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After 30 minutes, the amount of salt remaining in the tank is 18.75 kg. This is because the brine entering the tank contains 0.03 kg of salt per liter of water, and 25 liters of brine are entering the tank every minute.

Thus, in 30 minutes, 750 liters of brine will have entered the tank, bringing with it 22.5 kg of salt. Since the tank initially contained 20 kg of salt, the amount of salt remaining after 30 minutes is 18.75 kg.

The theory behind the amount of salt remaining in the tank after a given amount of time is based on the idea that the amount of salt entering the tank is equal to the amount of salt leaving the tank. The amount of salt entering the tank is determined by the concentration of salt in the brine solution and the rate at which the brine enters the tank. The amount of salt leaving the tank is determined by the same rate at which the brine enters the tank.

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Answer:

see explanation

Step-by-step explanation:

3

(f + g)(x)

= f(x) + g(x)

= 2x² - 4x - 5 + 3x - 13 ← collect like terms

= 2x² - x - 18

4

(f - g)(x)

= f(x) - g(x)

= 2x² - 4x - 5 - (3x - 13) ← distribute parenthesis by - 1

= 2x² - 4x - 5 - 3x + 13 ← collect like terms

= 2x² - 7x + 8

If number of cases of a disease is reduced by 7% every year and there are initially 10000 cases, then "y" as a function of "t" is expressed as  y=10000×(1 - 0.07[tex])^{t}[/tex]  .

the number of cases of a disease is reduced = 7% per year,

so , the rate of change can be expressed as a negative 7%.

The function "y" ,which represents number of cases of disease after "t" years, can be expressed as:

⇒ y = 10000×(1 - 0.07[tex])^{t}[/tex]  ;

where ; t = number of years elapsed and

⇒ (1 - 0.07) represents the factor by which number of cases decreases each year.

This equation gives the number of cases of the disease after "t" years, assuming that the 7% reduction rate remains constant over time.

The given question is incomplete , the complete question is

Suppose , the number of cases of a disease, is reduced by 7% per year ,  if there are initially 10,000 cases, express "y" as a function of "t" , the number of years elapsed ?

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Answer:

SAS because you have two congruent sides surrounding one congruent angle

Answer:

5

Step-by-step explanation:

Hope it helps! =D

The equivalent value of sin{D} is -

sin{D} = √13/10.

Given is a right angled triangle.

In the given right angle triangle, we can use the Pythagoras theorem as -

{FD}² = {√13}² + {√87}²

{FD}² = 13 + 87

{FD}² = 100

FD = 10

So, we can write that -

sin{D} = √13/10

Therefore, the equivalent value of sin{D} is -

sin{D} = √13/10.

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The approximate surface area of a cone is 204 inches².

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

We have,

The surface area of a cone is πr (r + √(h² + r²) )

Now,

Diameter = 10 inches

Radius = 5 inches

Slant height = 8 inches

Now,

The surface area of a cone is πr (r + √(h² + r²) )

Slant height = √(h² + r²) = 8 inches

So,

= πr (r + √(h² + r²) )

= π x 5 (5 + 8)

= 3.14 x 5 x 13

= 204 inches²

Thus,

The surface area of a cone is 204 inches².

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The approximate surface area of the cone is 227 square inches.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The diameter of a cone's circular base measures 10 inches

Radius of cone is 5 inches.

Slant height = 8 inches

A=πr(r+√h²+r²)

A=3.14×5(5+√64+25)

A=3.14×5(5+√89)

A=3.14×5(5+9.43)

A=3.14×5(14.43)

A=226.61

Hence, the approximate surface area of the cone is 227 square inches.

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The general solution of the given differential equation is y = sin x + c. cos x

What is Equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

cos (x) dy/dx +sin (x) y =1

now, divide with cos x on both the sides

cos(x)/cos x dy/dx + sinx.y/cos x = 1/cos x

dy /dx + sinx/cosx .y = 1/cos x

= dy/dx +tanxy =secx

the above equation is linear differentiation equation in y

so, now integrating factor

IF= secx

now the solution is

y secx = (secx .secxdx+c)

y secx = (sec[tex]x^{2}[/tex]dx+c)

= y* secx = tanx+c

y = 1/secx(tanx+c)

y = cos x (tanx+c)

we know that, tanx = sinx/cosx

y = cosx(sinx/cosx +c)

y = cos x .sinx/cosx +cosx (c)

Solution of the given differential equation y = sin x + c. cos x

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South Carolina can produce 26x26x10x10x10 = 676,000 different license plates with the configuration digit, letter, digit, letter, digit, digit.

Permutations are arrangements of objects in a specific order. For example, if you have the letters A, B, and C, the possible permutations are ABC, ACB, BAC, BCA, CAB, and CBA. Permutations are often used to calculate the total number of possible combinations for a given set of objects, as each permutation is a unique combination. For example, if you have three letters and three digits, the total number of permutations is 26x10x10x26x26x10 = 17576000.

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The number of hours worked multiplied by the hourly wage of an employee is how gross wages for hourly workers are determined is 318.8

Employees' gross pay is their salary before any payroll deductions such as taxes, benefits, and other expenses are made. Net pay, often known as take-home pay, is the amount that is left over once all withholdings have been taken into account.

Here,

Given :

=> 290

=> interest = 3% of 500

=> 960 * 3/100 =  28.8

=> 28.8 + 290 = 318.8

The total amount of money a person makes each year, whether they work or invest, is their gross income. In the case of a self-employed person, earned income is restricted to salaries, commissions, bonuses, and business income after deducting expenses.

The total of your earnings at a certain employment before deductions is your gross salary. Before any deductions from your pay are made, this is often listed at the top of your pay slip.

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The measure of the angle JKH is 19 degrees

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

m/LJK= 38° and m/KLJ= 71°.

Start by calculating the external angle of  JKL

So, we have

External = LJK + KLJ

External = 38 + 71

External = 109

The measure of angle JKH is then calculated using:

JKH + 90 = External

This gives

JKH + 90 = 109

Evaluatet the like terms

JKH = 19

Hence, the angle has a value of 19 degrees

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Answer:

y = 12

Step-by-step explanation:

I believe that you can use the geometric mean theorem to solve for y

y is the geometric mean of the segments of the hypotenuse, so

24/y = y/6

simplify using means and extremes property: y^2 = 144

simplify: y=12

Answer: C; $5 for 40 ounces

Step-by-step explanation: To find the lowest cereal amounts, we need to find the unit price. To find the unit price, you ALWAYS divide the price by the amount. In this case, we need to divide the money by the ounces. So, the prices for each (in cents) are:

[tex]\frac{3.20}{20} = 0.16[/tex]

[tex]\frac{4.50}{25} = 0.18[/tex]

[tex]\frac{5}{40}[/tex] ≈ 0.13 (0.125)

So, the decimals are the prices (in cents) and the last one was 0.125, but we need to round up to the nearest cent. This would be $0.13. This makes the 40 ounces of cereal for $5 the cheapest of the 3 deals. I hope this helped!

Answer:

1/6

Step-by-step explanation:

1-1/2 = 1/2

night = x

1/2 - x = 1/3

3/6 - x = 2/6

so x = 1/6

Answer: if your account has more liquidity

Answer:

О  B.  more

Step-by-step explanation:

You can access your funds easier if ypur account has more liquidity.

...

The measure of∠SAU = 92°,

SV  = 22, ∠SBV = 18°.

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is that the sum of its internal angles to 180 degrees. This quality is referred to as the angle sum property of triangles.

Given  a triangle ABC

and AV, BV, and CV are angle bisectors,

TV = 22 and CV = 27

∠TCU = 52°, ∠SAV = 46°

A: to find ∠SAU,

as we know angle bisector divides an angle into two equal parts,

so ∠SAV = ∠VAU = 46°

∠SAU = ∠SAV + ∠VAU

∠SAU =  46 + 46 = 92°

B: to find ∠SBV,

we have ∠SAU =  92° and ∠TCU = 52°

from angle sum property,

∠SAU + ∠TCU +  ∠SBT = 180°

∠SBT + 92 + 52 = 180

∠SBT = 180 - 92 - 52

∠SBT = 36°

so  ∠SBV = ∠BVT = ∠SBT/2 (due to angle bisector)

∠SBV = ∠BVT = 36/2

∠SBV = ∠BVT = 18°

C: to find SV,

since V is the incenter, Due to the junction point of the central axis being the center of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides.

so TV = UV = SV  = 22

Hence ∠SAU = 92°,

SV  = 22,

∠SBV = 18°

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The probability that airline b detected it will be 0.22.

The probability that airline B detected the weapon can be calculated using Bayes' Theorem, which states that:

P(airline B detected the weapon | weapon detected) = P(weapon detected | airline B detected the weapon) * P(airline B) / P(weapon detected)

where P(airline B) is the prior probability that a passenger was serviced by airline B (30%) and P(weapon detected) is the total probability that a weapon was detected (sum of the probabilities that a weapon was detected by each airline).

The numerator can be calculated as P(weapon detected | airline B detected the weapon) * P(airline B) = 0.5 * 0.3 = 0.15.

The denominator can be calculated as the sum of the probabilities that a weapon was detected by each airline, weighted by their respective prior probabilities:

P(weapon detected) = P(weapon detected | airline A detected the weapon) * P(airline A) + P(weapon detected | airline B detected the weapon) * P(airline B) + P(weapon detected | airline C detected the weapon) * P(airline C)

= 0.9 * 0.5 + 0.5 * 0.3 + 0.4 * 0.2

= 0.45 + 0.15 + 0.08

= 0.68

Finally, the answer is P(airline B detected the weapon | weapon detected) = 0.15 / 0.68 = 0.22.

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Answer:

The area of a trapezium with parallel sides of length 19 cm and 21 cm, and a distance of 14 cm between them, is 280 square cm.

Step-by-step explanation:

A) The change in entropy of the ice is 0.346 kJ/K.

B) The change in entropy of the stone slab is -1.257 kJ/K.

C) The total change in entropy of the system is -0.911 kJ/K.

Part A:

The change in entropy of the ice can be calculated using the formula:

ΔS_ice = Q_ice / T

where Q_ice is the heat transferred to the ice and T is the temperature at which the heat transfer occurs.

In this case, the ice is absorbing heat from the stone slab until it reaches thermal equilibrium.

The amount of heat transferred can be calculated using the formula:

Q_ice = m_ice c_ice ΔT

where, m_ice is the mass of the ice, c_ice is the specific heat of ice, and ΔT is the change in temperature of the ice.

Since the ice is initially at -10∘C and the final temperature is 0∘C (the melting point of ice), ΔT is 10∘C.

Substituting these values into the equations, we get:

Q_ice = (4.5 kg) (2100 J/kg⋅K) (10 K)

          = 94.5 kJ

ΔS_ice = Q_ice / T = (94.5 kJ) / (273 K)

           = 0.346 kJ/K

Therefore, the change in entropy of the ice is 0.346 kJ/K.

Part B:

The change in entropy of the stone slab can be calculated using the same formula as before:

ΔS_stone = Q_stone / T

where, Q_stone is the heat transferred to the stone and T is the temperature at which the heat transfer occurs.

In this case, the stone is losing heat to the ice until both reach thermal equilibrium.

The amount of heat transferred can be calculated using the same formula as before:

Q_stone = m_stone c_stone ΔT

where m_stone is the mass of the stone slab, c_stone is the specific heat of the stone, and ΔT is the change in temperature of the stone.

Since the stone slab is initially at +10∘C and the final temperature is 0∘C, ΔT is 10∘C.

Substituting these values into the equations, we get:

Q_stone = -(4.5 kg) (790 J/kg⋅K) (10 K) = -355.5 kJ

ΔS_stone = Q_stone / T = (-355.5 kJ) / (283 K) = -1.257 kJ/K

Therefore, the change in entropy of the stone slab is -1.257 kJ/K.

Part C:

The total change in entropy of the system can be calculated by adding the changes in entropy of the ice and the stone slab:

ΔS_tot = ΔS_ice + ΔS_stone

Substituting the values we calculated earlier, we get:

ΔS_tot = 0.346 kJ/K + (-1.257 kJ/K) = -0.911 kJ/K

Therefore, the total change in entropy of the system is -0.911 kJ/K.

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The values of x = 10√3 derived using the trigonometric ratio of cosine.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the larger acute angle, if we represent it by θ then for the bigger right triangle with adjacent x and hypotenuse 30;

cosθ = x/30

for the smaller right triangle with adjacent 30 - 20 = 10 and hypotenuse x

cosθ = 10/x

x/30 = 10/x

x² = 300 {cross multiplication}

x = √300 {take square root of both sides}

x = √100 × √3

x = 10√3.

Therefore, the values of x = 10√3 derived using the trigonometric ratio of cosine.

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Answer:

The first side = 2x = 2(4) = 8 cm

The second side = 5x = 5(4) = 20 cm

The third side = 8x = 8(4) = 32 cm

Step-by-step explanation:

We can use the fact that the ratio of the sides of the triangle is 2:5:8 and the perimeter of the triangle is 60 cm to find the length of each side of the triangle.

First, we can use the ratio to find the ratio of the perimeter to the sides of the triangle: 2:5:8. Since the perimeter is 60 cm, we can set up the following equation:

2x + 5x + 8x = 60

where x represents the length of one side of the triangle in cm.

We can then simplify the equation:

15x = 60

To find the value of x, we can divide both sides of the equation by 15:

x = 4

So each side of the triangle is 4 cm long.

Therefore,

The first side = 2x = 2(4) = 8 cm

The second side = 5x = 5(4) = 20 cm

The third side = 8x = 8(4) = 32 cm

The exact value for the tangent of 240° is -0.422618261740699.  The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. In order to calculate the tangent of 240°, first, find the ratio of the length of the opposite side to the length of the adjacent side. Then, use a calculator to convert the ratio into a decimal. To do this, simply divide the length of the opposite side by the length of the adjacent side. The decimal that is produced is the exact value for the tangent of 240°. In this case, the value is -0.422618261740699.

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This cannot be determined with the information given. To calculate the sample size, we would need to know the population means, the population standard deviation, and the confidence interval.

The confidence interval is 97%, which is the likelihood that the mean of the receipts is less than $38. We can use this information to calculate the margin of error and then use this to calculate the sample size.   The margin of error is calculated by taking the critical value (in this case, 1.96) and multiplying it by the standard deviation of the population. We then divide this by the square root of the sample size to get the margin of error.  

Once we have the margin of error, we can then calculate the sample size by taking the population means minus the margin of error and dividing this by the desired confidence interval. In this case, the desired confidence interval is 97%.   Therefore, without the population means, standard deviation, and confidence interval, it is impossible to calculate the sample size.

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Answer: 2x + 4mi >=10 , 3

Step-by-step explanation:
x=days after monday

Since Joseph ran 4 miles the first day, that number stays constant. The 2miles depends on the amount of days he runs for so that is the coefficient. Atleast means greater than or equal to. Using the inequality, we can solve that x >= 3.

2x+4>=10

    -4    -4

2x>=6

/2     /2

x>=3

The product is equivalent to $72 and its unit is $

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The rate,

8hx$9/h

In simple words,

$9 per hour for 8 hours.

Now, for 1 hour, the cost is $9.

Therefore, for 8 hours,

It can be written as -

x = 9 x 8

x = $72

Hence, the product is equivalent to $72.

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To find the value of the constant and the exponent so that is the solution of this initial value problem, you need to solve the differential equation, which can be written in the form y' + p(x)y = q(x).

To determine the largest interval of the form on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution, you need to ensure that the coefficients p(x) and q(x) are continuous on the interval and that p(x) does not change sign on the interval. The actual interval of existence for the solution is from the lower bound of the given interval to either the upper bound of the given interval or the point where p(x) changes sign.

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Answer:

Step-by-step explanation:

The percentage of 7th graders students that spend less than an hour a day on social media is 51.8%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

7th graders:

Number of students that spend less than an hour = 29

Number of students = 56

The percentage of students that spend less than an hour.

= 29/56 x 100

= 51.785

= 51.8 %

Thus,

The percentage of students that spend less than an hour is 51.8%.

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The volume of the cube as a polynomial is 8x³ + 12x² + 6x + 1.

The volume of a cube is expressed as;

V = a³

Where a is the side of the cube.

Given that;

Plug the given value into the above equation and simplify.

V = a³

V = ( 2x + 1 )³

Expand using FOIL method

V = ( 2x + 1 )( 2x + 1 )( 2x + 1 )

V = ( 2x( 2x + 1 ) + 1( 2x + 1 ) )( 2x + 1 )

V = (4x² + 4x + 1 )( 2x + 1 )

V = 2x(4x² + 4x + 1 ) + 1(4x² + 4x + 1 )

V = 8x³ + 8x² + 2x + 4x² + 4x + 1

Collect and add like terms

V = 8x³ + 12x² + 2x + 4x + 1

V = 8x³ + 12x² + 6x + 1

Therefore, the volume is 8x³ + 12x² + 6x + 1.

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