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2 years ago

Find the smallest number such that the remainder is 3 when it is divided by 16,20 or 24.

Mathematics

1 answer:

schepotkina [342]2 years ago

4 0

Answer: 123

Step-by-step explanation:

Foe us to solve this, we have to find the lowest common multiple of 16, 20 and 24 first and then add 3 to the LCM. This goes thus:

Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160

Multiples of 20 = 20, 40, 60, 80, 10, 120, 140, 160

Multiples of 24 = 24, 48, 72, 96, 120

Therefore, the Lowe's common multiple is 120.

We then add the remainder of 3 and this will give:

= 120 + 3

= 123

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A. What is the explicit definition for this sequence?<br><br>b. How far does she run on day 19?

creativ13 [48]

Answer:

(a) $a_n=1+\frac{1}{6}(n-1)$

(b) 4 miles

Step-by-step explanation:

Given:

The sequence of run is an arithmetic sequence.

Miles traveled on day 1 = 1 mile

Miles traveled on day 7 = 2 miles

(a).

Explicit formula for an arithmetic sequence is given as:

$a_n=a_1+(n-1)d\\a_n\to n^{th}\ term\\a_1\to first\ term\\n\to number\ of\ terms\\d\to \textrm{common difference}$

Here, $a_1=1,a_7=2$

So,

$a_7=a_1+(7-1)d\\2=1+6d\\6d=2-1\\d=\frac{1}{6}$

Therefore, the explicit definition of the above sequence is given as:

$a_n=1+\frac{1}{6}(n-1)$

Where, $a_n$ is the miles covered on $n^{th}$ day.

(b)

In order to find the distance covered by her on day 19, we plug in 19 for n in the above formula. This gives,

$a_{19}=1+\frac{1}{6}(19-1)\\\\a_{19}=1+\frac{1}{6}(18)\\\\a_{19}=1+3=4\ mi$

Therefore, the number of miles covered by her on day 19 is 4 miles.

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3 years ago

What does x/4=3/2 equal?

MrRissso [65]

x/4 = 3/2
x/2 = 3 (multiply both sides by 2)
x = 6 (multiply both sides by 2)
Therefore 6/4 = 3/2

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3 years ago

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ivann1987 [24]

Answer:

x = 44

Step-by-step explanation:

sqrt(x+5) -3 =4

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sqrt(x+5) -3+3 =4+3

sqrt(x+5) =7

Square each side

(sqrt(x+5))^2 =7^2

x+5 = 49

Subtract 5 from each side

x+5-5 = 49-5

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3 years ago

Read 2 more answers

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strojnjashka [21]

Answer: 49/9

Step-by-step explanation:

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2 years ago

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Crazy boy [7]

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3 years ago

Find the smallest number such that the remainder is 3 when it is divided by 16,20 or 24.​

Find the smallest number such that the remainder is 3 when it is divided by 16,20 or 24.