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3 years ago

. A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential model for the population.

Mathematics

1 answer:

larisa86 [58]3 years ago

4 0

Answer: $A=6000(1.012)^t$

Step-by-step explanation:

General exponential function:

$A=P(1+r)^t$

, where P= current population

r= rate of growth

t= time period

A= population after t years

As per given , we have P=6,000

r= 1.2% = 0.012

Then, the required exponential function: $A=6000(1+0.012)^t$

or $A=6000(1.012)^t$

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The Pyraminx is a Rubik's cube-type toy in the shape of a tetrahedron. The Pyraminx shown below has edges 15\,\text{cm}15cm long

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Answer:

8.727

Step-by-step explanation:

Since the below edge, d = 15 cm, and the height, h = 12.2 cm, we will use the Pythagorean theorem to find the distance r.

$d^2=r^2+h^2$

$(15)^2 = r^2+(12.2)^2$

$r^2 = (15)^2-(12.2)^2=225-148.84=76.16$

$r=\sqrt{76.16}=8.727$

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3 years ago

What is the volume of the composite figure? (Round to the nearest hundredth. Use 3.14 for x.)

marshall27 [118]

The volume of the composite figure is the third option 385.17 cubic centimeters.

Step-by-step explanation:

Step 1:

The composite figure consists of a cone and a half-sphere on top.

We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.1415.

The radius is 4 cm and the height is 15 cm.

The volume of the cone :

$V = \frac{1}{3} \pi r^{2} h = \frac{1}{3} (3.1415)(4^{2} )(15) = 251.32$ cubic cm.

Step 3:

The area of a half-sphere is half of a full sphere.

The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 4 cm. We take π as 3.1415.

The volume of a full sphere $\frac{4}{3} \pi r^{3} = \frac{4}{3} (3.1415) (4^{3}) = 268.07$ cubic cm.

The volume of the half-sphere $=\frac{1}{2} (268.07) = 134.037$ cubic cm.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume $251.32+134.037 = 385.357$ cub cm. This is closest to the third option 385.17 cubic centimeters.

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3 years ago

A bus travels two different routes: the Green Route and the Blue Route.

Alex17521 [72]

Answer:4.5

Step-by-step explanation: Check the file for my explanation

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2 years ago

10. A manufacturer wanted to know if more coupons would be redeemed if they were mailed to the

Mandarinka [93]

Using the t-distribution, it is found that the data does not provide convincing evidence that the mean number is greater when the coupons were addressed to a female.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if there is no difference, that is, the mean is of 0, hence:

$H_0: \mu = 0$

At the alternative hypothesis, it is tested if the mean number is greater for females, that is, the mean is greater than 0, hence:

$H_1: \mu > 0$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the null hypothesis.

s is the standard deviation of the sample.

n is the sample size.

In this problem, the parameters are given as follows:

$\overline{x} = 1.5, \mu = 0, s = 4.75, n = 50$ .

Hence, the test statistic is given by:

$t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{1.5 - 0}{\frac{4.75}{\sqrt{50}}}$

t = 2.23

<h3>What is the conclusion?</h3>

Considering a <em>right-tailed test</em>, as we are testing if the mean is greater than a value, with a <em>significance level of 0.01 and 50 - 1 = 49 df</em>, the critical value is given by $t^{\ast} = 2.4$ .

Since the test statistic is less than the critical value for the right-tailed test, the data does not provide convincing evidence that the mean number is greater when the coupons were addressed to a female.

More can be learned about the t-distribution at brainly.com/question/26454209

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2 years ago

A company will lease office space in two buildings. The annual cost of $21.75 per square foot in the first building and cost $17

lbvjy [14]

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