If each collection consists of at most 3 books on each subject, the number of collection that can be made of 3 English, 4 Economics, and 5 Business Mathematics books are 40.
What is a combination?A combination, as a mathematical technique, determines the number of possible arrangements in a collection of items.
In the combination, the order of the selection does not matter.
The implication is that in combinations, one can select the items in any order, unlike permutations, where the order of selection matters.
Data and Calculations:English books on shelf = 3
Economics books on shelf = 4
Business Mathematics books on shelf = 5
Collections to be made = 3 books on each subject
The solution can be set up as a combination problem, as follows:
3 C 3 x 4 C 3 x 5 C 3
3! / 3! (3 – 3)! The solution is 1.
4! / 3! (4 – 3)! The solution is 4.
5! / 3! (5 – 3)! The solution is 10.
1 x 4 x 10
= 40
Thus, if each collection consists of at most 3 books on each subject, the number of collections that can be made of 3 English, 4 Economics, and 5 Business Mathematics books is 40.
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p, q and r are prime numbers such that pqr3=270.
Work out the values of p, q and r.
b. Work out the highest common factor of 270 and 105.
The highest common factor of 270 and 105 is 15.
How to find the highest common factorfinding the prime factorization of 270.
The prime factorization of 270 can be written as:
270 = 2 * 3^3 * 5
From the equation pqr^3 = 270, we can see that p, q, and r are prime numbers. Therefore, p must be 2, q must be 3, and r must be 5.
So the values of p, q, and r are:
p = 2
q = 3
r = 5
Moving on to part B, let's work out the highest common factor (HCF) of 270 and 105.
The prime factorization of 270 is:
270 = 2 * 3^3 * 5
The prime factorization of 105 is:
105 = 3 * 5 * 7
To find the HCF, we need to find the common factors and choose the highest one.
The common factors of 270 and 105 are 3 and 5.
The highest common factor of 270 and 105 is 3 * 5 = 15.
Therefore, the highest common factor of 270 and 105 is 15.
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14. The graph below represents the number of books checked out at a library. What
is the constant of proportionality (unit rate per hour)?
The required constant of proportionality is 5.
A graph is shown, we have to find out the constant of proportionality.
In the given case, the constant of proportionality is given by the slope of the curve.
So, the slope is given as,
m = rise/run
From the graph put the value for any point, we choose (2, 10)
So,
m = 10/2
m = 5
Thus, the required constant of proportionality is 5.
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A TV station is going to air a movie marathon with 11 movies. It will consist of 6 science fiction movies and 5 horror movies. The horror movies will be aired later in the evening. So, all of the horror movies will be aired last (after all of the science fiction movies). In how many ways can the station air the movie marathon?
The solution is: In 86400 ways can the station air the movie marathon.
Given:
Number of total movies = 11
Number of science fiction movie = 6
Number of horror movie = 5
Computation:
Number of science fiction movies way air = 6!
so, we get,
Number of science fiction movies way air = 720
Number of horror movies way air = 5!
so, we have,
Number of horror movies way air = 120
The number of ways the station air the movie marathon is:
720 * 120
=86400
so, we get,
Final answer is 86400 ways.
Hence, The solution is: In 86400 ways can the station air the movie marathon.
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Harper recorded the heights of plants, in inches, as shown in the table.
nd the mean of the data.
11 12 13 14 15 16 17 18 19 20 21
Heights of Plants (in.)
The mean height of the plants whose heights are shown by the data set is 16 in.
Calculation of meanTo find the mean:
Sum of the values = 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 176
Total number of values = 11 (since there are 11 values in the data set)
Mean = Sum of the values / Total number of values
= 176 / 11
= 16
In other words, the mean of the given data set is 16 in and thus, the mean height of the plant is 16 in.
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PLEASE HELP ON VOLUME! ASAP❗️ I BEG❗️❗️❗️
The volume of the cylinder A = 1006.76 m³
The volume of the cylinder B = 2893.82 ft³
The volume of the cylinder C = 2712.96 in³
The volume of the cylinder D = 111.78 in³
The Volume of the cylinder = πr²h
Where r = radius , h = height
A) r = 15/2 = 7.5
h = 5.7
Volume = 3.14 × (7.5)² × 5.7
Volume = 1006.76
B) r = 8
height = 14.4
Volume = 3.14 × (8)² × 14.4
Volume = 2893.82
C) r = 6
h = 24
Volume = 3.14 × (6)² × 24
Volume = 2712.96
D) r = 2
h = 8.9
Volume = 3.14 × (2)² × 8.9
Volume = 111.78
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Which point is located at 2,1
Answer: Point P
Step-by-step explanation: over 2 up 1 (2,1)
Answer: M
Step-by-step explanation:
What is the total cost of 20 books at R25 each?
Answer:
R500
Step-by-step explanation:
20 books x R25 each = R500.
The scatterplot above displays the relationship between the amount of food hippopotamuses eat per day and their age. Describe and explain any associations and data features on the scatterplot. Then, use the variables on the graph to interpret the relationship that is shown.
The scatter plot shows a [positive linear] association.
How to determine the association of the scatterplotFrom the question, we have the following parameters that can be used in our computation:
The image of the scatter plot
On the scatter plot, we can see that
The points appear to be on a straight line
Also, we can see that
As the x values increases the y values increases
This represents a positive linear association.
Hence, the association is a positive linear association.
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c) Mrs. Chamling earns Rs 6,000 in a week. She spends Rs 250 for food Rs 75 for transportation everyday. (i) Write a mathematical expression to show this information. (ii) How much money does she save in a week? Cl LC and she divided the In this way, whole prime and compos of numbers, set of are the subset of 3.2 Prime and Prime numbe
(i) The mathematical expression to show Mrs. Chamling's earnings and expenses can be written as:
Weekly earnings = Rs 6,000
Daily food expenses = Rs 250
Daily transportation expenses = Rs 75
Total weekly expenses = (Rs 250 + Rs 75) x 7 = Rs 2,275
Total weekly savings = Weekly earnings - Total weekly expenses
= Rs 6,000 - Rs 2,275
= Rs 3,725
(ii) Mrs. Chamling saves Rs 3,725 in a week.
As for the second part of the question, I am not sure what is being asked. The sentence is incomplete and unclear. Please provide more information or context so I can assist you better.
helpppppppppp meeeeee please
The missing sides of the triangle are given as follows:
[tex]SX = 4\sqrt{3}[/tex]RS = 12.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:
Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.For the angle of 30º, we have that:
6 is the opposite side.RS is the hypotenuse.Hence the hypotenuse RS is obtained as follows:
sin(30º) = 6/RS
1/2 = 6/RS
RS = 6 x 2
RS = 12.
Applying the cosine, we have that:
cos(30º) = 6/SX
[tex]\frac{\sqrt{3}}{2} = \frac{6}{SX}[/tex]
[tex]SX = \frac{12}{\sqrt{3}}[/tex]
[tex]SX = 4\sqrt{3}[/tex]
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A recipe uses 5 cups of flour to 1-1/10 cups of milk. If you have two cups of flour, how much milk should you use.
The quantity of milk that should be used for the given amount of flour would be = 11/25
How to calculate the amount of milk to use for the recipe?The following steps are being taken to calculate the amount of milk that would be needed for the recipe.
The number of cups of flour for 1⅒ of milk = 5
The quantity of milk needed for 2cups of flour= X
That is;
1⅒milk = 5 flour
X milk = 2 flour
cross multiply;
X milk = 2×1⅒/5
= 11/25
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You deposit $5000 in an account earning 6% interest compounded monthly. How much will you have in the
account in 15 years?
Answer:
$12270.46----------------------
Use the compound interest formula:
[tex]A = P(1 + r/n)^{nt}[/tex]Where:
A = final amount;P = initial deposit = $5000;r = annual interest rate = 6%;n = number of times the interest is compounded per year = 12;t = time period in years = 15.Plugging in the values, we get:
A = 5000(1 + 0.06/12)¹²*¹⁵ A = 12270.46Select the correct answer. Consider this quadratic equation. x2 + 1 = 2x – 3 Which expression correctly sets up the quadratic formula? A. B. C. D.
The expression x = (2 ± √(-12)) / 2 is negative, this quadratic equation does not have real solutions.
The quadratic formula, we need the quadratic equation in the form ax^2 + bx + c = 0. The given equation is x^2 + 1 = 2x - 3. To set it up correctly, we need to move all terms to one side of the equation to have a zero on the other side.
Rearranging the equation, we get x^2 - 2x + 4 = 0. Now we can identify the coefficients a, b, and c.
The correct expression to set up the quadratic formula is:
B) x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation x^2 - 2x + 4 = 0, we have:
a = 1
b = -2
c = 4
Plugging these values into the quadratic formula, we have:
x = (-(-2) ± √((-2)^2 - 4 * 1 * 4)) / (2 * 1)
Simplifying further, we get:
x = (2 ± √(4 - 16)) / 2
x = (2 ± √(-12)) / 2
Since the expression inside the square root is negative, this quadratic equation does not have real solutions.
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Note the full question may be :
Consider the quadratic equation 2x^2 + 5x - 3 = 0. Which expression correctly sets up the quadratic formula?
A) x = (-b ± √(b^2 - 4ac)) / (2a)
B) x = (-b ± √(b^2 + 4ac)) / (2a)
C) x = (-b ± √(4ac - b^2)) / (2a)
D) x = (b ± √(b^2 - 4ac)) / (2a)
The table shows ordered pairs of the function y=8-2x. What is the value of y when x=8?
0-20
X
-3
-1
-
1
4
8
10
Mark this and return
y
14
10
6
0
?
-12
Save and Exit
Next
Submit
Answer:
The Value of Y is -8
Step-by-step explanation:
I believe it is -8 because giving the function, y = 8 - 2x, given that x = 8, we can replace the value into a function. y = 8 - 2(8) = 8 - 16 = -8.
So therefore, the value of y is -8. Hopes this helps :p
STRUCTURE Gustavo sets up tables for a caterer on weekends. Each round table can seat 8 people. Each rectangular table can seat 10 people. One weekend, his boss asked him to set up tables for 124 people. He uses 2 more round tables than rectangular tables. Write a system of equations to find the number of round tables and rectangular tables Gustavo used. Then graph the system on a separate sheet of paper to solve the system. Let x = the number of round tables and let y = the number of rectangular tables. y = x+ x+ y= WHAT DO I PUT IN THE BOXES
The system of equation of the tables used is 8x + 10y = 124 and x = y + 2
He used 8 round tables and 6 rectangular tables
How to determine the system of equation of the tables usedFrom the question, we have the following parameters that can be used in our computation:
Each round table = 8 peopleEach rectangular table = 10 peopleTotal number of table = 124Using the above as a guide, we have the following:
8x + 10y = 124
Where
x = round tables
y = rectangular tables
We understand that
He uses 2 more round tables than rectangular tables
This means that
x = y + 2
So, the system of equations is 8x + 10y = 124 and x = y + 2
The graph of the system is attached, where we have x = 8 and y = 6
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Intro
Nautilus Clothing's stock has a 50% chance of producing a 15% return, a 20%
chance of producing a 21% return, and a 30% chance of producing a -13% return.
Part 1
What is the stock's expected return?
Can someone help me? The velocity of a sound in air is given by the equation v=20 radical273+t where v is the velocity in meters per second and t is the temperature in degrees Celsius find the temperature when the velocity is 348 meters per second round the answer to the nearest degree
when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.
How to find the temperature when the velocity is 348 meters per secondTo find the temperature when the velocity is 348 meters per second, we can substitute the given velocity into the equation v = 20√273 + t and solve for t.
Given: v = 348 meters per second
Substituting this value into the equation:
348 = 20√273 + t
Now, let's solve for t. We can start by isolating the term with t:
t = 348 - 20√273
Calculating the value:
t ≈ 348 - 20 * 16.523
t ≈ 348 - 330.46
t ≈ 17.54
Rounding the answer to the nearest degree, we have:
t ≈ 18 degrees Celsius
Therefore, when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.
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Can someone help find the surface area, then round the answer to the nearest whole number please?
The Surface Area of cylinders are: 100 yd² , 264 m², 226 mm²
The Surface Area of Can is 219 cm².
We know the formula for Surface Area of Cylinder
= 2πrh
1. Radius = 2 yd
Height = 8 yd
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 2 x 8
= 100 yd²
2. Radius = 7 m
Height = 6 m
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 6 x 7
= 264 m²
3. Radius = 3 mm
Height = 12 mm
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 3 x 12
= 226 mm²
4. Radius = 3.5 cm
Height = 10 cm
So, Surface Area of Can
= 2πrh
= 2 x 3.14 x 3.5 x 10
= 219 cm²
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Find the solution set for the equation. |9x-5|+3=8
Answer: 10/9, 0
Step-by-step explanation:
Find the percentage and round to the nearest hundredth
7.2% of $ 8,650,00
The percentage is given by the expression A = ( 7.2 % ) ( 8650.00 ) and the value of A = $ 622.80
Given data ,
Let the initial amount be represented as P
Now , the value of P is
P = $ 8,650.00
On simplifying the equation , we get
Let the percentage value be d = 7.2 %
On simplifying the percentage , we get d = 0.072
So , A = 0.072 ( 8,650.00 )
Multiplying the expression , we get
A = $ 622.80
Therefore , the value of A is A = $ 622.80
Hence , the expression is A = $ 622.80
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HELP PLS DUE IN 5 MINUTES!!!!!!!!!!
Answer:
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.
Step-by-step explanation:
What is 1/3 of 343???????????
The number that is one-third of 343 is 49.
1/3 of 343 can be found by multiplying 343 by 1/3:
1/3 x 343 = (1/3) x (343) = 343/3
To simplify the result, we can divide both the numerator and denominator by the greatest common factor (GCF) of 343 and 3, which is 7:
343/3 = (343 ÷ 7) / (3 ÷ 7) = 49/1
Therefore, 1/3 of 343 is 49.
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The sum of Jerry's and Carrie's ages is 52. Jerry is 4 years older than Carrie. What is Jerry's age?
Answer:
28
Step-by-step explanation:
let's assumed that
x = Jerry's age
y = Carrie's age
if Jerry 4 years older that Carrie
x = y + 4
x + y = 52
(y + 4) + y = 52
2y + 4 = 52
2y = 48
y = 24
x = y + 4
x = 24 + 4
x = 28
#CMIIWPlease help me out on this question
The relative frequency distribution is:
Income ($) | Frequency Relative | Frequency200-300 | 51 | 18.82%301-400 | 58 | 21.40%401-500 | 74 | 27.30%501-600 | 69 | 25.46%More than 600 | 19 | 7.01%The correct option is A.
What is a relative frequency?A relative frequency is the proportion of the total number of outcomes to the number of times a certain value of the data happens in the set of all outcomes.
Relative frequency = frequency of given data/total frequency * 100%The relative frequency distribution of the given data is constructed below:
Total number of students = 51 + 58 + 74 + 69 + 19
Total number of students = 271
The relative frequency of each class interval will be:
200-300; 51/271 * 100% = 18.82%
301-400; 58/271 * 100% = 21.40%
401-500; 74/271 * 100% = 27.30%
501-600; 69/271 * 100% = 25.46%
More than 600; 19/271 * 100% = 7.02%
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Graph
�
<
0
x<0x, is less than, 0.
The graph of the inequality is x < 0 and is plotted
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
A = x is less than 0
So , on simplifying , we get
x < 0
Hence , the inequality of x is all numbers less than 0 without including 0
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Xavior took a total of 124 quarters and dimes to trade in for cash at the bank. He got exactly $25 back. How many quarters did he have?
A.
40
B.
62
C.
84
D.
100
four students are trying to find the rule that translates point N(-2,-4) to N'(2,4)
The student that gets the rule of the transformation correctly is Raheem
How to determine the student that gets the rule correctlyFrom the question, we have the following parameters that can be used in our computation:
Point N = (-2, -4)
Image of the point N = (2, 4)
This means that
N = (-2, -4)
N' = (2, 4)
From the above, we can see that
N' = -1 * N
This means that
N' = (-2, -4) * -1
So, we have
N' = (-2* -1 , -4 * -1)
So, the rule is (x * -1, y * 1)
Hence, the student that gets the rule correctly is Raheem
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Question
Four students are trying to find the rule that translates point N(-2,-4) to N'(2,4). Each student’s reasoning is shown below.
Raheem: The rule is (x * -1, y * -1)
Casey: The rule is (x + 2, y + 4)
Andrew: The rule is (x + 4, y + 0)
Lo: The rule is (x + 4, y + 8)
Which student is correct?
Raheem
Casey
Andrew
I NEED HELP WITH STATISCTICS
Answer:
20cm
Step-by-step explanation:
What is 692837 divided by 28736
Answer:24.1104189866
Step-by-step explanation:
the answer to What is 692837 divided by 28736 is 24.1104189866
Please help. Any unnecessary answers will be reported.
You are in a competition that involves building card towers. The quickest person to reach 100 stories wins the competition. After reaching 5 stories of cards as shown in the picture below, you needed to use 40 cards.
How many cards will be necessary to build , in a similar way, a tower with 100 stories. Make sure you include work.
Answer:
To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.
From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:
Number of stories: 5
Number of cards used: 40
To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).
Ratio = Number of stories / Number of cards used
Ratio = 5 / 40
Now, we can use this ratio to calculate the number of cards needed for 100 stories:
Number of cards for 100 stories = Ratio * Number of stories
Number of cards for 100 stories = (5 / 40) * 100
Calculating the result:
Number of cards for 100 stories = (0.125) * 100
Number of cards for 100 stories = 12.5
Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.
Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.