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I don't understand how to work out this question.

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

[tex]\int p(t)dt = \int\frac{1}{400}dt[/tex][tex]\int p(t)dt = \frac{1}{400}t[/tex]

[tex]\mu=e^{\int p(t)dt}[/tex]

[tex]\mu=e^{\frac{t}{400}}[/tex]

So, S(t) = [tex]\frac{\int\mu q(t)dt+C}{\mu}[/tex]

S(t) = [tex]\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)[/tex]

Now solving the bracket

S(t) = 4000 + [tex]e^{\frac{-t}{400}}[/tex]C.....(1)

At S(0) = 100

100 = 4000 + [tex]e^{\frac{-0}{400}}[/tex] C

100 = 4000 + [tex]e^{0}[/tex] C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Used the distributive property a(b+c)=ab+ac, the value of x is x>1/2

Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Curran:

-4(x-6)< 22

Used the distributive property a(b+c)=ab+ac

-4x+24<22

Then subtracted 24 from bot the sides

-4x<22-24

-4x< -2

Divide both sides by -4 ( inequality changes because of dividing by negative number)

x>1/2

Anjani:

-4(x-6)< 22

Divide both sides by -4

x-6> -22/4

add 6 on both sides

x> -22/4 + 6

x> -11/2 + 6

x> 1/2

Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.

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A. We can see that the intersection made by lines C and D classifies ∠7 and ∠8 as vertically opposite angles.

B. The special angles created by intersection of lines C and D can be used to solve for y by equating the expressions, 5y-29 and  3y+19 as they are vertically opposite angles.

C. Solving for y, we have: y = -5

Intersection, in mathematics, refers to the common elements or overlap between two sets. For example, if set A contains the elements 1, 2, and 3, and set B contains the elements 2, 3, and 4, then the intersection of set A and set B would be the set containing the element 2 and 3. In general, intersection is represented by the symbol ∩. Lines can also intersect to form angles.

Vertically opposite angles are actually known to be equal. It then means that:

∠7 = ∠8 (Vertically opposite angles)

Also, 5y-29 = 3y+19 (Vertically opposite angles)

Thus, solving for y, we have:

5y-29 = 3y+19

5y - 29 -29 = 3y + 19 - 29

5y -3y = - 10

2y = -10

y = -10/2 = -5

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The measurement of indicated angle is 20 degree.

Here opposite angles are congruent .

Therefore the indicated angle is 20 degree.

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The number of days before she mows the lawn and washes her window on the same day is 60 days.

The day she would mow the lawn and wash her window on the same day would be the least common multiple of 12 and 20.

A multiple of a number is the product of an integer and that number. A common multiple is a multiple that two or more numbers share. The least common multiple is the smallest multiple that two or more numbers share.

Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 120

Multiple of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200

Least common multiple = 60

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The person being called is a function of the phone number, as for each phone number, there is only one person associated with the number.

A relation represents a function when each input value is mapped to a single output value.

The input and output variables for this problem are given as follows:

Each phone number is mapped to a single person, meaning that the relation is in fact a function.

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Answer:

9

Step-by-step explanation:

9x9=81

Answer:

Step-by-step explanation:

So the rectangle is 9 units wide.

becuase given that the area of the rectangle is 81m'n' square units and the length of the rectangle is 9mn', we can set up the equation as:

81 = 9 x width

To solve for width, we can divide both sides of the equation by 9:

width = 81/9

width = 9

Answer:

Step-by-step explanation:

35

Answer:

is try ur hardest

Step-by-step explanation:

Based on the information, it can be concluded Isabella bought  2 paintbrushes and 3 jars of paint.

The average of buying a product is 0.97, which means Isabella can buy a total of 5 items (0.97 x 5 = 4.85)

Based on this different combinations of products are possible, for example, 1 paintbrush and 4 jars or 3 jars and 2 paintbrushes. However, the one that fits the final price is:

2 paintbrushes x 0.95 = $1.9

3 jars of paint x 0.99 = $2.97

$2.97 + 1.9 = $4.87

Note: This question is incomplete, here is the missing information

The paintbrushes cost $0.95 and the jar of paint cost $.099

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Answer:

cotθ=√21/2

Step-by-step explanation:

we have,

sinθ= 2/5= perpendicular/hypotenuse

here,

perpendicular=2

hypotenuse = 5

Now using Pythagorean theorem,

h^2 = p^2+ b^2

(5)^2 = 2^2 +b^2

b= √21

so,

cotθ= base/perpendicular = √21 /2

Hope you like the explanation.

Marlon's height is 42.52 inches.

Since the heights of four-year-old's are normally distributed with a mean of 40 inches and a standard deviation of 3 inches, we can use the z-score formula to find Marlon's height.

z = (x - mean) / standard deviation

where x is Marlon's height, mean is the population mean of 40 inches, and standard deviation is the population standard deviation of 3 inches.

We know that Marlon's height is taller than 70% of boys his age, so we can find his z-score using the cumulative standard normal distribution table, which tells us the proportion of the population that is less than a given value.

A z-score of 0.84 corresponds to a cumulative probability of 0.70.

So we can substitute this value into the z-score formula:

0.84 = (x - 40) / 3

Solving for x, we get:

x = 40 + (3 * 0.84) = 40 + 2.52 = 42.52 inches

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The side length of AC is 6 units for the shown triangle. The correct answer would be an option (C).

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The right triangle is given in the question, as shown.

AD = 4 cm and BD = 5

In ΔACD and ΔABC

∠ACD = ∠ABC

∠ACD = ∠BAC = 90°

∠CAD = ∠ACD (remaining)

So ΔACD and ΔABC are similar

Hence

AD / AC = AC/ BC

Apply the cross-multiplication operation, and we get

AC² = AD × BC

AC² = 4 × 9

AC² = 36

AC = 6 cm

So, the side length of AC is 6 units.

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Answer: We can start by using algebra to represent the given information. Let's call the number we're trying to find "x".

We know that:

quotient = (3x)/5

quotient + 4 <= 34

We can simplify the first equation:

(3x)/5 + 4 <= 34

We can then solve this inequality for x:

(3x)/5 + 4 <= 34

3x/5 <= 30

3x <= 150

x <= 50

So the quotient of three times a number and five is no more than 34 if that number is less than or equal to 50.

Step-by-step explanation:

The time taken by the submarine to make the descent when the equation of descent is given is 0.677 hours.

Submarine's descent can be represented by the equation, y = -3100 x

where,  

y is elevation

x is time in hours

We need to determine how long it will take this submarine to travel 2,100 feet below the surface of the ocean.

Since the submarine to make the descent to the seafloor 2,100 feet below the surface

So, y = - 2100

y = - 3100x gives

- 2100 = - -3100 x

Divide both sides by -3100,

x = 2100/3100 = 0.677 hours

As a result, the submarine will need 0.677 hours to complete the descent.

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Answer: i think y =  x + 5

Step-by-step explanation:

Answer: -15x - 9

Step-by-step explanation:

(2x ×2 −6x−5)+(−9x ×2 +5x−4)

(4x-6x-5)+(-18x+5x-4)

(-2x-5)+(-13x-4)

-2x-5-13x-4

-15x -

The value of the given equation is −7x2−x−9.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The equation (2x 2 −6x−5)+(−9x 2 +5x−4)

Now,

We need to add the two polynomials by combining like terms. Like terms are terms that have the same variable and exponent. For example, 2x2 and −9x2 are like terms because they both have x2

To add like terms, we just add their coefficients. For example, 2x2+(−9x2)=(−7x2)

We can apply this rule to each pair of like terms in the problem and get:

(2x2−6x−5)+(−9x2+5x−4)

=(2x2+(−9x2))+(−6x+5x)+(−5+(−4))

=(−7x2)+(−x)+(−9)

=−7x2−x−9

Therefore, by algebra the answer will be −7x2−x−9.

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The triangle types is impossible to draw is

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.

Given:

First, a scalene with right-angled triangle is possible to make.

Now, an isosceles with acute-angled triangle is possible to make such triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement.

Now, an isosceles with obtuse-angled triangle is not possible to make because if two angles are greater than 90 then sum of angles exceed 180.

and, an equilateral with right-angled triangle is not possible to make because in Equilateral triangle are angles are of equal measurement 60.

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People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

Pi, which is represented by the Greek letter π, is an irrational number that starts with 3.14 and continues for an infinite amount of digits. The numerical value of pi is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.1415926535897932384626433832795. The date and time of March 14th, 1:59 is a way to represent the first four digits of pi (3.14). People celebrate Pi Day by eating pie, making pi-related crafts, and sharing facts about pi. People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

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Answer:

I think 9/10 but I am not sure

The simplification of the given expression after addition would be = 163.241.

Addition is the combination of two or more given values and it's one of the major arithmetic operations in mathematics.

The given expression is a s follows;

127.98+35.261 = 163.241

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The lateral area for the prism is equal to 54 square inches. (Correct choice: B)

Herein we have the case of a prism with five faces, two triangles and three rectangles. The lateral area for the prism is the sume of the areas of the three rectangular faces, whose formula is described below:

Rectangle

A = w · l

Where:

Finally, we proceed to determine the lateral area of the prism:

A = 3 · (3 in) · (6 in)

A = 54 in²

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An artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.  

Now, According to the question:

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Here, we have

FH ≅ GH

FH = EG = 28in

If diagonals bisect each other then, an artist connects stained glass pieces with lead strips

1/2(EG) = JG

1/2 (28) = JG

14 = JG

Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.  

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When it's a quarter full, the shipping container holds a volume of 350 cubic feet.

Bassically, we want to find one quarter (1/4) of the volume of the rectangular prims.

The dimensions are 20ft by 8ft by (8ft + 9in)

Let's rewrite that last part only using feet.

Remember that 12 in = 1ft

Then:

9 in = (9/12)ft = 0.75 ft

Then we can rewrite the dimensions as:

20ft by 8ft by 8.75 ft

The volume is the product between these numbers, and we want one fourt of the volume, so we need to find:

V = (1/4)*(20ft)*(8 ft)*(8 .75 ft) = 350ft³

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The surface area of the pyramid is 5,685 ft².

To find the surface area of the pyramid, we need to find the area of the base and the area of the four triangular faces. Since the base is a rectangle, we can find its area by multiplying the length and width:

length, l = 25 ft

width,w = 22 ft

Area = l x w

Area = 25 ft x 22 ft

Area = 550 ft².

To find the area of each triangular face, we first need to find the slant height of the pyramid, which can be found by using the Pythagorean theorem on the net dimensions. The slant height is the square root of

Net dimensions of the pyramid:

length, l = 74.8 ft

width, w = 70.4 ft

h = [tex]\sqrt{l ^{2} +w^{2} }[/tex]

h = [tex]\sqrt{(74.8^{2} + 70.4^{2} ) }[/tex]

h = 102.7 ft.

Now, we can use the formula for the area of a triangle:

Area = (1/2) x base x height,

where,

base,b = the length of the rectangular base (25 ft)

height = the slant height (102.7  ft).

So, the area of each triangular face is:

A = (1/2) x 25 ft x 102.7  ft

A = 1283.75 ft².

Since there are four triangular faces, the total area of all the triangular faces is:

A= 4 x 1283.75 ft²

A = 5,135 ft².

To find the surface area of the pyramid, we add the area of the base to the area of the triangular faces:

SA= 550 ft² +  5,135 ft² = 5,685 ft².

Hence, the surface area of the pyramid is 5,685 ft².

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The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.

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Answer:

A ratio in words compares a whole to a part. For example, the ratio of apples to oranges in a basket is "three to one." This can also be written as "3:1" or "3/1."

Another example: is the ratio of students to teachers in a class is "twenty to one." This can also be written as "20:1" or "20/1."

Step-by-step explanation: