The number of ways 3 courses can be selected is 3654.
What are the Permutation and Combination?
Permutations and combinations are the various ways in which objects from a set can be selected to form subsets, generally without replacement. When the order of selection is a factor, this selection of subsets is called a permutation; when it is not, it is called a combination.
Total no. of courses available = 29
Courses needed to graduate = 3
No of ways these courses can be selected:
= ²⁹C₃
= 29!/ [(29-3)! - 3!]
= 29! / 26! 3!
= 29 * 28 * 27 * 26!/ 26! 3*2
= 29* 14* 9
= 3654
So, the number of ways 3 courses can be selected is 3654.
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Divide and state the quotient in simplest form.
[tex]\cfrac{x^2-4x-45}{x+6}\div\cfrac{x^2-3x-40}{x+6}\implies \cfrac{x^2-4x-45}{~~\begin{matrix} x+6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} x+6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{x^2-3x-40} \\\\\\ \cfrac{x^2-4x-45}{x^2-3x-40}\implies \cfrac{(x-9)~~\begin{matrix} (x+5) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{(x-8)~~\begin{matrix} (x+5) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x-9}{x-8}[/tex]
What is the unit rate for 9 pages in 3 hours? Which answer is correct?
(1): 1 page/3 hours
(2): 3 pages/1 hour
(3): 6 pages/1 hour
(4): 9 pages/3 hours
Answer:
(2) 3 pages in 1 hour
Step-by-step explanation: Simply dividing 9/3 we get, 3/1 by unitary method this is the right answer.
tinga says 6:8 is equivalent to 36:72. what did tina do wrong?
suppose there are n independent trials of an experiment with k>3 mutually exclusive outcomes, where p i represents the probability of observing the ith outcome. what would be the formula of an expected count in this situation?
The probability for observing the expected count will be given by [tex]E_i = nP_i[/tex]
Consider an experiment with n independent trials and k > 3 mutually incompatible outcomes.
Where [tex]P_i[/tex] stands for the likelihood of seeing the i-th result.
Hence for the nth expected result on i will be given by multiplying the i-th probability with the expected variable n.
Hence [tex]E_i = n\times P_i[/tex]
∴ [tex]E_i = nP_i[/tex] provides the predicted numbers for each potential outcome.
where pi is the likelihood of seeing the i-th result.
The predicted count of the i-th result is called [tex]E_i[/tex].
When two events cannot occur concurrently at the same moment, they are said to be mutually exclusive in accordance with probability theory. Or, to put it another way, discontinuous events are said to be mutually exclusive.
There is no possibility of two occurrences occurring simultaneously if they are viewed as separate events. If two events do not take place at the same time, they are said to be mutually exclusive. If a coin is tossed, the outcome will always be either head or tail; we cannot get both.
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Oliver and his little brother made up a game using coins. They flip the coins toward a cup and receive points for everyone that makes it in. Oliver starts with 16 points, and his little brother starts with 27 points. Oliver gets 2 points for every successful shot, and his brother, since he is younger, gets 1 point for each successful shot. Eventually, the brothers will have a tied score in the game. How many additional shots will each brother have made? How many points will they both have?
Oliver and his little brother will have an additional shot of 11shots and they both have 38points
What are Simultaneous equations?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 and 4x − 4y = 4.
Represent the number of additional shot made by the brothers as x and the common point made by both of them be y
therefore,
16+2x=y equation 1
27+x= y equation 2
subtract equation 1 from 2
11-x= 0
therefore x= 11
substitute 11 for x in equation 2
y = 27+ 11
y= 38
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Determine whether the pairs of functions in Problems 20 through 26 are linearly independent or linearly dependent on the real line. 20. f(x) = g(x) = cos? x + sinx 21. f(x)=x,8() = x+|x| 23. f(x) = xe", g(x) = |x|e" 22. f(x) = 1 + x, 8(x) = 1 + x 24. f(x) = sinx, g(x) = 1 - cos 2x 25. f(x) = e sinx, g(x) = e* cos x 26. f(x) = 2 cos x + 3 sinx, g(x) = 3 cos x - 2 sin x
The pairs of function which are linearly independent are f(x) = 2cos x + 3 sin x and g(x) = 3cox x - 2 sin x.
We need to determine the pairs of functions are linearly independent or linearly dependent on the real line
f(x) = 2cos x + 3 sin x
g(x) = 3cox x - 2 sin x
Let c₁f(x) and c₂g(x) = 0
using wornkskin method
w(f, y) = [tex]\left[\begin{array}{cc}f(x)&g(x)\\f'(x)&g'(x)\\\end{array}\right] \\\left[\begin{array}{cc}2cosx + 3sin x&3cos x - 2 sin x\\-2sin x + 3 cos x&-3sin x - 2 cos x\\\end{array}\right][/tex]
= - (2cos x + 3sin x) (3 sinx + 2 cos x) - (3cos x - 2sin x) (3cos x - 2sin x)
= - (9sin²x + 4cos² x + 12cos x sin x) + 9cos² x + 4 sin² x - 12 sin x cos x
= - (13 sin² x + 13 cos² x )
= - 13
since,
w(f , g) ≠ 0
f, g are linearly independent
Therefore, the function f(x) = 2cos x + 3 sin x and g(x) = 3cox x - 2 sin x are linearly independent.
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a store sold a case of scented candles for $ 17.85 that had been marked up 110 % what was the original price
The original Price of a case of scented candles was 8.5
What is percentage increase?A percent increase refers to how much a percentage has gone up over time.
In order to reach this number, you would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease.
The formula for calculating Percentage increase is:
(ΔPrice/Original price) × 100
change in price (new price - original price)/original price) × 100
From the question:
Percentage increase = 110%
New price = 17.85
Original price = X
so it we can substitute in the formula
((17.85 - X)/X) * 100 = 110%
Opening brackets
(17.85*100 - X*100)/ X =110
1785 - 100X = 110X (we balance the equation)
(we collect like terms)
1785 = 210X
to find X we divide both sides by 210
1785/210 = X
8.5
The original Price was $8.5
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f(x) = −2|x + 4|; h(x) = f(-x) describe the transformation
The vertex of the function is transformed from (-4,0) to (4,0). The expression will be transformed from f(x) = −2|x + 4| to h(-x) = -2|-x + 4|.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the absolute function is f(x) = −2|x + 4|. The transformed function is calculated as,
f(x) = −2|x + 4|
h(-x) = −2|-x + 4|
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the following data on price ($) and the overall score for 6 stereo headphones that were tested by consumer reports were as follows. brand price ($) score bose 180 72 scullcandy 150 78 koss 96 66 phillips/o'neill 72 54 denon 72 42 jvc 48 24 a. does the t test indicate a significant relationship between price and the overall score?
There is significant relation between price and overall score.
Given that,
Following are details on the cost ($) and final rating for the six stereo headphones that Consumer Reports examined. ($) brand price Score: Bose 180, 72 Scullcandy 150, 78 Koss, 96, 54 Phillips/O'Neill, 72, 42 Denon, 48, 24.
a) t =3.54
The P value is less than 0.2
There is significant relation between price and overall score.
P value is between 0.01 and 0.025.
Because p value is less than or equal to 0.05 , we reject H₀ : β₁ is equal to zero.
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convert these unlike fractions to equivalent like fractions and add them. you must use the lcd to get the answer correct. if possible, reduce the final sum.1523
The simplest form expression for the addition of the fractions given using the lowest common multiple of the denominator is 2/3.
A fraction is a numerical value that is a part of a whole. It is evaluated by dividing a whole into a number of parts.In Mathematics, a fraction is defined as a part of the whole thing. For example, ½ represents half of a whole number or a thing
Given the fractions :
1/4 + 5/12
The lowest common multiple of the denominator ;
A lowest common multiple of 4 and 12 = 12
1/4 + 5/12 = (3 + 5) / 12
1/4 + 5/12 = 8/12
Expressing in simplest form :
8/12 = 2/3
Therefore, the simplest form expression of the addition is 2/3
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you observe 40 crickets on an island after crickets were first introduced 2 years ago. at how many crickets must have been introduced?
Crickets must have been introduced at the lambda = 2 is 20.
Given:
you observe 40 crickets on an island after crickets were first introduced 2 years ago , at the lambda = 2 how many number of crickets must have been introduced .
Let x be the crickets must have to been introduced.
Number of crickets = observed crickets / lambda value
we know that,
Observed crickets = 40
lambda value = 2
substitute these values
Number of crickets = observed crickets / lambda value
= 40 / 2
= 20 crickets.
Therefore Crickets must have been introduced at the lambda = 2 is 20.
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Full question:
you observe 40 crickets on an island after crickets were first introduced 2 years ago. at lambda = 2 how many crickets must have been introduced?
jaime is preparing for a bicycle race. his goal is to bicycle an average of at least 280280280 miles per week for 444 weeks. he bicycled 240240240 miles the first week, 310310310 miles the second week, and 320320320 miles the third week. which inequality can be used to represent the number of miles, xxx, jaime could bicycle on the 4^\text{th}4 th 4, start superscript, start text, t, h, end text, end superscript week to meet his goal?
The inequality that can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal is 240 + 310 + 320 + x ≥ 4 (280).
What is inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.
For the next four weeks, Jaime wants to log at least 280 miles per week on average. Jamie's objective can be graphically expressed by the inequality: T4, or alternatively T 4 if T is the total number of miles he will pedal his bicycle for four weeks (280).
The sum of the distances Jamie has covered and has yet to cover is the total number of miles Jamie will cycle during this time. Hence, T = 240 + 310 + 320 + x. Replacing this term into the inequality T ≥ 4(280) gives 240 + 310 + 320 + x ≥ 4(280). Therefore, choice D is the correct answer.
Thus, the correct answer is 240 + 310 + 320 + x ≥ 4 (280).
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Software companies work hard to produce software without bugs. A particular company claims that 85% of the software it produces is bug free. A random sample of size 200 showed 156 softwareprograms were bug free.
a. Calculate the mean of the sampling distribution of the sample proportion.
the sample proportion under probability has a mean sampling distribution of 82.
The population percentage is the major variable in the sampling distribution of this proportion, which has a quarter-um normal distribution. Variants include population proportion times one and population proportion divided by sample size. Additionally, we are aware that the population proportion is under the null hypothesis. 200 is the sample soil. When we enter the value of P into this calculation without normalisation, we can obtain the standing ovation as the variance's root. 025 in excess. The probability that we got a sample result of 188/58 or less is then calculated. We simply need to determine this left tail probability after that.
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a pair of fair dice is cast. what is the probabiliy that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even? a) 0.4545 b) 0.3056 c) 0.3667 d) 0.2778 e) 0.1389 f) none of the above.
The probability that at least one of them is a 1 is 0.2778 when a fair set of dice is thrown and the total of the numbers falling above them is even.
Given that,
A fair set of dice is thrown.
We have to find given that the total of the numbers falling above them is even, what is the probability that at least one of them is a 1.
We know that,
A fair set of dice is thrown.
The total of the numbers falling above them is even.
The probability that at least one of them is a 1 is
(5/36)/(8/36)
5/18
0.2778
Therefore, The probability that at least one of them is a 1 is 0.2778 when a fair set of dice is thrown and the total of the numbers falling above them is even.
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Find the area of the figure. 16 cm 9 cm
REALLY EASY!! BRAINIEST FOR THE FASTEST AND THE CORRECT ANSWER! NO NEED TO EXPLAIN! I WILL REPORT IF WRONG OR IF YOU COPIED AN ANSWER
Answer: 26%
Step-by-step explanation:
23 + 52 + 34 + 61 + 30 = 200
do 52/200 because theres 52 gumballs and times it by 100
52/200 x 100 = 26% on calculator
(- 9x³-7x²-3x - 1) − (6x³ + 5x² + 2x + 2)
Find the difference
Answer:
(-15x^3 -12x^2 -5x-3)
Step-by-step explanation:
You can't add/subtract numbers that have different exponent numbers so you have to stick with the ones that have the same number
So then the coefficients would be:
x^3 : -9 - 6 = -15
x^2 : -7 -5 = -12
x: -3 -2 =-5
0: -1 - 2 = -3
Tammy has $20 to spend at the movie theater. She spends $9.50 on a movie ticket. If the snack counter sells bags of candy for $3.50 each, how many bags of candy can Tammy buy with the money she has left?
Answer:3
Step-by-step explanation:
20-9.50=11-3.50
Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 45 bacteria are present o begin with the total number present after a days is f(x) = 45 - 64* Find the total number present after 1, 2 and 3 days. There will be bacteria present after 1 day, after 2 days and after 3 days.
A certain bacteria strain needs 4 hours to double its population. If in the beginning there are 45 bacteria, after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.
The problem can be solved using the exponential growth model.
In the given problem, the formula for the growth model is given, that is:
f(x) = 45 (64)^(x)
Where:
f(x) = total number of bacteria present after x days
To find f(x) for 1 day, 2 days, and 3 says, substitute x = 1, x = 2, and x = 3 into the formula.
f(1) = 45 (64)¹ = 2,880
f(2) = 45 (64)² = 184,320
f(3) = 45 (64)³ = 11,796,480
Hence,
after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.
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Find the Sum.
1/6+2/3=?
Answer:
5/6
Step-by-step explanation:
1. Line up the fractions
1/6
+ 2/3
_____
2. Find the common denominator
1/6 x 1/1
+ 2/3 x 2/2
_____
Thus, we get:
1/6
+ 4/6
_____
3. Add
1/6
+ 4/6
_____
5/6
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 5 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
5/6 which is also 0.833
Step-by-step explanation:
(The whiteboard below)
which of the following expressions are equivalent to…
Answer: none of the above
Explanation: as it's - -8/-4 it means the answer is negative which none of the answers provided are so it's none of the above
Find the length of the third. If necessary, round to the nearest tenth 18 12
Answer:
Since it appears that you are talking about a triangle, if the third side that you are looking for is the hypotenuse, then you can use the Pythagorean theorem, a^2 + b^2 = c^2. In this case, the length of the side, if it would be the hypotenuse, would be approximately 21.63.
Step-by-step explanation:
Hope this helped! :D
A right triangle has one angle that measures 54°. What is the measure of the other acute angle?
Answer: 36
Step-by-step explanation:
Since all triangle angles add up to 180 we just add up both the angle measure we know and then subtract by 180.
54+90=144
180-144=36
The acute angle measure is 36 degrees.
answer:
36 degrees
step-by-step explanation:
all the angles of a triangle add up to be 180 degrees. so subtract 90 and 54 degrees to get the answer. hope that helps!
g 2. the following series can be written with a shorthand form of sigma notation (a). use for loop syntax to calculate this arithmetic series: ; n
Using for loop we can get the syntax in order to calculate this arithmetic series n is A = 0.9999.
An arithmetic collection is the sum of the phrases in an mathematics collection with a specific range of phrases. Following is a easy system for locating the sum: Formula 1: If S n represents the sum of an mathematics collection with phrases.
This system calls for the values of the primary and ultimate phrases and the range of phrases. Finite Sequence- Finite sequences have countable phrases and do now no longer cross as much as infinity. An instance of a finite mathematics collection is 2, 4, 6, 8. Infinite Sequence- Infinite arithmetic collection is the collection wherein phrases cross as much as infinity.
using while
A=0; n=1; while n<=10000 A=A+(1/(n*(n+1))); n=n+1; end A
output
A = 0.9999
using for loop
A=0; for n=1:10000 A=A+(1/(n*(n+1))); end A
output
A = 0.9999.
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Correct Question:
The following series can be written with a shorthand form of sigma notation (A). Use while syntax to calculate this arithmetic series:
1/(1x2) + 1/(2x3) + 1/(3x4) + ... + 1/(n x (n+1)) ......1
A = ∈ 1/(n x (n+1)); n=[1:10000]
Find an expression which represents the difference when (2x − 6) is subtracted
from (7-5) in simplest terms.
Answer:
-2x + 8
Step-by-step explanation:
(2x - 6) is subtracted from (7 - 5).
First term that into an equation.
Because our first term is being subtracted from our second one, our equation is written as:
(7 - 5) - (2x - 6).
Simplify the first term by subtracting:
7 - 5 = 2
Now simplify the second term by multiplying 2x - 6 by -1 to get them out of the parenthesis. We do this because there is a negative sign in front of it.
-1 (2x - 6)
-2x + 6
Now our equation is:
2 - 2x + 6
Combine like terms:
2 + 6 = 8
So -2x + 8
(2x - 6) subtracted from (7 - 5) is -2x+8
(b)(3) an annealing process is provided for the sample after cold work, what are the three stages during annealing (in sequence)?
The three stages of an annealing process in the sequence is recovery, recrystallisation, and gain growth.
Sequence:
In math, a series is defined as the sum of the elements of a sequence.
Given,
Here we need to find the are the three stages during annealing when an annealing process is provided for the sample after cold work.
In order to find the stages of the annealing process, first we have to know the definition of annealing process,
A process which is used to enhance ductility and counter the increase in hardness by cold working is known as annealing.
This one is to deal with residual stresses we first can reheat the glass to a high temperature known as annealing point and let it cool slowly so that the outside and inside cool at about the same rate.
And the resultant will have little to no residual stresses making annealed glass.
In the first stage recovery stage of annealing recovers the physical properties of the metals.
Second stage is recrystallisation, and gain growth.
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What’s higher -12 or -24
The length
17inches
more than half of its width. Which expression
represents the area of Nadine's new bed?
A) L+17
B) L + 34
C)2L² - 34L
D)2L² – 34
Answer:
C
Step-by-step explanation:
length = 17 + width/2
2×length = 34 + width
width = 2×length - 34
area of a rectangle
length × width = length × (2×length - 34) =
= 2×length² - 34×length
which is the answer option C.
7. towers a lookout tower sits on a network of struts and posts. leslie measured two angles on the tower. if m∠1=7x-7°, m∠2=4x 2°, and m∠3=2x 6°, what is m∠1?
The measure of the ∠1 for the given angles of the triangle are found as 1162/13.
Explain the angle sum property of the triangle?The internal angle of a triangle is just the angle formed by two of its sides. It is often referred to as the triangle's interior angle property. Because of this characteristic, a triangle's interior angles add up to 180 degrees.The given angles are-
∠1 = 7x - 7.
∠2 = 4x + 2
∠3 = 2x + 6
By the angle sum property of the triangle.
∠1 + ∠2 + ∠3 = 180
Thus,
7x - 7 + 4x + 2 + 2x + 6 = 180
Simplifying,
13x = 179
x = 179/13
So, ∠1 becomes-
∠1 = 7x - 7
∠1 = 7(179/13)- 7
∠1 = 1162/13
Thus, the measure of the ∠1 for the given angles of the triangle are found as 1162/13.
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I’m wondering why my teacher marked me wrong on these two problems. Was there something in my work that was wrong?
(Just check 1 and 2)
On #1, you used the side of 18 twice.
You should have had
[tex]\dfrac{40.5}{18}=\dfrac{49.5}{22}=\dfrac{54}{\boldsymbol{24}}[/tex]
with 24 in that last denominator. And with 24 in the last denominator, they're all equal to 2.25.
On #2, you should have compared 90 to 40 and then 81 to 36:
[tex]\dfrac{90}{40}=\dfrac{81}{36}[/tex]
Those are both equivalent to 9/4.