Answer:
[tex]\displaystyle y' = 2(2x - 5)(x^5 - 5)(12x^5 - 25x^4 - 10)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x⁵)²
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x^5)^2 + (2x - 5)^2\frac{d}{dx}[(5 - x^5)^2][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2-1} \cdot \frac{d}{dx}[2x]](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5)^{2-1} \cdot \frac{d}{dx}[-x^5]][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot \frac{d}{dx}[-x^5]][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1(2x^{1 - 1})](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot -5x^{5 - 1}][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x^5)^2 + (2x - 5)^2[2(5 - x^5) \cdot -5x^4][/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x^5)^2 - 10x^4(2x - 5)^2(5 - x^5)[/tex]Factor: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[2(5 - x^5) - 5x^4(2x - 5)][/tex][Distributive Property] Distribute 2: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[10 - 2x^5 - 5x^4(2x - 5)][/tex][Distributive Property] Distribute 5x⁴: [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)[10 - 2x^5 - 10x^5 + 25x^4][/tex][Addition] Combine like terms (x⁵): [tex]\displaystyle y' = 2(2x - 5)(5 - x^5)(10 - 12x^5 + 25x^4)[/tex]Rewrite: [tex]\displaystyle y' = 2(2x - 5)(x^5 - 5)(12x^5 - 25x^4 - 10)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
At Western University the historical mean of scholarship examination scores for freshman applications is 900. Ahistorical population standard deviation \sigmaσ= 180 is assumed known.
Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a. State the hypotheses.
b. What is the 95% confidence interval estimate of the population mean examination
score if a sample of 200 applications provided a sample mean \overline x
x
= 935?
c. Use the confidence interval to conduct a hypothesis test. Using \alphaα= .05, what is your
conclusion?
d. What is the p-value?
Answer:
(910.053 ; 959.947)
Pvalue = 0.00596
Step-by-step explanation:
Given :
Population mean, μ = 900
Sample size, n = 200
Population standard deviation, σ = 180
The hypothesis :
H0 : μ = 900
H0 : μ ≠ 900
The 95% confidence interval:
Xbar ± Margin of error
Margin of Error = Zcritical * σ/√n
Since the σ is known, we use the z- distribution
Zcritical at 95% confidence = 1.96
Hence,
Margin of Error = 1.96 * 180/√200
Margin of Error = 24.947
95% confidence interval is :
935 ± 24.947
Lower boundary = 935 - 24.947 = 910.053
Upper boundary = 935 + 24.947 = 959.947
(910.053 ; 959.947)
Hypothesis test :
Test statistic
(935- 900) ÷ (180/√(200))
Test statistic = 2.750
Pvalue from Test statistic ;
Pvalue = 0.00596
Pvalue < α ; Reject H0 and conclude that score has changed
Hence, we can conclude that the score has changed
Use the exact values of the ratios and find the value of tan 45° + sin 30°
Answer:
1.5
tan45=1
sin30=1/2
so 1+1/2=1.5 or 3/2
a principios de un mes, el precio de la gasolina de 95 octanos era de 750 el litro. si aunmento en un 12% el dia 10 y luego disminiyo un 5% el dia 24 ¿cual es el precio a fin de mes?
Answer:
750/100*12=90. 640, 37.5 O 32, entonces seria 670.5 o 673, tu decides, porque no se si el aumento o disminuyo del segundo es a base del valor inicial, pero yo diria que si, asi que suerte! espero te ayude
Decide if the following probability is classical, empirical, or subjective.
You guess that there is a 30% chance that you will be assigned homework in your English class on Tuesday
Answer:
Subjective.
Step-by-step explanation:
Classical probability:
A classical probability is a probability based on a formal reasoning, for example, probability of getting heads/tails on a coin toss.
Empirical probability:
An empirical probability is the same as experimental probability, that is, suppose 7 out of 10 people you meet are Buffalo Bills fans, so the next person has a 7/10 = 0.7 = 70% probability of being a Buffalo Bills fan.
Subjective probability:
Probability of somthing happening based on "intuition", that is, based on the person's own experience. In this exercise, we have an example of subjective probability.
Helpppp plsss I’m trying to get my grade up
This converts to the improper fraction 7/4
======================================================
Work Shown:
3/4 = 0.75
area of triangle on the left = base*height/2 = 0.75*2/2 = 0.75 sq ft
area of triangle on the right = base*height/2 = 1*2/2 = 1 sq ft
total area = 0.75+1 = 1.75 sq ft
This converts to the improper fraction 7/4 because
1.75 = 1 + 0.75
1.75 = 1 + 3/4
1.75 = 4/4 + 3/4
1.75 = (4+3)/4
1.75 = 7/4
Avery's piggy bank has 300 nickels
Answer:
Step-by-step explanation:
?
how to solve 4 > 11 - x/3
Answer:
21 < x
Step-by-step explanation:
4 > 11 -x/3
Subtract 11 from both sides
4 - 11 > -x/3
-7 > -x/3
Multiply both sides by 3
-7*3 > -x
-21 > -x
Multiply both sides by (-1)
21 < x
When we are multiplying by negative, then inequality sign changes.
Can I get some help with this question? I have attempted several times and failed.
9514 1404 393
Answer:
B. relative maximum of 8.25 at x=2.5
Step-by-step explanation:
A quadratic of the form ax²+bx+c has an absolute extreme at x=-b/(2a). For your quadratic, that is ...
x = -5/(2(-1)) = 5/2
The value of the extreme is ...
f(5/2) = (-5/2 +5)(5/2) +2 = 25/4 +2 = 33/4 = 8.25
The negative leading coefficient tells you the graph opens downward, so the extreme is a maximum.
The function has a relative maximum of 8.25 at x = 2.5.
__
A graphing calculator can show this easily.
Answer these please!!!
Answer:
(upper left) 3 triangles
(upper right) 5 triangles
(lower left) 9 rectangles
(lower right) next pattern is a grid that is 8 by 8.
The pattern is the previous side multiplied by 2
first block is 1x1
second block is 2x2
third block is 4x4
next block would be 8x8
Step-by-step explanation:
The amount of time needed to complete a certain roadtrip, t, varies inversely with the speed of a vehicle, s. At a speed of 52 miles per hour, the trip will be complete in 12 hours. How many hours would it take at a speed of 48 miles per hour?
Answer:
The time it will take is 13 hours
Step-by-step explanation:
From the given statement, we can generate the following inverse proportion relationship between t and s
t ∝ 1/s
[tex]t = \frac{k}{s} \\\\where;\\\\k \ is \ constant\\\\k = t_1s_1 = t_2s_2 \\\\t_2 = \frac{t_1s_1}{s_2} \\\\t_2 = \frac{12 \times 52}{48} \\\\t_2 = 13 \ hours[/tex]
The time it will take is 13 hours
if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line
Answer:
The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation the equation of the straight line will be.
Step-by-step explanation:
ANYONE KNOW THE ANSWER TO THIS??
Answer:
x = 14 is your answer
Step-by-step explanation:
76 = 7x-22, so to figure it out, you first move -22 to the other side and get
76+22 = 7x.
add them together and you get 98 = 7x
7x would be your equation, so divide 98 by 7 and you get your solution
x = 14 is your answer
The first five terms of a sequence are 34, 35, 36, 37, 38.
Write down the general term of the sequence
33+n
Hope it helps you...
log (3x+5)=log (2x-7)
Answer:
x=-12 (BUT IS EXTRENUS)
Step-by-step explanation:
If u dont know what extraneous is, dont worry about it...
Write a recursive formula for the following sequence:10, 5, 0, -5,... *
Answer:
decrease by 5
Step-by-step explanation:
n= 10
then in sequence,
n= n-5
I have a mix of 12 nickels and dimes in my pocket. All together I have $1 . How many nickles and dimes do I have?
(Create a system of equations and solve that system)
Answer:
Step-by-step explanation:
n + d = 12
0.05n + 0.1d = 1 ║ × ( - 10 )
n + d = 12 ..... (1)
- 0.5n - d = - 10 ..... (2)
(1) + (2)
0.5n = 2 ⇒ n = 4
d = 12 - 4 = 8
There are 4 nickels and 8 dimes in the pocket.
PLEASE HELP
A salesperson works 40 hours per week at a job where has two options for being paid. Option A is an hourly wage of $25. Option B is a commission rate of 5% on weekly sales. How much does need to sell this week to earn the same amount with the two options?
he needs to sell$___this week
Answer:
He must sell 20,000 to make the same amount
Step-by-step explanation:
Option A
25 h where hourly rate time number of hours ( 40 hours)
25 * 40 = 1000
Option B =
.05 * s where s is the amount of sales and 5% commission
We want them to be equal
1000 = .05s
Divide each side by .05
1000/.05 = .05s/.05
20000 = s
He must sell 20,000 to make the same amount
There are 750 identical plastic chips numbered 1 through 750 in a box. What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Answer:
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
There are 750 identical plastic chips numbered 1 through 750 in a box
This means that [tex]a = 1, b = 750[/tex]
What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?
[tex]P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358[/tex]
0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627
Two similar triangles are shown below:
Which two sets of angles are corresponding angles
Answer:
angle w and angle v; angle x and angle y (option 1)
Step-by-step explanation:
the little arc things are what tell you two angles are corresponding m
angles w and v both have two arc drawing things.
angle x and y have one
and the other angles that aren't labeled have three
YA is the angle bisector of ZXYZ. If mZXYZ = 52°, what is mZZYA?
Given:
[tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex].
[tex]m\angle XYZ=52^\circ[/tex]
To find:
The measure of [tex]m\angle ZYA[/tex].
Solution:
It is given that [tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex]. It means
[tex]m\angle XYA=m\angle ZYA[/tex] ...(i)
Now,
[tex]m\angle XYA+m\angle ZYA=m\angle XYZ[/tex]
[tex]m\angle ZYA+m\angle ZYA=52^\circ[/tex] [Using (i)]
[tex]2m\angle ZYA=52^\circ[/tex]
Divide both sides by 2.
[tex]m\angle ZYA=\dfrac{52^\circ}{2}[/tex]
[tex]m\angle ZYA=26^\circ[/tex]
Therefore, the required value is [tex]m\angle ZYA=26^\circ[/tex].
A scale model of a building has a scale of 3 : 79.
The height of the real building is 24 m.
Find the height of the scale model.
Give your answer in cm to 2 dp.
Answer:
The height of the scale model is of 91.14 cm.
Step-by-step explanation:
Scale problems are solved by proportions, using rule of three.
A scale model of a building has a scale of 3 : 79.
This means that 3m on the drawing represent 79m of real height.
The height of the real building is 24 m.
3m - 79m
xm - 24m
Applying cross multiplication
[tex]79x = 72[/tex]
[tex]x = \frac{72}{79}[/tex]
[tex]x = 0.9114[/tex]
In centimeters:
Multiplying by 100:
0.9114*100 = 91.14 cm.
Helppppo plsssssssssss I need helppp with thissss
Answer:
82 is what r equals
Step-by-step explanation:
So, lets go over what we know:
D equals rt, or r * t:
D=r*t
The table shows:
t=2 - d=164
t=3 - d=246
These are the only 2 values we need to look at.
We know that D= r*t, and we can just plug in the values found in the table for t and d to solve for r. So:
164= r * 2
Divide both sides by 2 to iscolate r:
82=r
So it seems like r is equal to 82, however this might be exponential or inaccurate, so lets double check witht the nexty values on the table:
246=r*3
Divide by 3 to iscolate the r:
82=r
So we know that r must equal 82.
Hope this helps!
Choose the correct vertex of the function f(x) = x2 - X + 2.
Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
f(x) = x² - X + 2.
Quadratic equation with [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]\Delta = b^2-4ac = (-1)^2 - 4(1)(2) = 1 - 8 = -7[/tex]
[tex]x_{v} = -\frac{(-1)}{2} = \frac{1}{2}[/tex]
[tex]y_{v} = -\frac{-7}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
What is the sample space for the suits of a standard 52-card deck of cards?
The sample space for the suits of a standard 52-card deck of cards is {Hearts, Diamonds, Clubs, Spades}.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The sample space for the suits of a standard 52-card deck of cards consists of four elements, one for each suit:
Hearts
Diamonds
Clubs
Spades
Each card in the deck belongs to one of these four suits. Therefore, the sample space for the suits of a standard 52-card deck of cards is {Hearts, Diamonds, Clubs, Spades}.
Hence, the sample space for the suits of a standard 52-card deck of cards is {Hearts, Diamonds, Clubs, Spades}.
To learn more on probability click:
https://brainly.com/question/11234923
#SPJ2
the terminal side of 0 passes through the point (8,-7) what is the exact value of cos 0 in simplified form
Answer: [tex]\cos(\theta) = \frac{8\sqrt{113}}{113}\\\\[/tex]
=================================================
Work Shown:
x^2+y^2 = r^2
(8)^2+(-7)^2 = r^2
113 = r^2
r = sqrt(113)
The distance from (0,0) to (8,-7) is exactly sqrt(113) units.
This is the exact length of the hypotenuse of the right triangle.
Next, we do the following steps:
[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(\theta) = \frac{x}{r}\\\\\cos(\theta) = \frac{8}{\sqrt{113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113}*\sqrt{113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113*113}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{\sqrt{113^2}}\\\\\cos(\theta) = \frac{8\sqrt{113}}{113}\\\\[/tex]
Side note: cosine is positive in quadrant Q4.
The annual demand for a product is 17,200 units. The weekly demand is 331 units with a standard deviation of 85 units. The cost to place an order is $31.50, and the time from ordering to receipt is six weeks. The annual inventory carrying cost is $0.10 per unit. a. Find the reorder point necessary to provide a 95 percent service probability. (Round your answer to the nearest whole number.)
Reorder point
b. Suppose the production manager is asked to reduce the safety stock of this item by 60 percent. If she does so, what will the new service probability be? (Round your answer to 3 decimal places.)
Service probability
Answer:
R = 2414 units
0.794
Step-by-step explanation:
Given:
Weekly demand, D = 331 units
Lead time (L)= 6 weeks
Standard Deviation (SD) = 85 units
The reorder point is calculated using the relation :
R = D*L + z*(SDw)
SDw = the standard deviation with lead time of 6 weeks ; √6 * 85 = 208.21
z = NORMSINV(0.98) = 2.05
R = (331 * 6) + (2.05 * 208.21)
R = 1986 + 428.122
R = 2414.122
R = 2414 units
The Safety stock, SS
SS = z * SDw
SS = 2.05 * 208.21
SS = 426.8305 units
60% reduction :
426.8305 * (1 - 60%)
= 170.7322
= 171 units
The new service probability ;
SS = z * SDw
171 = z * 208.21
z = 171 / 208.21
z = 0.82
P(Z < 1.02) = 0.7938 = 0.794 = 79.4%
Alix is 10 years older than tamia. Alanna is twice as old as tamia. If the sum of their ages is 74, how old is alanna
Answer:
Alanna is 32 years old
Step-by-step explanation:
Hi there!
We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.
Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x
Alix is 10 years older than Tamia, so Alix must be x+10 years old
Alanna is twice as old as Tamia, so she must be 2x years old
We're also given that Alix+Alanna+Tamia=74
When we substitute it with the expressions we have, it becomes:
x+x+10+2x=74
now combine like terms
4x+10=74
subtract 10 from both sides
4x=64
divide both sides by 4
x=16
We found the value of x (Tamia's age)
However, the problem asks for Alanna's age, which we have set as 2x
So Alanna is 2*16, or 32 years old
Hope this helps! :)
Answer:
32 years
Step-by-step explanation:
that is the procedure above
A square-based tent covers an area of 64 square feet. What is the length of one side of the tent?
Answer:
8 feet
Step-by-step explanation:
A square's area can be expressed as l², with l representing one side of the tent. Therefore, as our area is 64, we can say that 64 = l². Taking the square root of both sides, we get that √64 = l, and l = 8 feet
Help. Volume question in math.
Answer:
c-635.25pi
Step-by-step explanation:
volume of cylinder is pi*radius squared*height(here they gave you the diameter so you'll have to divide it by 2 to get the radius)
so pi*(11/2)^2*21
and you end up with 635.25pi
A delivery truck manager takes a sample of 25 delivery trucks and calculates the sample mean and sample standard deviation for the cost of operation. A 95% confidence interval for the population mean cost is constructed and found to be $253 to $320. He reasons that this interval contains the mean operating cost for the entire fleet of delivery trucks since the sample mean is contained in this interval.
Required:
a. Do you agree with his reasoning?
b. How would you interpret this confidence interval?
c. Is this an appropriate use of a confidence interval?
d. Concerning your answers to parts a through c, what assumptions did you make (if any)? Does the Central Limit Theorem apply? Why or why not?
e. How does this apply or could apply to your profession?
Answer:
a) No.
b) Lies between 253 and 320.
c) No.
d) Central limit theorem is not applicable here.
e) The process of estimation can always help us make the right prediction about future sales, demands, costs, profits, and so on based on the past data or any such data available and hence take the correct decision
Step-by-step explanation:
1) No I do not agree, it's just because the mean should be always within the confidence interval. in this case, the above statement doesn't satisfy the condition.
2)The true mean values at 95% confidence interval lies between 253 and 320.
3) No, because this is only used for the difference in mean. If there is a difference then the mean is different.
4) Central limit theorem is not applicable here. Since the sample size is very small, it better to use t distribution rather which indicated normal data.
in case the sample size is greater than 30, we can then apply the central limit theorem.
5) The process of estimation can always help us make the right prediction about future sales, demands, costs, profits, and so on based on the past data or any such data available and hence take the correct decision.
