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3 years ago

If 10 to the power of 2 is 100, then what is 10 to the power of 40? Sorry for the complicated question.

Mathematics

2 answers:

max2010maxim [7]3 years ago

8 0

Answer:

10000000000000000000000000000000000000000

Step-by-step explanation:

If you are doing 10 to the power of something just write 1 and then the amount of zeros as the power.

So for this question I wrote 1 and the 40 zeros.

ozzi3 years ago

5 0

Answer:

1 0000000000 0000000000 0000000000 0000000000.

Step-by-step explanation:

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At a certain coffee shop, all the customers buy a cup of coffee and some also buy a doughnut. The shop owner believes that the n

wolverine [178]

Answer:

(1) The probability that the shop owner sells over 2000 cups of coffee in a week is 0.2514.

(2) The shop owner has no reasonable chance to expect earning a profit more than $300.

(3) The probability that the shop owner will sell a doughnut to more than half of his coffee customers is 0.2611.

Step-by-step explanation:

Let X = number of cups of coffee sold and Y = number of donuts sold.

The random variable X follows a Normal distribution with parameters μ = 320 and σ = 20.

The random variable Y follows a Normal distribution with parameters μ = 150 and σ = 12.

The shop owner opens the shop 6 days a week.

(1)

Compute the probability that the shop owner sells over 2000 cups of coffee in a week as follows:

$P(X>2000)=P(\frac{X-\mu}{\sigma}>\frac{2000-(6\times320)}{6\times20})\\=P(Z>0.67)\\=1-P(Z$

Thus, the probability that the shop owner sells over 2000 cups of coffee in a week is 0.2514.

(2)

The equation representing the profit earned on selling 1 cup of coffee and 1 doughnut in a day is:

P = 0.5X + 0.4Y

Compute the probability that the shop owner earns more than $300 as profit as follows:

$P(Profit>300)=P(\frac{Profit-\mu}{\sigma}>\frac{300-((0.5\times320)+(0.4\times150))}{\sqrt{0.5^{2}(20)^{2}+0.4^{2}(12)^{2}}})\\=P(Z>7.21)\\\approx0$

The probability of earning a profit more then $300 is approximately 0.

Thus, the shop owner has no reasonable chance to expect earning a profit more than $300.

(3)

The expression representing the statement "he'll sell a doughnut to more than half of his coffee customers" is:

Y > 0.5X

Y - 0.5X > 0

Compute the probability of the event (Y - 0.5X > 0) as follows:

$P(Y - 0.5X > 0)=P(\frac{(Y - 0.5X) -\mu}{\sigma}>\frac{0-(150-(0.5\times320}{\sqrt{12^{2}+0.5^{2}20^{2}}})\\=P(Z>0.64)\\=1-P(Z$

Thus, the probability that the shop owner will sell a doughnut to more than half of his coffee customers is 0.2611.

8 0

3 years ago

A piece of wire of length 5050 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the

algol [13]

Answer:

x should be cut at 2221.5 to minimize the total combined area, and at 5050 to maximize it.

Step-by-step explanation:

Let x be the length of wire that is cut to form a circle within the 5050 wire, so 5050 - x would be the length to form a square.

A circle with perimeter of x would have a radius of x/(2π), and its area would be

$A_c = \pir^2 = \pi (\frac{x}{2pi})^2 = \frac{x^2}{4\pi}$

A square with perimeter of 5050 - x would have side length of (5050 - x)/4, and its area would be

$A_s = (\frac{5050 - x}{4})^2 = \frac{(5050 - x)^2}{16}$

The total combined area of the square and circles is

$\sum A = A_c + A_s = \frac{x^2}{4\pi} + \frac{(5050 - x)^2}{16}$

To find the maximum and minimum of this, we just take the 1st derivative, and set it to 0

$A' = \frac{2x}{4\pi} + \frac{-2(5050-x)}{16} = 0$

$\frac{x}{2\pi} - \frac{5050 - x}{8} = 0$

Multiple both sides by 8π and we have

$4x - 5050\pi + x\pi = 0$

$x(4 + \pi) = 5050\pi$

$x = \frac{5050\pi}{4 + \pi} = 2221.5$

At x = 2221.5:

$A = \frac{x^2}{4\pi} + \frac{(5050 - x)^2}{16}$ = 392720 + 500026 = 892746 [/tex]

At x = 0, $A = 5050^2/16 = 1593906$

At x = 5050, $A = \frac{5050^2}{4\pi} = 2029424$

As 892746 < 1593906 < 2029424, x should be cut at 2221.5 to minimize the total combined area, and at 5050 to maximize it.

3 0

3 years ago

Find the area of a triangle whose base is 10 mm, and its height is 15 mm.

hjlf

Answer:

75mm²

Step-by-step explanation:

Area of a triangle

1/2 × base × height

= 1/2 × 10mm × 15mm

= 75mm²

5 0

3 years ago

Use the numbers 2,4,6,8 to make 60. You can use any operations and use brackets as well.

lesya692 [45]

Answer:

Below

Step-by-step explanation:

4+6=10

8-2=6

10*6=60

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3 years ago

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Park County, Wyoming, has a population of approximately 28,205 people. There are two main cities in Park County: Cody, with a po

-BARSIC- [3]

The answer is A, 13,535 people.

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3 years ago

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