The times for the mile run of a large group of male college students are approximately Normal with mean 7.11 minutes and standar
1 answer:
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Answer:
Option C is correct
The ratio of green to red marbles is, 3 : 1
Step-by-step explanation:
As per the statement:
A bag contains 44 marbles, some red and some green.
⇒Total marbles = 44
If there are 11 red marbles.
then;
Green marbles = Total marbles - red marbles.
Substitute the given values we have;
Green marbles = 44 - 11 = 33
We have to find the ratio of green to red marbles.
Therefore, the ratio of green to red marbles is, 3 : 1
1. For this item we just refer to the prompt to know the conjectures of Ernest and Denise. According to Ernest, they should swim 1 kilometer on the first week then add 0.25km every week while Denise believes that they should swim 1 kilometer on the first week then add 0.5km every week.
2. Yes, these distances make an arithmetic sequence. It's because an arithmetic sequence is defined as a group of increasing or decreasing numbers where the difference between any two consecutive numbers is constant. This just means that every number has the same interval. In the case of their schedule, this is true.
3. For this item we just follow the descriptions of Ernest's and Denise's schedule in item number 1. For Ernest, we just keep adding 0.25 from 1 kilometer until we added it thrice. For Denise, we also keep adding a number thrice but this time it's 0.5 instead of 0.25.
Ernest's Schedule: 1, 1.25, 1.5, 1.75
Denise's Schedule: 1, 1.5, 2, 2.5
4. Here we are asked to determine a formula that will describe the schedules of Ernest and Denise. In the given formula
, 
refers to the next term in the sequence, 
refers to the previous term, while 
refers to the common difference. In the recursive formula all we need is to insert the value of d to the equations.
Ernest:
Denise:
5. For this item we basically do the same thing but this time we are given another formula. Our formula is in the form
where is still the nth term of the sequence, 
is the very first time, 
is the number of terms, and is the common difference.
Ernest:
Denise:
6. In this item we will just basically substitute numbers to one of the equations that we've set up in item #5. For this we need Ernest's explicit formula first. To know how far they will be swimming on week 10, the number of elements (n) must be 10.
7. Here, we just do the same thing as item #6 but this time we will consider Denise's explicit formula. Since we are also asked how far the students will be swimming on week 10, the number of elements would also be 10 and this would also be our value for n.
8. The answer for this question is obvious. You would just need to look at the 10th element in Ernest's and Denise's sequences and tell whose schedule had more than or equal to 5 as an answer. Following Ernest's schedule, you will just get 3.5 kilometers on the 10th week so it's definitely a no. Denise's schedule, on the other hand, would get you to 5.5 kilometers on week 10 so her training schedule should be followed.
2. Yes, these distances make an arithmetic sequence. It's because an arithmetic sequence is defined as a group of increasing or decreasing numbers where the difference between any two consecutive numbers is constant. This just means that every number has the same interval. In the case of their schedule, this is true.
3. For this item we just follow the descriptions of Ernest's and Denise's schedule in item number 1. For Ernest, we just keep adding 0.25 from 1 kilometer until we added it thrice. For Denise, we also keep adding a number thrice but this time it's 0.5 instead of 0.25.
Ernest's Schedule: 1, 1.25, 1.5, 1.75
Denise's Schedule: 1, 1.5, 2, 2.5
4. Here we are asked to determine a formula that will describe the schedules of Ernest and Denise. In the given formula
Ernest:
Denise:
5. For this item we basically do the same thing but this time we are given another formula. Our formula is in the form
Ernest:
Denise:
6. In this item we will just basically substitute numbers to one of the equations that we've set up in item #5. For this we need Ernest's explicit formula first. To know how far they will be swimming on week 10, the number of elements (n) must be 10.
7. Here, we just do the same thing as item #6 but this time we will consider Denise's explicit formula. Since we are also asked how far the students will be swimming on week 10, the number of elements would also be 10 and this would also be our value for n.
8. The answer for this question is obvious. You would just need to look at the 10th element in Ernest's and Denise's sequences and tell whose schedule had more than or equal to 5 as an answer. Following Ernest's schedule, you will just get 3.5 kilometers on the 10th week so it's definitely a no. Denise's schedule, on the other hand, would get you to 5.5 kilometers on week 10 so her training schedule should be followed.
Answer:
See explanation
Step-by-step explanation:
Required
Effect of replacing with
f(x) is represented as: (x,y)
While
f(x - h) is represented as (x - h, y)
Notice the difference in both is that, the x value in f(x - h) is reduced by a constant h while the y value remain unchanged.
This means that the graph of f(x) will shift horizontally (i.e. along the x-axis) to the left by h units