Answer:
<em>2.5 hours</em>
<u>Skills needed: Speed, distance, time problems</u>
Step-by-step explanation:
1) We are given speed and distance, and have to find out the the time (in hours).
- In terms of units, everything is matched up (Since distance and speed use kilometers, and speed and time use hours).
- Time is always the distance you travelled (how far) divided by how fast you travelled (the rate/speed)
---> We can use the formula for time: 
t= time
d=distance
r=rate/speed
2) Now, let's plug in for distance and rate.
---> 
2.5 hours is the answer.
Reading the question carefully, "<span>He draws the diameter of the circle through center P using a straight edge. Next he opens his compass to a width equivalent to the radius of the circle." - that implies that Mateo is still in the process of drawing the circle by which the equilateral is inscribed to.
The next steps should be:
*He should draw the upper and lower arcs using the compass opened to a width equivalent to the radius of the sircle.
*Make a vertical diameter using centroid P as basis.
*Draw two right triangles facing the opposite directions using the top most point by which the vertical diameter of the circle touches the top most circumference of the circle.
Doing these steps, Mateo will be able to draw an equilateral triangle inscribed in a circle.
</span>
Expanding the given expressions using Foil:
1)(–7x + 4)(–7x + 4) =
2) (–7x + 4)(4 – 7x)=
3)(–7x + 4)(–7x – 4)=
=
4)(–7x + 4)(7x – 4)=
The third option that is (–7x + 4)(–7x – 4) is difference of two squares.
Answer:
you should accept the $1,000 bill
Step-by-step explanation:
Given the information:
- $500 for rolling 1 or 2
- $400 for rolling 3
- lose $300 for rolling 4,5,6
P (rolling 1 or 2) = 1/6 + 1/6 = 2/6 = 1/3
P (rolling a 3) = 1/6
P (rolling 4 or 5 or 6) = 3/6 = 1/2
Hence, the expected value for 1 time is:
E = (1/3)*500 + (1/6)*400 - (1/2)*300
E = $166 + $66 - $150
E = $82
Expected value is linear so if you roll the die 10 times, expected value is: 10*82 = $820
The expected value is $82, meaning you should accept the $1,000 bill
