Answer:
The following classification is found:
[tex](0.2, 6)[/tex] - Absolute minimum
[tex](-0.2, 10)[/tex] - Absolute maximum
Step-by-step explanation:
Let be [tex]f(x) = 125\cdot x^{3}-15\cdot x + 8[/tex], we need to find first and second derivatives of this expression at first:
First derivative
[tex]f'(x) = 375\cdot x^{2}-15[/tex] (Eq. 1)
Second derivative
[tex]f''(x) = 750\cdot x[/tex] (Eq. 2)
Critical points are points that equals first derivative to zero and that may be maxima or minima. That is:
[tex]375\cdot x^{2} -15 = 0[/tex]
[tex]x = \pm \sqrt{\frac{15}{375} }[/tex]
Which leads to the following critical points:
[tex]x_{1}\approx 0.2[/tex] and [tex]x_{2} \approx -0.2[/tex]
Now we evaluate each result in second derivative expression:
[tex]f''(x_{1}) = 750\cdot (0.2)[/tex]
[tex]f''(x_{1})=150[/tex] (Absolute minimum)
[tex]f''(x_{2})= 750\cdot (-0.2)[/tex]
[tex]f''(x_{2}) = -150[/tex] (Absolute maximum)
Lastly we evaluate the function at each critical point:
[tex]f(x_{1})= 125\cdot (0.2)^{3}-15\cdot (0.2)+8[/tex]
[tex]f(x_{1})= 6[/tex]
[tex]f(x_{2})= 125\cdot (-0.2)^{3}-15\cdot (-0.2)+8[/tex]
[tex]f(x_{2}) = 10[/tex]
And the following classification is found:
[tex](0.2, 6)[/tex] - Absolute minimum
[tex](-0.2, 10)[/tex] - Absolute maximum
5,049 +48=105
MD Model with Mathematics A comic store sells two rare
comic books for $1,824. The price of one comic book is
11 times as much as the price of the other.
• 'Write an equation to model the price of the less expensive
comic book. Then find the price.
• Write an equation to model the price of the more expensive
comic book. Then find the price.
Let the cost of the less expensive comic book be x .
Then :-
[tex]1284 - 11x = x[/tex]
Using this equation , we can find the cost of the less expensive comic book .
Price of the less expensive book :-
[tex]1284 - 11x = x[/tex]
[tex]11x + x = 1284[/tex]
[tex]12x = 1284[/tex]
[tex]x = \frac{1284}{12} [/tex]
[tex]x = 107[/tex]
Cost of the less expensive book is 107 .
Therefore , the epice of the less expensive book = $ 107 .
Solution (b) :-Cost of the more expensive book = 11x
Which means :-
[tex]1284 - x = 11x[/tex]
[tex]11x + x = 1284[/tex]
[tex]12x = 1284[/tex]
[tex]x = 107[/tex]
[tex]11x = 11 \times 107[/tex]
[tex] = 1177[/tex]
Therefore , the price of the more expensive book = $ 1177 .
Forty discrete math students are to be divided into eight discussion groups, each consisting of five students. In how many ways can this be done?
There are 65,800,850,944,000 ways to divide the 40 students into 8 discussion groups, each consisting of 5 students.
To find the number of ways to divide 40 students into 8 discussion groups of 5 students each, we'll use a combination formula.
The number of ways to choose 5 students out of 40 for the first group is given by C(40, 5).
After choosing 5 students for the first group, there will be 35 students left for the second group.
The number of ways to choose 5 students out of these 35 for the second group is C(35, 5).
We continue this process until all 8 groups are formed.
The total number of ways to divide the students into groups is the product of the combinations for each group. So, the total number of ways is:
Total ways [tex]=^{40}C_5 \times ^{35}C_5 \times^{30}C_5 \times ^{25}C_5 \times ^{20}C_5 \times ^{15}C_5 \times ^{10}C_5 \times ^{5}C_5[/tex]
Total ways = 65800850944000
Hence, there are 65,800,850,944,000 ways to divide the 40 students into 8 discussion groups, each consisting of 5 students.
To learn more on Combinations click here:
https://brainly.com/question/19692242
#SPJ4
Sandra sets the cruise control in her car to 67 miles per hour when she goes on road trips. Which equation can be used to find how many hours, h, it will take her to drive m miles at her constant speed?
Answer:
A. [tex]\frac{m}{65} = h[/tex]
I hope this helps!
Travel time data is collected on an arterial. With 30 runs, an average travel time of 152 seconds is computed over the 2.0 miles length, with a computed standard deviation of 17.3 seconds.
Required:
a. Compute 95% confidence bounds on your estimate of the mean.
b. Was it necessary to make any assumption about the shape of the travel-time distribution?
Answer:
a
The 95% confidence bounds is [tex] 145.80 < \mu < 158.19 [/tex]
b
It was not necessary to make any assumption about the shape of the travel time distribution
Step-by-step explanation:
From the question we are told that
The sample size is n = 30
The sample mean is [tex]\=x = 152[/tex]
The standard deviation is [tex]\sigma = 17.3 \ second[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{17.3 }{\sqrt{30} }[/tex]
=> [tex]E = 6.19 [/tex]
Generally 95% confidence bounds is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]152 -6.19 < \mu < 152 -6.19[/tex]
=> [tex] 145.80 < \mu < 158.19 [/tex]
This 95% confidence bounds show that there is 95% confidence that the true mean lies within this bound hence there is it was not necessary to make any assumption about the shape of the travel time distribution
At a particular university, statistics students miss a mean of 2.1 days of school each semester with a standard deviation of 2.5 days. What is the probability that the mean number of days missed for a random sample of 64 students will be more than 3
Answer:
0.0018
Step-by-step explanation:
P(z>2.88)=1-0.9980= 0.0018
Solve the inequality. Graph the solution. -4s<6s +1
Answer:
Step-by-step explanation:
First solve the inequality by writing it.
-4s < 6s + 1
Now subtract -1 on both sides.
-4s - 1 < 6s
Now add 4s on both sides to combine like terms.
-1 < 10s
Now divide 10 on both sides.
-0.1 < s
Now flip it over properly.
s > -0.1
Hope this helped! <3
A sample of size 100 is selected from a population with p = .40.
a. What is the expected value of p(bar)?
b. What is the standard error of p(bar)?
c. Show the sampling distribution of p(bar)?
d. What does the sampling distribution of p show?
Answer:
(a) 0.40
(b) 0.049
(c) [tex]\bar p\sim N(0.40,0.049^{2})[/tex]
(d) Explained below
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]E(\bar p)=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]SE(\bar p)=\sqrt{\frac{p(1-p)}{n}}[/tex]
Given:
n = 100
p = 0.40
As n = 100 > 30 the Central limit theorem is applicable.
(a)
Compute the expected value of [tex]\bar p[/tex] as follows:
[tex]E(\bar p)=p=0.40[/tex]
The expected value of [tex]\bar p[/tex] is 0.40.
(b)
Compute the standard error of [tex]\bar p[/tex] as follows:
[tex]SE(\bar p)=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.40(1-0.40)}{100}}=0.049[/tex]
The standard error of [tex]\bar p[/tex] is 0.049.
(c)
The sampling distribution of [tex]\bar p[/tex] is:
[tex]\bar p\sim N(0.40,0.049^{2})[/tex]
(d)
The sampling distribution of p show that as the sample size is increasing the distribution is approximated by the normal distribution.
Solve −3−4x≤21.
A
x≤−6
B
x≥6
C
x≥−6
D
x≤4
Answer: A
Step-by-step explanation:subtract then multipy the see which one is least to greaest
The Complex Conjugate of 2 + 5i is equal to: _______+_________i
Answer:
2 - 5i
Step-by-step explanation:
For any complex number like say "z" written in rectangular form as;
z = a + ib, then from definitions the complex conjugate is given by the relation:
z* = a − ib
Now, from our question, we want to find the complex conjugate of 2 + 5i.
From the relationship above, it's clear that the complex conjugate here is;
2 - 5i
Please help me for a TEST review tomorrow!!
Answer:
Hope you understand my writing!
A bus holds 30 people, and a van holds 10 people. Write an expression that shows the number of people that could fill b buses and v vans?
Answer:
30b+10v
Step-by-step explanation:
9. Verizon offers a cell phone plan that includes a flat fee of $85 per month for the first phone and $7.50 a
month for each additional phone. If Maria's phone bill was $115, how many extra phone lines does she
have?
Answer:
She has 4 extra phone lines
Step-by-step explanation:
85 + 7.5p = 115
115-85 = 30
7.5p ÷ 7.5
30 ÷ 7.5
p = 4
Rename 2 1/2 as an improper fraction
Answer:
5/2
Step-by-step explanation:
Because that is the answer
Answer:
5/2
Step-by-step explanation:
Because it is an improper fraction so you move it to the top.
Pls Brainliest! ;) It would mean a lot!
there are 5,280 feet in 1 mile. if Riley ran 26,400 feet how many miles did she run
Given m||n, find the value of x.
t
>m
(x+14)
(9x-8)"
Answer:
1st one
Step-by-step explanation:
Answer:
1st one
Step-by-step explanation:
-9 - 11 = 2q + 4
Solve?
Answer:
q = -12
Step-by-step explanation:
-9 - 11 can be written as -9 + (-11)
-20 = 2q + 4
Subtract 4 from both sides.
-24 = 2q
Divide both sides by 2
-12 = q
Hope I helped :)
Please consider Brainliest :)
I needs help how do i shave my ba. lls
Answer:
WHAT THE FAWK SRE YOU SAYING AND WRITING
Answer:
truste me dont!
Step-by-step explanation:
A bee flies at 10 feet per second directly to a flowerbed from its hive. The bee stays at the
flowerbed for 16 minutes, and then fies directly back to the hive at 8 feet
per second it is away from the hive for a total of 20 minutes
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
a. Write the equation Leld be the distance of the flowerbed from the hive
(Type an equation Use integers of fractions for any numbers in the equation. Do not simplity)
Answer:
a. s = [tex]\frac{d}{t}[/tex]
b. 9600 ft
Step-by-step explanation:
In the given question, the motion of the bee involves speed (s), distance (d) and its time of flight (t).
a. The equation required to determine the distance of the flowerbed from the hive/ hive to flowerbed is;
speed = [tex]\frac{distance}{time}[/tex]
i.e s = [tex]\frac{d}{t}[/tex]
b. Given that: the bee flies back at 8 feet per second, and in 20 minutes (1200 seconds);
s = [tex]\frac{d}{t}[/tex]
⇒ d = s x t
= 8 ft/s x 1200 s
= 9600 ft
The flowerbed is 9600 feet from the hive.
Hey! I'm having trouble with this one problem in precalc.
Verify the identity: cot x minus pi divided by two = -tan x
Answer:
O-O is this highschool stuff sorry couldnt help
Step-by-step explanation:
1. which group weighed the most per item on the scale? how much did it weigh?
which group weighed the least per item on the scale? how much did it weigh?
And also complete the table.
Please help it is due right now ASAP
Answer:
cars weighed the most per item and desks the least
f(x) = 2( x ) + 10, Solve when given f(x) = -22 sorry it’s just I didn’t get function notation
Answer:
x=-16
Step-by-step explanation:
[tex]2x + 10 = - 22[/tex]
[tex]2x = - 22 - 10 = - 32[/tex]
[tex]x = - 32 \div 2 = - 16[/tex]
Bryce orders the following items from a catalog. What is the total price he charges to his credit card if the sales tax is 6 percent and nontaxable shipping costs $5 for the order? Round to the nearest cent if necessary.
Answer:
The answer is C : $115.54
Step-by-step explanation:
If you add every single items cost together, the total is $109.00
60 + 14 = 74
10 + 25 = 35
74 + 35 = $109
You then caculate what 6% percent of 109 is = $6.54
After that, you add the total and percent together
$6.54 + $109.00 = $115.54
Answer:answer is c
Step-by-step explanation:I took edge 2022
Pleas help I am brainliesting
Answer:
$2.22 i think
Step-by-step explanation:
Answer:
You would have $2.22 left.
Step-by-step explanation:
6.96 - (0.79 * 6)
6.96 - 4.74
2.22
Sub to SZ Lexrn if that does not show search up shiyo on vr and first vid is them please help out , thx bye . If you do it cmt and ill make a post for yall for 100 points, please bro..
Answer:
Ooooook?
Step-by-step explanation:
Fine
In ΔCDE, \text{m}\angle C = (x-4)^{\circ}m∠C=(x−4) ∘ , \text{m}\angle D = (11x-11)^{\circ}m∠D=(11x−11) ∘ , and \text{m}\angle E = (x+13)^{\circ}m∠E=(x+13) ∘ . Find \text{m}\angle C.m∠C.
Answer:
The measure of C is 10°
Step-by-step explanation:
In a triangle CDE, its internal angles are given:
C=x-4
D=11x-11
E=x+13
Since the sum of the internal angles of a triangle is 180°:
x-4+11x-11+x+13=180
Simplifying:
13x-2=180
Adding 2:
13x=182
Solving:
x=182/13
x=14°
The measure of the angles is:
C=x-4 =10°
D=11x-11=143°
E=x+13=27°
The measure of C is 10°
Bryce forgot how much he spent on a new video game but he did remember meer de palo 8.57% tax and that came to be $12.75. What is the original price of the video game?
Answer:
11.66
Step-by-step explanation:
Suppose that 28 crayons, of which four are red, are divided randomly among Jack,Marty, Sharon, and Martha (seven each). If Sharon has exactly one red crayon, what is the probability that Marty has the remaining three?
Answer:
0.0263
Step-by-step explanation:
A population’s instantaneous growth rate is the rate at which it grows for every instant in time. Function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.
r(x) = 0.05(x^2 + 1)(x - 6)
Consider the graph of function r.
Function r has (blank) and (blank). Based on the instantaneous growth rate, the population decreased (blank) hours and the population increased (blank) hours.
Answer:
Decreased 4 days-96 hours
Increased 6 days-144 hours
Step-by-step explanation:
In order to solve this you just have to look at the graph and after the start of the experiment which is basically the origin of the graph and as you can see immidiately goes down after the start and it reaches the turning point in the day four which is when the graph starts to go up in the Y axis, so that day it would start the increase, and it increases from day 4 to 10 that would be 6 days, and the decrease would be from the origin to day 4.
what is the slope of (-3,4) (-2,0)
Answer:
m = − 4
Step-by-step explanation:
Use the slope formula to find the slope m
Hope this helps :)
Five more than Bob’s age is 23. How old is Bob? equation
Answer:
18 Years OldStep-by-step explanation:
23 - 5 = 18 Years Old
Hope this helps! <3
Answer:
18 yeara old
Step-by-step explanation:
let Bob's age be 'x'
5 more than Bob's age means
5+x ...is 23
Therefore, 5+x=23
x= 23-5
18
Bob is 18 years old.
Hope it helped.