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anyanavicka [17]

3 years ago

12

In 2000 the population of a small village was 2,400. With an annual growth rate of approximately 1.68%, compounded continuously,

what will the population be in 2020 according to the exponential growth function?

1 answer:

Triss [41]3 years ago

3 0

Answer:

$3,358\ people$

Step-by-step explanation:

The formula to calculate the exponential growth function is equal to

$f(x)=P(e)^{rx}$

where

f(x) is the population

P is the population in the year 2000

r is the rate in decimal

x is number of years since 2000

e is the mathematical constant number

we have

$x=2020-2000=20\ years\\ P=2,400\\ r=0.0168$

substitute in the formula above

$f(x)=2,400(e)^{0.0168*20}$

$f(x)=3,358\ people$

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In a right triangle the lengths of the legs are a and b. Find the length of a hypotenuse, if: a=3, b=4;

prohojiy [21]

Answer:

The hypotenuse is 5

Step-by-step explanation:

We can use the Pythagorean theorem to find the hypotenuse of a right triangle

a^2 +b^2 =c^2 where a and b are the legs and c is the hypotenuse

3^2 +4^2 =c^2

9+16=c^2

25=c^2

Take the square root of each side

sqrt(25) =sqrt(c^2)

5 = c

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3 years ago

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80X3 PLUS 2x3 that is awnser

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The cost (in dollars) of a custom made sweatshirt is represented by 3.5n +29.99, where n is the number of different colors in th

juin [17]

Answer:

$52.5n+449.85$

Step-by-step explanation:

The cost is given for <em>1 sweatshirt</em>. To find the cost of 15 sweatshirts, we need to multiply the expression by 15. Let's do this:

$15(3.5n+29.99)\\=15(3.5n+29.99)\\=15(3.5n)+15(29.99)\\=52.5n+449.85$

This is the expression that represents the cost of 15 sweatshirts.

8 0

3 years ago

Which statement about the following equation is true?<br>2x2-9x+2-1

Furkat [3]

Complete Question:

Which statement about the following equation is true?

$2x^2-9x+2 = -1$

A) The discriminant is less than 0, so there are two real roots

B) The discriminant is less than 0, so there are two complex roots

C) The discriminant is greater than 0, so there are two real roots

D) The discriminant is greater than 0, so there are two complex roots

Answer:

C) The discriminant is greater than 0, so there are two real roots

Step-by-step explanation:

The given equation is $2x^2-9x+2 = -1$ which by simplification becomes

$2x^2 - 9x + 3 = 0$

For a quadratic equation of the form $ax^2 + bx + c = 0$ , the discriminant is given by the equation, $D = b^2 - 4ac$

If the discriminant D is greater than 0, the roots are real and different

If the discriminant D is equal to 0, the roots are real and equal

If the discriminant D is less than 0, the roots are imaginary

For the quadratic equation under consideration, a = 2, b = -9, c = 3

Let us calculate the discriminant D

D = (-9)² - 4(2)(3)

D = 81 - 24

D = 57

Since the Discriminant D is greater than 0, the roots are real and different.

3 0

3 years ago

Consider the probability that greater than 96 out of 153 DVDs will work correctly. Assume the probability that a given DVD will

ICE Princess25 [194]

Answer:

0.3594 = 35.94% probability that greater than 96 out of 153 DVDs will work correctly.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 153, p = 0.62$

So

$\mu = E(X) = np = 153*0.62 = 94.86$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.62*0.38} = 6$

Probability that greater than 96 out of 153 DVDs will work correctly.

97 or more DVDs, which is 1 subtracted by the pvalue of Z when X = 97. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{97 - 94.86}{6}$

$Z = 0.36$

$Z = 0.36$ has a pvalue of 0.6406

1 - 0.6406 = 0.3594

0.3594 = 35.94% probability that greater than 96 out of 153 DVDs will work correctly.

3 0

3 years ago