Answer:
y' = 3x² + 6x - 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationCalculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
y = x³ + 3x² - 5x
Step 2: Differentiate
Basic Power Rule: y' = 3x³⁻¹ + 2 · 3x²⁻¹ - 1 · 5x¹⁻¹Simplify: y' = 3x² + 6x - 5Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
A pizza company runs a marketing campaign based on their delivery time for pizzas. They claim that they will deliver a pizza within 30 minutes of ordering or it is free. In practice the time it takes to prepare a pizza and it being delivered is normally distributed with mean 25 minutes and standard deviation 3 minutes. What is the probability a pizza is delivered for free?On a particular Sunday, 40 pizzas were ordered. What is the probability that more than 2 were delivered for free?If the company wants to reduce the proportion of pizzas that are delivered free to 1%, what should the delivery time be advertised as?
Answer:
0.0475 = 4.75% probability a pizza is delivered for free.
0.2955 = 29.55% probability that more than 2 were delivered for free.
The delivery time should be advertised as 32 minutes.
Step-by-step explanation:
To solve this question, we need to understand the binomial distribution and the normal distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean 25 minutes and standard deviation 3 minutes.
This means that [tex]\mu = 25, \sigma = 3[/tex]
What is the probability a pizza is delivered for free?
More than 30 minutes, which is 1 subtracted by the p-value of Z when X = 30.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 25}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525
1 - 0.9525 = 0.0475
0.0475 = 4.75% probability a pizza is delivered for free
What is the probability that more than 2 were delivered for free?
Multiple pizzas, so the binomial probability distribution is used.
0.0475 probability a pizza is delivered for free, which means that [tex]p = 0.0475[/tex]
40 pizzas, which means that [tex]n = 40[/tex]
This probability is:
[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{40,0}.(0.0475)^{0}.(0.9525)^{40} = 0.1428[/tex]
[tex]P(X = 1) = C_{40,1}.(0.0475)^{1}.(0.9525)^{39} = 0.2848[/tex]
[tex]P(X = 2) = C_{40,2}.(0.0475)^{2}.(0.9525)^{38} = 0.2769[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1428 + 0.2848 + 0.2769 = 0.7045[/tex]
[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.7045 = 0.2955[/tex]
0.2955 = 29.55% probability that more than 2 were delivered for free.
If the company wants to reduce the proportion of pizzas that are delivered free to 1%, what should the delivery time be advertised as?
The 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{X - 25}{3}[/tex]
[tex]X - 25 = 2.327*3[/tex]
[tex]X = 32[/tex]
The delivery time should be advertised as 32 minutes.
In a bag of mini candy bars, 40% of the candy bars are Snickers. There are 120 Snickers in the bag. How many total mini candy bars are in the bag?
Answer:
The amswer is 48.
Step-by-step explanation:
120×0.40=48
Use the frequency distribution to construct a histogram. Using a loose interpretation of the requirements for a normal distribution, does the histogram appear to depict data that have a normal distribution? Why or why not?
Answer: hello the complete question is attached below
answer:
Histogram B is the right histogram
Yes it approximately depict data that have a normal distribution
Step-by-step explanation:
The histogram when plotted is symmetric which means/depicts that the data provided have a normal distribution ( approximately )
A histogram is one of the graphical ways of representing data for easy reading and interpretation.
I NEED HELP WITH THIS, THANKS
9514 1404 393
Answer:
g(x) = 3|x|
Step-by-step explanation:
Each value of g is 3 times the corresponding value of f:
g(x) = 3·f(x)
g(x) = 3|x|
Please help ASAP ASAP
Step-by-step explanation:
[tex] \sqrt{53} [/tex]
Represent the following sentence as an algebraic expression, where "a number" is the letter x.
\text{7 is added to a number.}
7 is added to a number.
Answer:
7+x
Step-by-step explanation:
X will be the unknown
By how much is the sum of 3 2/3 and 2 1/5 less than 7
Step-by-step explanation:
32/3+21/5÷7
14.87÷7
2.124
Susan was posting gifts to her family. She weighed three envelopes before posting them. Geace Envelope A Envelope B Envelope C • Envelope A weighed x grams. Envelope B was 50 grams lighter than Envelope A. • Envelope C was three times as heavy as Envelope A. If the total weight of the three envelopes was 840 grams, write an equation in x and solve it to find the weight of Envelope A. (
Answer:
5x+50
Step-by-step explanation:
you have one x. An x plus fifty. And 3 mire x's. So 5 x's and a 50.
The formula for the surface area of a cylinder is:
SA = 2π r 2 + 2πrh note: that π= 3.14
a. Solve for h showing all work.
b. If the height of a can of soup is 5 inches and the radius is 1.5 inches, what is the surface area?
Answer:
Below in bold.
Step-by-step explanation:
a. SA = 2π r^2 + 2πrh
2πrh = SA - 2π r^2
h = (SA - 2πr^2)/2πr
When π = 3.14 we have
h = (SA - 6.28r^2)/ 6.28r
b. SA = 6.28*1.5^2 + 6.28*1.5* 5
= 61.23 in^2
If a product normal retails for $40, and a customer has a coupon for 15% off, what will the discounted price of the product be?
Answer:
$34
Step-by-step explanation:
price of the product = $40
coupon = 15% off
discount price = 15% of price of a product
=15/100 * $40
=$600/100
=$6
New price of the product = original price - discount
=$40 - $6
=$34
express as a single decimal:4+9/100+6/10
Answer:
4.69
Step-by-step explanation:
4+9/100+6/10
4 is a whole number
9/100 = .09
6/10 = .6
Adding together
4+.09+.6
4.69
Answer:
4.69
Step-by-step explanation:
[tex] \small \: 4 + \frac{9}{100} + \frac{6}{10} \\ [/tex]
[tex] \small4 + \frac{9}{100} + \frac{3}{5} \\ [/tex]
[tex] \small \frac{100 \times 4}{100 \times 1} + \frac{9}{100} + \frac{ 3 \times 20}{5 \times 20} \\ [/tex]
common denominator is 100[tex] \small \frac{400}{100 \times 1} + \frac{9}{100} + \frac{ 60}{100} \\ [/tex]
Add the numerator[tex] \small \frac{400 + 9 + 60}{100 \times1} \\ [/tex]
[tex] \small \frac{469}{100 \times 1} \\ [/tex]
Divide we get
4.69
Let r be the binomial random variable corresponding to the number of people that will live beyond their 90th birthday,
r ≥ 15.
We want to find
P(r ≥ 15)
using the normal approximation given 625 trials and a probability of a 4.4% success on a single trial.
Answer:
P(r ≥ 15) = 0.9943.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
625 trials and a probability of a 4.4% success on a single trial.
This means that [tex]n = 625, p = 0.044[/tex]
Mean and standard deviation:
[tex]mu = E(X) = np = 625*0.044 = 27.5[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{625*0.044*0.956} = 5.13[/tex]
P(r ≥ 15)
Using continuity correction, this is [tex]P(r \geq 15 - 0.5) = P(r \geq 14.5)[/tex], which is 1 subtracted by the p-value of Z when X = 14.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14.5 - 27.5}{5.13}[/tex]
[tex]Z = -2.53[/tex]
[tex]Z = -2.53[/tex] has a p-value of 0.0057
1 - 0.0057 = 0.9943
So
P(r ≥ 15) = 0.9943.
What is cos 0 when sin 0= 2/3
Answer:
your answer is √7/3
Step-by-step explanation:
your answer is √7/3
How many ways can five people, A, B, C, D, and E, sit in a row at a movie theater if A and B must sit
together?
Answer:
The total number of ways A, B, C, D, and E can sit together is 5
Step-by-step explanation:
My sister’s house is 1 2/4 times as high as my house. My house is 5 feet high. How high is my sister’s house?
Answer:
Sister's house is 7.5 feet high
Step-by-step explanation:
Given :
My house = 5 feet
Sisters house = [tex]1\frac{2}{4}[/tex] [tex]times[/tex] [tex]my \ house[/tex]
= [tex]\frac{6}{4} \times 5[/tex]
[tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]
A business is interested in employees’ job satisfaction. The regional manager places a name card for every employee into a bowl and randomly selects 10 cards. Which sampling method was used?
cluster sampling
simple random sampling
stratified random sampling
systematic random sampling
Answer:
B
Step-by-step explanation:
Answer: simple random sampling
AKA: B
Step-by-step explanation: guy above me is correct :)
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than and draw a sketch of the region.
Answer:
0.5000
Step-by-step explanation:
According To The Question,
The Area under the Standard Normal Curve, We Can Use the Statistical Tables , That Reported Area As P(z < a) .
Thus, We need to use the following Relationship.
P(z > a) = 1 - P(z < a)Now solve, P(z > 0) = 1 - P(z < 0) ⇔ 1 - 0.5000 ⇔ 0.5000
(Diagram, Please Find in Attachment)
An elevation of - 12 m is higher than an elevation of -17 m. An elevation of - 17 mis lower than an elevation of -14 m. Which set of inequalities correctly
expresses these relationships?
-12-17 and -17<-14
-12-17 and -17 > -14
-12<-17 and -17 < -14
-12-17 and -17 > -14
help plss
Given:
An elevation of - 12 m is higher than an elevation of -17 m.
An elevation of - 17 m is lower than an elevation of -14 m.
To find:
The set of inequalities that correctly expresses these relationships.
Solution:
An elevation of - 12 m is higher than an elevation of -17 m.
We know that, higher than means greater than and it is represented by the inequality ">". So,
[tex]-12>-17[/tex]
An elevation of - 17 m is lower than an elevation of -14 m.
We know that, lower than means less than and it is represented by the inequality "<". So,
[tex]-17<-14[/tex]
Therefore, the required set of inequalities is [tex]-12>-17[/tex] and [tex]-17<-14[/tex].
Note: The inequality signs are not proper in the options.
Express square root 4x – 7 as a power .
Answer:
It's answer is 4x-7^1/2
Choose the system for the graph.
========================================================
Explanation:
The darkest shaded region is in the northern most region. This region is above both blue boundary lines.
A sample point from this region is (5,2)
We'll plug these coordinates into the first inequality of choice A
[tex]3x+4y \le 12\\\\3(5)+4(2) \le 12\\\\23 \le 12\\\\[/tex]
which is false. So we can rule out choice A.
We can rule out choice B for the exact same reason.
The answer is between C and D
---------------------------
Let's plug those x,y coordinates into the first inequality of choice C
[tex]3x+4y \ge 12\\\\3(5)+4(2) \ge 12\\\\23 \ge 12\\\\[/tex]
which is true. So far, so good.
Now repeat for the second inequality of choice C
[tex]2x-5y \ge 10\\\\2(5)-5(2) \ge 10\\\\0 \ge 10\\\\[/tex]
which is false. We rule out choice C. Choice D is the only thing left, so it must be the answer.
---------------------------
Let's check the second inequality of choice D just for the sake of completeness
[tex]2x-5y \le 10\\\\2(5)-5(2) \le 10\\\\0 \le 10\\\\[/tex]
which is true.
We can see that (x,y) = (5,2) makes both inequalities of choice D to be true, and therefore we have found the final answer.
Answer: TRUST ITS THE CHOICE D
Step-by-step explanation:
Give an
example of a set of data that has more than one mode.
Answer:
Step-by-step explanation:
To calculate the mode, we simply count the number of times that each value appears in the data set and then find the value that appears most often.
A data set can have more than one mode if there is more than one value with the highest count. For example, both 2 and 3 are modes in the data set {1; 2; 2; 3; 3}.
Example of a set of data having more than one node is {1; 2; 2; 3; 3}.
What is Node?
An example S of the data type node. set is a subset of the nodes of a graph G. S is said to be valid for the nodes of G.
Given,
To calculate the mode, we simply count the number of times that each value appears in the data set and then find the value that appears most often.
Now,
A data set can have more than one mode if there is more than one value with the highest count.
For example, both 2 and 3 are modes in the data set {1; 2; 2; 3; 3}.
Learn more about node,
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11 Roger has m toy cars. Don has twice as many cars as Roger. Larry has five more cars than Roger. Write down an expression, in terms of m, to complete each statement. Don has cars H Larry has cars
Step-by-step explanation:
Roger has m toy cars.→ Number of cars Roger has = m
Don has twice as many cars as Roger.→ Number of cars Don has = 2(Cars Roger has)
→ Number of cars Don has = 2m
Larry has five more cars than Roger.→ Number of cars Larry has = 5 + (Cars Roger has)
→ Number of cars Larry has = 5 + m
This is my last one I’m happy
Answer:
105
Step-by-step explanation:
So, we know the formula is:
D=rt or D=r*t
We only need 2 of the 3 sets of values given in the table, one to find our answer, and the other to double check our answer.
Here are the two sets we can look at:
t=2, d=210
t=3, d=315
Lets plug these in and solve:
210=r*2
Divide both sides by 2 to get r alone:
105=r
Now lets check if this is true by pluggin in 105 for r in the second set, and seeing if it works:
D=r*t
315=105*3
=
315=315
So 105 is our answer.
Hope this helps!
if (x) - **4, g(x) = x= 2, and h(x) = 4x+1, what is (f• Hºg)(x)?
2x+16
o (fe hºg)(x) =
2x+4
o (fonog)(x)=
4x-3
o (f• hºg)(x)- Ax=1
4x-5
o (f• nºg)(x) = AX-
Answer:
c
Step-by-step explanation:
How many liters each of a 25% acid solution and a 50% acid solution must be used to produce 80 liters of a 40% acid solution?
Answer:
32 and 48 litersStep-by-step explanation:
Let 25% solution is x liters, then 50% solution is (80 - x) liters.
Acid content is going to be same:
0.25x + 0.5(80 - x) = 80*0.40.25x - 0.5x + 40 = 320.25x = 8x = 8/0.25x = 32 litersSo 32 liters of 25% solution and 80 - 32 = 48 liters of 50% solution
PLEASE HELP ME ASAP! ILL GIVE YOU ALL OF MY POINTS PLEASE HELP.
A large container of breath mints has a mass of 50 g. A small container has a mass of 10 g. What is the percent decrease from the mass of the large container to the mass of the small container? Show your work.
Answer:
80 percent decrease
Step-by-step explanation:
80% of 50 = 40 and 50 - 40 = 10
Answer:
It decreases 80%
Step-by-step explanation:
If the 50g one is 100%, and the 10g one is a fraction of that, find out what 10/50 is as a percent.
10/50= 20%
Because this is the remaining mass, the other 80% has been deducted meaning that the mass of the large container has decreased 80% to get to the mass of the smaller one.
Is 4 over 5 equals 48 over 60 a true proportion?
Answer:
0.8 you yes both of them has the same answer , so it is a true portion
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
[tex]\frac{4}{5} =\frac{48}{60}[/tex]
This is a true proportion because when you cross multiply you get the same product.
[tex]48*5=240[/tex]
[tex]4*60=240[/tex]
cos(x+pi/3)-sin2x=0 ahihihihihihiihihihihihih
Answer:cos(x+pi/3) - sin2x=0
<=> cos(x+pi/3)=sin2x
<=> cos(x+pi/3)=cos(pi/2-2x)
<=>x+pi/3=pi/2-2x+k2pi
Or x+pi/3=-pi/2 +2x+k2pi
<=>x=pi/18 + k2pi/3
Or x=5pi/6 +k2pi
Step-by-step explanation:
Which of the following represents the difference between ten and a number is the sum of eight and a number"?
10 - N(8 + N)
08-N = 10 +N
10 -N = 8+N
9514 1404 393
Answer:
(c) 10 -N = 8 +N
Step-by-step explanation:
The difference between 10 and a number is (10 -N).
The sum of 8 and a number is (8 +N).
In this context, "is" means "equals," so we have ...
10 -N = 8 +N
I need help thanksss
Explanation:
We replace x with x-1 to shift 1 unit to the right. This is because we're making each new input 1 smaller than the old input, which means we're moving the xy axis 1 unit to the left while keeping the f(x) curve fixed in place. That gives the illusion f(x) is moving 1 unit to the right.
The -1 at the end will subtract 1 from the y coordinate and shift everything down by 1 unit.
Answer:
D
Step-by-step explanation:
1 unit Right ³√x-1
unit down (³√x-1)-1