hsksebhssv hnshsnsjdndj ldgehsiw c 3072729 lvwjaiwn sj. +a iwiwirbfhx ska hamd +675196 = $ 20000 solved
In the expansion of (1 + ax)24 where a > 0, the coefficient of x² is 1104. Find the value of a.
The required value of a is 2 if the coefficient of x² is 1104 of the expansion (1 + ax)²⁴.
What is the Binomial Theorem?According to the binomial theorem, it is possible to expand any non-negative power of binomial (x + y) into a sum of the form,
(x+y)ⁿ = ⁿC₀xⁿy₀ + nC₁ xⁿ⁻¹y₁ + nC₂ xⁿ⁻² y2 + ... + nC x¹yⁿ⁻¹ + nCn x°yⁿ
where n ≥ 0 is an integer and each ⁿCₓ is a positive integer known as a binomial coefficient.
We have been given that the expansion as
(1 + ax)²⁴
As per the binomial theorem expansion of the term 3,
T₃ = ⁿC₂ a² x²
Since the coefficient of x² = 1104
⇒ n!/2!(n-2)a² x² = 1104
Here n = 24
⇒ 24!/2!(24-2)a² = 1104
⇒ 276a² = 1104
⇒ a² = 1104/276
⇒ a² = 4
⇒ a = 2
Therefore, the required value of a is 2 if the coefficient of x² is 1104 of the expansion (1 + ax)²⁴.
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which expression represents an irrational number
See your levels
Mr. Camacho has 275 rubber stamps. He wants to give the same number of stamps to
each of his 8 students. If he gives away as many stamps as he can, how many stamps will be
left over?
Submit
rubber stamps
I do
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Answer:
3 Stamps left
Step-by-step explanation:
275/8=34.375
34*8=272
275-272=3
Answer: 3
If P=5+7+9+11+...+101 and Q=9+11+13+15+...+103 are sums of arithmetic sequences, determine which
is greater, P or Q, and by how much.
In the sequence, Q is greater by 115.
How to calculate the value?From the information, P=5+7+9+11+...+101 and Q=9+11+13+15+...+103.
It should be noted that by looking at the figures the greater value will be Q as it began with a higher number.
The difference will be:
= 5 + 7 + 103
= 115
Therefore, in the sequence, Q is greater by 115.
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if it takes 6 men 25 hours to dig 5 holes, how many hours does it take to dig 5 holes with 10 men
Answer: Answer is 15 hours
Step-by-step explanation:Given 6 men dig 5 holes in 25 hours
Therefore 10 men will take to dig 5 holes is
workers(1) × time(1) = workers(2)×time(2)
(This formula is used when Total work is same)
where workers(1)= 6 men
Time (1) = 25 hours
workers (2) = 10 men
We have find out Time(2)=T(2)
by applying above formula
6×25=10×T2
after simplify
T2= 15 hours
A textbook store sold a combined total of 414 physics and psychology textbooks in a week. The number of physics textbooks sold was 68
more than the number of psychology textbooks sold. How many textbooks of each type were sold?
HELP ASAP!!!
Evaluate the polynomial for the given value by using synthetic division.
P(x) = 3x4 - x³ + 7x - 2 for x = 4 and x = -2
A.802; 52
B.-238; 32
C.730; 40
D.202; -44
Answer:
I'm assuming that is 2x squared, and not 2 multiplied by 2, as a given question usually wouldn't come in such a silly format. I do wish people would start using (2x^2) or (2x²), though.Just substitute the value of x (-3) in to the equation to find the value of y, or P(x).2(-3)² + 7(-3) - 1 = -4
Step-by-step explanation:
Find the equation of a line whose graph passes through the points (8,1) and (0,1)
Answer: y=1
Step-by-step explanation:
Slope formula: m=(y2-y1)/(x2-x1)
m=(1-1)/(0-8)
m=0/(-8)
m=0
y=mx+b
1=0(0)+b
b=1
y=0x+1
y=1
Find an equation of variation in which y varies jointly as x and z, and y= 48 when x = 8 and z=6
Answer:
y = xzStep-by-step explanation:
Joint variation equation:
y = kxz, where k- coefficient of variationGiveny = 48,x = 8,z = 6Find the value of k by plugging in the given values:
48 = 8*6k48 = 48kk = 1The equation is:
y = xzA charter tours bus driver can fit an average of 54 passengers on his bus for each tour. He is scheduled to run 9 tours over the next month. At this rate, how many passengers will he give tours to on his bus?
The number of passengers that he will give tours to on his bus is 486 passengers.
How to compute the value?From the information, the charter tours bus driver can fit an average of 54 passengers on his bus for each tour and he is scheduled to run 9 tours over the next month.
The number of passengers that he will be able to carry will be:
= 54× 9
= 486
There'll be 486 passengers.
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Find the area and perimeter. The figure shows a triangle. One side is given by x minus 7 units. The second side is given by 2 x plus 5 units. The third side is equal to 12 units. The height from the third side is given by x plus 6 units. Hint: The height of a non-right triangle is the length of the segment of a line that is perpendicular to the base and that contains the opposite vertex. 12x + 72; 3x + 10 6x + 36; 3x + 10 6x + 36; 10x + 3 12x + 72; 10x + 3
Area of the triangle = 6x + 36
Perimeter of the rectangle = 3x + 10
How to Find the Area and Perimeter of a Triangle?Given the following parameters of a triangle as shown in the image attached below, its area and perimeter is calculated as shown below?
Area of the triangle = 1/2(base)(height) = 1/2(12)(x + 6)
Area of the triangle = 6(x + 6)
Area of the triangle = 6x + 36
The perimeter of the triangle = sum of all the three sides of the given triangle = (x - 7) + (2x + 5) + (12)
Perimeter= x - 7 + 2x + 5 + 12
Add like terms
Perimeter= x + 2x - 7 + 5 + 12
Perimeter= 3x + 10
Therefore, we have:
Area of the triangle = 6x + 36
Perimeter of the rectangle = 3x + 10
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Find the next item in the
pattern:
-3, 6, -12, 24, ...
........... what is a day of the week that you do not like? and why. Just curious!
In 7 days of a week, most of us do not like Monday because all the work starts again on monday after a weekend.
We need to tell the day in a week which we do not like in a week.
What is the first day of a week?Sunday is the first day of a week.
In a week there will be 7 days, sunday, monday, tuesday, wednesday, thursday, friday and Saturday. In this most of the people dont like monday because after a weekend the starting would be monday where one has to start the work.
Therefore monday is a day of week which i do not like.
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Find all x-intercepts of the function. Express your answer as a list of x-values.
f(x)=-2x^5+10x^3
Answer:
Step-by-step explanation:
45
6t^2/5+11t^1/5+3=000
You didn't provide a lot of info regarding the given question, however if you are looking to solve for t:
_______________________________________________
Isolate the variable by dividing each side by factors that do not contain the variable.
Solution's Exact Form:
[tex]t=-\frac{1}{243},-\frac{243}{32}[/tex]
_______________________________________________
Hope this helps! If not, please provide further info if you can regarding this question and I'll see what else I can do to help. If this did help however, lmk! Thanks and good luck!
2. Last week, Abe's carpet store sold 160 square feet of a particular carpet for $878.40. Bob's carpet store sold 85 square feet of the same carpet for $466.65
a. Is Cost proportional to area for this carpet? Show all relevant calculations and then explain your conclusion in a full sentence.
b. Answer ONE of the questions below depending on whether or not cost is proportional to area for this carpet
if cost is proportional to area, what is the cost of 118 square feet of carpet? Show your work. Use dimensional analysis
if cost is not proportional to area, which store has the better unit price for carpet explain your choice.
Consequently, the carpet's price is diversely correlated with its size. Then the cost of the carpet will be $647.82.
What are ratio and proportion?160 square feet of a certain carpet were purchased for $878.40 last week at Abe's carpet shop. The identical carpet, measuring 85 square feet, cost $466.65 at Bob's Carpet.
The cost of carpet per square foot in both cases will be
In the First case, we have
⇒ 878.40 / 160
⇒ $5.49 per square foot
In the second case, we have
⇒ 466.65 / 85
⇒ $5.49 per square foot
Consequently, the carpet's price is directly correlated with its size. Then the equation will be
Cost = 5.49 x Area
Then the cost of the carpet when the area is 118 square feet will be
Cost = 5.49 x 118
Cost = $647.82
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About how many pizzas does Mr. T's Pizzeria sell each week? Remember, there are 7 days in a week.
Mr. T's Pizzeria Daily Sales
Types of Pizza Number of Pizzas
Pepperoni 29
Sausage 35
Veggie 42
Cheese 28
A.
about 1,000 pizzas
B.
about 1,200 pizzas
C.
about 1,400 pizzas
D.
about 2,000 pizzas
Answer: a
Step-by-step explanation: hope it helps.
Refer to the number line. Find the coordinate of point X such that the ratio of MX to XJ is 3:1.
The coordinate of point X such that the ratio of MX to XJ is 3:1 is 12
How to determine the coordinate of point X?The coordinates are given as:
M = 2
J = 18
The ratio is given as:
Ratio = 3 : 1
The location of the point X is then calculated as:
X = Ratio * (J - M)
This gives
X = 3/(3 + 1) * (18 - 2)
Evaluate
X = 3/4* 16
This gives
X = 12
Hence, the coordinate of point X such that the ratio of MX to XJ is 3:1 is 12
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Step-by-step explanation:
show how to work out the question
Is -1.5 greater than 2.1
Question -: If ( 1 + tan θ ) ( 1+ ∅ ) = 2 , then what is ( θ + ∅ ) ?
a . 30⁰ b. 45⁰ c. 60⁰ d. 90⁰
Answer this question
Please Give Explanation
thanks
Correct choice is B.) 45°
The solution is in attachment ! do check it
Step-by-step explanation:
6.25 points
Find the GCF for the list.
10m4, 40m⁹
10m5
40m4
10m4
6.25 points
hey
list
Can someone please help Find the perimeter of each
figure using the given side lengths?????????
The perimeter of the figure using the given side lengths is 12x - 10
What are perimeters?The perimeter of a shape is the sum of the side lengths of the shape.
For all regular quadrilaterals, you add up the side lengths to determine the area
How to find the perimeter of the figure using the given side lengths?From the given figure, we have the side lengths to be:
x, 2x + 5, 6x - 17 and 3x + 2
Add these side lengths
So, we have
Perimeter = x + 2x + 5 + 6x - 17 + 3x + 2
Evaluate the like terms
Perimeter = 12x - 10
Hence, the perimeter of the figure using the given side lengths is 12x - 10
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When you draft a budget, you should include an _________________. This is extra money set aside to be used for unpredictable expenses, such as medical bills and vehicle repairs.
Group of answer choices
annual expenses
expense summary
fixed expenses
Emergency fund
Answer:When you draft a budget, you should include an _________________. This is extra money set aside to be used for unpredictable expenses, such as medical bills and vehicle repairs
Step-by-step explanation:
Are 12 17 and 14 19 determined ratio are proportional
No, 12 17 and 14 19 determined ratio are not proportional.
What are proportional ratios?If two ratios depict the same connection, they are said to be proportionate. By writing two ratios as fractions and then reducing them, one may determine if they are proportionate. Your ratios are proportional if the reduced fractions are equal.
We can observe that 17 and 19 are prime numbers,
So, 12 : 17 cannot be simplified further,
Neither 14 : 19 can be simplified.
⇒ 12 : 17 ≠ 14 : 19
∴ We can say that 12 17 and 14 19 determined ratio are not proportional.
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Use the given domain to find the range of each function. F(x)=|x|, D={-4,0,-3}
Answer:
[tex]R=\{0,3,4\}[/tex]
Step-by-step explanation:
We can find the range by finding the set of values the function takes for each element in the domain.
[tex]F(-4)=|-4|=4 \\ \\ F(0)=|0|=0 \\ \\ F(3)=|3|=3 \\ \\ \therefore R=\{0,3,4\}[/tex]
The domain and the range of the function are
Domain, D = {-4,0,-3}Range, R = {4,0,3}Calculating the domain and range of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = |x|
The rule of a function is that
The domain is the x valuesThe range is the f(x) valuesUsing the above as a guide, we have the following:
Domain, D = {-4,0,-3}
Range, R = {4,0,3}
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Helppp!
h(x)=x^2-6
Evaluate h(-3)
Answer:
3
Step-by-step explanation:
input -3 into h(x)=x^2-6
h(-3)=-3^2-6=9-6=3
A divided by b is 4, then what’s is b divided by a?
Answer:
the answer is
Step-by-step explanation:
A is more likely to be 12 and B could be 3
so 12/3=4
and
3/12= 0.25
A function, fx), represents the height of a plant x months after being planted. Students measure and record the height on a monthly basis.
Select the appropriate domain for this situation.
OA
the set of all integers
OB. the set of all positive real numbers
OC. the set of all positive integers.
OD. the set of all real numbers
Answer:
C. the set of all positive integers
Step-by-step explanation:
You want to know the appropriate domain of the function f(x) where x is months after a plant was planted, and f(x) is the height of the plant.
DomainThe domain of a function is the set of values of the independent variable for which the function is defined. In this case, the independent variable is x, the number of months after the plant was planted. Months are counted using the natural numbers, the set of all positive integers.
The appropriate domain is the set of all positive integers.
__
Additional comment
As a practical matter, the domain will have an upper limit, so will not actually be all positive integers.
The range of function values is likely the set of positive real numbers, though it might be integers if the measurements are recorded as integer values (mm or cm or in, for example).
please help, Solve K-PRT for R.
Answer:
r = [tex]\frac{k}{pt}[/tex]
Step-by-step explanation:
I think that you mean
K = PRT Divide both sides by pr
[tex]\frac{k}{pr}[/tex] = [tex]\frac{prt}{pr}[/tex] On the right sides the pr's on the top and bottom cancel each other out and you are left with
r = [tex]\frac{k}{pr}[/tex]
Lizzy had #500, John has #50
FIFI will have #700.Who has more money amongst the three.
Answer:
John
Step-by-step explanation:
it says Lizzy had which means we don’t know how much she has now. It says Fifi will have so we don’t know how much they have right now. But it says John has so we know what he has so therefore he has the most as of right now
3/4 + 7/8 + 3/4 + 1/2 + 7/8
Answer:
=
15/4
(Decimal: 3.75)
Step-by-step explanation: