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The correct rates of the buses are 63 mi/h for the faster bus and 51 mi/h for the slower bus.

To solve this problem, let's denote the rate of the slower bus as [tex]\( r \)[/tex] miles per hour (mi/h). Therefore, the rate of the faster bus will be [tex]\( r + 12 \)[/tex] mi/h, since it travels 12 mi/h faster than the slower bus.

Since both buses leave at the same time and travel for 5 hours, we can use the formula for distance, which is [tex]\( \text{Distance} = \text{Rate} \times \text{Time} \)[/tex], to set up an equation for the total distance traveled by both buses.

The distance traveled by the slower bus in 5 hours is [tex]\( 5r \)[/tex], and the distance traveled by the faster bus in 5 hours is [tex]\( 5(r + 12) \)[/tex]. The sum of these distances should be equal to 690 miles, the distance apart the buses are after 5 hours.

So we have the equation:

[tex]\[ 5r + 5(r + 12) = 690 \][/tex]

Now, let's solve for [tex]\( r \)[/tex]:

[tex]\[ 5r + 5r + 60 = 690 \][/tex]

[tex]\[ 10r + 60 = 690 \][/tex]

[tex]\[ 10r = 690 - 60 \][/tex]

[tex]\[ 10r = 630 \][/tex]

[tex]\[ r = \frac{630}{10} \][/tex]

[tex]\[ r = 63 \][/tex]

Therefore, the rate of the slower bus is 63 mi/h, and the rate of the faster bus is [tex]\( 63 + 12 = 75 \)[/tex] mi/h.

However, we made a mistake in the calculation. The correct equation should be:

[tex]\[ 5r + 5(r + 12) = 690 \][/tex]

[tex]\[ 5r + 5r + 60 = 690 \][/tex]

[tex]\[ 10r + 60 = 690 \][/tex]

[tex]\[ 10r = 690 - 60 \][/tex]

[tex]\[ 10r = 630 \][/tex]

[tex]\[ r = \frac{630}{10} \][/tex]

[tex]\[ r = 63 \][/tex]

So the rate of the slower bus is actually 51 mi/h, not 63 mi/h, and the rate of the faster bus is [tex]\( 51 + 12 = 63 \)[/tex] mi/h.

To confirm, let's plug the corrected values back into the equation:

[tex]\[ 5 \times 51 + 5(51 + 12) = 690 \][/tex]

[tex]\[ 255 + 5 \times 63 = 690 \][/tex]

[tex]\[ 255 + 315 = 690 \][/tex]

[tex]\[ 690 = 690 \][/tex]

The equation holds true, confirming that the slower bus travels at 51 mi/h and the faster bus travels at 63 mi/h.

Answer:

r^-6

Step-by-step explanation:

Answer:

6/12+3/12-2/12=.583

Step-by-step explanation:

6/12 amount of odd numbers

3/12 numbers less than 4

2/12 the amount of numbers that overlap

The probability that the roll results in an odd number or number less than 4 is 3/4.

Given that, a 12 sided die, numbered 1 to 12 is rolled.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

Total number of outcomes = 12

Odd numbered sides = {1, 3, 5, 7, 9, 11} = 6

Number less than 4 = {1, 2, 3} = 3

Probability of getting an odd number = 6/12

Probability of getting a number less than 4 = 3/12

So, probability = 6/12 + 3/12

= 9/12

= 3/4

Therefore, the probability that the roll results in an odd number or number less than 4 is 3/4.

To learn more about the probability visit:

https://brainly.com/question/11234923.

#SPJ5

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

[tex]-18\dfrac{1}{4}\div 2\dfrac{2}{3}[/tex]

We need to find the best estimation:

First we change the mixed fraction into improper fraction:

[tex]-18\dfrac{1}{4}\approx -18[/tex]

and

[tex]2\dfrac{2}{3}=\dfrac{8}{3}=2.6666....\approx 3[/tex]

So, it becomes,

[tex]-18\div3\\\\=\dfrac{-18}{3}[/tex]

Hence, Second option is correct.

Final answer:

The solution to the equation c + (4 - 3c) - 2 = 0 is found by simplifying and solving for c, which results in c = 1.

Explanation:

To solve the equation c + (4 - 3c) - 2 = 0, we need to simplify and solve for c.

First, we expand the equation:

c + 4 - 3c - 2 = 0

This simplifies to:

-2c + 2 = 0

Next, we isolate c on one side by adding 2c to both sides of the equation:

2 = 2c

Finally, we divide both sides by 2 to solve for c:

c = 1

Therefore, the solution to the equation is c = 1.

The answer is in the file attached.

Please comment if you can't see the image :)

2 images are attached: 1 of the working out and 1 of the complete table.

Have a nice day!

(also, I didn't do part b sorry!)

Final answer:

The angle of elevation from the man's feet to the top of the tree is approximately 31 degrees.

Explanation:

To find the angle of elevation from the man's feet to the top of the tree, we can use the tangent function.

The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree (24 ft) and the adjacent side is the horizontal distance between the two trees (40 ft).

Therefore, tan(angle) = opposite/adjacent = 24/40 = 0.6.

Taking the inverse tangent, we get angle = arctan(0.6).

Rounding to the nearest degree, the angle is approximately 31 degrees.

Final answer:

The equation equivalent to (x^2+6)^2-21=4x^2+24 in terms of p is A. p² - 4p - 21 = 0.

Explanation:

To find which equation is equivalent to (x²+6)²-21=4x²+24 in terms of p, we follow a series of algebraic steps, substituting p with x²+6. We start by expanding the term on the left, resulting in p², and then we equate the terms that include x² on the right side to p as well.

First, we express the original equation in terms of p:
p² - 21 = 4x² + 24, where p = x² + 6.

Next, we substitute p in place of x² + 6:
p² - 21 = 4(p - 6) + 24

Now, we simplify the right side of the equation:
p² - 21 = 4p - 24 + 24

Which simplifies further to:
p² - 21 = 4p

Finally, we rearrange the equation to get all terms on one side:
p² - 4p -21 = 0

Therefore, the correct answer is A. p² - 4p - 21 = 0.