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3 years ago

Solve for y 3x + 2y=37

Mathematics

1 answer:

kolezko [41]3 years ago

3 0

Answer and Step-by-step explanation:

$y=\frac{-3}{2}x+\frac{37}{2}$

Step 1: Add -3x to both sides

$3x+2y+-3x=37+-3x$

$2y=-3x+37$

Step 2: Divide both sides by 2.

$\frac{2y}{2}=\frac{-3x+27}{2}$

$y=\frac{-3}{2}x+\frac{37}{2}$

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A tank contains 120 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu

gtnhenbr [62]

If A(t) is the amount of salt in the tank at time t, then A(0) = 50 g and

A'(t) = (1 g/L)*(3 L/min) - (A(t)/120 g/L)*(3 L/min)

$\implies A'+\dfrac A{40}=3$

Multiply both sides by $e^{t/40}$ , so that the left side can be condensed as the derivative of a product:

$e^{t/40}A'+\dfrac{e^{t/40}}{40}A=3e^{t/40}$

$\left(e^{t/40}A\right)'=3e^{t/40}$

Integrate both sides and solve for A(t).

$e^{t/40}A=120e^{t/40}+C$

$\implies A(t)=120+Ce^{-t/40}$

Given that A(0) = 50 g, we have

$50=120+C\implies C=-70$

so that the amount of salt in the tank at time t is

$\boxed{A(t)=120-70e^{-t/40}}$

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3 years ago

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these inte

stich3 [128]

The probability of winning a lottery by selecting the correct six integers, are

$\begin{aligned}&(a) 1.68 \times 10^{-6} \\&(b) 5.13 \times 10^{-7} \\& (c) 1.91 \times 10^{-7} \\&(d)8.15 \times 10^{-8}\end{aligned}$

<h3>What is binomial distribution?</h3>

The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.

Part (a); positive integers not exceeding 30.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other twenty-four.

$\frac{\left(\begin{array}{c}6 \\6\end{array}\right)\left(\begin{array}{c}24 \\0\end{array}\right)}{\left(\begin{array}{c}30 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}30 \\6\end{array}\right)}=1.68 \times 10^{-6}$

Part (b); positive integers not exceeding 36.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other thirty.

$\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}30 \\0\end{array}\right)}{\left(\begin{array}{c}36 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}36 \\6\end{array}\right)}=5.13 \times 10^{-7}$

Part (c); positive integers not exceeding 42.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the 36 other integers.

$\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}36 \\0\end{array}\right)}{\left(\begin{array}{c}42 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}42 \\6\end{array}\right)}=1.91 \times 10^{-7}$

Part (d); positive integers not exceeding 48.

To calculate the probability, use binomial coefficients. Choose six of the six accurate integers and none of the other 42.

$\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}42 \\0\end{array}\right)}{\left(\begin{array}{c}48 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}48 \\6\end{array}\right)}=8.15 \times 10^{-8}$

To know more about binomial probability, here

brainly.com/question/9325204

#SPJ4

The complete question is-

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 30. b) 36. c) 42. d) 48.

5 0

2 years ago

Solving Rational equations. LCD method. Show work. Image attached.

Dmitry [639]

Answer:

$b=1$

Step-by-step explanation:

The given rational equation is

$\frac{2b-5}{b-2} -2=\frac{3}{b+2}$

The Least Common Denominator is $(b+2)(b-2)$ .

Multiply each term in the equation by the LCD.

$(b+2)(b-2)\times \frac{2b-5}{b-2} -(b+2)(b-2)\times2=(b+2)(b-2)\times\frac{3}{b+2}$

Simplify;

$(b+2)\times \frac{2b-5}{1} -2(b+2)(b-2)=(b-2)\times\frac{3}{1}$

$(b+2)(2b-5) -2(b+2)(b-2)=3(b-2)$

Expand and group similar terms

$2b^2-5b+4b-10 -2(b^2-4)=3b-6$

$2b^2-5b+4b-10 -2b^2+8=3b-6$

$-b-2=3b-6$

$3b+b=-2+6$

$4b=4$

$b=1$

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2 years ago

At a track meet, 50 people ran the 100-meter dash. 2 people finished in 11 seconds, 5 people finished in 12 seconds, 8 people fi

adoni [48]

You have to do a histogram here:

<span>11 sec: 2 people: probability is 2/50 = 1/25 = 0.04
12 sec: 5 people: probability is 5/50 = 1/10 = 0.1
13 sec: 8 people: probability is 8/50 = 4/25 = 0.16
</span>14 sec: 10 people: probability is 10/50 = 1/5 = 0.2
15 sec: 21 people: probability is 21/50 = 2.38
16 sec: 2 people: probability is 2/50 = 1/25 = 0.04
17 sec: 2 people: probability is 2/50 = 1/25 = 0.04

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2 years ago

The sum of the first n consecutive even numbers can be found using S = n2 + n, where n ≥ 2.

viktelen [127]

The following are the choices on this question:
A.6
B. 39
C. 26
D. 12
The answer is option D. 12.

Check this out:
S=n² + n
S= 12² + 12
(you can get the square of 12 by multiplying 12 by itself: 12 × 12)
S=144 +12
S=156

3 0

3 years ago

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Solve for y 3x + 2y=37​

Solve for y 3x + 2y=37