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3 years ago

14

Harry reads that a particular element has an atom with a mass of 0.000000000012 grams. What is the weight of the atom expressed

in scientific notation?

1 answer:

Arlecino [84]3 years ago

8 0

1.2 e⁻¹¹

Because you need a number between 1 and 10 for scientific notation. So you move the decimal over 11 places. Since you move it to the right, it becomes a negative exponent.

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The gross weekly sales at a certain restaurant are a normal random variable with mean $2200 and standard deviation $230.What is

Lesechka [4]

Answer:

a) The total gross sales over the next 2 weeks exceeds $5000 is 0.0321.

b) The weekly sales exceed $2000 in at least 2 of the next 3 weeks is 0.9033.

Step-by-step explanation:

Given : The gross weekly sales at a certain restaurant are a normal random variable with mean $2200 and standard deviation $230.

To find : What is the probability that

(a) the total gross sales over the next 2 weeks exceeds $5000;

(b) weekly sales exceed $2000 in at least 2 of the next 3 weeks? What independence assumptions have you made?

Solution :

Let $X_1$ and $X_2$ denote the sales during week 1 and 2 respectively.

a) Let $X=X_1+X_2$

Assuming that $X_1$ and $X_2$ follows same distribution with same mean and deviation.

$E(X)=E(X_1+X_2)=E(X_1)+E(X_2)$

$E(X)=2\mu = 2(220)=4400$

$\sigma_X=\sqrt{var(X_1+X_2)}$

$\sigma_X=\sqrt{2\sigma^2}$

$\sigma_X=\sqrt{2}\sigma$

$\sigma_X=230\sqrt{2}$

So, $X\sim N(4400,230\sqrt{2})$

$P(X>5000)=1-P(X\leq5000)$

$P(X>5000)=1-P(Z\leq\frac{5000-4400}{230\sqrt{2}})$

$P(X>5000)=1-P(Z\leq1.844)$

$P(X>5000)=1-0.967$

$P(X>5000)=0.0321$

The total gross sales over the next 2 weeks exceeds $5000 is 0.0321.

b) The probability that sales exceed teh 2000 and amount in at least 2 and 3 next week.

We use binomial distribution with n=3.

$P(X>2000)=1-P(X\leq2000)$

$P(X>2000)=1-P(Z\leq\frac{2000-2200}{230})$

$P(X>2000)=1-P(Z\leq-0.87)$

$P(X>2000)=1-0.1922$

$P(X>2000)=0.808$

Let Y be the number of weeks in which sales exceed 2000.

Now, $P(Y\geq 2)$

So, $P(Y\geq 2)=P(Y=2)+P(Y=3)$

$P(Y\geq 2)=^3C_2(0.8077)^2\cdot (1-0.8077)+^3C_3(0.8077)^3$

$P(Y\geq 2)=0.37635+0.52692$

$P(Y\geq 2)=0.90327$

The weekly sales exceed $2000 in at least 2 of the next 3 weeks is 0.9033.

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3 years ago

Determine whether the following claims could be true. Explain your answer. Your computer has 200% less storage than mine. true o

Alla [95]

Answer:

Step-by-step explanation:

8 0

3 years ago

five more than the product of a number n and 8 is at least 100. Write an inequality that can be used to find all positive values

hjlf

"More than" indicates addition, and "product" indicates multiplication.

The inequality is:

5 + 8n >= 100

Now we can solve for all positive values of n:

5 + (-5) + 8n >= 100 + (-5)

8n >= 95

8n/(8) >= 95/(8)

n >= 11.875

So all positive values of n include everything between 11.875 and positive infinity, inclusively.

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3 years ago

8. Line ZX and Line WY are secants of circle V, as shown below.

lisabon 2012 [21]

Answer: take a protractor to the unkown sides to find the angle degrees and to check add them up and see if it is 360 degrees

Step-by-step explanation:

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3 years ago

Can anyone help me with this, please?

zloy xaker [14]

9514 1404 393

Answer:

C. 3x∛(y²z)

Step-by-step explanation:

The relevant rules of exponents are ...

$\sqrt[n]{a^m} = a^\frac{m}{n}\\\\(a^b)^c=a^{bc}$

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Your expression can be rewritten and simplified as follows.

$\displaystyle\sqrt[3]{27x^3y^2z}=(3^3x^3y^2z)^\frac{1}{3}=3xy^\frac{2}{3}z^\frac{1}{3}=3x(y^2z)^\frac{1}{3}=\boxed{3x\sqrt[3]{y^2z}}$

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3 years ago

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