Imagine a sphere. if the sphere is cut three times at right angles, the resulting pieces would be what fraction of the original sphere?

The correct option is:  A.  2 years

Explanation

The given growth equation is:   [tex]20000e^0^.^1^5^t = 28000[/tex], where  [tex]t[/tex] is the number of years the population has been growing.

For finding the number of years, we will solve the above equation for  [tex]t[/tex].

First, dividing both sides by 20000, we will get........

[tex]\frac{20000e^0^.^1^5^t}{20000}=\frac{28000}{20000}\\ \\ e^0^.^1^5^t = 1.4[/tex]

Now taking 'natural log' on both sides, we will get........

[tex]ln(e^0^.^1^5^t)=ln(1.4)\\ \\ 0.15t*ln(e)= ln(1.4)\\ \\ 0.15t*1=ln(1.4)\\ \\ t=\frac{ln(1.4)}{0.15}=2.243..... \approx 2[/tex]

So, the population of the town has been growing about 2 years.

The town has been growing for 17 years

Given the exponential function

Given the expressions 20,000e^0.15t=28,000

We are to find the value of "t" which is the time.

e^0.15t = 28000/20000

e^0.15t = 7/5

e^0.15t = 1.4

Take the ln of both sides

lne^0.15t = ln 1.4

0.15t = 2.639

t = 2.639/0.15

t = 17years

Hence the town has been growing for 17 years

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Answer:

The volume flow rate of the air being pumped into the football is approximately [tex]\( 5.261 \times 10^{-7} \)[/tex] cubic feet per second.

Explanation:

To find the volume flow rate of the air being pumped into the football, we first need to calculate the cross-sectional area of the needle of the pump.

Given:

- The radius of the needle, [tex]\( r = 4.5 \)[/tex] millimeters.

The cross-sectional area, [tex]\( A \)[/tex], of the needle can be calculated using the formula for the area of a circle:

[tex]\[ A = \pi r^2 \][/tex]

Converting the radius from millimeters to feet:

[tex]\[ r = \frac{4.5}{1000} \text{ feet} \][/tex]

Now, let's calculate the cross-sectional area:

[tex]\[ A = \pi \left( \frac{4.5}{1000} \right)^2 \][/tex]

[tex]\[ A \approx \pi \left( \frac{0.0045}{1000} \right)^2 \][/tex]

[tex]\[ A \approx \pi \times 2.025 \times 10^{-8} \text{ square feet} \][/tex]

Now, we can find the volume flow rate, [tex]\( Q \)[/tex], of the air being pumped into the football. The volume flow rate is the product of the cross-sectional area of the needle and the speed of the air:

[tex]\[ Q = A \times \text{Speed} \][/tex]

Given:

- Speed of the air, [tex]\( \text{Speed} = 8.2 \)[/tex] ft/s

Now, let's calculate the volume flow rate:

[tex]\[ Q = \pi \times 2.025 \times 10^{-8} \text{ square feet} \times 8.2 \text{ ft/s} \][/tex]

[tex]\[ Q \approx 5.261 \times 10^{-7} \text{ cubic feet/s} \][/tex]

The mean and the standard deviation of y are given as follows:

For the multiplication, we have that both the mean and the standard deviation are multiplied by the constant.

For the subtraction, we have that the mean is subtracted by the constant, while the standard deviation remains constant, since all observations are subtracted by the constant, the differences squared between each observation and the mean remain constant.

The original mean and standard deviation are given as follows:

After the multiplication, they are given as follows:

After the subtraction, they are given as follows:

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Final answer:

The mean and standard deviation of the new random variable y, derived from a distribution x with a given mean and standard deviation, are calculated by applying transformations, resulting in a mean of 47 and a standard deviation of 12.

Explanation:

The question asks us to find the mean and standard deviation of a new random variable y = 4x - 5, given a distribution, x, with a mean of 13 and a standard deviation of 3. To calculate the mean of y, we use the transformation y = 4x - 5. The mean of y can be found by substituting the mean of x into this equation, giving us 4(13) - 5 = 52 - 5 = 47. To find the standard deviation of y, we multiply the standard deviation of x by the coefficient of x in the equation, resulting in 3 * 4 = 12. Therefore, the mean of y is 47, and the standard deviation is 12.

Answer:

26.89 seconds

Step-by-step explanation:

Any number with an 8 in the tenths place will have an 8 with 10 times the value of the 8 in the hundredths place in Armand's time.

Answer:

cosθ =  [tex]\frac{3}{5}[/tex] .

Step-by-step explanation:

Given : If sinθ =4/5 .

To find :  cosθ = _____.

Solution : We have given that sinθ =4/5 .

By the trigonometric identity

cos²θ + sin²θ = 1.

Plugging the value of sinθ =4/5 .

cos²θ + [tex](\frac{4}{5}) ^{2}[/tex] = 1.

cos²θ + [tex]\frac{16}{25}[/tex] = 1.

On subtracting  [tex]\frac{16}{25}[/tex]  from both sides

cos²θ = 1 -  [tex]\frac{16}{25}[/tex] .

cos²θ =  [tex]\frac{25 -16}{25}[/tex] .

Taking square root both sides.

[tex]\sqrt{cos^{2}theta}  = \sqrt{\frac{9}{25}}[/tex] .

cosθ =  [tex]\frac{3}{5}[/tex] .

Therefore, cosθ =  [tex]\frac{3}{5}[/tex] .

Answer: 2900 Square Feet

Step-by-step explanation: i took the test

Answer:

72 possible combinations

Step-by-step explanation:

The features in a computer (C) are:

All the possible combinations can be found using the following expression.

C = h × a × v × m = 3 × 4 × 2 × 3 = 72

There are 72 possible combinations to set up a computer.

Answer:

The circumference of a circle is  [tex]72\pi [/tex] .

Step-by-step explanation:

Forrmula

[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]

Where r is the radius of the circle .

As given in the question

The radius of the circle is 36 inches .

Put all the values in the formula

[tex]Circumference\ of\ a\ circle = 2\times 36\pi [/tex]

[tex]Circumference\ of\ a\ circle = 72\pi [/tex]

Therefore the circumference of a circle is  [tex]72\pi [/tex] .

Answer:

0.1151

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 500, \sigma = 75[/tex].

What is the probability that a family spends less than $410 per month?

This probability is the pvalue of Z when X = 410. So:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{410 - 500}{75}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151. This is the answer.

The length of the third side of the triangle Misty is building should be more than 3 feet and less than 13 feet, according to the Triangle Inequality Theorem.

This question pertains to the numerical properties of a triangle, in which two side lengths of the triangle are provided, specifically eight feet and five feet. The length of the third side of the triangle is not set, but it has certain parameters due to the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the possible lengths of the third side would be greater than the absolute difference of the two given sides (eight feet and five feet), and less than the sum of the lengths of the two given sides. Thus, the third side's length should be more than 3 feet (8 - 5) and less than 13 feet (8 + 5).

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Answer:

Conditional  and Converse.

Step-by-step explanation:

If a polygon is regular, then it has congruent angles and congruent sides.

We can say that;

Hypothesis is : If a polygon is regular

Conclusion is : then it has congruent angles and congruent sides.

A conditional statement will not be true when the hypothesis is true but the conclusion is false. In  the given statement, the above conditional statement has a truth value of true.

We can write the converse statement as : If it has congruent angles and congruent sides, then the polygon is regular.  

This also has a truth value of true.

So, correct options are :

Conditional  and converse