All categories

3 years ago

Four bottles of powerade cost $3.88. Find the unit price of each bottle

Mathematics

2 answers:

Naddik [55]3 years ago

8 0

Since 4 = $3.88
Then 1 = 3.88/4
= $ 0.97

timofeeve [1]3 years ago

7 0

The answer will be 0.97
i think

You might be interested in

A bacteria culture starts with 400 bacteria and grows at a rate proportional to its size. After 4 hours, there are 9000 bacteria

Kaylis [27]

Answer:

A) The expression for the number of bacteria is $P(t) = 400e^{0.7783t}$ .

B) After 5 hours there will be 19593 bacteria.

C) After 5.55 hours the population of bacteria will reach 30000.

Step-by-step explanation:

A) Here we have a problem with differential equations. Recall that we can interpret the rate of change of a magnitude as its derivative. So, as the rate change proportionally to the size of the population, we have

$P' = kP$

where $P$ stands for the population of bacteria.

Writing $P'$ as $\frac{dP}{dt}$ , we get

$\frac{dP}{dt} = kP$ .

Notice that this is a separable equation, so

$\frac{dP}{P} = kdt$ .

Then, integrating in both sides of the equality:

$\int\frac{dP}{P} = \int kdt$ .

We have,

$\ln P = kt+C$ .

Now, taking exponential

$P(t) = Ce^{kt}$ .

The next step is to find the value for the constant $C$ . We do this using the initial condition $P(0)=400$ . Recall that this is the initial population of bacteria. So,

$400 = P(0) = Ce^{k0}=C$ .

Hence, the expression becomes

$P(t) = 400e^{kt}$ .

Now, we find the value for $k$ . We are going to use that $P(4)=9000$ . Notice that

$9000 = 400e^{k4}$ .

Then,

$\frac{90}{4} = e^{4k}$ .

Taking logarithm

$\ln\frac{90}{4} = 4k$ , so $\frac{1}{4}\ln\frac{90}{4} = k$ .

So, $k=0.7783788273$ , and approximating to the fourth decimal place we can take $k=0.7783$ . Hence,

$P(t) = 400e^{0.7783t}$ .

B) To find the number of bacteria after 5 hours, we only need to evaluate the expression we have obtained in the previous exercise:

$P(5) =400e^{0.7783*5} = 19593.723 \approx 19593$ .

C) In this case we want to do the reverse operation: we want to find the value of t such that

$30000 = 400e^{0.7783t}$ .

This expression is equivalent to

$75 = e^{0.7783t}$ .

Now, taking logarithm we have

$\ln 75 = 0.7783t$ .

Finally,

$t = \frac{\ln 75}{0.7783} \approx 5.55$ .

So, after 5.55 hours the population of bacteria will reach 30000.

6 0

3 years ago

I need a thorough explanation, if not, only an answer with some steps would be fine.

Darya [45]

Answer:

$92.25

Step-by-step explanation:

If Diego spent $20.50 and Sandy spent 4.5x as much as Diego, that means that Sandy spent 20.5x4.5, which equals 92.25. Sandy spent $92.25

7 0

2 years ago

1. Which of the following is an example of a system of equations?

Anni [7]

Answer: (1)

Step-by-step explanation:

A system of equations must have two equations. The first option is the only one that satisfies this.

7 0

2 years ago

On one day a rickshaw puller earned 80.out of his earning he spent 68÷5 on tea and snacks,51÷2 on food and 22÷5 on repair of the

Alexeev081 [22]

Answer: $56.50
==================================
(instead of dividing each of them individually and them subtracting them one by one, combine them together as a fraction first and then subtract)

80 - (68/5 + 51/2 + 22/5)
= 80 - (136/10 + 255/10 + 44/10)
= 80 - (435/10)
= 80 - 43.5
= 56.5

He saved $56.50 on that

7 0

3 years ago

The Holiday Rush gets really intense. You work from 7am to 11pm on the Friday and Saturday just before Xmas, selling clothes and

Vlada [557]

Weekend just includes Saturdays and Sundays, so you don't have to count the earnings on Friday. You simply have to count the number of hours that passed from 7 am to 11 pm on Saturday. That would be a total of 16 hours. While on Sunday, the time from 9 am to 9 pm is a total of 12 hours. Hence, the total time would be 16 hours + 12 hours = 28 hours

Gross Wage = $20(28 hours) = $560

4 0

3 years ago