Answers
[tex]9\sqrt{56 x^7 y^{12}}\qquad \begin{cases} 56=7\cdot 2\cdot 2\cdot 2\\ \qquad 7\cdot 2^2 \cdot 2\\ \qquad 2^2\cdot 14\\ x^7=x^{(3)(2)+1}\\ \qquad (x^3)^2\cdot x^1\\ y^{12}=y^{(6)(2)}\\ \qquad (y^6)^2 \end{cases}\hspace{5em} \begin{array}{llll} 9\sqrt{2^2(14)(x^3)^2 x (y^6)^2} \\\\\\ 9(2)(x^3)(y^6)\sqrt{14x} \\\\\\ {\Large \begin{array}{llll} 18x^3y^6\sqrt{14x} \end{array}} \end{array}[/tex]
Answer:
[tex]\textsf{1.} \quad 18\;x^3\;y^{6}\sqrt{14x}[/tex]
[tex]\textsf{2.} \quad -8\sqrt{2}[/tex]
Step-by-step explanation:
Question 1Given expression:
[tex]9\sqrt{56x^7y^{12}}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies 9\sqrt{56}\sqrt{x^7}\sqrt{y^{12}}[/tex]
Rewrite 56 as 4·14:
[tex]\implies 9\sqrt{4 \cdot 14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies 9\sqrt{4}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
Rewrite 4 as 2²:
[tex]\implies 9\sqrt{2^2}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
Simplify:
[tex]\implies 9\cdot 2\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
[tex]\implies 18\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]
[tex]\implies 18\sqrt{14}\;(x^7)^{\frac{1}{2}}\;(y^{12})^{\frac{1}{2}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^{\frac{12}{2}}[/tex]
[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^6[/tex]
Rewrite ⁷/₂ as 3 + ¹/₂
[tex]\implies 18\sqrt{14}\;x^{(3+\frac{1}{2})}\;y^{6}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}= a^b \cdot a^c:[/tex]
[tex]\implies 18\sqrt{14}\;x^3 \; x^{\frac{1}{2}}\;y^{6}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]
[tex]\implies 18\sqrt{14}\;x^3 \; \sqrt{x}\;y^{6}[/tex]
Rearrange:
[tex]\implies 18\;x^3\;y^{6}\sqrt{14x}[/tex]
Question 2Given expression:
[tex]7\sqrt{32}-6\sqrt{72}[/tex]
Rewrite 32 as 16·2 and 72 as 36·2:
[tex]\implies 7\sqrt{16 \cdot 2}-6\sqrt{36 \cdot 2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies 7\sqrt{16}\sqrt{2}-6\sqrt{36}\sqrt{2}[/tex]
Rewrite 16 as 4² and 36 as 6²:
[tex]\implies 7\sqrt{4^2}\sqrt{2}-6\sqrt{6^2}\sqrt{2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies 7 \cdot 4\sqrt{2}-6\cdot 6\sqrt{2}[/tex]
Simplify:
[tex]\implies 28\sqrt{2}-36\sqrt{2}[/tex]
[tex]\implies -8\sqrt{2}[/tex]
Related Questions
Let f(x)=(x−7)(x+6)(x−5). Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0. Do not sketch the graph.
1. Find the y-intercept(s). List your answers as points in the form (a,b)
2.Find the x-intercept(s). List your answers as points in the form (a,b)
3. What are the values of x where f(x)>0?
4. What are the values of x where f(x)<0
Answers
Part 1
The y-intercept is when x=0, and [tex]f(0)=(0-7)(0+6)(0-5)=210[/tex]. So, the y-intercept is at (0, 210).
Part 2
The x-intercept(s) are when y=0, so:
[tex]f(x)=0\\\\(x-7)(x+6)(x-5)=0\\\\x-7=0, x+6=0, x-5=0\\\\x=-6, 5, 7[/tex]
So, the x-intercepts are: (-6, 0), (5, 0), (7, 0)
Using our roots from Part 2, we know that:
Part 3: [tex](-6, 5) \cup (7, \infty)[/tex]
Part 4: [tex](-\infty, -6) \cup (5, 7)[/tex]
which representation shows y as a function of x?if you can't see c, is says: -1,0 -1,5-1,10-1,15
Answers
At first ,we should know that :
The relation between x and y will be a function when each value of x appeared one time
We will check the options:
A. for the figure of option A, each value of x connected one time to a value of y
B . there are 2 arrows from 0 and 1
C. the values of x = -1 , connected four times to the value of y
So, the answer is option A
2. Tony's bill at a restaurant was $47.24. He planned to leave an 18% tip for the waiter. How muchdid he pay overall? (2 points)
Answers
Determine the amount paid by the Tony overall.
[tex]undefined[/tex]help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
A triangle has side lengths measuring 10m, 24m, and 26m. Explain how you use Pythagorean Theorem to determine whether or not the triangle is a right triangle.
Answers
Hello there. To solve this question, we'll have to remember some properties about the pythagorean theorem and right triangles.
Given a triangle with side lengths 10 m, 24 m and 26 m, we have to determine whether this is a right triangle or not.
First, let's assume these are the sides lengths of a right triangle, as follows:
Notice in this case we choose the largest side to be the hypotenuse. We know that the largest side of a triangle has to be less than the sum of the legs and any combination would do, but since we'll apply the Pythagorean theorem, we already know that the hypotenuse has to be the largest side of the triangle.
For a right triangle with legs a, b and hypotenuse c, the Pythagorean theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, that is
[tex]a^2+b^2=c^2[/tex]Hence we plug a = 10, b = 24 and c = 26.
We have to see if this equality will hold for the values;
[tex]10^2+24^2=26^2[/tex]On the right hand side, square the number
[tex]676[/tex]On the left hand side, square and add the numbers
[tex]100+576=676[/tex]Notice we got the same answer, then we say that these values satisfy the Pythagorean theorem.
Therefore, this is a right triangle.
If there is more then one element in the set, separate them with commas
Answers
Answer:
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Event that the number chosen is 2 = {2A, 2B, 2C}
Explanation:
The sample space is the set with all the possible outcomes, if she can select any number from 1, 2, or 3 and she can select any letter of A, B, or C, we get that the sample space is
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Then, the outcome for the event that the select number is 2 is
Event that the number chosen is 2 = {2A, 2B, 2C}
Therefore, the answers are:
Sample space = {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}
Event that the number chosen is 2 = {2A, 2B, 2C}
Describe the transformation of f(x)= x2 represented by g. then graph.
Answers
Determine the distance between M(4, 0) and N(-2, -3).
Answers
Explanation
Step 1
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Step 2
let
P1=M(4,0)
P2=N(-2,-3)
replace
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{distance}=\sqrt[]{(-2-4)^2+(-3-0)^2} \\ \text{distance}=\sqrt[]{(-6)^2+(-3)^2} \\ \text{distance}=\sqrt[]{36+9} \\ \text{distance}=\sqrt[]{45} \\ \end{gathered}[/tex]I hope this helps you
5
一堆
2
If log₁/2x = -1, then the value of x is
a) 2
b) 1/2
c)-1
Answers
The value of the variable 'x' in logarithmic expression is: 2
What is logarithm?
In mathematics, the term logarithmic expression can be explained as the exponent or the power which is raised on the base value of the logarithmic expression.
According to the question, the given logarithmic expression are as follows:
[tex]log_{1/2}x = -1[/tex]
Using standard logarithmic property, we get
x = (1/2)^-1
⇒x = 2
Hence, the logarithmic value of the variable 'x' is: 2
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I really need a clear, step-by-step explanation
Answers
1) 1/6
3) -7/6
what is the difference between rational and fractional numbers?Any number with the formula a/b, where both "a" and "b" are whole numbers, and where "b" ≠ 0, is a fraction. A rational number is one that has the pattern p/q, where p and q are both integers, and q≠0.Use equivalent fractions that do have a shared denominator if the denominators are not the same. To accomplish this, you must identify the two denominators' least common multiples (LCM). Rename the fractions having a common denominator before adding those with different denominators. Later, include and simplify.To learn more about : fractional numbers
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Calculate the total loss after 4 years if 299000 is reduced by 4% per annum
Answers
The total loss after 4 years is $47840.
How to calculate the value?From the information, we want to calculate the total loss after 4 years of 299000 is reduced by 4% per annum.
It should be noted that this simply means the calculation using the interest formula. In this case, the total loss will be gotten by knowing the interest.
In this case, the interest formula can be illustrated as:
Interest = PRT / 100
where P = Principal = 299000
R = Rate = 4%
T = Time = 4 years
Interest = (299000 × 4 × 4) / 100
Interest = 4784000 / 100
Interest = 47840
In this case, the calculation of the interest is the loss that the person gets.
Therefore, the loss is $47840.
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If ∆ABC is congruent to ∆PQR, find the length of QR.
Answers
If ∆ABC is congruent to ∆PQR, find the length of QR.
Given that If ∆ABC is congruent to ∆PQR:
The simplest way to prove that triangles are congruent is to prove that all three sides of the triangle are congruent.
When all the sides of two triangles are congruent, the angles of those triangles must also be congruent.
From the triangle ABC, the side BC = 4,
Hence the PQR, the side QR = 4 since they are congruent
Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30N, and the other east and at an angle of 30 degrees northward and a tension force of 40 N. Find the components of the net force on the cart. Show all work.
Answers
The net force on the cart is 62N
and the vertical component =36.64 N
the horizontal component= 50N
What is revolution of vector?
The process of splitting a vector into its components is called resolution of the vector. We resolve a vector into two components which are. component along the x-axis called horizontal component. component along the y-axis called vertical component
30N tension on the cart is westward which mean the vertical component will be 0 and the horizontal component will be 30N.
40N tension isN 30° E which means
the vertical component= 40 sin60=36.64N
Horizontal component= 40 cos 60= 20N
sum of vertical = 36.64N +0= 36.64N
sum of horizontal= 30N+20N= 50N
60° was used for tension 40N because the angle of vector must always lie on the horizontal axis
therefore the net force F is obtained by using Pythagoras theorem
F= √(50^2+36.64^2)
= 62N to the nearest whole number.
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Find two different ways to show that one third+ one fourth is not equal to 3/7. You can use numbers words and labels sketches.
Answers
We can show that one third + one fourth is not equal to 3/7 by following two ways.
By Calculation.By Analysis. By Calculation.We are given to prove that the one third and one forth combination of any object/value does not equals to the 3/7 of that same value/object.
let's Consider we have value as 1.
∴ one third of value will be [tex] \frac{1}{3} [/tex]
∴ one forth of value will be [tex] \frac{1}{4} [/tex]
∴ three of seven of value will be [tex] \frac{3}{7} [/tex]
Now we can do the mathematic calculation on one third and one forth of the value.
As given we have to calculate the addition of one third and one forth of the value
∴ [tex] \frac{1}{3} + \frac{1}{4} [/tex]
= [tex] \frac{4}{12} + \frac{3}{12} [/tex] --(make base same )
= [tex] \frac{4\ + 3}{12}[/tex]
= [tex] \frac{7}{12}[/tex]
∴ By the calculation we clearly got that the addition of one third and one forth of the value is equal to the seven of twelve of the value.
We can also prove it by analysis as follows ;
Proof by analysis:-Consider a number say 120.
∴ 1/3 of 120 will be 40
∴ 1/4 of 120 will be 30
∴ 3/7 of 120 will be 51.42
Now Addition of 1/3 and 1/4 of 120 will be 40 + 30 = 70
Comparing it with 3/7 i.e 51.42 ≠ 70
Hence proved 1/3 + 1/4 ≠ 3/7 .
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Write the linear inequalities that this graph represent in slope - intercept form
Answers
Solution
For the solid line we can select two points:
(0,2) and (1,0)
We can calculate the slope and we have:
[tex]m=\frac{0-2}{1-0}=-2[/tex]Then we can find the intercept and we got:
0= -2*1+ b
b =2
Then the equation is:
y= -2x +2
For the dashed line we can select (0,1) and (1,2) then the slope is:
[tex]m=\frac{2-1}{1-0}=1[/tex]The intercept is:
2= 1*1 +b
b=1
Then the equation is:
y= x +1
5. Which equation is solved for the height of the cone based on theinformation given below ?
Answers
The equation for the Volume (V) of the cone given is,
[tex]V=\frac{1}{3}\pi r^2h[/tex]We are to isolate 'h' in the equation above
SOLUTION
Multiply both sides by 3
[tex]3V=3\times\frac{\pi}{3}r^2h[/tex]Simplify
[tex]3V=\pi r^2h[/tex]Divide both sides by πr²
[tex]\frac{3V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex]Simplify
[tex]h=\frac{3V}{\pi r^2}[/tex]Hence, the answer is
[tex]h=\frac{3V}{\pi r^2}\text{ (OPTION D)}[/tex]What would the simplified form be to-√12+3√3
Answers
In a single throw of a fair die, what is the probability that an odd number or a perfect square greater than one shows up?
Answers
The probability that an odd number or a perfect square greater than one shows is 2/3.
Probability - The area of mathematics known as probability deals with numerical representations of the like that an event will occur or that a statement is true.
The probability of an event is a value between 0 and 1.total no. of outcomes - 1,2,3,4,5,6
odd number = 1,3,5
or a perfect square = 4
probability - dividing the favorable number of outcomes by the total number of possible outcomes.
probability = favorable outcomes / total no. of outcomes
= 4/6
= 2/3
The probability that an odd number or a perfect square greater than one shows is 2/3.
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Find the greatest common factor (GCF) of 64 and 72.A. 8B. 9C. 4D. 12
Answers
Okay, here we have this:
Let's decompose each number and then we see their common factors:
64=2*2*2*2*2*2
72=2*2*2*3*3
The factors common to both are: 2*2*2, and by multiplying we obtain that the greatest common divisor is 8. The correct answer is option A.
Write the augmented matrix for the following system of equations.
9y-5+9z = 0
7x=-3y+7+z
5x + 7y = 5
Answers
The augmented matrix is [tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex].
What is a matrix?
A rectangular array or table containing numbers, symbols, or phrases that are arranged in rows and columns is known as a matrix.
The given system of equations is:
9y - 5 +9z = 0
7x = -3y +7 + z
5x + 7y = 5
Rewrite the equations as:
0x + 9y + 9z = 5
7x +3y -1z = 7
5x + 7y + 0z= 5
Therefore, the augmented matrix for the system of equations is:
[tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex]
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Analyze the graph of the function f(x)=4|x+7|+8 compared to the graph of the absolute value function g(x)=|x| .
Answers
Given:
The functions
[tex]\begin{gathered} g(x)=|x| \\ f(x)=4|x+7|+8 \end{gathered}[/tex]Required:
Determine changes made in g(x) to get f(x).
Explanation:
The steps are:
[tex]\begin{gathered} f(x)=4|x+7|+8 \\ Shift\text{ the graph to the left }7\text{ units.} \\ Shift\text{ the graph upwards }8\text{ units.} \\ Apply\text{ a vertical stretch of }4\text{ units.} \end{gathered}[/tex]So. fourth option is describing the f(x).
The graph
Answer:
Completed the answer.
What can you conclude from the information in the diagram?
Answers
Answer:
Triangle UVT and TSR are isosceles triangles (two equal sides).
Angle WUV = Angle WTV (base angles of isosceles triangle)
Angle RTS = Angle TRS (base angles of isosceles triangle)
Line VW is perpendicular to line UT.
Angle WTV = Angle RTS (vertically opposite angles)
Angle WTR = Angle VTS (vertically opposite angles)
If 2 + √3 is a polynomial root, name another root of the polynomial, and explain how you know it must also be a root.
Answers
If 2+[tex]\sqrt{3}[/tex] is a polynomial root, then the another root of the polynomial will be 2 -[tex]\sqrt{3}[/tex]
The root of the polynomial = 2 +[tex]\sqrt{3}[/tex]
We know by using the quadratic equation we can find the solution of the polynomial
The quadratic equation of the polynomial
= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Then the root of the polynomial is [tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
Here one root is given that 2 + [tex]\sqrt{3}[/tex]
Then using the quadratic equation of the polynomial, the other root of the polynomial will be the conjugate of the given root.
The other root of the polynomial = 2 - [tex]\sqrt{3}[/tex]
Hence, If 2 + [tex]\sqrt{3}[/tex] is a polynomial root, then the another root of the polynomial will be 2 - [tex]\sqrt{3}[/tex]
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Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
y = 0.75x + 2
Step-by-step explanation:
Take two distinct points on the graph
Compute the slope m and y-intercept b
Equation of line in slope-intercept form is
y = mx + b
Take points (0, 2) and (4, 5)
Slope m = (5 - 2) /(4-0) = 3/4
y-intercept from the graph is 2
So y = 3/4 x + 2 =0.75x + 2
A large pizza pie with 15 slices is shared among x students such that each student's share is 3 slices. Write it as a mathematical statement.
Answers
15/x = 3
Explanation:Total number of slices = 15
Number of students = x
Each student's share = 3
(Total number of slices)/(Number of students) = Each student's share
Therefore, the mathematical statement representing the illustration is:
15/x = 3
A teacher was helping me but I got force quite the app due to lag can you help me with question C, D, and E !!!
Answers
Parts C, D and E
Answer:
Explanation:
C) The maximum height is the highest point on the graph. On the x axis of the graph, each small square is 0.25 units. Thus, the x coordinate of the maximum height is is 1.25. The ball reached maximum height after 1.25 seconds
D) There were two different times when the ball was at 10m.
When y = 10 m, x = 0.5
when y = 10, x = 2
At 0.5 and 2 seconds, the ball was at 10m
E) A the time the when the ball hit the ground, the height is 0. Thus, the time when the ball hits the ground is 3 seconds
x over 3=2
Can the value of x be 13
Answers
Answer:
no
Step-by-step explanation:
because 3*2 isnot equal to13
the recommended amount of meat to serve 1 and 1/2 dozzen people is 4 and 1/2 pounds. how many pounds of meat are recommended to feed 1 dozzen people? how many pounds are recommended to feed 4 people? and how many pounds are recommended to feed 1 person
Answers
First, 1 dozen is 12 units, so
[tex]1\frac{1}{2}\text{ dozen people }=\text{ 12 people + 6 people = 18 people}[/tex]Now, to solve the exercise you can use the rule of three. So, you have
*How many pounds of meat are recommended to feed 1 dozen people?
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 12\text{ people}\rightarrow x\text{ pounds} \\ x=\frac{12\text{ people }\ast\text{ 4.5 pounds}}{18\text{ people}} \\ x=\frac{54}{18}\text{ pounds} \\ x=3\text{ pounds} \end{gathered}[/tex]Therefore, 3 pounds of meat is recommended to feed a dozen people.
*How many pounds are recommended to feed 4 people?
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 4\text{ people}\rightarrow x\text{ pounds} \\ x=\frac{4\text{ people }\ast\text{ 4.5 pounds}}{18\text{ people}} \\ x=\frac{18}{18}\text{ pounds} \\ x=1\text{ pound} \end{gathered}[/tex]Therefore, 1 pound of meat is recommended to feed 4 people.
*How many pounds are recommended to feed 1 person
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 1\text{ person}\rightarrow x\text{ pounds} \\ x=\frac{1\text{ person}\ast4.5\text{ pounds}}{18\text{ people}} \\ x=\frac{1}{4}\text{ pounds} \end{gathered}[/tex]Therefore, 1/4 pound of meat is recommended to feed 1 person.
A student is initially outside. He is given the choice with a probability of 0.4 of going to the playground, 0.3 of shopping in the mall and 0.3 of returning home. If he is in the playground, he takes 2 hrs of time and then decides to stay in the playground again or return back home. (he can continue to decide to stay in playground like a recursive process) Similarly, If he is in the mall, he takes 3 hrs of time and then decides to stay in the mall again or return back home. (he can continue to decide to stay in mall like a recursive process) For all cases, it takes 1 hr to return home. what is the expected hours the student was outside home?
Answers
Based on the probability values, it will take the student 2 hours to stay outside the home
How to determine the expected value of the student?The given parameters are:
Probabilities
P(1) = 0.4
P(2) = 0.3
P(3) = 0.3
Time
Time 1 = 2 hours
Time 2 = 3 hours
Time 3 = 1 hour
When the above are represented on a table, we have the following table of values
Time (x) | 2 3 1
Probability (P(x)) | 0.4 0.3 0.3
The expected value of the student is then calculated as
E(x) = ∑ x * P(x)
Substitute the known values in the above equation
E(x) = 2 * 0.4 + 3 * 0.3 + 1 * 0.3
Evaluate the products
E(x) = 0.8 + 0.9 + 0.3
Evaluate the sum
E(x) = 2
Hence, the expected value is 2
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Construct a difference table to predict the next term of sequence. 6, 1, 0, 10, 38, 91,.......
Answers
Number..................Difference1........... Difference 2.....Difference 3
6...........................................................................................
1................................ -5......................................................
0.............................. -1....................................4..............
10.............................. 10..................................11......................7
38.............................. 28................................18..................... 7
91.............................. 53................................25................... 7
176............................85..............................32
Answer:
Next number in sequence 176