In the binomial development, the main problem is calculation of binomial coefficients.
If we want to get term a∧8*b∧2 we see that this is the third member in binomial development (n 2) a∧n-2*b∧2
The given binomial is ((1/3)a∧2 - 3b)∧6, the first element is (1/3)a∧2, the second element is (-3b) and n=6 when we replace this in the formula we get
(6 2) * ((1/3)a∧2)∧(6-2) * (-3b)2 = (6*5)/2 * ((1/3)a∧2)∧4 *9b∧2= 15*(1/81)*9 *(a∧8b∧2) =
= 15*9* a∧8b∧2 = 135*a∧8b∧2
We finally get numerical coefficient 135
Good luck!!!
The numerical coefficient of the [tex]a^8*b^2[/tex] term in the expansion of [tex]((1/3)a^2 - 3b)^6[/tex] is -45/16.
Explanation:The numerical coefficient of the [tex]a^8*b^2[/tex] term in the expansion of [tex]((1/3)a^2 - 3b)^6[/tex] can be found using the binomial theorem, which states that [tex](x+y)^n = \sum (n choose k) x^(^n^-^k^) y^k[/tex] where the sum is from k=0 to n. Here, x = [tex](1/3)a^2[/tex], y = -3b, and n = 6.
In the term [tex]a^8*b^2, a^2[/tex] is raised to the 4th power and -3b is raised to the 2nd power. Hence, we are looking for the coefficient in the term in the binomial expansion where [tex](1/3)a^2[/tex] is raised to the 4th power and -3b is raised to the 2nd power.
This can be calculated by multiplying together the coefficient '6 choose 4', the 4th power of [tex](1/3)a^2[/tex], and the 2nd power of -3b.
That leads to coefficient =[tex](6 choose 4)*((1/3)^4)*(-3)^2 * a^8 * b^2[/tex]. After calculation this simplifies to -45/16.
Learn more about Binomial Theorem here:https://brainly.com/question/30100273
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Georgia bought a pair of flip-flops that cost $3.46 and a pair of slip-on shoes that cost $9.87. She paid a total of what dollars for the two pairs of shoes.
Answer:
13.33
Step-by-step explanation:
Solve the system equation.
Answer:
A) (0, 2)
Step-by-step explanation:
Rewriting the second equation to the same form as the first, it becomes
... 1/2y = x + 1
... y = 2x + 2
Now, it is clear that both equations have the same y-intercept at y=2, so that is the solution.
... (x, y) = (0, 2)
John recieves £173 per week after working for 25 hours. How much does he get per hour
Answer:
Amount John gets paid per hour [tex]6.92[/tex] Dollars per hour ,
Step-by-step explanation:
To find how much he gets paid per hour we need to divide the total payment he received by the total number of hours he worked.
Amount John gets paid per hour = [tex]\frac{173}{25}[/tex] Dollars per hour.
=[tex]6.92[/tex] Dollars per hour
Jim has answered 7 e-mails this is 35% of the e-mails he must answer how many emails does he need to answer?
Answer: He needs to answer 20 emails.
Step-by-step explanation:
Given : Jim has answered 7 e-mails . (1)
This is 35% of the e-mails he must answer .
We can write 35% as 0.35.
Let x be the number of emails he need to answer.
Then, Number of mails he has answered = 0.35x (2)
From (1) and (2), we have
[tex]0.35=7\\\\\Rightarrow\ x=\dfrac{7}{0.35}=\dfrac{700}{35}=20[/tex]
Hence, he needs to answer 20 emails.
Are O, N, and P collinear? If so, name the line on which they lie.
We are given a figure where M, N , O and P points are given.
We need to explain if points O, N, and P collinear or not.
Note: All co-linear points are in a straight line.
From the figure, we can see that O and N points are in a straight line but point P is aside.
So, the points O, N, and P are not collinear.
Therefore, correct option is "No, the three points are not collinear".
please help on this one?
I think it is B. If you drew a graph of this and the x axis was time and the y axis is the enrollment then you would get 3 different x values and 1 y value. That's still a function. I've drawn it below.
Help With Proving Theorems
20 POINTS
1. If two vertical angles are supplementary, what is the measure of each angle?
Remember that when two angles are vertical angles, their angle measurements are the same, as the angles are congruent.
Note the Vertical Angle Theorem. Angles vertically opposite (directly opposite) when two lines intersect are congruent with each other.
Now note that supplementary means 180°
Set the equation. Let the angles = x
2x = 180
Isolate the x. Note the equal sign. What you do to one side, you do to the other. Divide 2 from both sides
(2x)/2 = (180)/2
x = 180/2
x = 90
90° is the measurement of each angle.
~Rise Above the Ordinary
Which of the following is the correct expansion of (x - 2)(x - 5)?
x2 + 7x + 10
x2 + 7x - 10
x2 - 7x - 10
x2 - 7x + 10
Use distributive property:
(a + b)(c + d) = ac + ad + bc + bd
(x - 2)(x - 5) = (x)(x) + (x)(-5) + (-2)(x) + (-2)(-5) = x² - 5x - 2x + 10
Answer: (x - 2)(x - 5) = x² - 7x + 10Can someone help me please?
Answer:
i think that the best answer to the question is b
Step-by-step explanation:
How do I find the zeros of x^4-10x^3-66x^2-94x-39
Answer: x = -1, -3, 7 + √62, 7 - √62
Step-by-step explanation:
q p
x⁴ - 10x³ - 66x² - 94x - 39
[tex]\frac{p}{q}[/tex] = +/- [tex]\frac{1*3*13*39}{1}[/tex]
possible rational factors: 1, -1, 3, -3, 13, -13, 39, -39
Use synthetic division or long division to see which factor will leave a remainder of 0.
try x + 1 = 0 ⇒ x = -1
-1 | 1 -10 -66 -94 -39
| ↓ -1 11 55 39
1 -11 -55 -39 0
(x + 1)(x³ - 11x² - 55x - 39)
next, try x + 3 = 0 ⇒ x = -3 for the new polynomial
-3 | 1 -11 -55 -39
| ↓ -3 42 39
1 -14 -13 0
(x + 1)(x + 3)(x² - 14x - 13)
Lastly: find the zeros by setting each factor equal to zero and solve.
x + 1 = 0 ⇒ x = -1
x + 3 = 0 ⇒ x = -3
x² - 14x - 13 = 0
[tex]x = \frac{-(b) +/- \sqrt{(b)^{2} -4(a)(c)}}{2(a)}[/tex]
[tex]= \frac{-(-14) +/- \sqrt{(-14)^{2} -4(1)(-13)}}{2(1)}[/tex]
[tex]= \frac{14 +/- \sqrt{196+52}}{2}[/tex]
[tex]= \frac{14 +/- \sqrt{248}}{2}[/tex]
[tex]= \frac{14 +/- 2\sqrt{62}}{2}[/tex]
[tex]= 7 +/- \sqrt{62}[/tex]
Denzel can mow 1/8 of his yard every 7 minutes. If he had 40 minutes to mow 3/4 of the yard, will he have enough time
Answer:
No. He is short by 2 minutes
Step-by-step explanation:
Given that Denzel can mow 1/8 of his yard every 7 minutes.
Hence he can mow the full yard in 7(8) = 56 minutes.
Now he has to do 3/4 of his yard and time is 40 minutes
For 3/4 of yard time taken would be = 3/4 (56) = 42 minutes.
If he had 40 minutes to mow 3/4 of the yard, he will not have enough time since he is short of time by 2 minutes.
mary pitches a ball. the initial height is 8 ft and velocity 80 ft per second. when will the ball hit the ground?
Initial velocity of the ball (u) = 80 ft/ sec
Final velocity of the ball after reaching the ground (v) = 0
Distance covered by the ball to reach the ground (s) = 8 ft
Let "a" be the acceleration of the ball.
We know, [tex]2as=v^{2}-u^{2}[/tex]
[tex]2a(8)=0-80^{2}=-6400[/tex]
[tex]a=-\frac{6400}{16}[/tex]
[tex]a=-400ft/s^{2}[/tex]
Let "t" be the time required to reach the ground.
We know,
[tex]v=u+at[/tex]
[tex]t=\frac{v-u}{a}[/tex]
[tex]t=\frac{0-80}{-400}[/tex]
[tex]t=0.2s[/tex]
The ball will hit the ground in 0.2 second.
Complete the two column proof
a. is Substitution Property
b. might be definition of supplementary angles
Answer:
B is the sum of adjacent angles is 180 degrees
Step-by-step explanation:
It is showing you that m∠3 and m∠4 "=" 180
During a promotional event a sporting good store gave a free t-shirt every eighth customer and a free water bottle every 10th customer which customer was the first to get a free t-shirt and a free water bottle
Answer:
40th customer
Step-by-step explanation:
Given that there is a promotional event
A sporting good store gave t shirt and free water bottle.
T shirt was given to 8th customer and water bottle to every 10th customer.
For the first person who should get both, he should have number as least common multiple of 8 and 10
8 = 2x2x2
10 = 2x5
Hence least common denominator = 2x2x2x5 = 40
Thus 40th customer will be the first to get both.
What is the number that has the same absolute value as 81
Martina works mowing lawns and babysitting. She earns 7.90 for mowing lawns and 6.90 for babysitting. How much will she earn for 7 hours of mowing and 1 hour of babystting
mowing lawns: 7 * $7.90 = $55.30
+ babysitting: 1 * $6.90 = $ 6.90
$62.20
Answer: $62.20
Geometry help , only answer if your sure please. The question is in the attached
Your answer would be D, The translation doesn't change the size or shape. Just location.
Hope this helped.
An urn contains 10 marbles: 4 red, 3 white, 2 blue, and 1 orange. (4 points) (a) What is the probability of drawing a marble that is red or white? (b) What is the probability of drawing a marble that is neither red nor white? (c) What is the probability of drawing a pair of marbles, one red and one white at the same time? (d) What is the probability of drawing a pair of marbles, one blue and one orange at the same time?
Answer:
a) 0.70
b) 0.30
c) 12/45 =4/15
d) 2/45
Step-by-step explanation:
a) Prob of drawing a marble red or white = No of red and white marbles/total marbles
= 7/10 = 0.70
b) Prob of drawing a marble neither red nor white = 1-7/10 = 0.30
c) Prob of drawing two marble one red and one white at the same time
= [tex]\frac{4C1 (3C1}{10C2 } =\frac{12}{45}[/tex]
d) Prob of drawing two marble one blue and orange white at the same time
= [tex]\frac{2C1 (1C1}{10C2 } =\frac{2}{45}[/tex]
Enter an equation that can be used to find x. (Picture below)
The equation ____ can be used to find x.
(2x+1)+89=180. 180 is the angle of a straight line. Set your two known sides equal to 180 and solve for x if needed.
PLEASE HELP ASAP
The length of a rectangle is 6m longer than its width. What are the possible widths if the area of the rectangle is at least 775cm^2?
Hey there!!
What is the area of a rectangle?
The area of a rectangle = Length × Breadth
Given :
Length is 6m longer than the width.
Hence, length = 6 + breadth
Area = ( 6 + breadth ) ( breadth )
Area = 6 breadth + breadth²
Area = 775
Hence, 775 = 6 breadth + breadth²
( Let's take the breadth as ' b ' )
775 = 6b + b²
... b² + 6b - 775 = 0
... b² - 25b + 31b - 775 = 0
... b ( b - 25 ) + 31 ( b - 25 ) = 0
... ( b + 31 ) ( b -25 ) = 0
There are two solutions found :
b + 31 = 0 and b - 25 = 0
Hence,
b = -31 and b = 25
As the values can not be in negatives, we take 25
Hence, the value of the breadth is 25.
Length = 6 + b
Length = 31
Hence, the value of the length = 31
Hope my answer helps!!
Multiply. (7x-4)(4x-3)
Your answer is 28x^2-37x+12
1) Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd
28x^2-21x-16x+12
2) Collect like terms
28x^2+(-21-16x)+12
3) Simplify
28x^2-37x+12
Use FOIL
28x-21x-16x+12
-9x+12
A box of 20 dictionaries costs $84. An individual dictionary costs $5. You need at least 55 dictionaries. Find the price of each combination of items.
55/20=2 as qutiont and 15 as remainder
2X84=168
15X5=75
answer=243
in how many ways can five girls and five boys stand in line if boys and girls must alternate?
[tex]5\cdot5\cdot4\cdot4\cdot3\cdot3\cdot2\cdot2\cdot1\cdot1\cdot2=28,800[/tex]
What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?
A.
x2 + y2 − 4x + 2y + 1 = 0
B.
x2 + y2 + 4x − 2y + 1 = 0
C.
x2 + y2 + 4x − 2y + 9 = 0
D.
x2 − y2 + 2x + y + 1 = 0
Answer:
B. x² + y² + 4x − 2y + 1 = 0Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the center (-2, 1) → h = -2 and k = 1.
The radius is the distance between the center and the given point.
Therefore put the coordinates of the points (-2, 1) and (-4, 1) to the formula of a distance between two points:
[tex]r=\sqrt{(-4-(-2))^2+(1-1)^2}=\sqrt{(-2)^2+0^2}=\sqrt{4}=2[/tex]
We have the equation in standard form:
[tex](x-(-2))^2+(y-1)^2=2^2\\\\(x+2)^2+(y-1)^2=4[/tex]
Convert to the genereal form using:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex](x+2)^2+(y-1)^2=4\\\\x^2+2(x)(2)+2^2+y^2-2(y)(1)+1^2=4\\\\x^2+4x+4+y^2-2y+1=4\\\\x^2+y^2+4x-2y+5=4\qquad\text{subtract 4 from both sides}\\\\\boxed{x^2+y^2+4x-2y+1=0}\to\boxed{B.}[/tex]
Can someone please help me?
The graph shows a journey in a car. Which of the statements most likely describes the start of the journey at the portion of the graph labeled I?
***PLEASE HELP WILL GIVE BRAINLIEST!!!***
If DG equals 88, DO = 5x+12 and OG =2x, find DO
.______________.________.
D O G
in the number line, the end points are DG, and the point in between is O
DG = 88
DO = 5x + 12
OG = 2x
Set the equation. The two parts (DO & OG) are equal to the whole (DG)
2x + 5x + 12 = 88
Simplify. Combine like terms
(2x + 5x) + 12 = 88
7x + 12 = 88
Isolate the x. Remember to do the opposite of PEMDAS. Subtract 12 from both sides
7x + 12 (-12) = 88 (-12)
7x = 76
Isolate the x. Divide 7 from both sides:
7x/7 = 76/7
x = 76/7
----------------------------------------------------------------------------------------------------------------------------
Find DO. Plug in "76/7" for x:
DO = 5x + 12
DO = 5(76/7) + 12
Simplify. Remember to follow PEMDAS. Multiply 76 with 5
DO = 380/7 + 12
Next, divide 380 with 7
DO = 54.29 (rounded)
Finally, add
DO = 54.29 + 12
DO = 66.29
66.29 is your answer
hope this helps
The probability of choosing two orange balls without replacement is 1/35 , and the probability of choosing one orange ball is 1/5 .
What is the probability of drawing a second orange ball, given that the first ball is orange?
1/7
11/75
2/7
1/6
Answer:
answer is 1/7
Step-by-step explanation:
Given that there were some orange balls in a bag.
The probability of choosing two orange balls without replacement is 1/35 , and the probability of choosing one orange ball is 1/5 .
We have to find out the probability of drawing a second orange ball, given that the first ball is orange
Let A - I ball orange
B = II ball orange
Then P(AB) = 1/35 (given)
P(A) = 1/5 (given)
The probability of drawing a second orange ball, given that the first ball is orange = P(B/A)
=P(AB)/P(A)
= 1/35 divided by 1/5
= 1/7
answer is 1/7
Answer: 1/7
Step-by-step explanation:
Picture of an inequality word problem. It says the answer is between 2 and 5 hours but I have no idea how to get that answer. Please help me with how to get that answer :(
it should be about 4-5 hours because her mom sleeps half the time that Mei sleeps!! you are welcome!
10 rubber stamps cost $10.30. What is the cost for 2 rubber stamps?
Answer:
2.06
Step-by-step explanation:
you should divide the 10.30 dollars by 10 which wlll give you the answer of one of them then you just multiply what you got by 2 ((:
To find the cost for 2 rubber stamps from the given information about 10 rubber stamps costing $10.30, the cost for 2 stamps is $2.06.
The cost for 10 rubber stamps is $10.30. To find the cost for 2 rubber stamps, we need to calculate the cost per rubber stamp and then multiply it by 2.
Cost per rubber stamp = Total cost / Number of rubber stamps = [tex]\frac{10.30}{10} = 1.03[/tex]
Cost for 2 rubber stamps = $1.03 per rubber stamp [tex]\times[/tex] 2 rubber stamps = $2.06
WILL GIVE BRAINLIEST
Marty ran 4 miles more than Shana ran. Write an expression for how far Shana ran using Marty’s variable “m”
Explain what the 4 inequality signs represent in your own words
The expression would be m - 4 because if Marty ran 4 more miles than Shana, that means that Shana ran 4 less miles than Marty.
The four inequalities are less than, less than or equal to, greater than, and greater than or equal to. Less than means that a number is less than the other number. For example, if you say 4 is less than 7 it is because 4 is less than 7 by 3 which makes 7 value more than 4. For less than or equal to, it means that the number or variable is less than or the same number as the other number. For example, if you say x is less than or equal to 9, that means that x is less than 9 or equal to 9. For greater than, it means that the variable is greater than the other number. For example, if x if greater than 10 than the variable has to be greater than 10 or 11 and so on. For greater than or equal to, it means that the variable is greater than the other number or equal to that number. For example, if x is greater than or equal to 12, then x is greater than 12 or 13 and up or x is equal to 12 or x is 12.