Answer:
12
Step-by-step explanation:
12 doesn't fit the data because it is so much farther from the general average of the others.
12 affects the median because with it, the median is 74. but without 12, the median is 76.
12 affects the mean because with it, the mean is 68.36. but without 12, the mean is 72.69.
Water
SA = 2tr2 + 2nrh
(Use 3.14 for 1.)
Find the surface area
of a water tower that is
40 feet tall and 20 feet
across the base.
square feet
Do NOT round your answer.
Answer:
the surface area is 3140 square feet
Step-by-step explanation:
The computation of the surface area is given below:
Given that
Diameter = 20 feet
radius = 20 ÷ 2 = 10 feet
Surface area = [tex]2\pi r^2 + 2\pi rh[/tex]
= 2 × 3.14 × (10)^2 + 2 × 3.14 × 10 × 40
= 6.28 × 100 + 6.28 × 400
= 628 + 25.12 × 100
= 628+ 2512
= 3140 square feet
hence, the surface area is 3140 square feet
state if polygons are similar
A light bulb is designed by revolving the graph of:
[tex]y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}[/tex]
Over the interval 0 ≤ x ≤ 1/3 about the x-axis, where x and y are measured in feet. Find the surface area of the bulb and use the result to approximate the amount of glass needed to make the bulb. (Glass is 0.015 inch thick).
Answer:
[tex]\displaystyle 0.251327 \ in. \ of \ glass[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringCalculus
Differentiation
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
Integration Property: [tex]\displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx[/tex]Fundamental Theorem of Calculus: [tex]\displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)[/tex]Area between Two CurvesVolumes of RevolutionArc Length Formula: [tex]\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx[/tex]Surface Area Formula: [tex]\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx[/tex]Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}][/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}[/tex][Derivative] Simplify: [tex]\displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}[/tex]Step 3: Integrate Pt. 1
Substitute [Surface Area]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx[/tex][Integral - √Radical] Expand/Add: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx[/tex][Integral - √Radical] Factor: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx[/tex][Integral - Simplify]: [tex]\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx[/tex][Integral] Integration Property: [tex]\displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx[/tex]Step 4: Integrate Pt. 2
[Integral] Define: [tex]\displaystyle \int {|9x + 1|(3x - 1)} \, dx[/tex][Integral] Assumption of Positive/Correction Factors: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx[/tex][Integral] Expand - FOIL: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx[/tex][Integral] Integrate - Basic Power Rule: [tex]\displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)[/tex][Expression] Multiply: [tex]\displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}[/tex]Step 5: Integrate Pt. 3
[Integral] Substitute/Integral - FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}[/tex][Integrate] Evaluate FTC: [tex]\displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})[/tex][Expression] Multiply: [tex]\displaystyle SA = \frac{\pi}{27} \ ft^2[/tex]It is in ft² because it is given that our axis are in ft.
Step 6: Find Amount of Glass
Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.
Convert ft² to in²: [tex]\displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2[/tex]Multiply: [tex]\displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass[/tex]And we have our final answer! Hope this helped on your Calc BC journey!
In the following equation, what is the y-intercept? y = -3.1 +7 03 o7
Answer:
the y-intercept, b, is 7
Step-by-step explanation:
Compare the given y = -3.1 +7 to y = mx + b. I must assume that you meant
y = -3.1x +7. It becomes evident that the slope, m, is -3.1 and the y-intercept, b, is 7.
Expand 2(c + 4).
Please help me
Answer:
2c+8
Step-by-step explanation:
this is because we are using 2 to open up the brackets. You will multiply c by 2 and 4 by 2.
what is the slope of the line graphed below? (3,3) (0,-6)
Answer:
Where is the line
Step-by-step explanation:
Answer:
The slope of the lines is 3.
Step-by-step explanation:
Since I can't actually graph it, we can make a table
x y
3 3
0 -6
From 3 to -6, you subtract 9 (for the y section)
From 3 to 0, you subtract 3 (for the x section)
Now all you need to do is divide y by x
y/x = -9/-3 = 3
It's a positive 3, because two negatives times each other will always result in a positive.
Slope = 3
Hope this helped!
Have a supercalifragilisticexpialidocious day!
Translate the sentence into an equation The sum of 5 times a number and 7 is 3
Use the variable b for the unknown number
HELPPPPPP
Answer:
Equation: 5b + 7 = 3
Step-by-step explanation:
Unknown number = b
5 times of number = 5b
Sum of 5b and 7 = 5b + 7
Equation;
5b + 7 = 3
heyyy wanna help mee
Answer: Only j = 2
============================================
Explanation:
Let's solve for j
[tex]\frac{96}{j} \ge 40\\\\96 \ge 40j\\\\\frac{96}{40} \ge j\\\\2.4 \ge j\\\\j \le 2.4[/tex]
In the second step, I multiplied both sides by j. If j is a positive number, then the inequality sign will not flip. All of the answer choices are positive numbers, so we don't have to worry about the inequality sign flipping.
The last step shows that j = 2.4 or j < 2.4
So j is 2.4 or smaller.
Of the list given to us, only j = 2 fits the description, since something like j = 8 is not 2.4 or smaller.
---------------------------
If j = 2, then,
[tex]\frac{96}{j} \ge 40\\\\\frac{96}{2} \ge 40\\\\48 \ge 40\\\\[/tex]
which is a true statement since 48 is larger than 40. This shows that j = 2 is a solution.
Something like j = 8 does not work because
[tex]\frac{96}{j} \ge 40\\\\\frac{96}{8} \ge 40\\\\12 \ge 40\\\\[/tex]
which is false because 12 is not equal to 40 or larger than 40. This means j = 8 is not a solution. You should find that j = 12 and j = 3 lead to similar false statements.
Of the list given, j = 2 is the only solution.
______________________________
1.) Solve using j = 12:Plug in 12: [tex]\frac{96}{12}[/tex] ≥ [tex]40[/tex]Divide 96 by 12: [tex]=8[/tex] Compare: [tex]8[/tex] ≥ [tex]40[/tex]
So this is False.
2.) Solve using j = 8:Plug in 8: [tex]\frac{96}{8}[/tex] ≥ [tex]40[/tex]Divide 96 by 8: [tex]=12[/tex] Compare: [tex]12[/tex] ≥ [tex]40[/tex]
So this is False.
3.) Solve using j = 2:Plug in 2: [tex]\frac{96}{2}[/tex] ≥ [tex]40[/tex] Divide 96 by 2: [tex]=48[/tex]Compare: [tex]48[/tex] ≥ [tex]40[/tex]So this is True.
4.) Solve using j = 3:Plug in 3: [tex]\frac{96}{3}[/tex] ≥ [tex]40[/tex]Divide 96 by 3: [tex]=32[/tex] Compare: [tex]32[/tex] ≥ [tex]40[/tex]So this is False.
______________________________
18 divided by 5 - (6-5)-1) pemdas
Answer:
The answer is 6
You want to add lace around the outside of your circular kitchen table cloth. If the diameter of the table cloth is 16 cm, then which of the following measurements would represent how much lace you need?
The length of lace would be the circumference of the circle.
Circumference = diameter x Pi
Circumference = 16pi cm
Circumference = 50.24 cm ( approximately)
Answer:
The circumference of the circle.
Step-by-step explanation:
Plz help I’m dumd and I can’t answer it
Answer:
11
Step-by-step explanation:
25% is 0.25 or 1/4
44 x 0.25 =11
Select the fraction that is equivalent to one half.
HOW DO I DO THIS PLZ HELP
Answer:
1/2 one half
Step-by-step explanation:
Answer:
Multiply both the numerator and the denominator by the same whole number.
For example;
If you multiply 1/2 by 2/2, this will equal 2/4. You can simplify 2/4 to 1/2.
So to find 1/2 to be equivalent to another fraction, multiply both the numerator and the denominator by the same number to find a fraction that equals 1/2.
Each month Javier takes his recycling to the local recycling center where he separates the glass bottles into different
colors. He would like to determine the proportion of glass his household recycles that is clear glass, so he mixes up
his container and randomly grabs 10 glass items and determines the proportion that are clear glass.
The population is
The sample is
The parameter is the proportion of
The statistic is the proportion of
Answer:
The population is: all glass recycled
The sample is: the 10 selected glass items.
The parameter is the proportion of: all his glass that is clear
The statistic is the proportion of: the selected glass that is clear
The population of a distribution is the entire group, while the sample is the selected group from the entire group.
The population is all glass recycled The sample is the 10 selected glass items. The parameter is the proportion of all his glass that is clear The statistic is the proportion of the selected glass that is clearThe population
From the question, we understand that glasses are recycled and then separated into colors.
This means that, the population is all glass recycled
The sample
From the question, we understand that he randomly grabs 10 glass items, and then determine the proportion of clear glasses.
This means that, the sample is the 10 selected glass items.
The parameter
This is the value that summarizes all the glasses that are being recycled.
So, the parameter is the proportion of all his clear glasses
The statistic
This is the value that summarizes the selected glasses.
So, the statistic is the proportion of the selected glass that is clear
Read more about samples and population at:
https://brainly.com/question/15683425
If the ratio of boys to girls is 1:2 and there are 10 girls in your class, how many boys are there?
Answer:
5
Step-by-step explanation:
divide 10 by 2
Answer:
There are 5 boys in the class
The graph below represents the linear equation y=1/2x-3 a second linear equation is represented by the data in the table. What is the solution to the system of e
ik its late but the correct answer is C:(2,-2)
Step-by-step explanation:
I got the answer correct on Edge 2020.
Hope this helps!!
Find the Y intercept of the line y-3=2(x + 1)
Answer:
y=2x+1
Step-by-step explanation:
Jocelyn walks her dog 5 days each week.Each Walk is 2 1/4 miles long. What is the total number of miles that Jocelyn walks her dog each week
Answer:the answer is c
Step-by-step explanation:
What are the like terms in the following algebraic expression? 5 - 3y + 2x - 5y + x - 2 + 3x^2
Answer:
3y+2x+5y+3x
Step-by-step explanation:
sepreate the varible numbers from the reguler
Jim buys a skateboard for $200. The value of the skateboard depreciates by 15% each year
since buying it. Create a function to represent the value of the skateboard, f(2), in dollars,
after 3 years since buying it.
Answer: f(x)=200•(0.85)^x
Step-by-step explanation:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the decaying rate, expressed in decimal
Depreciation is often modeled as an exponential decay function. Since Jim bought a skateboard for Co=$200, its value will depreciate by r=15% = 0.15 each year since buying it.
Please help me with this one ☝️
Answer:
D
Step-by-step explanation:
add them together
Translate quadrilateral ABCD 5 units to the right and 6 units down.
What are the coordinates of the vertices of the image?
Please help and give an answer with in depth information. +15 points
Answer:
D. A'(1,-7), B'(2,-1), C'8,-2) and D'(7,-5)
Step-by-step explanation:
Probably too late, but I took the quiz
Answer:
D
Step-by-step explanation:
Keep it simple, but correct :)
Help will make branliest
Answer:
I like that you watch wwe for one. but lets get started
the answer itself is m< 4=87
Step-by-step explanation:
Answer:
The answer is 87°
Step-by-step explanation:
A quadrilateral has an interior angle sum of 360°.
Given that three of the four angles in a quadrilateral are 89°, 80°, and 104°, we can create the following equation where x is the missing angle:
89° + 80° + 104° + x° = 360°.
All you have to do is add all the measures up and subtract from 360°.
89° + 80° + 104° + x° = 360° →
273° + x° = 360° →
x° = 87°.
Also, for any polygon, the interior angle sum is (n – 2) × 180°, where n is the number of sides.
A quadrilateral is a polygon with four sides so it's interior angle sum must be
(4 – 2) × 180° = 2 × 180° = 360°.
Which expression is equivalent to 3 the 5th power?
Answer:
The expression equivalent to 3 to the 5th power is 3^5.
The number 3 raised to the 5th power is represented through the expression 3 ^ 5, which means that the number 3 is multiplied by itself 5 times (3x3x3x3x3), which results in the number 243, which is can be corroborated by the following calculations:
3x3 = 9
9x3 = 27
27x3 = 81
81x3 = 243
The solution is: The expression equivalent to 3 to the 5th power is 3^5.
Here, we have,
The number 3 raised to the 5th power is represented through the expression 3 ^ 5,
which means that the number 3 is multiplied by itself 5 times (3x3x3x3x3),
which results in the number 243,
which is can be corroborated by the following calculations:
3x3 = 9
9x3 = 27
27x3 = 81
81x3 = 243
Hence, The solution is: The expression equivalent to 3 to the 5th power is 3^5.
To learn more on Expression click:
brainly.com/question/14083225
#SPJ6
Is this an example of a function?
Yes or no?
Answer:
Yes.
Step-by-step explanation:
A steel ball is dropped from a height and hits the ground 6.7 seconds after its release. From what height (in feet) was the ball released?
Step-by-step explanation:
Acceleration = g = 32.17ft/s²
Initial velocity = 0ft/s
Time taken = 6.7s
Using Kinematics,
we have s = ut + 0.5at².
=> s = (0)(6.7) + 0.5(32.17)(6.7)²
=> s = 722.06ft.
Amanda is decorating you new house. She found a table at Pottery Barn for $425. If the table is 45% off, what will it cost?
Please Please Help ME!!! its so hard 50 points
Brainiest for correct answer.
Answer:
hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
y-intercept: (___,___)
r-intercept: (___,___)
Answer:
y= 0,4 x=0,3
Step-by-step explanation:
find the equation of the line that is parallel y= 2x+10 and passes through the point (6,-4)
Answer:
The equation of the parallel line to the given line
y = 2 x - 16
Step-by-step explanation:
Step(i):-
Given equation of the straight line y = 2 x +10
2x - y + 10 =0
The equation of the parallel line to the given line is
a x + by + k=0
The equation of the parallel line to the given line is
2x - y + k=0
Step(ii):-
Given point ( 6,-4)
The equation of the parallel line to the given line is
2x - y + k=0
This line passing through the point ( 6,-4)
2(6) - (-4)+ k=0
12 + 4 +k =0
16 + k=0
k = -16
Final answer:-
The equation of the parallel line to the given line
y = 2 x - 16
10 pts+ brainliest if correct
Answer:
C.
Step-by-step explanation:
Answer:
c.
Step-by-step explanation:
