Answers
This is a telescoping sum. The K-th partial sum is
[tex]S_K = \displaystyle \sum_{k=1}^K \left(\frac1{\sqrt{k+1}} - \frac1{\sqrt{k+3}}\right) \\\\ ~~~= \left(\frac1{\sqrt2} - \frac1{\sqrt4}\right) + \left(\frac1{\sqrt3} - \frac1{\sqrt5}\right) + \left(\frac1{\sqrt4} - \frac1{\sqrt6}\right) + \left(\frac1{\sqrt5} - \frac1{\sqrt7}\right) + \cdots \\\\ ~~~~~~~~+ \left(\frac1{\sqrt{K-1}} - \frac1{\sqrt{K+1}}\right) \\\\ ~~~~~~~~+ \left(\frac1{\sqrt K} - \frac1{\sqrt{K+2}}\right) + \left(\frac1{\sqrt{K+1}} - \frac1{\sqrt{K+3}}\right)[/tex]
[tex]\displaystyle = \frac1{\sqrt2} + \frac1{\sqrt3} - \frac1{\sqrt{K+2}} - \frac1{\sqrt{K+3}}[/tex]
As [tex]K\to\infty[/tex], the two trailing terms will converge to 0, and the overall infinite sum will converge to
[tex]\displaystyle \sum_{k=1}^\infty \left(\frac1{\sqrt{k+1}} - \frac1{\sqrt{k+3}}\right) = \lim_{k\to\infty} S_k = \boxed{\frac1{\sqrt2} + \frac1{\sqrt3}}[/tex]
By the limit comparison test, the expression √[1 / (1 + 1 / k)] - √[1 / (1 + 3 / k)] has a limit, then the expression [1 / √(k + 1)] / [1 /√k] - [1 / √(k + 3)] / [1 /√k] has a limit and the series ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)] is convergent.
Is the series convergent?
Herein we have a series that involves radical components. First, we simplify the expression given:
∑ [1 / √(k + 1) - 1 / √(k + 3)] = ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)]
The convergence of the series can be proved by the limit comparison test, where each component of the subtraction of the series is compared with a series that is convergent. We notice that both 1 / √(k + 1) and 1 / √(k + 3) resembles the expresion 1 /√k. Then, we have the following subtraction of ratios:
[1 / √(k + 1)] / [1 /√k] - [1 / √(k + 3)] / [1 /√k]
√k / √(k + 1) - √k / √(k + 3)
√[k / (k + 1)] - √[k / (k + 3)]
Then, by using the limit property for rational functions we find the following result for n → + ∞:
√[1 / (1 + 0)] - √[1 / (1 + 0)]
√1 - √1
1 - 1
0
By the limit comparison test, the expression √[1 / (1 + 1 / k)] - √[1 / (1 + 3 / k)] has a limit, then the expression [1 / √(k + 1)] / [1 /√k] - [1 / √(k + 3)] / [1 /√k] has a limit and the series ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)] is convergent.
Remark
The statement is incomplete and complete form cannot be found, therefore, we decided to determine if the series is convergent or not.
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Related Questions
The measure of central angle qrs is startfraction 8 pi over 9 endfraction radians. what is the area of the shaded sector?
Answers
The area of the shaded sector is 144π units squared.
What is a sector?A circular sector, also known as a circle sector or disk sector, is a piece of a disk bounded by two radii and an arc, with the smaller area known as the minor sector and the larger area known as the major sector.To find the area of the shaded sector:
Given - The central angle of the sector is, θ [tex]=\frac{8\pi }{9} rad[/tex].
The radius of the circle is, [tex]R=18 units[/tex].
We know that the area of a sector of a circle of radius 'R' and central angle θ is given as:
[tex]A=\frac{1}{2} R^{2}[/tex]θ
Insert, θ [tex]=\frac{8\pi }{9} ,R=18[/tex] and obtain:
[tex]A=\frac{1}{2} *18^{2} *\frac{8\pi }{9} \\A=\frac{(324*4)}{9} \pi \\A=(36*4)\pi \\A=144\pi units^{2}[/tex]
Therefore, the area of the shaded sector is 144π units squared.
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The complete question is given below:
The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared
A group of 15 teenagers owes $75 at a pizza parlor. If they split the bill evenly, how much will each person owe?
Answers
Answer:
$5 each teenager
Step-by-step explanation:
divide 75 by 15
75 divided by 15= 5
pls help i don’t know how to do this
Answers
Answer: [tex]\displaystyle\\\frac{2\pi }{3},\ \frac{5\pi }{3} .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\tan\theta=-\sqrt{3}\ \ \ \ 0\leq \theta\leq 2\pi \\\theta =\frac{2\pi }{3}+\pi N\ \ \ (N=0,\ 1,\ 2,\ 3\ ...)\\ N=0\\\theta=\frac{2\pi }{3} +\pi *0\\\theta=\frac{2\pi }{3}\ \ \ \ ( 0\leq \theta\leq 2\pi)\\ N=1\\\theta=\frac{2\pi }{3}+\pi *1 \\\theta=\frac{2\pi }{3} +\pi \\\theta=\frac{2\pi +3\pi }{3} \\\theta=\frac{5\pi }{3} \ \ \ ( 0\leq \theta\leq 2\pi)\\[/tex]
[tex]N=2\\\theta=\frac{2\pi }{3}+2\pi \\ \theta=\frac{2\pi +3*2\pi }{3}\\ \theta=\frac{2\pi +6\pi }{3} \\\theta=\frac{8\pi }{3} \\\theta=2\frac{2}{3} \pi \ \ \ \ (\notin0\leq \theta\leq 2\pi).\\[/tex]
Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x 3y=108
Answers
For given f(x, y) the extremum: (12, 24) which is the minimum.
For given question,
We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108
We use the constraint to build the constraint function,
g(x, y) = 3x + 3y
We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:
[tex]f_x=8x[/tex]
[tex]f_y=4y[/tex]
[tex]g_x=3[/tex]
[tex]g_y=3[/tex]
Setting up the Lagrange multiplier equations:
[tex]f_x=\lambda g_x[/tex]
⇒ 8x = 3λ .....................(1)
[tex]f_y=\lambda g_y[/tex]
⇒ 4y = 3λ ......................(2)
constraint: 3x + 3y = 108 .......................(3)
Taking (1) / (2), (assuming λ ≠ 0)
⇒ 8x/4y = 1
⇒ 2x = y
Substitute this value of y in equation (3),
⇒ 3x + 3y = 108
⇒ 3x + 3(2x) = 108
⇒ 3x + 6x = 108
⇒ 9x = 108
⇒ x = 12
⇒ y = 2 × 12
⇒ y = 24
So, the saddle point (critical point) is (12, 24)
Now we find the value of f(12, 24)
⇒ f(12, 24) = 4(12)² + 2(24)²
⇒ f(12, 24) = 576 + 1152
⇒ f(12, 24) = 1728 ................(1)
Consider point (18,18)
At this point the value of function f(x, y) is,
⇒ f(18, 18) = 4(18)² + 2(18)²
⇒ f(18, 18) = 1296 + 648
⇒ f(18, 18) = 1944 ..............(2)
From (1) and (2),
1728 < 1944
This means, given extremum (12, 24) is minimum.
Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.
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Find the value of x.
OA. 66
OB. 122
OC. 98
O D. 76
SUBMIT
Answers
Answer:
C) 98
Step-by-step explanation:
Hope this helps! sry if I'm wrong
The value of x in the given equation 15x + 120 = 5x + 1100 is 98. Option C is correct.
An equation is a combination of numbers, variables, mathematical operations, and functions. It is basically a statement emphasising that the two or more expressions are equal to each other.
The given equation is
15x + 120 = 5x + 1100
Take the like terms together,
15x - 5x = 1100 - 120
10x = 980
x = [tex]\frac{980}{10}[/tex]
x = 98.
Thus, the option C is correct stating that the value of x in the given equation is 98.
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The complete question is as follows:
Find the value of x in the equation:
15x + 120 = 5x + 1100.
A. 66
B. 122
C. 98
D. 76
SUBMIT.
Need help with my math please. 31-41.
Answers
Step-by-step explanation:
31) the answer is (98765x9) +3=888888
why if u look at the equation is descending and if u verify the cinjecture u will find out is correct
41)½+¼+⅛+1/16+1/32=1-1/32
just d same reason with (31)
The graph of the function f(x)= 5/4 sin(x)+1 is shown. What are the key features of this function?
- The maximum value of the function is....(2pi,2.25,1)
- The minimum value of the function is...(pi/2,-0.25,-1)
- On the interval (0,pi/2), the function is...(increasing, decreasing)
-the range of the function is...([-0.25,2.24],all real numbers, [-1,1])
Answers
The answers to this question can be given as
The maximum value of the function is 2.25- The minimum value of the function is -0.25- On the interval (0,pi/2), the function is increasing-the range of the function is ([-0.25,2.25]What is the maximum value of a function?This is the point of the function while is it shown on the graph where it is said to be at its highest point or it is at its highest vertex.
When you trace the graph, the highest point is at 2.25.
What is the minimum value of a function?This is the point or the part of the function where it is at the vertex that is the lowest in the graph.
This is at -0.25
This is a function that can be said to be increasing from the behavior of this graph.
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of
Given the triangle ABC at points A=(1,6) B=(-3,5) C=(7,1), and if the triangle is first reflected over the
y axis, and then over the x axis, find the new point A".
Select one:
O a. (1,-6)
Ob. (3,5)
Oc. (-1,-6)
O d. (1,6)
Answers
After reflected over the triangle the point a become A = (-1,-6). The option c is correct.
According to the statement
we have given that the a triangle ABC at the points A=(1,6) B=(-3,5) C=(7,1), and we have to find the points of a when the triangle is first reflected over the y axis.
So, For this purpose
we know that the when the triangle is at the x axis then the point A is A=(1,6).
But when the triangles reflected over the y - axis then the point A goes to the negative side of the graph. In other words whole of the triangle shift to the negative side of the graph. That's why the point become negative.
So, The option c is correct. After reflected over the triangle the point a become A = (-1,-6)
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Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. if he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings? a. $40 b. $60 c. $74 d. $55
Answers
The total amount he puts towards emergency savings is $74
The correct option is C.
According to the given information:His total weekly deposits are as follows: 219+115+40+20+10+40+15 = 459
Now
that we are aware, his weekly deposits total $459 in total.
His total remuneration is $498 due to an error in his addition of the numbers.
The amount he has each week will be determined by deducting his deposits from his paycheck:
498-459 = 39
He contributes two equal payments of $20 and $15 to his emergency fund.
His entire contribution to emergency savings is = 20 + 15 = 35.
Only need to add the additional $39
To determine how much he can set aside each week for emergency savings, multiply his total emergency savings by 35 dollars:
39+35 = 74
the total per week that he can put towards emergency savings = $74
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I understand that the question you are looking for is:
Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Pictable) Education investment fund $10 Other (Pictable) Retirement investment fund $40 Other (Pictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?
a. $40
b. $60
c. $74
d. $55
Answer: C. $74
Step-by-step explanation: C. $74.00
A gardener wants to design a rectangular garden and has 100 feet of fencing available. A house is on one side of the garden, so no fencing will be needed there. What dimensions will give the maximum area?
Answers
Answer:
50 ft and 25 ft give the maximum area
Step-by-step explanation:
Let l and w be the dimensions of rectangle.
The length of fencing is 100 ft:
l + 2w = 100Then:
l = 100 - 2wThe area is:
A = lw = w(100 - 2w) = 100w - 2w²In order to have the maximum area we need to find the vertex of the quadratic function:
y = - 2w² + 100wThe vertex has x-coordinate:
w = - b/(2a) It comes from quadratic function y = ax² + bx + cor
w = - 100/(2*(-2)) = 25So the width is 25 ft.
Find the length:
l = 100 - 2*25 = 50 ftThe area is:
A = 50*25 = 1250 ft²See the attached graph.
Rewrite the function by completing the square. f(x) = x2 - 8x + 7
Answers
The function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x + 16 = 9.
Rewrite the function by completing the square?Given the function; f(x) = x² - 8x + 7
To rewrite by completing the square.
We simplify the function into a proper form to completing the square.
x² - 8x + 7 = 0
x² - 8x = -7
We create a trinomial square on the left side of the equation that is equal to the square of the half of b.
(b/2)² = (-4)²
Next, we add the term to both side of the equation.
x² - 8x + (-4)² = -7 + (-4)²
x² - 8x + 16 = 9
Therefore, the function f(x) = x2 - 8x + 7 rewritten by completing the square is x² - 8x + 16 = 9.
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Given the function f(x) = -5x²-x+ 20, find f(3).
O-28
O-13
O62
O64
Answers
Answer: [tex]\Large\boxed{First~Choice.~-28}[/tex]
Step-by-step explanation:
Given function expression
f(x) = -5x² - x + 20
Requirement of the question
Find the value of f(3)
Substitute the values into the function
f(x) = -5x² - x + 20
f(3) = -5(3)² - (3) + 20
Simplify the exponents
f(3) = -5(9) - 3 + 20
Simplify by multiplication
f(3) = -45 - 3 + 20
Simplify by subtraction and addition
f(3) = -48 + 20
[tex]\Large\boxed{f(3)=-28}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Is (1, 3) a solution to the system of inequalities below?
y> 2x + 1
y <-3x
Why or why not?
Answers
[tex]y > 2x + 1 \\ 3 > 2(1) + 1 \\ 3 > 3 \\ false[/tex]
We can stop here and conclude that ( 1 , 3 ) is not a solution to this system, since it does not even satisfy the first equation, but check for the other one just in case:[tex]y < - 3x \\ 3 < - 3(1) \\3 < - 3 \\ also \: false[/tex]
Classify the following function.
Answers
The equation is neither geometric nor arithmetic
How to classify the function?The function is given as
f(x) = 2x^2 + 6x - 9
As a general rule, arithmetic functions or sequences have a common difference while geometric functions or sequences have a common difference
Set x = 0, 1 and 2
f(0) = 2(0)^2 + 6(0) - 9 = -9
f(1) = 2(1)^2 + 6(1) - 9 = -1
f(2) = 2(2)^2 + 6(2) - 9 = 11
Calculate the common difference (d)
d = 11 --1 = -1--9
d = 12 = 8 ---- false equation i.e. no common difference
Calculate the common ratio (r)
r = 11/-1 = -1/-9
d = -11 = 1/9 ---- false equation i.e. no common ratio
The above function is not an arithmetic function.
This is so because it does not have a common difference
Also, the function is not a geometric function.
This is so because it does not have a common ratio
Hence, the true statement about the function is (c) the equation is neither geometric nor arithmetic
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When the shape of a bst approaches that of a perfectly balanced binary tree, what is the worst case performance characteristic of searches and insertions?
Answers
The shape of a bst approaches that of a perfectly balanced binary tree, (log2n) is the time complexity for a balanced binary search tree in case of insertions and search.
In computing, binary bushes are mainly used for looking and sorting as they offer a way to save statistics hierarchically. a few common operations that may be conducted on binary trees encompass insertion, deletion, and traversal.
A binary tree has a special situation that each node could have a most of two youngsters. A binary tree has the benefits of each an ordered array and a linked listing as search is as brief as in a taken care of array and insertion or deletion operation are as fast as in related listing.
In pc science, a binary tree is a tree information shape in which every node has at maximum two youngsters, that are known as the left baby and the proper toddler.
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A shape has an area of 37 mm², of which 60%
is green.
The shape is enlarged so that all its side lengths
increase by 45%.
Work out the area of the green part of the larger
shape.
If your answer is a decimal, give it to 1 d.p.
Answers
If the side are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].
Given that area of a shape of 37 [tex]mm^{2}[/tex] in which 60% is green.
We are required to find the area of green region if the side is increased by 45%.
Area is basically part of a surface covered by a shape.
When the side is increased by 45% then the area will increase by 45%*45%=20.25%.
Increased area =37*20.25%=7.4925
New area=37+7.4925
=44.4925
We have been given that 60% is the area of green.
Area of green region=44.4925*60/100
=26.6955 [tex]mm^{2}[/tex]
Hence if the sides are increased by 45% then the area of green part will be 26.6955 [tex]mm^{2}[/tex].
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G
Which point is located at (-3.5.-4.5)?
Y
A
(1
-5-4-3-2-1
point A
point K
point R
4
-3-
2
10
-I ? ? + 4
2
3
2 3 4
en.
5
X
Answers
this is because if you go left 3.5 and down 4.5, you will reach point A
please help i dont understand
Answers
The box and whisker plot is a 71 and 53 and 89 which represent the
median, upper value and lower value.
According to the statement
we have given that the some data of the marks of 18 students and we have to make the plot of that data.
So, For this purpose, we have given that the
A box and whisker plot is a visual tool that is used to graphically display the median, lower and upper quartiles, and lower and upper extremes of a set of data.
And it is used to find the median and the lower value and the maximum value.
So, The median become:
median = n /2
median = 18/2
median = 9th term and
median value is 71.
And then the lower value of the data is a 53.
And the upper value of the data is a 89.
So, overall we can say that the combination of median, upper value and lower value is called the box and whisker plot.
So, The box and whisker plot is a 71 and 53 and 89 which represent the
median, upper value and lower value.
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Draw at least six different sized rectangles that have an area of 64 square units then find the perimeter of each rectangle.
Answers
Six different sized rectangles that have an area of 64 square units:
1) 64 units x 1 unit
2) 32 units x 2 units
3) 16 units x 4 units
4) 40 units x 1.4 units
5) 20 units x 3.2 unit
6) 10 units x 6.4 units
For given question,
Let l be the length of the rectangle and w be the width of the rectangle.
We know that, the area of a rectangle is equal to
A = l × w
Here, A = 64 square units
So, we get an equation
l × w = 64 ...............................(1)
let's assume different values of l to get the different values of w.
Case 1) For l = 64 units
substitute in the equation 1
⇒ 64 × w = 64
⇒ w = 64/64
⇒ w = 1 units
The dimensions of the rectangle are 64 units x 1 unit
See the draw in the attached figure 1
Case 2) For l = 32 units
substitute in the equation 1
⇒ 32 × w = 64
⇒ w = 64/32
⇒ w = 2 units
The dimensions of the rectangle are 32 units x 2 unit
See the draw in the attached figure 2
Case 3) For l = 16 units
substitute in the equation 1
⇒ 16 × w = 64
⇒ w = 64/16
⇒ w = 4 units
The dimensions of the rectangle are 16 units x 4 unit
See the draw in the attached figure 3
Case 4) For l = 40 units
substitute in the equation 1
⇒ 40 × w = 64
⇒ w = 64/40
⇒ w = 1.4 units
The dimensions of the rectangle are 40 units x 1.4 unit
See the draw in the attached figure 4
Case 5) For l = 20 units
substitute in the equation 1
⇒ 20 × w = 64
⇒ w = 64/20
⇒ w = 3.2 units
The dimensions of the rectangle are 20 units x 3.2 unit
See the draw in the attached figure 5
Case 6) For l = 10 units
substitute in the equation 1
⇒ 10 × w = 64
⇒ w = 64/10
⇒ w = 6.4 units
The dimensions of the rectangle are 10 units x 6.4 unit
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A die is rolled. if it rolls to a 1 or 2, you win 2 usd. if it rolls to a 3, 4, 5, or 6, you will lose 1 usd. what is the expected payoff from rolling this die?
Answers
The expected payoff from rolling the die is 0 usd.
According to the given question.
A die is rolled.
So, the possiblbe outcomes for a dice = {1, 2, 3, 4, 5, 6}
⇒ Total number of outcomes = 6
Also, it is given that
If a die is roll to a 1 or 2, we win 2usd and if it rolls to 3, 4, 5, or 6 we lose 1 usd.
As, we know that "Probability denotes the possibility of the outcome of any random event". And probability of any event can be calculated as
P(E) = total number of favorable outcomes/ Total number of outcomes
So,
The probability that die rolls 1 or 2 = 1/6 + 1/6 = 2/6 = 1/3
And, the probability thet die rolls 3, 4, 5, or 6
= 1/6 + 1/6 + 1/6 + 1/6
= 4/6
= 2/3
Therefore, the excepted payoff from rolling this die
= [tex]2\times\frac{1}{3} - 1\times\frac{2}{3}[/tex]
[tex]= \frac{2}{3} - \frac{2}{3}[/tex]
= 0 usd
Hence, the expected payoff from rolling the die is 0 usd.
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9/[tex]9/3-6/10[/tex]-6/10
Answers
The value of expression 9/9/3-6/10-6/10 is 9/5.
Given an expression 9/9/3-6/10-6/10.
We are required to simplify the expression 9/9/3-6/0-6/10.
Expression is combination of numbers,fraction, coefficients, determinants,indeterminants, symbols.It is mostly not found in equal to form. It also includes algebraic operations also.
Expressions: 9/9/3-6/10-6/10
This is present in fraction which is combination of two numbers one is numerator and denominator. The numbers above division sign are known as numerator and the numbers below division sign are known as denominator.
Invert the fraction which is given in denominator.
=(9*3)/9-6/10-6/10
=27/9-6/10-6/10
Taking LCM now.
=(270-54-54)/90
=(270-108)/90
=162/90
=9/5
Hence the value of expression 9/9/3-6/10-6/10 is 9/5.
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Please answer quickly! Several questions from Algebra 2, on a unit about Sequences and Series, most of these have to do with Arithmetic and Geometric Series-screenshots of the questions are linked below. It would be great if you could include the question # and the answer in the answer section, and then explain it below. Thank you in advance!
Answers
The sum of the geometric series is 2199; option E.
The 36th term of the arithmetic series is -60.5 option CThe sum of the arithmetic series is 2547; option EThe missing geometric sequence are; 1.614375, 3.30946875, 6.7844109375. option EArithmetic and Geometric seriesa1 = 1458r = 1/3a6 = 6S6 = a(rⁿ - 1) / r -1
= 1468(1/3^6 - 1) / (1/3 - 1)
= 1468(0.00137174211248 - 1) / -2/3
= 1468(-0.9986282578875) / -0.66666666666666
= -1,465.98628257885 / -0.66666666666666
= 2198.97942386829
Approximately,
S6 = 2199
Arithmetic series
a36a1 = 27d = -5/2Sn = n/2{2a + (n -1)d}
= 36/2 {2×27 + (36-1)-5/2}
= 18{54 + (35)-5/2}
= 18(54 + 175/2)
= 18(54 + 87.5)
= 18(141.5)
s36 = 2547
a36 = a + (n - 1) d
= 27 + (36 - 1)-5/2
= 27 + (35)-5/2
=27 + -175/2
= 27 - 87.5
= -60.5
S20 = n/2{2a + (n -1)d}
= 20/2{2×27 + (20-1)-5}
= 10(54 + (19)-5)
= 10{54 + (-95)}
= 10(54-95)
= 10(-41)
s20 = -410
Missing terms of the geometric sequence:
nth term = ar^n-1
448/135 = 63/80×r^(6-1)
448/135 = 63/80×r^5
r^5 = 448/135 ÷ 63/80
= 448/135 × 80/63
= 35,840/8,505
r = 5√35,840/5√8505
= 946.57/461.11
r = 2.05
Second term = a×r
= 63/80×2.05
= 1.614375
Third term = ar²
= 63/80×2.05²
= 63/80×4.2025
= 3.30946875
Fourth term = 63/80 × 2.05³
= 63/80×8.615125
= 6.7844109375
Therefore, none of these are correct
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A vase in the shape of an oblique cylinder has the dimensions shown. What is the volume in the vase in liters?round nearest tenth
Answers
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Cylinder is solid geometrical figure with straight parallel sides and a circular or oval cross section
Let us assume that the vase has a base with radius of 1 m and height of 7 m, hence:
Volume of vase = π * radius² * height
Volume of vase = π * (1)² * 7 = 22 m³ = 22000 L
The volume of a vase with a radius of 1 m and height of 7 m is 22000 L
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Please help! What is the equation for g(x)? According to the graph ?
Answers
Answer: [tex]g(x)=2^{x-3}[/tex]
Step-by-step explanation:
The graph of y=g(x) is the graph of y=f(x) shifted 3 units right.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the properties to the regular polygons they describe.
Answers
A polygon is a figure that has a given number of sides.
What is a polygon?A polygon is an n - sided figure. The number of sides in a polygon is almost infinite. Let us now match the properties with the type of polygon.
a. 12.gon - An interior angle measures 150°
The polygon that has 12 sides is called the Dodecagon.
Given that the sum of the interior angles in a dodecagon is 1800, then each interior angle is; 1,800/12
= 150°
b. 15-gon - An exterior angle measures 24°
The polygon that contains 15 sides is called pentadecagon. Given that the sum of the exterior angles of polygon is 360 degrees and each exterior angle is 24° then;
360/ 24° = 15 sides
c. 16-gon - The sum of the interior angles is 2,520°
The polygon that contains 16 sides is called the hexadecagon. The sum of its interior angles is 2,520° hence each interior angle measures; 2,520°/16 = 157.5°
d. 18-gon - An interior angle measures 160°
A polygon that contains 18 sides is called an octadecagon .
We have;
160 = (n−2) × 180° / n
160n = 180n - 360
360 = 20n
n = 18
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Missing parts;
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the properties to the regular polygons they describe.
An interior angle measures 150".
An exterior angle measures 24.
The sum of the interior angles is 2520°.
An interior angle measures 160".
The sum of the exterior angles is 180º.
The sum of the interior angles is 2160°.
15-gon
16-gon
12.gon
18-gon
Answer:
15 gon = An exterior angle measure 2416 gon = The sum of the interior angles is 2,52012 = An interior angle measure 15018 = An interior angle measure 160Step-by-step explanation:
A Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. Which Equations Can Be Used To Find The Numbers Of Miles Driven For A Truck That Cost A Total Of $42.50 To Rent For One Day?
A)$25m + 0.35m = $42.50
B)$0.35 + $25m = $42.50
C)$42.50 + $0.35m = $25
D)$0.35 = $42.50
Answers
The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
According to the statement
we have given that the Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. and a Truck That Cost A Total Of $42.50 To Rent For One Day.
And we have to find the equation for this.
So, for given purpose,
we know that the A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
And from the given values the equation formed that the
In the equation the charges per mile is added to the original charges is equal to the total charges per day.
So, The equation become
$25m + 0.35m = $42.50
And by this equation we represent the all given conditions related charges.
So, The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
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Question 3 of 10
Which of the following must be true for an expression to be a difference of
two squares?
a. all variables are raised to an even power
b. there are only two terms
c. both terms have negative coefficients
OA. a, b, and c
B. a and b
OC. a and c
D. b and c
Answers
B is true: you cannot have a trinomial, only binomial or two terms
C is FALSE: you cannot take a square root of a negative and get a real number
B. a and b
Several properties are used to evaluate this expression. identify the property used in each step. 21 + (19 + 36): (21 + 19) + 36:
Answers
21 + (36 + 0 + 19) Equals 76.
What is the property of addition?A final result is obtained by adding two or more integers together. Commutative, associative, distributive, and additive identity are the four major characteristics of b. b means that even if the order changes, the addition result will remain the same.
Equation to be used: 21 + (36 + 0 + 19)
The identity property of addition states that a + 0 = a.21 + (36 + 0 + 19) = 21 + (36 + 19)Using the commutative property of addition, a + b equals a + b.21 + (36 + 19) Equals 21 + (19 + 36)By using the associative property of addition, the formula is: a + (b + c) = a + b + c.21 + (19 + 36) Equals (21 + 19) + 36Put two more numbers within the bracket now.(21 + 19) + 36 = 40 + 36A + B Equals C, any number, using the closure property of addition.40 + 36 = 76Hence 21 + (36 + 0 + 19) Equals 76.To know more about property of addition visit:
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I understand that the you are looking for is :
Several properties are used to evaluate this expression. Identify the property used in each step.
21 + (36 + 0 + 19)
21 + (36 + 19):
21 + (19 + 36):
(21 + 19) + 36:
40 + 36
76
Complete the equivalent ratio. How many ounces are in 2 cups?
StartFraction 48 ounces Over 6 cups EndFraction = StartFraction question mark ounces Over 2 cups EndFraction
Answers
2 Cups = (8 Ounces) x 2
2 Cups = 16 Ounces
I hope that this helps! :)
A day care program has an average daily expense of $75.00. the standard deviation is $5.00. the owner takes a sample of 64 bills. what is the probability the mean of his sample will be between $70.00 and $80.00? step 1. calculate a z-score for $70.00 - step 2. give the probability for step 1. % step 3. calculate the z-score for $80.00 step 4. give the probability for step 3. % step 5. add the probabilities from steps 2
Answers
Answer:
B. 68
Step-by-step explanation:
x is a raw score to be standardized;
μ is the mean of the population;
σ is the standard deviation of the population.
Therefore the mean is zero. Seventy is -1z, or -1 standard deviation.
Step 2: 34.13% of the cases fall between -1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 70 and 75. This, of course, assumes a normal curve.
Step 3: An 80 is +1z or +1 standard deviation assuming a normal curve.
Step 4: Thirty four percent of the cases fall between +1 standard deviation and the mean. Thus there is a 34.13% chance that the score will fall between 75 and 80. This, of course, assumes a normal curve.
Step 5: Score between +1z and -1z, or +1 and -1 standard deviation account for 68.26% of the cases.
