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Otrada [13]
3 years ago
8

The quotient of 4 and the difference of an integer and 3 is the same as two-thirds. Find the integer.

Mathematics
1 answer:
quester [9]3 years ago
7 0
To find the integer, you must cross multiply, group the same terms, then divide both side by 2:

Solution:
4/(x-3)= 2/3
12 = 2x-6
18=2x
x= 9

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James was trying to sleep one night but there was too much noise around him. His clock ticked every
g100num [7]

Answer:

<em>It will occur zero times between midnight and one o'clock.</em>

Step-by-step explanation:

<u>Least Common Multiple (LCM)</u>

Three events keep James from sleeping: his clock ticking every 20 seconds, a tap dripping every 15 seconds, and his dog snoring every 27 seconds.

All three events happened together at midnight. They will happen together again the first time the numbers 20, 15, and 27 have a common multiple. This is the LCM.

List the prime factors of each number:

20: 2,2,5

15: 3,5

27: 3,3,3

Now multiply all the factors the maximum number of times they appear:

LCM=2*2*3*3*3*5=540

(a) All the events will happen together again after 540 minutes.

(b) Since 540 minutes = 9 hours, this event won't happen again until 9 am. Thus, it will occur zero times between midnight and one o'clock.

4 0
2 years ago
PLEASE ANSWER IMMEDIATELY <br>find the area of the following shape​
STatiana [176]

Answer:

i think the answer is 51

6 0
3 years ago
HELP ME ASAP!!!!!!!!!
Arte-miy333 [17]

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6 0
2 years ago
The graph shown represents the number of bacteria in a dish after a certain number of minutes. It is a function in the form f(x)
SSSSS [86.1K]

Answer:

The number of bacteria in the dish after 9.9 minutes is 478

Step-by-step explanation:

The form of the function is f(x)=a.b^{x} , where a is the initial amount (value f(x) at x = 0)

To find a and b let us use two points from the graph and substitute their coordinates in the equation

∵ The graph passes through point (1 , 1)

∴ x = 1 and y = 1

- Substitute them in the equation

∵ 1=a.b^{1}

∴ a.b = 1 ⇒ (1)

∵ The graph passes through point (1 , 1)

∴ x = 3 and y = 4

- Substitute them in the equation

∵ 4=a.b^{3}

∴ a.b³ = 4 ⇒ (2)

Use equation (1) to find a in terms of b

∵ a.b = 1

- Divide both sides by b

∴ a=\frac{1}{b} ⇒ (3)

- Substitute a in equation (2) by equation (3)

∴ \frac{1}{b} . b³ = 4

- Remember the rule \frac{a^{m}}{a^{n}}=a^{m-n}

∵ \frac{1}{b} . b³ = b^{3-1} = b²

∴ b² = 4

- Take √  for both sides

∴ b = 2

Substitute the value of b in equation (3) to find a

∵ a = \frac{1}{2}

∴ a = 0.5

∴ f(x)=0.5(2)^{x}

∵ f(x) represents the number of bacteria after x minutes

∵ x = 9.9 minutes

- Substitute x by 9.9 to find the number of bacteria

∵ f(9.9)=0.5(2)^{9.9}

∴ f(9.9) = 477.7128917

- Round it to the nearest whole number

∴ f(9.9) = 478

∴ The number of bacteria in the dish after 9.9 minutes is 478

4 0
3 years ago
How many liters are in a gallon of water?
Alenkasestr [34]
In 1 gallon there are 3.8 liters 
3 0
3 years ago
Read 2 more answers
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