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maw [93]
3 years ago
6

A tank contains seven liters of 10% alcohol solution. how many liters of 6% alcohol should be added to have 8% alcohol solution?

Mathematics
1 answer:
kow [346]3 years ago
7 0

Answer:

b

Step-by-step explanation:

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Evaluate each of the following. (a) P(11,5) (b) C(11,5) (a) P(11,5) = (Simplify your answer.) (b) C(11,5) = (Simplify your answe
Hunter-Best [27]
<h2>Answer:</h2>

(a)   P(11,5)= 55440

(b)  C(11,5)=462

<h2>Step-by-step explanation:</h2>

We know that the permutation is the number of ways of arranging r items out of a total of n items and is given by:

P(n,r)=\dfrac{n!}{(n-r)!}

and the combination is the number of ways of choosing r items out of a total of n items and is given by:

C(n,r)=\dfrac{n!}{r!\times (n-r)!}

(a)

               P(11,5)

P(11,5)=\dfrac{11!}{(11-5)!}\\\\P(11,5)=\dfrac{11!}{6!}\\\\P(11,5)=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{6!}\\\\P(11,5)=11\times 10\times 9\times 8\times 7\\\\P(11,5)=55440

(b)

                 C(11,5)    

C(11,5)=\dfrac{11!}{5!\times (11-5)!}\\\\C(11,5)=\dfrac{11!}{5!\times 6!}\\\\C(11,5)=\dfrac{11\times 10\times 9\times 8\times 7\times 6!}{5\times 4\times 3\times 2\times 1\times 6!}\\\\C(11,5)=462

8 0
3 years ago
John could not decide, but he had 9 dollars he could spend on fruit kabobs that cast 1.75 dollars and smoothies that cost 2.50 d
IrinaK [193]

Answer:

One fruit kabob and one smoothie

Two fruits kabobs and two smoothies

Three fruit kabobs and one smoothie

One fruit kabob and two smoothies

Explanation:

In this situation, the basic combination John can afford is simply to buy one fruit kabob and one smoothie ( $1.75 + $ 2.50 = $4.25) because he wants at least one unit of each item. Additionally, it is possible to add more units of each item to create new combinations or possibles, just make sure they do not total more than 9 dollars, which is the money John has. Here are some of the possible combinations:

Two fruit kabobs and two smoothies

Fruit kabobs: $1.75 x 2 = $3.5

Smoothies: $ 2.50 x 2 = $5

Total: $8.5

Three fruit kabobs and one smoothie

Fruit kabobs: $1.75 x 3 = $5.25

Smoothie: $2.50

Total: $7.75

One fruit kabob and two smoothies

Fruit kabob: $1.75

Smoothies: $2.50 x 2 = $5

Total: $6.75

5 0
3 years ago
What is the equation of a circle with a center (3, 3) and a area of 219π
katrin2010 [14]

Answer:

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8 0
3 years ago
I need help with the following problem
nikdorinn [45]
Factor both the numerator and the denominator before attempting to divide /reduce/ simplify. 
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3 years ago
the local theater is showing a matinee and offering a special deal for the community. A ticket for an adult costs $11 and a tick
Montano1993 [528]
We will call an adult ticket <em>a</em>, and a child ticket <em>c</em>.

Since they sold 60 tickets in total, we can form the equation:
a + c = 60

We can also say that the sum of money from the adult tickets and child tickets combined is 460.
Thus we can say
11a + 6c = 460

Now, we must solve our system.

a + c = 60
11a + 6c = 460

6a + 6c = 360
11a + 6c = 460

-5a = -100
a = 20

Thus, (20) + c = 60
c = 40

a = 20 and c = 40
4 0
3 years ago
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