The number of different collections of 6 books which can be taken on vacation of 11 possible books is 462.
What is combination?Combination is the way of arrangement or the collection of items in the particular order. The order of this group of items does not matter in the combination type of arrangement.
Here, in the original problem, the number of book selection is6.
Of 11 possible books, one plans to take 6 with on vacation. The number of different collections of 6 books can be taken has to be found out.
The total number of books=11.The total number of selection of book=6.Thus, the number of combination to select 6 books collection from 11 is,
[tex]^{11}C_6=\dfrac{11!}{(11-6)!6!}\\^{11}C_6=\dfrac{11\times10\times9\times8\times7\times6!}{5\times4\times3\times2\times1\times6!}\\^{11}C_6=462[/tex]
Thus, the number of different collections of 6 books which can be taken on vacation of 11 possible books is 462.
Learn more about the combination here;
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The diagram shows the shape of a schools auditorium stage. What is the area of the stage?
Do number 5
Answer:
100 square feet (100 ft²)
Step-by-step explanation:
Formula
Area (trapezoid) = 1/2 x sum of parallel sides x heightArea (parallelogram) = base x heightArea of stage
Area (trapezoid) + Area (parallelogram)1/2 x (8 + 12) x 4 + 4 x 152 x 20 + 6040 + 60100 square feetArea of trapezoid:-
1/2(Sum of parallel sides×Height)1/2(8+12)×42(20)40ft²Area of parallelogram
BH15(4)60ft²Total:-
60+40=100ft²pls answer i need to answer it in 10-15 mins plsss
Answer:
The sum of two even numbers is an even number
Step-by-step explanation:
Hey there!
As you can see in the table, all the even numbers when added up are equal to an even number
This make the statement "The sum of two even numbers is an even number" true
From a club of 20 people, in how many ways can a group of three members be selected to attend a conference?
=============================================================
Reason:
There are 20 ways to pick the first person, 19 for the next, and 18 for the last. We count down by one each time we fill up a slot since we cannot reselect any person more than once.
If order mattered, then we'd have 20*19*18 = 6840 permutations.
However, order does not matter because no member has a special seat or role. The individual members don't matter and instead it's all about the group.
Notice that for any group of 3 people, there are 3*2*1 = 6 ways to arrange such individuals. We have to divide by 6 to go from 6840 permutations to 6840/6 = 1140 combinations.
-------------------------
Here's a more formulaic approach using the nCr combination formula.
Plug in n = 20 and r = 3
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\20 C 3 = \frac{20!}{3!*(20-3)!}\\\\20 C 3 = \frac{20!}{3!*17!}\\\\20 C 3 = \frac{20*19*18*17!}{3!*17!}\\\\ 20 C 3 = \frac{20*19*18}{3!}\\\\ 20 C 3 = \frac{20*19*18}{3*2*1}\\\\ 20 C 3 = \frac{6840}{6}\\\\ 20 C 3 = 1140\\\\[/tex]
CAN SOMEBODY SOLVE THIS EQUATION
Answer:
The tank starts with 32300 gallons and is decreasing by -16.15 gallons per minute
A restaurant has a soup-and-salad lunch with the choices listed in the table below. A soup and a salad are selected at random.
What is the probability that tomato soup and a garden salad are selected?
A 1/6
B 1/5
C 1/3
D 5/6
Answer:
I think it is B) 1/5, but I am not sure.
I NEED HELP ASAP, I NEED BOTH QUESTIONS ANSWERED THIS IS WORTH 50 POINTS SO PLS HELP ASAP~~
5:8:12 of 1,220,000
organize in least to greatest
1.
2.
3.
Answer:
244,000390,400585,600Step-by-step explanation:
The total number of parts is 5+8+12 = 25, so the fractions are ...
5/25 × 1,220,000 = 244,000
8/25 × 1,220,000 = 390,400
12/25 × 1,220,000 = 585,600
Least to greatest, the parts are ...
244,000390,400585,60010 men can do the work in 8 days. how many men should be reduced to finish the work in 10 days
If Reducing 2 men will bbe enough too finish the work in 10 days
For rate of work use the formualar
rate of work = quantity of work / duration
10 men can do the work at a rate of = 1 / 8
x men can do same work at a rate of = 1 / 10
x * ( 1 / 8 ) = 10 * ( 1 / 10 )
x = 1 * 8 = 8
therefore 8 men can do the work in 10 days
number of men reduced = 10 men - 8 men = 2 men
Hope it helped
. Assuming that the pool is 10 ft deep, approximately how many cubic heters of water will this pool hold when filled? (3.3 feet 1 meter)
Answer:
The answer is true
Step-by-step explanation:
hope this helps
A cable company charges $130 for digital cable and internet service. It charges $160 for digital cable, Internet service, and three premium movie channels. What part of the $160 charge for the second package is due to the three movie channels?
Answer:
$30
Step-by-step explanation:
Since the $130 has everything except the 3 premium movies, i subtracted 160 with 130 to get $30.
how do i simplify this: (8 2/3)^4
Answer:
5641 55/81
Step-by-step explanation:
you can simplify the equation by removing the parenthesis.
this means that you also have to solve the ^4 part.
this would be
5641 55/81
I know that this is a large number but that is what happens when you do ^4.
Can you help me solve this
Answer:
27 miles
Step-by-step explanation:
27 miles is your answer
if 8 pieces is 180 calories how many calories would one piece be?
Answer:
22.5
Step-by-step explanation:
8 pieces is 180 calories to find the calorie of one piece :
180/8 to get 22.5
Enter the solution (x, y) to the system of equations shown.
y=4x−3
y=−x−13
Answer:
x=-2
y=-11
Step-by-step explanation:
4x-3=-x-13
5x-3=-13
5x=-10
x=-2
y=4(-2)-3
y=-11
A fruit company guarantees that 94% of the pineapples it ships will ripen within four days of delivery. Find the probability that at least 10 pineapples in a case of 12 are ripe within four days.
The probability that at least 10 pineapples in a case of 12 are ripe within four days as described in the task content is; 0.783
Probability of PercentageFrom the task content;
It follows that 94% of the pineapples shipped will ripen within four days of delivery.On this note, the probability for ripening of each apple is; 0.94.
Ultimately, the probability that at least 10 pineapples in a case of 12 are ripe within four days is therefore; 0.94 × 10/12 = 0.783.
Read more on probability;
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the ratio of the sides of a certain triangle is 2:7:8 if the longest side of the triangle is 40cm how long are the other two sides
The length of the other two sides is 10 and 35 respectively.
What is a ratio?A ratio is a quantitative relation showing the comparison between two or more numbers. It can also be written in the fractional form where the first part is the numerator and the second part is called the denominator.
From the given information:
The sides of the triangle = 2:7:8The total sides of the triangle = 2+7+8 = 17We are being told that the longest side is the triangle is equal to 40.
i.e.
[tex]\mathbf{\to\dfrac{8}{17}\times x = 40}[/tex]
[tex]\mathbf{x = 40 \div \dfrac{8}{17}}[/tex]
[tex]\mathbf{x = 40 \times \dfrac{17}{8}}[/tex]
x = 85
Now for the other two sides 2 and 7, their length is as follows.
[tex]\mathbf{\dfrac{2}{17}\times 85 = 10}[/tex]
[tex]\mathbf{\dfrac{7}{17}\times 85 = 35}[/tex]
Therefore, we can conclude that the length of the other two sides is 10 and 35 respectively.
Learn more about ratios here:
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6x + y=4x+ 11y, write a formula for h(x) in terms of x
Answer:
[tex]h(x)=\frac{1}{5}x[/tex]
Step-by-step explanation:
To write a formula for a function, such as h(x), you need to solve for y.
[tex]6x+y=4x+11y[/tex]
[tex]-4x[/tex] [tex]-4x[/tex]
[tex]2x+y=11y[/tex]
[tex]-y[/tex] [tex]-y[/tex]
[tex]2x=10y[/tex]
[tex]/10[/tex] [tex]/10[/tex]
[tex]\frac{2}{10}x=y[/tex]
[tex]y=\frac{1}{5}x[/tex]
y and h(x) mean the same thing, so you can subsitute h(x) for y in order to fit the question.
Therefore, [tex]h(x)=\frac{1}{5}x[/tex]
write 156/51 as a mixed number in simplest terms
A) 3 1/17
B) 3 3/51
C) 3 2/51
D) 3 1/27
Answer:
B option is the answer, hope this helps!!
Which of the following tables represent linear relationships?
Answer:
Table 2 and 3
Step-by-step explanation:
A linear relationship should show a straight line, showing that it's linear.
*View the attached graphs*
Hope this helps!
Evaluate the following integral or state that it diverges.
*integral 0 to 1 (ln x)do
Answer:
-1
Step-by-step explanation:
so firstly we solve by integrating by parts.
lnX × X - the integral of x/x
so the integral is Xln(X) - X
so the value should converge at -1
What is an externality
Answer:
Externalities refer to situations when the effect of production or consumption of goods and services imposes costs or benefits on others that are not reflected in the prices charged for the goods and services being provided.
the picture below is an example of what it looks like
WHAT EXTERNALITY IS : externality is a economic cost or sometimes a benefit that is the´´by product´´ of the economic activity. the activity that is allacated outside of the system. the resources are likely to be misallocated when there is a externality.
the fact of existing outside the perceiving subject.
5
Type the correct answer in the box. Use numerals instead of words.
New York City has a population of approximately 8.8 million people with a population density of approximately 29,300 people per square mi
What is the approximate area of New York City to the nearest square mile?
The area of New York City is approximately
square miles.
Answer:
300
Step-by-step explanation:
help i dont know how to do this and i forgot the study guide
Answer:
number 1 is a
Step-by-step explanation:
I don’t know the rest tho but good luck
Find csc theta if sin theta = 4/5
Answer:
5/4
Step-by-step explanation:
csc theta is essentially 1/sintheta
so you can say that csc theta is 5/4.
another way to do this is to draw the right triangle and find the values of all the sides. this way you'll be able to find all the trig values of the triangle.
post a comment if you want any further guidance or help.
PLEASE HELP PLEASE HELP
Answer:
Option D - Line P
Step-by-step explanation:
Look at the coordinates in the (x, y) column of Max's table and see which line has the same points.
In a new video game, Franky had -16 1/2 points. He was able to earn 3/4 of the points he lost back. How many points did he have?
Answer:
slightly confused on the wording if he got back 3/4 from 16.5 then he earned back 12.375 points
if -16.5 is the 1/4 he didnt get back then he had 66 points
Step-by-step explanation:
Will someone please help <3
Answer:
area of base is 9pi
circumference of base is 6pi
lateral surface 24
surface area is 42
Step-by-step explanation:
In which data set is the mean greater than the median?
According to the skewness of each data-set, the first histogram has a mean greater than the median.
What is the relation between mean, median and skewness?If the mean is greater than the median, the data is positively(right) skewedIf the mean is less than the median, the data is negatively(left) skewedIn this problem, for the mean greater than the median, we want a right-skewed data, which is given by the first histogram.
More can be learned about a data-set skewness at https://brainly.com/question/1446134
Answer:
B
Step-by-step explanation:
took test
Questione Simplify Cosa + 2Cos(a +240")
Step-by-step explanation:
[tex] \cos(a) + 2 \cos(a + 240) [/tex]
[tex] \cos(a) + 2 \cos(a) \cos(240) - \sin(a) \sin(240) [/tex]
[tex] \cos(a) + 2( - \frac{ \cos(a) }{2} + \frac{ \sqrt{3} }{2} \sin(a) )[/tex]
[tex] \cos(a) - \cos(a) + \sqrt{3} \sin(a) [/tex]
[tex] \sqrt{3} \sin(a) [/tex]
If you graph the new identity, and the og identiy, they will be conciding graphs, so they are the same identity.
10) Complete the net worth statement by determining the total assets and total liabilities. What is the net worth? A) $178,000 B) $180,338 C) $1,052,662 D) $1,233,000
Answer:
C) $1,052,662
Step-by-step explanation:
Sorry the answer was late and also this is the right answer because i did the test