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Usimov [2.4K]
4 years ago
12

The table below lists the capacity, in quarts, of four different fish tanks at a pet store.

Mathematics
1 answer:
Ilya [14]4 years ago
5 0

Given:

Table of fish tank capacity

To find:

Which fish tank has a capacity of 60 gallons.

Solution:

In the given table, the capacity is mentioned in quarts.

Let us convert gallon to quarts.

1 gallon = 4 quarts

60 gallon = 60 × 4

                = 240 quarts

In the table Pacific fish tank has 240 quarts capacity (60 gallons).

Therefore Pacific fish tank has a capacity of 60 gallons.

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How many positive integers $n$ from 1 to 5000 satisfy the congruence $n \equiv 5 \pmod{12}$?
irga5000 [103]
The equivalence n \equiv 5 \pmod{12}

means that n-5 is a multiple of 12.

that is

n-5=12k, for some integer k

and so

n=12k+5


for k=-1, n=-12+5=-7

for k= 0, n=0+5=5 (the first positive integer n, is for k=0)


we solve 5000=12k+5 to find the last k

12k=5000-5=4995

k=4995/12=416.25

so check k = 415, 416, 417 to be sure we have the right k:

n=12k+5=12*415+5=4985

n=12k+5=12*416+5=4997

n=12k+5=12*417+5=5009


The last k which produces n<5000 is 416


For all k∈{0, 1, 2, 3, ....416}, n is a positive integer from 1 to 5000,

thus there are 417 integers n satisfying the congruence.


Answer: 417

6 0
4 years ago
What is five times that quantity​
yawa3891 [41]

Answer:

basically multiplication, (that quantity) times 5

Step-by-step explanation:

6 0
3 years ago
The circle passes through the point (−2, 3) with a center of (-4,6). What is its radius?
Ganezh [65]

Answer:

<u>radius = √13</u>

Step-by-step explanation:

Forming the equation :

<u>(x - h)² + (y - k)² = r²</u>

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  • (h, k) = center of circle
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Solving :

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7 0
2 years ago
PLEASE HELP!!!!
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A) \frac{2 \frac{1}{4}}{ \frac{1}{2}}
b)\frac{1}{2} • 2 = 1
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5 0
3 years ago
two pools are being drained.To start,the first pool had 3100 liters of water and the second had 3472 liters of water.Water is be
miss Akunina [59]
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5 0
3 years ago
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