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2 years ago

The population of a town is growing exponentially and can be modeled by the

Mathematics

1 answer:

svp [43]2 years ago

7 0

The population of the town in 1960 is 48.80 thousands

<h3>How to determine the population in 1950?</h3>

The equation of the model is given as:

f(t) = 42e^(0.015t)

1960 is 10 years after 1950.

This means that:

t = 10

Substitute t = 10 in f(t) = 42e^(0.015t)

f(10) = 42e^(0.015 * 10)

Evaluate

f(10) = 48.80

Hence, the population of the town in 1960 is 48.80 thousands

Read more about exponential functions at:

brainly.com/question/11464095

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Find an equation of the line parallel to y=2x+3 and that passes through the point (5,3)

timama [110]

Answer:

y = 2x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 3 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes , then

y = 2x + c ← is the partial equation

To find c substitute (5, 3 ) into the partial equation

3 = 10 + c ⇒ c = 3 - 10 = - 7

y = 2x - 7 ← equation of parallel line

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3 years ago

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Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random

Katen [24]

Answer:

$CI = (0.17 - 0.27)\± 1.65\sqrt{\frac{(0.17)*(0.83) + (0.27)*(0.73)}{200}}$

Step-by-step explanation:

Given

$n = 200$

$x_1 = 34$ -- City C

$x_2 = 54$ --- City K

Required

Determine the 90% confidence interval

This is calculated using:

$CI = \bar x \± z\frac{\sigma}{\sqrt n}$

Calculating $\bar x$

$\bar x = \bar x_1 - \bar x_2$

$\bar x = \frac{x_1}{n} - \frac{x_2}{n}$

$\bar x = \frac{34}{200} - \frac{54}{200}$

$\bar x = 0.17 - 0.27$

For a 90% confidence level, the z-score is 1.65. So:

$z = 1.65$

Calculating the standard deviation $\sigma$

$\sigma = \sqrt{(\bar x_1)*(1 - \bar x_1) + (\bar x_2)*(1 - \bar x_2) }$

So:

$\sigma = \sqrt{(0.17)*(1 - 0.17) + (0.27)*(1 - 0.27) }$

$\sigma = \sqrt{(0.17)*(0.83) + (0.27)*(0.73)}$

So:

$CI = (0.17 - 0.27)\± 1.65\frac{\sqrt{(0.17)*(0.83) + (0.27)*(0.73)}}{\sqrt {200}}$

$CI = (0.17 - 0.27)\± 1.65\sqrt{\frac{(0.17)*(0.83) + (0.27)*(0.73)}{200}}$

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3 years ago

At a little-known vacation spot, taxi fares are a bargain. A 42 -mile taxi ride takes 49 minutes and costs $29.40. You want

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Answer:

about 13.50$

Step-by-step explanation:

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An object at the top of a building with height 110 feet is thrown upward with an initial speed of 23 ft/s. Find its position z(t

alina1380 [7]

Answer:

Step-by-step explanation:

Given

Height of building is $h=110\ ft$

Initial upward velocity $u=23\ ft/s$

height of object is given by

$z(t)=ut+\frac{1}{2}gt^2$

but building is already at a height of 110 ft so z(t) must be given by

$Z(t)=ut+\frac{1}{2}(-g)t^2+110$

$Z(t)=23\times t-\frac{1}{2}\times 9.8\times t^2$

$Z(t)=-16t^2+23t+110$

Time when it hits is given by when Z(t)=0[/tex]

$-16t^2+23t+110=0$

$t=\frac{-23\pm \sqrt{(23)^2-4\times (-16)\times 110}}{2\times (-16)}$

$t=\frac{-23\pm 87}{-32}$

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Figs come in 2.4 lb bags. Apples come in 7.2 lb bags. How many times as many pounds are the apple bags as the fig bags?

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Answer:

Step-by-step explanation:

7.2 ÷ 2.4 = 3

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