median of 27,29,18,25,32,21,26

Answer:

590mph

Step-by-step explanation:

Speed with wind = 5525÷ 8.5

= 650mph

speed against wind = 4505÷8.5

= 530mph

speed without wind = (650mph+530mph)÷2

= 590mph

Answer:

11/10 i think... may be wrong

Step-by-step explanation:

Answer:

10/9 is the answer.

Step-by-step explanation:

The maximum amount of water that the pool can hold is 1000 cubic feet.

To find the maximum amount of water that the rectangular prism swimming pool can hold, we need to calculate its volume.

The volume of a rectangular prism is given by:

V = l x w x h

where l is the length, w is the width, and h is the height of the prism.

Given the dimensions of the swimming pool, we have:

l = 16 feet

w = 12.5 feet

h = 5 feet

Therefore, the volume of the swimming pool is:

V = l x w x h

V = 16 feet x 12.5 feet x 5 feet

V = 1000 cubic feet

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Answer:

D: A

Step-by-step explanation:

It is not CD as it doesn't cover the whole line, D is just a proportion of the line and AC is only less than half.

The equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Amount of ammonia in the solution 16%  x 22 gallons  =  3.52 gallons

The proportion of ammonia remains the same as the water evaporates, but the total composition of the solution is decreased by the amount of water that evaporates.

Quantity of ammonia = 3.52 gallons

Quantity of water after evaporation = 22 - n

Composition of ammonia after evaporation of water, 24% = 24/100

Now the percentage of ammonia after evaporates
Quantity of ammonia / Remaining water = 24%
3.52 / (22 - n) = 24 / 100

Thus, the equation that he used to find n, the number of gallons of water he should remove is 3.52 / (22 - n) = 24 / 100.

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Answer:

f(- 2) = - 4

Step-by-step explanation:

Step-by-step explanation:

To evaluate f(- 2) substitute x = - 2 into f(x) , that is

f(- 2) = (- 2)² + 3(- 2) - 2 = 4 - 6 - 2 = - 4

Answer:

I say its 14 because it says  times more" so u would divide 70 by 5 but im debating between 14 and 65

Step-by-step explanation:

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\(e^{\frac{-t}{400}}\)

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

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

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

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

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

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

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

Now solving the bracket

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

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

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

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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) =

The function that describes the fund that was raised is 0.05³ - 30x - 12425

The revenue is  R (z) = 0.05x³ + 75

the cost = C(z) = 30x + 12,500.

Please note that the equation for revenue missed a sign in the question so I made use of the plus sign

We would have revenue - cost

Hence ( 0.05x³ + 75) - (30x + 12,500)

We would open the bracket

0.05x³ + 75 -30x -12500

We would take the like term to

0.05³ - 30x -12500 + 75

0.05³ - 30x - 12425

The function that describes the fund that was raised is 0.05³ - 30x - 12425

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Answer: F(x)=0.05x^3-30x-12,575

Step-by-step explanation:

Correct on test.

Answer:

The answer is B.

I think I answered the wrong answer.

The equation of motion is given by ∂LD/∂ψ - ∂(∂LD/∂(∂μψ))/∂μ = 0, and the effective action is obtained by integrating the Lagrangian over space and time: S_eff = ∫∫∫∫ LD d^4x.

To determine the equation of motion and the effective action for the given Lagrangian, we can follow these steps:

Calculate the Euler-Lagrange equation by taking the variation of the Lagrangian with respect to the field ψ and its conjugate ψˉ:

∂LD/∂ψ - ∂(∂LD/∂(∂μψ))/∂μ = 0

Compute the derivative term ∂(∂LD/∂(∂μψ))/∂μ using the given Lagrangian:

∂(∂LD/∂(∂μψ))/∂μ = ∂(iψˉ∂μψ)/∂μ = i∂μ(ψˉ∂μψ)

Substitute the derivative term and the Lagrangian into the Euler-Lagrange equation and simplify to obtain the equation of motion.

To find the effective action, integrate the Lagrangian over space and time:

S_eff = ∫∫∫∫ LD d^4x

By following these steps, you can determine the equation of motion and the effective action for the given Lagrangian.

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Answer:

Step-by-step explanation:

-1 = 7 - x

On this case, what you want to achieve is for all the constants to go to one side of the equation and all the variables would be on the other side of the equation. Let us transpose 7 to the left side of the equation.

subtract 7 on both sides

-1 = 7 - x

-1 - 7 = 7 - 7 - x

Simplify

-8 = -x

Divide both sides by -1

-8/-1 = -x/-1

8 = x

The answer to the question is x=8. It is an example of a linear equation.

A linear equation is an algebraic equation that represents a straight line when graphed on a coordinate plane. It consists of variables, constants, and coefficients, with the variables raised to the power of 1 (i.e., they are not squared or cubed).

A general form of a linear equation with one variable, let's say x, is:

ax + b = 0

Here, 'a' and 'b' are constants, and 'x' is the variable. The coefficient 'a' represents the slope or gradient of the line, while the constant term 'b' represents the y-intercept, which is the point where the line crosses the y-axis.

In this question,

-1 = 7-x (Given)

so, x = 7+1

        =8

Therefore, the solution to the equation is x=8.

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Answer:

try to look in desmos graphic calculator

Step-by-step explanation:

Answer:

the drawing would be 46 inches

We are given the following information

Carlos works a total of 86 hours in four weeks.

He works 18.5 hours each week for three weeks.

To determine how many hours Carlos work in the fourth week, we can set up the equation

We can make x the subject of the formula

Simplifying further

Therefore in the fourth week, Carlos will work 30.5 hours

The square pyramid paper weight takes up approximately 10.663 cm^3 more volume than the cone paper weight.

To determine the volume difference between the cone and the square pyramid paper weights, we need to calculate the volumes of both shapes and find the difference.

The volume of a cone can be calculated using the formula V_cone = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height of the cone.

Given that the diameter of the cone is 7.4 cm, we can find the radius by dividing the diameter by 2: r_cone = 7.4 cm / 2 = 3.7 cm. The height of both the cone and the square pyramid is 7.5 cm, as stated.

Substituting the values into the cone volume formula, we have:

V_cone = (1/3) * π * (3.7 cm)^2 * 7.5 cm

The volume of a square pyramid can be calculated using the formula V_pyramid = (1/3) * base area * h, where the base area is calculated by squaring one side of the base.

Given that one side of the square base is 7.4 cm, the base area is (7.4 cm)^2.

Substituting the values into the square pyramid volume formula, we have:

V_pyramid = (1/3) * (7.4 cm)^2 * 7.5 cm

Now we can calculate the volumes of the cone and the square pyramid:

V_cone = (1/3) * 3.14159 * (3.7 cm)^2 * 7.5 cm ≈ 145.798 cm^3 (rounded to 3 decimal places)

V_pyramid = (1/3) * (7.4 cm)^2 * 7.5 cm ≈ 135.135 cm^3 (rounded to 3 decimal places)

To find the volume difference, we subtract the volume of the square pyramid from the volume of the cone:

Volume difference = V_cone - V_pyramid ≈ 145.798 cm^3 - 135.135 cm^3 ≈ 10.663 cm^3 (rounded to 3 decimal places)

Therefore, the square pyramid paper weight takes up approximately 10.663 cm^3 more volume than the cone paper weight.

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TRUE. As one performs multiple separate hypothesis tests, the risk of committing a Type I error (rejecting a true null hypothesis) accumulates.

This overall risk is referred to as the experiment-wise alpha level or family-wise error rate (FWER). It represents the probability of making at least one Type I error among all the conducted tests.

When multiple hypothesis tests are performed simultaneously or sequentially, the individual alpha levels (typically set at 0.05) for each test may no longer be appropriate. This is because if we conduct, for example, 20 separate tests with an alpha level of 0.05 for each test, the cumulative chance of committing at least one Type I error can be much higher than the desired 5%.

To control the experiment-wise error rate, various multiple comparison procedures and adjustments can be employed, such as the Bonferroni correction or the Holm-Bonferroni method. These methods aim to maintain a desired level of significance for the entire set of tests, reducing the risk of accumulating Type I errors.

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Answer:

Step-by-step explanation:

7(x-2) -3(x+3) = 5(x-3) +x , distribute in parenthesis

7x -14 -3x -9 = 5x -15 +x , isolate like terms

7x -3x -5x -x = 14 +9 -15, combine like terms

-2x = 8, divide both sides by -2

x= -4

The net outward flux across the boundary of the tetrahedron is 5, using the concept of the gradient of a function.

The gradient  function in a vector field

The gradient function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z). The gradient is a fancy word for derivative or the rate of change of a function. It's a vector (a direction to move) that. Points in the direction of greatest increase of a function are zero at a local maximum or local minimum because there is no single direction of increase

Vector field:

F = ( -x, 3y, 2 z )

Δ . F = (i δ/δx + j δ/δy + k δ/δz) (-x, 3y, 2 z )

Δ . F = [δ/δx(-x)] + δ/δy (3y) + δ/δz (2z)]

Δ . F = - 1 + 3 + 2

Δ . F = 4

According to divergence theorem

Divergence Theorem

The divergence theorem states that the surface integral of the normal component of a vector point function F over a closed surface S is equal to the volume integral of the divergence. F  took over the volume V enclosed by the surface S. The divergence theorem says that when adding up all the little bits of outward flow in a volume using a triple integral of divergence, the total outward flow from that volume, as measured by the flux through its surface.

Flux =  ∫∫∫ Δ. (F) DV

x+ y +z = 1; so, 1st octant

x from 0 to 1

y from 0 to 1 -x

z from 0 to 1-x-y

∫₀¹∫₀¹⁻ˣ∫₀¹⁻ˣ⁻y (4) dz dy dx

= 4 ∫₀¹∫₀¹⁻ˣ (1 - x - y) by dx

= 5

Therefore, conclude that the net outward flux across the boundary of the tetrahedron is  5

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Answer: 6:4

Step-by-step explanation: The total of marbles doesn't change just the green total total.

Answer:

3 marbles of what are removed (green red or blue)

Step-by-step explanation:

60 marbles=red+blue+green

red:blue

(13 : 3)

blue:green

( 3 : 4)

red:blue:green

13 : 3 : 4

13/20×60=39 red marbles

3/20 × 60=9 blue marbles

4/20× 60= 12 green marbles

60-3

=57

x-3

Answer: 400 miles

Step-by-step explanation: every hour, his distance decreases by 50 miles. After 4 hours, his distance is 200 miles, so 50 miles times 4 hours = 200 miles+the original 200 miles =400 miles.

Answer: 11136 grams

≈ 11.14 kilograms  

Step-by-step explanation:

Given, Each package has 126 grams of granola, 245 grams of chocolate chip cookies , and 325 grams of nuts in it.

Total weight of each package =  126 grams + 245 grams +  325 grams

= 696 grams

If they have 16 care packages, then total weight of packages = 16 x (Total weight of each package)

= 16 x 696 grams

=  11136 grams

≈ 11.14 kilograms   [ 1 kilogram = 1000 grams]

To convert 800 mm to inches, divide 800 by 25.4. The result is 2 feet and 7.5 inches.

The metric and imperial systems are two ways to measure length, with the metric system being more widely used in the world and the imperial system being predominantly used in the United States.

800mm (millimeters) can be converted to inches and feet by using the conversion factors: 1 inch = 25.4mm, and 1 foot = 12 inches.

To convert 800 mm to feet, first convert 800mm to inches as described above (800/25.4 = 31.5 inches). Then divide 31.5 by 12 to get the equivalent length in feet. The result is 2 feet and 7.5 inches.

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The particular solution for the given non-homogeneous system of first-order linear differential equations is:

\(Y = 54x - (5/3)x^3 + 3x^2 + 25x + 16\)

To find the particular solution for the non-homogeneous system of first-order linear differential equations, we need to substitute the given values into the system and solve for the unknown coefficients.

The given system is:

\(Y' = 54 - 5x^2 + 6x + 25\\Y(0) = 12 - x^2 + 2x + 4\)

Differentiating the second equation, we have:

\(Y'(0) = -2x + 2\)

Now, let's substitute these values into the first equation:

\(Y' = 54 - 5x^2 + 6x + 25\)

Since there are no derivatives of Y in the equation, we can integrate both sides with respect to x to find the particular solution:

\(\int Y' dx = \int (54 - 5x^2 + 6x + 25) dx\)

Integrating each term separately, we get:

\(Y = 54x - (5/3)x^3 + 3x^2 + 25x + C\)

Now, using the initial condition\(Y(0) = 12 - x^2 + 2x + 4\), we can substitute x = 0 and \(Y = 12 - x^2 + 2x + 4\) into the equation to solve for the constant C:

\(12 - 0 + 2(0) + 4 = 54(0) - (5/3)(0^3) + 3(0^2) + 25(0) + C\)

16 = C

C= 16

Therefore, the particular solution for the given non-homogeneous system of first-order linear differential equations is:

\(Y = 54x - (5/3)x^3 + 3x^2 + 25x + 16\)

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Answer:

x - y =9

x^2 + y^2 = 125

2^2 + 11^2 = 125

11-2 = 9

Thus, the two numbers are 2 & 11.

Hope this helps!

Answer:

(2y + 1) • (y - 3)

?

Step-by-step explanation:

Answer:

4.81 m

Step-by-step explanation:

area of Equilateral triangle with side length a : area = (√3/4) a²

10 = (√3/4) a²

a² = 40√3 / 3 = 23.09

a = 4.81 m

if you are in Trigonometry: h/a = sin 60°

h = (√3 / 2) a

The first three nonzero terms of two linearly independent solutions about x = 0 can be obtained by Taylor expanding the solutions in terms of the exponent r and truncating the series to the desired order.

To determine if x = 0 is a regular singular point of the differential equation xy'' + y = 0, we substitute y = x^r into the equation and solve for the exponent r. Differentiating y twice with respect to x, we have y'' = r(r - 1)x^(r - 2). Substituting these expressions into the differential equation, we get \(x(x^r)(r(r - 1)x^(r - 2)) + x^r = 0\). Simplifying, we obtain r(r - 1) + 1 = 0, which yields r^2 - r + 1 = 0. Solving this quadratic equation, we find that the exponents at the singular point x = 0 are complex and given by r = (1 ± i√3)/2.

To find the first three nonzero terms of two linearly independent solutions about x = 0, we can use the Taylor series expansion. Let's consider the solution y1(x) corresponding to the exponent r = (1 + i√3)/2. Expanding y1(x) as a series around x = 0, we have y1(x) =\(x^r = x^((1 +\)i√3)/2) = x^(1/2) *\(x^(i√3/2\)). Using the binomial series expansion and Euler's formula, we can write \(x^(1/2) and x^(i√3/2)\) as infinite series.

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