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Math Questions from Jan 20,2025

Browse the Math Q&A Archive for Jan 20,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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When a particular type of thumbtack is dropped, it will land point up ( \( \perp \) ) or point down ( \( \langle \) ). This experiment was repeated 100 times with the following results: point up: 50 times; point down: 50 times. a. What is the experimental probability that a particular type of thumbtack will land point up? b. What is the experimental probability that a particular type of thumbtack will land point down? c. If the experiment was tried another 100 times would the same results occur? Why? d. Is it expected that nearly the same results occur on a second trial? Why? a. The experimental probability that a particular type of thumbtack will land point up is (Type an integer or a simplified fraction.) If \( A \) and \( B \) are mutually exclusive, and if \( P(A)=0.2 \) and \( P(B)=0.7 \), what is \( P(A \cup B) \) ? \( P(A \cup B)=\square \) 90 men and 80 women are enrolled in calculus. There are 40 business majors, 20 biology majors, 55 computer science majors, and 55 mathematics majors. No person has a double major. If a single calculus student is chosen, find the following probabilites. Find the probability that the student is a man. P (man) \( =\frac{9}{17} \) (Type an integer or a simplified fraction.) Find the probability that the student is a mathematics major P (mathematics) \( =\frac{11}{34} \) (Type an integer or a simplified fraction.) Find the probability that the student is not a computer science major. P(not computer science) \( =\frac{23}{34} \) (Type an integer or a simplified fraction.) Find the probability that the student is a mathematics major or a computer science major. P(mathematics \( u \) computer science) \( =\square \) (Type an integer or a simplified fraction.) 5(a) (a) Using Cramer's rule to determine \( x+y \), if \( \left[\begin{array}{cc}5 & -3 \\ 4 & 2\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}-1 \\ -8\end{array}\right] \) (b) Given IS equation \( 0.4 Y+100 I-255=0 \) and the \( L M \) equation \( 0.25 Y-200 \mathrm{I}-177=0 \). Use matrix form to find the equilibrium level of income and rate of interest. Find the slope of the line that would pass through the ordered pairs below. \( (-7,9) \) and \( (14,-18) \) The value of a painting \( n \) years after it was painted is given by this formula: value in pounds \( (£)=300 \times 1.24^{n} \) a) What was the original value of the painting? b) By what percentage does the value of the painting increase each year? Find the slope and reduce. \[ \mathrm{P}=(-8,3) \mathrm{Q}=(-6,2) \] Slope \( =-\frac{[?]}{[]} \) 7.4 Suppose the average length of stay in a chronic disease hospital of a certain type of patient is 60 days with a standard deviation of 15 . If it is reasonable to assume an approximately normal distribution of lengths of stay, find the probability that a randomly selected patient from this group will have a length of stay: \( \begin{array}{ll}\text { (a) Greater than } 50 \text { days } & \text { (b) Less than } 30 \text { days } \\ \text { (c) Between } 30 \text { and } 60 \text { days } & \text { (d) Greater than } 90 \text { days }\end{array} \) 90 men and 80 women are enrolled in calculus. There are 40 business majors, 20 biology majors, 55 computer science majors, and 55 mathematics majors. No person has a double major. If a single calculus student is chosen, find the following probabilities. Find the probability that the student is a man. \( P \) (man) \( =\frac{9}{17} \) (Type an integer or a simplified fraction.) Find the probability that the student is a mathematics major. P(mathematics) \( =\frac{11}{34} \) (Type an integer or a simplified fraction.) Find the probability that the student is not a computer science major. P(not computer science) \( =\square \) (Type an integer or a simplified fraction.) Determine whether the statement below is true or false. The slope of the line \( 2 y=4 x+5 \) is 4 . Choose the correct answer below. False
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