The number of possible permutations of 8 objects taken 3 at a time is 336.
The formula for PermutationThe formula to calculate the permutation of 'n' object taken 'r' at a time is [tex]P_{r}=\dfrac{n!}{(n-1)!}[/tex].
How to find the number of possible permutations?The formula for calculating the permutation is [tex]P_{r}=\dfrac{n!}{(n-r)!}[/tex] where 'n' is the number of distinct objects taken 'r' at a time.
Thus we will substitute n=8 and r=3, we will get
[tex]P_{3}=\dfrac{8!}{(8-3)!}\\P_{3}=\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5!}\\P_{3}=\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{5\times 4\times 3\times 2\times 1}\\P_{3}=8\times 7\times 6\\P_{3}=336[/tex]
So, the number of possible permutations of 8 objects taken 3 at a time is 336.
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which expression is equivalent to 7/12?
if i understand correctly what you mean by this question the answer could be
14/24
28/48
you can just keep multiplying the top and the bottom by the same number to get an equivalent fraction
im sorry if i understood the question wrong, i hope this helped a little bit
Disclaimer: The options are missing. The options to the question are:
A.7x1/12; B.7/7x12/12; C.1/7x7/12; D.12x1/7
The expression equivalent to 7/12 is 7x1/12. So, option A. is the right choice.
What are equivalent fractions?Two fractions are said to be equivalent fractions when they both give the same value in their reduced or simplest form.
How do we solve the given question?We are asked to find the expression equivalent to 7/12 from the given options.
To solve the question, we reduce all the options to their simplest form. The option = 7/12 will be our answer.
A. 7 * 1/12 = 7/12B. 7/7 * 12/12 = 1*1 = 1C. 1/7 * 7/12 = 1/12D. 12 * 1/7 = 12/7As we can see only option A. 7 * 1/12 = 7/12 in its simplest form, so it is the right option.
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Suck at maths! HELP!
Answer:
Step-by-step explanation: you can use a protractor if you have 1 or seeing as the bottom left is 65, the bottom right will be the same, mostly a guess but half 65 and try that.
solve the inequality
[tex]2(4 + 2x) \geqslant 5 + 5[/tex]
Answer:
Step-by-step explanation:
8 + 4x ≥ 10
4x ≥ 2
x ≥ 2/4
x ≥ 1/2
Dr.Chavez drew a rectangle on a coordinate plane to estimate the size of a lake. Each unit represents 1 mi. The coordinates of the rectangle are the origin, (0,7.65), (12.8, 7.65) and (12.8,0). Based on the information, what is the perimeter of the lake?
Answer:
40.9 mi
Step-by-step explanation:
The four points will make the rectangle, and each pair of points in sequence will create a side of the rectangle. So, to find the length of each side, we need to find the distances between each pair of points in sequence:
distance between (0,0) and (0, 7.65) -> |7.65 - 0| = 7.65 mi
distance between (0,7.65) and (12.8, 7.65) -> |12.8 - 0| = 12.8 mi
distance between (12.8, 7.65) and (12.8, 0) -> |0 - 7.65| = 7.65 mi
distance between (12.8, 0) and (0, 0) -> |0 - 12.8| = 12.8 mi
So the perimeter is 7.65 + 12.8 + 7.65 + 12.8 = 40.9 mi
Answer:
40.9 mi
Step-by-step explanation:
will make it simple and short
in a surveying measurements with coordinates, we always take it from the Zero. So each coordinates must be subtracted from Zero to get the length of each point.
therefore the perimeter = 0 + 7.65 + 12.8 + 7.65 + 12.8 + 0 = 40.9 mi
URGENT PlZ Help
which statement is an example of the transitive property of congruence
[tex]the \: answer \: is \: of \: option \: a \\ \\ for \: example \\ \\ if \: a = b \: and \: b = c \\ then \: we \: can \: say \: a = c \\ hope \: it \: helps[/tex]
Answer:
A is the answer
Step-by-step explanation:
The transitive property is if ABC=DEF and DEF=GHI, then ABC=GHI. The concept is the same here, just with different letters.
Lou's Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers. Determine which equation represents how much Kayla will spend on sandals after the discount. $13.50 = 0.75(x + 10) $13.50 – 10 = 0.75x $13.50 + 10 = 0.75x $13.50 = 0.25(x + 10)
Answer:
13.50=0.75(x+10)
Step-by-step explanation:
From the options given, it seems the price of either of Sandals or sneakers is given as 10 and the other is x
If Price of Sandals or sneakers=x
And the price of the other one is 10
Total price=(x+10)
25% discount is given
So she will pay 75% of the total cost
75%=0.75
Total cost =$13.50
She would pay 75% of (x+10)
Which is
0.75(x+10)=13.50
13.50=0.75(x+10)
Answer:
The answer is $13.50 = 0.75(x + 10)
Step-by-step explanation:
I am doing the assignment right now
Your Welcome :)
A sequence is defined by the recursive function f(n + 1) = –10f(n). If f(1) = 1, what is f(3)?
Answer:
f(3) = 100
Step-by-step explanation:
Using the recursive formula and f(1) = 1 , then
f(2) = - 10 f(1) = - 10 × 1 = - 10
f(3) = - 10 f(2) = - 10 × - 10 = 100
Answer:
100
Step-by-step explanation:
B. Nina buys a variety of cereal bars. The box contains 5 blueberry bars, 3 strawberry bars, and
2 apple bars. Write the ratio that represents each relationship in words, in colon form, and in
fractional form.
1. strawberry bars to blueberry bars
2. apple bars to blueberry bars
3. strawberry bars to total bars
4. apple bars to total bars
5. blueberry bars to total bars
6. apple bars to strawberry bars
Answer:
The requested ratios in words, colon form, and fraction form are:
1. strawberry bars to blueberry bars = 3 : 5 = 3/5
2. apple bars to blueberry bars = 2 : 5 = 2/5
3. strawberry bars to total bars = 3 : 10 = 3/10
4. apple bars to total bars = 2 : 10 = 2/10= 1/5
5. blueberry bars to total bars = 5 : 10 = 5/10 = 1/2
6. apple bars to strawberry bars =2 : 3 = 2/3
Step-by-step explanation:
Let's start by doing an inventory of what Nina has:
Apple bars = 2
Blueberry bars = 5
Strawberry bars = 3
Total bars = 10
The requested ratios then are:
1. strawberry bars to blueberry bars = 3 : 5 = 3/5
2. apple bars to blueberry bars = 2 : 5 = 2/5
3. strawberry bars to total bars = 3 : 10 = 3/10
4. apple bars to total bars = 2 : 10 = 2/10= 1/5
5. blueberry bars to total bars = 5 : 10 = 5/10 = 1/2
6. apple bars to strawberry bars =2 : 3 = 2/3
pls help me I need to finish it!!
Answer:
2/7
Step-by-step explanation:
7/8 ÷ 3 1/16
Change to an improper fraction
3 /16 = (16*3+1)/ 16 =49/16
7/8 ÷49/16
Copy dot flip
7/8 * 16/49
Rewrite
7/49 * 16/8
Simplify
1/7 * 2/1
2/7
how to find the distance from a velocity-time graph?
Answer:
Calculating the distance travelled
Calculate the total distance travelled by the object - its motion is represented by the velocity-time graph below.
Here, the distance travelled can be found by calculating the total area of the shaded sections below the line.
½ × base × height.
½ × 6 × 2 = 12 m 2
(10 – 6) × 2 = 8 m 2
Answer:
Calculate the total distance travelled by the object - its motion is represented by the velocity-time graph below.
Here, the distance travelled can be found by calculating the total area of the shaded sections below the line.
½ × base × height.
½ × 4 × 8 = 16 m 2
(10 – 4) × 8 = 48 m 2
Step-by-step explanation:
How fast did the truck consume its fuel?
Pro
Choose 1 answer:
Tea
60 liters per kilometer
0.6 liters per kilometer
40 liters per kilometer
0.4 liters per kilometer
Answer: 0.6 liters per kilometer
Step-by-step explanation:
(A) 475L - 50km
(B) 375L - 200km
Subtract liters.
475-375=100L
Subtract km
200-50=150km
Divide liters per km
100/150=0.6L/km
Simplify square root of c^2d^6 / square root of 4c^3d^-4
a. d^2 / 2 square root c
b. d^5 / 2 square root c
c. d^5 / 2-c
d. d^2 / 4c
Answer: B on ed, i just took my test
Step-by-step explanation:
Answer:
on edge 2021
Step-by-step explanation:
just took the test :)
Simplify 3x(2x + 4y)
Answer:
[tex]6x^2+12xy[/tex]
Step-by-step explanation:
By the distributive property:
[tex]3x(2x+4y)= \\\\3x(2x)+3x(4y)=\\\\6x^2+12xy[/tex]
Hope this helps!
Find the area of the shaded region. Can I have the steps explained please?
Answer:
76.3 cm²
Step-by-step explanation:
step 1
area of circle= πr²= 3.14*5²= 78.6 cm²step 2
area of 60° sector= 60/360*area of circle= 1/6*78.6= 13.1 cm²step 3
Area of equilateral triangle = √3/4a²= √3/4*5²= 10.83 cm²step 4
Area of circle - area of sector + area of triangle= 78.6 - 13.1 + 10.8= 76.3 cm²factorise 32 x cube minus 8 y square
Answer: [tex]8(4x^3-y^2)[/tex]
Step-by-step explanation:
[tex]32x^3-8y^2[/tex]
[tex]8(4x^3-y^2)[/tex]
If g(x)=2x-1 and h(x)= swuare root x, find (g o h) (9)
Answer:
5
Step-by-step explanation:
To evaluate (g ￮ h)(9), evaluate h(9) , then use this value to evaluate g(x)
h(9) = [tex]\sqrt{9}[/tex] = 3, then
g(3) = 2(3) - 1 = 6 - 1 = 5
How many inches are in a square foot?
Answer:
144 inches.
Step-by-step explanation:
One foot = 12 inches
One square foot = 144 inches.
Answer:
144
Step-by-step explanation:
Foot=12 inch
Square foot= foot times foot
Square foot= 12 inch times 12 inch
Square foot= 144 square inch.
If h(x)=x-7and g(x)=x^2, which expression is equivalent to(g*h)(5)?
Answer:
(g*h)(5) is g(h)=x
Step-by-step explanation:
because if h(x)=x-7 and g(x)=x^2.
Help pls! I ended up getting the wrong answer, so an explanation would help! (:
Answer:
4p squared - 28pqStep-by-step explanation:
4p(p−7q)
=(4p)(p+−7q)
=(4p)(p)+(4p)(−7q)
=4p squared −28pq
May someone please help me with this question
Answer:
2+i or 2-i (D)
Step-by-step explanation:
First you use the quadratic formula. X= (-b +/- [tex]\sqrt{b^{2}-4ac }[/tex])/2a
a=1
b=-4
c=5
X= (4 +/- [tex]\sqrt{16-20}[/tex])/2
X=(4 +/- [tex]\sqrt{-4}[/tex])/2
The square root of -4 is 2i. i=√-1. Therefore 2i= 2√-1 .If you simplify that, it becomes √-4i.
X= (4+/- 2i)/2
X= 2+/-i
X= 2+i or 2-i
which expression is equivalent to: -9x^-1y^-9/-15x^5y^-3
Answer:
3 / 5x^6y^6
Step-by-step explanation:
= -9x^-1y^-9/-15x^5y^-3
= -9y-9 / -15x^6y^-3
= -9 / -15x^6y^6
= 3 / 5x^6y^6
Answer:
b on edge
Step-by-step explanation:
Divide 21a^3-14a by -7
Answer:
A
Step-by-step explanation:
[tex]\dfrac{21a^3-14a}{-7}= \\\\\\\dfrac{-7(-3a^3+2a)}{-7}= \\\\\\-3a^3+2a[/tex]
Hope this helps!
80 people were asked which was their favourite animal.
The pictogram shows the results.
The key is missing.
Cat
a)
Which animal was the least popular?
b)
How many people does
represent?
Dog
Giraffe DDI
Monkey D.
Dolphin
c)
How many more people preferred
giraffes than dogs?
Answer:
(a)Cat
(b)8 animals
(c)6 people
Step-by-step explanation:
From the attached diagram:
Let the [tex]\square[/tex] be x.
Half of [tex]\square[/tex] =x/2
From the pictogram, we then have:
[tex]Cat = x+\frac{x}{4} \\Dog=x+\frac{3x}{4}\\Giraffe=2x+\frac{x}{2}\\Monkey =x+\frac{x}{2}\\Dolphin=3x[/tex]
Therefore:
[tex]x+\frac{x}{4} +x+\frac{3x}{4}+2x+\frac{x}{2}+x+\frac{x}{2}+3x=80\\8x+\frac{x}{4}+\frac{3x}{4}+\frac{x}{2}+\frac{x}{2}=80\\10x=80\\x=8[/tex]
So we have the following numbers
[tex]Cat = x+\frac{x}{4} =8+\frac{8}{4}=10\\Dog=x+\frac{3x}{4}=8+\frac{3*8}{4}=14\\Giraffe=2x+\frac{x}{2}=2*8+\frac{8}{2}=20\\Monkey =x+\frac{x}{2}=8+\frac{8}{2}=12\\Dolphin=3x=3*8=24[/tex]
(a)Cat was the least popular
(b) [tex]\square[/tex] represents 8 animals
(c)
Number of People who preferred giraffe=20
Number of People who preferred dogs=14
Difference=20-14=6
Therefore, 6 more people preferred giraffes than dogs.
A pictogram is a simple drawing that represents something
(a). Cat is least popular animal
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.
Let us consider that a large complete square represented by variable y .
Since, peoples whose favourite animal is cat is represented by a complete square and one fourth of square.
It means, Peoples who like cat = [tex]y+\frac{y}{4}[/tex]
Similarly,
People who like dog = [tex]y+\frac{3}{4}y[/tex]
Peoples who like Giraffe = [tex]2y+\frac{y}{2}[/tex]
Peoples who like monkey = [tex]y+\frac{y}{2}[/tex]
Peoples who like Dolphin = [tex]3y[/tex]
Since, total people = 80
Therefore,
[tex]y+\frac{y}{4}+y+\frac{3}{4}y+2y+\frac{y}{2}+y+\frac{y}{2} +3y=80\\\\10y=80\\\\y=\frac{80}{10}=8[/tex]
So, a complete large square is equivalent to 8 peoples.
Peoples who like giraffes = [tex]2y+\frac{y}{2}=2(8)+\frac{8}{2}=20[/tex]
Peoples who like dog = [tex]y+\frac{3}{4}y=8+(\frac{3}{4} ) 8=14[/tex]
So, 20 - 14 =6 more people preferred giraffes than dogs.
Thus,
(a) Cat is least popular animal
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.
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James has a bicycle. Each wheel has diameter 45cm. James cycles his bicycle in a straight line in the playground. The front wheel makes 15 complete revolutions. How far does the bicycle travel? Give your answer in metres.
Answer: 21.21 meters
Step-by-step explanation:
Hi, to answer this, first we have to calculate the circumference (C) of the wheel:
C = π x diameter
Replacing with the values given:
C = π x 45 = 141.37 cm
Then we multiply it by the number of revolutions:
141.37 x 15 = 2,120.6 cm
Since
1 cm = 0.01 m
2,120.6 x 0.01 = 21.21 meters
Feel free to ask for more if needed or if you did not understand something.
Three tickets to attend an Off-Broadway show cost $81, 4 tickets cost $108, and 5 tickets cost $135. Show that the relationship between number and the cost is a proportional relationship by making a table of tickets for 1 to 5 tickets. Show your work. Number of Tickets 1 2 3 4 5 Total Cost ($) What is the constant of proportionality, k? Write and Equation for the relationship. (Remember to state what the variables represent)
Answer:
k=27y=27xStep-by-step explanation:
3 tickets to attend an Off-Broadway show cost $81,
4 tickets cost $108; and
5 tickets cost $135.
Let the price of a ticket=k
Therefore:
3k=814k=1085k=135Solving any of the equation above gives: x=27
We therefore have:
[tex]\left|\begin{array}{c|c|c|c|c|c}$Tickets&1&2&3&4&5\\$Total Cost(\$)&27&54&81&108&135\end{array}\right|[/tex]
Let y be the total cost of x tickets
From the above, the constant of proportionality, k=27An equation for the relationship is therefore:
y=27x (where x is the number of tickets and y is the total costs (in $)).
Please help ASAP! Correct answer only! I need to finish this assignment today.
There are 9 college students running for student government class president. The candidates include 5 biology majors.
If 5 of the candidates are randomly chosen to give the first 5 speeches, what is the probability that exactly 3 of the chosen candidates are biology majors?
Write your answer as a decimal rounded to four decimal places.
Answer:
0.4762
Step-by-step explanation:
There are 9C5 = 126 ways to choose 5 candidates to give speeches. There are (5C3)(4C2) = 60 ways that 3 of those candidates can be biology majors (and the other two can be non-biology majors). The probability of interest is ...
60/126 ≈ 0.4762
__
nCk = n!/(k!(n-k)!)
use the discriminant to determine the nature of the roots of the quadratic equation
The given equation is in the form ax^2 + bx + c = 0, where
a = 2
b = -12
c = 18
Those a,b,c values are plugged into the discriminant formula below
d = b^2 - 4ac
d = (-12)^2 - 4(2)(18)
d = 144 - 144
d = 0
The discriminant is zero, so there is only one real root. This root is specifically a rational number.
The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 3km?
Answer:
47.12388
Step-by-step explanation:
Wheel Diameter = Wheel 2 x Radius; 50 cm / 2 = 25 cm.
For one rotation of the wheel, the distance travelled = circumference of the wheel.
Circumference = 2 x pi x radius = 2 x 3.1415926858 x 25 cm = 157.07 cm approx.
Distance travelled with 30 turns of the wheel = 30 x 157.07 = 4712.39cm approx.
Distance in meters = 4712.39cm / 100 = 47.12388 meters approximate (1 cm = 1/100th of a meter).
hope it helps you
The requried bicycle wheel makes approximately 1910 complete rotations over a distance of 3 km.
What is the circumference?The circumference of the bicycle wheel is equal to its diameter multiplied by π (pi).
Here
Circumference = diameter x π = 50 cm x 3.14 ≈ 157 cm
To find the number of rotations, we need to divide the distance traveled by the circumference of one rotation:
Number of rotations = Distance ÷ Circumference
Number of rotations = 300000cm ÷ 157 cm = (3000 m ÷ 157 cm) ÷ (100 cm ÷ 1 m) = 1910.82
Therefore, the bicycle wheel makes approximately 1910 complete rotations over a distance of 3 km.
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Which expression is equivalent to -36 – 8?
Choose 1 answer:
A.36 + 8
B.-36 + (-8)
C.8 – 36
D.-8+36
Answer:B
Step-by-step explanation:
-36 – 8=-44
36+8=44
-36 + (-8)=-44
8 – 36=-28
-8+36=28
As you can see only B equals -44 just like the expression given,
Hope my explanation helps
Find the surface area of a cylinder with a diameter of 4 cm, and a height of
8 cm. (use 3.14 for Pi) *
Answer:
125.66
Step-by-step explanation: