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2 years ago

Over time, the number of organisms in a population increases exponentially. The table below shows the approximate number of

Mathematics

2 answers:

Sphinxa [80]2 years ago

6 0

Answer:

We write the generic form equation:

y = A (b) ^ t

We must use two points in the table to find the constants A and b

We have then:

For: t = 1, y = 55

55 = A (b)

For: t = 2, y = 60

60 = A (b) ^ 2

We solve the system of equations:

We divide both equations:

(60 = A (b) ^ 2) / (55 = A (b))

((60) / (55)) = b

b = 1.091

We substitute in any of the equations:

55 = A (b)

55 = A (1,091)

A = (55) / (1,091)

A = 50.41

The equation that models the problem is:

y = 50.41 * (1.09) ^ t

For t = 29 we have:

y = 613.5996987 (> 600)

Answer:

Assuming the trend continues the environment will not last until the population after 24 years.

Answer:

vlada-n [284]2 years ago

5 0

Answer:

Step-by-step explanation:

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A random sample of 6 homes in Gainesville, Florida between 1800 and 2200 square feet had a mean of 212990 and a standard deviati

Andrej [43]

Answer:

The 95% confidence interval for the average price of a home in Gainesville of this size is between 183,772.5 square feet and 242,207.5 square feet.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the students t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of 0.95( $t_{95}$ ). So we have T = 2.015

The margin of error is:

M = T*s = 2.015*14500 = 29217.5.

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 212990 - 29217.5 = 183,772.5 square feet

The upper end of the interval is the sample mean added to M. So it is 212990 + 29217.5 = 242,207.5 square feet

The 95% confidence interval for the average price of a home in Gainesville of this size is between 183,772.5 square feet and 242,207.5 square feet.

3 0

2 years ago

A while back, either James borrowed $12 from his friend Rita or she borrowed $12 from him, but he can’t quite remember which. Ei

Tamiku [17]

Answer:

First option is correct.

Step-by-step explanation:

Let amounts of money James may have after he sees Rita be x.

It is given that either James borrowed $12 from his friend Rita or she borrowed $12 from him.

So meeting Rita second time either he will $12 or he will receive $12.

The amounts of money James may have after second meeting with Rita is:

Case 1: If he pays $12.

$x=42.80-12$ .... (1)

Case 1: If he receives $12.

$x=42.80+12$ .... (2)

On combining equation (1) and (2), we get

$x=42.80\pm 12$

Subtract 42.80 from both sides.

$x-42.80=\pm 12$

It can be written as

$|x-42.80|=12$

Therefore first option is correct.

4 0

2 years ago

Read 2 more answers

Sam put $2,000 in a savings account at his bank. After 10 years, his account balance was $4,000. The interest rate on the saving

kkurt [141]

rule of 70:

number of years for savings to double = 70/ interest rate

account doubles in 10 years

so you have 10 = 70/x

x = 70/10 = 7%

7 0

2 years ago

Read 2 more answers

Jason ran 5/7 of the distance around the school track. Sara ran 4/5 of Jason's distance. What fraction of the total distance aro

masha68 [24]

Jason: 5/7
Sara: 4/5

Think of it this way: if the total track is a mile, and Jason runs 5/7 of it, he has run 5/7 of a mile. Then Sara runs 4/5 OF 5/7, with "of" meaning "times," so she runs 4/5 x 5/7, which gives you 20/35, which simplifies to 4/7. You can also think of Sara's distance as 80 percent of Jason's. If she runs "80 percent of the sevenths that Jason ran," that means she ran 4 out of his 5 sevenths.

7 0

2 years ago

The percent of a country's households with broadband Internet access can be modeled by the function f left parenthesis x right

mojhsa [17]

Answer:

a) The function has a maximum at x = 29,59

b) 99,32 %

Step-by-step explanation:

f(x) = -0,11*x² + 6,51*x + 3

Then:

f´(x) = -0,22*x + 6,51

If f´(x) = 0 then - 0,22*x + 6,51 = 0

0,22*x = 6,51

x = 6,51/0,22 ⇒ x = 29,59

if we get the second derivative

f´´(x) = - 0,22 f´´(x) < 0 then we have a maximun at x = 29,59

a) the function has a maximum

b) 29,59 years after 2000 ( in 2030 )

c) f(x) = - 0,11*x² + 6,51*x + 3

f(29,59) = - (0,11)* (29,59)² + 6,51*29,59 + 3

f(29,59) = 99,32 %

5 0

2 years ago