1. Marbles are to be removed from a jar that contains 12 red marbles and 12 black marbles. What is the least number of marbles that could be removed so that the ratio of red marbles to black marbles left in the jar will be 4:3?
(If someone can extent further with this that will be great, like how to tackle ratio problems.. I have hard time with ratios...)
2. If 0 <= (less than or equal to) x <= (less than or equal to) y and (x+y)^2 - (x-y)^2 >= 25, what is the least possible value of y?
3. If (p+1)(t-1)=0 and p is positive, what is the value of t?
a) -3
b) -1
c) 0
d) 1
e) 3
4. A stamp collecting club calculated that the average (arithmetic mean) number of stamps in its members' 10 collections was 88. However, it was discovered that 2 numbers in the calculations were entered incorrectly. The number 55 was entered as 75 and the number 78 as 88. What is the correct average number of stamps in the 10 collections?
a) 91
b) 89
c) 87
d) 86
e) 85
5. R is the midpoint of line segment PT, and Q is the midpoint of line segment PR. If S is a point between R and T such that the length of segment QS is 10 and the length of segment PS is 19, what is the length of segment ST?
a) 13
b) 14
c) 15
d) 16
e) 17
6. The interior dimensions of a rectangular fish tank are 4 feet long, 3 feet wide, and 2 feet high. The water level in the tank is 1 foot high. All of the water in this tank is poured into an empty second tank. If the interior dimensions of the second tank are 3 feet long, 2 feet wide, and 4 feet high, what is the height of the water in the second tank?
a) 0.5 ft
b) 1 ft
c) 1.5 ft
d) 2 ft
2) 4 ft
7. Each of the following inequalities is true for some values of x EXCEPT?
a) x< x^2 < x^3
b) x< x^3 < x^2
c) x^2 < x^3 < x
d) x^3 < x < x^2
e) x^3 < x^2 < x
Please explain thoroughly (I just don't want the answers, because I have the answers ... duh), step by step. Thank you!
Haha did not see this thread... so I had made a thread with these questions already before I saw this (I just copied and pasted from my other thread).
I answered your questions in your thread, but I'll post them here in a bit.
EDIT: here we go
1.) 12/x = 4/3
x = 9. So we want to remove 3 marbles to get this ratio.
2.) Expand and you'll see that the squared terms go away and you're left with 4xy > 25
xy = 25/4
Least possible value of y occurs at the equality of x and y, so xy = 25/4 = y^2; y = +-5/2, but since they want a positive value only 5/2 works.
3.) 1. Since the expression needs to multiply to zero, and since the term with p in it can't be 0, the t term needs to equal 0. t - 1 = 0 -> t = 1
4.) Incorrect sum of stamps: 88*10 = 880. Subtract 20 and 10 to correct for this to yield a sum of 850 for the 10 stamps. To average, 850/10 -> 85.
5.) PQ = QR; Since QS is 10 and PS in 19, we know that adding on PQ adds an additional 9 units, which means that QR is also 9. We also now know that RS is 1. Since PR = RT, we know that 18 = ST + 1, which means ST = 17.
6.) Volume of tank 1 is 4*3*2 = 24, but since it's half full we know the water volume is 12 ft^3 . so now we take the volume of the new container, 3*2*4 = 24, which is the same before, but the distribution along the axes is different, so we must halve the height of the new box to get 2 ft.
7.) Analyze it case by case.
(a) True for any integer n, where n > 1.
(b) True a negative number in the interval -1 < x < 0
(c) Fails.
(d) True for any negative integer.
(e) True for any number on the interval 0 < x < 1
In a mixture of peanuts and cashews, the ratio by weight of peanuts to cashews is 5 to 2. How many pounds of cashews will there be in 4 pounds of this mixture?
You can recognize that a basic parabola (y=x2) has been vertically shifted down 1 unit. Then, the absolute value reflects the part of the parabola that was below the x-axis, folding it up.
I know that it's alot of questions to ask help with, but I've been going through the book and circling the ones that I just couldn't understand on my own, and I have finnaly gathered enough problems I think lol. If someone would be willing to help, me with these, that would be wonderful.
A salesperson's commision is k percent of the selling price. While of the following represents the commision, in dollars, on 2 cars that sold at 14,000
A. 280k
B. 7,000k
C. 28,000k
D. 14,000/ (100+2k)
E. 28,000+k/ 100
I have a bunch: Not providing the choices, no point.
1) A restaurant has 19 tables that can seat a total of 84 people. Some of the tables seat 4 people and the others seat 5 people. How many tables seat 5 people?
2) In an election, 2.8 million votes were cast and each vote was for either Candidate I or Candidate II. Candidate I received 28,000 more votes than Candidate II. What percent of the 2.8 million votes were cast for Candidate I?
3) Five different point A, B, , D, and E lie on a line in that order. The length of AD is 4.5 and the length of BE is 3.5. If the length of CD is 2, what is one possible value for the length of BC?
4) Each term of a certain sequence is greater than the term before before it. The difference between any two consecutive terms in the sequence is always the same number. If the third and sixth terms of the sequence are 17 and 77, respectively, what is the eighth term?
5) What is the least value of x that satisfies the equation?
|x-3| = 1/2
6) A four-digit integer, WXYZ, in which W, X, Y, and Z each represent a different digit, is formed according to the following rules.
1. X = W + Y + Z
2. W = Y + 1
3. Z = W -5
What is the four-digit number?
A salesperson's commision is k percent of the selling price. While of the following represents the commision, in dollars, on 2 cars that sold at 14,000
A. 280k
B. 7,000k
C. 28,000k
D. 14,000/ (100+2k)
E. 28,000+k/ 100
the answer is A
Pick numbers, I chose his commission to be 10% to make it easy.
First establish what his commission should be in $.
$14,000 + $14,000 = $28,000 x .1 (.1 = 10/100) = $2,800 (salesperson should make)
A) 280 x 10 = 2,800 7,000 x 10 = 70,000
C) 28,000 x 10 = 280,000
D) 14,000 / (100 + 20) = 116
E) 28,000 + 10 / 100 = 280.1
The question states k is a percent so make sure k is a percent not a decimal. C could easily trick you with 28,000 x .1 = 2,800.
Not that important, but here's another way to do the restaurant problem without algebra and without guess and check:
There are 19 tables. Say you put 4 at each table. That would be enough for 19 x 4 = 76 people. But you have 84 people to seat, so that leaves 84 - 76 = 8 people unseated. You distribute them among the tables, 1 at each of 8 tables, so now 8 tables have 5 and that's the answer.
As a tutor, I've seen this problem like 10 times without thinking of this. Oh well...
g(x) = k(x+3)(x-3) for some constant k. If g(a-1.2) = 0 and a > 0, what is the value of a?
Assuming k is not 0 (we can safely assume this as the graph provided clearly reflects this - if k = 0 all values would be 0), we can assume either (x+3) or (x-3) = 0.
So, if g(a-1.2) = 0, a-1.2 equals either -3 or 3, resulting in values of a = -1.8 and a = 4.2 respectively. a must be 4.2 as it is stated that a > 0.
Replies to: Math help center
(If someone can extent further with this that will be great, like how to tackle ratio problems.. I have hard time with ratios...)
2. If 0 <= (less than or equal to) x <= (less than or equal to) y and (x+y)^2 - (x-y)^2 >= 25, what is the least possible value of y?
3. If (p+1)(t-1)=0 and p is positive, what is the value of t?
a) -3
b) -1
c) 0
d) 1
e) 3
4. A stamp collecting club calculated that the average (arithmetic mean) number of stamps in its members' 10 collections was 88. However, it was discovered that 2 numbers in the calculations were entered incorrectly. The number 55 was entered as 75 and the number 78 as 88. What is the correct average number of stamps in the 10 collections?
a) 91
b) 89
c) 87
d) 86
e) 85
5. R is the midpoint of line segment PT, and Q is the midpoint of line segment PR. If S is a point between R and T such that the length of segment QS is 10 and the length of segment PS is 19, what is the length of segment ST?
a) 13
b) 14
c) 15
d) 16
e) 17
6. The interior dimensions of a rectangular fish tank are 4 feet long, 3 feet wide, and 2 feet high. The water level in the tank is 1 foot high. All of the water in this tank is poured into an empty second tank. If the interior dimensions of the second tank are 3 feet long, 2 feet wide, and 4 feet high, what is the height of the water in the second tank?
a) 0.5 ft
b) 1 ft
c) 1.5 ft
d) 2 ft
2) 4 ft
7. Each of the following inequalities is true for some values of x EXCEPT?
a) x< x^2 < x^3
b) x< x^3 < x^2
c) x^2 < x^3 < x
d) x^3 < x < x^2
e) x^3 < x^2 < x
Please explain thoroughly (I just don't want the answers, because I have the answers ... duh), step by step. Thank you!
Haha did not see this thread... so I had made a thread with these questions already before I saw this (I just copied and pasted from my other thread).
EDIT: here we go
1.) 12/x = 4/3
x = 9. So we want to remove 3 marbles to get this ratio.
2.) Expand and you'll see that the squared terms go away and you're left with 4xy > 25
xy = 25/4
Least possible value of y occurs at the equality of x and y, so xy = 25/4 = y^2; y = +-5/2, but since they want a positive value only 5/2 works.
3.) 1. Since the expression needs to multiply to zero, and since the term with p in it can't be 0, the t term needs to equal 0. t - 1 = 0 -> t = 1
4.) Incorrect sum of stamps: 88*10 = 880. Subtract 20 and 10 to correct for this to yield a sum of 850 for the 10 stamps. To average, 850/10 -> 85.
5.) PQ = QR; Since QS is 10 and PS in 19, we know that adding on PQ adds an additional 9 units, which means that QR is also 9. We also now know that RS is 1. Since PR = RT, we know that 18 = ST + 1, which means ST = 17.
6.) Volume of tank 1 is 4*3*2 = 24, but since it's half full we know the water volume is 12 ft^3 . so now we take the volume of the new container, 3*2*4 = 24, which is the same before, but the distribution along the axes is different, so we must halve the height of the new box to get 2 ft.
7.) Analyze it case by case.
(a) True for any integer n, where n > 1.
(b) True a negative number in the interval -1 < x < 0
(c) Fails.
(d) True for any negative integer.
(e) True for any number on the interval 0 < x < 1
So your answer is choice (c)
[url]http://i31.****.com/11bneao.gif[/url]
Which of the following could be the equation of the function graphed in the xy-plane above?
A) y= (x)2 + 1
y= x2 + 1
C) y= x2 + 1|
D) y= |x2 1|
E) y = |(x 1)2|
I have no clue.
You can recognize that a basic parabola (y=x2) has been vertically shifted down 1 unit. Then, the absolute value reflects the part of the parabola that was below the x-axis, folding it up.
Peanut to Cashew is 5:2, which implies Cashew to Total is 2:7, so set up a proportion 2/7 = x/4, which gives 8/7 lbs.
(The answer is 183, but I got 13...)
First, ([email protected]) = 3^2 + 3(1) + 1^2 = 9 + 3 +1 = 13
Know we can replace ([email protected]) with 13, so what's left is [email protected]
13^2 + 13(1) + 1 = 169 + 13 + 1 = 183
You probably just had a computation error.
p.400;18
p.401;19
p.418;17
p.424;16
p.456;15
p.457;18,19
p.484;11
p.519; 19,20
I know that it's alot of questions to ask help with, but I've been going through the book and circling the ones that I just couldn't understand on my own, and I have finnaly gathered enough problems I think lol. If someone would be willing to help, me with these, that would be wonderful.
A salesperson's commision is k percent of the selling price. While of the following represents the commision, in dollars, on 2 cars that sold at 14,000
A. 280k
B. 7,000k
C. 28,000k
D. 14,000/ (100+2k)
E. 28,000+k/ 100
the answer is A
1) A restaurant has 19 tables that can seat a total of 84 people. Some of the tables seat 4 people and the others seat 5 people. How many tables seat 5 people?
2) In an election, 2.8 million votes were cast and each vote was for either Candidate I or Candidate II. Candidate I received 28,000 more votes than Candidate II. What percent of the 2.8 million votes were cast for Candidate I?
3) Five different point A, B, , D, and E lie on a line in that order. The length of AD is 4.5 and the length of BE is 3.5. If the length of CD is 2, what is one possible value for the length of BC?
4) Each term of a certain sequence is greater than the term before before it. The difference between any two consecutive terms in the sequence is always the same number. If the third and sixth terms of the sequence are 17 and 77, respectively, what is the eighth term?
5) What is the least value of x that satisfies the equation?
|x-3| = 1/2
6) A four-digit integer, WXYZ, in which W, X, Y, and Z each represent a different digit, is formed according to the following rules.
1. X = W + Y + Z
2. W = Y + 1
3. Z = W -5
What is the four-digit number?
Thank you.
Question One
Let x = number of tables seating four people
Let y = number of tables seating five people
There are a total of 19 tables
The total number of people that can be seated at these tables is 84
Therefore,
x + y = 19
4x + 5y = 84
Let's put this in terms of only one variable, y:
x = 19 - y
Therefore,
4(19 - y) + 5y = 84
76 - 4y + 5y = 84
76 + y = 84
y = 8
There are eight tables seating five people, and 19 - 8 = 11 tables seating four people.
Let x = number of votes for Candidate I
Let y = number of votes for Candidate II
The total number of votes was 2,800,000
Candidate I received 28,000 more votes that Candidate II.
Therefore,
x + y = 2,800,000
x = y + 28,000
Putting equation one in terms of one variable,
y = 2,800,000 - x
Now substitute:
x = 2,800,000 - x + 28,000
x = 2,828,000 - x
2x = 2,828,000
x = 1,414,000
Candidate I received 1,414,000 votes.
1,414,000 / 2,800,000 x 100 / 1 = 50.5%.
Pick numbers, I chose his commission to be 10% to make it easy.
First establish what his commission should be in $.
$14,000 + $14,000 = $28,000 x .1 (.1 = 10/100) = $2,800 (salesperson should make)
A) 280 x 10 = 2,800
7,000 x 10 = 70,000
C) 28,000 x 10 = 280,000
D) 14,000 / (100 + 20) = 116
E) 28,000 + 10 / 100 = 280.1
The question states k is a percent so make sure k is a percent not a decimal. C could easily trick you with 28,000 x .1 = 2,800.
There are 19 tables. Say you put 4 at each table. That would be enough for 19 x 4 = 76 people. But you have 84 people to seat, so that leaves 84 - 76 = 8 people unseated. You distribute them among the tables, 1 at each of 8 tables, so now 8 tables have 5 and that's the answer.
As a tutor, I've seen this problem like 10 times without thinking of this. Oh well...
g(x) = k(x+3)(x-3) for some constant k. If g(a-1.2) = 0 and a > 0, what is the value of a?
Assuming k is not 0 (we can safely assume this as the graph provided clearly reflects this - if k = 0 all values would be 0), we can assume either (x+3) or (x-3) = 0.
So, if g(a-1.2) = 0, a-1.2 equals either -3 or 3, resulting in values of a = -1.8 and a = 4.2 respectively. a must be 4.2 as it is stated that a > 0.
I hope this makes sense!