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lakkis [162]
3 years ago
9

A town hasapopulation of p people based on a 2010 census. According to research conducted by the town council, the population of

the city is expected to increase by 5 percent per year. According to the estimate, the expected population of the town in 2020 is 810. To the nearest whole number, what is the value of p ?
Mathematics
1 answer:
jasenka [17]3 years ago
4 0

Answer:

p = 497 ( to the nearest whole number)

Step-by-step explanation:

In order to do this calculation, we will apply the principle of accounting, where a certain amount is compounded periodically and yielding a future value. Compound interest is used because the percentage growth rate is added on the new amount gotten each year, and not on the first or original amount.

Hence:

FV = PV × (1+ \frac{r}{n}) ^{n*t}

where FV = future value = population in 2020 = 810

PV = present value = population in 2010 = p

r = percentage growth rate in decimal = 5% = 5/100 = 0.05

n = growth rate period per year = once = 1

t = time in years = 2010 to 2020 = 10 years

∴ 810 = p * (1+ \frac{0.05}{1}) ^{1*10}

810 = p * (1.05) ^{10}\\810= p(1.6289) (dividing both sides by 1.6289)

p = 810 ÷ 1.6289 = 497.2 = 497 (to the nearest whole number)

∴ population in 2010 = 497

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3 0
3 years ago
8 customers entered a store over the course of 16 minutes. At what rate were the customers entering the store in minutes per cus
lilavasa [31]

Answer:

<h3>2min/customer</h3>

Step-by-step explanation:

If 8 customers entered a store over the course of 16 minutes, then;

8 customers = 16 minutes.

The rate at which the customers are entering is expressed as;

Rate = Time (in minutes)/amount of customers;

Given

Time = 16 minutes

Amount of customers = 8 customers

Rate = 16min/8customers

Rate = 2min/customer

Hence the rate at which the customers entering the store in minutes per customer is 2min/customer.

4 0
3 years ago
Y=x^2-6x-16 in vertex form
satela [25.4K]

Answer:

y=(x-3)^{2} -25

Step-by-step explanation:

The standard form of a quadratic equation is y=ax^{2} +bx+c

The vertex form of a quadratic equation is y=a(x-h)^{2} +k

The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.

To find the h-value of the vertex, you use the following equation:

h=\frac{-b}{2a}

In this case, our quadratic equation is y=x^{2} -6x-16. Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.

h=\frac{-b}{2a} ⇒ h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3

Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is y=x^{2} -6x-16

y=x^{2} -6x-16 ⇒ y=(3)^{2} -6(3)-16 ⇒ y=9-18-16 ⇒ y=-25

This y-value that we just found is our k-value.

Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: y=a(x-h)^{2} +k

a: 1

h: 3

k: -25

y=(x-3)^{2} -25

Hope this helps!

3 0
4 years ago
What is the probability that a randomly selected male will have a foot length between 8 and 12.5 inches? P(8 &lt; r &lt; 12.5)=
melisa1 [442]

Answer:

0.8185 or 81.85%

Step-by-step explanation:

The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.

The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive  and if the raw score is below the mean the z sore is negative. It is given by:

z=\frac{x-\mu}{\sigma}

To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.

For 8 inches:

z=\frac{x-\mu}{\sigma}=\frac{8-11}{1.5}=-2

For 12.5 inches:

z=\frac{x-\mu}{\sigma}=\frac{12.5-11}{1.5}=1

From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1)  - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%

4 0
3 years ago
Is 16=3 one, no, or many solutions?
elixir [45]

Answer:

No solutions; parallel

Step-by-step explanation:

The equations x=16 and x=3 both have a slope of 0. So when graphed, they would be parallel and there are no solutions between parallel lines.

3 0
3 years ago
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