There are 40,320 ways, in which 8 books can be arranged on a shelf.
Solution:Here, we are to find the number of ways in which 8 books can be arranged on a shelf. The total number of books is 8 and the way of arranging books is also 8.
If one book is placed in the first place, then 7 books will be placed in front of it. If 2 books are placed in the 2nd place, then only 6 books can be placed after that book. This sequence will continue till 1 .Permutations :
A permutation is an arrangement of objects in a definite order.➲ P ( n, r )= n ! / ( n - r ) !
n = total number of objectsr = number of objects selectedThe number of ways to arrange 8 books on a shelf will be :
➝ P ( n, r ) = n ! / ( n - r ) !
➝ P ( n, r ) = 8 ! / ( 8 - 8 ) !
➝ P ( n, r ) = 8 ! / 0 !
➝ P ( n, r ) = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 / 1
➝ P ( n, r ) = 40, 320
ㅤㅤㅤㅤㅤㅤ~ Hence, there are 40,320 ways in which 8 books can be arranged on a shelf !
If the 3 books can't be together (but any 2 of the 3 can be) then it's 36,000 ways. If any one of the 3 books can't touch either of the other 2, it's 15,840 ways.
Explanation:I'm not sure if the question is saying that all three books can't be together in a group (and so biology and history can be together, but biology, history and programming can't), or if the books in that group can't sit next to other books in the group (and so biology and history can't be together). Let's do it both ways - case 1 will be all three together and case 2 will be any 2 together.
Before we work this, let's first see the number of ways we can have all 8 books arranged. Order matters and so we can approach this using a permutation equation. Moreover, since we're using all the books, we'll end up with the total number being:
8 ! = 40 , 320 .
What resolution should images for a nature magazine have?
neutral
high
low
According to a weather report, there is a 11% chance it will rain tomorrow. What is the probability that it will not rain tomorrow?
Answer:
0.78
Step-by-step explanation:
P(R)=22/100=0.22
R=1
1-0.22=0.78
According to a weather report on the probability that it will rain tomorrow, the probability that it will not rain tomorrow is 89%.
What is Probability?
Probability is simply the likelihood that something or an event is to happen.
Now, the probability that an event will not occur is one minus the probability that the event will occur.
Given the data in the question;
Probability that it will rain tomorrow p = 11%Probability that it will not rain tomorrow p⁰ = ?The probability that it will not rain tomorrow is one minus probability that it will rain tomorrow.
p⁰ = 1 - p
p⁰ = 1 - 11%
p⁰ = 1 - ( 11 / 100 )
p⁰ = 1 - 0.11
p⁰ = 0.89
p⁰ = 89%
Therefore, According to a weather report on the probability that it will rain tomorrow, the probability that it will not rain tomorrow is 89%.
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Tammy cuts four identical circles from a square piece of black poster board as shown. What is the area of the leftover poster board?
a) 6.240 square feet
b) 5.375 square feet
c) 18.760 square feet
d) 19.625 square feet
Answer:
B) 5.375
Step-by-step explanation:
The circles are half the square so their diameter will be half the length of the square
d=5/2=2.5
the formula is
area of shaded portion-area out unshaded portion
area of a square= l×l
5×5=25
area of a circle=πr^2
but since there are 4 circles it becomes 4πr^2
r=d/2=2.5/2=1.25
area of unshaded portion= 4×3.14×1.25×1.25
=19.625
area of leftover=25-19.625
= 5.375
You can rewrite the trajectory equation as y = -16(x-1)^2 + 19
I believe the answer is -16x+35
Find the median, first quartile, third quartile, and interquartile range of the data.
84,75,90,87,99,91,85,88,76,92,94
median:
first quartile:
third quartile:
interquartile range:
am confused :/
Answer:
Median: 88, First Quartile: 84, Third Quartile: 92, IQR (interquartile range): 8
Step-by-step explanation:
1. Sort the numbers in numerical order (like 1, 2, 3, etc.)
2. Find the number that is in the middle
3. Find all the quartiles by finding the median of the lower and upper halves of the list
4. Subtract Q1 (quartile 1) and Q3 (quartile 3) like this: Q3 - Q1 to get IQR
The sum of two consecutive odd numbers is 28. Find their product
We will see that the first odd number is 13 and the second odd number is 15, the product is:
P = 13*15 = 195
How to find the two consecutive odd numbers?
Let's say that the first number is x, the next odd number will be x + 2.
The sum of these two odd numbers must be 2, then we need to solve the linear equation:
x + (x + 2) = 28
We can solve that for x:
2x + 2 = 28
2x = 28 - 2 = 26
x = 26/2 = 13
Then the first number is x = 13 and the second number is x + 2 = 13 + 2 = 15.
The product of these two numbers is:
13*15 = 195
IF you want to learn more about linear equations:
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PLS HELP ITS ONLY 2 QUESTIONS
For number 6, Cylinder formula 3.14r^2*h (h=height)
For 5, pyramid formula 1/3b*h
5) base=33
Length=34
Height=21
6) pi=3.14
Radius=20
Height=31
Answer:
Cylinder: 3.14(20)^2*31
3.14(400)*31
1,256*31
becomes the answer 38,936!
Pyramid: 1/3(33)^2*21
1/3(1,089)*21
363*21
7,623!!!
Please answer number 2. I don’t understand I’m very stressed right now I need help please.
Answer:
Smaller
Step-by-step explanation:
Because 7/8 is less than 1 and the sides are smaller which makes the volume smaller
:thumbsup:
Which of the following correctly shows the first step when factoring 3wx + 3wy - 4zx - 4zy by grouping? Please show explanations - also please do not ask any further question other than answering from what is questioned.
A) 3w(x + y) - 4z(x + y)
B) 3w(x + y) + 4z(x - y)
C) 3w(x + y) + 4z(x + y)
D) w(3x + 3y) - z(4x + 4y)
3w(x+y) - 4z(x+y)
Step-by-step explanation:
Hope it helps......
3w(x + y) + 4z(x - y) correctly shows the first step when factoring 3wx + 3wy - 4zx - 4zy by grouping. Option B
How to solve thisTo factor by grouping, we first pair up the terms and then check if there is a common factor in each pair.
The given expression is 3wx + 3wy - 4zx - 4zy
First, put the terms into pairs.
The simplified version of the expression (3wx + 3wy) - (4zx + 4zy) is 3wx + 3wy - 4zx - 4zy.
Next, separate and remove the terms that are the same from each group.
The expression 3w(x + y) - 4z(x + y) can be simplified to (3w - 4z)(x + y).
This is a summary:
In option B, we have correctly put the terms together in pairs and found the common factors in each group. In the first group, we take out 3w from 3wx and 3wy, and in the second group, we take out 4z from 4zx and 4zy. This means that the expression is correct when it is written as factors.
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Find the value of f(5) for the function.
f(x) = 6+3x
Answer: 21
Step-by-step explanation:
This means we can substitute x=5 into f(x), so f(5)=6+3(5)=21.
83250/?=74*25
options are:
a) 50
b) 45
c) 40
d) 55
e) none of these
Answer:
B. 45
Step-by-step explanation:
Simplyfy 74*25
1850
Now blug in all the values for the "?".
83250/45=1850
This is the only value that staifies this equaton so therefore, B 45
Answer:
45.
Step-by-step explanation:
83250/x=74*25
83250/x=1850
1850 * x = 83250
x = 83250 /1850
= 45
Write an expression equivalent to the expressions 12x+16y using the gcf
pls help
Answer:4(3x+4y)
Step-by-step explanation: the gcf of 12x+16y is 4. we factor out 4 by dividing both terms by 4.
Answer:
[tex]4(3x+4y)[/tex]
Step-by-step explanation:
Hey there!
This would be the correct answer because the GCF of 12 and 16 is 4.
Now that we know that it is 4 we can divide the eqiasion by 4 and then you get
[tex]4(3x+4y)[/tex]
If you need to ckeck if this answer is corret then you will need to use the distributive property to distribute 4 to 3y and 4y.
The equasion would then look like this
[tex](4(3x)) (4(4y))[/tex]
Next you would need to solve the equasion to get the origional equasion
[tex]12x+16y[/tex]
A washer and dryer cost a total of $964 . The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Answer:
A washer and dryer cost a total of $964 . The cost of the washer is three times the cost of the dryer. Find the cost of each item.
Answer: 96$
Answer:
The washer costs $723 and the dryer $241.
Step-by-step explanation:
Represent the cost of the washer by w and that of the dryer as d.
Then w = 3d.
Since w + d + $964, we get 3d + d = $964, or 4d = $964, or d = $241.
Three times that is $723.
The washer costs $723 and the dryer $241.
Last year a company spent a total of £2400 on advertising. This year they spent £2796 What was the percentage increase in their spending on advertising?
Answer:
16.5%
Step-by-step explanation:
[tex] \frac{396}{2400 } \times 100[/tex]The percentage increase in their spending on advertising will be 16.5%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Last year an organization spent a sum of £2400 on publicizing. This year they burned through £2796.
Then the percentage increase in their spending on advertising will be given as,
P = [(2796 - 2400) / (2400)] x 100
P = (396 / 2400) x 100
P = 0.165 x 100
P = 16.5%
The percentage increase in their spending on advertising will be 16.5%.
More about the percentage link is given below.
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What is the distance between points (8,3) and (53,31) on a coordinate plane?
Answer:
53 units
Step-by-step explanation:
Let [tex](x_1,y_1)\rightarrow(8,3)[/tex] and [tex](x_2,y_2)\rightarrow(53,31)[/tex] to use the distance formula:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\\\\d=\sqrt{(31-3)^2+(53-8)^2}\\\\d=\sqrt{(28)^2+(45)^2}\\\\d=\sqrt{784+2025}\\\\d=\sqrt{2809}\\\\d=53[/tex]
Thus, the distance between the two points is 53 units
PLEASE SOLVE. I NEED IT TO BE CORRECT!
Answer:-4,000/ -20
Step-by-step explanation:
hopefully this is right, so you have multiple choice and if so is this up their?
Answer:
198
Step-by-step explanation:
Someone Plss Help!!!! The dot plots compare the number of raffle tickets sold by students for a school fundraiser.
Answer:
That's just the way of the world
Somewhere in the world, they think they're working for themselves
They get up everyday to go to work for someone else
And somebody works for them and, so, they think they got it made
But they're all just working to get paid the very same
And so, they keep on twiddlin' them thumbs.
Three moons are in the same circular orbit around a planet. The moons are each 98,000 kilometers from the surface of the planet, located at points A, B, and C. The planet is 12,000 kilometers in diameter and m∠ABC=90°. How far is point A from point C?
Answer:
The distance between points A and C is 275000 kilometers
Which of the following isatangent
Answer:
can you re word this i dont understand
cany anybody give me the awnser to this?
Have a look at the attached image.
what is this
please help
Answer:
The answers are the 2nd box, 4th box, and 5th box.
What is the value of the expression (2^4)^2?
Answer:
256Explanation:
[tex]\dashrightarrow \sf \left(2^4\right)^2[/tex]
apply exponent rule: [tex]\bold{\left(a^b\right)^c=a^{bc}}[/tex]
[tex]\dashrightarrow \sf 2^{4*2}[/tex]
[tex]\dashrightarrow \sf 2^{8}[/tex]
[tex]\dashrightarrow \sf 256[/tex]
[tex]\large{\boxed{(\sf 2^{4})^2 \ \ = \ \ 256}[/tex]
James is participating in a 8-mile walk to raise money for a charity. He has received $600 in fixed pledges
and raises $11 extra for every mile he walks. Use a point-slope equation to find the amount he will raise if
he completes the walk.
If he finishes the race, James will raise
Answer:688
Step-by-step explanation:600+(11x8)=x
x=total
600+88=x
x=688
Pls help me !! Pls help me !!
Answer:
x= -2
Step-by-step explanation:
Make denominator same
3*(x+10)/12 - 2*(x-10)/12 = 6*(x+10)/12
denominators are same so numerators has to same as well
3*(x+10)-2*(x-10)=6*(x+10)
expand brackets
3x+30-2x+20 = 6x+60
x+50=6x+60
x-6x=60-50
-5x=10
x= -2
Victoria is at an elevation of 150 feet. She hikes down to an elevation of 120 feet in 40 minutes. Then she hikes down to an elevation of 100 feet in 30 minutes.
Answer:
Answer: First portion is greater than second portion.
Step-by-step explanation:
Time taken to hiked down a trail = 10 minutes
Change in elevation = (-) 170 feet
Speed is given by
\begin{gathered}Speed=\frac{Distance}{Time}\\\\Speed=\frac{170}{10}\\\\Speed=17\text{ feet per minute}\end{gathered}
Speed=
Time
Distance
Speed=
10
170
Speed=17 feet per minute
Similarly,
Time taken to hiked down a trail = 20 minutes
Change in elevation = (-)220 feet
Speed is given by
Speed=\frac{Distance}{Time}Speed=
Time
Distance
\begin{gathered}Speed=\frac{220}{20}\\\\Speed=11\text{ feet per minutes}\end{gathered}
Speed=
20
220
Speed=11 feet per minutes
So, we can see that first portion of the hike where he hiked down a trail at a steady rate for 10 minutes and her change in elevation was (-) 170 feet, was her rate of change in elevation greater.
As 17 feet per minutes is greater than 11 feet per minutes.
i think it’s #1 but what’s the work?
Evaluate 49x - 2 when x = 1
Answer:
49(1) - 2 =
49x1=49
49 - 2 = 47 is your answer
Answer:
47
__________________________________________________________
SolveIf the variable, x has an assigned value, you must multiply the number behind x by the assigned value.
[tex]49 * 1 = 49[/tex]
Lastly, subtract by 2
[tex]49 - 2 = 47[/tex]
________________________________________________________
Questions?Ask me in the comments box.
SOMEONE PLEASE HELP ME WITH THIS!!
IMAGE DOWN BELOW!!
ILL GIVE YOU BRAINLIST ANSWER!!
Answer:
7.235 cm
Step-by-step explanation:
Pythagorean theory
A^2 + B^2 = C^2
A = 4.7
B = 5.5
4.7^2 + 5.5^2 = C^2
22.09 + 30.25 = C^2
√52.34 = √C^2
7.235 cm ≈ C
A department store buys 300 shirts at a cost of $8,100 and sells them at a selling price of $30 each. Find the percent markup.
Answer:
11.11%
Step-by-step explanation:
C.P = $8,100
S.P =$30 ×300
=$9,000
Markup = $9000-$8100
=$900
% markup = 900/8100 × 100
=11.11%
is 90,000 mg greater than 90 kg
Answer:
No, 90 kg is more
Step-by-step explanation:
90 Kilograms is about 198 pounds while 90,000 milligrams is about 0.198 of a pound
Answer:
No 90kg is greater
Step-by-step explanation:
1000mg= 1 g
90,000/1000= 90
100g= 1 kg
90/100= 0.9kg
