Question

1 - 76. renaes mp3 player can be programmed to randomly play songs from her playlist without repeating a single song. currently, renaes mp3 player has 5 songs loaded on it, which are listed below. as she walks between class, she only has time to listen to one song. a. is each song equally likely to be chosen as the first song? b. what is the probability that her mp3 player will select a country song? c. what is the probability that renae will listen to a song with \mama\ in the title? d. what is the probability she listens to a duet with hank tumbleweed? e. what is the probability she listens to a song that is not r & b? playlist i love my mama (country) by the strings of heaven dont call me mama (country) duet by sapphire and hank tumbleweed carefree and blue (r & b) by sapphire and prism escape go back to mama (rock) duet by bjorn free and sapphire smashing lollipops (rock) by sapphire 1 - 77. use what you learned about the slopes of parallel and perpendicular lines to find the equation of a line that would meet the criteria given below. a. find the equation of the line that goes through the point (0, - 3) and is perpendicular to the line y = -\frac{2}{5}x + 6. b. find the equation of the line that is parallel to the line - 3x + 2y = 10 and goes through the point (0, 7). 1 - 78. examine the diagram at right. which angle below is another name for \angle abc? note: more than one solution is possible a. \angle abe b. \angle gbd c. \angle fbg d. \angle ebc e. none of these

Explanation:

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Step1: Determine equal - likelihood

Since the MP3 player randomly selects a song without repeating and there are no biases mentioned, each of the 5 songs has an equal chance of being chosen first. So the answer to part a is Yes.

Step2: Calculate probability of country song

There are 2 country songs ("I Love My Mama" and "Don't Call Me Mama") out of 5 total songs. The probability formula is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So the probability of selecting a country song is $\frac{2}{5}$.

Step3: Calculate probability of "Mama" in title

There are 3 songs with "Mama" in the title ("I Love My Mama", "Don't Call Me Mama", "Go Back to Mama") out of 5 total songs. So the probability is $\frac{3}{5}$.

Step4: Calculate probability of duet with Hank Tumbleweed

There is 1 duet with Hank Tumbleweed ("Don't Call Me Mama") out of 5 total songs. So the probability is $\frac{1}{5}$.

Step5: Calculate probability of non - R&B song

There is 1 R&B song ("Carefree and Blue") and $5 - 1=4$ non - R&B songs. So the probability of listening to a non - R&B song is $\frac{4}{5}$.

Step1: Find slope of perpendicular line (for part a)

The slope of the line $y =-\frac{2}{5}x + 6$ is $m_1=-\frac{2}{5}$. For a line perpendicular to it, the slope $m_2$ satisfies $m_1m_2=-1$. So $m_2=\frac{5}{2}$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(0,-3)$ (where $x_1 = 0$ and $y_1=-3$), we get $y+3=\frac{5}{2}(x - 0)$, which simplifies to $y=\frac{5}{2}x-3$.

Step2: Find slope of parallel line and equation (for part b)

Rewrite the line $-3x + 2y=10$ in slope - intercept form $y=mx + b$. We have $2y=3x + 10$ or $y=\frac{3}{2}x+5$. The slope of a line parallel to it is $m=\frac{3}{2}$. Using the point - slope form with the point $(0,7)$ (where $x_1 = 0$ and $y_1 = 7$), we get $y - 7=\frac{3}{2}(x - 0)$, which simplifies to $y=\frac{3}{2}x+7$.

An angle can be named in different ways. $\angle ABC$ and $\angle FBG$ are the same angle because they share the same vertex $B$ and the same set of rays forming the angle.

Answer:

a. Yes
b. $\frac{2}{5}$
c. $\frac{3}{5}$
d. $\frac{1}{5}$
e. $\frac{4}{5}$

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