when using the binomial formula which of the following is the correct step in the expansion of (x+y)^4

Answers

Answer 1

Final answer:

The correct step in the expansion of (x+y)^4 is to determine the coefficients for each term using the binomial formula.

Explanation:

The correct step in the expansion of (x+y)^4 using the binomial formula is to determine the coefficients for each term.

In this case, the coefficients can be found using the formula n choose k, where n is the exponent (4) and k is the power of either x or y in each term.

For example, the term with x^3*y would have a coefficient of 4 choose 3, which is equal to 4.

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Related Questions

how do you solve log base 3 (27) by hand

Answers

[tex]\bf \textit{Logarithm Cancellation Rules}\\\\ \boxed{log_a a^x= x}\qquad \qquad a^{log_ax}=x\\\\ -------------------------------\\\\ log_3(27)\qquad \boxed{27=3^3}\qquad log_3(3^{\underline{3}})\implies \underline{3}[/tex]

The log base 3 of 27 is equal to 3.

To solve log base 3 of 27 by hand, we need to determine the exponent to which the base 3 must be raised to obtain 27.

In this case, 3 raised to the power of what exponent equals 27?

By observing that [tex]3^3[/tex] equals 27, we can conclude that:

log base 3 of 27 = 3.

Therefore, the solution to log base 3 of 27 is 3.

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Mr.gleasons math class lasts 40 minutes . Math class starts at 9:55 a.m. At what time does math class end

Answers

Hello,

The answer is "10:35am".

Reason:

Just add 9.55 and 40 mins:

9.55+40=10:35a.m

=10:35am

If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit

Answer:

10:35

Step-by-step explanation:

Just add 9.55 and 40 mins:

9.55+40=10:35a.m

Bryan is paid $32 per hour and works 8 hours per day. He receives one paid day off for each 16 days that he works. What is his true hourly wage?

A. $40 per hour
B. $34 per hour
C. $32 per hour
D. $48 per hour

Answers

I am taking the test the answer is B $34 hope this helps

$40 per hour is his true hourly wage, option A is correct.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Bryan works 8 hours per day, so he works 16 x 8 = 128 hours during the 16-day period.

His pay for the 16-day period is 16 x 8 x $32 = $5,120.

He receives one paid day off for each 16 days that he works, so he gets 16/1 = 16 paid days off for every 16 days worked.

Therefore, he actually works for 16 - 16/1 = 0 days during those 16 days.

His true hourly wage is his total pay divided by the actual number of hours he works:

True hourly wage = $5,120 / 128 hours = $40 per hour

Hence, $40 per hour is his true hourly wage, option A is correct.

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Explain how to find the degree of a polynomial.

Answers

The degree of a polynomial is the highest number as an exponent in a term, for example, 5x^3+5x^2, 3 is the degree. To find it, you need to either just find the highest number or add up multiple degrees in one term. An example of this is 5x^3y^3+4x^3y^2. Since 3+3=6 and 3+2=5, the first term has the highest degree.

Answer:

The Degree of a Polynomial is the largest of the degrees of the individual terms. Add the degrees of the variables of each term to decide what is the Degree of the Polynomial. Degree of term 1 is 2 (1+1= 2), Degree of term 2 is 6 (2+4 = 6), Degree of term 3 is 7 (5+2 = 7) 7 is the Degree of the Polynomial.

A cell phone plan charges $15$15 per month for 300300 text messages. The plan charges $0.08$0.08 for each additional text message. You use 6060 additional texts this month. What is your bill for the month?

Answers

The company charges 15 dollars per month for first 300 text messages and thereafter 0.08 dollars for any additional text message.

It says that we used additional 60 text messages (after fair usage of first 300 messages in the plan).

Our bill for this month would be sum of charges for 300 messages and charges for additional 60 messages.

Total bill = 15 dollars + 60x0.08 dollars = (15 + 4.80) dollars.

Total bill = 19.80 dollars.

Hence, our bill this month would be 19.80 dollars.

Consider the function f (x) = (2x - a)(x - b)/5(x - b)(x - c). Determine where the following features of its graph
are located in terms of a, b, and/or c. Explain your reasoning for each situation.
a. the x-intercepts
b. the y-intercepts
c. any vertical asymptotes
d. any horizontal asymptotes
e. any “holes” in the graph

Answers

a) The function simplifies to
.. f(x) = (2x -a)/(5(x -c)) . . . . . . x ≠ b
The x-intercept will be located where f(x) = 0, at x = a/2.

b) The y-intercept is located where x = 0, at f(0) = a/(5c)

c) The vertical asymptote is where the denominator is zero, at x = c

d) The horizontal asymptote is the value that results when x gets large, y = 2/5.

e) There is a "hole" in the graph at x=b, where the function is undefined.

PLEASE HELP ASAAAAAPPPP

Answers

equation = y = 9800 * 1.02^x

y = 9800 * 1.02^7 = 11257

Answer is 2nd choice

https://screenshots.firefox.com/cxfIjV7PcUHa4HAl/lms.thinkthroughmath.com

Please give answer and explain how to solve.

Answers

volume of rectangular prism is first edge*second edge*third edge (product of
prism dimensions)
1st edge has 4 small cubes , edge of the small cube=1/4,
so 1st edge of the large cube =1/4*4=4/4 (it could be written as 1)
2d edge has 3 small cubes , so 2d edge= 3*1/4=3/4
3d edge has also 3 small cubes , so 3d edge= 3*1/4=3/4
Volume= first edge*second edge*third edge=4/4*3/4*3/4=1*3/4*3/4=9/16
Answer 4/4*3/4*3/4=9/16

**PLEASE HELP**

The area of a rectangle is 3x^2 + 14x + 8, and the length is x + 4. Which expression best describes the rectangle's width?

A.) 2x + 2

B.) 3x - 2

C.) 3x + 2

D.) 2x + 4

Answers

----------------------------------------------------------
Given information
----------------------------------------------------------
Area = 3x² + 14x + 8
Length = x + 4

----------------------------------------------------------
Formula
----------------------------------------------------------
Area = Length x Width

----------------------------------------------------------
Find Width
----------------------------------------------------------
3x² + 14x + 8 = (x + 4) x width
width = (3x² + 14x + 8) ÷ (x + 4)
width = (x+4)(3x+2) ÷ (x + 4)
width = 3x + 2

----------------------------------------------------------
Answer: The width is 3x + 2 (Answer C)
----------------------------------------------------------

According to Okun's law, if the unemployment rate goes from 2% to 5%, what will be the effect on the GDP?

Answers

According to this law, when unemployment goes up by 1%, GDP drops by 2%. In the question, unemployment rate goes from 2% to 5%, meaning unemployment goes up by 3%, so the GDP drops by 6%. Thus the effect is a drop in GDP by 6%.

Answer: decreases by 3%

Step-by-step explanation:

Help Please

Tamara needs to buy motor oil to fill the 3 empty cylindrical barrels at her oil service center each barrel is 7 ft deep and has a radius of 4 ft what is the volume of oil needed use 3.14 for the radius.

Answers

the answer is seven times 4 times three and then you will get your answer

Answer:

1055.04 volume

Step-by-step explanation:

The histogram shows the number of hours volunteers worked one week.

What percent of the volunteers worked 8 to 11 hours or 16 to 19 hours?

Enter your answer in the box.

%

Answers

I have the CORRECT answers to the quiz. I have the correct answer to number 4, but the snip doesn't include the question, so here is the question it is for: "Ramon recorded how many miles he biked each day in the table. Distance (mi) Frequency 1 2 2 2 3 4 4 4 5 2 6 2 Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots."

If dewayne answered 38 items correctly on a test, and received a score of 76%, How Many items were on the test?

Answers

The answer is 50 questions

please help asap!!! brainliest to best/right answer!!!!!!

Answers

The answer is C, I hope this helps!

Please help me out! :)

Answers

The area for that Equilateral triangle is 110.851
if you round it, you get 110.9

I need to know what 8(ii) because I don’t know the method

Answers

notice y° and y° and 50°, are all three angles in a flat-line, namely "linear angles", and since a flat-line is always 180°.

[tex]\bf y+y+50=180\implies 2y=180-50\implies 2y=130 \\\\\\ y=\cfrac{130}{2}\implies y=65[/tex]

Extra points to the person who answer first
Mandana is ordering new tile for her kitchen floor. The area of the floor is 116.9 square feet, and she wants to order between 15% and 20% extra of the materials. Which of the following is a reasonable amount of tile for Mandana to order?

A. 131 square feet B. 138 square feet C. 133 square feet D. 141 square feet

Answers

In order to know what is the reasonable amount of tile for Mandana to order, you have to divide the choices with the area of the floor and deduct with 1 and multiply by 100. You have to assess if the answer you will get will fall between 15% and 20% which is the goal of Mandana.

a. 131/116.9 = (1.1206 – 1) x 100 = 12.06%, this does not fall between 15% and 20%

b. 138/116.9 = (1.1805 – 1) x 100 = 18.05%, this fall between 15% and 20%

c. 133/116.9 = (1.1377 – 1) x 100 = 13.77%, this does not fall between 15% and 20%

d. 141/116.9 = (1.2062 – 1) x 100 = 20.62%, this does not fall between 15% and 20%

Therefore, the reasonable amount of tile for Madana to order that is between 15% and 20% extra of the materials is 138 square feet.

The histogram below shows the age distribution of Elizabeth’s grandchildren.

The box-and-whisker plot below shows the same data.

Which of the following best explains why one graph appears skewed and one graph appears symmetric?

A. The intervals on the x-adis of the histogram are too large

B. The interval on the y-axis of the histogram is too small

C. The interval on the x-axis of the histogram is inconsistent

D. The interval in the box-and-whisker plot is too small

Answers

С.

I hope helped`` ^-^

Answer:

Option: C is the correct answer.

C. The interval on the x-axis of the histogram is inconsistent

Step-by-step explanation:

Clearly after looking at the histogram we see that the interval on the x-axis are inconsistent.

Since, the intervals given are:

0-4 ( length of interval is 4)

5-9 ( length of interval is 4)

10-14 ( length of interval is 4)

But the intervals:

(15-19) is missing in the given histogram.

And then a interval of length 4 is given i.e. (20-24)

Hence, option: C is the correct answer.

Jerry starts to save at age 35 for a vacation home that he wants to buy for his 50th birthday. He will contribute $300 each month to an account, which earns 1.7% interest, compounded annually. What is the future value of this investment, rounded to the nearest dollar, when Jerry is ready to purchase the vacation home? Answers: $61,960 $60,924 $5,077 $5,163 This is the only question I couldn't figure out , I just need help with it please. Thanks

Answers

Here we shall use the future annuity formula
FV of annuity= P{[(1+r)^n-1]/r}
monthly contribution is $300
yearly contribution will be 300*12=$3600
hence P=$3600
r=1.7%=0.017
t=n=50-35=15 years
Therefore:
FV of annuity=3600{[(1+0.017)^15-1]/0.017}
=$60924.45
Hence the answer is $60924

What is 2 (log₃8+log₃z) - log₃(3⁴-7²) written as a single logarithm?

Answers

Before we start solving this problem we need to make sure that all logarithms have same base. They do. Base is 3.

We start by solving first brackets. We will use the rule:
[tex]log a + log b = log (a*b)[/tex]

[tex] log_{3} 8 + log_{3} z = log_{3} (8z)[/tex]

Now we are left with:
[tex]2log_{3} (8z)- log_{3} ( 3^{4} - 7^{2} )[/tex]

To get rid of 2 we will use rule:
[tex]a* log_{b} c= log_{b} c^{a} [/tex]

[tex]2log_{3} (8z)= log_{3} (8z)^{2} [/tex]

Now we are left with:
[tex] log_{3} (8z)^{2}-log_{3} ( 3^{4} - 7^{2} )[/tex]

To solve this we will use rule:
[tex]log a -logb = log \frac{a}{b} [/tex]

[tex]log_{3} (8z)^{2}-log_{3} ( 3^{4} - 7^{2} )= log_{3} \frac{64 z^{2} }{3^{4} - 7^{2}} =log_{3} \frac{64 z^{2} }{32} =log_{3} 2z^{2}[/tex]

The options for number two is
31.5 m^2
63 m^2
84 m^2
126 m^2

Please help! I will give brainliest to the best explained answer.

Answers

the area of any quad = the base* height
for q 1:
the base=12 in
the height= 3 in
then the area = 12*3 = 36 sq in

for q 2:
the base= 14 in
the height = 4.5 in
then the area =4.5*14 =63

Use the data to create a scatter plot.

Stretch distance

(cm)

Weight

(Newtons)

2.0

1

3.5

2

4.0

2

4.5

3

5.5

5

6.0

6

7.5

8

9.0

9
Weight vs. Stretch Distance

Point
Move

Undo
Redo
Reset

Stretch distance (cm)
Weight (N)

Answers

Final answer:

To create a scatter plot for the given data, label the axes with 'Stretch distance (cm)' and 'Weight (Newtons)', plot the points, and observe the correlation. A positive trend is expected as weight increases with stretch distance.

Explanation:

To create a scatter plot with the given data of stretch distance versus weight, you would typically use graphing software or graph paper. Here's a step-by-step explanation on how to plot the data:

Label the x-axis as 'Stretch distance (cm)' and the y-axis as 'Weight (Newtons)'.Mark even increments on both axes according to your data range. For stretch distance, you might use increments of 1 cm, and for weight, you could use increments of 1 Newton.Plot each pair of values from the table onto the graph. For example, you would place a point at (2.0 cm, 1 N), (3.5 cm, 2 N), and so on.Once all points are plotted, you may observe a pattern or trend which can be indicated by drawing a line of best fit if appropriate.

After plotting all the points, your scatter plot might show a positive correlation between stretch distance and weight, indicating that weight increases as the stretch distance increases.

Jenna is a professional typist.she can type 22,500 words in 5 hours of typing.in one hour how many words can she type?in one minute how many words can she types?

Answers

In addition you have answer :)

Which function increases at a faster rate on 0 to infinity, f(x)=x^2 or g(x)=2^x?Explain your reasoning.

Answers

Answer:

g(x) increase at a faster rate.

Step-by-step explanation:

Given : Two functions [tex]f(x)=x^2[/tex] or [tex]g(x)=2^x[/tex]

To find : Which function increase at a faster rate on 0 to infinity

Solution :

We put some value of x in the functions and note down the observation.

x → 0 1 2 3 4 5 6 7

[tex]f(x)=x^2[/tex] → 0 1 4 9 16 25 36 49

[tex]g(x)=2^x[/tex] → 1 2 4 8 16 32 64 128

Comparing the values of f(x) and g(x), we can see that that g(x) increases at a faster rate on 0 to infinity.

Reason - The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function f(x).

1. Find the product of 2x4(2x2 + 3x + 4).
2x8 + 3x4 + 4x4
4x6 + 6x5 + 8x4
4x4 + 3x5 + 2x6
3x6 + 4x5 + 5x4

2. Find the product of (3x 4)(2x2 + 2x 1)
6x3 + 2x2 - 5x + 4
6x3 + 14x2 - 11x + 4
6x3 - 14x2 - 5x + 4
6x3 - 2x2 - 11x + 4

3. Find the product of (x2 + 4x 3)(2x2 + x + 6).
2x4 + 9x3 + 4x2 + 21x 18
2x4 + 9x3 + 10x2 + 21x 18
2x4 + 7x3 + 4x2 + 21x18
2x4 + 9x3 + 4x2 + 27x 18,

Answers

A) So 2x4(2x2 + 3x + 4)
4x^(4 + 2) + 6x^(1 + 4) + 8x4
4x^6 + 6x^5 + 8x^4
B) (3x 4)(2x2 + 2x 1)
6x^(4 + 2) + 6x^(4 + 1)
6x^6 + 6x^5
C) (x2 + 4x3)(2x2 + x + 6)
Expanding we have:
2x^4 + x^3 + 6x^2 + 8x(3 + 2) + 4x^4 + 24x^3
2x^4 + x^3 + 6x^2 + 8x5 + 4x^4 + 24x^3
8x^5 + 6x^4 + 25x^3 + 6x^2

List the first five terms of each of the following geometric sequence.

A_1 = 10; r = 5

Answers

10, 50, 250, 1250, 6250

1. Suppose that the amount of algae in a pond triples every 2 hours. If the pond initially contains 80 pounds of algae, how much algae will be in the pond after 8 hours? (1 point)
a) 720
b) 1,280
c) 6,480
d) 320

Answers

Initially = 80 pounds

It triples every 2 hours

2 hours later = 3(80)
4 hours later = 3(3(80)))
6 hours later = 3(3(3(80)))
8 hours later = 3(3(3(3(3(80)))))
8 hours later = [tex] 3^{4} [/tex] x 80
8 hours later = 6480 (Answer C)

OR

We find the number of 2 hours period in that 8 hours
8 ÷ 2 = 4
It starts at 80 pounds
It tripes every 2 hours
Total algae = [tex] 3^{4} [/tex] x 80 = 6480 (Answer C)

If it triples every 2 hours, it will triple 4 times. 80x3x3x3x4=6480

A triangle with one obtuse angle must also have two acute angles.a. trueb. false

Answers

(a) True

Because the sum of the angles in a triangle is 180°

Obtuse angle = angle greater than 90°.

180° - Obtuse angle = less than 90°

So there cannot be another obtuse angles, therefore both the other angles will be acute.

Answers

Final answer:

Ursula, swimming at 60 meters per minute, and given Andre a 1-minute head start who swims at 48 meters per minute, will catch up to Andre 4 minutes after she starts.

Explanation:

Ursula and Andre competed against each other in a swimming race. Ursula swam at a rate of 60 meters per minute and Andre swam at a rate of 48 meters per minute. Ursula gave Andre a 1-minute head start. To determine who wins the race, we need to calculate the time it takes for Ursula to catch up to Andre, given the head start.

Let's denote the time it takes for Ursula to catch up to Andre as t (in minutes). Since Andre has a 1-minute head start, he would have swum 48 meters before Ursula starts. Therefore, the distance Andre swims in t+1 minutes is 48(t+1). Ursula's swimming distance in t minutes is 60t.

To find out when Ursula catches up to Andre, we set these distances equal to each other:

60t = 48(t+1)60t = 48t + 4860t - 48t = 4812t = 48t = 4

Thus, Ursula will catch up to Andre 4 minutes after she starts swimming, which is 5 minutes after Andre starts.

PLEASE HELP! An organization surveyed a random sample of their employees about their new vacation policy. Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%.

What does the margin of error imply?

A.It can be concluded, with 81% confidence, that between 93% and 97% of all employees will rate the vacation policy as "delightful."

B.It can be concluded, with 95% confidence, that at least 81% of all employees will rate the vacation policy as "delightful."

C.It can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."

D.It can be concluded, with 81% confidence, that at least 95% of all employees will rate the vacation policy as "delightful."

Answers

The answer is C.

Let me know if you have any other questions! ♥

Answer:

The answer is option C.

Step-by-step explanation:

Here, according to the given question, margin of error means that the number of people who rated the vacation as 'delightful' ranges between 81% (83-2) and 85% (83+2) of the population at a 95% confidence interval. The range is formed as 81% to 85% as its given that the margin of error is ±2% .

Therefore, only option C is having both the ranges, 81% and 85%. So, option C is the correct answer.

C.It can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."

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