Answers
The second derivative of the first function is s"(x) = = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³.
The second derivative of the second function is; k''(t) = (36t² - 6)e^(-3t²)
How to find the second derivative?1) We are given the function;
s(x) = 4/(1 + 2e^(-0.2x)
First derivative is;
ds/dx = [8e^(x/5)]/5(e^(x/5) + 2)²
Second Derivative is;
d²s/dx² = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³
At x = 0;
d²s/dx² = -[8e^(0/5) - 2]e^(0/5)/25(e^(0/5) + 2)³
d²s/dx² = 8/675
B) We are given the function;
k(t) = e^(-3t²)
The first derivative is;
dk/dt = -6te^(-3t²)
The second derivative is;
k''(t) = (36t² - 6)e^(-3t²)
At t = 1, we have;
k''(t) = (36(1)² - 6)e^(-3(1²))
k"(t) = 1.494
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Related Questions
Please help! thank youuuu
Use polynomial long division to divide. Determine whether the divisor evenly divides into the dividend.
(8x-5)/(2x+1)
Answers
Answer:
The solution is 4 - 9/(2x + 1)
No, the divisor does not evenly divide into the dividend
Step-by-step explanation:
Please see the attached image
Statement: "Three less than four times a number is greater
than or equal to 41."
Answers
Answer:
x≥11
Step-by-step explanation:
4x-3≥41
4x≥41+3 -44
x≥44/4 = 11
Comparing Fractions Choose the correct symbol to compare the fractions please see attached image
Answers
Answer:
>
Step-by-step explanation:
Given: [tex]\frac{1}{2} ? \frac{1}{3}[/tex]
Want: Which fraction is larger?
To identify the size of a fraction, converting it into a fraction is easier
[tex]\frac{1}{2}[/tex] = 0.5
[tex]\frac{1}{3}[/tex] = 0.33
where 0.5 is greater than 0.33
Choices:
< is less than symbol
> is greater than symbol
= is equal to
[tex]\frac{1}{2} > \frac{1}{3}[/tex]
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Visual Representation:
Assuming two hikers begin at a trail start, which scenarios must be true based on the table? Check all that apply.
Melissa and Corey started on different trails.
Melissa hiked up the trail for a longer period of time than Corey.
Melissa and Corey crossed paths between 60 and 90 minutes.
Corey began his descent before Melissa.
As Melissa’s time increased from 0 to 60 minutes, her elevation decreased.
Answers
The true statements are (A), (B) and (D)
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
As, from the given table we can see that
Melissa and Corey started on different trails.Melissa hiked up the trail for a longer period of time than Corey.Corey began his descent before Melissa.Learn more about this concept here:
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What number comes next in the sequence?
1, 1, 2, 3, 5, 8, 13, 21, 34, ?
Answers
Answer:
55
Step-by-step explanation:
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
5+8 = 13
8+13 = 21
13+21 = 34
21 +34 = 55
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The following excerpt comes from the International Bottled Water Association
"In 2012, total U.S. bottled water consumption increased to 9.67 billion gallons, up from 9.1 billion gallons in 2011. In fact, 2012's consumption growth was the strongest it has been in five years. In addition,
per-capita consumption is up 5.3 percent in 2012, with every person in America drinking an average of 30.8 gallons of bottled water last year. Bottled water increased in absolute volume more than any other
beverage category in the U.S. Bottled water sales increased by 6.7 percent in 2012, and now total $11.8 billion."
(i) Estimate the per capita consumption from 2011 from data in the statement. Express your answer rounded correctly to the nearest tenth of a gallon.
Answers
Using proportions, the estimate of the per capita consumption from 2011 is of 29.2 gallons.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
From the data, the 2012 consumption was 5.3% percent higher than in 2011, that is 105.3% of 1.053x. This consumption was of 30.8 gallons, hence:
1.053x = 30.8.
x = 30.8/1.053
x = 29.2.
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Ahmed is three times as old as Suad. Deeqa is three times o Ahmed. If Deeqa is 39 years old. How old is Suad?
Answers
Answer:
Suad is 4.333 years old.
Step-by-Step explanation:
let x = Suad's age
let y = Deeqa's age
let z = Ahmed's age
y = 3x
z = 3y = 3(3x)
but z = 39
3(3x) = 39
x = 4.33333
What is the equation for a cosecant function with vertical asymptotes found at x equals pi over 3 plus pi over 3 times n comma such that n is an integer?
f (x) = 3csc4x
g(x) = 3csc2x
h(x) = 4cscx
j (x) = 4csc3x
Answers
Despite not being a part of the function graph, a vertical asymptote is a vertical line that serves as a guide f (x) = 3csc4x.
How do you find a vertical asymptote?The denominator of the function, n(x), is the place where vertical asymptotes can be located.
If the numerator, t(x), is not zero for the same value of x, then the vertical asymptotes can be determined by solving the equation n(x) = 0 where n(x) is the denominator.
f (x) = 3csc4x.
Periodicity of 3csc(4x) : π / 2
Domain of 3csc(4x) :
Solution : π / 2 n<x < π / 4 + π / 2 n or π /4 + π / 2 n< x < π /2 + π /2 n
Interval Notation : ( π / 2 n,π /4 + π /2)n) ∪ (π / 4 + π /2 n, π / 2 + π /2 n)
Range of 3csc(4x) :
Solution : f(x) ≤ -3 or f(x) ≥ 3
Interval notation : ( - ∝ , -3 ) ∪ (3,∝)
Axis interception points of 3csc(4x) : None
Asymptotes of 3csc(4x) : vertical: x = π / 2 n, x = π / 4 + π/2 n
extreme points of 3csc(4x) :
Minimum (π /8 + π / 2 n,3 ),
Maximum ( 3π / 8 + π/2n, -3).
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Despite not being a part of the function graph, a vertical asymptote is a vertical line that serves as a guide f (x) = 3csc4x.
How do you find a vertical asymptote?The denominator of the function, n(x), is the place where vertical asymptotes can be located.
If the numerator, t(x), is not zero for the same value of x, then the vertical asymptotes can be determined by solving the equation n(x) = 0 where n(x) is the denominator.
f (x) = 3csc4x.
Periodicity of 3csc(4x) : π / 2
Domain of 3csc(4x) :
Solution : π / 2 n<x < π / 4 + π / 2 n or π /4 + π / 2 n< x < π /2 + π /2 n
Interval Notation : ( π / 2 n,π /4 + π /2)n) ∪ (π / 4 + π /2 n, π / 2 + π /2 n)
Range of 3csc(4x) :
Solution : f(x) ≤ -3 or f(x) ≥ 3
Interval notation : ( - ∝ , -3 ) ∪ (3,∝)
Axis interception points of 3csc(4x) : None
Asymptotes of 3csc(4x) : vertical: x = π / 2 n, x = π / 4 + π/2 n
extreme points of 3csc(4x) :
Minimum (π /8 + π / 2 n,3 ),
Maximum ( 3π / 8 + π/2n, -3).
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This year, a teacher graded 83 more final exams than last year. If the teacher graded 625 final exams this year, how many final exams did the teacher grade last year?
Answers
Answer:
542
Step-by-step explanation:
So X is the number of finals graded by teacher last year
she graded 83 more finals than the last year
and the total number of finals she graded this year is 625 so we have an equation
X + 83 = 625
and as you solve it for X
X = 625-83
x = 542
Answer:
542,
Step-by-step explanation:
You could solve these types of problems with inverse operations, so if you subtract 83 from 625, you'd get 542.
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company
manufactures is 14%. Suppose a random sample of 10 LED light bulbs is selected. Complete parts (a) through (d) below.
a. What is the probability that none of the LED light bulbs are defective?
The probability that none of the LED light bulbs are defective is
(Type an integer or a decint. Round to four decimal places as needed.)
Answers
A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability that none of the LED light bulbs are defective is 0.2213.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given the probability of a bulb being a failure is 14%, therefore, the probability of bulb passing the quality check is 86%.
Let the probability of success be defined as 0.14 for binomial distribution, and the probability for failure be 0.86. Therefore, The probability that none of the LED light bulbs are defective is
P(x=0) = ¹⁰C₀ (0.14)⁰ (0.86)¹⁰ = 0.2213
Hence, The probability that none of the LED light bulbs are defective is 0.2213.
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What is the equation of the line that has a slope of 3 and passes through the point (1,-2)?
Y=3x+5
Y=3x-5
Y=3x+1
Answers
Answer:
y = 3x - 5
Step-by-step explanation:
y = mx + b
y - b = mx
-b = mx - y
b = -mx + y
b = -3(1) -2
b = -5
a triangle has wo sides of lengths 6 and 9. what value could the length of the third side be?
Answers
knowed that the 3rd side of a triangle need being greater than the difference of the given two sides length and less that the sum of the given two sides length
so with these knowledge we get
x > (9-6) so x > 3
and
x < (9+6) so x < 15
from these result that the 3rd side length can being choice B. 4 ,C. 7,F. 10,
E. 12,
hope this will help you .
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You invest $1000 in an account that has an annual interest rate of 4%, compounded monthly for 12 years. What is the equivalent interest rate and how many times will the money be compounded?
Answers
The equivalent interest rate is 4.07%.
The money will be compounded 12 times.
What is the equivalent interest rate?
The equivalent interest rate is the actual interest rate that an account earns after accounting for number of compounding.
Effective interest rate = (1 + APR / m ) ^m - 1
M = number of compounding
(1 + 0.04/12)^12 - 1 = 4.07%
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Find the midpoint of the line segment whose endpoints are given. (9,3), (10,- 10)
Answers
Answer:
Step-by-step explanation:
(xm , ym ) = x1 + x2 / 2 and y1 + y2 / 2
= 9 +3 / 2 = 10 -10 / 2
= 12/2 = 0/2
= 6 = 0
So midpoints are (6 , 0)
Answer:
midpoint = [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
Step-by-step explanation:
To find the midpoint of a line segment, you have to find the average of the x and y-values of the end-points, i.e., add the x-coordinate values and divide the answer by 2, and do the same for the y-coordinate values.
• midpoint = [tex](\frac{x_{2} + x_1}{2}, \frac{y_2 + y_1}{2} )[/tex]
= [tex](\frac{9 + 10}{2}, \frac{3 + (-10)}{2} )[/tex]
= [tex](\frac{19}{2}, \frac{-7}{2} )[/tex]
= [tex](9\frac{1}{2} , -3\frac{1}{2} )[/tex]
In 2010, the number of clown costumes sold at a single costume shop was 11. By 2015, that number had grown to 23. Assuming a constant increase in clown costume sales, calculate the average rate of change (the slope) from 2010 to 2015.
Answers
The average rate of change = 109%
What is the meaning of Rate of Change ?Rate of Change is the measure of the increase or decrease in the value with respect to the initial value.
It is given that
No of clown sold in 2010 = 11
No of clown sold in 2015 = 23
The average rate of change = ((23-11)/11 ) *100 %
The average rate of change = 109%
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John needs to put the set of numbers below in ascending order.
3, -1, √5, 13, -11
Which number should John write first?
A. -1
B. -11
C. √5
D. 13
Answers
Reason
Ascending order means smallest to biggest
-11 is the furthest from 0 to the left (negative numbers)
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?
y – 1=-3/2(x + 3)
y – 1=-2/3(x + 3)
y – 1=2/3(x + 3)
y – 1=3/2(x + 3)
Answers
The equation of the line parallel to given line and passing through (-3, 1) will be y – 1 = (3/2)(x + 3). Then the correct option is D.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The slope of the parallel lines are equal.
m = (2 + 4) / (2 + 2)
m = 6/4
m = 3/2
Then the equation of the line will be
y = (3/2)x + c
The line is passing through (-3, 1). Then the value of c will be
1 = (3/2)(-3) + c
c = 9/2 + 1
Then the equation will be
y = (3/2)x + 9/2 + 1
y – 1 = (3/2)(x + 3)
Then the correct option is D.
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If the odds against an event are 3:5, then the probability that the event will fail to occur is
Answers
Answer:
3/8
Step-by-step explanation:
probability = wanted outcomes / total outcomes
odds = wanted outcomes / unwanted outcomes
Odds of 3:5 losing means 3 losing outcomes and 5 winning outcomes.
The total outcomes is 8
The probability of losing which is the probability that the event will fail to occur is 3/8.
6z + 10= -2 solve this problem
Answers
Answer:
z = -2
Step-by-step explanation:
Answer:
[tex]\boxed{\bf z = - 2}[/tex]
Step-by-step explanation:
[tex]\bf 6z + 10 = - 2[/tex]
Subtract 10 from both sides.
[tex]\bf 6z + 10 - 10= - 2 - 10[/tex]Simplify.
[tex]\bf 6z = - 12[/tex]Divide both sides by 6.
[tex]\bf \cfrac{6z}{6} = \cfrac{ - 12}{6} [/tex]Simplify.
[tex]\bf z = - 2[/tex]_________________________
Graph the inequality.
y > |x-2| -5
Answers
Here is the graph! I hope this helps!
Answer:
^this means graph C.
Step-by-step explanation:
Based on statistics from a worldwide health organization, in there were million people worldwide living with a certain disease, and million deaths from the disease. By , the number of people living with the disease had grown to million, and million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw.
Answers
Based on the statistics from the worldwide health organization, the percentage change in those living with the disease is 19.7% and the change in those who have died is 70%.
This shows that the disease is getting worse and not being treated effectively.
What do the statistics on the disease show?The number of those living with the disease went from 71 million to 40 million:
= (85 - 71) / 71
= 19.7% increase
The percent change in those who have died is:
= (6.8 - 4) / 4
= 70% increase
This shows that the measures being implemented against the disease are not working because both the number of people who have the disease and have died from it has increased.
Full question is:
Based on statistics from a worldwide health organization, in 1999 there were 71 million people worldwide living with a certain disease, and 4 million deaths from the disease. By 2015, the number of people living with the disease had grown to 85 million, and 6.8 million deaths were reported. Find the percent change for each statistic, and write any conclusions you can draw.
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e total cost, in dollars, for a company to produce r headsets per day is modeled by the function C,
where C(r) = (-5)2 + 35 for 5 < r ≤ 25. The company sells each headset for $20. On one day, the
company produced 15 headsets. According to the model, what will be the profit on the sale of these
headsets? (Profit equals total sales minus total cost.)
O $215
O $225
O $240
O $300
Answers
‐10+35=25 and 25 × 20=300
Solve: 12x- +5x-4-_ = 172x+6 O x=2 0 x==5 O x=2 x=-5 no solution
Answers
The solution to the equation 12x + 5x - 4 = 172x + 6 is D. No solution.
How to calculate the equation?The information given is 12x + 5x - 4 = 172x + 6 and we are told to find the value of x.
12x + 5x - 4 = 172x + 6
Collect like terms
12x + 5x - 4 = 172x + 6
12x + 5x - 172x = 6 + 4
-155x = 10
x = 10/-155
x = -0.0645
Therefore, the correct option is no solution as the correct answer isn't given.
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Help me with this question please!!!
Answers
a) 2/8 = 1/4
b) There are 3 females who can speak French and 2 males who can speak French, so the probability is 3/5
Dwayne is selling hamburgers and cheeseburgers. he has 100 burger buns. each hamburger sells for $3, and each cheeseburger sells for $3.50. which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80? h c ≤ 80 3h 3.5c ≤ 100 h c ≤ 80 3h 3.5c ≥ 100 h c ≤ 100 3h 3.5c ≤ 80 h c ≤ 100 3h 3.5c ≥ 80
Answers
Let h represent hamburgers and c represent cheeseburgers
h + c ≤ 100 - The number of burgers sold
3h + 3.5c ≥ 80 - Amount that each burger sells for
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. what is the value of this function
Answers
The range of y will be all real numbers such that 0≤y≤40
The complete question is:
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute. The table shows that the amount of water remaining in the bathtub, y, is a function of the time in minutes, x, that it has been draining. What is the range of this function? all real numbers such that y ≤ 40 all real numbers such that y ≥ 0 all real numbers such that 0 ≤ y ≤ 40 all real numbers such that 37.75 ≤ y ≤ 40
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
Raj’s bathtub is clogged and is draining at a rate of 1.5 gallons of water per minute.
The amount of water remaining in the bathtub = y
The function of time in minutes, that it has been draining = x
At 0 minutes the amount of water is 40 gallons.
The highest volume of water is 40 which is decreasing at the rate of 1.5 gallons per minute.
The given function is a linear function
y = 0
However, the volume of water can be 0 but cannot ever be negative.
Therefore the range of y will be all real numbers such that 0≤y≤40
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I will give lots of points please help
Answers
Answer:
a) 81π in³
b) 27 in³
c) divide the volume of the slice of cake by the volume of the whole cake
d) 10.6%
e) see explanation
Step-by-step explanation:
Part (a)The cake can be modeled as a cylinder with:
diameter = 9 inheight = 4 in[tex]\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in[/tex]
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
[tex]\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}[/tex]
If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.
[tex]\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}[/tex]
Part (c)The volume of each slice of cake is 27 in³.
The volume of the whole cake is 81π in³.
To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:
[tex]\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}[/tex]
Part (d)Probability is approximately 10.6% (see above for calculation)
Part (e)If the four slices of cake are cut and passed out before anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, until the marble is found. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.
Clara is building a triangular garden. She wants the length of the longest side to be three more than twice as long as the length of the shortest side, and the third side will be twelve feet long.
What expression could she write to determine the perimeter of the triangle if s represents the length of the shortest side?
Answers
The garden's perimeter = 3+2s+12+s.
The simpler version of the expression = 15+3s.
The variable's frequency in the abbreviated statement is 3.
Calculation of a triangle's perimeter:The triangle's perimeter is equivalent to the sum of its edges, where a, b, and c are its sides.
Let the triangle's longest edge be 'a'shorter one to be 's'the opposite side 'b'With the information provided, the formula will become 'a = 3+2s'
and 'b' is also 12 ft.
Triangle perimeter =the total of its edges
= a + b + s
= 3 + 2s + 12 + s
= 15 + 3s
As a result, the garden's perimeter = 3+2s+12+s.
Therefore,the simpler version of the formula is 15+3s.
The variable's coefficient in the abbreviated statement is 3.
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f(x) = x². What is g(x)?
Answers
g(x) is the inverse of f(x)
[tex]f(x) = {x}^{2} [/tex]
[tex]g(x) = \sqrt{x} [/tex]
Which expression is equivalent to 36x² - 25?
O (18x)²+(-5)²
O (18x)²-(5)²
O (6x)²+(-5)²
O (6x)²-(5)²
Answers
Answer:
[tex] \boxed{ \rm(6x)²-(5)²}[/tex]
Step-by-step explanation:
Given expression/polynomial :
[tex]3 6{x}^{2} - 25[/tex]
Let's evaluate.
We can re-write the polynomial as
[tex]6 {}^{2} x {}^{2} - 5 {}^{2} [/tex]Further
[tex]{(6x) {}^{2} - 5 {}^{2} }[/tex]Hence, the expression is equivalent to last Choice, (6x)²-(5)².
-Regards, Hannah :)
