Answer:
$201.99
Step-by-step explanation:
Given that:
Amount held on Monday = $61.72
Amount withdrawn on Tuesday = $57.00
Amount deposited on Thursday = $197.27
Final balance :
Amount held on Monday - Amount withdrawn on Tuesday + Amount deposited on Thursday
$61.72 - $57.00 + $197.27 = $201.99
Hence, final balance = $201.99
Use the Binomial Theorem/Pascal's Triangle to expand (2a + 2b)^5
Answer:
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
============================================================
Explanation:
Let's use Pascal's Triangle
In the row that starts with 1,5,... we have the values 1,5,10,10,5,1
These will be the coefficients of the terms.
Let x = 2a and y = 2b
We want to expand out (x+y)^5
Using pascals triangle, we get the following expansion
(x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5
The numbers in bold are the coefficients 1,5,10,10,5,1 found earlier.
Note how the exponents for x start at 5 and count down to 0; while the y exponents start at 0 and count up to 5. For any term, the x and y exponents always add to 5 for the expansion of (x+y)^5. In general, the exponents of any term will add to n for (x+y)^n.
At this point, we plug in x = 2a and y = 2b
Since this will clutter things a bit, I'll do it term by term
1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^55x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^210x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^35x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^41x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5So in the end, the expression (2a+2b)^5 expands out to
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
The binomial theorem uses the same basic idea, but instead of using Pascal's Triangle to get the coefficients, you'll use the nCr combination formula.
Answer: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex].
Using Pascal's triangle we get:
[tex](x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5[/tex]
Here, x = 2a and y = 2b
So the terms become:
[tex]1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^5\\5x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b\\10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^2\\10x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^3\\5x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^4\\1x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5\\[/tex]
Hence: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex]
Learn more: https://brainly.com/question/13769924
I need help on this question!
Answer:
110 cookies in 180 minutes
Step-by-step explanation:
Write the slope intercept form of the equation of the line through the given point with the given slope through (-2,5),slope-3/2
Answer:
Slope Intercept Form: y= -3/2× + 2
7. Find the slope of the line.
Answer:
5
Step-by-step explanation:
take 2 points on the graph, for example (4,20) and (2,10) use y2-y1/x2-x1 to solve ,plug in the values 20-10/4-2= 10/2 = 5
write 600 as a product of a prime factor give your answer in index form
Answer:This is problems on common factors.
(a) 600 = 2 × 2 × 2 × 3 × 5 × 5
= 2³ˣ 3 ˣ 5²
(b) The highest common factors could be calculated using factors methods and the divisional methods.
Here we go.
(i) 600 = 2³ ˣ 3 ˣ 5²
1050 = 2 ˣ 3 ˣ 5² ˣ 7, the highest common factor HCF will be
HCT = 2 ˣ 3 ˣ 5²
= 150.
The divisional methods.
600) 1050 ( 1
- 600
------
450 ) 600 ( 1
- 450
------
150 ) 450 ( 3
- 450
------
000
So the answer is 150, the principle is that you continue to divide and subtract until you arrive at zero.
Answer = 150
If this is incorrect you should report my answer... Hope this was helpful... Stay safe and have a great weekend!!! :D
Need Help ASAP I’m having trouble
Answer:
ok
Step-by-step explanation:
nerd nerd nerd nerd lolololollool
Name the point of concurrency shown. Please please don’t answer if you don’t know it!!!
Answer:
Circumcenter
Step-by-step explanation:
Which of the following is equivalent to the addition problem below?
27.93 +61.63
If a ∥ b and e ∥ f, what is the value of y?
87
88
91
92
Answer:
88 i believe
Step-by-step explanation:
Answer:
92
Step-by-step explanation:
Angle (x+1) is equal to 92 degrees, and x equals 91. If x equals 91, then (x+1) equals 92. (x+1) and angle y are equal angles, so therefore, you can determine that angle y is equal to 92 degrees.
-I got the question right on the test
Hope this helps!
If a toy rocket is launched vertically upward from the ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation:
h(t) = -16t^2 + 128t
What is the maximum height the rocket reaches?
Answer:
The maximum height of the rocket is 256 feet
Step-by-step explanation:
The vertex form of the quadratic function f(x) = ax² + bx + c is
f(x) = a(x - h)² + k, where
(h, k) is the vertex pointh = [tex]\frac{-b}{2a}[/tex] and k = f(h)(h, k) is a minimum point if a > 0 and a maximum point if a < 0Let us use these rules to solve the question
∵ h(t) = -16t² + 128t
→ Compare it by the form of the quadratic function above
∴ a = -16 and b = 128
∵ a < 0
∴ The vertex (h, k) is a maximum point
∴ The maximum height of the rocket is the value of k
→ Use the rule of h above to find it
∵ h = [tex]\frac{-128}{2(-16)}[/tex] = [tex]\frac{-128}{-32}[/tex]
∴ h = 4
→ Substitute x in the equation by the value of h to find k
∵ k = h(h)
∴ k = -16(4)² + 128(4)
∴ k = -256 + 512
∴ K = 256
∴ The maximum height of the rocket is 256 feet
Plz answer these two and I will give you brainliest
Answer:
1. -9. 2.i cant see what all the options are but the slope is y= 1/2x -3
Step-by-step explanation:
Hope this helps :)
how to write thirty six thousanths in standard form
Answer:
36,000
Step-by-step explanation:
Answer:
3600
Step-by-step explanation:
because that's how you write it so yes do it please this is the answer s itch wi guy if i.p.o fallacy hallmark plz upload pda fool jsa xxl la all pda all jazz dlp jazz all
The number one selling item at Sam’s Swim Shop is a beach towel. It is priced at $7.50 , How much will Mrs. Wilson spend if she purchases 4 beach towels and pays 6% sales tax ?
Answer:
$31.80
Step-by-step explanation:
Need help ASAP please give answer in cm squared
Answer:
17×15=255
Step-by-step explanation:
you do base times height
simplify each expression
(e^2)(g)(g^4)(e^3)
(e)(e^2)(e)
9514 1404 393
Answer:
e^5g^5e^4Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
__
[tex](e^2)(g)(g^4)(e^3)=e^{(2+3)}g^{(1+4)}=\boxed{e^5g^5}\\\\(e)(e^2)(e)=e^{(1+2+1)}=\boxed{e^4}[/tex]
Write the equation for a parabola with the focus at
(-1, 4) and the equation of the directrix x = 5.
(x + 1)2 = 3(y-4)
(y-4)2 = 12(x + 1)
(y-2)2 = -3(x – 4)
(y-4)2 = –12(x - 2)
Jeff has two sticker-printing machines. Each machine can print 42 stickers per minute. On day 1, only the first machine was used, and it printed 89 stickers. On the following day, the first machine printed for x minutes and the second machine printed for y minutes. Which expression shows the total number of stickers printed by both machines during these two days? (1 point) a 131x + 42y b 42 + 89x + y c 89 + 42x + 42y d 89x + 84y
Answer:
c 89+42x+42y
Step-by-step explanation:
On day 1 :
First Machine= 89 stickers
Second Machine= none
On day 2 :
First Machine= ? stickers ( if in 1min = 42stickers
x min=?
( x min/1 min × 42stickers)
=42x stickers.
Second Machine=?stickers ( if in 1min = 42stickers
y min=?
( y min/1 min × 42stickers)
=42y stickers.
Total = 89 + 42x + 42y
3
..
4) through: (-2,5), slope
2.
Answer:
y - 5 = 2(x + 2)
General Formulas and Concepts:
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate
y₁ - y coordinate
m - slope
Step-by-step explanation:
Step 1: Define
Slope m = 2
Point (-2, 5)
Step 2: Create equation
y - 5 = 2(x + 2)
I REALLY NEED HELP WITH ALL OF THESE!!
Label each type of slope ( Positive, Negative, Zero, Undefined)
Answer:
1. negative 2. zero 3 undefined 4 positive
Step-by-step explanation:
If the movie theater seats 328 people, what is the maximum amount of money the theater can bring in during a showing? (Do not include labels with your answer, just type in the number.)
The answer would be 3900 money
Determine the value of x.
find the LCM and HCF of 110 and 220 by prime factorization, what do u observe
Answer:
GCF= 2 x 5 x 11 = 110
LCM= 2 x 2 x 5 x 11 = 220
Step-by-step explanation:
please help im so confused at math pls help
Answer:
where is the question ??
Just answer correctly to get brainleist and 10 pts! :)
Answer:
B
Step-by-step explanation:
x is repeated
What is the distance between (4,-1) and (0,1)
Answer:
answer is in the image below
Step-by-step explanation:
Use the distance formula to determine the distance between two points.
What percent of 202 is 34
Answer:
Result: 68.68
68.68 is 202% of 34.
Step-by-step explanation:
:
202% × 34 = 68.68
Hope it helps :)
Answer:
16.8%
Step-by-step explanation:
We can write this as: is over of equals percent over 100. We need the percentage, so we leave the percent part blank.
34 = p Multiply across: 34*100=3,400
202 100 Divide: 3,400/202=16.8 (rounded)
Hope this helps!! Have a great day C:
The larger of two numbers is sixteen less than twice the smaller number. If the sum of the numbers is 44, find the two numbers. Write your answer as two numbers separated by a coma.
Answer:
20, 24
Step-by-step explanation:
smaller: x
larger: 2x - 16
x + 2x - 16 = 44
3x -16 = 44
3x = 60
x = 20
smaller: x = 20
larger: 2x - 16 = 2(20) - 16 = 24
2 points
2) Mark bought a new suit for $139. The sales tax was 8.5%. What is the
total cost of the suit?*
the perimeter of an isosceles triangle in which the equal sides measures 12cm each and third side is 8cm_____. please show the working too ^^
Use the formula P = 2a+ b.
Let a = 12
Let b = 8
P = 2(12) + 8
P = 24 + 8
P = 32
I need help please!!
Answer:
1
Step-by-step explanation:
The line goes through the point 1, so that will be the slope.