGENT WILL GIVE BRAINLIEST!!!!
Answer:
7/10
Step-by-step explanation:
Answer:
7/10
Step-by-step explanation:
There is a total of ten numbers, and only seven of them are odd numbers (1, 3, 7, 9, 15, 19, 21)
You have a 70% chance of picking an odd number.
The dimensions of two square pyramids formed of sand are shown. How much more sand is in the pyramid with the greater volume?
I will ONLY give brainliest to whoever answer FIRST AND whoever answers CORRECTLY!
Answer:
There is 32in² more sand in the pyramid with greater volume.
Step-by-step explanation:
Volume of rectangular pyramid = l²*h/3, where l is the base length and h is height.
Volume of left pyramid=l²*h/3=8²*(6/3)=64*(2)=128in³
Volume of right period=l²*h/3=6²*(8/3)=36(8/3)=96in³
128-96=32, there is 32in² more sand in the pyramid with greater volume.
I need help please :)
Step-by-step explanation:
The given equation is :
2x = 10
We need to find the value of x.
This equation has one solution as it is a linear equation having one variable i.e. x.
Dividing both sides by 2,
x = 5
So, the value of x is equal to 5.
Put x = 5. So,
2(5) = 10
10 = 10
Hence, this is the required solution.
De la siguiente sucesión: – 1, – 3, – 5, – 7, – 9,…, ¿Cuál es la regla general para n=1, 2, 3,…?
The general rule for the given Sequence is a_n = 1 – 2n, where n = 1, 2, 3, ... This equation allows us to calculate any term in the sequence by substituting the corresponding value of n.
The given sequence –1, –3, –5, –7, –9,... follows a specific pattern or rule. To determine the general rule for n = 1, 2, 3,..., we can observe the sequence and identify the relationship between the terms.
Looking at the sequence, we notice that each term is decreasing by 2. Starting with –1, we subtract 2 to get the next term –3. Then, we subtract 2 again to get –5, and so on. Therefore, the rule for generating the terms in this sequence is to start with –1 and subtract 2 from each subsequent term.
We can express this rule algebraically as follows:
a_n = a_1 + (n – 1) * d
Where:
a_n represents the nth term of the sequence,
a_1 represents the first term of the sequence,
n represents the position of the term in the sequence,
d represents the common difference between the terms.
In this case, a_1 = –1 and d = –2 (since each term is decreasing by 2). Plugging these values into the equation, we get:
a_n = –1 + (n – 1) * (–2)
Simplifying further, we have:
a_n = –1 – 2n + 2
a_n = 1 – 2n
Therefore, the general rule for the given sequence is a_n = 1 – 2n, where n = 1, 2, 3, ... This equation allows us to calculate any term in the sequence by substituting the corresponding value of n.
For more questions on Sequence .
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Note the full question may be :
From the following sequence: – 1, – 3, – 5, – 7, – 9,…, What is the general rule for n=1, 2, 3,…?
convert 32.1% to an equivalent decimal.
Answer:
0.321
Step-by-step explanation:
32.1 / 100 = 0.321 = [tex]\frac{321}{1000}[/tex]
The decimal equivalent of 32.1% is 0.321.
Converting a percentage to a decimal is a breeze.
To convert 32.1% to its decimal equivalent, all you have to do is divide the percentage value by 100.
In this case,
it would be 32.1 ÷ 100 = 0.321.
So, the decimal equivalent of 32.1% is 0.321.
Converting percentages to decimals is a simple concept that allows us to represent numbers in different form.
It's like translating one language into another.
By dividing the percentage by 100, we scale it down to a decimal representation.
Learn more about the percent visit:
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