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expand (x-4)^5 using the binomial theorem and pascal’s triangle show all necesssry steps
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The binomial expansion of the [tex](x-4)^5[/tex] is [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
According to the statement
we have given that a equation and we have to expand it by use of the binomial theorem.
So, For this purpose we know that the
A binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form.
And the general formula is
[tex](x+y)^n= ^nC_0x^ny^0+^nC_1x^(n-1)y^1+^nC_2x^(n-2)y^2+...+^nC_nx^0y^n[/tex]
And we have to solve it with the given equation (x-4)^5.
Then
[tex](x-4)^5=x^5+20x^4+(20)/(2)x^3(4^2)+(60)/(6)x^2(4)^3+(120)/(24)x^1(4)^4+(120)/(120)x^0(4)^5[/tex]
Now after solving the equation become
[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
So, The after expanding the given statement with the binomial theorem the result output is
[tex](x-4)^5=x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
So, The binomial expansion of the [tex](x-4)^5[/tex] is [tex]x^5+20x^4+160x^3+640x^2+1280x+1024[/tex]
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f Tanisha has $ 1,000 to invest at 5 % per annum compounded , how long will it be before she has $1,400 ? If the compounding is continuous, how long will it be?
Question content area bottom
Part 1
Compounding , it will be about
enter your response here years before Tanisha has $1,400.
Answers
With annual compounding, the number of years for 1000 to become 1400 is 6.7 years
With continous compounding, the number of years for 1000 to become 1400 is 1.35 years
How long would it take $1000 to become $1,400?With annual compounding, the formula that would be used is:
(In FV / PV) / r
Where:
FV = future value PV = present value r = interest rate(In 1400 / 1000) / 0.05 = 6.7 years
With continous compounding, the formula that would be used is:
(In 1400 / 1000) / (In e^r)
Where r = interest rate
((In 1400 / 1000) / (In e^0.05) = 1.35 years
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give answer please too hard to solve
Answers
Answer:
see explanation
Step-by-step explanation:
to evaluate f(a) substitute x = a into f(x)
f(a) = 5a + 4
---------------------
2f(a) = 2(5a + 4) = 10a + 8
-----------------------
to evaluate f(2a) substitute x = 2a into f(x)
5(a + 2) + 4 = 5a + 10 + 4 = 5a + 14
--------------------------
f(a) + f(2) ← substitute x = 2 into f(x)
= 5a + 4 + 5(2) + 4 = 5a + 4 + 10 + 4 = 5a + 18
What are the sums? Complete the equations. 12 +15= -12+(-15) = help 36 points
Answers
-12+(-15)= -27
A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.
12 + 15= 27
-12 + (-15)= -12 -15
= -27
☆...hope this helps...☆
_♡_mashi_♡_
The following table shows the cost of 4 party favor packs. For example, the Slinky costs $9 for a pack of 5. Which toy pack has a cost of $2.50 per toy
Answers
Answer:
yo-yo cost 2.50 dollar because if we divide 15 and 6 the answer will be 2.50
The Chief Operating Officer (COO) of the City Hotel has three people reporting to him: The Hotel Manager, The Retreat Coordinator and the Program Manager. The Hotel Manager has responsibility for the Front Desk, Housekeeping, Maintenance and Security. The Program Manager has responsibility for the Massage Therapists, the Yoga Instructors and the Dance Instructors. Draw a tree diagram representing these reporting relationships.
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The tree diagram representing these reporting relationships is attached.
What is a tree diagram?It should be noted that a tree diagram is a planning tool that is used to show the hierarchy of tasks that are needed to be completed.
In this case, the tree diagram shows the way the employees report to each other.
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If f(x) = 10 – x2 and g(x) = 3f (x) – 8, then which of the following is the value of g(-2)?
Answers
Answer:
10
Step-by-step explanation:
g(x) = 3(10-x^2)-8=>30-3x^2-8=>-3x^2+22
then substitute -2 in x
-3(-2)^2+22
-3(4)+22=-12+22=10
Find A when p= 2000, r= 7%, n= 4, and t= 4
Answers
A=prt
A=2000×7%×4
=560
Which of the following statements does NOT adequately describe a developmental progression?
A-The order in which skills and concepts build on one another as children develop is called a developmental progression.
B- A developmental progression provides a specific sequence of instruction to support children as they build their math knowledge.
C- A developmental progression is a skill check- list that four-years- olds must master to be prepared for kindergarten.
Answers
The statement which does not adequately describe a developmental progression is Choice C- A developmental progression is a skill check- list that four-years- olds must master to be prepared for kindergarten.
What is developmental progression?The Developmental Progression of Functional Skills is a concept which describes the child's growth in which case, the child's develops relationship with family members and a sense of self in the process and this concept in discuss is not limited to four-year olds.
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Write an Algebra equation to the following question: Stephen and Lauren bought a home to flip for a profit. After budgeting a total of $23,150 for improvements, they started by spending $10,350 on subbing out some of the work. They would like to replace all thirty-two of the windows in the home. What is the maximum amount they can afford to spend on each window?
Answers
The maximum amount they can afford to spend on each window is $400
EquationTotal budget = $23,150Amount spent on subbing = $10,350Number of windows = 32Amount spent on each window = x23,150 = 10,350 + 32x
23,150 - 10,350 = 32x
12,800 = 32x
divide both sides by 32x = 12,800 / 32
x = $400
Therefore, the amount spent on each window is $400
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Use a graphing calculator or other technology to write the quadratic equation that best fits the data set. X 0 -1 -2. y 3 -3 -5
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The quadratic equation of the data is y = 7x^2 + 13x + 3
How to determine the quadratic equation?The table of values is given as:
X 0 -1 -2.
y 3 -3 -5
When the above values are added to the graphing calculator, we have the following summary
a = 7
b = 13
c = 3
A quadratic equation is represented as:
y = ax^2 + bx + c
So, we have:
y = 7x^2 + 13x + 3
Hence, the quadratic equation of the data is y = 7x^2 + 13x + 3
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Which set of ordered pairs could be generated by an exponential function?
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The set of ordered pairs that could be generated by an exponential function is; C: (-1,1/2), (0, 1), (1, 2), (2, 4)
How to find the ordered pairs?An exponential function is represented by the general form;
y = abˣ
The above equation means that the value (0, 0) cannot be an ordered pair in an exponential function.
The highlight above means that, the options A, B and D cannot generate an exponential equation because they contain the point (0,0).
Thus, the set of ordered pairs that could be generated by an exponential function is option C: (-1,1/2), (0, 1), (1, 2), (2, 4)
The missing options are;
A. (-1,-1/2), (0, 0),(1,1/2), (2, 1)
B. (–1, –1), (0, 0), (1, 1), (2, 8)
C. (-1,1/2), (0, 1), (1, 2), (2, 4)
D. (–1, 1), (0, 0), (1, 1), (2, 4)
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The sum of five consecutive integers equals 5.5 times the middle integer. Find the integers.
Answers
The integers are therefore -2, -2, 0, 1 and 2
Linear equationLet the five consecutive integers be x-3, x-2, x-1, x and x+1
If the sum of five consecutive integers equals 5.5 times the middle integer, then;
x-3+x-2+x-1+x+x+1 = 5.5(x-1)
5x - 5 = 5.5x - 5.5
Collect the like terms
5x-5.5x = -5.5 + 5
-0.5x = -0.5
x = 1
The integers are therefore -2, -2, 0, 1 and 2
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6m + 2 - 4m =
help with this please
Answers
The answer is: 2(m+1)
First combine like terms.
we do 6m-4m which is 2m
2m+2=?
Second we factor. We notice that both terms have 2.
2(m+1)
by distributive law, the 2 is distributed to m and 1.
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 18 houses that sold in their neighborhood took an average time of 100 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 20 days. (You may find it useful to reference the z table.)
a. What assumption regarding the population is necessary for making an interval estimate for the population mean?
multiple choice
Assume that the central limit theorem applies.
Assume that the population has a normal distribution.
b. Construct the 99% confidence interval for the mean sale time for all homes in the neighborhood. (Round final answer to 2 decimal places.)
Answers
The 99% Confidence interval for the mean sale time for all homes in the neighborhood is:87.857, 112.143.
Confidence intervala. The assumption is: Assume that the population has a normal distribution.
The CI is exact for the normal populations and for small samples the z-interval method should be used in a situation where the variable is normally distributed.
b. Confidence interval:
CI=Sample mean±z-score×Standard deviation/√Size of the sample
CI=100-2.576×20/√18, 100+2.576×20/√18
CI=100-12.143, 100+12.143
CI=87.857, 112.143
Therefore the 99% Confidence interval is 87.857, 112.143.
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differentiate with respect to x (6-2x)^3
Answers
Answer:
- 6(6 - 2x)²
Step-by-step explanation:
using the chain rule
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{du}[/tex] × [tex]\frac{du}{dx}[/tex]
let y = (6 - 2x)³
let u = 6 - 2x , then y = u³
[tex]\frac{du}{dx}[/tex] = - 2 and [tex]\frac{dy}{du}[/tex] = 3u²
then
[tex]\frac{dy}{dx}[/tex] = 3u² × - 2 = - 6(6 - 2x)²
Find the value of x. Round to the
nearest tenth.
X
26
12
X
x = [?]
Answers
Answer:
Step-by-step explanation:
This is classic right triangle trig, cos specifically. Our reference angle is the one marked 26°, the hypotenuse is given as 12, and the side adjacent to the reference angle is our unknown. This is the cosine ratio. Setting up to solve for x:
[tex]cos26=\frac{x}{12}[/tex] and
12cos(26) = x Plug this into your calculator in degree mode to get that
x = 10.8
The area of a square quilt is 35 ft 2. How will it look stretched across a queen sized bed measuring 60 inches wide and 80 inches long?
Answers
The quilt will be 10.99 inches wider and 9.01 inches shorter than the bed.
What is the relationship between the quilt and the bed?The first step is to determine the dimensions of the quilt.
Dimensions = √35 = 5.92 feet
Now convert the dimensions of the quilt to inches
1 feet = 12 inches
5.92 x 12 = 70.99 inches
Difference in the width of the bed and the quilt = 70.99 - 60 = 10.99
Difference in the length of the bed and the quilt = 80 - 70.99 = 9.01
Here are the options:
A. The quilt will cover half of the surface of the bed.
O B. The quilt will match up with the length of the bed, but 20 inches will hang over the length. °
C. The quit will be 14.6 inches wider and 15.4 inches shorter than the bed. O D. The quilt will be 10.99 inches wider and 9.01 inches shorter than the bed.
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Question 13 (5 points)
Find the greatest common factor of 48a²b7 and 48a6b5z.
a.) 12a²b5
b.) 12a8b¹2
c.) 18a6b7
d.) 48a²b5
Answers
The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The greatest common factor is the highest number that all the numbers share.
The greatest common factor of 48a²b⁷ and 48a⁶b⁵z is the number 48a²b⁵
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9) Find the median of the data set.
O a.) 8
Ob.) 5
Oc.) 10
O d.) 13
Data:
5, 8, 12, 6, 7, 10, 14, 6, 13
Answers
Answer:
a
Step-by-step explanation:
the median is the middle value of the data arranged in ascending order
5 , 6 , 6 , 7 , 8 , 10 , 12 , 13 , 14 ← ascending order
↑ middle value
median = 8
Answer:
8
Step-by-step explanation:
To find the median, we must put all of the data in order and select the middle number. Since there are 9 terms, the median will be the 5th term.
5, 6, 6, 7, 8, 10, 12, 13, 14
Brainliest, please :)
3) A communications company is planning a new network of specialty ZTX cables linking the major cities noted below. The cost to complete the project is $150 per mile. Draw a diagram of the minimum spanning tree and the cost associated with it.
Answers
The Minimum Spanning Tree diagram associated with ZTX's project is indicated as attached. The total cost associated with it is $1,664,550
What is a Minimum Spanning Tree?A graph spanning tree is a set of linked edges that encompass every vertex in the graph but do not create a cycle. A graph may have several such spanning trees.
The Minimum Spanning Tree, on the other hand, has the least cumulative edge weights.
What is the calculation for the attached minimum spanning tree?The starting point is Seattle.
The total minimum cost is given as:
(1306 + 629 + 435 + 1983 + 1225 + 1483 + 661 + 1145 + 1709 + 183 + 338) x 150
= $1,664,550
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Write the equation for the following relation. D = {(x, y ): (3, 9), (5, 25), (-2, 4), . . .}
Answers
The equation for the given relation is a quadratic equation:
[tex]y = x^2[/tex]
How to write an equation for the given relation?
Here we have the relation:
D = {(x, y); (3, 9), (5, 25), (-2, 4), ...}
Notice that for each coordinate point, we can see that the output is equal to the square of the input:
[tex]3^2 = 9\\5^2 = 25\\(-2)^2 = 4[/tex]
Then the equation is just:
[tex]y = x^2[/tex]
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Simplify the expression using the proper order of operations
5[6 ÷ 2^2 ∙ 3 - 1]
Answers
The simplification of the expression 5(6 ÷ 2² × 3 - 1) using the proper order of operation is 3.75
Simplification5(6 ÷ 2² × 3 - 1)
Bodmas
B - BracketO - ofD - divisionM - MultiplicationA - AdditionS - Subtraction= 5(6 ÷ 4 × 3 - 1)
= 5(6 ÷ 4 × 2)
= 5(6 ÷ 8)
= 5(0.75)
= 3.75
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A(-3,-2), B(12, 3); 3 to 2
Answers
Answer:
(6, 1)
Step-by-step explanation:
The formula for dividing segment AB into parts in the ratio M:N is ...
P = (M·B +N·A)/(M+N)
ApplicationUsing the above formula with the given values, we have ...
P = (3(12, 3) +2(-3, -2))/5 = (36 -6, 9 -4)/5 = (30, 5)/5
P = (6, 1)
The point P that divides segment AB into parts in the proportion 3:2 is ...
P = (6, 1)
evaluate 5(x-1)-2 when x=3 (urgent)
Answers
Answer: 8
Step-by-step explanation:
Since x=3, we can plug in 3 for x in the equation:
[tex]5(3-1)-2\\5(2)-2\\10-2\\8[/tex]
⊱________________________________________________________⊰
Answer:
8
Step-by-step explanation:
Plug in 3 for x
[tex]\sf{5(3-1)-2}[/tex]. [tex]\large\textbf{[Perform the operation in parentheses]}[/tex][tex]\sf{5(2)-2} \ \ \ \ \ \large\textbf{[Multiply 5 by 2 next]}[/tex]
[tex]\sf{10-2} \ \ \ \ \large\textbf{[Subtract]}[/tex]
[tex]\sf{8}[/tex]
Done !! Hope this made sense to you !!
⊱________________________________________________________⊰
[tex]\small\pmb{\tt{CALLIGRAPHY}}[/tex]
how tell me how you got answer 5.9 and also if you do at calculate can show me how to do pls thanks.
Answers
The steps you have are correct. I'll fill in the gap between step 2 and step 3.
[tex]0.4245 = \frac{2.5}{\text{x}}\\\\0.4245\text{x} = 2.5\\\\\text{x} = \frac{2.5}{0.4245}\\\\\text{x} = 5.8892815\\\\\text{x} = 5.9\\\\[/tex]
I multiplied both sides by x, then divided both sides by 0.4245 to isolate the variable.
With the exception of 2.5, every other decimal value mentioned is approximate.
8 through 10 thank you answers only
Answers
Answer:
8) - 8z^3 - 3z^2 - 2z + 13
9) g^3 - 3g^2 + 3g + 6
10) (14n + 21) - (8n + 7) = 6n + 14
a box contains 7 red balls and 2 blue balls. how many more blue balls do you need to add to the box to make the probobility of pulling a red ball 0.5
A) 2
B) 3
C) 4
D) 5
E) None Of The Above
Answers
Using the probability concept, the number of blue balls you need to add is:
D) 5.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
A probability of 0.5 is reached if the number of red balls is the same as the number of blue balls. Current the difference is of 7 - 2 = 5, hence 5 blue balls must be added.
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If p is the probability of success of a binomial experiment, then the probability of failure is what?
Answers
Answer:
1 - p
Step-by-step explanation:
1 - p
A sum of money is shared between Aaron and Betty in the ratio 2:5 Aaron received $60.How much money was shared altogether?
Answers
Answer:
The answer is $210.
Step-by-step explanation:
60/2 = 30. 30*5= 150. 150+60=210.
well, we know Aaron received $60, and we also know that Aaron and Betty are sharing the total on a 2:5 ratio, thus
[tex]\cfrac{Aaron}{Betty}~~ = ~~\cfrac{2}{5}\implies \cfrac{60}{Betty}~~ = ~~\cfrac{2}{5}\implies (60)(5)=(Betty)(2) \\\\\\ \cfrac{(60)(5)}{2}=Betty\implies 150=Betty~\hfill \underset{\textit{total money shared}}{\stackrel{60~~ + ~~150}{210}}[/tex]