If pr=5 in and pt=8in what is rs

The population of a town with a 20162016 population of 87 comma 00087,000 grows at a rate of 1.91.9% per year. a. Find the rate

SCORPION-xisa [38]

Answer:

Given,

The initial population, P = 87,000,

Annual rate of increasing, r = 1.9 %,

a) Thus, the population after t years,

$A=P(1+\frac{r}{100})^t$

$A=87000(1+\frac{1.9}{100})^{t}$

$=87000(1+0.019)^t$

$=87000(1.019)^t$

$87000(1.019)^t=87000e^{kt}$

Where, k is the rate constant,

By comparing,

$\implies k=log(1.019)=0.00817418400643\approx 0.00817$

Hence, the approximate value of k is 0.00817.

And, the exponential growth function would be,

$A=87000e^{0.00817t}$

b) If A = 145,000,

$145000=87000(1.019)^t$

By using graphing calculator,

We get,

$t=27.14\approx 27$

The year after 27 years from 2016 is 2043.

Hence, in 2043 the population reach 145,000.

6 0

4 years ago

Si tenemos un cuadrado cuyos lados miden 1/3 en 7 partes iguales, ¿Cuál es su área?

Nataly_w [17]

Answer:

English please?

Step-by-step explanation:

...........

8 0

3 years ago

At the deli, 2 turkey subs and 5 veggie subs cost $29. 4 turkey subs and 3 veggie subs cost

MrMuchimi

Answer:

4/9 of sales are veggie 5/9 are turkey

4/(4+5)=4/9

5/(4+5)= 5/9

4/9 x 27 = 12

5/9 x 27 = 15

12 veggie subs sold and

15 turkey subs sold

12+15=27 total sold

Step-by-step explanation:

3 0

3 years ago

(1 point) The cost of unleaded gasoline once followed an unknown distribution with a mean of $4.59 and a standard deviation of $

marin [14]

Answer:

a) unknown

b) 1.43% probability that the average price for 30 gas stations is less than $4.55.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 4.59, \sigma = 0.1$

a) What's the approximate probability that the average price for 16 gas stations is over $4.69?

Sample size less than 30 and unknow distribution. Therefore, the central limit theorem cannot be applied and the answer is unknown.

b) Find the probability that the average price for 30 gas stations is less than $4.55.

Now $n = 30, s = \frac{0.1}{\sqrt{30}} = 0.0183$

This probability is the pvalue of Z when X = 4.55. So

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

By the Central Limit Theorem

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

$Z = \frac{4.55 - 4.59}{0.0183}$

$Z = -2.19$

$Z = -2.19$ has a pvalue of 0.0143

1.43% probability that the average price for 30 gas stations is less than $4.55.

5 0

4 years ago

A cardboard box has a square base and an open top. the four sides are made of wood that costs 2 dollars per square foot, while t

serious [3.7K]

Answer:

$300

Step-by-step explanation:

Let x represent the side length of the square base in feet. Then the height of each side is ...

... h = (50 ft³)/(x ft)² = (50/x²) ft

The cost of the sides of the box is then ...

... (4 sides) × (x ft)(50/x² ft)/side × $2/ft² = $400/x

The cost of the bottom is ...

... (x ft)² × $25/ft² = $25x²

So, the total dollar cost is

... C = 400/x + 25x²

This will be a minimum where its derivative with respect to x is zero.

... 0 = -400/x² +50x

... 400/50 = 8 = x³ . . . . . add 400/x²; multiply by x²/50

... x = ∛8 = 2

For this value of x, the minimum cost is ...

... C = 400/2 + 25·2² = 300

The minimum possible cost is $300.

_____

<em>Comments on the problem</em>

1) Cardboard boxes are usually made of cardboard. They are rarely made of wood and alumninum.

2) The cost of the bottom is half the cost of the sides. When the dimensions are unconstrained, you will find (as here) the cost is shared equally between the bottom and pairs of opposite sides—each being 1/3 the total cost.

4 0

4 years ago