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Related Questions
Calculus helpppppppppppppppp
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Answer:
[tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
FunctionsFunction NotationExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Logarithms and Natural LogsLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Logarithmic Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x\sqrt[3]{1 + x^2}[/tex]
Step 2: Rewrite
[Equality Property] ln both sides: [tex]\displaystyle lny = ln(x\sqrt[3]{1 + x^2})[/tex]Logarithmic Property [Multiplying]: [tex]\displaystyle lny = ln(x) + ln(\sqrt[3]{1 + x^2})[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle lny = ln(x) + ln \bigg[ (1 + x^2)^\bigg{\frac{1}{3}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = ln(x) + \frac{1}{3}ln(1 + x^2)[/tex]Step 3: Differentiate
ln Derivative [Implicit Differentiation]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx} \bigg[ ln(x) + \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{d}{dx} \bigg[ \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{1}{3}\frac{d}{dx}[ln(1 + x^2)][/tex]ln Derivative [Chain Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \frac{d}{dx}[(1 + x^2)][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \bigg( \frac{d}{dx}[1] + \frac{d}{dx}[x^2] \bigg)[/tex]Basic Power Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot (2x^{2 - 1})[/tex]Simplify: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot 2x[/tex]Multiply: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{2x}{3(1 + x^2)}[/tex][Multiplication Property of Equality] Isolate y': [tex]\displaystyle y' = y \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex]Substitute in y: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex][Brackets] Add: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{5x^2 + 3}{3x(1 + x^2)} \bigg][/tex]Multiply: [tex]\displaystyle y' = \frac{(5x^2 + 3)\sqrt[3]{1 + x^2}}{3(1 + x^2)}[/tex]Simplify [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Implicit Differentiation
Book: College Calculus 10e
If Jamal currently has 2000 in saving, he will need to Save________each month
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PLZ needed now plz URGENT!
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Answer:
Realtionship B
Step-by-step explanation:
Relationship A doesn't pass the line test
Plz answer now Presenting your findings best fits which step of the statistical process?
a) Form a question that can be answered by data.
b) Design and implement a plan that collects data.
c) Analyze the data using graphical and numerical methods.
d) Interpret and compare the data.
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Answer:
Interpret and compare the data
Step-by-step explanation:
when you compare you are presenting your information and data to others and they present theirs to you.
Answer:
Interpret and compare the data
Step-by-step explanation:
A high school basketball coach wants to see whether there is a linear relationship between player height, x , and the number of points scored in a game by basketball players in the coach’s state, y. The 96 percent confidence interval to estimate the slope of the linear regression line relating player height to points scored in a game is calculated to be (−0.432,1.844) . Assume all conditions for inference for the slope of a regression line were met. Based on the confidence interval, which of the following claims is supported by the confidence interval?
A. Each player scored at most 1.844 points in a game.
B. The average difference between actual points scored and predicted points scored is between -0.432 and 1.844.
C. There is a positive linear relationship between player height and number of points scored for basketball players in the coach's state.
D. There is a negative linear relationship between player height and number of points scored for basketball players in the coach's state.
E. It cannot be determined whether the linear relationship between player height and number of points scored for basketball players in the coach's state is positive or negative
Answers
Answer:
E
Step-by-step explanation:
Since 0 is in confidence interval, and negative and positive values are also, we are 96% confident in all possible answers in this interval so since true slope could be negative or positive in our interval, we cannot determine it
It cannot be determined whether the linear relationship between player height and number of points scored for basketball players in the coach's state is positive or negative (Option E)
How to interpret the confidence interval?Suppose the confidence interval at P% for some parameter's values is given by
[tex]x \pm y[/tex]
That means, that parameter's estimated value is P% probable to lie in the interval
[tex][x-y,x+y][/tex]
For this case, the slope of the linear regression line relating player height to points scored in a game is in the interval (−0.432,1.844) with 96% confidence.
So, we are 96% sure about the slope of the considered linear regression being in this interval. There is nothing more conveyed by this confidence interval about the slope.
Option A, B, C and D therefore are false as they state facts about slope which are not obtainable from the given data.
Thus, "it cannot be determined whether the linear relationship between player height and number of points scored for basketball players in the coach's state is positive or negative "(Option E) is corect here.
Learn more about confidence interval here:
https://brainly.com/question/16148560
amber deposits $870 in an account that has a simple interest rate of 8% per year. After 5 years, how much interest will Amber have learned and what will the total balance be in the account
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Your information:
I = (870)(0.08)(5)
I = 348
Add the interest to the principal for your total balance
348 + 870 = $1218 will be the total balance in the account.
10. Beth has a wooden box. The inside of the box is 5 inches wide, 8.25 inches
long, and 4.5 inches tall. The box has not top. Beth wants to line the box with fest
to protect the items she puts in the box. How many square inches of felt will she
need?
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Answer:
the answer is 41.25
Step-by-step explanation: You multiply 5 x 8.25 at least thats
what I think
If you apply the changes below to the quadratic parent function, f(x) = x?,
what is the equation of the new function?
• Shift 1 unit right.
• Vertically stretch by a factor of 5.
• Reflect over the x-axis.
O A. g(x) = (-5x + 1)2
O B. g(x) = -5(x + 1)2
O C. g(x) = 5x2 - 1
O D. g(x) = -5(x - 1)2
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Answer:
The answer is A
Step-by-step explanation:
(D) g(x) = -5(x-1)² is the correct answer for the given changes in function.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
The starting parent function is f(x) = x².
To shift 1 unit right, we need to replace x with (x-1).
To vertically stretch by a factor of 5, we need to multiply the function by 5.
To reflect over the x-axis, we need to multiply the function by -1.
So the new function g(x) can be written as:
g(x) = -5(x-1)²
Therefore, the correct answer is (D) g(x) = -5(x-1)².
Learn more about function here:
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for the following problems do at least one problem using unit form and at least one problem using fraction form 3.2 x 1.4=
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Order the numbers from least to greatest!
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Answer:
edcafgb
Step-by-step explanation:
-2 1/2 = -5/2 < -2 < -1.75 < -1 < 1.75 < 9/4
*-2 1/2 and -5/2 are the same.
Last year 5200 people entered a contest to win free swimming lessons at the rec center. This year there was a 14% increase in the number of entrees. How many entries were there this year?
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Answer:
There were 5928 entries
Step-by-step explanation:
You multiply 14% by 5200, which is 0.14 in decimal form, and you get 728. Then you add 5200 and 728 together, since 14% of 5200 is 728
243 to the 1/5 power
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Answer:
-3
Step-by-step explanation:
Answer: 3
How I know I use this app called Cymath.
draw to show 5- 2 on the number line
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Answer:
the image is there
Step-by-step explanation:
Someone know this? Pls I really need help
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Answer:
Step-by-step explanation:
d₃₄ = Value in the 3rd row and 4th column
= 0
m₁₃ = Value in the 1st row and 3rd column
= 2
k₂₁ = Value in the 2nd row and 1st column
= 1
1. In a fishing contest, the two largest bass weighed a total
of 22 pounds. The first-place bass weighed 8 pounds
more than the second-place bass. Find the weights of
the first-place and second-place bass.
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Answer:
First place fish weights 15 pounds.
Second place fish weights 7 pounds.
Step-by-step explanation:
7+8=15
15+7=22
Hope this helped!
Find the slope and the y intercept
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Y intercept = (0,2)
Find the slope.
help me find the answer,real answers only!
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-2
step-by-step explanation:
rise over run
so down two over one = negative two
Need the answer for x and y
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Answer:
See below
Step-by-step explanation:
There is no 'y' in your question but I will answer the Q in the pic:
the two sides are equal so
10x-1 = 8x+11
2x = 12
x = 6 then CD = 8x+11 = 8(6)+ 11 = 59 units
Find the surface area or i will kiII myseIf (I give brainliest! :D)
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Answer:
I'll cya in h.e.l.l
ima k.i.l.l. myself as well if they don't give us the answer
Step-by-step explanation:
Answer:
I believe its 122
Step-by-step explanation:
122 total surface area
The area of a rectangular living room is 264 square feet. The length of the room is 2 feet less than twice the width.
What is the width of the living room in feet?
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9514 1404 393
Answer:
12 ft
Step-by-step explanation:
Let the width of the room be represented by w. Then the length is (2w-2), and the area is ...
A = LW
264 = (2w-2)w
132 = w² -w . . . . . . . divide by 2, eliminate parentheses
132.25 = w² -w +.25 . . . . . add (-1/2)² to complete the square
√132.25 = w -0.5 . . . . . take the square root
0.5 +11.5 = w = 12 . . . . . add 0.5; use the positive root
The width of the living room is 12 feet.
Jonas has 16 carnations and 12 roses. He wants to make identical bouquets for a party. How many bouquets can he make?
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Answer:
Jonas can make 4 bouquets, each containing 4 carnations and 3 roses.
Step-by-step explanation:
Given that Jonas has 16 carnations and 12 roses, and he wants to make identical bouquets for a party, to determine how many bouquets can he make the following calculation must be performed, obtaining the largest common divisor between both numbers:
12 = Divisible by 2, 3, 4, 6 and 12
16 = Divisible by 2, 4, 8 and 16
Thus, the common greatest divisor between the two numbers is 4.
12/4 = 3
16/4 = 4
So, Jonas can make 4 bouquets, each containing 4 carnations and 3 roses.
Mr. Sonny's science class is calculating the average number of blinks per minute. Jan blinks 72 times in 4 minutes. What is her
blinking rate, in blinks per minute?
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Answer:
18
Step-by-step explanation:
6 friends are going to a bowling alley. They have to pay a fee per game and $2 to
rent shoes. If they plan on only playing one game, the cost is $48.
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Answer:
3
Step-by-step explanation:
Let x be the number of games they bowled.
Then, we know that each shoe rental was $2.50. So, the total cost for shoes was 3 * $2.50 = $7.50
The total number of games they bowled was 3 * x (since there were 3 persons).
Now, the cost per game was $5.30. So, the total cost for games bowled (minus shoes) was:
3x($5.30) = $15.90x
Now, add the cost of the shoes ($7.50) and you have the total cost ($55.20):
$15.90x + $7.50 = $55.20
Subtract $7.50 from both sides:
$15.90x = $47.70
Divide both sides by $15.90:
x = 3 (the number of games they bowled)
URGENT HELP
Solve for X
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Answer:
x = 3
Step-by-step explanation:
95 + 85 + 100 + 27x -1 = 360
280 + 27x - 1 = 360
279 + 27x = 360
27x = 81
x = 3
Double check your work:
95 + 85 + 100 + 27(3) - 1 = 360
95 + 85 + 100 + 81 -1 =360
360 = 360
In a survey at a shoe store, 200 customers were asked whether they have
running shoes or basketball shoes. The results are in the relative frequency
table.
Total
Have running shoes
0.23
Have basketball shoes
No basketball shoes
Total
No running shoes
0.31
0.32
0.14
What percentage of the people surveyed have basketball shoes?
A. 37%
B. 54%
O C. 46%
O D. 63%
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Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?
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At a school health fair, individual pieces of fruit are placed in paper bags and distributed to students randomly. There are 20 apples, 15 apricots, 25 bananas, 25 pears, and 30 peaches. Write the answer as a fraction in simplest form. Find the probability of NOT getting an apple.
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Answer:
Around 82%
Step-by-step explanation:
95/115
Help with my assignment please
I couldn’t fit part b in the picture so can you please answer this too
Part B
Write the length of the hypotenuse rounded to
nearest hundredth.
The length of the hypotenuse is
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Answer:
the answer ti the first one is B
Step-by-step explanation:
hypotenuse is 12.649
Help me please it’s for math class
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Answer:
No solution
Step-by-step explanation:
To start, a solution requires the lines to intersect
However both lines share a slope of -3 and are thus parallel
Since parallel lines dont intersect, there is no solution
Answer:
Hi! The answer to your question is A. No solution, i also have a picture to help you if u need it.
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
What is the perimeter of a square with side length: 3 cm Do not include units (cm) in your answer. I also will be reporting any links as answers
Answers
Answer:
perimeter of a square is 3 + 3 + 3 + 3 = 12 (cm)
Step-by-step explanation:
Or use the formula P = 4a = 4(3) = 12 (cm)