[tex]x=2y[/tex] and [tex]x=y^3[/tex] intersect when
[tex]2y=y^3\implies y^3-2y=y(y^2-2)=y(y-\sqrt2)(y+\sqrt2)=0[/tex]
[tex]\implies y=0\text{ or }y=\sqrt2\text{ or }y=-\sqrt2[/tex]
We omit the negative root, since we only care for [tex]y\ge0[/tex].
In the interval (0, √2), we have [tex]y^3<2y[/tex]. Then the volume is given by the integral
[tex]\displaystyle\pi\int_0^{\sqrt2}(2y)^2-(y^3)^2\,\mathrm dy=\pi\int_0^{\sqrt2}4y^2-y^6\,\mathrm dy[/tex]
and so the volume is (32√2)/21 π.
A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. (Round your answers to four decimal places.) (a) Compute the probability that 2 or fewer will withdraw. (b) Compute the probability that exactly 4 will withdraw. (c) Compute the probability that more than 3 will withdraw. (d) Compute the expected number of withdrawals.
Answer:
(a) Probability that 2 or fewer will withdraw is 0.2061.
(b) Probability that exactly 4 will withdraw is 0.2182.
(c) Probability that more than 3 will withdraw is 0.5886.
(d) The expected number of withdrawals is 4.
Step-by-step explanation:
We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.
Assume that 20 students registered for the course.
The above situation can be represented through binomial distribution;
[tex]P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 20 students
r = number of success
p = probability of success which in our question is probability
that students withdraw without completing the introductory
statistics course, i.e; p = 20%
Let X = Number of students withdraw without completing the introductory statistics course
So, X ~ Binom(n = 20 , p = 0.20)
(a) Probability that 2 or fewer will withdraw is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}[/tex]
= [tex]1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}[/tex]
= 0.2061
(b) Probability that exactly 4 will withdraw is given by = P(X = 4)
P(X = 4) = [tex]\binom{20}{4} \times 0.20^{4} \times (1-0.20)^{20-4}[/tex]
= [tex]4845\times 0.20^{4} \times 0.80^{16}[/tex]
= 0.2182
(c) Probability that more than 3 will withdraw is given by = P(X > 3)
P(X > 3) = 1 - P(X [tex]\leq[/tex] 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
= [tex]1-(\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}+\binom{20}{3} \times 0.20^{3} \times (1-0.20)^{20-3})[/tex]
= [tex]1-(1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}+1140\times 0.20^{3} \times 0.80^{17})[/tex]
= 1 - 0.4114 = 0.5886
(d) The expected number of withdrawals is given by;
E(X) = [tex]n\times p[/tex]
= [tex]20 \times 0.20[/tex] = 4 withdrawals
What can be determined by looking at the factored form of the polynomial f(x) = (x + 7)(x - 2) ?
A
The graph of the polynomial has zeros at (0,-7) and (0,2)
В
The graph of the polynomial has zeros at (7,0) and (-2,0)
C
The graph of the polynomial has zeros at (-7,0) and (2,0)
D
The graph of the polynomial has zeros at (0,7) and (0,-2)
Answer:
C . The graph of the polynomial has zeros at (-7,0) and (2,0)
Step-by-step explanation:
f(x) = (x + 7)(x - 2)
Zero's obtained:
(x+7)(x-2) = 0x+7 = 0 ⇒ x = -7x-2 = 0 ⇒ x = 2Coordinates:
(-7, 0) and (2, 0)Correct answer choice is:
C . The graph of the polynomial has zeros at (-7,0) and (2,0)
Solve the inequality
Math question
Answer:
AAAAAAAAAAAAAAAAAAAA
Step-by-step explanation:
x < 7
the length of a rectangle is 4 unit less than the width. which expression represents the perimeter of the rectangle
Answer:
Length: 11
Width: 5
Step-by-step explanation:
Let W = width
Let L = length
Length is 4 less than 3 times the width ==> L = 3*W - 4
Let P = Perimeter = 2*W + 2*L
Perimeter is 22 more than twice the width ==> P = 2*W + 22
Setting the 2 expressions for the perimeter equal to each other gives
2*W + 2*L = 2*W + 22
2*L = 22
L = 11
So 11 = 3*W - 4
3*W = 15
W = 5
The length is 11 and the width is 5
Check: 3*W - 4 = 11 = Length
Perimeter = 32 = 22 more than 2*5 = 10
if a line is perpendicular to y=-2/3x+2, will it be perpendicular to 2x+3y=12?
Answer:
3x + 2y = -2
Step-by-step explanation:
Given Equation is − 2 x + 3 y = 12
3 y = 2 x + 12
y = ( 2 /3 ) y + 12
Slope of this line is m = 2/ 3
Slope of Line A m a = 2
Slope of Line B m b = 2/ 3
Slope of Line C m c = − ( 2 /3 )
Slope of Line D m d = − ( 3 /2 )
since m d = − 1 /m , D is perpendicular to the given line
The complement of 20°17' is
Answer:69°43'
Step-by-step explanation:
Complementary angles add up to 90
Let them complement be y
y+20°17`=90°
Collect like terms
y=90-20°17' 20°17'=1217/60
y=90-1217/60
y=(60x90 -1 x 1217)/60
y=(5400-1217)/60
y=4183/60
y=69°43'
At Silver Gym, membership is $35 per month, and personal training sessions are $30 each. At Fit Factor,
membership is $85 per month, and personal training sessions are $20 each. In one month, how many
personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Sarah would have to buy
equal.
personal training sessions to make the total cost at the two gyms
Answer:
5 sessions each
Step-by-step explanation:
Let the personal training sessions be x.
Then at Silver Gym Sarah would spend:
35 + 30xAnd at Fit Factor she would spend:
85 + 20xSince total costs are same, the amounts will be equal:
35+30x = 85 + 20x30x - 20x = 85 - 3510 x = 50x= 50/10x= 5So Sarah would buy 5 training sessions for each of the gyms.
And she would spend $185 at each.
Which best describes a fraction?
» A fraction is the denominator divided by the numerator.
» A fraction is the numerator divided by the denominator.
1.) A fraction is the numerator multiplied by the denominator.
()) A fraction is the denominator multiplied by the numerator.
A fraction is the numerator divided by the denominator best describes a fraction.
Given,
- A fraction is the denominator divided by the numerator.
- A fraction is the numerator divided by the denominator.
- A fraction is the numerator multiplied by the denominator.
- A fraction is the denominator multiplied by the numerator.
We need to find which option best describes a fraction.
What is a fraction?A fraction has two parts: Numerator and Denominator.
It is in the form of Numerator / Denominator.
We have,
- A fraction is the denominator divided by the numerator.
It is written as denominator / Numerator.
- A fraction is the numerator divided by the denominator.
It is written as Numerator / Denominator
- A fraction is the numerator multiplied by the denominator.
It is written as Numerator x Denominator.
- A fraction is the denominator multiplied by the numerator.
It can be written as Denominator x Numerator.
We see that the option "a fraction is a numerator divided by the denominator" is the correct answer.
Thus A fraction is the numerator divided by the denominator best describes a fraction.
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The number of new contributors to a public radio station's annual fund drive over the last ten years is 63, 58, 61, 72, 98, 103, 121, 147, 163, 198 Using Microsoft Excel, develop a linear regression model that predicts the number of new contributors. Explain the slope of this model. Based on this model, how many new contributors would you predict for the following year?
Answer:
The number of potential members predicted in next year's estimate becomes 193. The further explanation is given below.
Step-by-step explanation:
The slope of the model,
m = 15.345
c = 24
After comparing with the equation,
⇒ [tex]y=mx+c[/tex]
we get,
⇒ [tex]=15.345x + 24[/tex]
The slope seems to be a positive value which also means that another always improves this as component decreases. Which ensures that perhaps the number of contributors rising as time went by.
So that the above is the right answer.
Which equation represents the hyperbola shown in the
graph?
10
8
(x - 2)2
(y + 3)
25
(-2,5) 6
(-7,3)
(1-21)
4-12-10 -8 -6 4-2
(3,3)
(x + 2)2
(y = 3) = 1
4
2 4 6
(x + 2)2
25
(y - 3)2
4
1
(232) - (7,31 = 1
(x - 2)2
25
Answer:
Step-by-step explanation:
A general equation of a hyperbola is
x^2 y^2
-------- - ------- = 1 (This applies only when the center of the hyperbola
a^2 b^2 is at (0, 0) ).
You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.
The equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
What is a hyperbola?A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
Given that, a graph, showing hyperbola, we need to find the equation,
We have the general equation for up - down facing hyperbola as
(y - k)² / b²- (x - h)² / a² = 1.
Let's start listing the properties of this graph -
Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).
Therefore, (h, k) = (- 4,1).
This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.
Therefore, a = 3.
That gives asymptotes. Now remember that it will be in the form
y = ± b / a.
We already know a = 3, so we have to find b.
Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).
Calculating the slope of the dotted line would be as follows,
Given: (- 4,1) and (- 2, - 2)
Slope = - 2 + 4 / - 2 - 1 = 2 / 3
We have the equation y = 2 / 3x.
Therefore, b = 2.
Let's substitute to equation...
h = - 4, k = 1, b = 2, a = 3
(y - 1)² / (3)²- (x + 4)² / (2)² = 1
(y - 1)² / 9 - (x + 4)² / 4 = 1
Hence, the equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
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The complete question is attached
Ollivanders stuffed bear shop has 456 bears in stock exactly half of them Are made from wool how many wool does Mr.oillvander have in stock
Answer:
228 of them are made from wool, but there is no enough information to determine how many would he has in stock.
Step-by-step explanation:
Mr Ollivander's stuffed bear shop has 456 bears in stock, and exactly half of them are made from wool, this means that 1/2 of 456 are made from wool
1/2 of 456 = 1/2 × 456 = 456/2 = 228.
That is 228 of them are made from wool.
However, nothing tells us that this is all he has in his stock. There is no information available to determine how many would he has in stock.
The altitude of an airplane is decreasing at a rate of 44 feet per second. What is the change in altitude of the airplane over a period of 34 seconds?
Answer:
1320 feet
Step-by-step explanation:
All we have to do is multiply the rate of change of altitude by the time it took the altitude to change.
The altitude of an airplane is decreasing at a rate of 44 feet per second. After 30 seconds, the change is altitude is:
44 * 30 = 1320 feet
The altitude of the airplane has changed by 1320 feet.
Solve the system of equations using the elimination method 4x+5y=40 6x+3y=42
Answer:
The solutions to the system of equations are [tex]y=4,\:x=5[/tex].
Step-by-step explanation:
To solve the system [tex]\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}[/tex]
First,
[tex]\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84[/tex]
[tex]\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}[/tex]
Subtract the first equation from the second equation
[tex]12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36[/tex]
Solve [tex]-9y=-36[/tex] for y:
[tex]\frac{-9y}{-9}=\frac{-36}{-9}\\y=4[/tex]
For [tex]12x+15y=12[/tex] plug in [tex]y=4[/tex] and solve for x
[tex]12x+15\cdot \:4=120\\12x=60\\x=5[/tex]
The solutions to the system of equations are:
[tex]y=4,\:x=5[/tex]
BRAINLIEST ASAP! LENGTH OF AC?
Answer:
2.33 units
Step-by-step explanation:
[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]
For the data 20, 40, 50, 20, 10, 70. What is there mean absolute deviation?
Answer:
18.333
Step-by-step explanation:
Nora made 15 gallons of lemonade for a community picnic.
Part A
Which of the following can be used to find the number of pints of lemonade that Nora made?
15 × 2 × 2
15 × 4 × 2
15 × 3 × 2
15 × 4 × 3
Part B
How many pints of lemonade did Nora make?
Enter your answer in the box.
pints
Answer:
I also belive for Part A the second one is the answer because it equals 120 Part B is 120 pints! Good Luck! And I hope this Helps!
Answer:
B
Step-by-step explanation:
A bag of colored marbles contains 16 blue marbles, 12 red marbles, and 8 yellow marbles.
What is the theoretical probability of drawing a red marble?
Enter your answer as a reduced fraction, like this: 3/14
Answer:
The theoretical probability of drawing a red marble is 1/3.
Step-by-step explanation:
1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.
2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.
3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.
What is the Surface Area of the figure below?
A
60 units2
B
60 units3
C
104 units2
D
104 units3
Answer:
D
Step-by-step explanation:
I'm really sry if it's wrong!
Which equation represents the black line?
Which equation represents the red line?
Explain a mathematical way to find the intersection of the lines without actually graphing the lines.
Answer:
Black Line y = 3 + 2x , y = 2x +3
Red Line y = -2 - .5x. y = -.5x -2
vice versa
Step-by-step explanation:
For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x
For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.
Determine which consecutive integers do not have a real zero of f(x) = x^3 + 9x^2 + 8x – 5 between them.
A.) (–8, –7)
B.) (4, 5)
C.) (0, 1)
D.) (–2, –1)
Answer:
Option B (4,5)
Step-by-step explanation:
The integers (4, 5) do not have real zero.
What is zero of a function?Knowing what zeros represent can assist us in determining when and how to locate the zeros of functions given their expressions and a function's graph. The value of x when the function itself reaches zero is typically referred to as a function's zero.
A function's zero can take many different forms, but as long as they have a y-value of zero, we will consider them to be the function's zero.
Given Expression
f(x) = x³ + 9x² + 8x - 5
to find which is not a real zero,
condition of real zero is for any function f(a , b) if f(a).f(b) < 0 the function have at least a zero.
1: (-8, -7)
f(-8).f(-7) = [(-8)³ + 9(-8)² + 8(-8) - 5][(-7³) + 9(-7)² + 8(-7) - 5]
f(-8).f(-7) = (-5)(37)
f(-8).f(-7) = -185 < 0 points have at least a zero
2: (4, 5)
f(4).f(5) = [(4)³ + 9(4)² + 8(4) - 5][(5³) + 9(5)² + 8(5) - 5]
f(4).f(5) = 235 x 385
f(4).f(5) = 94,475 > 0
points do not have any zeros
3: (0, 1)
f(0).f(1) = [(0)³ + 9(0)² + 8(0) - 5][(1³) + 9(1)² + 8(1) - 5]
f(0).f(1) = -5 x 13
f(0).f(1) = -65 < 0
points have a zero
4: (–2, –1)
f(-2).f(-1) = [(-2)³ + 9(-2)² + 8(-2) - 5][(-1³) + 9(-1)² + 8(-1) - 5]
f(-2).f(-1) = 7 x (-5)
f(-2).f(-1) = -35 < 0
points have a zero
Hence only point (4, 5) do not have a zero.
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A 5000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $153 comma 200?
Answer:
Let's denote:
x: number of ticket 28$
y: number of ticket 40$
Then, we have:
x + y =5000
28x + 40y = 153200
=> 28(5000 - y) + 40y = 153200
=> 12y = 153200 - 140000
=> 12y =13200
=> y = 1100 (ticket 40$)
=> x = 5000 - 1100 = 3900 (ticket 28$)
What’s the correct answer for this?
Answer:
c
Step-by-step explanation:
Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of
modeled by the function r(s)=315, where sis time in seconds.
The area of the spill when s=5 seconds is
1 square inches.
Reset
Reset
Next
Next
Answer:
[tex]45\pi$ square inches[/tex]
Step-by-step explanation:
The radius, r of the expanding circle of oil is modeled by the function:
[tex]r=3\sqrt{s}[/tex] , where s is time in seconds.
When s=5
Radius [tex]r(5)=3\sqrt{5}$ inches[/tex]
Area of a circle [tex]=\pi r^2[/tex]
Therefore, the area of the oil spill when s=5 seconds
[tex]=\pi* (3\sqrt{5})^2\\=45\pi$ square inches[/tex]
The area of the spill when s=5 seconds is 45pi square inches.
In the right triangle shown DF=EF=3. How long is DE?
Answer:
4.24
Step-by-step explanation:
To solve this, use the Pythagorean therom. A^2 + b^2 = C^2
in this case a = 3 and b = 3
so 9 + 9 = sqrt 18
4.24
Answer:3√(2)
Step-by-step explanation:
DF=3
EF=3
DE=√(3^2 + 3^2)
DE=√(3x3 + 3x3)
DE=√(9+9)
DE=√(18)
DE=√(2 x 9)
DE=√(2) x √(9)
DE=√(2) x 3
DE=3√(2)
An angle whose measure is -102° is in standard position. Which quadrant does the terminal side of the angle fall?
Quadrant 1
Quadrant 2
Cuadrant 3
Cuadrant 4
Answer:3
Step-by-step explanation:
edg
A bag contains 3 red marbles and 6 blue marbles. A second bag contains 6 green marbles and 4 yellow marbles. You choose a marble from bag A and then a marble from bag B, what would be the probability of selecting one blue marble and one yellow marble?
Answer:
4/15
Step-by-step explanation:
Bag A
3 red marbles and 6 blue marbles. = 9 marbles
P(blue) = blue/total =6/9 = 2/3
Bag B
6 green marbles and 4 yellow marbles. = 10 marbles
P(yellow) = yellow/total=4/10 = 2/5
P(blue,yellow) = 2/3 * 2/5 = 4/15
if u dont know dont worry about it
Answer:
4/15
Step-by-step explanation:
The total number of spins completed is 6+8+7+9 = 30
The letter B came up 8 times
P(B) = number of B's over total
P(B) = 8/30 = 4/15
Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000, select the correct answer. Note that the profit is distributed proportionally based on the respective amount each invested. A. The ratio of the investment of Bob, Paula and Sam is 11:15:10. B. The ratio of the investment of Bob, Paula and Sam is 12:17:21. C. The ratio of the investment of Bob, Paula and Sam is 12:5:4. D. The profit of Paula was $23,800
Answer:
D
Step-by-step explanation:
since sam invest the least, let a be the amount invested by sam
sam = a
paul = a + 5000
bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
a = 12000
thus sam is 12000, paul is 17000 and Bob is 21000
therefore the ratio of B:P:S is 21:17:12
profit by paula is 17/50 x 70000 = 23800
The profit by Paula is 17/50 x 70000 = 23800.
We have given that Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000
Since sam invest the least, let a be the amount invested by sam
Therefore we get,
sam = a
What is the investment of Paul?
The investment of Paul = a + 5000
Bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
divide both sides by 3 so we get,
a=36000/3
a = 12000
Therefore, sam is 12000,
paul =5000+12000=17000 and
Bob =12000+9000= 21000
Therefore the ratio of B:P:S is 21:17:12
The profit by Paula is 17/50 x 70000 = 23800.
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BRAINLIST+11 Pts!!!
Jim just found a job with a take-home pay of $950 per month. He must pay $400 for rent and $100 for groceries each month. He also spends $100 per month on transportation. If he budgets $50 each month for clothing, $100 for restaurants and $50 for everything else, how long will it take him to save $1,800?
Answer:12 months
Step-by-step explanation:
400+400=800 so 950-800=150 1800/150=12
True or false
Writing a check on an account with insufficient funds is allowed under certain conditions?
