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3 years ago

a linear function passes through the point (1,5)and (7,23)what are the rate of change and initial value?

Mathematics

1 answer:

Vlada [557]3 years ago

4 0

Answer:

The rate of change = 3

Initial value = 2

Step-by-step explanation:

The linear function has the form ⇒ y = mx + c

Where m is the slope or the rate of change, and c is y-intercept.

Given: A linear function passes through the point (1,5)and (7,23)

So, m = (y₂-y₁)/(x₂-x₁) = (23-5)/(7-1) = 18/6 = 3

So, y = 3x + c

By substitution with the point (1,5)

So, at x = 1 , y = 5

5 = 3*1 + c

c = 5 - 3 = 2

∴ y = 3x + 2

so, the rate of change = 3

And initial value = 2

initial value is the value at which x = 0 which is the y-intercept

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Step-by-step explanation:

r - 18 = 27

r = 27 + 18

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3 years ago

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The exponential model A = 661.7 e^0.011t describes the population, A, of a country in millions, t years after 2003. Use the mode

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Answer:

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Step-by-step explanation:

Given the exponential model :

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The general form of an Exponential model is expresses as :

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Where A = final value ; A0 = Initial value ; r = growth rate and t = time elapsed

From the question t = time after 2003

Therefore, A0 = initial population, which is the population in 2003

Therefore, A0 = 661.7

Or we could put t = 0 in the equation and solve for A

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Hence, population in 2003 is 661.7 million

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3 years ago

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2 years ago

The cost for admission to go to the amusement park is $13 plus $1.50 for each ride. If you have a total of $35.50 to spend, what

Mandarinka [93]

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3 years ago

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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard devia

gtnhenbr [62]

Answer:

$n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547$

So the answer for this case would be n=22547 rounded up to the nearest integer

Step-by-step explanation:

Let's define some notation

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=58.2$ represent the population standard deviation

n represent the sample size

$ME =1$ represent the margin of error desire

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =+1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. The significance would be $\alpha=0.01$ and the critical value $z_{\alpha/2}=2.58$ , replacing into formula (b) we got:

$n=(\frac{2.58(58.2)}{1})^2 =22546.82 \approx 22547$

So the answer for this case would be n=22547 rounded up to the nearest integer

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3 years ago