The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone? A) 299m + 261j => 1000 B) 299m + 261j > 1000 C) 299/m + 261/j => 1000 D) 299/m + 261/j > 1000
After reading the problem, note that it mentions "inequalities", which automatically gives clues as to what the question will be asking. The key words in the question is that it says "meet or exceed". This should lead you to think what kind of inequality it will be. "Meet or exceed" means greater than or equal to. This automatically rules out B and C since these are inequalities that express only "greater than", and does not include "equal to". Looking at A and C, the only difference is what is left of the inequality. To figure out which is the correct answer, read back the question. To get the total amount of calcium, we multiply the number of mg of calcium in one cup of milk or juice by the number of cups (m and j). A is the correct answer because it is multiplying mg of calcium by m and j.
Find x and y so that the ordered data set has a mean of 42 and a median of 35. 17 , 22 , 26 , 29 , 34 , x , 42 , 67 , 70 , y
1) Make sure the data set is listed in numerical order since the question asks for median and median requires the data to be listed in numerical order. The data is already listed in numerical order so we can proceed. 2) We can start off with finding what x can be to make the data set have a mean of 35. The reason why is because by finding the x first, we find what one of the missing numbers are, so when it comes time to find the mean, we only need to find out what y is. 3) Median is the middle number in the data set, but in this set, there are two numbers in the middle since it is an even amount of numbers in the data set. We find the median by finding the average of these two middle numbers, which are 34 and y in this case. 4) (34 + x) / 2 = median = 35. Solve for x, which turns out to be 36. We can double check this answer by plugging 36 back into x in the expression and seeing if it equals 35. 5) To find a mean, we find the sum of the data set and divide by n, the number of values in the data set: sum/n = mean. In this case, n = 10. (17 + 22 + 26 + 29 + 34 + 35 + 42 + 67 + 70 + y) / 10 = 42. Note that we replaced x with 35 since we now know what it is. We set sum/n = 42 because 42 is the mean we are trying to achieve. 3) When we add up all the values in the data set, the equation becomes (342 + y) / 10 = 42. Just like with the median, we solve for y, which turns out to be 78. We can check if this is correct by plugging in 78 into this equation and seeing if it equals 42.
Evaluate 10(x - 3)^3 - (7 - x^2) at x = -5.
1) Plug in -5 for x in the expression. Expression becomes 10(-5-3)^3 - (7-(-5)^2). 2) Solve what is inside the parentheses first. Remember that for (7-(-5)^2), we can take off the parentheses around -5 because it is alone inside its parentheses and we need to square it since exponents are evaluated first in the order of operations. 3) The expression now becomes 10(-8)^3 - (7 - 25). There are still parentheses so we need to still evaluate those parts of the expression. For 10(-8)^3, the -8 is in the parentheses alone so we see what the next operation that is to be done to it next is the exponent. Remember that -8^3 is -8*-8*-8 = (-8^2) * -8 = 64 * -8 = -512. The answer is negative when we bring a negative number to an odd exponent. 4) The expression now becomes 10(-512) - (-18). Multiply 10 * -512 since multiplication is the next operation in the order of operations since -512 is in the parentheses by itself with no other operation inside the parentheses. 5) Expression is now -5120 - (-18). We can remove the parentheses around -18 and add it to -5120 because subtracting a negative is the same as adding its positive. This expression is equal to -5102.