Explain why you cannot use mass or volume alone to identify substances.

A company manufactures three types of cabinets. It makes 110 cabinets each week. In the first week, the sum of the number of typ

miss Akunina [59]

Answer:

In the first week, the number of type-1 cabinets produced was 15,
the number of type-2 cabinets produced was 30,
the number of type-3 cabinets produced was 65.

Step-by-step explanation:

If we let a, b, c represent the numbers of type-1, type-2, and type-3 cabinets produced in the first week, respectively, we can write three equations in these unknowns:

a + b + c = 110 . . . . . total cabinets for the first week
a + 2b - c = 10 . . . . relationship of quantities in the first week
3a +0b +c = 110 . . . . total cabinets in the second week

It can be convenient to let a machine solver find the solution to this set of equations. Most graphing calculators can handle it, along with several web sites.

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Solving by hand, we can subtract the second equation from twice the first. This gives ...

2(a +b +c) -(a +2b -c) - 2(110) -(10)

a +3c = 210 . . . . simplify

Subtracting this from 3 times the third equation gives ...

3(3a +c) -(a +3c) = 3(110) -(210)

8a = 120 . . . . . simplify

a = 15 . . . . . . . divide by 8

Using this in the third equation of the original set, we have ...

3·15 +c = 110

c = 65 . . . . . . subtract 45

Then, in the first equation, we get ...

15 + b + 65 = 110

b = 30 . . . . . . . subtract 80

The solution is (type-1, type-2, type-3) = (15, 30, 65) for the first week.

4 0

4 years ago

Read 2 more answers

A bicycle has a listed price of $577.98 before tax. If the sales tax rate is 6.5%, find the total cost of the bicycle with sales

Salsk061 [2.6K]

Answer:

$615.54

Step-by-step explanation:

Step 1

Write your problem.

577.98 x 6.5% = ?

Step 2

Convert the % to a decimal:

6.5% to 0.065

Step 3

Rewrite the problem with decimal replacing the percentage.

Now the problem looks like this:

577.98 x 0.065 = 37.56

This problem gives the amount of the tax.

Step 4

Add the original price with the tax amount:

577.98 + 37.56 = $615.54 (total cost)

3 0

3 years ago

A survey conducted by the Consumer Reports National Research Center reported, among other things, that women spend an average of

Nookie1986 [14]

Answer:

(a) The probability that a randomly selected woman shop exactly two hours online is 0.217.

(b) The probability that a randomly selected woman shop 4 or more hours online is 0.0338.

(c) The probability that a randomly selected woman shop less than 5 hours online is 0.9922.

Step-by-step explanation:

Let <em>X</em> = time spent per week shopping online.

It is provided that the random variable <em>X</em> follows a Poisson distribution.

The probability function of a Poisson distribution is:

$P (X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!} ;\ x=0,1,2,...$

The average time spent per week shopping online is, <em>λ </em>= 1.2.

(a)

Compute the probability that a randomly selected woman shop exactly two hours online over a one-week period as follows:

$P (X=2)=\frac{e^{1.2}(1.2)^{2}}{2!} =0.21686\approx0.217$

Thus, the probability that a randomly selected woman shop exactly two hours online is 0.217.

(b)

Compute the probability that a randomly selected woman shop 4 or more hours online over a one-week period as follows:

P (X ≥ 4) = 1 - P (X < 4)

= 1 - P (X = 0) - P (X = 1) - P (X = 2) - P (X = 3)

$=1-\frac{e^{1.2}(1.2)^{0}}{0!}-\frac{e^{1.2}(1.2)^{1}}{1!}-\frac{e^{1.2}(1.2)^{2}}{2!}-\frac{e^{1.2}(1.2)^{2}}{3!}\\=1-0.3012-0.3614-0.2169-0.0867\\=0.0338$

Thus, the probability that a randomly selected woman shop 4 or more hours online is 0.0338.

(c)

Compute the probability that a randomly selected woman shop less than 5 hours online over a one-week period as follows:

P (X < 5) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)

$=\frac{e^{1.2}(1.2)^{0}}{0!}+\frac{e^{1.2}(1.2)^{1}}{1!}+\frac{e^{1.2}(1.2)^{2}}{2!}+\frac{e^{1.2}(1.2)^{3}}{3!}+\frac{e^{1.2}(1.2)^{4}}{4!}\\=0.3012+0.3614+0.2169+0.0867+0.0260\\=0.9922$