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notka56 [123]
2 years ago
5

Paint costing $19 per gallon is to be mixed with thinner costing $3 per gallon. How much of each should be added to make 16 gall

ons of a mix that costs $14 per gallon?
Mathematics
1 answer:
Evgen [1.6K]2 years ago
4 0
Let x represent gallons of $19 paint
let y represent gallons of $3 paint

first you make your 2 equations

x+y=16, y=16-x
(19x+3y) ÷ 16 = 14

then you use substitution

14 = (19x + 3(16-x) ) ÷16
224 = 19x + 48 - 3x
176 = 16x
11 = x, so there's 11 gallons of $19 paint
recall that x+y=16
11+y=16
5=y

so there are 11 gallons of $19 paint and 5 gallons of $3 paint


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Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $
STatiana [176]

Answer:

For this case, the first thing we must do is define variables:

x: number of hammers

y: number of wrenches

We write the system of inequations:

10x + 6y <= 120

x + y> = 14

Step-by-step explanation:

5 0
2 years ago
Problem 5 (4+4+4=12) We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely. 1) Fin
tekilochka [14]

Answer:

1

p(b) =  \frac{1}{6}

2

p(k) =  \frac{1}{3}

3

P(a) =  \frac{1}{3}

Step-by-step explanation:

Generally when two fair 6-sided dice is rolled the doubles are

(1 1) , ( 2 2) , (3 3) , (4 4) , ( 5 5 ), (6 6)

The total outcome of doubles is N = 6

The total outcome of the rolling the two fair 6-sided dice is

n = 36

Generally the probability that doubles (i.e., having an equal number on the two dice) were rolled is mathematically evaluated as

p(b) =  \frac{N}{n}

p(b) =  \frac{6}{36}

p(b) =  \frac{1}{6}

Generally when two fair 6-sided dice is rolled the outcome whose sum is 4 or less is

(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)

Looking at this outcome we see that there are two doubles present

So

The conditional probability that doubles were rolled is mathematically represented as

p(k) =  \frac{2}{6}

p(k) =  \frac{1}{3}

Generally when two fair 6-sided dice is rolled the number of outcomes that would land on different numbers is L = 30

And the number of outcomes that at least one die is a 1 is W = 10

So

The conditional probability that at least one die is a 1 is mathematically represented as

P(a) =  \frac{W}{L}

=> P(a) =  \frac{10}{30}

=> P(a) =  \frac{1}{3}

3 0
2 years ago
According to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market. A random sample of 70 users
Natalija [7]

Answer:

Probability that 32 or more from this sample used Internet Explorer as their browser is 0.9015.

Step-by-step explanation:

We are given that according to Net Market Share, Microsoft's Internet Explorer browser has 53.4% of the global market.

A random sample of 70 users was selected.

Let \hat p = <u><em>sample proportion of users who used Internet Explorer as their browser.</em></u>

The z score probability distribution for sample proportion is given by;

                            Z  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, p = population proportion of users who use internet explorer = 53.4%

           \hat p = sample proportion = \frac{32}{70} = 0.457

           n = sample of users = 70

Now, probability that 32 or more from this sample used Internet Explorer as their browser is given by = P( \hat p \geq 0.457)

      P( \hat p \geq 0.457) = P( \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } \geq \frac{0.457-0.534}{\sqrt{\frac{0.457(1-0.457)}{70} } } ) = P(Z \geq -1.29)

                            = P(Z \leq 1.29) = <u>0.9015</u>

The above probability is calculated by looking at the value of x = 1.29 in the z table which has an area of 0.9015.

4 0
2 years ago
in triangleABC the side lengths are b=13, ac=21 and bc=x. write a compound inequality the represents the range of possible value
tankabanditka [31]

Answer:

8 < x < 34

Step-by-step explanation:

ab = 13, ac = 21, bc = x

The longest side of a triangle must be less than the sum of the other two sides.

If 21 is the longest side:

21 < 13 + x

8 < x

If x is the longest side:

x < 13 + 21

x < 34

Therefore, 8 < x < 34.

3 0
2 years ago
A dartboard has 8 sections of equal area. The letters represent colors red (R), yellow (Y), blue (B), and green (G). Complete th
Alla [95]
Since the sum of all probabilities of all all elementary events will always be equal to 1. Furthermore, the probabilities of all mutually exclusive set of events that is part of the entire sample space will always be total of 1.

So in the problem, the answer is 1/8.
1/8 for red + 3/8 for green + 3/8 for yellow + 1/8 for blue = 8/8 or 1.
4 0
2 years ago
Read 2 more answers
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