The fourth term of the given expansion is [tex]-280x^{3}[/tex].
What is binomial expansion?
The binomial expansion is used to expand and write the terms which are equals to the natural number exponent of the sum or differences of two terms.
The general term of the binomial expansion is given by[tex]T_{r+1} =nC_{r} x^{n-r} y^{r}[/tex]
According to the given question
We have,
A binomial expression, [tex](1-2x)^{n}[/tex]
and, the binomial coefficients are taken from the row of Pascal's triangle 1 6 15 20 15 6 1
⇒ n = 7
Therefore,
The fourth term of the expansion of [tex](1-2x)^{n}[/tex] is given by
[tex]T_{3+1} = 7C_{3} 1^{7-3} (-2x)^{3}[/tex]
[tex]T_{4} =\frac{(7)(6)(5)(4)(3!)}{3!(4)(3)(2)} (1)(-2x)^{3}[/tex]
[tex]T{4} = -280x^{3}[/tex]
Hence, the fourth term of the given expansion [tex](1-2x)^{3}[/tex] is [tex]-280x^{3}[/tex].
Learn more about the binomial expansion here:
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Can y’all help on question 29?!
Answer:
Option C: 20 cm^2
Step-by-step explanation:
Essentially, surface area is just area added up. In this question, there are 4 same rectangles and 2 squares with the areas given. So you have to figure out the total.
Since there are 4 rectangles and each of them has an area of 4cm just multiply 4 by 4 to get 16.
Then, since there are 2 squares with an area of 2 cm each just multiply 2 by 2 to get 4.
Add both numbers, 16 + 4 = 20 and you get your answer.
The total surface area would be 20cm^2.
if jane give £2 pounds to charlotte they will have equal amount of money. instead
charlotte give £4 to jane the ratio of jane's money to charlotte will be 2:1. how much
do jane and charlotte each have to start with
One number is 5 more than eight times another. Their sum is 104. Find the numbers. Enter your answer as a list of numbers separated by a comma: a,b
Answer:
la conclave Tu pa I ya me tiene dcado esta ndjfjejcuejfn
Step-by-step explanation:
jdjfiifw rjfje djfje fjdjje fjejrj cjdjrn d djdjjff jddjd bdbdjrjrbd. dbebdb d d dbrbdbd. d dd rjrj I'd. drbdbdb. ffbdjjdjdb. d f. bdjdbd bdjdjdjd d dbdhn
find the probability of spinning an A 3 times
The height of the tank is 11 m and the radius of the tank is 5 m. the height of the water is 6 m and the radius of the water is 3 m. how much more water in cubic meters could you fit in the tank?
Answer:
221 cubic metre.
Step-by-step explanation:
Volume of water in tank (v) = π × {3}^{2} × 6
= 54π cubic metre
Volume of tank (v') = π × {5}^{2} × 11
= 275π cubic metre
More Water that can be fit in the tank = v' - v
=275π - 54π
= 221π cubic metre.
ANS.
According to a NY Times article on December 13, 2009, The average selling price of a 32-inch LCD TV was $600. Use the annual CPI values from your text to compute the cost of that same TV in 2010 dollars. Express your answer rounded to the nearest cent.
Answer:
Your answer should be 647.51
Explanation : the price was 215.949 in December, 2009.
the price was 233.049 in December, 2013.
divide 233.049 by 235.949 and got 1.079185363.
multiply that by 600 and got 647.5112179.
The cost of the TV in 2010 is $647.5
Calculations and ParametersGiven that the complete information contains the Consumer Price Index values:
To find the CPI,
CPI= [tex]\frac{C_t}{C_0}[/tex]
Where C_t= cost of the market basket in the current period
C_0 = cost of the market basket in the base period
In December 2009, the price was 215. 949
In December 2013, the price was 233.049
Hence,
215. 949/233.049
= 1.079185363.
Then we would multiply by the base selling price
[tex]1.079185363 * 600 = 647.5112179.[/tex].
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Có 6 quyển sách và 7 quyển vở. Hỏi có bao nhiêu cách chọn
một trong các quyển nói trên?
Answer:
eeeeeee
Step-by-step explanation:
xdddddddudjdjdjdjdjdjsjsjsjsjsjsjsjjsjsjsjsjsjsjsjsjsjsjjs
look at pic 10 pts will mark brainilest
Answer:
111
Step-by-step explanation:
y-18=14
y=14+18
y=32
substitute the vale of y
3(y+5)
3(32+5)
3*37
111
There were 436 tickets purchased for a major league baseball game. The general admission tickets cost $6.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $3284.00. How many of each kind of ticket were purchased?
How many general admission tickets were purchased? ____
How many upper reserved tickets we purchased? ___
Answer:
How many general admission tickets were purchased? __136__
How many upper reserved tickets we purchased? _300_
Step-by-step explanation:
Let the number of general tickets = g.
Let the number of reserved tickets = r.
6.5g + 8r = 3284
g + r = 436
6.5g + 8r = 3284
(+) -8g + -8r = -3488
--------------------------------
-1.5g = -204
g = 136
g + r = 436
136 + r = 436
r = 300
Answer:
How many general admission tickets were purchased? __136__
How many upper reserved tickets we purchased? _300_
Answer:
136 general admission tickets were purchased
300 upper reserved tickets were purchased
Step-by-step explanation:
This is a classic system of equations problem. Let the number of general admission tickets sold be [tex]g[/tex] and the number of reserved tickets sold be [tex]r[/tex]. We can write the following system of equations:
[tex]\begin{cases}6.50g+8.00r=3284,\\g+r=436\end{cases}[/tex]
Multiply the second equation by -8 and add both equations to isolate [tex]g[/tex]:
[tex]-8(g+r)=-8(436),\\-8g-8r=-3488,\\\begin{cases}6.50g+8.00r=3284,\\-8g-8r=-3488\end{cases},\\-1.5g=-204,\\g=\frac{-204}{-1.5}=\boxed{136}[/tex]
Now substitute [tex]g=136[/tex] into [tex]g+r=436[/tex] to find the number of reserved tickets sold:
[tex]g+r=436,\\136+r=436,\\r=436-136=\boxed{300}[/tex]
Angles D and G are complementary. What statement must always be true about angles D and G?
Answer:
They will never intersect. I'm pretty sure that is right
In circle R, What is the name of line segment BE and AD?
a diameter is a line that starts from the circumference to the other part of the circumference
Wei has 150.00 to make a garland using 60-cent balloons
Answer:
The answer is 0.60b + 0.30w = 150; 60 + 0.30w = 150
Step-by-step explanation:
1. Jeremy has $12000 cash to invest in the bank compounded at 4% interest annually.
a.
What equation will calculate the value in x years? y =
Answer:
[tex]A(x) = 12000(1.04)^x[/tex]
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
$12000 cash
This means that [tex]P = 12000[/tex]
Compounded at 4% interest annually.
This means that [tex]r = 0.04, n = 1[/tex]
What equation will calculate the value in x years?
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(x) = P(1 + \frac{r}{n})^{nx}[/tex]
[tex]A(x) = 12000(1 + 0.04)^x[/tex]
[tex]A(x) = 12000(1.04)^x[/tex]
Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.
Answer:
x=3 and x=-2 is the root of given eq
Answer:
Use the zero product property to find the solutions to the equation x2 – x – 6 = 0.?
x = –2 or x = 3 is the answer
Step-by-step explanation:
verify that A(3, 1), B(0, 5), and C(-1, -1) are the vertices of a right triangle.
Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?
O 1+√211
O-1+ 19;
O 1+2 V19;
O 1+ 19;
Answer:
1 ± √19i
Step-by-step explanation:
Circle O has a circumference of approximately 25077 ft.
Nhat is the approximate length of the diameter o?
40 ft
O 80 ft
0 125 ft
250 ft
Answer:
7,982 ft
Step-by-step explanation:
c = πd
25077 = πd
Divide both sides by π
25077/π = d
d = 7,982 ft
----------------------
I think the 25077 number in the question might be a typo
Just divide the correct number by 3.14 to get the diameter.
Help me out plsssssss
Answer:
125
Step-by-step explanation:
the bearing of b to a is equal to 85+45
What I Can Do
Directions: How can we help minimize the amount of electricity and water
to be consumed in a month? List down at least 3 ways each. Write your
answers on a sheet of paper.
ಠ_ಠ (눈‸눈) (⌐■-■)
(ب_ب) ¯\_ಠ_ಠ_/¯
By the distributive law, 49 * 17 + 49 * 3 =
Answer:
980
hope it helps
solve 14a-3b+9c=18 for a. Do not use a= in your answer
Answer:
9/7 + 3/14b - 9/14c
Step-by-step explanation:
See image below:)
Find the integer solutions that
satisfy the inequality, 2 < x + 5<7.
Give your answer as an inequality.
Use the < or > signs to represent your
inequality
Given:
The compound inequality is:
[tex]2<x+5<7[/tex]
To find:
The integer solutions that satisfy the given inequality.
Solution:
We have,
[tex]2<x+5<7[/tex]
Subtracting 5 from each side, we get
[tex]2-5<x+5-5<7-5[/tex]
[tex]-3<x<2[/tex]
All the real numbers between -3 and 2 are in the solution set but -3 and 2 are not included in the solution set.
The integers between -3 and 2 are -2, -1, 0, 1.
Therefore, the integer solution of the given inequality are -2, -1, 0, 1. The answer as an inequality is [tex]-3<x<2[/tex].
Which ones are correct?
Answer:
Th answer is D
Step-by-step explanation:
A rectangle has a length of 16
inches and a width of 6 inches. A similar rectangle has a length of 24 inches. What is the width of the similar rectangle?
Answer:
9 inches
Step-by-step explanation:
Given
Let;
[tex]L = Length; W= Width[/tex]
So:
[tex]L_1=16in; W_1 = 6in[/tex]
[tex]L_2 = 24[/tex]
Required
Determine [tex]W_2[/tex]
To do this, we make use of the following equivalent ratios
[tex]L_1 : W_1 = L_2:W_2[/tex]
This gives
[tex]16 : 6= 24:W_2[/tex]
Express as fraction
[tex]\frac{6}{16}= \frac{W_2}{24}[/tex]
Multiply by 24
[tex]W_2 = 24 * \frac{6}{16}[/tex]
[tex]W_2 = 9[/tex]
Are the triangles congruent? Why or why not?
Answer:
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Step-by-step explanation:
(d) 4 – 0.2 x (0.4 + 0.7)
Answer:
4d - 0.22
Step-by-step explanation:
Find the size of the of angle x.
Answer:
80 degrees
Step-by-step explanation:
Since a triangle is 180 degrees
you then add to 2 degrees given and subtract it from 180
65+35=100
180-100=80 degrees
Calculating area of rectangle
Your measurments Another student's measurements
Length (cm) 20.70 20.74
Width (cm) 10.44 10.46
Area (cm2)
Required:
Why might two students have different calculated areas when measuring the same rectangle?
Answer:
[tex]Area = 216.108cm^2[/tex] --- You
[tex]Area = 216.940cm^2[/tex] --- Another student
Reason: Because there is a variation in the given dimensions
Step-by-step explanation:
Given
Your measurement
[tex]Length = 20.70cm; Width =10.44cm[/tex]
Another students'
[tex]Length = 20.74cm; Width =10.46cm[/tex]
Solving (a): The area
Area is calculated as:
[tex]Area = Length * Width[/tex]
For you
[tex]Area = 20.70cm * 10.44cm[/tex]
[tex]Area = 216.108cm^2[/tex]
For the other student
[tex]Area = 20.74cm * 10.46cm[/tex]
[tex]Area = 216.940cm^2[/tex]
Solving (b): Reason for the variation in the areas
The given measurements are estimates of the dimensions of the rectangle.
Since there is a variation in the estimates, there will be some level of variation in the calculated area.
Write the slope-intercept form of the equation of the line through the point (-1,-4) with the slope of 6.
Answer:
y-y1=m(x-x1)
y+4=6(x+1)
y=6x+2
factorise y^3- 7y+6
Answer:
(y−1)(y−2)(y+3)
Step-by-step explanation:
Factor y3−7y+6
y3−7y+6
=(y−1)(y−2)(y+3)
Answer:
(y - 2) (y-1) (y+3)
Step-by-step explanation:
y³-7y+6
= y³ +2y² - 2y² - 3y - 4y +6
= ( y³ +2y² - 3y) - (2y² + 4y -6)
= y( y² +2y -3) - 2( y² + 2y -3)
= (y² +2y -3)(y-2)
= ( y² +3y -y -3)(y-2)
= [ y( y+3) -(y+3)] ( y-2)
= (y-1)(y+3)(y-2)
