1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
erastovalidia [21]
3 years ago
9

QUESTION

Mathematics
1 answer:
Lorico [155]3 years ago
7 0
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 a_{n}= a_{n-1}+d, a_{n} refers to the next term in the sequence, a_{n-1} refers to the previous term, while d refers to the common difference. In the recursive formula all we need is to insert the value of d to the equations.

Ernest: a_{n}= a_{n-1}+0.25
Denise: a_{n}= a_{n-1}+0.5

5. For this item we basically do the same thing but this time we are given another formula. Our formula is in the form a_{n}= a_{1}+(n-1)d where a_{n} is still the nth term of the sequence, a_{1} is the very first time, n is the number of terms, and d is the common difference. 

Ernest: a_{n}= 1.0+0.25(n-1)
Denise: a_{n}= 1.0+0.5(n-1)

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.

a_{10}= 1.0+0.25(10-1)
a_{10}= 1.0+0.25(9)
a_{10}= 1.0+2.25
a_{10}= 3.25

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.

a_{10}= 1.0+0.5(10-1)
a_{10}= 1.0+0.5(9)
a_{10}= 1.0+4.5
a_{10}= 5.5

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.
Bdbhdjdjsjs
2 years ago
What’s 8 ?
You might be interested in
Adam is painting the outside of a 4-walled shed. The shed is 5 feet wide, 4 feet deep, and 7 feet high. How many square feet of
Olenka [21]
He will nedd alot of sqaure feer
5 0
3 years ago
Read 2 more answers
The cost of 3 scarves is $72.75. What is the unit price?
sergejj [24]

Answer:

$24,25

Step-by-step explanation:

72.75 ÷ 3 = 24,25

3 0
2 years ago
Two angles are complementary. The first angle is 2x degrees. The second angle is (3x +5) degrees. Determine the measure of each
bixtya [17]

Answer:

70 and 110

Step-by-step explanation:

First angle -- 2x

Second angle -- 3x + 5

Therefore,

2x + 3x + 5 = 180

5x = 175

x = 35

Therefore, 2x -- 70

3x + 5 -------------110

Thenks and mark me brainliest :)

8 0
3 years ago
Someone good with trigonometry please help
serg [7]
Tan(52°) = opposite/adjacent = x/35  ⇒ 

x = 35 * tan(52°) = 35 * 1.2799 ≈ 44.80
3 0
3 years ago
Can I get some help please
Mamont248 [21]
-2(-2)+3=7
-2(0)+3=3
-2(4)+3=-5
3 0
3 years ago
Other questions:
  • Pleas help me if you can’t see the picture it’s h over 10 as a fraction then it says=100 what is h?
    8·2 answers
  • Multiply these binomials, (x+2) and (3x-4)
    8·1 answer
  • Name the property of real numbers illustrated by the following equation.
    11·1 answer
  • MechNerd has 3 dollars. He loses 1 dollar because he is dumb. How much does he have left?
    15·2 answers
  • I need help pleaseeeeeeeeeeeeeeeeeeeeee ill be in trouble if i get it wrong
    13·1 answer
  • Miyo works for an ice cream vendor. She receives $25 for taking
    7·1 answer
  • Please help spring break homework!!
    15·1 answer
  • 15)<br> 125°<br> ?<br> Help me plzzz
    10·1 answer
  • Answer this please Answer
    12·2 answers
  • in how many ways can a club choose a president, a treasurer, a secretary, and three other committee members (with identical duti
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!