A tank initially contains 200 gallons of brine, with 50 pounds of salt in solution. brine containing 2 pounds of salt per gallon is entering the tank at the rate of 4 gallons per minute and is is flowing out at the same rate. if the mixture in the tank is kept uniform by constant stirring, find the amount of salt in the tank at the end of 40 minutes. the amount of salt in the tank at the

The length of the shorter piece of wire is 12 cm, which is found by setting up the equation x + (x + 6) = 30, where x is the length of the shorter piece.

The student has asked to find the length of the shorter piece of wire when a 30 cm long wire is cut into two pieces, with the longer piece being 6 cm longer than the shorter piece. To solve this, we need to set up a simple equation based on the information given.

Let's represent the length of the shorter piece as x cm. Since the longer piece is 6 cm longer than the shorter piece, we can represent the longer piece as (x + 6) cm

We are told that the total length of the wire before it was cut was 30 cm. Therefore, the sum of the lengths of both pieces must equal 30 cm. This gives us the equation:

x + (x + 6) = 30

Simplifying the equation, we get:

2x + 6 = 30

Subtracting 6 from both sides of the equation gives us:

2x = 24

Dividing both sides by 2 to solve for x gives us:

x = 12

The probability of drawing a green card on both the first and second draw, with replacement, is 25/64, as each draw is an independent event with the same probability of 5/8 for drawing a green card.

The problem is asking us to compute the probability of drawing two green cards in succession, with replacement, from a deck that contains eight cards of which five are green and three are yellow. Since the draws are independent and with replacement, the probability of an event occurring on the first draw is not affected by the second draw, and vice versa.

To calculate the probability of drawing a green card on the first draw, denoted as P(G₁), we look at the number of green cards and the total number of cards. There are 5 green cards out of 8 total cards, so P(G₁) = 5/8.

Because we are replacing the drawn card before the second draw, the probability of drawing a green card on the second draw, denoted as P(G₂), remains the same as for the first draw, thus P(G₂) = 5/8.

The probability of both events happening, denoted as P(G₁ and G₂), is the product of the individual probabilities since the draws are independent. Therefore, we have:

P(G₁ and G₂) = P(G₁) * P(G₂) = (5/8) * (5/8) = 25/64.

Answer:

=

Step-by-step explanation:

When solving this, we just have to remember that the zero´s to the right after the decimal point are meaningless, so basically 0.700 is the same as 0.7 so in this case both number are the same, 0.700 and 0.7 are the same number expressed in different ways.

Answer:

150 lbs

Step-by-step explanation:

set up proportion

400/120 = 500/x

cross multiply
120x500 = 400x

then simplify

60000 = 400x

solve for x

60000/400 = x

x = 150

The volume of the solid generated is 218.01 cubic units

The curves are given as:

[tex]y = 9x^3[/tex], y = 9

[tex]x = 0[/tex]

Start by calculating x at [tex]y = 9x^3[/tex]

Substitute 9 for y

[tex]9x^3 = 9[/tex]

Divide both sides by 9

[tex]x^3 = 1[/tex]

Take the cube roots of both sides

[tex]x = 1[/tex]

So, the equation of the volume is then represented as:

[tex]V = \pi \int\limits^a_b {9^2 - (9x^3)^2} \, dx[/tex]

[tex]V = \pi\int\limits^a_b {81 - 81x^6} \, dx[/tex]

Where [a,b] = [1,0]

So, we have:

[tex]V = \pi\int\limits^1_0 {81 - 81x^6} \, dx[/tex]

Factor out 81

[tex]V = 81\pi\int\limits^1_0 {1 - x^6} \, dx[/tex]

Integrate

[tex]V = 81\pi [x - \frac 17x^7]|\limits^1_0[/tex]

Expand

[tex]V = 81\pi ([1 - \frac 17(1)^7] - [0 - \frac 17(0)^7] )[/tex]

[tex]V = 81\pi ([1 - \frac 17] )[/tex]

[tex]V = 81\pi * \frac 67[/tex]

So, we have:

[tex]V = 81 * 3.14 * \frac 67[/tex]

[tex]V = 218.01[/tex]

Hence, the volume of the solid generated is 218.01 cubic units

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The correct answer is that Jenny's ball bounced 32 inches.

To solve the problem, let's denote the distance that Clark's ball bounced as [tex]\( d \)[/tex] inches. According to the problem, Jenny's ball bounced 8 times farther than Clark's ball, so the distance Jenny's ball bounced is [tex]\( 8d \)[/tex] inches.

The total distance bounced by both balls is the sum of the distances each ball bounced, which is given as 36 inches. Therefore, we can set up the following equation:

[tex]\[ d + 8d = 36 \][/tex]

Combining like terms, we get:

[tex]\[ 9d = 36 \][/tex]

To find the value of [tex]\( d \)[/tex], we divide both sides of the equation by 9:

[tex]\[ d = \frac{36}{9} \][/tex]

[tex]\[ d = 4 \][/tex]

Now that we have the distance Clark's ball bounced, which is 4 inches, we can find the distance Jenny's ball bounced by multiplying [tex]\( d \)[/tex] by 8:

[tex]\[ 8d = 8 \times 4 \][/tex]

[tex]\[ 8d = 32 \][/tex]

So, Jenny's ball bounced 32 inches.

Option C correctly applies the Law of Syllogism. By combining the hypothesis from the first statement, 'If it is springtime, you will plant flowers in the garden' with the conclusion of the second, 'If you plant flowers in the garden, your yard will smell good' we form 'If it is springtime, then your yard will smell good'.

The question deals with logical reasoning, specifically the laws of syllogism and detachment. The Law of Syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. The Law of Detachment, also known as Modus Ponens, applies when a single conditional statement and the affirmation of its hypothesis lead to the affirmation of its conclusion.

Looking at the options:
A. The statement does not apply the law of syllogism.
B. The statement does not apply the law of detachment.
C. This statement correctly applies the Law of Syllogism. We have two statements: 'If it is springtime, you will plant flowers in the garden' and 'If you plant flowers in the garden, your yard will smell good'. Combining the hypothesis of the first with the conclusion of the second gives us 'If it is springtime, then your yard will smell good'.
D. This accurately applies the law, but the law it uses is not mentioned.

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The vertical asymptotes are x = 4 and x = 2, and the horizontal asymptote is y = -3.

The given function is f(x) = −3(x + 3)(x − 2) / (x − 4)(x − 2).

To find the vertical asymptotes, we need to determine the values of x for which the function approaches positive or negative infinity. The denominator of the rational expression cannot be equal to zero, so we set it equal to zero and solve for x: (x − 4)(x − 2) = 0. This gives us two vertical asymptotes at x = 4 and x = 2.

To find the horizontal asymptote, we need to examine the highest power of x in the numerator and denominator. In this case, both the numerator and denominator have the same highest power, which is x^1 or simply x. Therefore, to find the horizontal asymptote, we compare the coefficients of the highest power of x. The coefficient of x in both the numerator and denominator is -3. So the horizontal asymptote is y = -3.

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The vertical asymptotes of this rational function are x = 4 and x = 2.

The horizontal asymptote is y = -3.

In Mathematics and Geometry, a rational function refers to a type of function which is expressed as a fraction.

By critically observing the rational function [tex]f(x)=\frac{-3(x + 3)(x - 2)}{(x -4)(x - 2)}[/tex] shown above, we can logically deduce that its vertical asymptote can be determined by solving the denominator as follows;

(x - 2)(x - 4) = 0

x = 2 and x = 4.

Since the degree of the numerator is the same as the degree of the denominator, we can reasonably infer and logically deduce that this rational function's horizontal asymptote can be calculated by dividing the leading coefficient of the numerator by the leading coefficient of the denominator as follows;

y = -3/1

y = -3.

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The answer should look something like this:

Answer:

Y-4 =2/5(x-(-2)) is answer on edge

Step-by-step explanation:

Use point slope equaction y-y1=m(x-x1)

y1= 4 x1= -2 and m= 2/5 just plug in numbers

Answer:

[tex]y=\frac{a}{(9+3x)}[/tex]

Step-by-step explanation:

we have

[tex]a=9y+3yx[/tex]

Solve for y

That means -----> isolate the variable y

Step 1

Factor the variable y in the right side

[tex]a=y(9+3x)[/tex]

Step 2

Divide by [tex](9+3x)[/tex] both sides

[tex]a/(9+3x)=y(9+3x)/(9+3x)[/tex]

Step 3

Simplify

[tex]y=\frac{a}{(9+3x)}[/tex]

The speed of Mercury around the Sun in kilometers/second is 48 kilometers/second.

In 2  seconds, Mercury will travel 96 kilometers.

The speed of an object is the ratio of the distance travelled by the object to the time taken by the object to travel that distance.

Given, the speed of Mercury around the Sun is 30 miles/second.

Therefore, the speed of Mercury around the Sun in kilometers/second

= (30 × 1.6) kilometers/second

= 48 kilometers/second

Now, in 2  seconds, Mercury will travel

= 48 × 2 kilometers

= 96 kilometers

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