Answer:
1) [tex]f'(t)=4t,\ g'(t)=3t^2+4[/tex]
2) [tex]p(t) =2t^5+8t^3[/tex]
[tex]p'(t)=10t^4+24t^2[/tex]
3) False
4)[tex]q(t) =\dfrac{1}{2}t+2t^{-1}[/tex]
[tex]q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
5) False
Step-by-step explanation:
Given that:
[tex]f(t) = 2t^2[/tex] and [tex]g(t) = t^3 + 4t[/tex]
Formula:
[tex]1. \dfrac{d}{dx}x^n=nx^{n-1}[/tex]
[tex]2. \dfrac{d}{dx}C.f(x)=C.f'(x)\ \{\text{C is a constant}\}[/tex]
1) Using above formula:
[tex]f'(t)=2\times 2 t^{2-1}=4t[/tex]
[tex]g'(t)=3t^{3-1}+4\times 1 t^{1-1}=3t^2+4[/tex]
2) [tex]p(t) =2t^2(t^3+4t)[/tex]
Rewriting the formula by distributing the [tex]2t^2[/tex] term:
[tex]p(t) =2t^2.t^3+2t^2.4t=2t^5+8t^3[/tex]
[tex]p'(t) = 10t^4+24t^2[/tex]
3) By using answers of part (1):
[tex]f'(t).g'(t)=12t^3+16t[/tex]
[tex]p'(t) = 10t^4+24t^2[/tex]
Therefore it is False that [tex]p'(t) = f'(t).g'(t)[/tex]
4) [tex]q(t)=\dfrac{t^3+4t}{2t^2}[/tex]
Writing by distributing:
[tex]q(t)=\dfrac{t^3}{2t^2}+\dfrac{4t}{2t^2}\\\Rightarrow q(t) =\dfrac{t}{2}+\dfrac{2}{t}\\\Rightarrow q(t) =\dfrac{1}{2}t+2t^{-1}[/tex]
Using the formula:
[tex]q'(t)=\dfrac{1}{2}t^{1-1}+2\dfrac{-1}{t^2}\\\Rightarrow q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
(5)By using answers in part (1):
[tex]\dfrac{g'(t)}{f'(t)}=\dfrac{3t^2+4}{4t}=\dfrac{3}{4}t+\dfrac{1}t[/tex]
[tex]q'(t)=\dfrac{1}{2}-\dfrac{2}{t^2}[/tex]
Therefore, it is False that:
[tex]q'(t)=\dfrac{g'(t)}{f'(t)}[/tex]
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145145 millimeters, and a standard deviation of 77 millimeters. If a random sample of 3131 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 33 millimeters
Answer:
The probability that the sample mean would differ from the population mean by greater than 33 millimeters is 0.0174
Step-by-step explanation:
[tex]Mean = \mu = 145 mm[/tex]
Standard deviation =[tex]\sigma = 7[/tex]
We are supposed to find the probability that the sample mean would differ from the population mean by greater than 3 millimeters
[tex]P(|x-\mu|>33)=1-P(|x-\mu|<3)\\P(|x-\mu|>33)=1-P(-3<|x-\mu|<3)\\P(|x-\mu|>33)=1-P(\frac{-3}{\frac{\sigma}{\sqrt{n}}}<\frac{|x-\mu|}{\frac{\sigma}{\sqrt{n}}}<\frac{-3}{\frac{\sigma}{\sqrt{n}}})\\P(|x-\mu|>33)=1-P(\frac{-3}{\frac{7}{\sqrt{31}}}<\frac{|x-\mu|}{\frac{\sigma}{\sqrt{n}}}<\frac{-3}{\frac{7}{\sqrt{31}}})\\P(|x-\mu|>33) =1-P(-2.38<z<2.38)\\P(|x-\mu|>33) =1-(P(z<2.38)-P(z<-2.38))\\[/tex]
Using Z table
= 1-(0.9913-0.0087)
=0.0174
Hence the probability that the sample mean would differ from the population mean by greater than 33 millimeters is 0.0174
Drag the tiles to go the boxes to form correct pairs
Answer:
math
Step-by-step explanation:
Answer: For Edmentum Multiply the sets of numbers and match them with their products.
(-3/4)(7/8)= -21/32
(5/16)(-2)(-4)(-4/5)= -2
(2/3)(-4)(9)= -24
(2 3/5) (7/9)= 91/45
Step-by-step explanation:
Generally accepted accounting principles require companies to use only one factor overhead rate for product costing True or False?
Answer:
i think its false :>
Step-by-step explanation:
ANSWER PLEASE 100 POINTS
Answer: multiplication property of equality
Step-by-step explanation:
in the equation 2(x-3)=18
it should be 2x-6=18
x=12 by the way
[tex]\begin{gathered} \: \: \: \footnotesize{\boxed{\begin{array}{c|c}\boxed {\bf {Statement}} & \boxed {\bf {Reason}} \\ \\\\ \text{2(x-3)=18} & \sf{Given} \\\\ \text{ 2x-6=18} &\sf{Multiplication ~property~ of~ equality } \\\\ \text{2x=18+6}& \sf \\\\ \text{2x=24} &\sf{Addition~ property~ of~ equality }\\\\ \text{x=24/2} & \sf{Division~ property ~of ~equality }\\\\ \text{X=12} & \sf \end {array}}}\end{gathered}[/tex]
Help please will give brainlest!!!
Answer:
1.55 or 31/20 which is 1 11/20 gallons
Step-by-step explanation:
Numbers between 380 and 410 divisible by 2,5, and 10
Answer:
Did you try this is a piece of cake
Step-by-step explanation:
Section 3 - Question 24
Maria's internet service costs 14.95 a month for the first 100 hours of usage and 0.50 for each additional hour. This could be written as y = 14.95 +0.50 (1 - 100).
In the equation, what does the represent?
A
the total cost of internet service
B
the cost per month for internet service
С
the number of hours of internet service
D
the number
months of internet service
EVO Illuminate Education Inc
O
hp
Answer: D. The Number of months of internet service
What is one other way to write 10x7 ?
A:10+7
B:(10)(7)
C:10-7
D:10/7
Answer
B
Step-by-step explanation:
Kia Read for a total of 60 minutes on Monday and Tuesday. He read for 60 minutes on Tuesday. How many minutes did he read on Monday?
Geometry: Write and solve an equation to find the value of x so that the figures have the same area.
Answer:
e
Step-by-step explanation:
e
Timmy's T-Shirts is having a huge back-to-school sale. All the T-shirts in the store are currently discounted by 15%. Let t represent the regular price of any T-shirt in the store. This discount can be represented by the expression Syntax error. Which expression can also be used to find the sales price of a T-shirt?
Answer:
1.15t
Step-by-step explanation:
I think
GET20 POINTS BY ANSWERING THE QUESTION!
ARE PRIME AND CO-PRIME NUMBERS SAME ? GIVE RIGHT ANSWER AS SOON AS POSSIBLE..
Answer:
[tex]yes \: \\ PRIME \: AND \: CO-PRIME \: NUMBERS \: are \: the \: SAME [/tex]
Label following study as either an observational study, an experiment, or neither.
Many parents have expressed concerns that pertussis vaccinations will cause wheezing disorders or asthma in later life. In 2009 the Journal of the American Academy of Pediatrics published research by the Institute of Social and Preventive Medicine in Bern, Switzerland. The researchers wanted to determine if routine childhood vaccination against pertussis (whooping cough) was associated with subsequent development of childhood wheezing disorders and asthma. The researchers studied 6811 children from the general population born between 1993 and 1997 in Leicestershire, UK. From birth through 2003, they conducted repeated questionnaire surveys about wheeze and asthma and then linked the respiratory symptom data to independently collected vaccination data from the National Health Service database. Then the researchers compared wheeze and asthma incidents for children of three different levels of vaccination (complete, partial, and no vaccination). The analyses were based on 6,048 children with available vaccination records.
a. observational study
b. an experiment
c. neither
Answer:
a. observational study
Step-by-step explanation:
An observational study is one in which the researcher seeks to discover the effect of a disease or treatment without interference on those who are affected or not affected by it. Observational studies could be of two types namely; the case-control, and the cohort study. The research given above is a cohort study because it compares a group of people born in the same time period and checks for the presence of a disease that could be linked to the vaccinations administered at birth.
A case-control study compares those affected by the disease to those not affected by it. An experimental study assigns the participants to groups and there is a control or placebo group. After this, the results from the groups are compared.
What is the equation?
Answer:
9/1 x 3/1
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
the second one would be the correct anwser i think.
Step-by-step explanation:
A store owner paid $15 for a book. She marked up the price of the book by 20% to determine its selling price. What is the selling price, in dollars, of the
books?
Answer:
18
Step-by-step explanation:
.2x15=3
3+15=18
Answer:
18$
Step-by-step explanation:
there are 3 people at a party if each person must shake hands with every other person at the party exactly once how many handshakes will there be
Answer:
there will be 9
Step-by-step explanation:
The mass of a teapot and 4 cups is 1,280 grams. The mass of the same teapot and 10 cups is 2,720 grams. Each cup has the same mass. What is the mass?
The mass per cup for the objects will be 320g and 272g respectively.
What is mass?Mass simply means the weight that an object contains.
The mass of a teapot and 4 cups is 1,280 grams. The mass per cup will be:
= Mass / Number of cups
= 1280 / 4
= 320g
The mass of the same teapot and 10 cups is 2,720 grams. The mass per cup will be:
= 2720 / 10
= 272g
Learn more about mass on:
brainly.com/question/19385703
#SPJ1
The ratio of boys to girls in ms Cunningham’s class is 2 to 3. There are 18 girls in the class. What is the total number of students in her class?
Answer:
30 students
Step-by-step explanation:
you have a ratio, and an unknown amount, so set up a proportion
[tex]\frac{2}{3} = \frac{x}{18}[/tex] I used x because the amount of boys is unknown
so then, cross multiply
(so do 3 times x, and 2 times 18)
[tex]3x=36[/tex]
then divide both sides by 3 to get x by itself, and you get
[tex]x=12[/tex]
this means there are 12 boys in the class. because the problem is asking for the total number of students, add 12 and 18 (the number of boys and girls).
you get 30, so there are 30 students in her class.
Find the area of the figure.
Answer:
I think its 38 however i could be wrong
Step-by-step explanation:
Self explanatory i just added them
**Put as brainliest if you wish**
Answer:
139yds
Step-by-step explanation:
area of a rectangle is length time width
9(11)=99
area of a triangle is length times width divided by 2
8(10) divided by 2=40
99+40=139
52x16 please add explaining to show me how to do it
Answer: 832
Step-by-step explanation:
Below is how I solved it
You do 2 times 6, then 2 times 10, then 6 times 50, then 50 times 10. Make a table!
2 x 6 = 12
2 x 10 = 20
6 x 50 = 300
50 x 10 = 500
500 + 300 + 20 + 12 = 832
52 x 16 = 832
9+10
A.21 B.19 C.1 D.90
Answer: 19 XD
Step-by-step explanation: u add
what is the answer to 2x+2x-9=19
Answer:
x = 7
Step-by-step explanation:
Answer:
x = 7
Step-by-step explanation:
We have to solve for [tex]x[/tex] so we isolate the value of x in the expression.
[tex]2x + 2x - 9 = 19[/tex]
[tex]2x + 2x - 9 + 9 = 19 + 9[/tex]
[tex]2x + 2x = 28[/tex]
[tex]4x = 28[/tex]
[tex]\frac{4x}{4} = \frac{28}{4}\\[/tex]
[tex]x = 7[/tex]
Please help this one will give you extra points
THE ANSWER IS B
A: 1/3*6,000,000 does NOT equal 18,000,000
C: However, 2/5*6,000,000 does equal 2, yet, $2.4*10^3 is a FALSE STATEMENT and it doesn't make sense
D: Not ALL statements are correct
If one Chinese yaun equals 13.2455 Japanese yen then one Japanese yen equals approximately how many Chinese yuan
Answer:
0.755 Yuan
Step-by-step explanation:
You already know it's going to be less than 1 since 1 yuan is 13.2455 yen.
Chinese Yaun : Japanese Yen
1 : 13.2455
divide both by 13.2455 to work out 1 Japanese Yen
0.0755 : 1
Multiply both 10
0.755: 10
HELP ME, its due at 9pm
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let(x,y) be the unknown endpoint. Apply the midpoint formula,
and solve the two equations for x and y)
midpoint (-24.18) endpoint (-19.10)
The other endpoint is
(Type an ordered pair
M = ( (x1 + x2) / 2 , (y1 + y2) / 2 )
(9, 0) = ( (x1 + 12) / 2 , (y1 + 3) / 2)
Break up this formula into two equations.
(x1 + 12) / 2 = 9 and (y1 + 3) / 2 = 0
Solve for x1 and y1 from the equations.
another way to explain it
the formula for finding the midpoint of a segment given the coordinates of its endpoints is:
((x1+ x2)/2, (y1 + y2)/2 {Average of the x coordinates, average of the y coordinates}.
For this problem we know the coordinates of the midpoint along with one of the endpoints.
So the x coordinate of the midpoint (9) must equal (12 + x2)/2.
That is: 9 = (12 + x2)/2 Solve for x2. Follow a similar pattern to find the y coordinate of the unknown endpoint.
and another way
The x's are 3 apart and the y's are 3 apart. The other endpoint is (9 - 3, 0 - 3), or (6,-3).
hope this helped you have a good day this was ez
i already know the answer can someone explain or show me how to do it on a numberline
Answer:
I'm not sure what the question is but an example question could be
"Take 5 away from 3."
For this you would go to three on the number line and then move left five gaps. You would land on -2
another example: "Add 4 to -3."
For this, you would go to -3 on the number line, and then move right 4 times. you would land on 1.
Answer:
4.5
Step-by-step explanation:
just move 1 1/2 steps to the left
-2x^2-20x-46
How would you solve this?
Answer:
-2x^2-20x-46
Step-by-step explanation:
-2(x^2)-20x-46
-2(x^2) -2(10x)-46
-2(x^2)-2(10x)-2(23)
-2(x^2+10x)-2(23)
-2x^2-20x-46
Mid point between (0,0) (11,9)
9514 1404 393
Answer:
(5.5, 4.5)
Step-by-step explanation:
The midpoint coordinates are the average of the end point coordinates.
((0, 0) +(11, 9))/2 = (11, 9)/2 = (5.5, 4.5) . . . midpoint
What is the 8th term of the sequence 12, 17, 22, 27, 32,...
Answer:
47
Step-by-step explanation:
just keep adding by 5