WhAt is the volume of the right circular cone with the radius of 4cm and a height of 12cm

The population of a certain species of insects increases exponentially according to the model, P(0) = 952e0.12t where P is the n

NeX [460]

Answer:

A) 952 insects are in the original colony

B) 10494 insects are in the colony after 20 weeks

C) 25 weeks

Explanations:

The model representing the population of the species of insects

$P(t)=952e^{0.12t}$

An exponential growth is of the form:

$P(t)=P_0e^{kt}$

where P₀ is the original population

t is the time taken in weeks

Comparing the two equations:

$P_0=\text{ 952}$

952 insects are in the original colony

B. The number of insects that will be in the colony after 20 weeks

Substituting t = 20 into the function given

$\begin{gathered} P=952e^{0.12(20)} \\ \text{P = }10494 \end{gathered}$

C) If the population, P = 20000

$\begin{gathered} 20000=952e^{0.12t} \\ e^{0.12t}=\text{ }\frac{20000}{952} \\ e^{0.12t}=21.008 \\ 0.12t\text{ = ln(21.008)} \\ 0.12t\text{ = }3.04 \\ t\text{ = }\frac{3.04}{0.12} \\ t\text{ = }25 \end{gathered}$

8 0

1 year ago

4|2x+7|=16<br> x=? and x=?

sammy [17]

4 | 2x + 7 | = 16...divide both sides by 4
| 2x + 7 | = 16/4
| 2x + 7 | = 4

2x + 7 = 4 -(2x + 7) = 4
2x = 4 - 7 -2x - 7 = 4
2x = -3 -2x = 4 + 7
x = -3/2 -2x = 11
x = -11/2

so x = -3/2 and x = -11/2

5 0

4 years ago

Let point C be on circle A. If ∠BAC 5 radians and segment BC is 12cm, what is the length of the radius

Genrish500 [490]

Answer:

2.4 cm

Step-by-step explanation:

The formula we would use

S = rθ

Where S = Arc length

θ = central angle in radians

r = radius of the circle or length of the radius.

From the question, we can see that if

If C = a point on circle A

The Segment BC = The arc length of the circle = 12cm

∠BAC = central angle in radians = 5 radians.

Since, S = rθ,

Length of the radius = S/θ

= 12cm/5 radians

Length of the radius = 2.4 cm

5 0

3 years ago

2. Members of a high school sports team are selling two popular items for a fundraiser:

vaieri [72.5K]

It would be E because.75 per candy bar

8 0

3 years ago

A researcher wishes to see if the average number of sick days a worker takes per year is less than 5. A random sample of 30 work

Lana71 [14]

Answer:

No. At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average number of sick days a worker takes per year is significantly less than 5.

Then, the null and alternative hypothesis are:

$H_0: \mu=5\\\\H_a:\mu< 5$

The significance level is 0.01.

The sample has a size n=30.

The sample mean is M=4.8.

The standard deviation of the population is known and has a value of σ=1.2.

We can calculate the standard error as:

$\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.2}{\sqrt{30}}=0.219$

Then, we can calculate the z-statistic as:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{4.8-5}{0.219}=\dfrac{-0.2}{0.219}=-0.913$

This test is a left-tailed test, so the P-value for this test is calculated as:

$\text{P-value}=P(z$

As the P-value (0.181) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.

3 0

3 years ago