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Aleksandr [31]
2 years ago
7

Jeff hiked for 2 hours and traveled 5 miles. If he continues at the same pace, which equation will show the relationship between

the time, t, in hours he hikes to distance, d, in miles? Will the graph be continuous or discrete?

Mathematics
2 answers:
lesya692 [45]2 years ago
5 0

Answer:

d

Step-by-step explanation:

Lady_Fox [76]2 years ago
3 0

Answer: The relationship between distance and time is d=2.5t and the graph is continuous.

Step-by-step explanation:

Since we have given that

Number of hours he hiked = 2 hours

Distance covered = 5 miles

Speed would be

\dfrac{Distance}{Time}\\\\=\dfrac{5}{2}\\\\=2.5\ mph

Let the distance be 'd'.

Let the time be 't'.

so, the relation between distance and time would be

distance=Speed\times time\\\\d=2.5t

The graph  is continuous because it is not based on counts and the points are  connected with a continuous line without any break.

Hence, the relationship between distance and time is d=2.5t and the graph is continuous.

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Estimate 1.9 times 4.4
lord [1]

Answer:

8.93

Step-by-step explanation:

3 0
2 years ago
Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solut
Murrr4er [49]
Let's say the number of days library book is late is X, and the total fee is Y.

Liability charges $0.30 dollars as a fee for being 1 day late,

For being 1 day late, fee charge is: 1* $0.30
So, for X days the charge would be: X*$0.30.

Total charge for being X days late is Y, Which means: Y= 0.30 * X.

Now We would have to check all the viable solutions in the answer to see if they satisfy the equation Y= 0.30 * X

Option one(-3, -0.9) and two (-2.5, -0.75) Would not be a viable solution because the value of number of days can not be negative and in option one and two, value of days -3 and -2.5 is negative.

Option three(4.5, 1.35) can not be correct because library charges fee for a full day so the number for days would be a whole number. Library would not charge for 4.5 days, they would either charge of 4 days or 5 days because 4.5 is not an whole number.


Option four(8, 2.40) is the correct answer because it satisfies our equation;

Y= 0.30 * X

2.40= 0.30 * 8

2.40 = 2.40.


Fourth option (8, 2.40) is the only viable solution to this question.
5 0
2 years ago
Read 2 more answers
The number of bacteria in a petri dish on the first day was 113 cells. If the number of bacteria increase at a rate of 82% per d
Tresset [83]

Answer:

4107 cells

Step-by-step explanation:

From the question, we have the following values:

Day 1 : 113 cells

Number of cells increases by day by 82%

Hence,

Day 2

113 × 82% = 92.66cells

Hence, Total number of bacteria cells for Day 2 = 113 + 92.66 = 205.66cells

Day 3

205.66 × 82% = 168.6412 cells

Hence, Total number of bacteria cells for Day 3 = 168.6412 + 205.66 = 374.3012 cells

Day 4

374.3012 × 82% = 306.926984 cells

Hence, Total number of bacteria cells for Day 4 = 306.926984 + 374.3012 = 681.228184 cells

Day 5

681.228184 × 82% = 558.60711088 cells

Hence, Total number of bacteria cells for Day 5 = 558.60711088 + 681.228184 = 1239.8352949 cells

Day 6

1239.8352949 × 82% = 1016.6649418 cells

Hence, Total number of bacteria cells for Day 5 = 1016.6649418 + 1239.8352949 = 2256.5002367 cells

Day 7

2256.5002367 × 82% = 1850.3301941 cells

Hence, Total number of bacteria cells for Day 7 = 1850.3301941 + 2256.5002367 = 4106.8304308 cells

Approximately to nearest whole number, the total number of bacteria cells that would be present after 7 days = 4107 cells

3 0
2 years ago
G identify the solution of the recurrence relation an = 6an − 1 – 8an − 2 for n ≥ 2 together with the initial conditions a0 = 4,
maksim [4K]
Via the generating function method, let

G(x)=\displaystyle\sum_{n\ge0}a_nx^n

Then take the recurrence,

a_n=6a_{n-1}-8a_{n-2}

multiply everything by x^n and sum over all n\ge2:

\displaystyle\sum_{n\ge2}a_nx^n=6\sum_{n\ge2}a_{n-1}x^n-8\sum_{n\ge2}a_{n-2}x^n

Re-index the sums or add/remove terms as needed in order to be able to express them in terms of G(x):

\displaystyle\sum_{n\ge2}a_nx^n=\sum_{n\ge0}a_nx^n-(a_0-a_1x)=G(x)-4-10x

\displaystyle\sum_{n\ge2}a_{n-1}x^n=\sum_{n\ge1}a_nx^{n+1}=x\sum_{n\ge1}a_nx^n=x\left(G(x)-a_0\right)=x(G(x)-4)

\displaystyle\sum_{n\ge2}a_{n-2}x^n=\sum_{n\ge0}a_nx^{n+2}=x^2\sum_{n\ge0}a_nx^n=x^2G(x)

So the recurrence relation is transformed to

G(x)-4-10x=6x(G(x)-4)-8x^2G(x)
(1-6x+8x^2)G(x)=4-14x
G(x)=\dfrac{4-14x}{1-6x+8x^2}=\dfrac{4-14x}{(1-4x)(1-2x)}=\dfrac1{1-4x}+\dfrac3{1-2x}

For appropriate values of x, we can express the RHS in terms of geometric power series:

G(x)=\displaystyle\sum_{n\ge0}(4x)^n+3\sum_{n\ge0}(2x)^n=\sum_{n\ge0}\bigg(4^n+3\cdot2^n\bigg)x^n

which tells us that

a_n=4^n+3\cdot2^n
3 0
2 years ago
You and three friends own a paint shop. The shop's profit was $536 in the first month. You always divide the profits equally. In
alexandr1967 [171]
C.  $360


$224x4=896 (total profit)

$896 (total) - $536 (first month profit) = $360 (second month profit)
4 0
2 years ago
Read 2 more answers
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