Answers
Answer:
The correct option is;
[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex]
Step-by-step explanation:
The given expression is presented as follows;
[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right )[/tex]
Which can be expanded into the following form;
[tex]\sum\limits _{n = 1}^{50} \left (4\cdot n^2 + 3 \cdot n\right ) = 4 \times \sum\limits _{n = 1}^{50} \left n^2 + 3 \times\sum\limits _{n = 1}^{50} n[/tex]
From which we have;
[tex]\sum\limits _{k = 1}^{n} \left k^2 = \dfrac{n \times (n+1) \times(2n+1)}{6}[/tex]
[tex]\sum\limits _{k = 1}^{n} \left k = \dfrac{n \times (n+1) }{2}[/tex]
Therefore, substituting the value of n = 50 we have;
[tex]\sum\limits _{n = 1}^{50} \left k^2 = \dfrac{50 \times (50+1) \times(2\cdot 50+1)}{6}[/tex]
[tex]\sum\limits _{k = 1}^{50} \left k = \dfrac{50 \times (50+1) }{2}[/tex]
Which gives;
[tex]4 \times \sum\limits _{n = 1}^{50} \left n^2 = 4 \times \dfrac{n \times (n+1) \times(2n+1)}{6} = 4 \times \dfrac{50 \times (50+1) \times(2 \times 50+1)}{6}[/tex]
[tex]3 \times\sum\limits _{n = 1}^{50} n = 3 \times \dfrac{n \times (n+1) }{2} = 3 \times \dfrac{50 \times (51) }{2}[/tex]
[tex]\sum\limits _{n = 1}^{50}n\times \left (4\cdot n + 3 \right ) = 4 \times \dfrac{50 \times (50+1) \times(2\times 50+1)}{6} +3 \times \dfrac{50 \times (51) }{2}[/tex]
Therefore, we have;
[tex]4 \left (\dfrac{50 (50+1) (2\times 50+1)}{6} \right ) +3 \left (\dfrac{50(51) }{2} \right )[/tex].
Related Questions
PLEASE HELP! WILL MARK BRAINLIEST! 13 POINTS! THX! Two bicycles are driving on the circle in the same direction with speeds of 9 mph and 5 mph respectively. How many points are there on the circle where the two bicycles meet.
Answers
Answer
The points where the two bicycles meet after every 6hr at 30 miles and 54 miles.
please hurry! ill give brainliest to the fastest answer!
Which expression would the model be most helpful in solving?
An area model has 5 shaded parts and 1 unshaded part. The shaded part is labeled 5/6.
A. 1/6 ÷ 5/6
B. 5/6 ÷ 1/6
C. 6 ÷ 1/6
D. 6 ÷ 5/6
Answers
5/6 divided 1/6, this is the correct answer
:))))
Answer:
5/6 ÷ 1/6
Step-by-step explanation:
The following table shows the results of a vote for Lola's dance team's color. Color Number of votes Blue 9 Green 4 Red 8 Yellow 3 Pink 5 Find the mean number of votes.
Answers
Answer:
5.8
Step-by-step explanation:
Mean= Sum of votes/No of Votes
Sum of votes: 9+4+8+3+5= 29
No of votes= 5 (9,4,8,3,5)
Mean= 29/5= 5 4/5
5 4/5= 5.8
The mean number of votes are 5.8.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The given table is below
Color Number of votes
Blue 9
Green 4
Red 8
Yellow 3
Pink 5
We have to find the mean number of votes.
Mean = sum of observations/total number of observations
=9+4+8+3+5/5
=29/5
=5.8
Hence, the mean number of votes are 5.8.
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Write an equation in the form y=mx for the following situation. Then give the three ordered pairs associated with the equation for x-values of 0, 5, and 10.
x represents the number of hours traveling at 60 mph, and y represents the distance traveled (in miles).
What is the equation?
Answers
Answer:
y = 60x
(0, 0)
(5, 300)
(10, 600)
Step-by-step explanation:
since x is the number of hours, 60 will represent m.
y = 60x.
Plug in x values.
Plug in 0 and get a y of 0. (0,0)
Plug in 5 and get a y of 300. (5, 300)
Plug in 10 and get a y of 600. (10, 600)
explain constraint of domain on parabola graphs
Answers
Answer:The set of possible values for the independent variable is called the domain. Similarly, there are constraints on the values for any dependent variable. ... Graphs of functions are traditionally drawn with the independent variable on the horizontal axis and the dependent variable on the vertical axis.
Step-by-step explanation:
Which of these numbers is the most precise approximation of?
Answers
Answer:
[tex]\boxed{3.464}[/tex]
Step-by-step explanation:
Calculate the square root.
[tex]\sqrt{12} = 3.46410161514[/tex]
Approximate the value.
[tex]\sqrt{12} \approx 3.464[/tex]
Answer:
d
Step-by-step explanation:
to find the square root of a # see how many times a # can go into the root, find the # with the greatest value
Which point is the image of R? Choose one answer: A B C D
Answers
Answer:
point D
Step-by-step explanation:
moving 270 degrees clockwise from point R would result in the point being in quadrant I
point D is the only point in quadrant I
These dot plots show the ages (in years) for a sample of sea turtles and a
sample of koi fish.
Age (in years)
What are the differences between the centers and spreads of these
distributions?
Select two choices: one for the centers and one for the spreads.
a A. Centers: The sea turtles have a lower median age than the koi.
3. B. Centers: The sea turtles have a greater median age than the koi.
c. Spreads: The ages of the sea turtles are more spread out.
D D. Spreads: The ages of the koi are more spread out.
Answers
*see attachment below for the dot plots that completes the question.
Answer:
B. Centers: The sea turtles have a greater median age than the koi.
D. Spreads: The ages of the koi are more spread out.
Step-by-step explanation:
The measure of center that can be used for comparison is the median, while the spread can simply be visualised by mere looking at how spread out the dots on the number line are. The spread of both can also be compared using their range. The greater the range, the more spread a data is.
=>Median Differences:
The median age for turtle = the middle value = 55
The median age for koi = 30
Therefore, sea turtles have a greater median age than the koi.
=>Spread Differences:
Range for turtle = the highest age - the least age represented on the dot plot = 65 - 45 = 20
Range for koi = 55 - 10 = 45
Koi has a greater range value than koi. Therefore, the ages of the koi are more spread out.
What is the equation of the ellipse with foci at (5, 0), (-5, 0) and vertices (9, 0), (-9, 0)?
Answers
Answer: [tex]\dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
Step-by-step explanation:
General equation of ellipse : [tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}[/tex]
Given: Vertices of ellipse : (± 9,0)
Since the vertices are of the form (± a, 0).
i.e. a=9
Thus, the major axis is along x-axis.
Also, foci of the ellipse = (±5,0)
Since, foci is of the form (± c,0), i.e. c=5
Since
[tex]c^2=a^2-b^2\\\\\Rightarrow\ 5^2= 9^2-b^2\\\\\Rightarrow\ b^2=81-25\\\\\Rightarrow\ b^2=56[/tex]
Equation of ellipse :
[tex]\dfrac{x^2}{9^2}+\dfrac{y^2}{56}=1\\\\\Rightarrow\ \dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
Hence, the required equation : [tex]\dfrac{x^2}{81}+\dfrac{y^2}{56}=1[/tex]
please help- my final is timed! xx Identify the graph of the triangle with vertices P(1,4), Q(1,1), R(3,1). Then identify the image that represents ΔPQR rotated 90° counterclockwise around vertex Q and the resulting image reflected across the x-axis.
Answers
Answer:
Since it is a negative degree it’s a counter clockwise meaning the fourth picture or D with the vertexs being p’(-2,-1),q’(1,-1),r’(1,-3)
Step-by-step explanation:
solve for y: y÷1 7/9 = 3/4
Answers
Answer:
y = 4/3
Step-by-step explanation:
The required value of fraction y is 4/3.
Given that,
[tex]\frac{y}{1\frac{7}{9} } = 3/4[/tex]
Fraction y is to be determined by simplification.
The process in mathematics to operate and interpret the function to make function simple or more understandable is called simplifying and the process is called simplification.
What is the fraction?Fraction is defined as the number of compositions that constitute the Whole. Fraction is represented as x = a / b where the upper value is termed as the numerator and the lower value is the denominator.
⇒Simplification
[tex]\frac{y}{1\frac{7}{9} } = 3/4[/tex] ( 1 + 7 / 9 = 16 / 9)
[tex]\frac{y}{\frac{16}{9} } = 3/4[/tex] (Transposition of 16/9 from the denominator to the right)
y = 3 / 4 * 16 / 9
y = 4 / 3
Thus, the required value of fraction y is 4/3.
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Which function has exactly one x- and y-intercept
Answers
Answer:
Step-by-step explanation:
The function represented by the yellow graph has exactly one y-intercept and one x-intercept. The y-intercept is (0, 4) and the x-intercept is (2, 0).
Answer:
Its the one shown
Step-by-step explanation:
6 x 10^-2 is how many times a large as 2 x 10^-8?
Answers
Answer:
the number [tex]6\,\,\,10^{-2}[/tex] is three million times larger than [tex]2\,\,\,10^{-8}[/tex]
Step-by-step explanation:
To answer this, just do the quotient of the first one over the second one, and use the rules for quotient of exponential expressions of the same base:
[tex]\frac{6\,\,\,10^{-2}}{2\,\,\,10^{-8}} =\frac{6}{2} \,\frac{10^{-2}}{10^{-8}} =3\,\,\,10^{-2+8}=3\,\,\,10^6=3000000[/tex]
So the answer is: the number [tex]6\,\,\,10^{-2}[/tex] is three million times larger than [tex]2\,\,\,10^{-8}[/tex]
2 x 10^-8= 0.00000002
Write the sentence as an equation: 220 is 48 and h more
Answers
Answer:
220=48+h or 220=48h
Step-by-step explanation:
the word more can refer to a greater degree or extent. possibly referring
to addition or multiplication.
Answer:
220=48+h
Step-by-step explanation:
We know that 220 is the sum of 48 and h so you just represent it in an equation/equality statement.
A farmer has the same number of chickens, cows and goats. Together, all these animals have 210 legs. How many chickens live on this farm?
Answers
Answer:
21
Step-by-step explanation:
Chickens - 2x
cows - 4x
goats = 4x
2x+4x+4x+210
10x=210
x=21
CHECK:
21 chickens = 42 legs
21 cows = 84 legs
21 goats = 84 legs
42+84+84=210 legs
210\3=70 animals of each
So 70 chicken I hope this helped
For the linear function ƒ(x) = 7x – 4, find the range of ƒ(x) at x = –2, 0, and 2.
Answers
Answer:range is -2
Step-by-step explanation:
IV
What is the range of the function on the graph?
5
4+
3+
all real numbers
O all real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
2+
1 +
-5 4 -3 -2 -11
1 2 3 4 5 X
h
-27
-37
I
-4
-5
Answers
Does the function ƒ(x) = (0.85)x represent exponential growth, decay, or neither? Question 8 options: A) Exponential decay B) Impossible to determine with the information given. C) Neither D) Exponential growth
Answers
Answer:
exponential decay
Step-by-step explanation:
The function f(x)=0.85ˣ is a exponential decay.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=0.85ˣ.
The function f of x is equal to zero point eight five to the power of x.
Exponential decay refers to a process in which a quantity decreases over time, with the rate of decrease becoming proportionally smaller as the quantity gets smaller.
The function f(x)=0.85ˣ is a exponential decay.
Hence, the function f(x)=0.85ˣ is a exponential decay.
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HELP ASAP!!! Alex bought a notebook containing 96 pages, and numbered them from 1 through 192. Bob tore out 25 pages of Alex’s notebook, and added the 50 numbers he found on the pages. Could Bob have gotten 2012 as the sum? Show your logic steps on how you draw your conclusion.
Answers
=====================================================
Explanation:
Page 1 is labeled with 1 and 2, which sum to 1+2 = 3
Page 2 is labeled with 3 and 4 which sum to 3+4 = 7
Page 3 is labeled with 5 and 6 which sum to 5+6 = 11
and so on until we reach
Page 96 is labeled with 191 and 192, which sum to 191+192 = 383
Note how each page has an odd page number label and an even number label (odd on the front side; even on the back side). Adding any odd number to an even number will result in an odd number. We can prove it as such
x = some odd number = 2m+1, m is any integer
y = some even number = 2n, n is an integer
x+y = 2m+1+2n = 2(m+n)+1 = some other odd integer because it is in the form 2p+1 with p = m+n as an integer
This explains why the results 3,7,11,..,383 are all odd.
------------------------
So we effectively have this set of values {3,7,11,...,383}. This is an arithmetic sequence with 3 as the first term and 4 as the common difference.
If we add two odd numbers together, we get an even number (proof is similar to one shown above)
odd + odd = even
But if we add in another odd number, then we'll go back to an odd result
odd + odd + odd = odd
If we have an odd number of odd numbers added up, then the result will be odd. In this case, we're adding 25 values from the set {3,7,11,...,383}. The value 25 is odd, so we have an odd number of values from {3,7,11,...,383} being added up. Therefore, the result Bob will get will always be odd. There is no way to get a sum of 2012 because this value is even.
A bag contains 5 blue marbles, 2black marbles ,and 3 red marbles. A marine is randomly drawn from the bag The probability of not drawing a red marble is___ . The probability of drawing a red marble is
Answers
The probability of not drawing a red marble is 7/10
The probability of drawing a red marble is 3/10
=======================================================
Explanation:
We have 3 red marbles out of 5+2+3 = 10 total. Therefore, the probability of selecting a red marble is 3/10.
The probability of not selecting a red marble is 7/10 because 3/10+7/10 = 1. Put another way, we have 7 marbles that aren't red (the 5 blue and 2 black ones) out of 10 total.
Please help i will make brainliest for correct answers! :)
Answers
Answer:
For 13, there are 25 possible words, and for 14, depending on what the meaning of leaves is in this, the answer is 590.
Answer:
The first one is 25 and the second is 1080.
Step-by-step explanation:
To find how many 5-letter words you can make out of the letters, H, Q, L, R, and S, find the answer to 5². 5² = 25, so we can make 25 5-letter words. To find the number of "leaves" on the tree, just multiply the number of choices for color, monitor size, hard-drive size, and battery type together. So, 5×9×12×2 = 1080, so there are 1080 "leaves" on the tree.
Hope this helps! Plz give me brainliest like you said, it will help me achieve my next rank.
Point D is on segment BC, Segment BC measures Bx
units in length
What is the length of segment BC?
units
Answers
Answer:
144 units
Step-by-step explanation:
3x + 8 + 4x + 10 = 8x
7x + 18 = 8x
8x - 7x = 18
x = 18
8x is length of BC
8 × 18 is length of BC
144 units
Answer:
What is the length of segment BC?
144 units
explanation:
<3
Write an exponential function y = abx for a graph that includes (–3, 16) and (–1, 4) f(x) = 2(0.5)x f(x) = 0.5(2)x f(x) = 4(0.3)x f(x) = 3(4)x
Answers
Answer: [tex]f(x)=2(0.5)^x[/tex]
Step-by-step explanation:
Given, the exponential function [tex]y = ab^x[/tex] for a graph that includes (–3, 16) and (–1, 4).
On putting these points, we will have
[tex]f(-3)=16=ab^{-3}\\\\ f(-1)=4=ab^{-1}[/tex]
Now,
[tex]\dfrac{f(-3)}{f(-1)}=\dfrac{16}{4}=\dfrac{ab^{-3}}{ab^{-1}}\\\\\Rightarrow\ \dfrac{4}{1}=\dfrac{b^{-3}}{b^{-1}}\\\\\Rightarrow\ \dfrac{4}{1}=\dfrac{b}{b^3}=\dfrac{1}{b^2}\\\\\Rightarrow\ b^2=\dfrac{1}{4}\\\\\Rightarrow\ b=\pm\dfrac{1}{2}=\pm0.5[/tex]
since the multiplicative factor cannot be negative, so b= 0.5.
At b= 0.5
[tex]4=a(0.5)^{-1}\\\\\Rightarrow\ 4=a(\dfrac{1}{2})^{-1}\\\\\Rightarrow\ 4=a(2)\\\\\Rightarrow \ a=2[/tex]
So, the required function is [tex]f(x)=2(0.5)^x[/tex].
Line 'L' is horizontal and passes through (-5,8). Line 'L is vertical and passes through $(4,-1)$. Find the point of intersection of $\ell_1$ and $\ell_2$.
Answers
Every y coordinate on the horizontal line is the same, so each point has a y coordinate of y = 8. This is to be able to pass through (-5,8)
Every x coordinate on the vertical line is the same, so each point has an x coordinate of x = 4. This is to be able to pass through (4,-1)
Put this together to get the answer (x,y) = (4,8)
Answer:
The two lines intersect at (4,8).
100 POINTS!!! Match each pair of points with the approximate distance between them. Round your answers to the nearest tenth. 7.07 units 5.1 units 2 units 2.83 units 5.39 units 13.15 units 12.5 units (3, -1) and (5, 4) (2, 3) and (4, 5) (-5, 7) and (8, 5) (-2, 4) and (3, -1)
Answers
Answer:
(3, -1) -> (5, 4) = √29 or 5.38516
(2, 3) -> (4, 5) = 2√2 or 2.82843
(-5, 7) -> (8, 5) = √173 or 13.1529
(-2, 4) -> (3, -1) = 5√2 or 7.07107
Step-by-step explanation:
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Simply plug the coordinates into the distance formula:
[tex]d=\sqrt{(5-3)^2+(4+1)^2} = \sqrt{29}[/tex]
[tex]d=\sqrt{(4-2)^2+(5-3)^2} = 2\sqrt{2}[/tex]
[tex]d=\sqrt{(8+5)^2+(5-7)^2} = \sqrt{173}[/tex]
[tex]d=\sqrt{(3+2)^2+(-1-4)^2} = 5\sqrt{2}[/tex]
To get the decimals, we evaluate the square roots:
√29 = 5.38516
2√2 = 2.82843
√173 = 13.1529
5√2 = 7.07107
Answer:
d = √[(x₂ - x₁)² + (y₂-y₁)²]
(3, -1) and (5, 4)
√(5−3)²+(4-(-1)²
√(2)²+(5)²
√4+25
√29 = 5.385164807134504 = 5.39
(2,3) and (4,5)
√(4-2)v+(5−3)²
√(2)²+(2)²
√4+4
√8 ≈2.8284271247461903 = 2.83
(-5, 7) and (8,5)
√(8−−5)²+(5−7)²
√(8++0)2+(5−7)²
√(13)²+(−2)²
√169+4
√173 ≈ 13.152946437965905 = 13.15
(-2, 4) and (3, -1)
(3− −2)²+(−1−4)²
√(3++0)²+(−1−4)²
√(5)² + (−5)²
√25+25
√50 ≈ 7.0710678118654755 = 7.07
The first entry of the resulting matrix is:
Answers
Answer:
[tex]\boxed{1}[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}1 \times 1&2 \times 1\\3 \times 5&4 \times 5 \end{array}\right][/tex]
A cougar can run 25 miles per hour. A cheetah can run 55 miles per hour. if they both run at 3 hours full speed, how much farther will the cheetah run
Answers
Answer:
Step-by-step explanation:
( in 3hrs calculate distance)
,the cheetah will run 90 miles farther the cougar
pls mark my answer as the brainliest
help! please I need the answer now !!
Answers
Answer:
(- 5, 0 ), (7, 0 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, - 108 ), thus
y = a(x - 1)² - 108
To find a substitute (0, - 105 ) into the equation
- 105 = a(- 1)² - 108 ( add 108 to both sides )
3 = a
y = 3(x - 1)² - 108 ← equation in vertex form
To find the x- intercepts, let y = 0, that is
3(x - 1)² - 108 = 0 ( add 108 to both sides )
3(x - 1)² = 108 ( divide both sides by 3 )
(x - 1)² = 36 ( take the square root of both sides )
x - 1 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 1 to both sides )
x = 1 ± 6, so
x = 1 - 6 = - 5
x = 1 + 6 = 7
x- intercepts are (- 5, 0), (7, 0)
Which of the follow is the best representation for the cross-section?
(a)
(b
(c)
Answers
Answer:
A
Step-by-step explanation:
Which logarithmic graph can be used to approximate the value of y in the equation 2y = 5? (5 points) The graph of function f of x equals negative log base 2 of x The graph of function f of x equals negative log base 2 of x, plus 3 The graph of function f of x equals log base 2 of x, plus 3 The graph of function f of x equals log base 2 of x
Answers
Answer:
Step-by-step explanation:
Taking the base 2 log of both sides, we get:
log-base 2 of 2 + log-base 2 of y = log-base 2 of 5, or
2 + log-base 2 of y = approx. 2.3, or
log-base 2 of y = approx 2.3 - 2, or
log-base 2 of y = approx 0.3
Please, if you are given a graph or graphs, share them along with all instructions for the problem at hand. Thank you.