How do you show your work of 47 divided by 6?

Please help on two math questions. I don’t understand how to do them.

Sidana [21]

When you represent intervals on the number line, you're including full dots, excluding empty dots, and you're considering numbers highlighted by the line.

In the first case, you've highlighted everything before -2 (full dot, thus included), and everything after 1 (empty dot, excluded). So, the set would be

$x\leq -2 \lor\ x>1$

or, in interval notation,

$(-\infty,-2]\cup (1,\infty)$

In the second case, you are looking for all numbers between -3 and 5. This interval is symmetric with respect to 1: you're considering all numbers that are at most 4 units away from 1, both to the left and to the right.

This means that the difference between your numbers at 1 must be at most 4, which is modelled by

$|x-1|\leq 4$

where the absolute values guarantees that you'll pick numbers to the left and to the right of 1.

3 0

3 years ago

A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second.

Ad libitum [116K]

Let $d_m,\ d_e$ represent the depth of the miner and equipments elevator, respectively. We know that equipment elevator descends with a velocity of $v_e = 4$ feet per second, and the miners one descends with a velocity of $v_m = 15$ feet per second.

If we start counting time ( $t=0$ ) when the equipment elevator begins to descend, after $t$ seconds its depth will be

$d_e(t) = v_et = 4t$

On the other hand, the miner elevator follows the same rule, but we have to use its velocity, and remember that it starts with a delay of thirty seconds:

$d_m(t) = v_m(t-30) = 15(t - 30)$

Now, we have to wait the 30 seconds of delay, and then another 14 seconds. This means that we want to know the positions of both elevators when $t = 44$ . Let's plug this value into the two equations:

$d_e(44) = 4\cdot 44 = 176$

$d_m(44) = 15(44-30) = 15\cdot 14 = 210$

So, the equipment elevator is 176 feet deep, and the miner elevator is 210 feet deep, and thus this is the deeper one.

7 0

3 years ago

Rita gets paid $16 per hour for the first 8 hours she works each day. She earns 1 1 2 times her hourly pay rate for time she wor

omeli [17]

<h3>The total money earned by Rita on Monday = $158</h3>

Step-by-step explanation:

The rate by which Rita is paid first 8 hours = $16

The next per hour rate after 8 hours = $1\frac{1}{2} = 1.5$ times the usual rate.

Now, 1.5 times $16 = 1.5 x 1 6 = $24

So, for each hour worked after 8th hour, Rita is paid $24 per hour.

Now, the intervals she has worked are:

(a) from 8:15 to 12: 45 pm

So, the number of hours worked = 45 minutes + 45 minutes + 3 hours

= 4 hours 30 minutes .... (1) (as 60 minutes = 1 hour)

(b) break of 45 minutes after 12: 45 = 12: 45 + 45 minutes

= 12 hour 90 minutes = 1 : 30 P M

So, she started working at 1: 30 and worked till 6: 15

So, the number of hours worked = 30 minutes + 15 minutes +4 hours

= 4 hours 45 minutes .... (2)

So, by adding (1) and (2) the total hours worked by Rita

= 4 hours 30 minutes + 4 hours 45 minutes

= 8 hours 75 minutes = 9 hours 15 minutes

9 hours 15 minutes = ( 8 + 1 .25 ) ( 15 minutes = 0.25 of an hour)

So, the payment is ( 8 x (16) + 1.25 (24) )

= 128 + 30 = 158

Hence, the total money earned by Rita = $158

6 0

3 years ago

Given the line 2x - 3y - 5 = 0, find the slope of a line that is perpendicular to this line.

mojhsa [17]

The Slope of "<span>2x - 3y - 5 = 0" is:

m = 2/3.

Use the mx+y formula to solve this question.

The correct answer is: B

This is a verified answer. </span>

3 0

3 years ago

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If a football team has a 90% chance of making a field goal for 3 points and a 35% chance of making a touchdown for 7 points, fin

Svetlanka [38]

2.7 points (my guess)

4 0

3 years ago

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