By Stokes' theorem,
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S[/tex]
where [tex]S[/tex] is the surface with [tex]C[/tex] as its boundary. The curl is
[tex]\nabla\times\vec F(x,y,z)=2\,\vec\imath-x\,\vec k[/tex]
Parameterize [tex]S[/tex] by
[tex]\vec\sigma(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+(8-u\cos v)\,\vec k[/tex]
with [tex]0\le u\le9[/tex] and [tex]0\le v\le2\pi[/tex]. Then take the normal vector to [tex]S[/tex] to be
[tex]\vec\sigma_u\times\vec\sigma_v=u\,\vec\imath+u\,\vec k[/tex]
Then the line integral is equal to the surface integral,
[tex]\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9(2\,\vec\imath-u\cos v\,\vec k)\cdot(u\,\vec\imath+u\,\vec k)\,\mathrm du\,\mathrm dv[/tex]
[tex]\displaystyle=\int_0^{2\pi}\int_0^9(2u-u^2\cos v)\,\mathrm du\,\mathrm dv=\boxed{162\pi}[/tex]
Please Explain and Show your work! Thank you!
Answer:
344 ft²
Step-by-step explanation:
The area of the square is (40 ft)² = 1600 ft².
The area of the four circles is ...
4×(πr²) = 4×3.14×(10 ft)² = 1256 ft²
Then the area that is not covered by the circles is ...
1600 ft² -1256 ft² = 344 ft²
The area not sprinkled is 344 ft².
The partial fraction decomposition of LaTeX: \frac{x-9}{x^2-3x-18} x − 9 x 2 − 3 x − 18 is LaTeX: \frac{A}{x-6}+\frac{B}{x+3} A x − 6 + B x + 3 . Find the numbers LaTeX: A\: A and LaTeX: B B . Then, find the sum LaTeX: A+B A + B , which is a whole number. Enter that whole number as your answer.
Not entirely sure what the question is supposed to say, so here's my best guess.
First, find the partial fraction decomposition of
[tex]\dfrac{x-9}{x^2-3x-18}[/tex]
This is equal to
[tex]\dfrac{x-9}{(x-6)(x+3)}=\dfrac a{x-6}+\dfrac b{x+3}[/tex]
Multiply both sides by [tex](x-6)(x+3)[/tex], so that
[tex]x-9=a(x+3)+b(x-6)[/tex]
Notice that if [tex]x=6[/tex], the term involving [tex]b[/tex] vanishes, so that
[tex]6-9=a(6+3)\implies a=-\dfrac13[/tex]
Then if [tex]x=-3[/tex], the term with [tex]a[/tex] vanishes and we get
[tex]-3-9=b(-3-6)\implies b=\dfrac43[/tex]
So we have
[tex]\dfrac{x-9}{x^2-3x-18}=-\dfrac1{3(x-6)}+\dfrac4{3(x+3)}[/tex]
I think the final answer is supposed to be [tex]a+b[/tex], so you end up with 1.
50 Points Please show graph
Solve the equation by graphing.
x^2+14x+45=0
First, graph the associated parabola by plotting the vertex and four additional points, two on each side of the vertex.
Then, use the graph to give the solution(s) to the equation.
If there is more than one solution, separate them with commas.
Answer:
The solutions are x = -9 , x = -5
Step-by-step explanation:
* Lets find the vertex of the parabola
- In the quadratic equation y = ax² + bx + c, the vertex of the parabola
is (h , k), where h = -b/2a and k = f(h)
∵ The equation is y = x² + 14x + 45
∴ a = 1 , b = 14 , c = 45
∵ h = -b/2a
∴ h = -14/2(1) = -14/2 = -7
∴ The x-coordinate of the vertex of the parabola is -7
- Lets find k
∵ k = f(h)
∵ h = -7
- Substitute x by -7 in the equation
∴ k = (-7)² + 14(-7) + 45 = 49 - 98 + 45 = -4
∴ The y-coordinate of the vertex point is -4
∴ The vertex of the parabola is (-7 , -4)
- Plot the point on the graph and then find two points before it and
another two points after it
- Let x = -9 , -8 and -6 , -5
∵ x = -9
∴ y = (-9)² + 14(-9) + 45 = 81 - 126 + 45 = 0
- Plot the point (-9 , 0)
∵ x = -8
∴ y = (-8)² + 14(-8) + 45 = 64 - 112 + 45 = -3
- Plot the point (-8 , -3)
∵ x = -6
∴ y = (-6)² + 14(-6) + 45 = 36 - 84 + 45 = -3
- Plot the point (-6 , -3)
∵ x = -5
∴ y = (-5)² + 14(-5) + 45 = 25 - 70 + 45 = 0
- Plot the point (-5 , 0)
* To solve the equation x² + 14x + 45 = 0 means find the value of
x when y = 0
- The solution of the equation x² + 14x + 45 = 0 are the x-coordinates
of the intersection points of the parabola with the x-axis
∵ The parabola intersects the x-axis at points (-9 , 0) and (-5 , 0)
∴ The solutions of the equation are x = -9 and x = -5
* The solutions are x = -9 , x = -5
A student answers a multiple-choice examination question that offers four possible answers. Suppose the probability that the student knows the answer to the question is 0.9 and the probability that the student will guess is 0.1. Assume that if the student guesses, the probability of selecting the correct answer is 0.25. If the student correctly answers a question, what is the probability that the student really knew the correct answer? (Round your answer to four decimal places.)
Answer: 0.9730
Step-by-step explanation:
Let A be the event of the answer being correct and B be the event of the knew the answer.
Given: [tex]P(A)=0.9[/tex]
[tex]P(A^c)=0.1[/tex]
[tex]P(B|A^{C})=0.25[/tex]
If it is given that the answer is correct , then the probability that he guess the answer [tex]P(B|A)= 1[/tex]
By Bayes theorem , we have
[tex]P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(C|A^c)P(A^c)}[/tex]
[tex] =\dfrac{(1)(0.9)}{(1))(0.9)+(0.25)(0.1)}\\\\=0.972972972973\approx0.9730[/tex]
Hence, the student correctly answers a question, the probability that the student really knew the correct answer is 0.9730.
1.What’s the least common multiple (LCM) for each group of numbers?
a. 6 and 15
b. 4 and 11
c. 6, 9, and 12
d. 8, 10, and 20
2.What’s the least common denominator (LCD) for each group of fractions?
a. 1⁄6 and 7⁄8
b. 3⁄4 and 7⁄10
c. 7⁄12, 3⁄8 and 11⁄36
d. 8⁄15, 11⁄30 and 3⁄5
3.Insert the “equal” sign or the “not equal” sign ( = or ≠) to make each statement true.
a. 18/36 _____ 1/2
b. 13/15 _____ 7/10
c. 3/5 _____ 5/9
d. 3/8 _____ 10/16
4.On a hot summer day, John drank 5⁄11 of a quart of iced tea; Gary drank 7⁄10 of a quart; and Carter drank 3⁄5 of a quart. Which man was the most thirsty?
5.What’s the largest fraction in each group?
a. 5⁄6 and 29⁄36
b. 5⁄12 and 3⁄8
c. 2⁄5 and 19⁄45
d. 5⁄7, 13⁄14, and 19⁄21
e. 7⁄11 and 9⁄121
f. 1⁄2, 3⁄18, and 4⁄9
6.Reduce each of the following fractions to its simplest form.
a. 12⁄18
b. 48⁄54
c. 27⁄90
d. 63⁄77
e. 24⁄32
f. 73⁄365
7.What is the next fraction in each of the following patterns?
a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .?
b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .?
c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .?
8.In each pair, tell if the fractions are equal by using cross multiplication.
a. 5⁄30 and 1⁄6
b. 4⁄12 and 21⁄60
c. 17⁄34 and 41⁄82
d. 6⁄9 and 25⁄36
9.This year, a baseball player made 92 hits out of 564 times at bat. Another player made 84 hits out of 634 times at bat. Did the two players have the same batting average?
10.On a test with 80 questions, Bob got 60 correct. On another test with 100 questions, he got 75 correct. Did Bob get the same score on both tests?
11.Find the missing numerators in each of the following problems.
a. 10⁄15 = ⁄60
b. ⁄108 = 4⁄9
c. 7⁄11 = ⁄121
d. ⁄144 = 2⁄6
12.This handy application of LCMs is used by astronomers.
All the planets in our solar system revolve around the sun. The planets occasionally line up together in their journeys, as shown in the illustration. The chart shows the time it takes each planet to make one trip around the sun.
Now, imagine that the planets Earth, Mars, Jupiter, Saturn, Uranus, and Neptune aligned last night. How many years will pass before this happens again? (Hint—Find the LCM of the planets’ revolution times.)
Solar System
Planet Revolution Time
Earth 1 year
Mars 2 years
Jupiter 12 years
Saturn 30 years
Uranus 84 years
Neptune 165 years
1.
a. 30
b. 44
c. 36
d. 40
2. I don't really remember how to do these but if you cant make the denominator smaller then I belive it's
a. 24
b. 20
c. 4
d. 5
3.
a. =
b. not =
c. not =
d. not =
4. Gary
5.
a. 5/6
b. 5/12
c. 19/45
d. 13/14
e. 7/11
f. 1/2
6.
a. 2/3
b. 8/9
c. 3/10
d. 9/11
e. 3/4
f. 1/5
7.
a. 36/40
b.
c.
8.
a. yes
b. no
c. no
d. no
9. no
10. yes
11.
a. 40
b. 48
c. 77
d. 48
12. 4,620
c. 27⁄90
d. 63⁄77
e. 24⁄32
f. 73⁄365
7.What is the next fraction in each of the following patterns?
a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .?
b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. . .?
c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. . .?
8.In each pair, tell if the fractions are equal by using cross multiplication.
a. 5⁄30 and 1⁄6
b. 4⁄12 and 21⁄60
c. 17⁄34 and 41⁄82
d. 6⁄9 and 25⁄36
1.
a. 30
b. 44
c. 36
d. 40
2.
a. 24
b. 20
c. 4
d. 5
3.
a. =
b. not =
c. not =
d. not =
4. Gary
5.
a. 5/6
b. 5/12
c. 19/45
d. 13/14
e. 7/11
f. 1/2
6.
a. 2/3
b. 8/9
c. 3/10
d. 9/11
e. 3/4
f. 1/5
7.
a. 36/40
b.
c.
8.
a. yes
b. no
c. no
d. no
9. no
10. yes
11.
a. 40
b. 48
c. 77
d. 48
12. 4,620
Step-by-step explanation:
Find the sum of the sequence 46+47+48+49+...+137
Answer:
8418
Step-by-step explanation:
1 + 2 + ... + n is (n^2 + n)/2
46 + 47 + ... + 137
is the same as
1 + 2 + ... + 137 - (1 + 2 + ... + 45)
or
(137^2 + 137)/2 - (45^2 + 45)/2
= 8418
The probability of winning something on a single play at a slot machine is 0.11. After 4 plays on the slot machine, what is the probability of winning at least once
Step-by-step explanation:
The probability of winning at least once is equal to 1 minus the probability of not winning any.
P(x≥1) = 1 - P(x=0)
P(x≥1) = 1 - (1-0.11)^4
P(x≥1) = 1 - (0.89)^4
P(x≥1) = 0.373
The probability is approximately 0.373.
Answer:
37.26% probability of winning at least once
Step-by-step explanation:
For each play, there are only two possible outcomes. Either you win, or you do not win. The probability of winning on eah play is independent of other plays. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability of winning something on a single play at a slot machine is 0.11.
This means that [tex]p = 0.11[/tex]
After 4 plays on the slot machine, what is the probability of winning at least once
Either you do not win any time, or you win at least once. The sum of the probabilities of these events is decimal 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]. So
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{4,0}.(0.11)^{0}.(0.89)^{4} = 0.6274[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.6274 = 0.3726[/tex]
37.26% probability of winning at least once
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 6.5% and the tax in the second city was 4.5% The total hotel tax paid for the two cities was $582.50
. How much was the hotel charge in each city before tax?
Answer:
First city: $5,500
Second city: $5,000
Step-by-step explanation:
Let's define x as the hotel price in the first city and y the hotel price in the second city. We can start with this equation:
y = x - 500 (The hotel before tax in the 2nd city was $500 lower than in the 1st.)
Then we can say
0.065x + 0.045y = 582.50 (the sum of the tax amounts were $582.50)
We place the value of y from the first equation in the second equation:
0.065x + 0.045 (x - 500) = 582.50
0.065x + 0.045x - 22.50 = 582.50 (simplifying and adding 22.5 on each side)...
0.11x = 605
x = 5,500
The cost of the first hotel was $5,500
Thus, the cost of the second hotel was $5,000 (x - 500)
When Jill Thompson received a large settlement from an automobile accident, she chose to invest $115,000 in the Vanguard 500 Index Fund. This fund has an expense ratio of 0.17 percent. What is the amount of the fees that Jill will pay this year? (Round your answer to 2 decimal places.) Annual fee
Answer:
$195.50
Step-by-step explanation:
0.17% × $115,000 = $195.50
Jill's account will be charged $195.50 in expense fees.
Answer:
Jill will have to pay $195.5 in fees this year.
Step-by-step explanation:
This question may be solved by a simple rule of three.
This fund has an expense ratio of 0.17 percent. This means that for each investment in this fund, there is a fee of 17% percent of the value.
$115,000 is 100%, that is, decimal 1. How much is 0.17%, that is, 0.0017 of this value. So
1 - $115,000
0.0017 - $x
[tex]x = 115000*0.0017 = 195.5[/tex]
Jill will have to pay $195.5 in fees this year.
A rectangular patio measures 20 feet by 30 feet. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
Answer:
2400sq ft
Step-by-step explanation:
20×2 and 30×2
40×60
2400 sq ft
Answer:
Length = 40 feet
Width =30 feet
Step-by-step explanation:
It is given that a rectangular patio measures 20 feet by 30 feet.
To find the area of first patio.
Area = length * breadth
= 20 * 30 = 600 square feet
To find the value of x
It is given that new area will be the double the area of first patio.
Here area = 2 * 600 = 1200 square feet
Here length = 30 + x
width = 20 + x
Area = (30 +x)(20 + x) = 1200
x² + 50x + 600 =1200
x² + 50x - 600 = 0
By solving this quadratic equation we get,
x = 10 and x = -60
take positive value x = 10
To find the dimensions of new patio
New length = 30 + x = 30 + 10 = 40 feet
width= 20 + x = 20 + 10 = 30 feet
A drawer contains 2 red socks, 4 white socks, and 8 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is red and the second sock is blue?
[tex]|\Omega|=14^2=196\\|A|=2\cdot8=16\\\\P(A)=\dfrac{16}{196}=\dfrac{4}{49}\approx8.2\%[/tex]
The AWP for a gallon (3785 ml) of antihistamine/ antitussive cough syrup is $18.75, with an additional 20% discount from the wholesaler. What is the cost of 1 pint of the medication?
Answer:
The cost of 1 pint of the medication would be $1.875.
Step-by-step explanation:
The AWP of 3785 ml ( 1 gallon ) cough syrup = $18.75
After an additional 20% discount from wholesaler the price would be
New price = 18.75 - (0.20 × 18.75)
= 18.75 - 3.75
= $15.00
Since 1 gallon ( 3785 ml) = 8 pints
Therefore, the price for 1 pint = [tex]\frac{15}{8}[/tex] = $1.875
The cost of 1 pint of the medication would be $1.875.
You're using your meter to make voltage measurements in the circuit shown in the figure above. Your meter is connected between points A and C, and you're getting a reading of 6 V on the display. What can you conclude from this reading? A. Switch S1 is open. B. Resistors R1 and R2 have equal resistance values. C. Resistor R2 has a resistance value that's twice the value of either R1. D. Switch S1 is closed.
Answer:
A. Switch S1 is Open
Step-by-step explanation:
I attach the missing figure in the image below
Since you are getting a reading of 6V which is the maximum voltage of your circuit, you can conclude that
A. Switch S1 is Open
- If the Switch S1 was closed, we would be getting a reading of 0V. This is not the case.
- Because the switch is open, there is no current going through the circuit and therefore there is not any voltage drop across the resistors. This is why their values don't affect the reading.
A radio station claims that the amount of advertising per hour of broadcast time has an average of 10 minutes and a standard deviation equal to 5 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 8.2 minutes. Calculate the z-score for this amount of advertising time. Round your answer to 2 decimal places.
Answer: -0.36
Step-by-step explanation:
Given: Mean : [tex]\mu=10\text{ minutes}[/tex]
Standard deviation : [tex]\sigma=5\text{ minutes}[/tex]
We know that the formula to calculate the z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x=8.2 minutes, we have
[tex]z=\dfrac{8.2-10}{5}=0.36[/tex]
Hence, the z-score for this amount of advertising time = -0.36
Final answer:
The z-score for the observed amount of advertising time (8.2 minutes) compared to the radio station's average of 10 minutes with a standard deviation of 5 minutes is -0.36, when rounded to two decimal places.
Explanation:
To calculate the z-score for the amount of advertising time observed on the radio station (8.2 minutes), we use the formula: Z = (X - μ) / σ, where X is the value to calculate the z-score for, μ is the mean of the data, and σ is the standard deviation. Plugging in the given values: X = 8.2 minutes (amount of advertising time observed), μ = 10 minutes (average advertising time), σ = 5 minutes (standard deviation).
So, the z-score is calculated as follows:
Z = (8.2 - 10) / 5 = -1.8 / 5 = -0.36.
Thus, the z-score of the amount of advertising time (8.2 minutes) is -0.36, rounded to two decimal places.
PLEASE HELP!!!!!!!!!!!!!!!
Answer:
d. (1, 5, 2)
Step-by-step explanation:
A suitable calculator can find the reduced row-echelon form for you. Some scientific calculators and many graphing calculators have this capability, as do on-line calculator. The one below is supported by ads.
In terms of x, find an expression that represents the area of the shaded region. The outer square has side lengths of (x+5) and the inner square has side lengths of (x-2), as shown.
Answer:
Area = 14x + 21 square unitsStep-by-step explanation:
The formula of an area of a square with side length a:
[tex]A=a^2[/tex]
The big square:
[tex]a=x+5[/tex]
Substitute:
[tex]A_B=(x+5)^2[/tex] use [tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex]A_B=x^2+2(x)(5)+5^2=x^2+10x+25[/tex]
The small square:
[tex]a=x-2[/tex]
Substitute:
[tex]A_S=(x-2)^2[/tex] use [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]A_S=x^2-2(x)(2)+2^2=x^2-4x+4[/tex]
The area of a shaded region:
[tex]A=A_B-A_S[/tex]
Substitute:
[tex]A=(x^2+10x+25)-(x^2-4x+4)=x^2+10x+25-x^2+4x-4[/tex]
combine like terms
[tex]A=(x^2-x^2)+(10x+4x)+(25-4)=14x+21[/tex]
The mean salary of 5 employees is $33700. The median is $34600. The mode is $35600. If the median paid employee gets a $3500 raise, then ...
Hint: It will help to write down what salaries you know of the five and think about how you normally calculate mean,median, and mode.
a) What is the new mean? (3 point)
New Mean = $
b) What is the new median?
New Median = $
c) What is the new mode?
New Mode = $
Step-by-step explanation:
Given:
Mean = 33700
Median = 34600
Mode = 35600
The mean is the average, the median is the middle number, and the mode is the most common number.
a)
First, we need to find the new mean (average) if one of the employees gets a 3500 raise. The average is the total salary divided by number of employees:
(5 × 33700 + 3500) / 5 = 34400
b)
The mode is the most common number in a set. Since there are only five employees, and the mode is different than the median, then the two highest earners must have the same salary. The salaries from smallest to largest is therefore:
?, ?, 34600, 35600, 35600
When the median gets the 3500 raise, the set becomes:
?, ?, 35600, 35600, 38100
So the new median is 35600.
c)
The most common number is still 35600. So the mode hasn't changed: 35600.
Factor out the GCF (greatest common factor)
8m^2 n^3 - 24m^2 n^2 + 4m^3 n +
Answer:
4m²n
Step-by-step explanation:
The GCF is the factor by which all the terms among the given can be divided.
In the expression 8m²n³-24m²n²+4m³n,
The GCF between 8,24 and 4 is 4
The greatest common factor between m²,m² and m³ is m²
The greatest common factor between n³, n² and n is n
Thus multiplying the three we get:
4×m²×n
=4m²n
All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .73, the probability the second truck is available is .59, and the probability that both trucks are available is .43: What is the probability neither truck is available
Answer: .11
Step-by-step explanation:
Let F be the event that the first truck is available and S be the event that the second truck is available.
The probability of neither truck being available is expressed as P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex]) , where P([tex]F^{C}[/tex]) is the probability that the event F doesn't happen and P([tex]S^{C}[/tex]) is the probability that the event S doesn't happen.
P([tex]F^{C}[/tex])= 1-P(F) = 1-0.73 = 0.27
P([tex]S^{C}[/tex])=1-P(S) = 1-0.59 = 0.41
Since [tex]F^{C}[/tex] and [tex]S^{C}[/tex] aren't mutually exclusive events, then:
P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex]) = P([tex]F^{C}[/tex]) + P([tex]S^{C}[/tex]) - P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex])
Isolating the probability that interests us:
P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex])= P([tex]F^{C}[/tex]) + P([tex]S^{C}[/tex])- P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex])
Where P([tex]F^{C}[/tex]∪[tex]S^{C}[/tex]) = 1 - 0.43 = 0.57
Finally:
P([tex]F^{C}[/tex]∩[tex]S^{C}[/tex]) = 0.27+ 0.41 - 0.57 = 0.11
The ratio of the areas of two similar polygons is 49:36. If the perimeter of the first polygon is 15 cm, what is the perimeter of the second polygon? Round to the nearest hundredth. 11.76 cm 11.02 cm 13.25 cm 12.85 cm
Answer:
12.85 cm
Step-by-step explanation:
Area ratio of 49:36 means a side length ration of 7:6.
7/6 = 15/x
7x = 90
x = 90/7
= 12.85
Answer: 12.85 cm
Step-by-step explanation:
There are 20 multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points, and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. If the student needs at least 40 points to pass the test, the probability the student passes is closest to
Ok, the student needs 40 points and each question is worth 5, so 40/5 = 8 questions are needed.
Each question has 4 possibilities, 1 is right, so the chances to guess it correctly is one in 4, or 1/4, or 25%.
[tex]\frac{8}{20} = \frac{2}{5}[/tex]
To know the probability to pass the exam we can do:
[tex]\frac{25}{100}*\frac{2}{5} = 10%[/tex]
Answer: 0.102 or 10.2%.
Step-by-step explanation:
Given : Number of multiple-choice questions = 20
Number of options in any question=4
Each question is worth 5 points and only one response per question is correct.
Probability of getting a correct answer = [tex]\dfrac{1}{4}=0.25[/tex]
If the student needs at least 40 points to pass the test, that mean he needs at-least [tex]\dfrac{40}{5}=8[/tex] questions correct.
Let x denotes the number of correct questions .
By using binomial distribution , we find
[tex]P(x\geq8)=1-P(x<8)\\\\ =1-P(x\leq7)\\\\=1-0.898\ \ \text{[By using binomial table for n= 20 , p=0.25 and x=7]}\\\\=0.102[/tex]
[Binomial table gives the probability [tex]P(X\leq x)=\sum_{x=0}^c^nC_xp^x(1-p)^{n-x}[/tex] ]
Hence, the probability the student passes is closest to 0.102 or 10.2%.
Last year, a person wrote 126 checks. Let the random variable x represent the number of checks he wrote in one day, and assume that it has a Poisson distribution. What is the mean number of checks written per day? What is the standard deviation? What is the variance?
Answer: The mean number of checks written per day [tex]=0.3452[/tex]
Standard deviation[tex]=0.5875[/tex]
Variance [tex]=0.3452[/tex]
Step-by-step explanation:
Given : The total number of checks wrote by person in a year = 126
Assume that the year is not a leap year.
Then 1 year = 365 days
Let the random variable x represent the number of checks he wrote in one day.
Then , the mean number of checks wrote by person each days id=s given by :-
[tex]\lambda=\dfrac{126}{365}\approx0.3452[/tex]
Since , the distribution is Poisson distribution , then the variance must equal to the mean value i.e. [tex]\sigma^2=\lambda=0.3452[/tex]
Standard deviation : [tex]\sigma=\sqrt{0.3452}=0.5875372328\approx0.5875[/tex]
George was given 11 grams of medicine, but the full dose is supposed to be 25 grams. What percent of his full dose did George receive? Solve with percent table and equivalent fractions
Answer: George receive 44 % of his full dose .
Step-by-step explanation:
Given : The amount for full dose : 25 grams
The amount received by George = 11 grams
Now, the percent of his full dose received by George :-
[tex]\dfrac{\text{Dose taken by George}}{\text{Full dose}}\times100[/tex]
[tex]=\dfrac{11}{25}\times100=44\%[/tex]
Hence, George receive 44 % of his full dose .
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 15.7% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? c. What is the probability of not being awakened if the student uses three independent alarm clocks?d. Do the second and third alarm clocks result in greatly improved reliability? (A) Yes, because you can always be certain that at least one alarm clock will work. (B) No, because the malfunction of both is equally or more likely than the malfunction of one. (C) Yes, because total malfunction would not be impossible, but it would be unlikely. (D) No, because total malfunction would still not be unlikely.
Step-by-step answer:
Given:
alarm clocks that fail at 15.7% on any day.
Solution
Probability of failure of a single clock = 15.7% = 0.157
(a)
probability of failure of a single clock on any given day (final exam or not)
= 15.7% (given)
(b)
probability of failure of two independent alarm clocks on the SAME day
= 0.157^2
= 0.024649 (from independence of events)
(c)
probability of failure of three independent alarm clocks on the SAME day
= 0.157^3
= 0.00387 (from independence of events)
(d)
Since the probability of failure has been reduced from 0.157 to 0.00387, we can conclude that yes, even though malfunction of all three clocks is not impossible, it is unlikely at a probability of 0.00387 (less than 1 %)
Using the binomial distribution, it is found that:
a) 15.7% probability that the student's alarm clock will not work on the morning of an important final exam.
b) 0.0246 = 2.46% probability that they both fail on the morning of an important final exam.
c) 0.0039 = 0.39% probability of not being awakened if the student uses three independent alarm clocks.
d)
(C) Yes, because total malfunction would not be impossible, but it would be unlikely.
---------------------------
For each alarm clock, there are only two possible outcomes. Either it works, or it does not. The probability of an alarm working is independent of any other alarm, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success on a single trial.
---------------------------
Item a:
15.7% probability of the alarm clock falling each day, thus, the same probability on the day of the final exam.---------------------------
Item b:
Two clocks, thus [tex]n = 2[/tex]Each with a 100 - 15.7 = 84.3% probability of working, thus [tex]p = 0.843[/tex].The probability of both falling is the probability that none works, thus P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.843)^{0}.(0.157)^{2} = 0.0246[/tex]
0.0246 = 2.46% probability that they both fail on the morning of an important final exam.
---------------------------
Item c:
Same as item b, just with 3 clocks, thus [tex]n = 3[/tex][tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.843)^{0}.(0.157)^{3} = 0.0039[/tex]
0.0039 = 0.39% probability of not being awakened if the student uses three independent alarm clocks.
---------------------------
Item d:
Each extra clock, the probability of malfunctions become increasingly smaller, thus very unlikely, which means that the correct option is:(C) Yes, because total malfunction would not be impossible, but it would be unlikely.
A similar problem is given at https://brainly.com/question/23576286
Graph the line that passes through the given point and has the given slope m. (3,10); m=-(5)/(2)
Step-by-step explanation:
given a slope and a point that the line passes through you have 2 options
Option 1: Solve for the equation of the line so you can just use that to graph the line. In this scenario it would be y=(-5/2)x - (20/13)
Option 2: plot the given point and, based on the slope, plot the next point that it crosses. In this case the next point would be (5, 7). Then you can just draw a line using these 2 points.
How is this equation completed? I cannot find any examples in the book.
Answer: Option D
[tex]t_{max} =19\ s[/tex]
Step-by-step explanation:
Note that the projectile height as a function of time is given by the quadratic equation
[tex]h = -12t ^ 2 + 456t[/tex]
To find the maximum height of the projectile we must find the maximum value of the quadratic function.
By definition the maximum value of a quadratic equation of the form
[tex]at ^ 2 + bt + c[/tex] is located on the vertex of the parabola:
[tex]t_{max}= -\frac{b}{2a}[/tex]
Where [tex]a <0[/tex]
In this case the equation is: [tex]h = -12t ^ 2 + 456t[/tex]
Then
[tex]a=-12\\b=456\\c=0[/tex]
So:
[tex]t_{max} = -\frac{456}{2*(-12)}[/tex]
[tex]t_{max} =19\ s[/tex]
You are playing with a standard deck of 52 playing cards. Each time you draw one card from the deck, and then you put the card back, and reshuffle the deck before choosing another card. What is the probability of selecting a number less than (but not including) 4? Count aces as equal to 1. (report a number rounded to the nearest two decimal places, but not a fraction)
Answer:
0.23
Step-by-step explanation:
A standard deck has 4 suits (spade, club, diamond, and heart), and each suit has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king).
We want to know the probability of drawing an ace, a 2, or a 3. There are four aces, four 2's, and four 3's in a deck (one for each suit). That's a total of 12 cards. So the probability is:
12 / 52 ≈ 0.23
Using the probability concept, it is found that there is a 0.2308 = 23.08% probability of selecting a number less than 4.
--------------------------
A probability is the division of the number of desired outcomes by the number of total outcomes.In a standard deck, there are 52 cards, and thus, the number of total outcomes is [tex]T = 52[/tex]Of those, 12 are less than 4, and thus, the number of desired outcomes is [tex]D = 4[/tex].Thus, the probability of selecting a number less than 4 is:
[tex]p = \frac{D}{T} = \frac{12}{52} = 0.2308[/tex]
0.2308 = 23.08%
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Combine the following expressions.
Answer right pls, thanks
a and c both have √x , so they will both be in brackets multiplied by √x.
b is the only term with √y so it will be outside of the brackets.
So the answer will be:
(a - c)√x + b√y
We can check this by expanding the brackets:
(a - c)√x + b√y
= a√x - c√x + b√y
We can rearrange this to get the same original expression:
a√x - c√x + b√y
= a√x + b√y - c√x
____________________________________
Answer:
Last option: (a - c)√x + b√y
Answer:
choice 3 is correct √x(a - c) + b√y
explanation:
You simplify by looking for the common multiplier which is √x
meaning it will be
√x(a - c) + b√y
A hypothesis is: a The average squared deviations about the mean of a distribution of values b) An empirically testable statement that is an unproven supposition developed in order to explain phenomena A statement that asserts the status quo; that is, any change from what has been c) thought to be true is due to random sampling order dA statement that is the opposite of the null hypothesis e) The error made by rejecting the null hypothesis when it is true
Answer:
b) An empirically testable statement that is an unproven supposition developed in order to explain phenomena.
Step-by-step explanation:
b) An empirically testable statement that is an unproven supposition developed in order to explain phenomena.
A hypothesis is an unproven supposition.This may be derived from previous research or theory and is developed prior to data collection.
Note:
Variance is the average squared deviations about the mean of a distribution of values.
Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0∘ and the coefficient of rolling friction is 0.30. How long the ramp should be to stop a truck of 15000 kg having a speed of 35 m/s.
The length of the ramp required can be determined by using conservation
of energy principle.
The length of the ramp should be approximately 154.97 meters.
Reasons:
Given parameters are;
The angle of inclination of the ramp, θ = 6.0°
Coefficient of friction, μ = 0.30
Mass of the truck, m = 15,000 kg
Speed of the truck, v = 35 m/s
Required;
The length of the ramp to stop the truck
Solution:
From the law of conservation of energy, we have;
Kinetic energy = Work done against friction + Potential energy gained by the truck at height
K.E. = [tex]W_f[/tex] + P.E.
Kinetic energy of the truck, K.E. = [tex]\frac{1}{2} \cdot m \cdot v^2[/tex]
Therefore;
K.E. = [tex]\frac{1}{2} \times 15,000 \times 35^2 = 9,187,500[/tex]
The kinetic energy of the truck, K.E. = 9,187,500 J
Friction force,[tex]F_f[/tex] = m·g·cos(θ)·μ
Therefore;
[tex]F_f[/tex] = 15,000 × 9.81 × cos(6) × 0.30 = 43,903.169071
Friction force,[tex]F_f[/tex] = 43,903.169071 N
Work done against friction = [tex]F_f[/tex] × d
Therefore;
Work done against friction, [tex]W_f[/tex] = 43,903.169071·d
Potential energy gained, P.E. = m·g·h
The height, h = d × sin(6.0°)
∴ P.E. = 15,000 × 9.81 × d × sin(6.0°) = 147150 × d × sin(6.0°)
Which gives;
9,187,500 J = 43,903.169071·d + 147150 × d × sin(6.0°)
[tex]d = \dfrac{9187500}{43,903.169071 + 147150 \times sin(6.0^{\circ})} \approx 154.97[/tex]
The length of the ramp, d ≈ 154.97 m.
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