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riadik2000 [5.3K]
3 years ago
12

You need 250 mL of a 90% alcohol solution. On hand, you have a 75% alcohol mixture. How much of the 75% alcohol mixture and pure

alcohol will you need to obtain the desired solution?
Mathematics
1 answer:
stich3 [128]3 years ago
8 0

9514 1404 393

Answer:

  • 100 mL of 75% solution
  • 150 mL of pure alcohol

Step-by-step explanation:

Let x represent the quantity (in mL) of pure alcohol needed for the mix. Then the amount of 75% needed is (250-x). The amount of alcohol in the mixture is ...

  1.00x +0.75(250 -x) = 0.90(250)

  0.25x +187.5 = 225 . . simplify

  0.25x = 37.5 . . . . . . . . subtract 187.5

  x = 150 . . . . . . . . . . . . . divide by 0.25

  (250 -x) = 100 . . . . mL of 75% solution

You need 100 mL of the 75% solution and 150 mL of pure alcohol to obtain the desired mixture.

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Two types of defects are observed in the production of integrated circuit boards. It is estimated that 6% of the boards have sol
aalyn [17]

Answer:

(a) 0.09

(b) 0.06

(c) 0.0018

(d) 0.9118

(e) 0.03

Step-by-step explanation:

Let <em>A</em> = boards have solder defects and <em>B</em> = boards have surface defects.

The proportion of boards having solder defects is, P (A) = 0.06.

The proportion of boards having surface-finish defects is, P (B) = 0.03.

It is provided that the events A and B are independent, i.e.

P(A\cap B)=P(A)\times P(B)

(a)

Compute the probability that either a solder defect or a surface-finish defect or both are found as follows:

= P (A or B) + P (A and B)

=P(A)+P(B)-P(A\cap B)+P(A\cap B)\\=P(A)+P(B)\\=0.06+0.03\\=0.09

Thus, the probability that either a solder defect or a surface-finish defect or both are found is 0.09.

(b)

The probability that a solder defect is found is 0.06.

(c)

The probability that both defect are found is:

P(A\cap B)=P(A)\times P(B)\\=0.06\times0.03\\=0.0018

Thus, the probability that both defect are found is 0.0018.

(d)

The probability that none of the defect is found is:

P(A^{c}\cup B^{c})=1-P(A\cup B)\\=1-P(A)-P(B)+P(A\cap B)\\=1-P(A)-P(B)+[P(A)\times P(B)]\\=1-0.06-0.03+(0.06\times0.03)\\=0.9118

Thus, the probability that none of the defect is found is 0.9118.

(e)

The probability that the defect found is a surface finish is 0.03.

6 0
3 years ago
What’s the explicit formula
zepelin [54]

Answer:

2.7g-1

Step-by-step explanation:

5 0
3 years ago
Rewrite the function f of x equals 7 times one half to the 3 times x power using the properties of exponents.
Artist 52 [7]

Answer:

f of x equals 7 times one eighth to the x power

Step-by-step explanation:

Given phrase,

function f of x equals 7 times one half to the 3 times x power,

\implies f(x) = 7(\frac{1}{2})^{3x}

By the power to power property of exponent,

That is,

(a^m)^n=a^{m.n}

f(x) = 7((\frac{1}{2})^3)^x

f(x) = 7(\frac{1}{8})^x

= f of x equals 7 times one eighth to the x power

8 0
3 years ago
The following events took place at a manufacturing company for the current year: (1) Purchased $115,000 in direct materials. (2)
Elden [556K]

The question was not written properly. Here is the appropriate form of question:

The following events took place at a manufacturing company for the current year:

(1) Purchased $115,000 in direct materials.

(2) Incurred labor costs as follows: (a) direct, $76,000 and (b) indirect, $33,600.

(3) Other manufacturing overhead was $127,000, excluding indirect labor.

(4) Transferred 75% of the materials to the manufacturing assembly line.

(5) Completed 60% of the Work-in-Process during the year.

(6) Sold 80% of the completed goods.

(7) There were no beginning inventories.

1- What is the company's Cost of Goods Sold?

Options:

a. $193,710

b. $154,968

c. $322,850

d. $258,280

Answer:

1- b. $154,968

Step-by-step explanation:

1- Cost of goods sold (COGS) is the is the expense of securing or assembling the items that an organization sells during a period, so the main costs remembered for the measure are those that are directly attached to the creation of the items, including the expense of work (labor cost), materials, and assembling overhead.

0.6*[$0 + 0.75*($115,000) + $76,000 + ($127,000 + $33,600)] <em>(because completed 60% of the Work-in-Process during the year)</em>

= $193,710

80% of $193,710 <em>(because sold 80% of the completed goods)</em>

0.8*$193,710

= $154,968

5 0
3 years ago
Polygon ABCD goes through a sequence of rigid transformations to form polygon A′B′C′D′. The sequence of transformations involved
Sever21 [200]
Polygon ABCD goes through a sequence of rigid transformations to form polygon A′B′C′D′. The sequence of transformations involved is a reflection across the _Y-axis _, followed by a reflection across the line _y=-x__.
5 0
3 years ago
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