From a barrel of colored marbles, you randomly select 4 blue, 5 yellow, 6 red, 2 green, and 5 purple marbles. Find the experimental probability of randomly selecting a marble that is not blue. A. The term shows 6 over 13. B. one-half C. start fraction 9 over 11 end fraction D. three-eighths

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.

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.

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.

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.

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

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!)

Answer:

r^-6

Step-by-step explanation: