Answer:
a) 840 different ways
b) 35 different choices of books
Step-by-step explanation:
We know that our literature class will read a total of 4 novels this year.
All novels chosen by class vote from a list of 7 possible books offered by the teacher.
Wherever we have an experiment [tex]''N''[/tex] which is formed by sub - experiments that can occurred in [tex]m_{1},m_{2},...,m_{n}[/tex] ways, the total number of ways in which the whole experiment [tex]''N''[/tex] can be developed is :
[tex]m_{1}[/tex] x [tex]m_{2}[/tex] x ... x [tex]m_{n}[/tex]
Then, for a) if it matters what order we read the books in, the total number of different ways could the course unfold is :
[tex](7).(6).(5).(4)=840[/tex] (I)
Because for the first book there are 7 different choices. Now, given that we choose the first book, we only have 6 different choices for the second one.
Continuing with the idea, we deduce the equation (I).
For item b) :
Wherever we have [tex]''n''[/tex] different objects and we want to find the ways that we can choose [tex]''r''[/tex] objects from that group, we need to use the combinatorial number.
We define the combinatorial number as :
[tex]nCr=\left(\begin{array}{c}n&r\end{array}\right)=\frac{n!}{r!(n-r)!}[/tex]
Then, if we apply this to the problem, the total different choices of books if we want 4 novels voting from a total of 7 possible books is :
[tex]7C4=\frac{7!}{4!(7-4)!}=35[/tex]
a) 840 different ways
b) 35 different choices of books
A store at the beach sells t-shirts for $19.99. If the shirts are 35% off, what is the amount of the discount
find the area of the circle round your answer to the nearest hundred
Answer:
what are the numbers shown?
43/(-12 + 22
( (2 x 3)2 + (-5 x 2 x 3) + 2
Give your answer in simplest form.
Answer:
I think it is -1
Step-by-step explanation:
Simplify the problem first.
Let's start with the numerator.
FYI, this, ^, means raised to the power of.
4^3 = 64
-12 + 2^2 = -12 +4 which equals -8
64/-8 = -8
Now simplify the denominator.
(2*3)^2 = 6^2 which equals 36.
-5*2*3 = -10*3 which equals -30
Then add the 2 to the end.
36 + (-30) + 2 = 6 + 2 which equals 8. This is the denominator.
Your fraction now is:
-8/8
Simplify this and you will get -1 as the simplest form.
Please forgive me if this is incorrect.
9514 1404 393
Answer:
-1
Step-by-step explanation:
A suitable calculator can find the value for you.
[tex]\dfrac{4^3/(-12+2^2)}{(2\times3)^2+(-5\times2\times3)+2}=\dfrac{64/(-12+4)}{6^2+(-5\times2\times3)+2}=\dfrac{64/(-12+4)}{36+(-5\times2\times3)+2}\\\\=\dfrac{64/(-8)}{36+(-30)+2}=\dfrac{-8}{6+2}=\boxed{-1}[/tex]
Please help its7to10 I be waiting like two hours
Answer:
Please check the explanation!
Step-by-step explanation:
Important factors to remember regarding the like terms:
'Like terms' are terms whose variables such as 2x and 6x are the same. Also if the variables contain the exponents such as 4 in x⁴, they must be the same too.Since the coefficient doesn't affect likeness, therefore we can say that all constant terms would be treated as the like terms.Question 7
Given the terms
2b b⁶ b x⁴ 3b⁶ 2x²
From the list of terms, there are two groups of like terms which are:
2b b (Like terms containing the variable b)
b⁶ 3b⁶ (Like terms containing the variable b with the same exponents)
The remaining two x⁴ and 2x² terms are different from each other and the rest of the termsQuestion 8
Given the terms
6 2n 3n² 3m² n/4 7
From the list of terms, there is one group of like terms which are:
6 7 (Constants Like terms)
2n n/4 (The terms with the same variable n)
All the remaining terms such as 3n², 3m² are all different from each other and the rest of the terms.Question 9
Given the terms
10k² m 3³ p/6 2m
From the list of terms, there are there is one group of like terms which are:
m 2m (The terms withe same variable m)
All the remaining terms such as 10k², 3³, p/6 are all different from each other and the rest of the terms.Question 10
Given the terms
6³ y³ 3y² 6² y 5y³
From the list of terms, there are two groups of like terms which are:
y³ 5y³ (The terms withe same variable m and exponent)
6³ 6² (Constant like terms. Plz don't confuse the power as all are the same constant terms)
All the remaining terms such as y and 3y² are all different from each other and the rest of the terms.If QS and TV are parallel lines and m<QRU=127, what is m<TUW? HELP ASAP
Based on the corresponding angles theorem, m<TUW = 127°.
What is the Corresponding Angles Theorem?If two angles on two parallel lines that are cut across by a transversal are corresponding to each other, the corresponding angles theorem states that they are congruent to each other.
Given:
m<QRU = 127
Angles QRU and TUW are corresponding angles. Therefore:
m<TUW = m<QRU = 127° [corresponding angles theorem]
m<TUW = 127°
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6.What is the radius of the circle?
Answer:
Radius is half the diameter of a circle
Step-by-step explanation:
If the diameter was 6, then the radius is 3
In this polygon, which angle is an interior angle?
pls answer 20 points
A. c°
B. a°
C. b°
D. d°
Answer:
Step-by-step explanation:
D
Answer:
C
Step-by-step explanation:
I took the quiz and got it correct
Perform the indicated operations:
-1
4
-4
4
-4
-1
6
-7
-4
-7
-4
2R2 + R3 R3
-4
6
2
-4
8
2
6
-4
30
Answer:
Step-by-step explanation:
The solution is, resulting matrix:[tex]\left[\begin{array}{ccc}4&-1&-4\\-4&6&2\\0&8&10\end{array}\right][/tex][tex]\left[\begin{array}{ccc}-7\\-4\\22\end{array}\right][/tex].
What is Matrix?In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns.
here, we have,
given that,
We are given a matrix,
Let A=[tex]\left[\begin{array}{ccc}4&-1&-4\\-4&6&2\\8&-4&6\end{array}\right][/tex]
and B=[tex]\left[\begin{array}{ccc}-7\\-4\\30\end{array}\right][/tex]
We have to find the resulting matrix after performing given row operations
2R2 +R3 ⇒ R3
Apply
we get,
:A=[tex]\left[\begin{array}{ccc}4&-1&-4\\-4&6&2\\0&8&10\end{array}\right][/tex]
and, B=[tex]\left[\begin{array}{ccc}-7\\-4\\22\end{array}\right][/tex]
Hence, resulting matrix
[tex]\left[\begin{array}{ccc}4&-1&-4\\-4&6&2\\0&8&10\end{array}\right][/tex][tex]\left[\begin{array}{ccc}-7\\-4\\22\end{array}\right][/tex]
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Is 3 x 1/2 greater than 5?
HELP For each triangle, find x and the measure of each side.
△FGH is an equilateral triangle with FG = x +5, GH = 3x – 9, and FH = 2x –2.
I DID ALGEBRA LAST YEAR HOW AM I SUPPOSED TO REMEMBER THIS AHHH
Answer:
5
Step-by-step explanation:
x-y> -3
2x + y<6
help plsss it’s for a quiz it’s algebra 2
Answer:
Hello!
Step-by-step explanation:
Ok so for X-y> -3, there are no solutions and for 2x + y<6, there are also no solutions. Hope this helped!
The weather forecast calls for a total of 16 inches of snow over the next week. If it is estimated that 2.8 inches of snow will fall on Monday, 3.4 inches of snow will fall on Tuesday, 1.6 inches of snow will fall on Wednesday, 2.1 inches of snow will fall on Thursday, 1.7 inches of snow will fall on Friday, and 2.9 inches of snow will fall on Saturday. How much snow should fall on Sunday?
A.
3.2 inches
B.
3.6 inches
C.
1.5 inches
D.
0.5 inches
A swim coach wants to test whether practicing with swim paddles improves swimmers' breaststroke times in the 100-
meter relay race. He asks the first member of the relay team to continue swimming without paddles. He asks the other
three members of the relay team to swim with paddles for two weeks. He records the swim times of the relay teams with
and without paddles. Which group of an experiment are the other three members of the relay team part of?
-single-blind
-confounding
-control
-experimental
Answer: experimental
Step-by-step explanation:
In a research design such as the one described in the scenario above, participants are separated into two distinct groups. The hypothesis (if swimming with paddles is faster than without paddles) being tested is applied on one of the two groups while the other group remains as before. Hence, the group which receives the treatment which is to be tested (those who swim with paddles) are called the experimental group. The other group of participants who continue to swim without paddles are the control group.
Hence, the other group of three member who were asked to swim with paddles for two weeks are the experimental group because they are the ones who received the actual treatment in the experiment.
A __________ names part of a whole, part of a set,
or a location on a number line.
A: decimal
B: fraction
Answer:
Fraction
Step-by-step explanation:
Tell me if im wrong
Answer
in this case its a fraction
Step-by-step explanation:
the give away in this question is that it says part of a whole. this just means what amount of the whole. for example 1/2
pls mark brainleist
WHAT IS THE PRODUCT OF 6 NEGATIVE AND 12 POSITIVE
INTEGERS
Answer:
-72
Step-by-step explanation:
-6*+12=-72
because - x + = -
Answer:
-72
Step-by-step explanation:
6×-12
-72 (because a×-a=-a)
The table shows which equation?
Answer:
C. I think I'm not sure
Step-by-step explanation:
PLEASE HELP ILL GIVE YOU DA BRAINLIESTTTTT
Answer:
x=2, And i think the 2nd one is reflexive
Step-by-step explanation:
Sometimes two transformations, one performed after the other, have a nice description as a single transformation. For example, instead of translating 2 units up followed by translating 3 units up, we could simply translate 5 units up. Instead of rotating 20 degrees counterclockwise around the origin followed by rotating 80 degrees clockwise around the origin, we could simply rotate 60 degrees clockwise around the origin.
Can you find a simple description of reflecting across the x-axis followed by reflecting across the y-axis?
Answer:
We rotate the point counterclockwise by an angle θ = tan⁻¹ (y/x)
Step-by-step explanation:
If we have the point (x, y), its reflection along the x-axis (x,-y). The reflection of the point (x, -y) along the y - axis is (-x, -y). So, the angle between the initial point (x, y) and the final point (-x, -y) is θ = tan⁻¹ [(-y - y)/(- x -x)] = tan⁻¹ [(-2y/(-2x)] = tan⁻¹(y/x).
So, the point (x, y) is rotated counterclockwise by an angle of θ = tan⁻¹ (y/x) to perform both reflections.
4 movie tickets cost $48. At this rate, what is the cost of 8 movie tickets?
Answer:
$60
Step-by-step explanation:
48/4=12
12*8=60.
So you'd pay 60 dollars for 8 movie tickets. ^^
PLEASE HELP ASAP 20 POINTS WILL GIVE BRAINLIEST
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Wind farms are a source of renewable energy found around the world. The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second). If a turbine generates 500 kW in a 10 m/s wind, how much power does it generate in a 12 m/s
wind?
Answer: P = 0.5 *(12)^3 = 864 kW
Step-by-step explanation:
We calculate the power as follows:
P=C*v^3,
where C = constant and v is the velocity,
lets find the C first, from the given conditions
P = C*v^3
500= C(10)^3
C=500/(10)^3 = 0.5
If a turbine generates 500 kW in a 10 m/s wind, then 864 KW power does it generate in a 12 m/s wind
What is Power?Power is the amount of energy transferred or converted per unit time.
Given,
The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v
P = kv³
Where k is the proportionality constant.
If a turbine generates 500kW in a 10m/s wind, we need to find how much power does it generate in 12m/s wind
first solve the proportionality constant k
500 = k (10³)
k = 500 / 10³= 0.5
so when v = 12 m/s
P = 0.5(12³)
p = 864 kW
Hence 864 kW is the power generated by a 12 m/s wind.
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I have never really watched anime but I have been thinking to start watching it soooo does anyone have suggestions?
Answer:
yeah watch my hero academy One punch man n Naruto also Dragon Ball Z
Answer:
It’s not really an amine but avatar the last airbender
Step-by-step explanation:
Attack on titan
One punch man
the devils a part-timer
HELP ME PLZZ SOMEONE DONT JUST ANSWER RANOMELLY I REALLY NEED HELP !!!!
Frankenstein is definitely a classic and he can still manage to get a few scares, but the also classic Werewolf has seen better days. The Werewolf is often the target of scares and has an equation perpendicular to Frankenstein's. Frankenstein's equation is`y=x+5` and the Werewolf's equation passes through the point `\left(-1,-2\right).` What is the Werewolf's equation?
Answer:
y = - x - 3Step-by-step explanation:
Given
Equation y = x + 5Perpendicular line that passes through the point (-1, -2)Perpendicular line has negative reciprocal slope, so the slope is -1
The line in slope-intercept form is:
y = -x + bUsing the given point, finding the y-intercept:
-2 = -(-1) + b-2 = 1 + bb = -2 - 1b = -3So the Werewolf's equation is:
y = - x - 3A store is advertising a 25% off sale. Mikale purchases a swimming pool for $225. What was the original price of the pool?
A.
$450.75
B.
$300.00
C.
$655.50
D.
$281.25
Answer:
B
Step-by-step explanation:
Stephanie started selling earrings online at a handmade shop. She makes a profit of $8.50 on each pair of earrings. If she wants to make a profit of no less than $765 this month, how many pairs of earrings does she need to sell? Write and solve an inequality to model this solution.
Answer:
90 pairs
Step-by-step explanation:
We can use clues from the problem in order to set up our inequality.
First, we know that a pair of earrings, [tex]p[/tex], costs $8.50. So, we can say that [tex]8.5p=[/tex] total profit.
That's a function we could use, but we need an inequality. Well, it says that Stephanie wants to make no less, or at least $765. This indicates that we need the 'greater than or equal to' symbol. Just replace the equal sign:
[tex]8.5p\geq 765[/tex]
Now we can isolate [tex]p[/tex] to find how many earrings she needs to sell to make a profit of at least $765.
[tex]8.5p\geq 765\\\\p\geq \frac{765}{8.5}\\\\p\geq 90[/tex]
Stephanie needs to sell at least 90 pairs of earrings.
Hope this helps!
is this relation a function? justify your answer.
please help!
Answer:
C
Step-by-step explanation:
No, because you can not use the same X more than once. It has to pass the vertical line test. So it'll be option C
plz I need help!!! will give brainlyyyyy
Find the unit rate. Round to the nearest hundredth, if necessary.
$4.99 for 18 lb
The unit rate is $ ? /lb.
Answer:
4.99 divided by 18
0.277222222
Rounded to $0.28
What value of x satisfies the equation below? Explain
how you know
- 6x=
36
Answer:
-6 because -6 times -6 is a positive 36 negative times negative is positive
Step-by-step explanation:
Answer:
x = -6
Step-by-step explanation:
Okay so basically. The "-6" and the fact that the answer is a positive number shows that X must be a negative number. So let us set "-6" as a positive number. Divide 36 by 6 and the answer is = 6. Add a negative sign and X is -6.
Below are two parallel lines with a third line intersecting them
Answer:
Z is 66. If you want an explanation, I could give it to you, FYI.
Answer:
x=66°
Step-by-step explanation:
Solve for x:
If the two vertical lines are parallel, then the given angles are same side interior angles that are supplementary angles. This means that their values add up to 180°:
∠1+∠2=180°
Substitute known values:
[tex]x+114=180[/tex]
Subtract 114 from both sides to isolate x:
[tex]x+114-114=180-114\\\\x=66[/tex]
The value of x is 66°.
:Done
What is the result of F (X) = - 3 × -3
Hello There this is your answer
and hope you a GREAT Thanksgiving :)
F ( X ) = 9