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2 years ago

A beaker contains 1 1/4 pints of a chemical. A scientist pours the chemical out of the beaker until only 3 fluid ounces remain.

Mathematics

2 answers:

Keith_Richards [23]2 years ago

6 0

Answer:

17 pints

Step-by-step explanation:

1 pint is 16 plus another quarter equals 20, 20 - 17 = 3 or 20 - 3 = 17

rusak2 [61]2 years ago

3 0

Answer:

Step-by-step explanation:

16 ounces in a pint, 16 divided by four is 4, so 1/4 a pint is four ounces.

so there is 20 ounces in total, 20 -3 = 17

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The vertices of ΔRST are R(–1,–1), S(–1,11) and T(4,11). Which could be the side lengths of a triangle that is similar but not c

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The side lengths could be 10, 24 and 26 units.

We must first find the side lengths. We use the distance formula to do this.

For RT:
$d=\sqrt{(11--1)^2+(-1--1)^2}
\\=\sqrt{(11+1)^2+(-1+1)^2}
\\=\sqrt{12^2+0^2}=\sqrt{144}=12$

For ST:
$d=\sqrt{(11-11)^2+(4--1)^2}
\\=\sqrt{0^2+(4+1)^2}=\sqrt{5^2}=\sqrt{25}=5$

For TR:
$d=\sqrt{(11--1)^2+(4--1)^2}
\\=\sqrt{(11+1)^2+(4+1)^2}=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13$

Our side lengths, from least to greatest, are 5, 12 and 13.

To be similar but not congruent, the side lengths must have the same ratio between corresponding sides but not be the same length. 10, 24 and 26 are all 2x the original side lengths, so this works.

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2 years ago

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It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry a

Sphinxa [80]

Answer:

(a) P(B) = 0.008, (b) P(A∩B) = 0, (c) Yes, A and B are mutually exclusive events, (d) P(A∪B)=0.948, (e) 0.948, (f) 0.06

Step-by-step explanation:

We have three different posibilities

A: fill to specification

B: underfill

C: overfill

in probability the sum of the different events which are mutually exclusive should sum to 1, so, we should have

(a) P(B) = 1 - P(A)-P(C) = 1-0.940-0.052=0.008

(b) P(A∩B)=probability that the machine fill to specification and underfill = 0 because a machine can't fill to specification and underfill at the same time

(c) Yes, A and B are mutually exclusive events, because a machine can't fill to specification and underfill at the same time

(d) Because A and B are mutually exclusive events we should have that

P(A∪B)=P(A)+P(B)=0.940+0.008=0.948

(e) The probability that the machine does not overfill is the same that the probability that the machine fill to specification plus the probability that the machine underfill, i.e, the probability that the machine does not overfill is P(A)+P(B)=0.948, because does not overfill is equivalent either to fill to specification or to underfill.

(f) The probability that the machine either overfill or underfills is

P(C∪B)=P(C)+P(B)=0.052+0.008=0.06 because C and B are mutually exclusive events.

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Step-by-step explanation: