Jean puts 12 books on a shelf in random order. Three are by the same author. What is the probability that those 3 books will be next to each other?
it's one of these...
4.55%
8.33%
Answer:
4.55
Step-by-step explanation:
AEight different books were put on a shelf in random order. Calculate probability that two specific books were put near each other.
My answer: Let's divide the space on the shelf into eight slots. Let's also name our two books, "A" and "B" respectively. We have two sets of combinations - in the first set of combinations we have AB (i.e. A goes first). For example, A is put into the first slot and B is put into the second slot. Next example, A is put into the second slot and B is put into the third slot. And so on. There are 7 such AB combinations in total. By the same logic there are also 7 BA combinations. Obviously there is no overlap between said combinations, thus we can sum them up and get 14 combinations in total where books A and B are put side by side.
As for number of total combinations of books on the bookshelf, it's equal to "n!", where n is equal to 8. Why? Because in order to calculate combinations when repetitions are forbidden and order is important we use this formula:
Which graph represents exponential decay?
On a coordinate plane, a straight line has a negative slope.
On a coordinate plane, a curve approaches y = 0 in quadrant 2 and curves up in quadrant 1.
On a coordinate plane, a straight line has a positive slope.
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2.
The graph which shows the function is exponential decay is on a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2 thus, option (D) is correct.
What is an exponential function?In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.
As per the given,
The exponential function is a function that changes rapidly, for example, y = 6^x here as x approaches higher the y approaches rapidly higher.
Exponential decay is the exponential function that rapidly decreases as x increases for example y = 6^(-x).
The graph of the exponential decay has been graphed below.
Hence "The graph which shows the function is exponential decay is on a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2".
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Answer:
D
Step-by-step explanation:
edge
hope this helps :)
QUICK HELP with the Image below
Answer:
12 8/11
Step-by-step explanation:
hope it helps you
What is 1/6 divided by 1/3 in simplest form
Answer:
1/2 or 0.5
Step-by-step explanation:
Answer:
1/18
Step-by-step explanation:
1/6÷1/3
1/3×1/6
1/3×6
1/18
The owner of a pet shop predicts that 10 out of 20 new puppies are male. He randomly selects 10 of the puppies, and notes that all 10 are male. Which of the following conclusions best supports his findings?
Select one:
10 of the puppies are male and 10 are female.
More than 10 of the puppies are male.
All 20 puppies are male.
Less than 10 of the puppies are male.
Answer:
A, 10 of the new puppies are male and 10 are female
Step-by-step explanation:
Really this is the one that makes the most since because if 10 of the puppies are male, then 10 must be female.
Answer: A
Step-by-step explanation:
What is the square root of –16?
A. –8i
B. –4i
C. 4i
D. 8i
Answer:
C. 4i
Step-by-step explanation:
Answer:
C. 4i
Step-by-step explanation:
[tex]\sqrt{-16} = \sqrt{16} \sqrt{-1}[/tex] (because [tex]\sqrt{ab} =\sqrt{a} \sqrt{b}[/tex])
Since [tex]\sqrt{16}[/tex]=4, and [tex]\sqrt{-1}[/tex]=i, [tex]\sqrt{-16}[/tex]=4i
pls help
#1
isjsbijsj
Answer:
The value of “Y” is (6)
Step-by-step explanation:
the x value unit of “5” has the y value of “6.”
Answer: 6
EXPLANATION:
The x axis is the one on the bottom that goes like this : ---
The y axis is the one that is like a vertical line up like this: |
If you look at the x axis you can see that one the 5 and you go up you can see there is a dot that is on the 6.
Collin bought one T-shirt for $7.90 and another T-shirt for $12.40. What is the total amount he spent?
answer this please!!!
Answer:
yes. It's a right triangle.
Step-by-step explanation:
According to the Pythagoras theorem,
a² + b² = c²
20² + 21² = 29²
400 + 441 = 841
841 = 841
LHS = RHS
Answer to this problem
The 3 deals are worth the same price per unit of $0.1 a pencil.
Price per unit of itemsBased on the given prices, we can calculate the price per pencil for each pack:
Pack of 12 pencils: $1.29Price per pencil = $1.29 / 12 = $0.1075 (approximately $0.11)
Pack of 24 pencils: $2.35Price per pencil = $2.35 / 24 = $0.0979 (approximately $0.10)
Pack of 50 pencils: $5.45Price per pencil = $5.45 / 50 = $0.109 (approximately $0.11)
In other words, the 3 deals are worth the same price per unit of the pencil.
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Find the equation of the line specified.
The slope is -7, and it passes through ( 5, -3).
a.
y = -7x - 3
c.
y = -14x + 32
b.
y = -7x + 32
d.
y = -7x - 38
The equation for the perimeter around Claire's garden is a:
Group of answer choices
Linear Function
Exponential Function
Quadratic Function
Absolute Value Function
Answer:
Linear Function
Step-by-step explanation:
I just took the test and got it right.
PLS HELP I NEED HELP SO SOOON PLEASEEDSrewrite without absolute value for the given condition y=|x-5|+|x+5| if -5
answer: i think i failed this part in class
Will give Brainly
Find the probability that a
randomly
selected point within the circle falls
in the red shaded area.
60°
60°
r= 4 cm
[? ]%
Round to the nearest tenth of a percent.
Answer: 33.3%
s Step-by-step explanation: The combined arc length of the red area is 120, which is 1/3 of 360, the full arc. So the probability is 1/3, or 33.3%. Hope this helps!
The probability that a randomly selected point within the circle falls
in the red shaded area will be 33.33%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that the shaded red sector has an angle of 60 degrees and the radius of the circle is 4 cm. The probability will be calculated as:-
The formula for a circle's sector's area is (Ф/360°) x π(r²), where r is the circle's radius and is the sector's angle.
Area of shaded region = (Ф/360°) x π(r²),
Area of shaded region = ( 60 / 360 ) x π (4²)
Area of shaded region = 8.377 square cm
Total shaded area = 2 x 8. 377 = 16.75 square cm
Total area of circle = π (4²) = 50.265 square cm
The probability is calculated by the formula below:-
Probability = Number of favorable outcomes / Number of sample
Number of favorable outcomes = 8.377
Number of sample = 50.265 square cm
Probability = 8.377 / 50.265 = 0.3333 = 33.33%
Therefore, the probability that a randomly selected point within the circle falls in the red-shaded area will be 33.33%.
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Find the area of the figure.
Answer:
91
Step-by-step explanation:
Answer:
91
Step-by-step explanation:
(11 + 15) × 7 ÷ 2 = 26 × 7 ÷ 2 = 91
Theo is using the Quadratic Formula to solve a quadratic equation. Which of the following is the next step for simplifying
x=−4±4√6/2
Answer: look at the picture
Step-by-step explanation:
Removing the denominator by dividing both the numerator's terms by 2 is the needed next step for simplification. The result is: x=−2±2√6
How to find the solution to a standard quadratic equation?Suppose the given quadratic equation is
[tex]ax^2 + bx + c = 0[/tex]
Then its solutions are given as
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Here, we're given the expression:
[tex]x = \dfrac{-4 \pm 4\sqrt{6}}{2}[/tex]
The next step to simplify is to make it look more simple.
[tex]x = \dfrac{-4}{2} \pm \dfrac{4\sqrt{6}}{2}\\\\x = -2 \pm 2\sqrt{6}[/tex]
Thus, removing the denominator by dividing both the numerator's terms by 2 is the needed next step for simplification. The result is: x=−2±2√6
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Rachel downloaded a movie at a constant speed.
After she downloaded 40% of the movie, the remaining download time was 40 seconds.
After she downloaded 40 mb, the remaining download time was 16 seconds.
Compute the total size of the movie (in mb) rounded to the nearest mb.
Answer:
The total weight of the file was 64 mb.
Step-by-step explanation:
Given that Rachel downloaded a movie at a constant speed, and after she downloaded 40% of the movie, the remaining download time was 40 seconds, while after she downloaded 40 mb, the remaining download time was 16 seconds, to determine the total size of the movie rounded to the nearest mb, the following calculation must be performed:
100 - 40 = 60
60% = 40 seconds
40 mb = 16 seconds left
16/40 = 4/10
60/40 = 1.5
1.5% for every 1 second of download.
16 x 1.5 = 24
40 + 24 = 64
Thus, the total weight of the file was 64 mb.
Does anyone have the answer key to this? Need it ASAP!
The Distance between point A and Point B is √10 units.
What is Distance?Distance is a numerical measurement of how far apart objects or points are. In Physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
Here, Coordinates of A is (1, 8) and B is (4, 9).
Distance formula = √(x₂-x₁)² + (y₂-y₁)²
= √(4 - 1)² + (9 - 8)²
= √9 +1
AB = √10
Thus, the Distance between point A and Point B is √10 units.
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Please help me with this
Answer: 20 inches
Step-by-step explanation: You will use the equation 48 x 28 x N = 26,880. To find the solution divide 48 and 28 from 26,880 to get N. To check your work just multiply what you got from N by 48 and 28.
someone please help me answer this
Answer:
It would be 20
Answer:
6.4 in is the answer.
Step-by-step explanation:
a = 5 in
b = 4 in
c = ?
According to the Pythagorean theorem,
a² + b² = c²
5² + 4² = c²
25 + 16 = c²
c² = 41
c = 6.403
Round to the nearest tenth,
c = 6.4 in
∴ the length of the pencil is 6.4 in
what is the equation that has an x intercept of 4 and yintercept of 2. Show your work please
Answer:
y = -1/2x + 2
Step-by-step explanation:
If you are talking about a linear equation then b=2
The slope is y2 - y1 / x2 - x1 so 2-0/0-4 = 2/-4 = -1/2
So put it all together in y = mx + b so y = -1/2x + 2
Pictures in order !
Answer:X=10
Step-by-step explanation: 3x-2=2x+8 If that's what you're looking for
simplify the following complex number, without changing the polar form and leave your answer in polar form:
[tex]\frac{(2\ \textless \ \frac{2\pi }{3})^{3} (3\ \textless \ \frac{3\pi }{2}) }{4\ \textless \ \frac{7\pi }{3} }[/tex]
The simplified form of the complex number in polar form is: 2 < (-7π/6)
How to simplify the complex numberTo simplify the given complex number in polar form, we can apply the rules of exponentiation and division for complex numbers:
First, let's simplify the numerator:
(2 < 2π/3)^3 = (2^3) < (2π/3 * 3) = 8 < (2π)
(3 < 3π/2) remains the same.
Now, let's simplify the denominator:
4 < (7π/3) remains the same.
Next, let's divide the numerator by the denominator:
[(8 < (2π)) * (3 < (3π/2))] / (4 < (7π/3))
Using the rules of division for complex numbers, we can divide the magnitudes and subtract the angles:
(8/4) < (2π - 7π/3 - (3π/2)) = 2 < (2π/3 - 3π/2 - π/6) = 2 < (-7π/6)
Therefore, the simplified form of the complex number in polar form is:
2 < (-7π/6)
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Denise made 1/2 of a liter of hot chocolate. Each mug holds 1/10 of a liter. How many mugs will Denise be able to fill?
Answer:
5 mugs
Step-by-step explanation:
1/2 converted into 10ths would be 5/10 ... meaning 5 mugs
someone please help me answer this!!
Answer:
100 in is the answer.
Step-by-step explanation:
a = 60 in
b = 80 in
c = ?
According to the Pythagorean theorem,
a² + b² = c²
60² + 80² = c²
3600 + 6400 = c²
c² = 10000
c = 100 in
∴ the distance between the opposite corners of the bed is 100 in
1) Which number line below
shows x 4?
a)
1 2 3 4 5 6
b)
0 1 2 3 4 5 6
C)26
O i 2 3 4
D)5
0 1 2
3 4 5
6
A
B
оооо
С
D
In the figure, lines a and b are parallel. Which statements are true? Select each correct answer. Responses m∠2=m∠1 measure of angle 2 equals measure of angle 1 m∠3=m∠1 measure of angle 3 equals measure of angle 1 m∠1=75° measure of angle 1 equals 75 degrees m∠2=105° measure of angle 2 equals 105 degrees
The correct statements from the line are given as follows:
m∠2=m∠1m∠1=75°What are corresponding angles?When two parallel lines are cut by a transversal, corresponding angles are pairs of angles that are in the same position relative to the two parallel lines and also to the transversal.
Corresponding angles are congruent, which means that they have the same angle measure.
Two corresponding angles for this problem are given as follows:
<2 and <1.
Hence:
m < 2 = m < 1.
Angles 1 and 105º form a linear pair, meaning that they are supplementary, hence the measure of angle 1 is given as follows:
m < 1 + 105º = 180º.
m < 1 = 75º.
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HELP! How many triangles can be made from the following three lengths: 1.6 centimeters, 7.4 centimeters, and 5.9 centimeters?
none
one
more than one
Answer: one
Step-by-step explanation:
Find the volume of a cone with a base diameter of 10 cm and a height of 9 cm
Answer:
235.71cm^2
Step-by-step explanation:
Volume of cone = 1/3 pie r^2 h
1/3*22/7*5*5*9
= 235.71cm^2
Volume of a cone is 235.6 cm³.
Why is the volume of a cone?The volume of a cone with height h and radius r is 1/3πr2h, which is exactly one third the volume of the smallest cylinder that it fits inside. This can be proved easily by considering a cone as a solid of revolution, but I would like to know if it can be proved or at least visual demonstrated without using calculus.The volume of a cone is calculated the using the formula:
[tex]V = \frac{1}{3} \pi r^{3} h[/tex]
Given,
height of the cylinder is, h=9cm.
The diameter of the base is 10cm. r = 5 cm
put the values into the formula to get -
V = [tex]\frac{1}{3} * \pi * 5^{2} * 9[/tex]
[tex]V = 75 \pi[/tex]
Put value of π = 3. 14 ,
V = 75 * 3.14
V = 235.6 cm³
Therefore, Volume of a cone is 235.6 cm³.
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aced or higher please hellp i beg :C
Answer:
A: Find the area of the outer trapezoid and then subtract the area of the inner trapezoid
B: 15 square units
Step-by-step explanation:
A:
Find the area of the outer trapezoid and then subtract the area of the inner trapezoid
(because if the inner trapezoid wasn't there and you were looking for the shaded region, you'd find the area of the outer trapezoid. since you have to take away the area the inner trapezoid takes up, the shaded region = area of outer trapezoid - area of inner trapezoid)
B
The area of a trapezoid is ((a+b)/2)h, where a is the top or the trapezoid, b is the bottom and h is the height.
The top of the outer trapezoid ranges from 4 to 6, so a=6-4=2. The bottom of the outer trapezoid ranges from 2 to 8, so b=8-2=6. The height of the outer trapezoid ranges from 2 to 8, so h=8-2=6.
The area of the outer trapezoid = ((a+b)/2)h = ((2+6)/2)(6) = 4(6) = 24
The top of the inner trapezoid ranges from 4 to 6, so a=6-4=2. The bottom of the inner trapezoid ranges from 3 to 7, so b=7-3=4. The height of the inner trapezoid ranges from 3 to 6, so h=6-3=3.
The area of the inner trapezoid = ((a+b)/2)h = ((2+4)/2)(3) = 3(3) = 9
The are of the shaded region = the area of the outer trapezoid - the area of the inner trapezoid = 24 - 9 = 15 square units