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3 years ago

53,806 in expanded form

Mathematics

1 answer:

mojhsa [17]3 years ago

5 0

50,000 + 3,000 + 800 + 6

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The birth rate of a population is b(t) = 2300e0.021t people per year and the death rate is d(t)= 1450e0.018t people per year, fi

Cerrena [4.2K]

Answer:

38,674.This area represents the increase in population over a 10-year period.

Step-by-step explanation:

When graphed over the interval 0 ≤ t ≤ 10, the birth rate is more than the death rate. This means the area between the two curves is the amount of births subtract the amount of deaths. This results in an area which means the increase of the population.

The birth rate is graphed in green and the death rate is graphed in blue.

To find the area, take the integral of the difference of the functions:

$\int\limits^{10}_0 {2300e^{0.021t} - 1450e^{0.018t} } \, dt \\\\\frac{2300e^{0.021t}}{0.021} - \frac{1450e^{0.018t}}{0.018} \\\\(\frac{2300e^{0.21}}{0.021} -\frac{1450e^{0.18}}{0.018} ) - (\frac{2300}{0.021}- \frac{1450}{0.018} ) \\\\135117.12 - 96442.51 \\\\38,674$

7 0

3 years ago

An elementary school teacher wants to know if the words in a book are too difficult for her students. She reads the first senten

raketka [301]

Answer:

d.every word in the first sentence of the first page of every chapter.

Step-by-step explanation

the sample space means the set of total possible outcomes or ALL possible outcomes.

so here, the situation is about the teacher reading a sentence.

the favorable outcome is the set which has all the words that the students would not know from all the words read by the teacher or simply from the sample space.

since the teacher reads the first sentence on the first page in every chapter , all the words in that sentence will be sample in this situation.

7 0

3 years ago

Mario has a remaining balance of $1,300 on his credit card his credit card has an APR of 20% how much will he pay in interest in

nydimaria [60]

The correct answer for this problem is 6,500 in one month

4 0

3 years ago

IXL!! I WILL ADD BRAINLIST!

klio [65]

Answer:

-3,3.1, 3 2/10

Step-by-step explanation:

When you are putting different numbers from least to greatest, you need to put them in the same form...

First things first we should put -3 wayy up front. negative numbers are worth less than positive numbers.

Then we need to turn 3 2/10 into a decimal.

3 2/10 -------> 3.2

3.2 is more than 3.1

Thus, the order is

-3,3.1, 3 2/10

Hope this helps and have a nice day.

8 0

3 years ago

Read 2 more answers

Two streams flow into a reservoir. Let X and Y be two continuous random variables representing the flow of each stream with join

zlopas [31]

Answer:

c = 0.165

Step-by-step explanation:

Given:

f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,

f(x, y) = 0 otherwise.

Required:

The value of c

To find the value of c, we make use of the property of a joint probability distribution function which states that

$\int\limits^a_b \int\limits^a_b {f(x,y)} \, dy \, dx = 1$

where a and b represent -infinity to +infinity (in other words, the bound of the distribution)

By substituting cx y(1 + y) for f(x, y) and replacing a and b with their respective values, we have

$\int\limits^3_0 \int\limits^3_0 {cxy(1+y)} \, dy \, dx = 1$

Since c is a constant, we can bring it out of the integral sign; to give us

$c\int\limits^3_0 \int\limits^3_0 {xy(1+y)} \, dy \, dx = 1$

Open the bracket

$c\int\limits^3_0 \int\limits^3_0 {xy+xy^{2} } \, dy \, dx = 1$

Integrate with respect to y

$c\int\limits^3_0 {\frac{xy^{2}}{2} +\frac{xy^{3}}{3} } \, dx (0,3}) = 1$

Substitute 0 and 3 for y

$c\int\limits^3_0 {(\frac{x* 3^{2}}{2} +\frac{x * 3^{3}}{3} ) - (\frac{x* 0^{2}}{2} +\frac{x * 0^{3}}{3})} \, dx = 1$

$c\int\limits^3_0 {(\frac{x* 9}{2} +\frac{x * 27}{3} ) - (0 +0) \, dx = 1$

$c\int\limits^3_0 {(\frac{9x}{2} +\frac{27x}{3} ) \, dx = 1$

Add fraction

$c\int\limits^3_0 {(\frac{27x + 54x}{6}) \, dx = 1$

$c\int\limits^3_0 {\frac{81x}{6} \, dx = 1$

Rewrite;

$c\int\limits^3_0 (81x * \frac{1}{6}) \, dx = 1$

The $\frac{1}{6}$ is a constant, so it can be removed from the integral sign to give

$c * \frac{1}{6}\int\limits^3_0 (81x ) \, dx = 1$

$\frac{c}{6}\int\limits^3_0 (81x ) \, dx = 1$

Integrate with respect to x

$\frac{c}{6} * \frac{81x^{2}}{2} (0,3) = 1$

Substitute 0 and 3 for x

$\frac{c}{6} * \frac{81 * 3^{2} - 81 * 0^{2}}{2} = 1$

$\frac{c}{6} * \frac{81 * 9 - 0}{2} = 1$

$\frac{c}{6} * \frac{729}{2} = 1$

$\frac{729c}{12} = 1$

Multiply both sides by $\frac{12}{729}$

$c = \frac{12}{729}$

$c = 0.0165 (Approximately)$

8 0

3 years ago