Business Mathematics & Statistics #2

Explanation
After solving the given linear equation, we can simplify it to 6x = 8. By dividing both sides of the equation by 6, we find that x = 8/6, which can be further simplified to x = 4/3. Therefore, the value of x after solving the equation is 4/3.

Explanation
An annuity is a series of equal periodic payments or receipts. The future value of an annuity refers to the total value of all the payments or receipts at a future point in time, taking into account compound interest. Therefore, the correct answer is "Future Value" because it represents the sum of all the payments or receipts in the future.

Explanation
The given question asks for the number of arrangements that can be made with the letters in the word "BUSINESS." To solve this, we need to consider that the word contains 8 letters, including 2 S's and 2 I's. The total number of arrangements can be calculated using the formula for permutations of a word with repeated letters, which is n!/(n1! * n2! * ... * nk!), where n is the total number of letters and n1, n2, etc. are the number of repetitions for each letter. In this case, the number of arrangements is 8!/(2! * 2!) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (2 * 1 * 2 * 1) = 6720.

Explanation
The RSQ (coefficient of determination) of any data is the square of the correlation coefficient. The correlation coefficient measures the strength and direction of the linear relationship between two variables. By squaring the correlation coefficient, we obtain the RSQ, which represents the proportion of the variance in one variable that can be explained by the other variable. Therefore, the square of the correlation coefficient is the correct answer.

Explanation
The answer 10C5 represents the number of ways to choose 5 letters out of 10 to be placed in the post boxes. This is because 10C5, also known as "10 choose 5" or the binomial coefficient, calculates the number of combinations without regard to the order in which the letters are placed in the boxes. Therefore, it is the appropriate choice for this question.

Explanation
When there is no linear correlation between two variables, the value of r, which represents the correlation coefficient, will be 0. This means that there is no relationship or association between the variables. A correlation coefficient of 0 indicates that there is no linear pattern in the data points, and they are scattered randomly.

Explanation
The mode of a set of data is the value(s) that appear(s) most frequently. In the word "CORRELATION," both the letters "R" and "O" appear twice, while the other letters appear only once. Therefore, both "R" and "O" are the mode of the word "CORRELATION."

Explanation
The point where a straight line cuts the X-axis is called the y-intercept. This is because the y-intercept is the value of y when x is equal to zero, which means it represents the point where the line intersects the y-axis. In other words, it is the point on the line where the x-coordinate is zero.

Explanation
The value of r=0.913 indicates a strong positive correlation. A correlation coefficient measures the strength and direction of the linear relationship between two variables. A correlation coefficient of 0.913 indicates a strong positive relationship, meaning that as one variable increases, the other variable also tends to increase. The closer the value of r is to 1, the stronger the positive correlation. Therefore, a value of 0.913 suggests a strong positive relationship between the variables being studied.

Explanation
The question asks for a type of graph, but "Median" is not a type of graph. It is a statistical measure used to find the middle value in a set of data. Therefore, it does not fit the criteria of being a type of graph.