Answers
Step-by-step explanation:
1. Given: a = 4t + 4
We know that
[tex] a = \frac{dv}{dt} \: \: or \: dv = adt[/tex]
By definition, the integral of a power function x^n is
[tex] \int {x}^{n} dx = \frac{ {x}^{n + 1} }{n + 1} + k[/tex]
Integrating the acceleration a, we get
[tex]v = \int adt = \int(4t + 4)dt = 2 {t}^{2} + 4t + k[/tex]
where k = constant of integration. We know that v = 10 when t = 0 so when we do the substitution, we get k = 10 therefore, the final expression for v is
[tex]v = 2 {t}^{2} + 4t + 10[/tex]
To find s, we need to integrate v. Knowing that
[tex]v = \frac{ds}{dt} \: \: or \: s = \int v \: dt[/tex]
[tex]s = \int(2 {t}^{2} + 4t + 10)dt[/tex]
[tex] = \frac{2}{3} {t}^{3} + 2 {t}^{2} + 10t + k[/tex]
where k once again is the constant of integration. We know that s = 2 when t = 0, which gives us k = 2. Therefore, the final expression for s is
[tex]s = \frac{2}{3} {t}^{3} + 2 {t}^{2} + 10t + 2[/tex]
2. The potential difference V between two boundaries a and b is given by
[tex]V = \frac{q}{2\pi \epsilon_0 \epsilon_r} \int_{b}^{a} \frac{dr}{r} [/tex]
Note that the integral in the expression above can be rewritten and the integrated as
[tex] \int_{b}^{a} \frac{dr}{r} =\int_{b}^{a} {r}^{ - 1} dr = \ln |a| - \ln |b| [/tex]
so the potential difference V is then J
[tex]V = \frac{q}{2\pi \epsilon_0 \epsilon_r} \int_{b}^{a} \frac{dr}{r}[/tex]
[tex] = \frac{2 \times {10}^{ - 6} }{2\pi (8.85\times {10}^{ - 12}) (2.77)}( \ln |20| - \ln |10| )[/tex]
[tex] = 9000 \: V[/tex]
Related Questions
Following is a portion of the regression output for an application relating maintenance expense (dollars per month) to usage (hours per week) for a particular brand of computer terminal. When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as
Answers
Answer:
Matched samples
Step-by-step explanation:
A matched sample is obtained when pairing of treatment values for each subject or observation is performed. This sample obtained from a matched pair is usually called dependent sample and is usually done when each subject in an experiment is subjected to two different treatments usually at different time or stage. Hence, matched samples are used in matching observations to tie different groups.
Classify the following triangle. Check all that apply.
Answers
Answer:
This triangle is a right triangle
Express the area of the entire rectangle.
Your answer should be a polynomial in standard
form. X+9 top x+2
Pls help i will mark the brainliest!
Answers
This prompt is telling you to find the area of the rectangle, so you multiply these two factors. (x + 9)(x + 2).
One way you can do this is by using the foil method.
Which is:
(a+b) (c+d) = ac + ad + bc + bd
Explanation:
The blue rectangle is x*x = x^2 in areaThe pink rectangle has area of x*9 or 9xThe green rectangle has area 2*x or 2xThe orange rectangle has area 2*9 = 18Add up those areas to get the final answer
x^2+9x+2x+18 = x^2+11x+18
note the like terms 9x and 2x combine to 11x
1. James and Alexis simplified the expression 5 + 42 - 6/3. James' said the answer is
10, while Alexis' said the answer is 19. Who is correct? How do you know? How
should you apply the order of operations to this problem to simplify?
Answers
Answer:
19
Step-by-step explanation:
5 + 4^2 - 6/3
= 5 + 16 - 2
= 21 - 2
= 19
Solve for x:
х/2 = 8
O A) X= 17
OB) x = 18
OC) x = 16
OD) x = 12
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
C) x = 16
»»————- ★ ————-««
Here’s why:
We will use inverse operations to solve for 'x'.⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\\frac{x}{2}=8\\-------\\\rightarrow{\frac{x}{2}=8}\\\\\rightarrow(\frac{x}{2}})*2=8*2\\\\\rightarrow\boxed{x=16}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x = 16
Step-by-step explanation:
х/2 = 8
Multiply each side by 2
x/2*2 = 8*2
x = 16
At the market, he spends $5.58 on red potatoes and $4.68 on yellow potatoes. If each type of potato costs $0.90 per pound, how many total pounds of potatoes does he buy?
Answers
Answer:
11.4pounds
Step-by-step explanation:
(5.58+4.68)÷0.90
＝11.4(pounds)
If f(x) = x2 + 4, find f(3)
Answers
Answer:
c. 13
Explanation:
f(x) = x² + 4
f(3) = (3)² + 4
= 9 + 4
= 13
what is the volume of this figure?
Answers
Answer:
23 blocks
Step-by-step explanation:
Count the blocks
The back wall has 3 blocks by 5 blocks which is 15 blocks
The front cubs has 4 blocks by 2 blocks = 8 blocks
Add them together = 15+8 = 23 blocks
What is the factored form of x2 − 4x − 5? (x + 5)(x − 1) (x + 5)(x + 1) (x − 5)(x − 1) (x − 5)(x + 1)
Answers
Item 22
The distance between Cleo's home and work is 9 kilometers. She travels between home and work 36 times each month.
How many kilometers does Cleo travel between home and work each month?
Answers
Answer:
324 kilometres
What I did was do 36x10 which is 360
Then I did 360-36=24 because the question wants 9x36 not 10x36
Determine the location and absolute maximum and absolute minimum for the given function f(x)=(_x+2)^4 where 0
Answers
Answer:
the minimum is 0 and the maximum is 16.
Step-by-step explanation:
For a function f(x), the maximum is defined as:
f(xₐ)
such that:
f(xₐ) ≥ f(x) for every value of x in the domain.
And the minimum is:
f(xₙ)
Such that:
f(xₙ) ≤ f(x)
for every value of x.
Now, in this case we have the function:
f(x) = (-x + 2)^4 in the range 0 < x < 3
First, let's analyze our function.
We can see that the exponent is even, then:
f(x) = (-x + 2)^4
Can be equal to zero or larger than zero.
Then the minimum will be f(x) = 0
To find this, we need to find the value of x such that:
-x +2 = 0
2 = x
Then the minimum is:
f(2) = (-2 + 2)^4 = 0
For the maximum, we can just play with the other values in the range and see which one gives the larger value of f(x).
Again, because f(x) = (-x + 2)^4 , the maximum will be at the value of x such that:
|-x + 2| is maximized.
As we have a negative sign multiplying x, the smaller value in the range:
x = 0
is the one that maximizes that:
|-0 + 2| = |2| = 2
Evaluating f(x) in x = 0 we get:
f(0) = (0 + 2)^4 = 16
Then the minimum is 0 and the maximum is 16.
Consider a different experiment: EXPERIMENT: A bag contains 3 red balls, 4 blue balls, 4 green balls and 3 yellow balls. One ball is drawn at random and then returned to the bag. Then a ball is drawn again, possibly the same one or a different one.
(a) Specify the sample space (set of outcomes) and probability distribution of the outcomes.
(b) What is the probability that both balls drawn were red balls?
(c) Starting over with all 14 balls back in the bag, what is the probability that both draws were balls of different colors?
Answers
Answer:
a) Sample space = RR, RB, RG, RY, BB, BR, BG, BY, GG, GR, GB, GY, YY, YR, YB, YG .
probability distribution of outcomes
= (3/14*3/14), (3/14*4/14), (3/14*4/14), (3/14*3/14), (4/14 *4/14 ), (4/14*3/14), (4/14 * 4/14), (4/14 * 3/14 ), ( 4/14 *4/14 ), (4/14*3/14), ( 4/14 *4/14 ),
(4/14*3/14), (3/14 *3/14 ), (3/14*3/14), (3/14 *4/14 ), ( 3/14 * 4/14 )
b) 0.0459
c) ( 3/14 * 4/14 ) + ( 3/14 * 4/14 ) + ( 3/14 * 3/14 ) + ------ ( 3/14 * 4/14 )
Step-by-step explanation:
Total number of balls = 3 + 4 + 4 + 3 = 14 balls
3 Red balls = 3/14
4 blue balls = 4/14
4 green balls = 4/14
3 yellow balls = 3/14
a) Determine the sample space and probability distribution of outcomes
since ball is drawn with replacement
Sample space = RR, RB, RG, RY, BB, BR, BG, BY, GG, GR, GB, GY, YY, YR, YB, YG .
i.e. The sample space has 16 possible combination
probability distribution of outcomes
= (3/14*3/14), (3/14*4/14), (3/14*4/14), (3/14*3/14), (4/14 *4/14 ), (4/14*3/14), (4/14 * 4/14), (4/14 * 3/14 ), ( 4/14 *4/14 ), (4/14*3/14), ( 4/14 *4/14 ),
(4/14*3/14), (3/14 *3/14 ), (3/14*3/14), (3/14 *4/14 ), ( 3/14 * 4/14 )
b) Determine P( R and R )
P ( R and R ) = 3/14 * 3/14
= 9/196 = 0.0459
C) Determine probability of drawing two different balls
P( R and B ) + P ( R and G ) + P ( R and Y ) + ------ P ( Y and G )
= ( 3/14 * 4/14 ) + ( 3/14 * 4/14 ) + ( 3/14 * 3/14 ) + ------ ( 3/14 * 4/14 )
onnie measures an object's mass in kilograms.
Which of the following objects is he most likely measuring?
A.
An apple
B.
A bicycle
C.
A paper clip
D.
A pencil
Answers
Answer:
a bicycle
Step-by-step explanation:
Answer:
B. A bicycle
Step-by-step explanation:
B. A bicycle
All the others would most likely be in grams
Will mark Brainlest help me to find the value of x (step by step) pls
Answers
Answer:
5 (cm)
Step-by-step explanation:
1. according to the condition in ΔABC: AC=BC, m∠C=90°. Then m∠B=m∠A=45° and
2. x=AC=AB/√2; ⇔ x=5 (cm).
Answer:
x=5 cm
Step-by-step explanation:
triangle ABC is an isoceles triangle
so BC=AC and angle A=angle B
BC=X and angle A=theta
angle B and angle A both is theta degree because base angles of an isosceles triangle are equal
to find angle A and B
angle A + angle B + angle c=180 degree (sum of interior angles of a triangle)
theta + theta +90=180
2theta=180-90
2theta=90
theta=90/2
theta=45 degree
sin both angle A and angle B are theta their value is 45 degree.
For side x
now using pythagoras theorem
take theta as reference angle
using sin rule
sin 45=opposite/hypotenuse
[tex]\frac{1}{\sqrt{2} }[/tex] =x/[tex]5\sqrt{2}[/tex]
[tex]\frac{1}{\sqrt{2} } *5\sqrt{2}[/tex]=x
[tex]\frac{5\sqrt{2} }{\sqrt{2} } }[/tex]=x
5=x
In the above figure, m∠P = 125° and m∠Q = 5x. If angles P and Q are supplementary angles.
what is the value of x and the measure of angle Q?
A. x = 61, m∠ Q = 55°
B. x = 11, m∠Q = 16°
OC. x = 11, m&angle: Q = 55°
D. x = 43, m∠Q = 215°
Answers
Answer:
C. x = 11, m∠Q = 55º
Step-by-step explanation:
125 + 5x = 180
5x = 55
x = 11
5x = 55
C. x = 11, m∠Q = 55º
x-1/x-4 =x+1/x-2
Solve.
Answers
Answer:
x=-1
Step-by-step explanation:
Daniel and Joe watched a beetle and a spider on the sidewalk. The beetle crawled 1/2 of a yard and the spider crawled 1/8 of a yard. How much farther did the beetle crawl than the spider?
Answers
Answer: 3/8 yard
Step-by-step explanation:
Since the beetle crawled 1/2 of a yard and the spider crawled 1/8 of a yard. To calculate how much farther the beetle crawl than the spider, we will have to subtract 1/8 from 1/2. This will be:
= 1/2 - 1/8
= 4/8 - 1/8
= 3/8 yard
Therefore, the beetle covered 3/8 yard more.
if loga (n) = 16, find loga (sqrtt n)
Answers
Answer:
8
Step-by-step explanation:
by definition:
[tex]log_an=16\\\\log_a\sqrt{n}=log_a n^{\frac{1}{2}}=\frac{1}{2}log_a n=\frac{1}{2}(16)=8[/tex]
What is the surface area of the rectangular prism?
5 ft
5 ft
8 ft
Answers
A recent study at Winthrop University was done to determine the ratio of democrats to republicans. Use the information in each problem to come up with an appropriate sample size to accurately estimate the mean. Let a republican represent a success r. If no preliminary sample is taken, how large should the sample be to be 90% sure that the estimate is within .03 of the population proportion?
Answers
Answer:
A sample of 752 should be taken.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
No preliminary sample is taken
This means that [tex]\pi = 0.5[/tex]
How large should the sample be to be 90% sure that the estimate is within .03 of the population proportion?
This is n for which M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645*0.5[/tex]
[tex]\sqrt{n} = \frac{1.645*0.5}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2[/tex]
[tex]n = 751.7[/tex]
Rounding up:
A sample of 752 should be taken.
What are the more appropriate measures of center and spread for this data
set?
5
18
22 24 26
H
02
4 B
3 10 12 14 16 18 20 22 24 26 28 30
Select two choices: one for the center and one for the spread.
A. Better measure of center: the mean
O B. Better measure of spread: the standard deviation
I c. Better measure of center: the median
I D. Better measure of spread the interquartile range (IOR)
Answers
Answer:
C and D
Step-by-step explanation:
The data is represented in a box plot given. In a box plot, the min, max, median, Q1, and Q3 are displayed.
If you want to measure the center of the data, you can make use of the median.
Also, an appropriate measure of spread to use is the interquartile range.
Interquartile range = Q3 - Q1.
Better measure of center to use is Mean while better measure of spread is interquartile range.
The correct options for measures of center and spread for the data set is option C and D
What are the best measures of center and spread of the data?The measures of center of data include the mean, median and mode.
The measures of spread include range, mean deviation, variance and standard deviation.
The give dat is a box plot where the min, max, median, Q1, and Q3 are shown.
The best measure of the center of the data, is the median.
The appropriate measure of spread is the interquartile range.
In conclusion, the more appropriate measures of center and spread for the data set is median and interquartile range respectively.
Learn more measures of center and spread at: https://brainly.com/question/10252810
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The terms central location or central tendency relate to the way quantitative data tend to cluster around some middle or central value.
a. True
b. False
Answers
Answer:
A: True
Step-by-step explanation:
It's true because central tendency is defined as a branch of descriptive statistics that shows the centre of the data distribution.
This central tendency could be mean, median or mode.
4th term of an arithmetic sequence is 23 and its 11th term is 65, what is its common difference
Answers
Answer:
d = 6
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₄ = 23 and a₁₁ = 65 , then
a₁ + 3d = 23 → (1)
a₁ + 10d = 65 → (2)
Subtract (1) from (2) term by term to eliminate a₁
10d - 3d = 65 - 23
7d = 42 ( divide both sides by 7 )
d = 6
Help me with my geometry homework
Answers
Answer:
10.5 is the answer
Step-by-step explanation:
i hope it helps u
Answer:
is the answer y=7? if correct its ok but if the answer didn't match then plesse let me know
Three coins are flipped. What is the probability that all three coins will match?
Answers
Answer:
25%
Step-by-step explanation:
We can also show this from the results table below: There are 8 possible outcomes for tossing three coins. Two of these outcomes are either all heads or all tails, Therefore there is a 28=14=0.25=25% chance of getting all heads or all tails.
I’m not sure of the answer.
Answers
Step-by-step explanation:
l hope it helps mark the brainliest plzz
Answer:
option c is correct
Step-by-step explanation:
(3x^2 + 3)(4 + x^3)
=3x^2(4 + x^3) +3(4 + x^3)
=12x^2 + 3x^5 +12 +3x^3
=3x^5 + 3x^3 + 12x^2 + 12
you and your four friends go to the water park. it is $10 each for tickets, and y dollars for lunch.
a. use the distributive property to write and simplify an expression for the total the group pays.
b. how much does the group pay when the lunches cost $4?
Answers
Answer:
56 dollars
Step-by-step explanation:
idfk 56 dollars is the answer tho
Judson collected information about the name length and the population of a random sample of 296 American cities. Here are the results:
Name length Less than Between 150,000 More than Total
150,000 and 250,000 250,000
Less than 8
characters 30 29 41 100
8 to 10
characters 43 41 33 117
More than 10
characters 26 28 25 79
Total 99 98 99 296
Judson wants to perform a X2 test of independence between name length and population. What is the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters?
Answers
The expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters is A = 33.45
What is the probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
The mean of probability distribution is also known as expected value. It is denoted by E ( X ). E(X), or mean μ of a discrete random variable X is calculated by multiplying each value of the random variable by its probability and taking the sum of the values.
E ( X ) = μ = ∑x P ( x )
Given data ,
To find the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters, we need to calculate the expected count for that cell using the formula:
Expected Count = (row total * column total) / grand total
The row total for cities with more than 250,000 residents is 99, and the column total for names with less than 8 characters is 100. The grand total is 296
Expected Count = (99 * 100) / 296
Expected Count ≈ 33.45
Therefore , the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters is approximately 26.67
Hence , the distribution is 33.45
To learn more about probability distribution click :
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The complete question is attached below :
Judson collected information about the name length and the population of a random sample of 296 American cities. Here are the results:
Judson wants to perform a X2 test of independence between name length and population. What is the expected count for the cell corresponding to cities with more than 250,000 residents whose name has less than 8 characters?
help pls find the coordinates for the midpoint of the segment with the end points given (5,6) (8,2)
Answers
Step-by-step explanation:
hear is your answer in attachment
convert into decimal 8%
Answers
Answer:
Percent to decimal conversion table
Percent Decimal
8% 0.08
