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2 years ago

The Mad Hatter is ordering cups from Teacups

Mathematics

1 answer:

Flura [38]2 years ago

3 0

a) The piecewise function is:

$C(n) = 12 + 1.40n, n \leq 20$

$C(n) = 15 + 1.1n, n > 20$

b) Applying the piecewise function, it is found that it will cost $40.

A piecewise function is a function that has different definitions based on the input.

Item a:

20 or fewer cups, fixed cost of $12 for shipping plus $1.40 per cup. Thus, the first definition of the function for the cost of n cups is:

$C(n) = 12 + 1.40n, n \leq 20$

For more than 20 cups, price of $1.1 per cup plus a shipping and handling fee of $15. Then:

$C(n) = 15 + 1.1n, n > 20$

Then, the piece-wise function is:

$C(n) = 12 + 1.40n, n \leq 20$

$C(n) = 15 + 1.1n, n > 20$

Item b:

The cost of 20 cups is C(20).
It is the first definition, which is valid for $n \leq 20$ .

Then:

$C(20) = 12 + 1.4(20) = 12 + 28 = 40$

It will cost $40.

A similar problem is given at brainly.com/question/24815096

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In the rhombus m<1=160. What are m<2 and <3? The diagram is not drawn to scale.

xxMikexx [17]

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3 years ago

a car purchased for $34,000 is expected to lose value, or depreciate, at a rate of 6% per year.using x for years and y for the v

Vika [28.1K]

Answer:

$y = 34000(1-0.06) ^ t$

After 7.40 years it will be worth less than 21500

Step-by-step explanation:

This problem is solved using a compound interest function.

This function has the following formula:

$y = P(1-n) ^ t$

Where:

P is the initial price = $ 34,000

n is the depreciation rate = 0.06

t is the elapsed time

The equation that models this situation is:

$y = 34000(1-0.06) ^ t$

Now we want to know after how many years the car is worth less than $ 21500.

Then we do y = $ 21,500. and we clear t.

$21500 = 34000(1-0.06) ^ t\\\\log(21500/34000) = tlog(1-0.06)\\\\t = \frac{log(21500/34000)}{log(1-0.06)}\\\\t = 7.40\ years.$

After 7.40 years it will be worth less than 21500

3 0

3 years ago

Can someone help me with this page please I have an exam tomorrow, I need to remember the answers unfortunately :)

zimovet [89]

Answer:

1. B. ∠2 and ∠6

2. 50°

3. Option 1, Option 5, and Option 6.

4. 133°

Work for question 4:

180°-47° = 133°

Step-by-step explanation:

Alternate means the angles are on different sides of the transversal (horizontal line in this case). Interior means they are between the parallel lines (lines a and b in this case). (∠2 and ∠6) and (∠3 and ∠7) are the alternate interior angles but only the first is an option.

∠10 = ∠8+∠7 (corresponding angles so they are congruent)

∠10 is 140° and ∠8 is a right angle

140-90 = 50

∠7 = 50°

∠4 = 50° (∠7 and ∠4 are vertical angles so they are congruent)

Sense all angles of a triangle add up to 180 and the ratio of angles is 3:3:6 the we can find the angle with the equation x+x+2x=180

Simplify.

4x=180

Solve by dividing 4 from both sides

x=45

so it is a 45, 45, 90 triangle. (right triangle because the 90 and icoceles because other 2 angles are congruent so option 5 is correct)

m∠J= 45°

m∠K= 45° (Option 1 is correct)

m∠L= 90° (Option 6 is correct)

I honestly don't see how you can solve this without making assumptions so I will make assumptions.

Assuming the whole figure is symmetrical vertically ∠1 is congruent to the same spot on the right side of the shape. This angle would be supplementary to the angle of the angle outside of the shape adjacent on the right making the angle (which is corresponding, therefore congruent to ∠2) 133°.

8 0

2 years ago

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

Lesechka [4]

Answer:

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

4 0

4 years ago