Mathematics High School

The mean weight of five complete computer stations is 167.2 pounds. The weights of four of the computer stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds respectively. What is the fifth computer station?

Answers

Answer 1

The mean weight of five complete computer stations is 167.2 pounds.

The weights of four of the computer stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds.

We have to determine the weight of fifth computer station.

Let the weight of fifth computer station be 'x' pounds.

Mean is calculated by sum of all the observations divided by the total number of observations.

So, [tex] \frac{158.4+162.8+165+178.2+x}{5}=167.2 [/tex]

[tex] \frac{664.4+x}{5}=167.2 [/tex]

[tex] {664.4+x}=167.2 \times 5 [/tex]

[tex] {664.4+x}=836 [/tex]

x= 171.6 pounds

The weight of fifth computer station is 171.6 pounds.

Answer 2
Final answer:

To find the weight of the fifth computer station, subtract the sum of the weights of the four given stations from the mean weight.

Explanation:

The mean weight of five complete computer stations is 167.2 pounds. To find the weight of the fifth computer station, we can calculate the sum of the weights of all five stations and then subtract the sum of the weights of the four given stations. The weight of the fifth station can be found by subtracting the sum of the weights of the four given stations from the mean weight.

Sum of the weights of all five stations = 5 * 167.2 pounds

Sum of the weights of the four given stations = 158.4 pounds + 162.8 pounds + 165 pounds + 178.2 pounds

Weight of the fifth station = Sum of the weights of all five stations - Sum of the weights of the four given stations

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Related Questions

Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin. Naturally, she wants to place the roof beams in such an angle that each pair of opposite beams would meet exactly in the middle. What is the angle of elevation, in degrees, of the roof beams?

Answers

Answer: The angle of elevation should be 38.9 degrees.

To find this answer, it is always best to draw a picture of the building. The point of the roof, will be directly over the middle of the cabin. Therefore, we could draw an altitude down from the top to the cabin and create a right triangle.

This would form a triangle with an adjacent side and hypotenuse with our needed angle.

We could write and solve the following cosine equation:

cos(x) = 21/27
x = 38.9

The angle of elevation is 38.9° if Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

Width of the cabin = 42 meters

Wooden beam length = 27 meters

Since opposite beams would meet exactly in the middle.

The half of the beam width = 42/2 ⇒ 21 meters

As we can see in the right angle triangle:

[tex]\rm cosx = \frac{21}{27}[/tex]

[tex]\rm x = cos^{-1}(\frac{21}{27} )[/tex]

x = 38.9°

Thus, the angle of elevation is 38.9° if Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roof of the cabin.

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Could someone please help me with this?

Answers

Answer: 
The exact answer is sqrt(170)
The approximate answer is roughly 13.0384

=======================================

Explanation:

We have a right triangle with two known sides. Use the pythagorean theorem to find the third side

Known sides:
a = 7
b = 11

Unknown side is c which is the hypotenuse (longest side)

a^2 + b^2 = c^2
7^2 + 11^2 = c^2
49 + 121 = c^2
170 = c^2
c^2 = 170
c = sqrt(170)
c = 13.0384
Note: the last value is approximate

Write the percent as a decimal and as a fraction.

215% (1 point)
2.15; 2 1/20
2.15; 2 3/20
21.5; 21,1/2
21.5; 21, 3/10
Just tell me what one what it is..

I'LL GIVE A MEDAL (:,

Answers

To write 215% as a decimal you can approach the problem two ways. You can divide 215 by 100. 215/100 = 2.15 You can also move the decimal two places to the left 215.0 = 2.15 To write 2.15 as a fraction you will place 215 over 100. {215/100}. You will then want to write this fraction in it’s simplest form. The greatest common denominator is 5 so you will then divide the numerator and denominator by 5. 215/5 = 43 100/5 = 20 215/100 = 43/20 To write this fraction as a mixed fraction you would divide 43 by 20. 43 ÷ 20 = 2 with a remainder of 3 This is written as: 2 3/20

F(x) = 2x2 – 4x – 3

0 = 2x2 – 4x – 3

3 = 2(x2 – 2x)

3 + 1 = 2(x2 – 2x + 1)

4 = 2(x – 1)2

2 = (x – 1)2

± = x – 1

1 ± = x

Mica is solving for the zeros of a quadratic function by completing the square. Her work is shown. What error did Mica make?




ANSWER CHOICES
Mica should have set each x = 0 instead of f(x).
Mica should have added 2 to 3 instead of 1.
Mica should have multiplied both sides by 2 instead of dividing.
Mica should have subtracted 1 from both sides instead of adding.

Answers

Mica should have added 2 to 3 instead of 1 to 3.

She factored out a 2 on the righthand side, so adding 1 within the parentheses is equivalent to adding 2 outside the parentheses. Since this is an equation, what we do to one side, we must do to the other, so Mica should've added 2 to the lefthand side.
Mica should have added 2 to 3 instead of 1.

PLEASE HELP ME QUICKLY!!!!!!!!!!!!!!

Answers

First answer because you had to do the elimination method
Hello,

ANSWER: The first choice

To get to the second equation, you have to multiply the first equation by 4. Then, add the 2 equations. Doing this will eliminate the y variable from the equations. 

This is called the elimination method. When you use this method, your goal is to eliminate 1 variable, so you can solve for the other variable.

Best of luck,
MrEQ

Suppose we deposit $73,000 into a savings account which compounds daily with 5% APY and we want to know how much the account will be worth after two days.

Answers

Let
I1-------------> interest first day
I2-------------> interest second day

we know that
P0=$73000----------> initial amount

first day
I1=73000*(5%/100)*(1/365)-----------> I1=$10
P1=P0+I1------> $73000+$10-------- P1=$73010

second day
P1=$73010
I2=73010*(5%/100)*(1/365)-----------> I2=$10
P2=P1+I2------> $73010+$10-------- P2=$73020

the answer is $73020

Anita says CD can also be called DC. Do you agree?Explain
I'm talking about line segments

Answers

CD can be called DC, since each letter represents a point on the line. If the line segment has two points, it may be referenced with the points in any order. In the same way, a segment with points A and B could be called AB or BA.

If f(x) = 9x – 7 and g(x) = 2x2 – 3x + 1, what is (f + g)(4)?
a. -8
b. 8
c. 34
d. 50

Answers

Answer:

D. 50

Step-by-step explanation:

[tex]f(x) = 9x - 7 \\ g(x) = 2x {}^{2} - 3x + 1 \\( f + g)(x) = 9x - 7 + (2x {}^{2} - 3x + 1) \\ (f + g)(x) = 2x {}^{2} + 6x - 6 \\ (f + g)(4) = 2(4 ){}^{2} + 6(4) - 6 \\ (f + g)(4) = 32 + 24 - 6 \\ (f + g)(4) = 56 - 6 \\ (f + g)(4) = 50[/tex]

Find the 7th term of the arithmetic sequence -5x-8,-x-14,3x-20,...

Answers

a₁ = -5x-8;  a₂ = -x-14; a₇=?

d = a₂ - a₁
  = x-14 - (-5x-8)
  = -x - 14 + 5x + 8
  = 4x-6

a(n) = a₁ + (n-1)d

a₇ = -5x-8 + (7-1)(4x-6)
    = -5x-8 + 6(4x-6)
    = -5x - 8 + 24x - 36
    = 19x - 44

Soon you will determine the right triangle connection the pythagorean theorem

Answers

I don't know I just need the points Lol sorry

Factor completely: 9ab + 12ax - 6b - 8x (1 point)
1. Prime
2. (3b - 4x)(3a - 2)
3. (3b + 4x)(3a - 2)
4. (3b + 4x)(3a + 2)

Answers

3. (3b + 4x)(3a - 2) is correct.
Use FOIL to expand each factored form, only #3 will result in 9ab + 12ax - 6b - 8x
the correct answer would be C or #3

If arc XV = 68° and ∠YUV = 36°, what is the measure of arc VY?

Answers

the complete question in the attached figure

we have
arc XV = 68°
∠YUV = 36°
 
we know that
The measure of the external angle is the semidifference of the arcs that it covers.
therefore
∠YUV =[arc VY-arc XV]/2
arc VY=[2*∠YUV]+arc XV----------> [2*36]+68---------> 140°

the answer is
the measure of arc VY is 140°

Circle 1: center (8, 5) and radius 6
Circle 2: center (−2, 1) and radius 2
What transformations can be applied to Circle 1 to prove that the circles are similar?
What scale factor does the dilation from Circle 1 to Circle 2 have?
Show your work.

Answers

we have that
Circle 1: center (8, 5) and radius 6
Circle 2: center (−2, 1) and radius 2

we know that
the equation of a circle is
(x-h)²+(y-k)²=r²
for the circle 1---------> (x-8)²+(y-5)²=36
for the circle 2---------> (x+2)²+(y-1)²=4

using a graph tool 
see the attached figure

Part A)What transformations can be applied to Circle 1 to prove that the circles are similar?

we know that
r1/r2---------> 6/2------> 3

to prove that the circle 1 and circle 2 are similar, the radius of circle 1 must be divided by 3 and  translate the center of the circle 1  (10) units to the left and (4) units down  

 the answer part A) is
the radius of circle 1 must be divided by 3 and  translate the center of the circle 1  (10) units to the left and (4) units down  


Part B) What scale factor does the dilation from Circle 1 to Circle 2 have?

the answer Part B) is 
the scale factor is (3/1)

Need Help. I will give a thanks and rate you 5 stars.
2. A tree that is 10 yards tall casts a shadow 14 yards long. Find the angle of elevation from the tip of the shadow to the top of the tree. Round to the nearest degree.
A. 54
B. 36
C. 46
D. 44
3. Use the Law of Sines to find the missing side of the triangle. Find b.
A. 70.1
B. 43.8
C. 57.1
D. 31.5
4. For a triangle ABC, find the measure of AB given m A. 45.22
B. 96.68
C. 88.19
D. 81.12
5. Use the Law of Cosines to solve the problem. On a baseball field, the pitchers mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet. the path of the ball makes a 34 angle with the line connecting the pitcher and the catcher, to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?
A. 207.4 ft
B. 224.3 ft
C. 169.3 ft
D.

Answers

The angle of elevation will be given by: 
tan θ=opposite/adjacent
tan θ=10/14
θ=arctan 10/14=
θ=35.5~26°

5. c^2=a^2+b^2-2abcos C
c^2=60.5²+216²-2*60.5*216cos34
c^2=28,648.524
c=169.255~169.3 ft

Fill in the scale dimensions in the table to the nearest thousandth. The scale of a blueprint is 1/4 inch = 1 foot. A house has 1 bedroom measuring 10 feet 6 inches by 11 feet, a living room measuring 25 feet by 18 feet 8 inches, a kitchen measuring 13 feet 6 inches by 8 feet, and a dining room measuring 12 feet by 10 feet. Put the shortest length in the first box for each room. Give all answers to three decimal places (thousandths place).
bedroom inches by inches
living room inches by inches
kitchen inches by inches
dining room inches by inches

Answers

The scale dimensions of the rooms on the blueprint using a scale of 1/4 inch = 1 foot are calculated by converting feet to inches, then dividing by the scale ratio (0.25 inches per foot) to find each room's dimensions in inches on the blueprint.

To calculate the scale dimensions of the rooms on the blueprint, you will use the given scale of 1/4 inch = 1 foot. This means for every 1/4 inch on the blueprint, it represents 1 foot in actual size.

Step-by-Step Calculation for Each Room

Convert the scale into a ratio that can be used for calculations (1/4 inch / 1 foot or 0.25 inches / 12 inches since there are 12 inches in a foot).

Calculate the scale dimension for each room by dividing the actual dimension in inches by the scale ratio.

For each room, ensure to convert feet to inches first (1 foot = 12 inches) and then apply the scale.

Bedroom: 10 feet 6 inches is (10 * 12) + 6 = 126 inches, 11 feet is (11 * 12) = 132 inches. Scale dimensions: (126 inches / 48) by (132 inches / 48) equals 2.625 inches by 2.750 inches.Living room: 25 feet is (25 * 12) = 300 inches, 18 feet 8 inches is (18 * 12) + 8 = 224 inches. Scale dimensions: (300 inches / 48) by (224 inches / 48) equals 6.250 inches by 4.667 inches.Kitchen: 13 feet 6 inches is (13 * 12) + 6 = 162 inches, 8 feet is (8 * 12) = 96 inches. Scale dimensions: (162 inches / 48) by (96 inches / 48) equals 3.375 inches by 2.000 inches.Dining room: 12 feet is (12 * 12) = 144 inches, 10 feet is (10 * 12) = 120 inches. Scale dimensions: (144 inches / 48) by (120 inches / 48) equals 3.000 inches by 2.500 inches.

Below is the scale dimensions for each room to the nearest thousandth:

Bedroom: 2.625 inches by 2.750 inchesLiving room: 6.250 inches by 4.667 inchesKitchen: 3.375 inches by 2.000 inchesDining room: 3.000 inches by 2.500 inches

A die is tossed. Find the odds against rolling a number greater than 4.
*the probability of rolling a # greater than 4 is 1/3.
*the probability that the event doesn't occur is 2/3.

What is the ratio?

Answers

The chance of rolling a number greater than 4 (a 5 and 6) is 2/6 = 1/3 after simplification. The probability it WON'T happen is 1 - 1/3 = 2/3. 
 The ratio of against to for is 2/3:1/3
 You can further simplify this ratio by multiplying each side by 3 and yielding
 2:1.
 The chance of it not happening is twice as likely as it is to roll a number greater than 4

please help I don't understand this
Solve for x
2/(9x) = 4/7

18/7
I don't know
- 18/7
7/18
- 7/18

Answers

The correct answer is:  [C]:  " [tex] \frac{7}{18} [/tex]" .
____________________________________________________
Explanation:
____________________________________________________
Given:
____________________________________________________
  
  2 / (9x) = 4 / 7 ;  solve for "x" ;
____________________________________________________

Cross-multiply:

        →   (9x)*4  = 2 * 7 ; 

        →   36x = 14 ; 

Divide each side of the equation by "36" ; 
 to isolate "x" on one side of the equation; & to solve for "x" ; 

        →   36x / 36 = 14 / 36 ; 

                   x = 14/ 36 ; 

                  → x = 14/36 = (14÷2) / (36÷2) = 7/18 ; 
______________________________________________________

The answer is:  " [tex] \frac{7}{18} [/tex]" ;

                       →  which is:  Answer choice:  [C]:  " [tex] \frac{7}{18} [/tex]" .
______________________________________________________

Find the radius of a circle with the equation 2x2+y2-6x+2y-45=0

Answers

2x²+y²-6x+2y-45=0
center:(3/2,-1)
vertex1:(3/2,-1+√202/2)
vertex2:(3/2,-1-√202/2)
focus1:(3/2,-1+√101/2)
focus2:(3/2,-1-√101/2)


I hope this helps!!!!!!!!!!

state whether the relationship between x and y in y=4x-5 is proportional or nonproportional

Answers

The relationship is proportional because it is in standard form
Its proportional it’s a standard form

find the exact value of cos285 using the fact that 285=330-45

Answers

[tex]\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\ -------------------------------\\\\ cos(285^o) \\\\\\ cos(330^o-45^o)=cos(330^o)cos(45^o)+sin(330^o)sin(45^o) \\\\\\ cos(330^o-45^o)=\left( \frac{\sqrt{3}}{2} \right)\left( \frac{\sqrt{2}}{2} \right)~~+~~\left( \frac{1}{2} \right)\left( \frac{\sqrt{2}}{2} \right) \\\\\\ cos(330^o-45^o)=\cfrac{\sqrt{6}}{4}+\cfrac{\sqrt{2}}{4}\implies cos(330^o-45^o)=\cfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]

What is cot theta when sin theta < 0 and cos theta = -5/13

Answers

If cos and sin are both minus, you are in quadrant III where the cot(theta) is plus.

The reason for that is that cot(theta) = cos(theta)/sin(theta) which means that the two minuses will cancel out.

Now all you have to do is calculate sin(theta).
a^2 + b^2 = c^2
cos = adjacent / hypotenuse

a = 5 The adjacent side
b = ????
c = 13 The hypotenuse
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 144
b = 12
sin(theta) = -12/13

cot(theta) = -5/13//-12/13
cot(theta) = -5/-12 = 5/12

In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots as shown. Explain why the ropes forms a right angle

Answers

The Egyptians used a rope with 13 equally spaced knots in it, which gave them 12 equal sections of rope.  These would be the units.  One of the most recognized Pythagorean triples is 3, 4, 5.  This comes from the Pythagorean theorem:
3²+4²=5²
9+16=25

With the sides of the triangle being 3, 4 and 5, the perimeter would be 3+4+5=12.
Final answer:

In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots. The tensions in the rope on either side of the right angle were equal, resulting in the formation of a right angle.

Explanation:

In ancient Egypt, surveyors made right angles by stretching a rope with evenly spaced knots. The ropes formed a right angle because the angles on either side of the rope were equal. When the rope was stretched taut, the tensions in the rope on either side of the right angle were equal. This resulted in the formation of a right angle.

10,11, and 12 please and show work

Answers

10).  5 x 10^6            5.3 x 10^-4
        5 x 1,000,000    5.3 x 0.0001
        5,000,0000    x    0.00053 = 2,650
 
2,650

Is the answer 85.3???????

Answers

Look at the picture below.

I hope this helps!

What is the coefficient of the term x7y in the expansion of (x + y)^8?

a1
b8
c28
d56,

Answers

The coefficient for x^7*y is equal to 8Choose7 which is 8!/7! which is 8, or answer b. Pascal's triangle may be used to capture this as well, or use the exponent as above.

The base 10 logarithm is called the _____ logarithm and is often written as log x instead of log10 x.,

Answers

A common logarithm is any logarithm with base 10. Our number system is base 10; there are ten digits from 0-9, and place value is determined by groups of ten. You can remember a “common logarithm,” then, as any logarithm whose base is our “common” base, 10.

4) A mountain climber climbed up a cliff 1/4 mile at a time. he did this 5 times in one day. How many miles did he climb up? *

Answers

He climbes 1 1/4 miles.
1/4+1/4+1/4+1/4+1/4= 1 1/4.

what steps transform the graph of y=x^2 to y= -(x+3)^2+5

Answers

[tex]\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)= A( Bx+ C)+ D \\\\ ~~~~y= A( Bx+ C)+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \\\\ f(x)= A sin\left( B x+ C \right)+ D \\\\ --------------------[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

now, with that template in mind, let's check this one

[tex]\bf y=x^2\implies y=\stackrel{A}{1}(\stackrel{B}{1}x\stackrel{C}{+0})^2\stackrel{D}{+0} \\\\\\ y=-(x+3)^2+5\implies y=\stackrel{A}{-1}(\stackrel{B}{1}x\stackrel{C}{+3})^2\stackrel{D}{+5}[/tex]

A = -1, reflection over the x-axis.

B = 1, C = +3, C/B = +3/1 = +3, horizontal shift to the left of 3 units.

D = 5, vertical shift up of 5 units.

Is the mean always a more accurate measure of center than the median

Answers

I want to say yes it is but it's been a little while since I have learned this

Ashley is digging for rocks at a geological site. She has 140 meters of rope and 4 stakes to mark off a rectangular area. Which set of dimensions will create a rectangle using all the rope Ashley has with her?

14 m × 10 m
70 m × 70 m
60 m × 10 m
55 m × 10 m

Answers

the answer is 60 m x 10 m

The total perimeter of the rectangle is P = 140m and the length and width of the rectangle is 60 m and 10 m respectively

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangle be represented as P

Now , the equation will be

Let the total perimeter of rectangle P = 140 m

The Perimeter P = 2 ( Length + Width )

Let the length of the rectangle L = 60m

Let the width of the rectangle be W = 10 m

So , Perimeter P = 140 m

140 = 2 ( L + W )

140 = 2 ( 60 + 10 )

140 = 2 ( 70 )

140 = 140

Therefore , the length and width is given by 60m x 10m

Hence , the perimeter of rectangle is P = 140 m

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If every cell in the body gets the same dna, how do the cells of an embryo make different structures and take on different roles? (select all that apply.)a. different transcription factors are active in different cells.b. different transcription factors are encoded in the dna.c. genes are spliced differently in different cells.d. translation is regulated so that different cells may make more of certain proteins.e. some cells lack ribosomes while others use them. f. cells delete a set of unused genes from their chromosomes. Mitosis, the process of cell division, is most important for an organism's what? The library is having a book sale. Hardcover books sell for $4 each, and paperback books are $2 each. If Connie spends $26 for 8 books, how many hardcover books did she buy? The perimeter of an equilateral triangle is 186 cm. what is the length of one side of the triangle? how do you find the volume of a square of 8 by 8 what is the correct answer to this question?abcd HELP ASAP!!!Review the following PowerPoint slide layout. What type of content would be most appropriate for this layout?A. ComparisonB. HeadingC. Title and contentD. Title Jesse has has n dollars in his bank account he deposits 132 write an expression that represents the total amount Jesse now has in his bank account Dillon is conducting a survey about whether or not people like a traffic law that is being passed.Can he publish his findings as a scientific study because he collected information? write a whole number as a fraction the number 5 In who knows if the moons, what is the moon seen as? (1 point) a city a balloon a cloud a sailboat What can you do to lessen the chances of being in an aggressive driving situation? What universal themes does Josephine Baker explore in her speech? What makes these themes universal? how does a ketone react with PCl5?, The iron in breakfast cereal is absorbed more readily when consumed with a glass of vitamin crich orange juice. (0,0), (5,-5), (-5,-5), (0,-10) Find the area of the polygon with the given coordinates.A)10 square unitsB)25 square unitsC)40 square unitsD)50 square unitsNeed help if anyone can show how they did it, it would help me a lot! thanks :D Two buses leave a station at the same time and travel in opposite directions. One bus travels 12 mi/h faster than the other. If the buses are 690 mi apart after 5 hours, what is the rate of each bus mi/h? Which type of map projection uses a cone-shaped piece of paper to depict the Earth? Research the battle known as Custers Last Stand. Why do you think the Native Americans felt so strongly? Why did Custer lose the battle? Find a linear differential operator that annihilates the given function. (use d for the differential operator.) ex + 8xex x2ex