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Mumz [18]
2 years ago
7

Jotham needs 70 liters of a 50% alcohol solution. He has a 30% solution and an 80% solution available. How many liters of

Mathematics
2 answers:
Nuetrik [128]2 years ago
6 0

x+y=70. (30x+80y)/(100x+100y)=50/100

lara31 [8.8K]2 years ago
5 0

Answer:

42 liters of 30% alcohol solution will be needed.

28 liters of 80% solution will be needed.

Step-by-step explanation:

Jotham needs 70 liters of a 50% alcohol solution.

Let the 30% solution needed be x.

We get the following equation:

70\times0.5=0.30x+0.80(70-x)

Solving this we get;

35=0.30x+56-0.80x

=> 35=56-0.50x

=> 0.50x=56-35

=> 0.50x=21

x = 42

Hence, 42 liters of 30% alcohol solution will be needed.

And 70-42=28 liters of 80% solution will be needed.

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22% of adults would pay more for environmentally friendly products he randomly select 10 adults find the probability that the nu
Anettt [7]

Answer: 0.383 and 0.6671

Step-by-step explanation:

Take 22%, that is 0.22 to be probability of success.

That means "1-0.22 = 0.78" is the probability of failure.

When dealing with selection in probability mathematics, the combination equation is used.

Probability of selecting number 'r' as a successful outcome from a given number 'n' is given as

nCr * p^r * q^n-r

Where p is the probability of success= 0.22

q is the probability of failure= 0.78

n is the total number of sample =10

r is the varying outcome of number of success.

For the first question, number of success is asked to be everything more than 2, that is probability of choosing 3,4,5,6,7,8,9,10 people with a successful outcome (adults who will pay more for environmentally friendly product.)

Instead of going through the long process of checking probability of success for choosing 3,4,5,6,7,8,9,10 adults who will pay more, we can simply find the probability of choosing 0,1,2 adults who will pay more and subtract the answer from 1.

By doing this, we first check for probability of choosing 0 adult that will pay More and this is gotten by putting r=0 in our probability Formula. The Formula becomes

=10C0 * 0.22^0 * 0.78^10

=1 *1 * 0.0834= 0.0834

Hence, Probability of Choosing 0 adult that will Pay more is 0.0834

To Check for probability of choosing 1 adult that will pay more becomes

=10C1 * 0.22^1 * 0.78^9

=10 * 0.22 * 0.1069 = 0.2352

Hence, Probability of choosing 1adult that will pay more = 0.2352

To Check for the probability of choosing 2adults that will pay more becomes

=10C2 * 0.22^2 * 0.78^8

=45 * 0.0484 * 0.1370 = 0.2984

Therefore the total sum of choosing 0,1,2 adults that are willing to pay more becomes

= 0.0834+ 0.2352+ 0.2984 = 0.617

So to determine the probability of choosing more than 2 adults, that is, 3,4,5,6,7,8,9,10 adults that are willing to pay more, we subtract 0.617 from 1.

This gives 1-0.617 = 0.383

Hence, probability of choosing more than 2 people that are willing to pay more than 2 = 0.383.

To determine the probability of choosing between two and five people inclusive, we follow the same probability formular but r becomes 2,3,4,5 differently.

For probability of choosing 2 adults, we already calculated it to be 0.2984 earlier.

For probability of choosing 3 adults, it becomes

10C3 * 0.22^3 * 0.78^7

=120* 0.0106 * 0.1757 = 0.2235

For the probability of choosign 4 adults, it becomes

10C4 * 0.22^4 * 0.78^6

= 210 * 0.0023 * 0.2252 = 0.1088

For the probability of choosing 5 adults, it becomes

10C5 * 0.22^5 * 0.78^5

= 252 * 0.0005 * 0.2887 = 0.0364

Hence, the probability of choosing between 2 and 5 adults becomes

0.2984 + 0.2235 + 0.1088 + 0.0364 = 0.6671

5 0
3 years ago
Y is inversely proportional to the square of (x + 2).<br>When x = 3, y = 2.<br>Find y when x = 8.​
VikaD [51]

Answer:

y = k/(x+2) squared

substitute y and x to find the value of k.

k =50

nxt used the value of k with same formula:.

y= 50/ (8+2) squared

y =1/2

6 0
2 years ago
Please answer the following attachment down below.<br><br> I would greatly appreciate it if you did.
zepelin [54]

Answer:

34.63

Step-by-step explanation:

A=a2+2aa2

4+h2=32+2·3·32

4+42≈34.63201

4 0
3 years ago
Expand: x(3 + 9). please
Oksi-84 [34.3K]

Answer:

x(3 + 9) = 3x + 9x = 12x

Step-by-step explanation:

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3 years ago
Your friend says she used a common
AfilCa [17]

Step-by-step explanation:

An equivalent fraction can be found by either multiplying the numerator and denominator by the same number or dividing the numerator and the denominator by the same number.

7 0
3 years ago
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