Answers
Each number in the sum is even, so we can remove a factor of 2.
2 + 4 + 6 + 8 + ... + 78 + 80 = 2 (1 + 2 + 3 + 4 + ... + 39 + 40)
Use whatever technique you used in (a) and (b) to compute the sum
1 + 2 + 3 + 4 + ... + 39 + 40
With Gauss's method, for instance, we have
S = 1 + 2 + 3 + ... + 38 + 39 + 40
S = 40 + 39 + 38 + ... + 3 + 2 + 1
2S = (1 + 40) + (2 + 39) + ... + (39 + 2) + (40 + 1) = 40×41
S = 20×21 = 420
Then the sum you want is 2×420 = 840.
Related Questions
The area of one triangle is 270 square centimeters when its height is 30 centimeters and its base length is 18 centimeters. What
is the area of a triangle having a height of 25 centimeters and a base length of 16 centimeters?
Answers
Answer:
[tex]200 cm^2[/tex]
Step-by-step explanation:
A = (1/2)bh
A = (1/2)(18)(30)
A = 270 square cm
A = (1/2)(16)(25)
A = 200 square cm
Answer:
200 square centimeters
Step-by-step explanation:
The area of a triangle can be calculated using the formula: [tex]A = \frac{1}{2}bh[/tex] where b is the base and h is the height. So if the base is 16 cm and the height if 25 cm you simply plug the values into the equation to find the area
Plug Values In:
[tex]A = \frac{1}{2}(16 cm)(25 cm)[/tex]
Multiply 16 cm and 25 cm:
[tex]A = \frac{1}{2}(400 cm^2)[/tex]
Multiply by 0.5 (or technically divide by 2)
[tex]A = 200 cm^2[/tex]
Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.
Enter the correct answer in the box by replacing the values of m and b.
Answers
Answer:
[tex]y = -2x + 5[/tex]
m = -1
b = 5
Step-by-step explanation:
Hello!
Slope - Intercept Form: [tex]y = mx+b[/tex]
m = slopeb = y-interceptSlopeThe slope of the line is the rate of change, or how the graph changes in y as it changes in x.
Slope can be calculated by the formula: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We need two points on the line to get the x and y-values. I'm going to choose points (0,5) and (4,-3).
Calculate Slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex][tex]m = \frac{5 - (-3)}{0 - 4}[/tex][tex]m = -\frac{8}{4}[/tex][tex]m = -2[/tex]The slope is -2.
Y-interceptThe y-intercept of the line is where the graph touches the y-axis (x = 0). It can be found by looking at the intersection of the graph and the axis.
The intersection happens at point (0,5), so the y-intercept is 5.
EquationWe found m, the slope, to be -2 and b, the y-intercept, to be 5. We can just plug it into the equation format.
Equation: [tex]y = -2x + 5[/tex]
Carnot heat engine receives heat at 900 K and rejects the waste heat to the environment at 300 K. The entire work output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at 215 °C at a rate of 250 kJ/min and rejects it to the same environment at 300 K. Determine (a) the rate of heat supplied to the heat engine and (b) the total rate of heat rejection to the environment.
Answers
A heat engine is a device that turns heat into mechanical energy that may subsequently be utilized to do mechanical labour. The total rate of heat rejection to the environment is 298.4458 kJ/min.
What is a Heat Engine?A heat engine is a device that turns heat into mechanical energy that may subsequently be utilized to do mechanical labour. It accomplishes this by transferring a functioning ingredient from a higher to a lower state temperature.
For the following condition, the diagram can be made as shown below. Also, the Heat Engine Sink temperature, [tex]T_H[/tex] = 900 K
Heat Engine surrounding temperature, [tex]T_L[/tex] = 300 K
Refrigerator surrounding temperature, [tex]T'_C[/tex] = 215 C + 273 = 488 K
Refrigerator sink temperature, [tex]T'_H[/tex] = 300 K
The heat removed by the refrigerator, [tex]Q'_{in}[/tex] = 250 kJ/min
A.) For a Carnot refrigerator, the COP or the coefficient of performance is given by,
[tex]COP = \dfrac{T'_C}{T'_H-T'C}[/tex]
COP = (488)/(488-300)
COP = 2.596
The COP is also the ratio of the Heat input and the work output.
[tex]COP = \dfrac{Q'_{in}}{W}[/tex]
2.596 = 250/W
W = 96.302 kJ/min
The Carnot engine efficiency is expressed as,
[tex]\eta = 1- \dfrac{T_C}{T_H}[/tex]
η = 1 - (300/900)
η = 0.6667
Also, the Carnot engine efficiency is defined as,
[tex]\eta = \dfrac{W}{Q_{in}}\\\\[/tex]
[tex]0.6667 = \dfrac{96.302}{Q_{in}}\\\\Q_{in} = \rm 144.4458\ kJ/min[/tex]
Hence, the rate of heat supplied to the heat engine is 144.4458 kJ/min.
B.) The total work done by the engine is 96.302 kJ/min, while the heat input is 144.4458 kJ/min. Therefore, the heat output of the system is,
[tex]W = Q_{in} - Q_{out}\\\\Q_{out} = 48.1438\rm\ kJ/min[/tex]
Thus, the total rate of heat rejection to the environment,
[tex]\text{Total Heat rejection} = Q_{out}+Q'_{in}\\[/tex]
= 48.4458 kJ/min + 250 kJ/min
= 298.4458 kJ/min
Hence, the total rate of heat rejection to the environment is 298.4458 kJ/min.
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Determine whether the triangle is a scalene, isosceles of equilateral
Answers
Answer:
Equilateral triangle: All three sides are equal.
Isosceles triangle: All two sides are equal.
Scalene triangle: No sides are equal.
Step-by-step explanation: Step 1: Label the given points as A, B, and C, and plot them as vertices of a triangle with connecting lines to draw the triangle we are working to identify.
Step 2: Calculate the side length AB using the distance formula.
Step 3: Calculate the side length BC using the distance formula.
Step 4: Calculate the side length AC using the distance formula.
Step 5: Compare the side lengths AB, BC, and AC from the previous steps to define the triangle type.
simplify the expression 1-cos^2(t) / cos^2(t)
Answers
Answer: [tex]\tan^2 t[/tex]
Step-by-step explanation:
[tex]\sin^{2} t+\cos^2 t=1 \implies 1-\cos^2 t=\sin^2 t\\\\\implies \frac{1-\cos^{2}t}{\cos ^2 t}=\frac{\sin ^2 t}{\cos^2 t}=\tan^2 t[/tex]
You work as an assistant for a local musical theatre group, the Main Street Theatre Company. The company is putting on a production of Les Misérables this year, and they need your help planning it.
Since the role of young Cosette is played by a child, the Main Street Theatre company must actually cast 3 girls in the role of young Cosette, and alternate girls from night to night. (This is because of restrictions on working hours for children.) You have received headshots and resumes from 25 girls who wish to audition for young Cosette.
Does order matter when casting the 3 young Cosettes? (In other words, are young Cosette 1, young Cosette 2, and young Cosette 3 different parts?)
No, all three girls will play the same part.
Yes, even though they will all be playing the same part, it will be on different nights.
No, all three girls will get paid the same amount.
Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.
Answers
The inference based on the information about ordering is that D. Yes, young Cosette 1, young Cosette 2, and young Cosette 3 are all different parts.
What is an inference?It should be noted that a inference simply means the conclusion that can be deduced based on the information given.
In the role of young Cosette for the drama, 3 girls should be casted.
If three are being casted then there is need for different parts because for same role there may be different stages of character.
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A bird can fly 5 miles in 15 minutes how many miles can it fly in 60 minutes?
Please show the process
Answers
The number of miles the bird can fly for 60 minutes is 20 miles.
How to find rate and distance?A bird can fly 5 miles in 15 minutes.
Let's find the rate before we can find the number of miles the bird can fly in 60 minutes.
Therefore,
rate = distance / time
rate = 5 / 15 = 1 / 3 miles per minutes
Therefore,
1 / 3 = d / 60
cross multiply
60 = 3d
d = 60 / 3
d = 20 miles
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Please help!! Find the solution for t in the equation:
Answers
Answer:
t = 1.322
Step-by-step explanation:
4×(2^t) = 10
2^t = 10/4 = 2.5
t = log2(2.5)
now, the logarithm to the base 2 of 2.5 must be larger than 1, as 2.5 is larger than 2.
so, it can be only the 4th answer option.
now, to actually calculate it :
log2(2.5) = log10(2.5) / log10(2) = 1.321928095... ≈
≈ 1.322
we were correct.
Answer:
t = 1.322
Step-by-step explanation:
Given equation:
[tex]4(2^t)=10[/tex]
Divide both sides by 4:
[tex]\implies \dfrac{4(2^t)}{4}=\dfrac{10}{4}[/tex]
[tex]\implies 2^t=2.5[/tex]
Method 1Take natural logs of both sides:
[tex]\implies \ln 2^t = \ln 2.5[/tex]
[tex]\textsf{Apply the natural log power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies t \ln 2 = \ln 2.5[/tex]
Divide both sides by ln 2:
[tex]\implies \dfrac{t \ln 2}{\ln 2} = \dfrac{\ln 2.5}{\ln 2}[/tex]
[tex]\implies t= \dfrac{\ln 2.5}{\ln 2}[/tex]
[tex]\implies t=1.321928095...[/tex]
Method 2[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]
[tex]\implies \log 2 (2.5)=t[/tex]
[tex]\implies t=1.321928095...[/tex]
SolutionTherefore, the solution that is nearest to the exact solution is t = 1.322
A collection of coins has a value of 64 cents. There are two more nickels than dimes and three times as many pennies as dimes. How many of each kind of coin are there?
Answers
There are 5 nickels, 3 dimes, and 9 pennies.
Let d = The number of dimes
Let n = number of nickels
Let p = The number of pennies
As given, there are two more nickels than dimes and three times as many pennies as dimes:
d+2=n
3d=p
0.10d+0.05n+0.01p=0.64
Plug in the value to find d
[tex]0.10d+0.05(d+2)+0.01(3d)=0.64[/tex]
[tex]0.10d+0.05d+0.1+0.03d=0.64[/tex]
[tex]0.18d=0.64[/tex]
[tex]d=3[/tex]
What is the value of p?The value of p is equal to 3d
p=3(3)=9
n=d+2
n=3+2
n=5
Hence, there are 5 nickels, 3 dimes, and 9 pennies.
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MATH: GRAPHING PIECE-WISE...HELP! 15 PTS
Answers
Answer:
Step-by-step explanation:
What happens to the surface area and volume if the lengths of the dimensions of the
prism are multiplied by a scale factor of 3?
Answers
Answer:
area is multiplied by 9volume is multiplied by 27Step-by-step explanation:
Area of a scaled figure is multiplied by the square of the scale factor; volume is multiplied by the cube of the scale factor.
AreaWhen dimensions are multiplied by 3, the area is multiplied by 3² = 9.
Area of the larger figure is 9 times that of the smaller one.
VolumeWhen dimensions are multiplied by 3, the volume is multiplied by 3³ = 27.
Volume of the larger figure is 27 times that of the smaller one.
__
Additional comment
In general, the area of a figure is the sum of the products of two orthogonal dimensions. If each of those is multiplied by 3, then the product is multiplied by 3 twice, or 3² = 9.
Similarly, the volume of a figure is the sum of products of three orthogonal dimensions. When those are each multiplied by 3, the product is multiplied by 3 three times, or 3³ = 27.
0,2,14,36,68,?
Find the next number in the sequence
Answers
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
Geometric sequenceGeometric sequence are sequence that increase in an exponential manner.
Given the recursive sequence 0, 2, 14, 36, 68
From the sequence
0 + 2 = 2
2 + 12 = 14
14 + 22 = 36
36 + 32 = 68
68 + 42 = 110
Note that the difference keeps increasing by a value of 10. Hence the next term of the sequence is 110
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find x and y
pls help
Answers
Step-by-step explanation:
(3x+6)= 48(Alternate angles)
3x=48-6
3x=42
x=14
2y+48=5y-9 (Sum of two opposite interior angles= exterior angle)
48+9=5y-2y
57=3y
y=19
What is the equation for the line of reflection
X=6
Y=6
Y=x
Y=2
Answers
Answer: x = 6
Step-by-step explanation:
B(7,3) maps onto B'(5,3).
The perpendicular bisector of [tex]\overline{BB'}[/tex] is x=6, so that is also the line of reflection.
Answer:
x = 6
Step-by-step explanation:
Taking test as we speak
(b) Write the next whole number after A59C thirteen in the base-thirteen system.
Answers
In base 13, we use the digits 0-9 along with A for 10, B for 11, and C for 12.
Then the number that comes after A59C₁₃ is
A59C₁₃ + 1₁₃ = A59(C + 1)₁₃
… = A59(10)₁₃
… = A5(9 + 1)0₁₃
… = A5A0₁₃
where I use parentheses to indicate we're adding C and 1 in the same digits place, then carry the 1 into the next digits place.
Whats the correct answer answer asap for brainlist
Answers
Answer:
option A: West Europe, East Europe, and Asia
Explanation: Europe and Asia as a whole are called Eurasia.
hope that helps...
Median weekly earnings for women with some college for an associate degree. 1980.......$231 2013.............$657 Using today's dollars, the data in the bar graph can be described by the mathematical model W = 13n + 231, Where W represents median weekly earnings n years after 1980. Does the formula underestimate or overestimate the median weekly earnings in 2013? By how much?
Answers
Using the linear function given in this problem, the formula underestimates the median weekly earnings in 2013 by $3, as 657 < 660.
What is the linear function?The function that estimates the median weekly earnings n years after 1980 is:
W = 13n + 231.
2013 is 2013-1980 = 33 years after 2000, hence the estimate is given by W when n = 33, that is:
W = 13 x 33 + 231 = 660.
657 < 660, hence the formula underestimates the median weekly earnings in 2013 by $3.
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What is the solution
Answers
Answer:
4
Step-by-step explanation:
5x + 2 = 2x + 14
5x-2x=14-2
3x=12
x=12/3
x=4
Answer:
The exact form: x = 4
Complete the equation of this circle:
(x − [?])²+(y - [ ])²=[ ]
Answers
Answer:
(x+2)²+(y-4)²=36
Step-by-step explanation:
1) to determine the coordinates of the centre of the given circle. It is point A (-2;4);
2) to determine the length of the radius: to calculate the distance between the point A(-2;4) and any point on the circle, it is 6 [units];
3) to make up the required equation according to the scheme:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - the coordinates of the centre, r - the length of the radius.
4) finally, (x+2)²+(y-4)²=6².
PS. for more details see the attachment.
e.Water has a density of about 0.0361 pounds/cubic inch. You might know that wood floats on water. What can you conclude about the densities of objects that float and the densities of objects that do not?
Answers
Answer:
Step-by-step explanation:
the objects which have less density than water will float
and the objects which have more density than the density of liquid will sink in liquid or will not float.
How many three-letter "words" can be made from 5 letters "FGHIJ" if repetition of letters
(a) is allowed?
Your answer is :
Correct
(b) is not allowed?
Your answer is :
Answers
The number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
How to determine the waysFormula for permutation with repetition
[tex]^nPr = n^r[/tex]
Formula for permutation without repetition
[tex]^nPr = \frac{n!}{n-r!}[/tex]
We have = 5
r = 3
a. If repetition is allowed,
Permutation = [tex]5^3[/tex] = 125 ways
b. If repetition is not allowed,
Permutation = [tex]\frac{5!}{5-3!}[/tex]
Permutation = [tex]\frac{5*4*3*2*1}{2*1}[/tex]
Permutation = [tex]\frac{120}{2}[/tex]
Permutation = 60 ways
Thus, the number of ways of the letters FGHIJ can be arranged with repetition and without repetition are 125 and 60 ways respectively.
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Deepak stacked 14 copies of the
same book. Each book is 13 inches
thick. How high is the stack of books?
8
inches
Answers
Answer:
182 inches
Step-by-step explanation:
1 book is 13 inches thick.
So when 14 of those books are stacked together (lets take the book cover has non-existent thickness since the question did not mention),
Height of stack of 14 books = 14 x Thickness of 1 book = 14 x 13inches
= 182 inches
MATH QUESTION HELP. Hhhhnh
Answers
Answer:
y
Step-by-step explanation:
that easy just isolate the variables
Which equation is equivalent to 162 - 32+³?
=
=
O 84 - 84+3
O 84-84+12
O 28 - 25p+15
=
O 28P = 25p+3
Answers
[tex]{ \red{ \bold{option \: (d)}}} \: { \green{ \tt{ {2}^{8p} = {2}^{5p + 3}}}} [/tex]
Step-by-step explanation:
I said option (d) is correct. Because, the answer of 2^8 is 256 i.e.,
[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2}}}[/tex]
[tex]{ \green{ \bold{ {2}^{8} }}} = { \green{ \tt{256}}}[/tex]
The value of 16^2 = 256.
Also, the answer of 2^5 is 32. i.e.,
[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{2 \times 2 \times 2 \times 2 \times 2}}}[/tex]
[tex]{ \green{ \bold{ {2}^{5} }}} = { \green{ \tt{32}}}[/tex]
PLS HELP ME Solve the following equation: five eighths plus two eighths equals
three eighths,
seven sixteenths,
seven eighths,
or eight sevenths.
Answers
Five eighths + two eighths = seven eighths
(5+2)/8 = 7/8
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median mark of 3,2,0,1,9,12,3,5
Answers
Answer: 3
Step-by-step explanation:
Median is a statistical measure that determines the middle value of a dataset listed in ascending order.
arranged data is 0,1,2,3,3,5,9,12
number of data terms=8
if data is even then
median=(3+3)/2=3
If it takes me 20 minutes to get to work while traveling at an average speed of 60 mph, but it took me 17 minutes to get to work today, what was my average speed today?
Answers
Answer:
if you are asking a real question the answer should be on your driving history on life 360 or maybe the average gps. How fast were you driving? I have no idea thats a answer only you know.
Step-by-step explanation:
Answer:
r = 70.59 miles / hour
Step-by-step explanation:
Comment
The first set of numbers gives you the distance you travelled.
Givens
t = 20 minutes = 20/60 = 1/3 of an hour
r = 60 miles / hour
d = ?
d = r * t
d = 60 * 1/3
d = 20 miles (The hours cancel)
So now you can find out what 17 minutes means
d = 20 miles
t = 17 minutes = 17/60 hours = 0.2833 hours.
r = d / t
r = 20 / 0.2833
r = 70.59 miles / hour
Least common multiple of 35 and 70
Answers
Answer:
70
Step-by-step explanation:
【Answer】The least common multiple of 35 and 70 is 70.
[tex]\orange{ {\hspace{50 pt}\above 1.2pt}\boldsymbol{\mathsf{Procedure}}{\hspace{50pt}\above 1.2pt}}[/tex]
To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.
This method consists of extracting the common and uncommon prime factors, then
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{35 \ \ \ 70}\\ 35 \ \ \ 35\\ 7 \ \ \ \ 7\\ 1 \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 5\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]
[tex]\sf{L.c.m.(35,70)=2\times5\times7}[/tex]
[tex]\boxed{\boxed{\sf{L.c.m.(35,70)=70}}}[/tex]
{ Pisces04 }Please help me out asap.
Answers
Using a calculator, the slope of the line of best-fit is of 7.2.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
In this problem, the points are given as follows:
(-4,-32), (-2,-8), (0,10), (2,8), (4,32).
Using the calculator, the equation is:
y = 7.2x + 2.
Hence the slope is of 7.2.
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Find an equation of the line. Write the equation using function notation.
Through (8,8); perpendicular to 5y = x - 10
Answers
Answer:
f(x) = -5x +48
Step-by-step explanation:
A fairly easy way to write the equation of the perpendicular line is to swap the x- and y-coefficients, negating one of them. Then choose the constant in the equation to make it true at the given point.
Swapped coefficientsIn this instance, we find it convenient to leave the coefficient of y as positive.
5y = x -10 . . . . . . original equation
y = -5x +c . . . . . . with coefficients swapped, x-coefficient negated
New constantAt the given point, the equation becomes ...
8 = -5(8) +c
48 = c . . . . . . . add 40
Equation of the perpendicular lineThe equation of the line is then ...
y = -5x +48
f(x) = -5x +48 . . . . . . in functional notation