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vodka [1.7K]
3 years ago
11

Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. he currently has a 40% solution and a 70% solution. ho

w many liters of each does he need to make the needed 30 liters of 60% acid solution?
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
7 0

x = liters of 40% solution

y = liters of 70% solution

Gabe needs 30 liters, so

x + y = 30

Each liter of 40% solution contributes 0.4x liter of acid; each liter of 70% solution contributes 0.7y liter of acid. Gabe needs a solution with concentration 60%, which from 30 liters amounts to a net volume of 0.6*30 = 18 liters of acid. So

0.4x + 0.7y = 18

Solve the system however you like. By substitution, we have

y = 30 - x

0.4x + 0.7(30 - x) = 18

0.4x + 21 - 0.7x = 18

3 = 0.3x

==> x = 10 ==> y = 20

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Galina-37 [17]
The given data is
t, h:            0     2     4     6     8   10
r(t), L/h:   8.6  7.9  6.8  6.4  5.7  5.3

The lower and upper estimates for the total amount that leaked may be computed as the Left and Right Riemann sums.

The shape of the graph of r versus will determine which of the two sums yields an upper or lower sum.
The plot of the graph is shown below.

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4 0
4 years ago
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The area of a rectangle having breadth 2.6m is 18.33 sq.m. Find the<br> length of rectangle.
ladessa [460]

Answer:

Length = 7.05m

Step-by-step explanation:

Breadth is just a fancy word for width. We know that the width is 2.6 m and the total area is 18.33 m². We also know that the formula for the area of a rectangle is l*w, length times width. Remember, we are looking for l.

Set up an equation: l*w=A

Where:

  • l = Length
  • w = Width
  • A = Area

Plug in the known values.

l*w=A

l * 2.6 = 18.33

Solve for l. Isolate the variable by dividing both sides of the equation by 2.6:

l = 7.05

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3 years ago
HW 5.2
Marizza181 [45]

Answer:

The probability of no correct answers is 0.125 = 12.5%.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent of any other question, which means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

3 trials, each with probability of success (correct) given by p=0.50.

This means that n = 3, p = 0.5

The probability of no correct answers is

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{3,0}.(0.5)^{0}.(0.5)^{3} = 0.125

The probability of no correct answers is 0.125 = 12.5%.

6 0
3 years ago
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