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2 years ago

Why is 3÷0.5 is 6, why is it?

Mathematics

1 answer:

Alekssandra [29.7K]2 years ago

3 0

Answer:

Step-by-step explanation:

A quick way to divide by 0.5 or ½ is to double the number (or multiply number by 2). The reason for this is that two halves go into a whole.

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I've already saved $68 for the $200 video game system. How many hours does raj need to work to earn the remainder of the money h

gladu [14]

Total amount needed for the video game = $200

Total amount of money saved = $68

Amount of money that is needed to be saved = 200-68 =132

So raj needs to work additional hours in order to earn the remaineder$132 for the video game

Hourly wage = $5.5

So, number of hours that Raj needs to work to earn $132 = $132/5.5 = 24 hours

Number of hours that Raj needs to work to earn the remainder of the money = 24 hours

6 0

2 years ago

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a

Anettt [7]

Answer:

1) The size of the colony after 4 days is 6553 mosquitoes

2) After $t = 4.9\ days$

Step-by-step explanation:

To answer this question you must use the growth formula

$N = N_0e ^ {kt}$

Where

$N_0$ is the initial population of mosquitoes = 1000

t is the time in days

k is the growth rate

N is the population according to the number of days

We know that when t = 1 and $N_0=1000$ then N = 1600

Then we use these values to find k.

$1600 = 1000e ^{k(1)}\\\\\frac{1600}{1000} = e ^ k\\\\ln(\frac{1600}{1000}) = k\\\\k = 0.47$

Now that we know k we can find the size of the colony after 4 days.

$N = 1000e ^ {0.47(4)}\\\\N = 6553\ mosquitoes$

To know how long it should take for the population to reach 10,000 mosquitoes we must do N = 10000 and solve for t.

$10000 = 1000e ^ {0.47t}\\\\10 = e ^ {0.47t}\\\\ln(10) = 0.47t\\\\t = \frac{ln(10)}{0.47}\\\\t = 4.9\ days$

6 0

2 years ago

2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0

2 years ago

Quentin buys a model car every year. The first time he bought a model car, in Year 0, it cost $19.40. He notices the price is ge

vitfil [10]

Answer: the graph increases from left to right, since the price goes up. If you were to actually graph this, the years would be on the bottom and the price would be on the left side, so since the price is going up, so is the graph. :)

6 0

3 years ago

Which of the following rational functions is graphed below?

Dennis_Churaev [7]

Can you provide a picture?

3 0

3 years ago

Why is 3÷0.5 is 6, why is it?​

Why is 3÷0.5 is 6, why is it?