How would you solve?

(X)^(1/2) = X^(1/8)

Raise each side to the power of 8 so that you have whole number exponents, then solve.

Which has higher standard deviation? Set A:{0.2, 0.4, 0.6, 0.8} Set B:{2, 4, 6, 8}

Set B

On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 24 miles on Saturday and Sunday, how many miles did Bill run on Sunday?

(Bill Saturday) + (Bill Sunday) + (Julia Sunday) = 24 x + (x + 4) + (2x + 8) = 24

We need to multiply 126.3 by a number, x, to get an integer. We have many options on what the integer could be. How do we select the right ones?

1. Take a look at that decimal. It is 3/10. Therefore, to get an integer, you must multiply by 10 OR a multiple of 10.3. 2. If it was 63.15, it would be 15/100, or 3/20. Therefore, the number would have to be divisible by 20

Six children will sit in a row of six chairs but Jackie and Marilyn cannot be seated next to each other. How many arrangements are possible?

1. Calculate 6! , or all the possible ways that they could sit next to each other, even if it breaks the restriction. 720 2. How many un-allowed seating arrangements are possible? In this case, 10. Remember that Jackie could sit to the right, or Marilyn could sit to the right. 3. In every scenario, the remaining chairs could be filled by 4! combos of children seating. 24 3. Multiply the number of unallowed seating arrangements by the number of ways the remaining chairs could be filled. 24*10 = 140 4. Subtract total combos - unallowed combos. 720 - 240.

We want to find out what other exponential phrases are equal to 8^24. The options have bases of all different sorts and various exponents.

1. Find out what the prime factorization is of the number you are trying to compare to. In this case, 2^72. 2. Eliminate options where the base can't boil down to a base of 2. For example, 12 is (3*2). However, 4 and 16 work. 3. Turn those options into their prime factor and see if it is equal to the first expression.

By approximately how much, in millions, was the population of Asia greater than the population of Africa in 1990?

1. Find the % population of both on the graph. 2. To save time on this problem, DO NOT multiply each percentage by the total population. First, subtract the percentages. 3. Then multiply THAT number by the total world population

Point A (-4, 2) and Point B (2, 4) lie in the xy-coordinate plane. If point C lies in the first quadrant and contains the coordinates (p, q), where p < 2 and q < 4, which of the following could be the area of triangle ABC?

1. Find the area of the triangle that would maximize the area. In this case, it is 12, and it is easy to find because the slope of 1 creates a 45:45:90 triangle. 2. Next, find the smallest possible case for the area. Since you really only have one line pre-determined, you can see that you can make the area infinitely closer to zero, since there was no specification that the area should be an integer.

A librarian has 7 books to arrange, 4 different novels, and 3 identical copies of the same dictionary, how many different orders could these 7 books be put on the shelf?

1. First, take the largest factorial of 7!. 2. In this arrangement, you have 3 items that are essentially the same. The factorial of 7 is 3! too big. 3. Divide 7! by 3!

Company has stock options. If 85% of the men and 77% of the women choose to participate in this plan, then which of the following could be the total number of employees?

1. For each option, what is the least amount of people that can fit this ratio without making half of a person? 2. For example, 77/100 cant be simplified, so the amount of women MUST be divisible by 100. However, 85/100 can be divided to 17/20, so the number of men must be divisibe by 20. 3. Therefore, the total of people must be divisible by 100 and also 20. Try out each option, but first get rid of things you know wont work.

From a group of 8 people, it is possible to create exactly 56 different k-person committees. Which of the following could be the value of k ?

1. Go step by step. First do 8 C 1, then 8 C 2, then 8 C 3 to see what each of those equals. When you find one that equals 56, that is one answer. 2. For the second answer, remember that xCr is equal to xCx-r. So, if 8 C 3 is one answer, 8 C 5 is the other answer.

Each student takes English, Math, History, Science, and Science Lab. In how many different orders can a student's schedule be arranged given that science lab must immediately follow the science class

1. How many spots can science class fall? Only four, because it can't be at the very end of the day, because it needs a lab. 4 2. How many spots can science lab fit? It can only fit in 1 -- the spot after science class. In practice, the simplest way to handle a problem that stipulates that X immediately precedes Y is to treat XY as a single item to be scheduled. In this problem, that means we act as though we have four classes to schedule, S/SL, E, M, and H.

Jennifer has $400 more than Brian has. If she were to give Brian 20% of her money, then Brian would have 2/3 of the amount of money that Jennifer would then have. How much money does Brian currently have (before exchanging money)?

1. J = B + $400. 2. (B+0.2J) = 23(0.8J) 3. Substitute

In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. What is the mean of the set?

1. Mean + (1.5)SD = 12.5 2. Mean - (0.5)SD = 8.9 3. Subtract equations from each other to find standard deviation. 4. Plug back into one of the equations to find the mean

Ten dice, each fair with six sides rolled simultaneously. What is the probability of getting exactly two fives?

1. Probability of getting a 5 is 1/6. We are looking for two, so (1/6^2. 2. This leaves eight dice. The probability of rolling NOT five is 5/6, so (5/6)^8. 3. Multiply both together 4. How many ways can those combinations be distributed across the coins? 10 choose 2 ways. Multiply the probability by that number.

A certain barrel is 1/5 full. When k liters of liquid are added to the barrel, it becomes 2/3 full. In terms of k, what is the capacity of the barrel, in liters?

1. The capacity of the barrel, written as C 2. To calculate how full the barrel is at different stages, multiply C by the fraction. 3. The barrell was 1/5C full, then you added k to it, and it became 2/3C full. Turn this into an equation 4. Isolate C

For which values of x is (x2 - 10x + 25)(x2 - 13x + 40) < 10?

1. You cant solve exactly for x 2. Factor the equaitons and then plug in the options

From a set of ten different items, Lisa is going to select three as a gift for someone. How many different sets of three items can she pick?

10*9*8 / 3*2*1

An amusement park has 12 different rides. Passholders can ride 3 for free. How many different sets of free rides are possible?

12*11*10 / 3*2*1

Set A: {1, 3, 4, 6, 9, 12, 15} If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?

5/7 chance of being divisible by 3 on first draw, then 4/6, then 3/5. Multiply together.

A knockoff website requires users to create a password using letters from the word MAGOSH. If each password must have at least 4 letters and no repeated letters are allowed, how many different passwords are possible?

6 C 4 + 6 C 5 + 6 C 6

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John's weekly allowance?

Go step by step. If he spends 3/5, he has 2/5 left. Next, if he spends 1/3, he has 2/3 of 2/5 left. This should equal 80 cents. solve for x.

Given that the length of each side of a quadrilateral is a distinct integer and that the longest side is not greater than 7, how many different possible combinations of side lengths are there?

How many different sets of four could be selected? 7C4 = 7*6*5/(3!) = 7*5 = 35 Of those 35, the only ones that don't work for sides of a quadrilateral are the ones in which the sum of the three smallest sides are equal to or less than the longest side.

8^n+1 + 8^n = 36,

Factor out 8^n from both sides to turn it into a multiplication thing

At the moment there are 54,210 tagged birds in a certain wildlife refuge. If exactly 20 percent of all birds in the refuge are tagged, what percent of the untagged birds must be tagged so that half of all birds in the refuge are tagged?

Fast way to solve it: ignore the first number given and make up your own, easier number! If the math is in percents and the final number is in percents, you dont even need to touch the real number.

Set X={a, b, c}, where a < b < c. If the average (arithmetic mean) of a and b is 3x-13, and the average of b and c is 3x+11, what is the range of set X?

Find a+b, then find b+c. Range is a - c. Subtract those equations from each other. You get = 26+ 22. Add them together for the range. If you get a negative, you are finding a-c.

In the standard x,y-plane, Line L passes through the point (1, 3). If Line L passes below the point (4, 5), then which of the following could be the slope of Line L?

First, figure out the slope from (1, 3) exactly through (4, 5). Rise = 2, and Run = 3, so slope = 2/3. This is the slope of the line that, starting at (1, 3), would go directly through (4, 5). If we want to go under (4, 5), we need a slope less than 2/3. In many cases, finding a common denominator makes the comparison quick & easy.

Six children will give presentations, one after the other. Luke's presentation makes a reference to something mentioned in Ruth's, so Ruth's presentation must come before Luke's, and not necessarily immediately before. How many orders are possible?

For every combo where Luke comes before Ruth (aka does not meet the restriction), there is a combo where Ruth comes before Luke (aka meets the restriction). Find 6! and divide by two. Think about problems where there might be similar symetry.

How many of the five continents shown experienced a population increase between 1950 and 1970? (shown world population and % of world population of each continent)

If world population and % of total population increase, then it definitely counts. If % of toal population falls for a country, need to find out whether there was a drop in actual population.

. How many diagonals does a regular 12-sided figure or regular dodecagon on half?

Multiply number of vertices by number of options for next vertices that make a diagonal. 12 vertices, 9 options for a diagonal (can't go to either adjacent vertex or itself). But with this number, you'd be counting ever diagonal twice. So divide by two. 12*9 / 2

Two quadratic functions are the same, except that one is x's and the other with y's. Each have the same two factors. Are they equal?

No! One could be one factor, the other could be the other factor.

Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/4 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used?

Note: you cannot multiply 360 by 1/4 and 1/5 to get the right answer. Either go step by step and calculate it out, OR convert the fractions to find out how much is left and subtract from original. 360 * 3/4 * 4/5

A certain plastic cup is manufactured by a robot. If 5 such robots, working at the same individual rate, can manufacture a combined total of 5 cups in 5 seconds, how many seconds will it take 25 robots to manufacture a total of 25 cups?

Notice that if 5 robots manufacture 5 cups in 5 seconds, then each robot manufactures 1 cup in 5 seconds. Using the RT = W formula, R(5) = 1, and the rate of production of 1 robot is 1/5, meaning it does 1/5 of a job in 1 second. Remember that when we have multiple "workers" performing a job, we add the individual rates, so 25 robots will work at a rate of cups/second. Therefore, since now the job is to manufacture 25 cups, our equation is 5(T) = 25, and T, or the time it will take the 25 robots to do the job, equals 5 seconds.

Every person in a certain group is either a Dodgers fan or a Yankees fan, but not both. The ratio of Yankees fans to Dodgers fans is 5 to 3. If 22 Yankees fans change teams to become Dodgers fans, the ratio of Dodgers fans to Yankees fans will be 1 to 1. How many people are in the group?

Set up a ratio with x in both the numerator and denominator: 5x/3x 22 Yankees left, 22 Dodgers added. (5x-22)/(5x+22) Set this equal to the new ratio, solve for x, and plug that back into the original ratio to find out the total number.

When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

Since water is filling the tank at a rate of 22 cubic meters per hour, after one hour there will be the equivalent of a "cylinder of water" in the tank (smaller than the tank itself) with a volume of 22 m3. Since the water level rises at 0.7 meters/hour, this "cylinder of water" will have a height of 0.7 meters. The radius of this "cylinder of water" will be the same as the radius of the cylindrical tank.

If a - b > a + b, where a and b are integers, which of the following must be true?

Solve inequality, which results in

Car X can come with any of these 5 additional features: sunroof, stereo, tinted windows, leather seats and cruise control. How many combinations are possible?

Think of this as each feature having two options -- included or not. Therefore, each feature is a "stage" where you have to decide whether or not to include it. So, the answer is 2 x 2 x 2 x 2 x 2

Marcia has 2 liters of a 60% concentrated solution of phosphoric acid. She wants to add 3 liters of less concentrated phosphoric acid solutions, so that she has 5 liters of a solution with a concentration less than 50%. Which could she add?

This is essentially weighted averages. We want a mean concentration of 50%. 60 percent is 10 percent over what we're aiming for, and we have two liters of that (20). What % do we need, in 3 units, to get an average of 50? Find this, and then get rid of all options that are above it.

From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

This is two stages, one of 5 C 2 and the other 4 C 2. Once you find the number of possibilities for each stage, MULTIPLY those two numbers together (don't add!)

ab ≠ 0 and a^x = b^x Is a or b bigger?

Usually they are equal. But what if one is the same number, but opposite sign? If x was even, then it would be the same. Not enough information.

What is bigger, 22 percent of x or 2/9 of x ?

Usually, it is 2/9 of x. However, if x is zero, they are equal, so we do not have enough information.

A weighted coin has a probability p of showing heads. If successive flips are independent, and the probability of getting at least one head in two flips is greater than 0.5, then what could p be?

We need to find a value where, when squared (or multiplied twice), 1 minus that value is greater than .5 Take all the options and find their inverse (this will be the probability of not showing heads). Square it. Subtract from one. If the value is greater than .5, the answer works.

2 ÷ 2 ÷ 2 ÷ 2 ÷ 2 = 2^x, then x =

x = -3