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3 years ago

Evaluate this piecewise function

Mathematics

1 answer:

ohaa [14]3 years ago

7 0

Answer:

f(-2) = 2 and f(0) = 0.

Step-by-step explanation:

The piece wise function is given by, f(x) = x³ for x ≠ - 2 and f(x) = |x| for x = - 2.

Now, as defined above at x = -2, f(x) = |- 2| = 2

So, f(-2) = 2

Again, at x = 0, f(x) = x³ = (0)³ = 0.

So, f(0) = 0.

Hence, f(-2) = 2 and f(0) = 0. (Answer)

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The Atlantic Salmon swim upstream at a steady rate of 2 miles every 3 minutes. Fill in the table to describe the relationship. R

Likurg_2 [28]

The distance traveled by the Salmon is proportional to the duration spent

swimming.

A table of the distance traveled by the Atlantic Salmon is presented as follows;

$\begin{tabular}{|c|c|c}\underline{Time in minutes}&\underline{Miles Traveled at 2/3 miles per minute } \\1&2/3 \\2&4/3\\3&2\\4&8/3\\5&10/3\\6&4\end{array}$

Reasons:

The given parameter are;

The steady rate at which Atlantic Salmon swims = 2 miles in 3 minutes

Distance the Salmon swims, d ∝ Time taken, t

Therefore;

d = s·t

Where;

s = The constant of proportionality = The speed

Which gives;

$\displaystyle s = \mathbf{\frac{Distance, \, d}{Time, \, t}}$

The speed with which the Atlantic Salmon swims per minute is therefore;

$\displaystyle The \ speed = \mathbf{\frac{2 \ miles}{3 \ minutes}} = \frac{2}{3} \ miles /minute$

The distance travelled, <em>d</em>, is given as follows;

$\displaystyle d = \mathbf{\frac{2}{3} \times t}$

A table showing the distance travelled by the fish with time is presented as follows;

$\begin{tabular}{|c|c|c|}\underline{Time, t, in minutes}&\underline{t \times d}&\underline{Miles Traveled, d, at 2/3 miles per minute } \\1&1 \times 2/3 = 2/3&2/3 \\2&2 \times 2/3 = 4/3&4/3\\3&3 \times 2/3 = 2&2\\4&4 \times 2/3 = 8/3&8/3\\5&5 \times 2/3 = 10/3&10/3\\6&6 \times 2/3 = 4&4\end{array}$

Learn more about constant of proportionality here:

brainly.com/question/11703625

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3 years ago

A small town currently has a population of 15,000. Each year the population decreases by 2.25%. What will the population be in 8

kolbaska11 [484]

Answer: 12,503 people

Step-by-step explanation:

This is an exponential decrease so to find the population in 8 years you have to use a future value formula:

= Amount * (1 + rate) ^ number of years

= 15,000 ( 1 + (-2.25%)) ⁸

= 15,000 * (1 - 2.25%)⁸

= 12,503.32

= 12,503 people

6 0

3 years ago

Help. I’m confused on this question and would like an answer. Thanks.

ikadub [295]

Answer:

Angle

Step-by-step explanation:

Since, the figure is in the final step of construction. So, it will have only two rays which as we can see are emerging from a common point.

So, it represents an angle.

An angle has two rays arising out of a common vertex point.

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3 years ago

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agasfer [191]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

According to a poll, 55 % of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Assume that thi

Ivenika [448]

Answer:

$\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}})$

The mean is given by:

$\mu_{\hat p} = 0.55$

And the deviation:

$\sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161$

Step-by-step explanation:

For this case we assume that the true population proportion of Americans do not know that GOP stands for Grand Old Party is 0.55 and we select a random sample of n = 953 americans

For this case we assume that we satisfy the conditions to use the normal approximation for $\hat p$

1) np >10 , n(1-p)>10

2) Independence

3) Random sample

4) The sample size is less than 10% of the population size

We assume that all the conditions are satisfied and the distribution for $\hat p$ would be:

$\hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}})$

The mean is given by:

$\mu_{\hat p} = 0.55$

And the deviation:

$\sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161$

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3 years ago