Answer:
a) [tex]\Delta A \approx 26.389\,cm^{2}[/tex], b) [tex]r_{A} \approx 0.019[/tex], c) [tex]\delta = 1.9\,\%[/tex]
Step-by-step explanation:
a) The area of the circular disk is modelled after this expression:
[tex]A = \pi \cdot r^{2}[/tex]
The total differential is given by the following formula:
[tex]\Delta A = 2\pi r \cdot \Delta r[/tex]
The maximum absolute error in the calculated area of the disk is:
[tex]\Delta A = 2\pi \cdot (21\,cm)\cdot (0.2\,cm)[/tex]
[tex]\Delta A \approx 26.389\,cm^{2}[/tex]
b) The relative error is given by:
[tex]r_{A} = \frac{\Delta A}{A}[/tex]
[tex]r_{A} = \frac{26.389\,cm^{2}}{\pi \cdot (21\,cm)^{2}}[/tex]
[tex]r_{A} \approx 0.019[/tex]
c) The percentage error is:
[tex]\delta = r_{A}\times 100\,\%[/tex]
[tex]\delta = 0.019 \times 100\,\%[/tex]
[tex]\delta = 1.9\,\%[/tex]
A typical classroom is a rectangle with dimensions of 20 feet wide by 25 feet long, and the area needed for each person in the room is approximately 28 square feet, what fraction of the total area in a classroom is needed for each person? What is the largest number of people that would fit in an average sized classroom while practicing good social distancing?
Answer:
A fraction of 0.056 of the classroom is needed for each student.
A typical classroom can acomodate up to 17 persons while practicing good social distancing.
Step-by-step explanation:
We have a classroom that is a recatngle with dimensions of 20 feet wide by 25 feet long.
The total area of the classroom is:
[tex]A=w\cdot l=20\cdot25=500[/tex]
As the area of the classromm is 500 square feet and we need 28 square feet for each student, the fraction that is needed for each student is:
[tex]f=\dfrac{A_{\text{student}}}{A_{\text{classroom}}}=\dfrac{28}{500}=0.056[/tex]
A fraction of 0.056 of the classroom is needed for each student.
The largest number of students that would fit in an average sized classroom while practicing good social distancing can be calculated dividing the area of the classroom by the area needed for each student. This is equal to the inverse of the fraction calculated previously:
[tex]n=\dfrac{1}{f}=\dfrac{1}{0.056}\approx17.86[/tex]
A typical classroom can acomodate up to 17 persons while practicing good social distancing.
Please help. I’ll mark you as brainliest if correct!
Answer:
product = 40
Step-by-step explanation:
The conjugate of (-2 + 6i) is (-2 - 6i)
You just need to change the sign
(-2 + 6i) (-2 - 6i)
Expand:
4 + 12i + -12i - [tex]36i^{2}[/tex]
4 + 12i + -12i + 36
product = 40
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
Answer:
The probability that a randomly selected boy in secondary school can run the mile in less than 368 seconds is P(X<368)=0.011.
Step-by-step explanation:
We have a normal distribution with mean 460 and standard deviation 40 to describe the time for the mile run in its secondary-school fitness test.
We have to calculate the probabiltiy that a randomly selected boy in secondary school can run the mile in less than 368 seconds.
To calculate this, we have to calculate the z-score for X=368:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{368-460}{40}=\dfrac{-92}{40}=-2.3[/tex]
Then, we can calculate the probability:
[tex]P(X<368)=P(z<-2.3)=0.011[/tex]
A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 155 while the ACT scores have a mean of 22 and a standard deviation of 4. Assuming the performance on both tests follows a normal distribution, determine which test the student did better on.
Answer:
Due to the higher z-score, he did better on the SAT.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Determine which test the student did better on.
He did better on whichever test he had the higher z-score.
SAT:
Scored 1070, so [tex]X = 1070[/tex]
SAT scores have a mean of 950 and a standard deviation of 155. This means that [tex]\mu = 950, \sigma = 155[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1070 - 950}{155}[/tex]
[tex]Z = 0.77[/tex]
ACT:
Scored 25, so [tex]X = 25[/tex]
ACT scores have a mean of 22 and a standard deviation of 4. This means that [tex]\mu = 22, \sigma = 4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{25 - 22}{4}[/tex]
[tex]Z = 0.75[/tex]
Due to the higher z-score, he did better on the SAT.
Suppose the demand for a certain brand of a product is given by D(p)equals=StartFraction negative p squared Over 116 EndFraction−p2116plus+200200, where p is the price in dollars. If the price, in terms of the cost c, is expressed as p (c )equals 2 c minus 10p(c)=2c−10, find the demand function in terms of the cost.
Answer:
The demand function in terms of cost is [tex]D(c) = [\frac{[40c- 100 -4c^2 \ ])}{116} ] + 200[/tex]
Step-by-step explanation:
From the question we are told that
The demand for a certain brand of a product is
[tex]D(p) = \frac{-p^2}{116} + 200 ----(1)[/tex]
The price, in terms of the cost c, is expressed as
[tex]p(c) = 2c -6 -----(2)[/tex]
Now substituting equation 2 into equation 1
So
[tex]D(c) = - [\frac{(2c -10 )^2)}{116} ] + 200[/tex]
[tex]D(c) = - [\frac{[4c^2 + 100 -40c \ ])}{116} ] + 200[/tex]
[tex]D(c) = [\frac{[40c- 100 -4c^2 \ ])}{116} ] + 200[/tex]
What value of b will cause the system to have an infinite number of solutions?
A system of equations. y equals 6 x plus b. negative 3 x plus StartFraction one-half EndFraction y equals negative 3.
A coordinate grid with a line labeled negative 3 x plus StartFraction one-half EndFraction y equals negative 3 and passes through the points (1, 0) and (0, negative 6).
-6
-3
3
6
Answer:
-6 on edge
Step-by-step explanation:
The value of b that causes the system of equations to have infinite solutions will be: b = -6
System with infinite solutions:A system of linear equations will have infinite solutions only when both equations represent the same line.
In this case our equations are:
y = 6x + b
-3x + (1/2)*y = -3
So the value of b needs to be such that these two equations are equal
Let's isolate y in the second equation:
(1/2)*y = -3 + 3x
y = -3*2 + 3x*2 = -6 + 6x
Then we must have:
6x - 6 = 6x + b
-6 = b
Thus, the value of b that causes the system to have infinite solutions is b = -6.
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FIND P(NOT 6) WHEN YOU ROLL A STANDARD NUMBER CUBE THEN DESCRIBE THE LIKELIHOOD OF THE EVENT WRITE IMPOSSIBLE ,UNLIKELY , EQUALLY LIKELY , LIKLEY OR CERAIN
Answer: LIKLEY
Step-by-step explanation:
Formula : Probability [tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]
A standard cube has six numbers on it (1,2,3,4,5 and 6).
P( NOT 6) =[tex]\dfrac{\text{Numbers that are not 6}}{\text{Total numbers}}[/tex]
[tex]=\dfrac{5}{6}=0.8333[/tex]
We know that when the probability of any event lies between 0.5 and 1then the event is said to be likely to happen.
Since , P(not 6)=0.8333 which lies between 0 and 0.5.
That means, it is likely to happen.
Note :
When probability of having A = 0 , we call A as uncertain event.
When probability of having A = 1 , we call A as certain event.
When probability of having A = 0.5 , we call A as equally likely event.
When probability of having A lies between 0 and 0.5 , we call A as unlikely event.
When probability of having A lies between 0.5 and 1 , we call A as likely event.
After the accounts have been adjusted at December 31, the end of the fiscal year, the following balances were taken from the ledger of Pioneer Delivery Services Co.:
Kerry Buckner, Capital. $9,556,300
Kerry Buckner, Drawing 80,000
Wages Expense 1,878,400
Rent Expense 1,415,500
Supplies Expense 125,000
Fees Earned 30,600
Miscellaneous Expense 22,100
Journalize the two entries required to close the accounts.
Help asap giving branlist!!!
Answer:
Option 2
Step-by-step explanation:
Because the slope is -0.09 the answer is the second option. A negative slope means a decrease.
Evaluate 1/2 + 1/2 ÷ 18
Answer:
1/18
Step-by-step explanation:
First you would add 1/2 and 1/2 to get 1 then you would divide it by 18 to get 1/18
Answer:
1/18
Step-by-step explanation:
plz mark me brainliest.
A rectangular field has an area of 1,764 m(squared). The width of the field is 13 m more than the length. What is the perimeter of the field?
Answer:
170m
Step-by-step explanation:
The answer to the above question is letter d which is 170 m. To get the 170 m, kindly check the below solution:
x^2 + 13x = 1764 so x = -49 and 36, we take 36 as its the positive value. And the other side is 49. Now use 2(l+b) to find perimeter. You get (36+49)*2 = 170
Please help me HURRY!!!!!!
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2013?
Answer: The population will be 408,000 people.
Step-by-step explanation:
So in 2000 there were 200,000 people and it started to grow 8% every year so up to 2013.
so find 8% of 200,000 and then multiply it by the the number of years.
8% * 200,000 = 16,000
Find the difference between the years.
2013 - 2000 = 13 years
13 * 16000 = 208000 This is the amount of new people from 2000 to 2013 so add it to the original population.
208,000 + 200,000 = 408,000
Parallelogram L M N O is shown. Angle M is (3 x minus 55) degrees, angle N is (5 y) degrees, and angle O is (2 x) degrees. In parallelogram LMNO, what are the values of x and y?
Answer:
x=55,y=14
Step-by-step explanation:
<M = <{opposite angles of a parallelogram are congruent and equal}
Hence 3x-55 = 2x=>3x-2x= 55 =>x=55
Simarly;
M+N=180°{ sum of angles in a parallelogram is 180°}
N= 180°-M=>N=180-(3x-55)=180-(3x55-55)= 180- 110=70°
N=70°=>5y=70=>y=70/5=14
therefore x=55,y=14
Answer:
55 and 14
Step-by-step explanation:
i just took the test
On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Find the probability expressions: (Round your answers to 2 decimal places.)
a. P(X=50)P(X=50).
b. P(X≤75)P(X≤75).
c. P(X>50)P(X>50).
d. P(X<100)P(X<100).
Answer:
a. P(X=50)= 0.36
b. P(X≤75) = 0.9
c. P(X>50)= 0.48
d. P(X<100) = 0.9
Step-by-step explanation:
The given data is
x 25 50 75 100 Total
P(x) 0.16 0.36 0.38 0.10 1.00
Where X is the variable and P(X) = probabililty of that variable.
From the above
a. P(X=50)= 0.36
We add the probabilities of the variable below and equal to 75
b. P(X≤75) = 0.16+ 0.36+ 0.38= 0.9
We find the probability of the variable greater than 50 and add it.
c. P(X>50)= 0.38+0.10= 0.48
It can be calculated in two ways. One is to subtract the probability of 100 from total probability of 1. And the other is to add the probabilities of all the variables less than 100 . Both would give the same answer.
d. P(X<100)= 1- P(X=100)= 1-0.1= 0.9
what value of x makes the equation true ? 9.68x + 21.6 -6.23x = 2.3x + 17
Answer:
-4 please brainliest me
Step-by-step explanation:
9.68x+21.6-6.23x=2.3x+17
lets move it to the left
9.68x+21.6-6.23x-(2.3x+17)=0
Then, We add all the numbers together, and all the variables
3.45x-(2.3x+17)+21.6=0
We get rid of parentheses
3.45x-2.3x-17+21.6=0
We add all the numbers together, and all the variables
1.15x+4.6=0
We move all terms containing x to the left, all other terms to the right
1.15x=-4.6
x=-4.6/1.15
x=-4
x= -8 makes the equation true.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
9.68x + 21.6 -6.23x = 2.3x + 17
Now, solving for x
9.68 x - 6.23x - 2.3x = 17 - 21.6
1.15x= -4.6
x= -4.6 / 1.15
x= -8
Hence, x= -8 makes the equation true.
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help me................
Answer:
x = 5. y = 4
Step-by-step explanation:
7x - 4 = 31
7x = 35
x = 5
4y + 8 = 24
4y = 16
y = 4
Solve for x
A) -8
B) 3.5
C) 8
D) 26
Answer:
C) 8
Step-by-step explanation:
By remote interior angle property of a triangle.
[tex] 19x - 3 = 94° + 7x - 1\\\\
19x - 7x = 94 + 3 - 1\\\\
12 x = 96\\\\
x = \frac{96}{12}\\\\
\huge \orange{\boxed {x = 8}} [/tex]
Which of the given shapes has a larger area?
Answer:
Rectangle
Step-by-step explanation:
Count the units. For the triangle, A=0.5bh. 0.5(4)(6)=A. A=12
Now, for the rectangle, A=bh. A=(3)(5). A=15. The rectangle is larger
Complete the synthetic division problem below.
2 1 6 -16
What is the quotient in polynomial form?
Answer: x + 8
Step-by-step explanation:
The required quotient in polynomial form is x + 8.
To determine the synthetic division of 2 | 1 6 -16 and quotient in polynomial function.
It is a method for performing division of polynomials, with little writing and lesser calculations than complex division.
2 | 1 6 -16
+2 +16
1 8 0
Its quotient in polynomial form is given as x + 8
Thus, The required quotient in polynomial form is x + 8.
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Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 12 ft high? (Round your answer to two decimal places.)
Answer:
0.13 ft/min
Step-by-step explanation:
We are given that
[tex]\frac{dV}{dt}=15ft^3/min[/tex]
We have to find the increasing rate of change of height of pile when the pile is 12 ft high.
Let d be the diameter of pile
Height of pile=h
d=h
Radius of pile,r=[tex]\frac{d}{2}=\frac{h}{2}[/tex]
Volume of pile=[tex]\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3[/tex]
[tex]\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}[/tex]
h=12 ft
Substitute the values
[tex]15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}[/tex]
[tex]\frac{dh}{dt}=0.13ft/min[/tex]
Solve:
|x-7|<-1.
zero solutions
one solution
infinite solutions
all real numbers
Step-by-step explanation:
In mathematics, the absolute value |x|, is the non-negative result of x without regard to its sign.
An absolute function, can never have a negative result.
By this alone, you can solve the question because the inequality is false, and therefore there are zero solutions.
Please see the attachment of f(x) = |x - 7|.
When you look at the graph, you can easily confirm that there is no value which can result in a negative y- coordinate like -2. In fact, that is the whole purpose of any absolute value or function. The result of an absolute function can never be negative.
The average score of all golfers for a particular course has a mean of 70 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 71.
Design and complete a frequency table for Belinda.
Belinda ask 20 people, how many hours of TV did you watch last week?
Here is the results
3,17,4,4,6,11,14,14,1,20,9,8,9,6,12,7,8,13,13,9.
Belinda wants to show these result in a frequency table.
She will use 4 equal groups.
The first group will start with 1 hour and the last group will end with 20 hours.
Answer:
Step-by-step explanation:
Since she will use 4 groups or class intervals, the the class width would be 20/4 = 5 hours
The class groups would be
1 to 5
5 to 10
10 to 15
15 to 20
The class mark for each class is the average of the minimum and maximum value of each class. Therefore, the class marks are
(1 + 5)/2 = 3
(5 + 10)/2 = 7.5
(10 + 15)/2 = 12.5
(15 + 20)/2 = 17.5
The frequency table would be
Class group Frequency
1 - 5 4
5 - 10 8
10 - 15 6
15 - 20 2
The total frequency is 4 + 8 + 6 + 2 = 20
A
B
C
D
Help me out
Answer:
2x^2 + 3/2x -5
Step-by-step explanation:
f(x) = x/2 -2
g(x) = 2x^2 +x -3
f(x)+ g(x) = x/2 -2+ 2x^2 +x -3
Combine like terms
= 2x^2 + 3/2x -5
Find f(g(−1)), f(g(−1))=___
Answer:
Find g(f(−1)).
g(f(−1)) = 64
Find f(g(−1)).
f(g(−1)) = -6
f(g(−1)) is - 8.
What is a composite function ?A composite functions is a function where two or more than two functions are combined.The output of the previous function is the input of the next function.
According to the given question we have to find a composite function.
Assuming f(x) = x² + 9x and g(x) = x³.
To find f(g(-1)) first we have to put x = -1 for g(x) which is
= g(-1) = (-1)³ = -1.
Now we put this value of g(-1) in f(x).
∴ f(g(-1))
= f(-1)
= (-1)² + 9(-1)
= 1 - 9
= - 8.
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A team of researchers published an article on the study of how vehicles are dispatched based on an airport-based taxi service. The researchers modeled this system with an underlying assumption that travel times of successive trips to and from the terminal are independent exponentially distributed random variables with β = 15 minutes. (a) Find the mean and standard deviation of trip time distribution (b) How likely is it for a particular trip to take more than 25 minutes? (c) If two taxis are dispatched together, what is the probability that both of them will be gone for more than 25 minutes? (d) what is the likelihood of at least of one of the taxis returning within 25?
Answer:
a. The mean would be 0.067
The standard deviation would be 0.285
b. Would be of 1-e∧-375
c. The probability that both of them will be gone for more than 25 minutes is 1-e∧-187.5
d. The likelihood of at least of one of the taxis returning within 25 is 1-e∧-375
Step-by-step explanation:
a. According to the given data the mean and the standard deviation would be as follows:
mean=1/β=1/15=0.0666=0.067
standard deviation=√1/15=√0.067=0.285
b. To calculate How likely is it for a particular trip to take more than 25 minutes we would calculate the following:
p(x>25)=1-p(x≤25)
since f(x)=p(x≤x)=1-e∧-βx
p(x>25)=1-p(x≤25)=1-e∧-15x25=1-e∧-375
c. p(x>25/2)=1-p(x≤25/2)=1-e∧-15x25/2=1-e∧-187.5
d. p(x≥25)=1-e∧-15x25=1-e∧-375
write any two numbers less than 15 , which has exactly four factors
Answer:
4 can be divided by 1 and 2
6 can be divided by 1 and 2
12 is wrong because it can be divided by 1,2, and 4 so it has 6 factors instead of 4
Step-by-step explanation:
A linear track begins at 0 meters and has a total distance of 100 meters to the finish line. Juliet starts at the 100 meter mark while practicing for a race. After running 45 meters how far is she from the beginning of the track?
Answer:
It’s D, 55.
Step-by-step explanation:
After running 45 meters, Juliet runs 55 meters from the beginning of the track
What’s the correct answer for this question?
Answer:
The last option is the correct choice 33.5
Step-by-step explanation:
[tex]V=\pi r^2\frac{h}{3} \\=\pi 2^2\frac{8}{3} \\=33.51\\=33.5[/tex]
Answer:
D
Step-by-step explanation:
In the attached file