A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the pr

Consider this system of equations. Which shows the second equation written in slope-intercept form? y = 3 x minus 2. 10 (x + thr

Leona [12618]

Question

Consider this system of equations. Which shows the second equation written in slope-intercept form?

$y = 3x - 2.$

$10(x + \frac{3}{5} ) = 2y$

A. $y = 5x + \frac{3}{10}$

B. $y = 5x + 3$

C. $y = \frac{1}{5} x + \frac{3}{25}$

D. $y = \frac{1}{2} x + 6$

Response:

B. $y = 5x + 3$

Detailed explanation:

Given

Equation 1: $y = 3x - 2.$

Equation 2: $10(x + \frac{3}{5} ) = 2y$

Required:

Equivalent of equation 2

To achieve an equivalence of equation 2 (in slope-intercept form), we must first simplify it

$10(x + \frac{3}{5} ) = 2y$

Open the brackets

$10*x + 10 *\frac{3}{5} = 2y$

$10x + \frac{30}{5} = 2y$

Simplify the fractions

$10x + 6 = 2y$

Divide by 2

$\frac{10x}{2} + \frac{6}{2} = \frac{2y}{2}$

$5x + 3 = y$

Re-arrange

$y = 5x + 3$

Next, we compare options A through D with $y = 5x + 3$

A. is not equal to $y = 5x + 3$

Next, we check the second option

B.

$y = 5x + 3$ matches $y = 5x + 3$

This option represents the second equation in slope-intercept format.

We check for further options

C.

$y = \frac{1}{5} x + \frac{3}{25}$

Convert the fraction into a decimal

$y = 0.2x + 0.12$

This does not equal $y = 5x + 3$

D.

$y = \frac{1}{2} x + 6$

Convert the fraction to decimal

$y = 0.5x + 6$

This also does not equal to $y = 5x + 3$

Therefore, the only option equivalent to the second equation in slope-intercept form is Option B

7 0

2 months ago

Read 2 more answers

A basketball player makes 90% of her free throws. what is the probability she will miss for the first time on the seventh shot?

Inessa [12570]

The likelihood she will miss on her first attempt is 52.17%.

4 0

3 months ago

44 students completed some homework and the histogram shows information about the times taken. Work out an estimate of the inter

tester [12383]

1.4×5=7

0.8×10=8

1.4×10=14

1×15=15

15+14+8+7=44

44÷4=11

LQ of 44=11

LQ=10 minutes

11×3=33

UQ= 29 minutes

The Range is 19 minutes

Detailed breakdown:

Commence with the individual boxes. For determining the number of students in each category, calculate Frequency density × The difference in the category. (if it's 5-15, the difference is 10)

This results in the counts of students in each range.

Next, determine the LQ of 44, which is 11.

Then locate the 11th student's score; in this instance, it resides in the 5-15 range. 7 students have already surpassed it, with 8 in the 5-15 range. Hence, the 11th lies within the bounds of 5-15, making the middle 10.

Repeat this process for the UQ.

The interquartile range is calculated as UQ-LQ, yielding 29-10=19 minutes.

I hope this helps, though I'm not entirely sure if my explanation is coherent and I'm unclear on the terminology I've used for these categories.

6 0

2 months ago