Jocelyn made a spinner If Jocelyn spins only one time what is the probability that the arrow will not land on a red section of the spinner?
3 parts are red
4 parts are blue
1 part is white
A.1/8
B.5/8
C.3/8
D.1/2
B
Palmer participated in sports for 8 hours and drama for 5 hours during a period of 2 weeks. If Palmer continues participating activities at this rate how many hours will he spend participating in them during 52 weeks
338?
Express 405 as a product of prime factors
A.3^4x5^4
B.5x9x9
C.3^4x5
D.3^4x5x9
C
I agree with your answers.
me to
To find the probability that the arrow will not land on a red section of the spinner, we first need to determine the total number of sections on the spinner. In this case, there are 3 red sections, 4 blue sections, and 1 white section, so the total number of sections is 3 + 4 + 1 = 8.
The probability of an event happening is calculated by taking the number of favorable outcomes (the desired event) divided by the number of possible outcomes. In this case, the favorable outcome is the arrow not landing on a red section, which is 4 (the number of blue and white sections). The number of possible outcomes is the total number of sections, which we determined to be 8.
Therefore, the probability that the arrow will not land on a red section is 4/8, which simplifies to 1/2.
For the second question, we know that Palmer participated in sports for 8 hours and drama for 5 hours during a period of 2 weeks. To find out how many hours he will spend participating in these activities during 52 weeks, we can set up a proportion.
Since there are 52 weeks in a year and we know Palmer spent 2 weeks participating in the activities, we can write the proportion:
2 weeks / 8 hours = 52 weeks / x hours
To solve for x, we can cross-multiply:
2x = 8 * 52
2x = 416
Dividing both sides by 2, we get:
x = 416 / 2
x = 208
Therefore, Palmer will spend 208 hours participating in sports and drama activities during 52 weeks.
To express 405 as a product of prime factors, we need to find the prime numbers that, when multiplied together, give us the original number.
We can start by dividing 405 by the smallest prime number, which is 2. However, 405 is not divisible evenly by 2.
Next, we try dividing by the next prime number, 3. 405 divided by 3 equals 135, which is divisible by 3.
Further dividing 135 by 3, we get 45, which is divisible by 3 again.
Lastly, dividing 45 by 3, we get 15, which is divisible by 3 one more time.
The result, 15, is not divisible by 3 anymore, so we move on to the next prime number, which is 5.
405 divided by 5 equals 81, which is not divisible by 5.
So, the prime factors of 405 are 3, 3, 3, and 5. Therefore, we can express 405 as 3^3 * 5, which corresponds to option C: 3^4 * 5.