a tank with a capacity of 400 l is full of a mixture of water and chlorine with a concentration of 0.05 g of chlorine per liter. in order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 4 lys. the mixture is kept stirred and is pumped out at a rate of 10 lys. find the amount of chlorine in the tank as a function of time.

Answer:

a = b - 2

Step-by-step explanation:

1) Subtract 2 from both sides.

a = b - 2

Thanks.

- Eddie

Answer:

Below

Step-by-step explanation:

a+2 = b        Solve for a :   subtract 2 from both sides of the equation

a = b-2      Done !

Answer:

700 cubic feet

Explanation:

The pool is to be filled with water until it is 1 1/2 feet from the top of the pool. Therefore, the height of the water in the pool is:

Therefore, the number of cubic feet of water it takes to fill the pool is the volume of water in the pool.

It takes 700 cubic feet of water to fill the pool.

Answer:

The point that lies in the solution set to the following system of inequalities is (1,10).

To check, substitute the values of x and y into each inequality:

ys > x-5

y < x+4

For the point (1,10):

10 > 1-5 is true (10 > -4)

10 < 1+4 is true (10 < 5)

Therefore, (1,10) satisfies both inequalities and lies in the solution set. The other three points do not satisfy at least one of the inequalities, and thus do not lie in the solution set.

Step-by-step explanation:

Step-by-step explanation:

Let A = {1, 2, 3}, B = {3, 4, 5}, and U = {1, 2, 3, 4, 5}.

a) We have:

(A∪B)′ = {1, 2, 4, 5} (taking the complement of the union of A and B)

A′∩B′ = {4, 5} (taking the intersection of the complements of A and B)

We can verify that (A∪B)′ = A′∩B′ by showing that both sets contain exactly the same elements, which they do in this case.

Another example: Let A = {a, b, c}, B = {c, d, e}, and U = {a, b, c, d, e}.

Then:

(A∪B)′ = {d, e}

A′∩B′ = {d, e}

Again, we can see that both sets contain exactly the same elements, so (A∪B)′ = A′∩B′ is true.

To prove this using Venn diagrams, we can draw a Venn diagram for the sets A, B, and (A∪B)′, and shade the region that represents the complement of the union of A and B. We can also draw a Venn diagram for A′, B′, and their intersection, and shade the region that represents this intersection. Then we can visually compare the two shaded regions to see that they are the same.

b) We have:

(A∩B)′ = {1, 2, 4, 5} (taking the complement of the intersection of A and B)

A′∪B′ = {1, 2, 4, 5} (taking the union of the complements of A and B)

We can see that (A∩B)′ = A′∪B′ in this case.

Another example: Let A = {a, b, c}, B = {c, d, e}, and U = {a, b, c, d, e}.

Then:

(A∩B)′ = {a, b, d, e}

A′∪B′ = {a, b, d, e}

Again, we can see that both sets contain exactly the same elements, so (A∩B)′ = A′∪B′ is true.

To prove this using Venn diagrams, we can draw a Venn diagram for the sets A, B, and their intersection, and shade the region that represents this intersection. We can also draw a Venn diagram for A′, B′, and their union, and shade the region that represents this union. Then we can visually compare the two shaded regions to see that they are the same.

The account balance after eleven years would be ₱14,925.08. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08. total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.

The account balance after eleven years would be ₱14,925.08.

1. Calculate the compounded interest rate: 5% per year compounded semi-annually = 2.5% per semi-annual period.

2. Calculate the total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.

3. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08.

The account balance after eleven years would be ₱14,925.08.

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a)  the solution to the simultaneous equations is x = 2 and y = 7.

b i) The value of y in each equation is 7.

ii) The value of y, which is 7, is the same for both equations. This means that the solution (x = 2, y = 7) satisfies both equations and is consistent across both equations.

a) To solve the simultaneous equations y = 2x + 3 and y = -x + 9, we can set them equal to each other:

2x + 3 = -x + 9

Adding x to both sides:

3x + 3 = 9

Subtracting 3 from both sides:

3x = 6

Dividing by 3:

x = 2

Now that we have the value of x, we can substitute it back into either equation to find the corresponding value of y. Let's use the first equation:

y = 2(2) + 3

y = 4 + 3

y = 7

Therefore, the solution to the simultaneous equations is x = 2 and y = 7.

b) Substituting the value of x = 2 into each equation:

For the equation y = 2x + 3:

y = 2(2) + 3

y = 4 + 3

y = 7

For the equation y = -x + 9:

y = -(2) + 9

y = -2 + 9

y = 7

i) The value of y in each equation is 7.

ii) The value of y, which is 7, is the same for both equations. This means that the solution (x = 2, y = 7) satisfies both equations and is consistent across both equations.

In summary, when solving the simultaneous equations, we find that x = 2 and y = 7. When substituting this solution back into the original equations, we notice that the value of y is the same (7) in each equation. This confirms the consistency of the solution.

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A brute-force approach to evaluate a polynomial of degree n involves directly substituting x into each term. The time complexity is O(n), increasing linearly with the degree.

A brute-force approach to evaluating a polynomial p(x) of degree n involves substituting the value of x into each term of the polynomial and summing them to obtain the final result. This method calculates the polynomial value directly based on its definition, without using any optimization techniques.

The time complexity of this approach is O(n), where n is the degree of the polynomial. Since we need to evaluate each term individually, the number of operations increases linearly with the degree of the polynomial. As a result, the time complexity grows proportionally with the degree of the polynomial.

For example, if the polynomial is of degree 3, evaluating p(x) using the brute-force approach requires three multiplications and two additions. Similarly, for a polynomial of degree 5, it would require five multiplications and four additions. Thus, the time complexity increases linearly with the degree of the polynomial.

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The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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The isosceles triangle of the maximum area is also an equilateral triangle.

Given, an isosceles triangle ABC is inscribed in a circle with center D and radius r.

We can obtain the side a in function of r and α by applying Law of Sines to triangle BCD,

a/sin(2α) = r/sin β

Since, 2α + β + β = 180°

2α + 2β = 180°

α + β = 90°

β = 90° - α

a = r(sin 2α/sin(90°-α))

a = r(2 sinα cosα)/cosα

a = 2r sinα

a = 4r sin(α/2) cos(α/2)

We can obtain the height h in function of r and α,

tan(α/2) = (a/2)/h

h = a/2tan(α/2)

Replacing with the value of a,

h = [4r sin(α/2) cos(α/2)/2][cos(α/2)/sin(α/2)]

h = 2r cos2(α/2)

Now, find the area of the triangle in function of a and r,

Area, A = (base)(height)/2

A = [4r sin(α/2) cos(α/2)][2r cos2(α/2)]/2

A = 4r2sin(α/2) cos3(α/2)

Now, take the derivative to find the maximum or minimum of the area of the triangle.

dA/dα = [4r2cos(α/2)(1/2)cos3(α/2)] + [4r2sin(α/2) 3cos2(α/2)(-sin(α/2))(1/2)]

On simplification,

= [2r2cos4(α/2)] - 6r2sin2(α/2) cos2(α/2)

Taking out common terms,

= 2r2cos2(α/2)[cos2(α/2) - 3sin2(α/2)]

Equating the derivative to zero, we get

2r2cos2(α/2)[cos2(α/2) - 3sin2(α/2)] = 0

2r2cos2(α/2) = 0

cos2(α/2) = 0

Thus, α/2 = 90°

α = 180°

Also, cos2(α/2) - 3sin2(α/2) = 0

cos2(α/2) = 3sin2(α/2)

[sin2(α/2)/cos2(α/2)] = 1/3

tan2(α/2) = 1/3

tan(α/2) = 1/√3

So, α/2 = 30°

α = 60°

This implies that ∠B = ∠C = 60°

Thus, the isosceles triangle of the maximum area that can be inscribed in a circle of radius r. is also an equilateral triangle.

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The option is B. Emerson is painting the outside of a cube for a math project. he knows the area of each face is 145 square inches.

the place is the quantity that expresses the quantity of vicinity on the plane or on a curved floor. The area of a plane vicinity or aircraft location refers to the area of a shape or planar lamina, while surface location refers to the region of an open floor or the boundary of a three-dimensional object. the place can be understood as the quantity of material with a given thickness that might be necessary to fashion a model of the shape, or the amount of paint essential to cowl the surface with a single coat. it's by far the 2-dimensional analog of the period of a curve (a one-dimensional concept) or the volume of a stable (a three-dimensional idea).

The region of a form can be measured by using comparing the form to squares of a set size. within the global system of devices (SI), the standard unit of the region is the rectangular meter (written as m²), which is the place of a rectangular whose aspects are one meter long. A shape with an area of 3 square meters might have an equal area to 3 such squares. In mathematics, the unit square is defined to have area one, and the place of some other form or floor is a dimensionless real number.

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Answer:

5 days

Step-by-step explanation:

15 servings per box / 3 servings per day = 5 days

Answer:

5 Days

Step-by-step explanation:

15 servings / 3 serving = 5

The magnification n can be found by using the formula n = -s'/s, where s' is the image distance and s is the object distance. The value of s' obtained from this new equation can be found by rearranging the formula to s' = -ns.

To find the magnification n, we can use the formula n = -s'/s, where s' is the image distance and s is the object distance. In this case, the object is placed 45.0 centimeters from the mirror, so s = 45.0 cm. The magnification can be found by calculating the ratio of the image distance to the object distance. By rearranging the formula, we get n = -s'/s.

To find the value of s' obtained from this new equation, we can rearrange the formula n = -s'/s to solve for s'. This gives us s' = -ns. By substituting the value of n calculated earlier, we can find the value of s'. The negative sign indicates that the image is inverted.

Using the given values, we can now calculate the magnification and the value of s'. Plugging in s = 45.0 cm, we find that s' = -ns = -(2/3)(45.0 cm) = -30.0 cm. This means that the image is located 30.0 centimeters from the mirror and is inverted compared to the object.

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Answer:

56/19

Step-by-step explanation:

I'll approach this using Substitution. Since 3X = 2Y, we know that 1.5X = 1Y. We can plug that into the first equation, which gives us...

2X + 5(1.5X) = 8

2X + 7.5X = 8

9.5X = 8

19X = 16

X = 16/19

While this is not 'pretty', it does match up with how most of the answers are written (four of the answers involve "nineteenths"). With this value of X, we can solve for Y...

3X = 2Y

3(16/19) = 2Y

48/19 = 2Y

24/19 = Y

With the value of X and the value of Y, we can answer the question that's asked:

2X + Y = ?

2(16/19) + 24/19 =

32/19 + 24/19 =

56/19

Final Answer: 56/19

Answer:

\(x = - 1\)

\(y = - 2\)

Step-by-step explanation:

\(3x + 2y = - 7\)

\(2x - 5y = 8\)

Apply elimination method. Let multiply the bottom equation by -3/2.

\(2 \times - \frac{3}{2} x = - 3\)

\( - 5 \times - \frac{3}{2} = 7.5\)

\(8 \times - \frac{3}{2} = - 12\)

Substitute new equation and add it to the top equation

\(3x + 2y = - 7\)

\( - 3x + 7.5y = - 12\)

\(9.5y = - 19\)

\(y = - 2\)

Now plug -2 for y into any equation and solve for x.

\(3x + 2( - 2) = - 7\)

\(3x - 4 = - 7\)

\(3x = - 3\)

\(x = - 1\)

Answer:

B

Step-by-step explanation:

x=4 so

2x4=8

8+5=13

Carlos's sister is 4 years old, therefore it is B.

Answer:

B

Step-by-step explanation:

Answer:

$25

Step-by-step explanation:

First you would add 27 and 9 to find the total number of games he sold, next you would divide 900 by 36 to get 25, then you would do 25 times 36 to check your answer.

Answer:

$41.00

Step-by-step explanation:

because you do the 27 and 9 add that to get 922 then divide that with 900 then you will get either 40 or 41 dollars. hope this helpss!!!:)

Answer:

Step-by-step explanation:

From ohms law the expression for voltage is given as

\(V= IR\)

Now given that

Voltage, V= \(2.4*10^3\) volts

Resistance R= \(2*10^6\) ohms

Applying ohms law the current can be calculated by making I the subject of formula

that is I= V/R

\(I= \frac{2.4*10^3}{2*10^6} \\\\I= \frac{2.4}{2} *10^(^3^-^6^)\\\\I=1.2*10^-^3\)

The current in amps is 1.2 milli amps

Answer:

2=2

Step-by-step explanation:

Answer:

y=2x +1 is already the equation,

but 2 is the slope and 1 is the y intercept

1. The amount of petrol L left is car engine is given by V=36-3t , then number of days required to empty the car engine is equal to 12 days.

2. From the graph ,

a. $8 Australian dollars equal to 10 British pounds and

b. 15 British pounds are equal to $12 Australian dollars.

As given in the question,

1.

Amount of petrol L left is car engine is given by V=36-3t

V  represents the amount of petrol in L and t represents the time number of days.

When car engine get empty amount of petrol V = 0

Therefore,

V= 36 -3t

⇒ 0 = 36 -3t

⇒ 3t = 36

⇒ t= 36 /3

⇒ t= 12 days

2.

From the given graph of Australian dollars and British pounds it is observed that :

a. $8 Australian dollars equal to 10 British pounds and

b. 15 British pounds are equal to $12 Australian dollars.

Therefore,

1. The amount of petrol L left is car engine is given by V=36-3t , then number of days required to empty the car engine is equal to 12 days.

2. From the graph ,

a. $8 Australian dollars equal to 10 British pounds and

b. 15 British pounds are equal to $12 Australian dollars.

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If the account earns 6.5% simple interest per year , Diego will give his granddaughter a sum of $1130

To calculate the simple interest earned on an initial amount of $500 at 6.5% for 18 years, you can use the formula:

$I = Prt$, where

$I$ = interest earned

$P$ = initial amount ($500)

$r$ = interest rate (6.5%)

$t$ = time in years (18)

So, $I = 500 * 6.5 * 18 / 100 = 630$.

Thus, on the granddaughter's 18th birthday, Diego will give her $500 + 630 = $1130.

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a) The actual distance between towns K and L is: 100 km

b) As shown in the attached file

c) The bearing of town L from town K is 117 degrees.

The scale of the map is given as:

1 cm to represent 50 km

Now, when we measure the distance between K and L on the map, we see that it gives us a distance of 2 cm.

Using the scale of 1 cm: 50 km, we can say that:

Actual distance between towns K and L = (2 * 50)/1 = 100 km

b) Using a compass and it’s 3cm aiming down {South} as seen in the attached photo. Then a line was drawn aiming {South} with a ruler. On the end of the line the (x) point was put there to get the mark.

c) Measuring the angle gives the bearing of town L from town K which is 117 degrees.

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Answer:

Step-by-step explanation:

The given points (6,4), (12,6), and (16,-6) do not form the vertices of a right triangle.

To determine if the given points form a right triangle, we can calculate the distances between the points and check if the squares of the distances satisfy the Pythagorean theorem. Let's calculate the distances between the points:

Distance between (6,4) and (12,6):

d₁ = √((12-6)² + (6-4)²) = √(36 + 4) = √40 ≈ 6.32

Distance between (12,6) and (16,-6):

d₂ = √((16-12)² + (-6-6)²) = √(16 + 144) = √160 ≈ 12.65

Distance between (16,-6) and (6,4):

d₃ = √((6-16)² + (4-(-6))²) = √((-10)² + (4+6)²) = √(100 + 100) = √200 ≈ 14.14

According to the Pythagorean theorem, if the points form a right triangle, then one of the distances squared should be equal to the sum of the squares of the other two distances. However, in this case, d₁² + d₂² ≠ d₃², d₁² + d₃² ≠ d₂², and d₂² + d₃² ≠ d₁². Therefore, the given points (6,4), (12,6), and (16,-6) do not form the vertices of a right triangle.

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Answer:

First picture - 20.42 m

Second picture - 12.9 m

Step-by-step explanation:

------------------------------------------------------------------------------------------------------------

Formula for pyramid:

\(V=b^2\frac{h}3\)

Where,

b = base - 3.5 m

h = height - 5 m

Thus,

\(V=3.5^2\frac{5}{3}\)

\(20.41667m^3\) ≈ \(20.42m^3\)

------------------------------------------------------------------------------------------------------------

Formula for pyramid:

\(V=b^2\frac{h}3\)

Where,

b = base - 3 m

h = height - 4.3 m

Thus,

\(V = 3^2\frac{4.3}{3}\)

\(12.9m^3\)

------------------------------------------------------------------------------------------------------------

Kavinsky

The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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Answer:

t=-3.7

Step-by-step explanation:

5 (t+3)=-3.5

solving the bracket we have;

5t+15=-3.5

collect like terms

5t=-3.5-15

5t=-18.5

divide both sides by 5;

t=-3.7

The value of t in the given algebraic expression is; t = -2.3

We are given the equation;

5(t + 3) = 3.5

Using distributive property on the left hand side, we have;

5t + (5 × 3) = 3.5

5t + 15 = 3.5

Using subtractive property of equality, subtract 15 from both sides to get;

5t + 15 - 15 = 3.5 - 15

5t = -11.5

Divide both sides by 5 to get;

5t/5 = -11.5/5

t = -2.3

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Each T shirt costs $21.

Since Martha takes her niece and nephew to a concert, and she buys T-shirts and bumper stickers for them, and the bumper stickers cost $ 1 each, and Martha's niece wants 1 shirt and 4 bumper stickers, and her nephew wants 2 shirts but no bumper stickers, to determine, if Martha's total is $ 67, what is the cost of one shirt, the following calculation must be performed, posing linear equations:

Therefore, each T shirt costs $21.

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ANSWER

0.667

EXPLANATION

We want to convert the rational number given to decimal number.

To do this, we divide the numerator by the denominator.

That is:

That is the answer, approximated to the nearest thousandth.

Answer:

63

Step-by-step explanation:

Answer:

A = 210 cm²

Step-by-step explanation:

Perimeter of the triangle = the sum of the sides of the triangle.

70 = (3x - 1) + (4x + 1) + (3x)

70 = 10x  

7 = x     The length of the sides of the triangle are 3x - 1 = 20;  4x + 1 = 29 and                

             3x = 21.

 Looking at the given information, this triangle is a special type of triangle because the area of a triangle is Area = 1/2 bh and you do not know which side is the base and height of the triangle.

Trying a² + b² = c² to see if it is a right triangle.   20² + 21² = 29 ² ; yes it is a right triangle and now we know that the base and height is 20 and 21.   The longest side is the hypotenuse in a right triangle

A = 1/2bh

A = 1/2 (20)(21)

A = 10 · 21

A = 210 cm²