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
Question : 3/4+ 0.6 = ? 1.15 1.35 1.45 or 1.05
Artyom0805 [142]

we have

\frac{3}{4} +0.6

we know that

\frac{3}{4}=0.75

and

0.75=0.40+0.35

substitute in the expression

0.40+0.35 +0.6

(0.40+0.60)+0.35

(1.00)+0.35=1.35

therefore

<u>the answer is</u>

1.35

3 0
3 years ago
Read 2 more answers
What is the product? 8(–1) A. –1.4 B. –8 C. 8 D. 11.2
enot [183]
B: -8
8 times 1 = 8, and since there is a negative in front of the 1 when you are multiplying, it should be -8/ 
7 0
3 years ago
Read 2 more answers
What is the value of the correlation coefficient r of the data set?
enyata [817]

The correct option will be:  C) 0.84

<u><em>Explanation</em></u>

Formula for Correlation coefficient :

r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}

First, for each point(x, y), we need to calculate x², y² and xy .

Then, we will find sum all x, y, x², y² and xy, which gives us Σx, Σy, Σx², ∑y² and Σxy

<em>(Please refer to the attached image for the table )</em>

Here we got, ∑x = 44 , ∑y = 183 , ∑x² = 362 , ∑y² = 6575 and ∑xy = 1480

'n' is the total number of data set, which is 7 here.

So, plugging those values into the above formula..........

r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}\\ \\ r=\frac{7(1480)-(44)(183)}{\sqrt{[7(362)-(44)^2][7(6575)-(183)^2]}}\\ \\ r=\frac{10360-8052}{\sqrt{(598)(12536)}}\\ \\ r=\frac{2308}{\sqrt{7496528}}\\ \\ r=0.84

So, the value of the correlation coefficient is 0.84

4 0
3 years ago
Read 2 more answers
What is the midpoint of a line segment with endpoints (-2, 6) and (4, 3) in the
Inessa05 [86]

Answer:

(1, 9/2) or (1, 4.5)

Step-by-step explanation:

To find the midpoint, take the x1 and x2 values and divide it by 2, same for the y values.

(4-2)/2  and (6 + 3)/2

1 and 4.5

(1, 4.5)

3 0
3 years ago
What is the range of this data?<br><br> {3, 3, 0, 8, 7, 10, 2, 6, 12, 0}
S_A_V [24]
12-0=12 that is the answer

4 0
3 years ago
Read 2 more answers
Other questions:
  • You are standing 45 meters from the base of the Empire State Building. You estimate that the angle of elevation to the top of th
    6·1 answer
  • The answer to number 27
    14·1 answer
  • A company has fixed monthly costs of $130,000 and production costs on its product of $32 per unit. The company sells its product
    6·2 answers
  • Michelle's class is handing out balloon arrangement consisting of 4 balloons each each balloon has and equally likely chance of
    6·1 answer
  • 2x10+6x13x(1/100)+9x(1/1000) into a decimal
    5·2 answers
  • Help me with this probability question for (7th grade math)​
    14·2 answers
  • Can someone please help me <br> With Geometry
    12·2 answers
  • Find the area? need help guys!!​
    11·1 answer
  • A teacher surveyed her class about their online accounts and wanted to know if they had “Fb” accounts or if they had “Snap ” acc
    8·1 answer
  • A pediatrician has smallpox vaccines numbered 1,2,3, chickenpox vaccines numbered 1,2,3,4,5,6, and influenza vaccines numbered 1
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!