the digits 1 2 3 and 4 are to be arranged randomly to make a positive four digit integer. What is the probability that the digits 1 2 and 3 will be directly next to each other in that order from left to right?
A)1/12
B)1/8
C)1/6
D)1/4
E)1/3
its either gonna be 4123 or 1234 so it will be 2/(1234) so 2/24 = 1/12. My question here is when do we do 44 instead of 123*4?
2)the cost of a price of a certain type of lumber is directly proportional to its length.A piece of this lumber that is 8 feet long costs 6.00 what is the cost in dollars of a piece of this lumber that is y yards long? (1 yard=3feet)
A)y-2
B)3y-2
c)3/4y
d)9/4y
e)4y
i did 6=8/k so k=4/3 then i didnt know how to continue :-/
3)At north High school, the ski club has 15 members and the debate club has 12 members. if a total of 11 students belong to only one of the two clubs how many students belong to both clubs?
A)2
B)7
C)8
D)12
E)16
4)in a certain high school there are three times as many band members as orchestra members and twice as many orchestra members as jazz choir members.if no student can be enrolled in more than one of the three activites and there are 108 members in the three activities,how many students are in the band?
5)A rectangular solid has length 20 centimeters width 5 cm and height 10 cm how many of these rectangular solids if combined have a volume of 1 cubic meter? 1 meter=100 cm
so this is how i solved and am not sure of the way ._.
20cm=0.2m 5cm=0.05m 10cm=0.1m
0.20.050.1=1/1000 m
(1/1000)*x=1m x=1000
6)Norman used 1/4 of his monthly allowance to purchase a book and saved 1/3 of the remaining allowance of a school trip to the museum .what fraction of norman’s monthly allowance was saved for the trip?
A)1/4
B)1/2
C)7/12
D)2/3
E)3/4
7)if x>0 n is nonnegative integer and 2x^n+1 + x^n+2=x^n+3
which of the following must equal x^3
A)2+2x+x^2
B)2x+x^2
C)2+x^2
D)2+x
E)3x
My question here is when do we do 44 instead of 1234?
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There are 4! = 432*1 ways to arrange (permute) the digits 1,2,3,4 to make a 4-digit number.
Clearly define your variables! We don't know what k is. Furthermore, note the units.
8 feet cost $6.00 so the cost per foot is $6.00/8 ft = $0.75/ft. Therefore it costs 3*0.75 = $2.25/yd. 2.25 as a fraction is 9/4, and the cost for y yards is therefore 9y/4. (there are several other ways of similar difficulty to do this problem)
We have 15+12 = 27 memberships in either club or both. Subtracting the 11 students who are a member of only 1 club, we have 27-11 = 16. But we must divide by 2, since the remaining students are members of both clubs; 16/2 = 8.
(The above explanation may or may not be intuitive; a more rigorous way is to use inclusion-exclusion).
This reduces to a simple algebra problem, but you need to read carefully. Let J = # jazz choir members, then there are 2J orchestra and 3*2J = 6J band members. 6J+2J+J = 108 --> J = 12. We want the number of band members, which is 6J = 72.
[quote]
20cm=0.2m 5cm=0.05m 10cm=0.1m
0.20.050.1=1/1000 m
(1/1000)*x=1m x=1000
[/quote]
That looks correct, as far as I can tell. But remember to use correct units (m^3) when explaining to someone else.
This is an easy one to plug in a number. Say she starts with $100. Then she buys a book for $25, and saves 1/3 of $75 (i.e. $25) for the trip, so 1/4.
Use parentheses or curly braces to separate exponents, i.e. 2x^{n+1} + x^{n+2} = x^{n+3}
Divide both sides by x^n to get 2x + x^2 = x^3, so the answer is B.
If there were replacements (meaning same digit can be reused) the problem SHOULD state this. For example, the problem might say something like “In a bag you have four balls marked 1 through 4. After pulling one out, the digit is marked and the ball is placed again in the bag. What are the chances that the four digit 1234 would be the result?” In this case, the chances would be 1/(4.4.4.4) because of the replacements.
In your problem, the questions deals with arranging four numbers without replacing it. In other words, when you use the first (4 chances to be 1,2,3,4) you only have 3 chances for the second number, and two chances for the third, and obviously one for the last. Hence the 4x3x2x1.
Fwiw, in almost all SAT problems you have the time to write them out and count the successes (matches the question). Try it with this problem
4321
4312
4123
4132
4213
4231
and so forth … you will see 24 possibilities (and you can deduce this after writing one series as I did - If there are six possibilities with 4. There are six more for 3, and for 2, and for 1)
Look at the question (you identified 2 successes, So your solution is 2/24 or 1/12.
It is O = 2J and B = 3O. There are 3 times as many band members (B) as orchestra (O) members, so B = 3O. A simple check: say O = 10, then B = 30.
No. First off, you should delimit the exponent using parentheses or curly braces (especially if the exponent is more than one character - if you typeset math using LaTeX, for example, you must use curly braces, e.g. 2x^{n+1}). Otherwise, the math major in me will interpret 2x^n+1 as 2x^n, plus 1.
You can’t simplify exponents like that. x^{n+1} is essentially the same as multiplying x n+1 times, i.e. xx…*x where there are n+1 x’s. You can say that x^{n+1} = x^n * x, though. Or x^{n+1} = x^3 * x^{n-2}. In general, a^{b+c} = a^b * a^c.
By the above rules, x^{n+1} divide by x^n is equal to x.
