Make things easier by expanding J(v) first:
[tex]J(v) = (v^3-2v) \left(\dfrac1{v^4}+\dfrac1{v^2}\right) = \dfrac1v - \dfrac2{v^3} - \dfrac2v + v = v - \dfrac1v - \dfrac2{v^3}[/tex]
Now differentiate term-by-term (power rule):
[tex]J'(v) = \boxed{1 - \dfrac1{v^2} + \dfrac6{v^4}}[/tex]
In case you're supposed to use the product rule first, we have
[tex]J'(v) = (3v^2 - 2) \left(\dfrac1{v^4} + \dfrac1{v^2}\right) + (v^3-2v) \left(-\dfrac4{v^5} - \dfrac2{v^3}\right)[/tex]
Expanding and simplifying will yield the same result as before.
1. Jenna and Marcus want to calculate who got the better score on different math quizzes. Jenna got 4 out of
5 questions correct. Marcus got 8 out of 10 questions correct. Who did better? Explain.
Answer:
Jenna got a better score
Step-by-step explanation:
She got a better score because Marcus missed 2 but Jenna only missed one.
The cost of a first-class postage stamp in 1962 was 4. In 1999 it is 33. The cost was (and is) growing exponentially. What was the growth rate? What will be the cost of a first-class postage stamp in 2010?
Answer:
The growth rate was 5.87%
Step-by-step explanation:
Time interval is t=1999−1962=37 yearsInitial cost in 1962 was a=4 unit Final cost in 1999 was y=33 unit Exponential growth function :y=a(1+r)t;a>0,r>0,ris rate of growth in decimal form.y=a(1+r)tor33=4(1+r)37 or(1+r)37=334or(1+r)37=8.25 , taking log on bothsides we get, 37log(1+r)=log(8.25) orlog(1+r)=log(8.25)37orlog(1+r)≈0.24769(1+r)=100.24769or1+r≈1.0587∴r=0.0587 orr%=0.0587⋅100≈5.87%The growth rate was 5.87% [Ans]
5(x - 20) = 1/2 (4x + 4)
Show your work
Help
Answer: 334
Step-by-step explanation: Find the steps in the file
Answer:
34
Step-by-step explanation:
1. Expand 5(x - 20):
Use the distributive property to distribute 5 to x and -205x - 100
2. Expand [tex]\frac{1}{2} (4x + 4)[/tex]:
Use the distributive property to distribute [tex]\frac{1}{2}[/tex] to 4x and 42x + 2
3. Add 100 to both sides:
5x - 100 = 2x + 2
5x - 100+100 = 2x + 2+100
5x = 2x + 102
4. Subtract 2x from both sides:
3x = 102
5. Divide both sides by 3:
x = 34
hope this helps!
HELP ME PLEASEEE URGENT I’ll mark the brainiest!!
216.66
169π-100π=69π
69*3.14= 216.66
Without graphing, find the slope of the line that goes through (-3, 1) and (1,3).
Answer:
1/2 i think using a app brjejfj
Find the arc length of the semicircle.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answer:
18.852
Step-by-step explanation:
Formula to find the arc of semi circle is :
Arc length = π r
Given that,
diameter ⇒ 12
So, the radius will be,
Radius ⇒ 12 / 2
⇒ 6
Let us solve now.
Arc length = π r
= 3.142 × 6
= 18. 852
You want to bake a 20" diameter pizza. Give exact answers.
a. What should be the circumference of the pan?
b. What is the area of the pizza?
c. If you cut the pizza into 8 congruent slices, what is the area of one slice?
d. What is the length of the crust of one slice?
Step-by-step explanation:
pizza = circle
the area of a circle is
pi×r²
r = radius (half of the diameter). in our case 20/2 = 10".
the circumference of a circle is
2×pi×r
again, r = radius.
in our case that gives us
a.
2×pi×r = 2×pi×10 = 20×pi = 62.83185307... "
b.
the area of the pizza is
pi×10² = 100×pi = 314.1592654... in²
c.
it is 1/8 of the whole area, of course.
314.1592654... / 8 = 39.26990817... in²
d.
it is 1/8 if the whole circumference, of course.
62.83185307... / 8 = 7.853981634... "
find the mean, median and mode of the following data set: 8, 12, 15, 3, 7, 10, 15
8, 12, 15, 3, 7, 10, 15
to find:mean, median and mode.
solution:mean:to find mean you'll have to add all of the numbers and divide by the number of numbers in the data set.
[tex] \frac{(8 + 12 + 15 + 3 + 7 + 10 + 15)}{7} [/tex]
[tex] = \frac{70}{7} [/tex]
[tex] = 10[/tex]
median:to find median you'll have to order the numbers either in descending or ascending, and find the number in the middle.
[tex]3 \: 7 \: 8 \: 10 \: 12 \: 15 \: 15[/tex]
=10
mode:most frequently occurred number is the mode.
[tex] = 15[/tex]
Choose the inequality represented in the graph.
A. y ≥ -4/5x - 3
B. y > -5/4x - 4
C. y > -4/5x - 3
D. y < -5/4x - 3
Answer:
C
Step-by-step explanation:
The line is dotted, so the sign is non-inclusive.
The dotted line is y = -(4/5)x - 3.
The section of the graph above the line is shaded so this inequality is "greater than".
So, putting these together, you get:
C. y > -(4/5)x - 3
A person with type O blood can donate red blood cells to anybody because type O blood is the universal blood type. About 44% of the US population has type O blood. University High held a blood drive where 50 students donated blood.
Part A: What is the probability that exactly 25 of the students had type O blood?
Part B: What is the probability that at least 25 of the students had type O blood?
Answer:
Part A.
k= 25
p= 44% = 0.44
n= 50
P(x = k) = (nk) p^k (1 - p) ^n - k
P(x = 25) = (50 25) (0.44)^25 (1 - 0.44) ^50 - 25
50!/25!(50 - 25)!
50!/25!(25)! = 1.264106 x 1014
P(x=25) = (1.264106 x 1014)(0.44)^25(0.56)^25
= 0.07812
= 7.8% probability that exactly 25 students have type O blood
Part B.
Do the same math you did above. Just replace 25 with 26 and 27 :)
25 = 7.8% probability
26 = 0.01851
= 1.8% probability
27 = 0.00405
= 0.4% probability
How many apples do you need to baked 3 apple pies if each pie need 5 apples?
Answer:
15
Step-by-step explanation:
Each pie requires 5 apples
5x3=15
Answer:
Step-by-step explanation:
1 apple pie = 5 apples
3 apple pies x 5 apples = 15 apples
Andrew wants to lay new turf in his garage.Andrews garden is a rectangle measuring 3m by 4m,New turf cost 12.50pr m2.
How much will it cost Andrew to get enough new turf for his garden?
I WOULD REALLY APPRECIATE YOUR HELP
Answer:
$150
Step-by-step explanation:
The area of the lawn is 12m so 12 x 12.50 is 150. It would cost $150
6. A circle has a circumference whose length is 25pi . Find the length of an arc whose
central angle is 90°.
Answer:
So, A 90° central angle cuts off an arc which has length 90/360 = 1/4 of the circumference. Therefore, length of arc = (1/4)(25π) = 25π/4.
Step-by-step explanation:
espero te sirva
Mr. Marsh plans to tile the floor in his 6-foot by 8-foot front hall. If each tile is an 8-inch square. what is the minimum number of tiles needed to cover the floor?
The division is one of the four fundamental arithmetic operations. The number of tiles that will be needed to cover the entire area of the hall is 864.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
The area of the hall with dimensions 6 feet by 8 feet are:
[tex]\rm \text{Area of the hall} = 6 feet \times 8foot =48\ feet^2[/tex]
The area of the tile is 8 square inches, therefore, the area of tile in square feet can be written as,
[tex]\rm \text{Area of the tile} = \dfrac8{12 \times 12}\ feet^2[/tex]
Noe, the number of tiles needed to tile the complete area of the hall is,
[tex]\text{Number of tiles needed} = \dfrac{\text{Area of the hall}}{\text{Area of the tile}}\\\\\\\text{Number of tiles needed} = \dfrac{48}{\frac8{12 \times 12}} = \dfrac{48 \times 12 \times 12}{8} = 864[/tex]
Hence, the number of tiles that will be needed to cover the entire area of the hall is 864.
Learn more about Division:
https://brainly.com/question/369266
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Pls pls pls pls help po
How can you use a
single measure to describe a data set?
Describing data Often we wish to describe a set of data with a single number, or a small set of numbers, in such a way that these values will yield enough information about the content of the data that we can produce a means of generating a similar set of data from this description.
If P is the incenter of triangle JKL, find PJ
can anyone help find the area pls ty
Answer:
53.72
Step-by-step explanation:
apply area of triangle and rectangle and add them
What is the vertex of f(x)=x2−8x+15 ?
Answer:
(4,-1)
i strongly believe that is the answer, pls mark as brainlist
HELP A marble paperweight shaped similar to a prism weighs 0.2 lb. How much does a similarly shaped marble paperweight weigh if its length, width, and height are tripled?
5.4 lb
0.6 lb
0.8 lb
1.8 lb
Answer:
0.6 lbs
0.2 ×3=0.6
explanation
Trust
Alguien podra ayudarme en pregunta numero 8
Answer:
jb
Step-by-step explanation:
9
What does "Y" equal? Answer ASAP and whoever gets it right can have brainliest
Answer:
Y = 21
To solve this, do the inverse of division, multiplication. Multiply 3 by the result, 7, and you get 21 as your answer to the missing digit.
What is the value of x? A=55 B=80
Answer:
x = 45°
Step-by-step explanation:
80° + 55° + x = 180°
135° + x = 180°
x = 45°
Help! I got it wrong the first time
Answer:
The correct correspondence is B.
The exam scores in Bryan's class are Normally
distributed with a mean of 88 points and a standard
deviation of 1.5 points.
Exam Scores
83.5 85 86.5 88 89.5 91 92.5
Score
Which statements are true? Check all that apply.
□ About 16% of all exam scores are less than 86.5
points.
About 16% of all exam scores are greater than 89.5
points.
About 68% of the test scores fall between 85 and 91
points.
About 84% of all exam scores are less than 89.5
points.
About 84% of all exam scores are greater than 89.5
points.
0
Using the Empirical Rule, it is found that the correct statements are given by:
About 16% of all exam scores are less than 86.5 points.About 16% of all exam scores are greater than 89.5 points.About 84% of all exam scores are less than 89.5 points.What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.We also have to consider that the normal distribution is symmetric. Then, alog with the mean of 88 and standard deviation of 1.5, the correct statements are given by:
About 16% of all exam scores are less than 86.5 points(more than 1 standard deviation below the mean, the percentage, considering the symmetry, is 0.5 x 32 = 16%).About 16% of all exam scores are greater than 89.5 points, due to the same explanation as above.About 84% of all exam scores are less than 89.5 points, as the percentage is 50%(all below the mean) + 50% x 68%(one standard deviation above the mean) = 84%.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Answer:
Step-by-step explanation:
Fill in the correct values in the statements.
About 68% of the observations will fall within
⇒ 1.5 points of the mean of
⇒ 88 points.
About
⇒ 95% of the observations will fall within 3 points of the mean.
About 99.7% of the observations will fall within
⇒ 4.5 points of the mean.
The annual number of burglaries in a town rose by 50% in 2012 and fell by 10% in 2013. hence the total number of burglaries increased by 40% over the two year period.
a. by what percent has the number of burglaries actually changed in the two-year period?
b. by what percent would the crime have to decrease in the second year in order for the change over the two-year period to actually be a 40% increase?
Answer:
a) 35%
b) 6.67%
Step-by-step explanation:
a) The annual number of burglaries in 2012 would be 150% and since in 2013, it fell by 10%:
10% of 150 is 15 so 150-15 = 135%.
The actual percentage increase of burglaries is 135% - 100% = 35% not 40%.
b) In the second year, the percentage would have to decrease by 10% of the initial 150% so [tex]\frac{10}{150}[/tex] = [tex]\frac{1}{15}[/tex] which as a percentage would be 6.66666....% or 6.67%.
The number of burglaries actually changed in the two-year period will be 35% and the crime have to decrease in the second year in order for the change over the two-year period to actually be a 40% increase will be 6.7%
BurglariesIt is act of breaking and entering a dwelling at night to commit a felony such as theft.
How to solve this problem?The steps are as follow:
Let us assume that the annual number of burglaries in 2011 are 100. After that there is 50% increase in 2012 so the number of burglaries will be: 100(1.50) = 150.Burglaries after the 10% reduction in 2013 would be: 150(.90) = 135So there will be change in burglaries over the two-year period = (135 / 100) - 1 = 35% To know how much burglaries would have to reduce in order to have a 40% change in burglaries we would be using the following formula:(x - 100) / 100 = 0.40
x - 100 = 40
x = 140
Change in burglaries over the two-year period to have 40% increase = (140 / 150) - 1 = 6.7%So, burglaries after the 10% reduction in 2013 would be 35% and change in burglaries over the two-year period to have 40% increase will be 6.7%.
Learn more about burglaries here:
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Zach's step counter tracked how many steps he took each day for a week. Number of steps 2,000 4,000 6,000 8,000 10,000 What was Zach's median number of steps?
Answer: 8,000
Step-by-step explanation: Did it on IXL
PLSSSSSSSSSSSSS HELPPPPPPPPPPPPPPP
Christine exercises more than 40 minutes per day.
Use t to represent Christine's amount of exercise (in minutes per day).
Answer:
t=40+
Step-by-step explanation:
I couldn't really tell what you meant by that question
a - 1 = 70; a = 71 solution or not a solution??
solution
hope it helps...!!!