Answer:
The answer is below
Step-by-step explanation:
Expansion using pascal triangle:
a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ =
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
Expansion using binomial where [tex]C(n,r)=\frac{n!}{(n-r)!r!}[/tex]
a) (x + 2)⁶ = C(6,0)[x⁶2⁰] + C(6,1)[(x⁵)(2)¹] + C(6,2)[(x⁴)(2²)] + C(6,3)[(x³)(2³)] + C(6,4)[(x²)(2⁴)] + C(6,5)[(x)(2⁵)] + C(6,6)[(2⁶)]
= x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = C(4,0)[x⁴] + C(4,1)[(x³)(-4)] + C(4,2)[(x²)(-4)²] + C(4,3)[(x)(-4)³] + C(4,4)[(x⁰)(-4)⁴]
= x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = C(5,0)[(2x)⁵] + C(5,1)[(2x)⁴(3)] + C(5,2)[(2x)³(3)²] + C(5,3)[(2x)²(3)³] + C(5,4)[(2x)(3)⁴] + C(5,5)[(2x)⁰(3)⁵]
= (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = C(4,0){(2x)⁴(-3y)⁰} + C(4,1)[(2x)³(-3y)] + C(4,2)[(2x)²(-3y)²] + C(4,3)[(2x)(-3y)³] + C(4,4)[(2x)⁰(-3y)⁴]
= 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
In the expansion of (3a + 4b)⁸, the only possible variable terms are a⁵b³, b⁸, a⁴b⁴, a⁸, ab⁷ because for each of them, the sum of there powers is eight. If the sum of the powers is not 8 then it is not correct.
For a²b³, the sum of the power is 5, for ab⁸ the sum of power is 9 and for a⁶b⁵ the sum of the power is 11 therefore thy are not correct.
As per the question expand the bimonoidal theorem and the pascal triangle. Showing the (x+2)6 (x-4)4 (2x+3)5 (2x-3y)4.
Expansion using pascal triangle:a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶) = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4) =x⁴-16x³+96x²-256x+256c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴ = 16x⁴- 96x³ + 216x² - 216x + 81.Learn more about the use the binomial theorem.
brainly.com/question/11995132.
. Error Analysis Describe and correct the error
a student made when ordering numbers from
least to greatest.
HELP ASAP
Answer:
Step-by-step explanation:
[tex]\sqrt{144} = 12[/tex]
the error was in not take the root of the number correctly
the student assumes that the root of 144 was equal to 72
Can someone please help me
Answer:
c
Step-by-step explanation:
come on ! you can literally see that in the chart.
how many parts of the gray 3/8 are covered by the gray 1/4 ?
2 parts = 2/8 are clearly covered by 1/4.
2/8 is what part of 3/8 ?
it is the same question as "2 is what part of 3" ?
is 2 a quarter (1/4) of 3 ? no, 1/4×3 = 3/4 and not 2.
is 2 one third (1/3) of 3 ? no, 1/3 of 3 = 1/3×3 = 1 and not 2.
is 2 two thirds (2/3) of 3 ? ah, 2/3 × 3 = 2. that is correct !
is 2 three quarters (3/4) of 3 ? no, 3/4×3 = 9/4 and not 2.
once you have the same denominator, you can easily compare the numerators and ignore the denominators for such problems.
Vanessa owed her friend $24. She paid back $8. How much more does Vanessa need to pay before her account is at zero?
Answer:
$16
Step-by-step explanation:
$24 - $8 = $16
Answer:
$ 16
Step-by-step explanation:
$ 24 - $ 8 = $ 16
Which number has the greatest value?
A) 12.2
B) 12.25
C) 12.5
D) 12.52
Answer:
The answer is letter D, 12.52
Witch of the following numbers are greater then or equal to 4/7
A 2/5
B .57
C 2/3
Answer:
2/3
Step-by-step explanation:
Its simple. Ona calculator, if you type in these fractions, you can compare then decimal form values and see which is the biggest:
4/7 = .5714
2/5 = .04
.5/7.0714
2/3 = .66667
Since .6667 is greater than .5714, 2/3 is greater than 4/7
Answer:
B: .57
C: 2/3
Step-by-step explanation:
Divide 4/7 = .57
A: divide 2/5 = 0.4, which is less than 4/7 so we won't include this number as one of the answers
B: .57, which is equal to 4/7
C: divide 2/3 = 0.67, which is greater than 4/7
This question has two answers (B and C), because it is asking which numbers are greater than or equal to.
Find the value of x and y
[tex]\\ \rm\Rrightarrow \dfrac{x}{2}=3[/tex]
[tex]\\ \rm\Rrightarrow x=2(3)[/tex]
[tex]\\ \rm\Rrightarrow x=6[/tex]
And
[tex]\\ \rm\Rrightarrow \dfrac{y}{2}+1=3[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{y}{2}=3-1=2[/tex]
[tex]\\ \rm\Rrightarrow y=2(2)[/tex]
[tex]\\ \rm\Rrightarrow y=4[/tex]
Answer:
x=6 y=4
Step-by-step explanation:
Equating corresponding terms , we get
x/2=3
or, x=6
Also,
y/2+1=3
or, (y+2/2)=3
or, y+2=6
or, y=6-2
y=4
Therefore, x=6 and y=4.
Still can’t get the answer
Answer:
Arliss needs [tex]4 \frac{1}{3}[/tex] yards more.
Step-by-step explanation:
We can look at the fractions [tex]2 \frac{1}{3}[/tex] and [tex]3 \frac{1}{3}[/tex] and add them up.
Looking at the whole numbers, [tex]2+3=5[/tex].
Looking at the fractional parts, [tex]\frac{1}{3} + \frac{1}{3} = \frac{2}{3}[/tex].
So all together, she currently has [tex]5 \frac{2}{3}[/tex] yards.
If she wants to get to 10, we need to find how many more yards we need.
Let's level it out quickly - having [tex]\frac{1}{3}[/tex] more of a yard will give is 6 yards.
[tex]10-6=4[/tex], so in total we added
[tex]4 \frac{1}{3}[/tex] more yards.
So she needs [tex]4 \frac{1}{3}[/tex] more yards.
Hope this helped!
I need help in this question
Answer:
Yes and 60 mi/h
Step-by-step explanation:
The slope of a distance-time graph represents the spped of an object. since the slope has been uniform, the body was travelling with a constant speed that is 120/2=60 mi/h
HAPLLAPLPAL! BRAINLIEST!
Answer:
D. 860 square inches
Answer:
D: 860 square inches
Step 1.
Remember:
w = 8
x = 5
y = 20
z = 11.3
Let's start with the bottom rectangular prism. The front and back of it is x * x
(5 * 5), so the from and back is 25 + 25 = 50.
The three long sides are x * y (5*20), so the three long rectangles are 100 * 3 = 300. The bottom shape is 350 in total.
Step 2.
The top two rectangles are w * y, (8 * 20) so the two top rectangles are 160 * 2 = 320.
The triangles are w * w / 2 (8 * 8/2) (64 / 2) (32), so the two triangles are 64.
We subtract x from z to get 6.3.
Then, we multiply 6.3 by 20. We get 126. Finally, we add all the values together to get our final answer.
350 + 384+126 = 860
Our answer is D: 860.
Helpp me pleaseeeeee
Answer:
On-time Buses: 75%
Running late Buses: 13.46%
Step-by-step explanation:
Part 1: Solve for the probability of Jerry owning an "on-time" bus
Of the 48 buses that run on time, Jerry owns 36 of them. Therefore, the probability of a bus running on time being owned by Jerry will be solved with the ratio of 36 buses to 48 buses.
This is represented by the fraction 36/48. Simplifying this fraction will give us 3/4. Convert to a decimal and then multiply by 100 to get a percentage - 75%.Part 2: Solve for the probability of Jerry owning a "running late" bus
Of the 52 buses that run late, Jerry owns 7 of them. Therefore, the probability of a bus running late & being owned by Jerry will be solved with the ratio of 7 buses to 52 buses.
This is represented by the fraction 7/52.Simplifying this fraction will give us 7/52 (cannot be simplified).Convert to a decimal and then multiply by 100 to get a percentage - 13.46%.Which value of x makes the following matrix equation true?
Answer:
[tex]\large \boxed{{x=-3}}[/tex]
Step-by-step explanation:
[tex]{\mathrm{view \ attachment}}[/tex]
In algebraic expression
Three-fourths the square of a number.
Answer:
3/4x^2
Step-by-step explanation:
Answer:
[tex] \frac{3}{4} \sqrt{x} [/tex]
where 'X' is the number
Step-by-step explanation:
hope this helps
Find the equation of a circle with PQ as diameter, where P(2,-6) and Q(-6,-4)
Answer:
y=-¼x+⁴⁴/8
Step-by-step explanation:
p(2,-6). Q(-6-4)
p (x¹,y¹). Q(x²,y²)
1) find the gradient(slope)
gradient=y²-y¹
x²-x¹
gradient = -4-(-6)
-6-2
gradient= -4+6
-6-2
gradient=²/-8
2)equation is supposed to be in the form of y=mx+c
where m is the gradient
thus.
gradient=y²-y¹
x²-x¹
when finding the equation we only use one of the values of the coordinates leaving the other as an unknown value.
2 = y-(-4)
-8 x-(-6)
2 =y+4
-8. x+6
remove the denominators by cross multiplying that is:
2(x+6)= -8(y+4)
2x+12= -8y-32
express in the format y=mx+c
2x+12+32=-8y
2x+44=-8y.
divide all sides by -8 to remain with y
²/-8x+⁴⁴/-8=y
-¼x+ -⁴⁴/8=y
y=-¼x-⁴⁴/8
Which expression can be used to model the phrase “the sum of three and a number”?
Answer:
3+x
Step-by-step explanation:
lol im doing this on edge too
hope it helps
Help please, all i know is that 4x:24 I will give brainliest
the question:
Heather is planning a dessert display. She needs 4 ounces of strawberries for each dessert.
Part A: Heather is not sure how many desserts she will make. Write an expression with a variable that represents the amount of strawberries Heather needs for the desserts. Identify what the variable represents.
Part B: If Heather has 24 ounces of strawberries, how many desserts can she make? Create an equation and show all work to solve it. (6 points)
Answer:
Let n be the total number of desserts.
Let s be the total ounces of strawberries.
S = 4n <- answer to part a.
24 = 4n
n = 6
If she has 24 ounces of strawberries, she can make 6 desserts.
Let me know if this helps!
plzzzzzzz help asap!!!!!! T.T
C
since the graph is almost symmetrical then the mode,median and mean are approximately equal
whats the gcf of 50,40
whats the gcf of 14,56,63
9514 1404 393
Answer:
107Step-by-step explanation:
The GCF can be no larger than the difference between the numbers. That would be the first value you want to check to see if it is a factor of the numbers.
GCF(40, 50)The difference is 10, which is a factor of both 40 and 50.
GCF(40, 50) = 10
__
GCF(14, 56, 63)You can figure the GCF pairwise, as GCF(14, 56) = 14; then GCF(14, 63) = 7. Or, you can look at the smallest difference between any pair of numbers. Here, that is 63 -56 = 7, which is a factor of all three numbers.
GCF(14, 56, 63) = 7
_____
Additional comment
Euclid's algorithm has you compute the remainder from division of the largest by the smallest. When that remainder is non-zero, it replaces the largest, and you repeat. When the remainder is zero, the smallest is the GCF.
For example, let's look at the GCF of 14 and 63.
63/14 = 4 r 7
14/7 = 2 r 0 . . . . . 7 is the divisor, so is the greatest common factor
Please answer this question now
Answer:
A≈422.37
You use the equation A=πr(r+h2+r2) to find the surface area of a cone
Answer:
373.99 sq cm
Step-by-step explanation:
formula for surface area of cone is: πr(r+s) where r is radius and s is slant height.
π*7(7+10) = π*7(17) = π*119 = 3.14*119 = 373.99 sq cm
please answer this!!!
Answer:
[tex]BC=40[/tex]
Step-by-step explanation:
Since AC is a tangent and PB is the raduis
[tex]\angle PBC= 9[/tex]
By pythagoras
[tex]PC^{2} =PB^{2} +BC^{2}[/tex]
[tex]41^{2} =9^{2} +BC^{2}[/tex]
[tex]1681-81=BC^{2}[/tex]
[tex]1600=BC^{2}[/tex]
[tex]BC=\sqrt{1600}[/tex]
[tex]BC=40[/tex]
OAmalOHopeO
Answer:
40
Step-by-step explanation:
A tangent to a circle is perpendicular to the radius intersection by definition. That makes BPC a right triangle at B. BP and PD are both equal (9) because every radius of a circle is equal. So
PC**2 = BP**2 + BC**2 or
41**2 = 9**2 + BC**2
1681 = 81 + BC**2
1681 - 81 = BC**2
1600 = BC**2
40 = BC
Which transformation shows a reflection across the y-axis? A) A B) B C) C D) D
Answer:
The answer is A
Step-by-step explanation:
This shows a mirroring effect over the vertical y axis.
Choices B and C are a translation (aka shifting)
Choice D is a reflection but over the horizontal x axis.
what seven divided by 4
Answer:
7 divided by 4 is 1 ¾ as a fraction, or 1.75 as a decimal.
Step-by-step explanation:
Pls mark as brainliest answer
The calculated division of the numbers seven divided by 4 is 1 3/4
How to calculate the division of the numbersFrom the question, we have the following parameters that can be used in our computation:
seven divided by 4
When represented as an equation, we have
seven divided by 4 = 7/4
Divide 7 by 4
So, we have the following result
seven divided by 4 = 1 3/4
Using the above as a guide, we have the following:
the result is 1 3/4
Read more about quotient at
brainly.com/question/11418015
#SPJ6
what is meaning of rate?
Answer:
1.a measure, quantity, or frequency, typically one measured against another quantity or measure.
Step-by-step explanation:
2.a fixed price paid or charged for something.
Answer:
a measure, quantity, or frequency typically one measured against another quantity or measure.
Assign a standard or value to (something) according to a particular scale.225 tickets were sold for a Schools Winter Play. The tickets for the adults cost $8.00 and for the children $4.50. The total receipts for the performance were $1275.00 How many of each type of ticket were sold?
Answer:
75 of the adult ones and 150 of the children ones.
40. Which families of plane figures given below are NOT always similar?
A. Squares
C. Equilateral triangles
B. Circles
D. rectangle
Answer:
Rectangle
Explanation:
Rectangles can be oblong, and square is also a rectangle.
Evaluate |3 - 5 + 7|. -5 5 -15 15
Answer:
5
Step-by-step explanation:
|3 - 5 + 7|
= |-2 + 7|
= |5| = 5
Answer:
The correct answer would be 5.
Step-by-step explanation:
An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.H0: The product does not change the height of the plant.Ha: The product makes the plant grow taller.Is the following an example of a type I or type II error?The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.a) Type Ib) Type II
Answer:
The error made here is a Type I error.
Step-by-step explanation:
A Type I error is the rejection of a null hypothesis (H₀) when indeed the null hypothesis is true. It is symbolized by α.
A Type II error is failing to discard a null hypothesis when indeed the null hypothesis is false. It is symbolized by β.
The hypothesis in this case is defined as follows:
H₀: The product does not change the height of the plant.
Hₐ: The product makes the plant grow taller.
The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.
So, the sample suggests to reject the null hypothesis when in fact the null hypothesis is true.
Thus, the error made here is a Type I error.
The number of pages per book on a bookshelf is normally distributed with mean 248 pages and standard deviation 21 pages. Using the empirical rule, what is the probability that a randomly selected book has less than 206 pages?
Answer:
The probability is 0.0228
Step-by-step explanation:
We proceed by calculating the z-score value
Mathematically;
z-score = (x - mean)/SD
where x = 206, mean = 248 and SD = 21
Substituting these values, we have;
z-score = (206-248)/21 = -42/21 = -2
So the probability we want to calculate is;
P(z < -2)
We can use the standard normal distribution table for this;
P(z < -2) = 0.0228
Answer:
i need this as a percentage
Step-by-step explanation:
Can someone please help? the answer is 5/12 but I have no idea how. Please explain the steps!
Answer:
5/12
Step-by-step explanation:
4√y√y / 3√y
The above equation can be simplified as follow:
4√y√y / 3√y
4√y × √y ÷ 3√y
Recall:
√a = a^1/2
m√a = a^1/m
Therefore,
4√y√y ÷ 3√y
y^1/4 × y^1/2 ÷ y^1/3
Recall:
a^m × a^n = a^(m+n)
Therefore,
y^1/4 × y^1/2 ÷ y^1/3
y^(1/4 + 1/2) ÷ y^1/3
y^3/4 ÷ y^1/3
Recall:
a^m ÷ a^n = a^(m–n)
Therefore,
y^3/4 ÷ y^1/3
y^(3/4 – 1/3)
y^5/12
Comparing the above with y^m, we have
y^5/12 = y^m
m = 5/12
Therefore, the value of m is 5/12
A fish jumps out of the water at a speed of 12 feet per second. The height y (in feet) of the fish above the surface of the water is represented by the equation y=-16x^2+12x, where x is the time (in seconds) since the jump began. The fish reaches its highest point above the surface of the water after 0.375 seconds. How far above the surface is the fish at this time?
Answer:
The fish is 2.25 ft above the surface at 0.375 seconds
Step-by-step explanation:
Given:
y=-16x^2+12x
x=0.375 seconds
Substitute x=0.375 into the equation
y=-16x^2+12x
= -16(0.375)^2 +12(0.375
= -16(0.140625) + 4.5
= -2.25 + 4.5
= 2.25
y=2.25 ft
The fish is 2.25 ft above the surface at 0.375 seconds
Find m<1
A. 70°
B. 65°
C. 50°
D. 40°
Question :- Find Angle 1 in diagram
Answer:- Exterior angle is equal to sum of two opposite interior Angle
so :- ATQ
[tex]140 = \angle1 + 90 \\ 140 - 90 = \angle1 \\ 50° = \angle1 \: \: ans[/tex]
so your answer is option (C) 50°