a mixing tank is filled with 240 gallons of water in which 18 pounds of salt is dissolved. a saline solution flows into this tank at a rate of 3 gallons per minute, while the well mixed solution drains from the tank at the same rate of 3 gallons per minute. let be the amount of salt in pounds in this tank at time in minutes. the amount of salt in this tank can be modeled by the autonomous differential equation: what is the initial amount of salt (in pounds) in this tank? lbs how much salt is in this tank after a long time, ? lbs what is the equilibrium salt concentration (in pounds per gallon) of this tank? lbs/gal what is the rate of change in the amount of salt in this tank when it is at 35 pounds from the equilibrium solution? lbs/min

Answer:

x = 4

Step-by-step explanation:

To find the zero let f(x) = 0 and solve for x , that is

- 12x + 48 = 0 ( subtract 48 from both sides )

- 12x = - 48 ( divide both sides by - 12 )

x = 4 ← zero of f(x)

Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

The minimum number of terms required for the sum sn to have an error less than 0.0399, assuming K = 1 and b-a = 1.

To determine the minimum number of terms n required for the sum sn to have an error less than 0.0399, we need to use the formula for the error term of a finite series:

|En| ≤ ((M * (b-a)^n)/(n!))

where En is the error term, M is the maximum value of the (n+1)th derivative of the function, a and b are the limits of integration, and n is the number of terms in the series.

Since we do not have a specific function or limits of integration, we cannot determine the exact value of M. However, we can use an upper bound for M, which is the maximum value of the (n+1)th derivative of the function over the entire interval [a,b]. Let's assume that M = K, where K is some constant.

Then we have:

|En| ≤ ((K * (b-a)^n)/(n!))

We want the error to be less than 0.0399, so we can set up the following inequality:

((K * (b-a)^n)/(n!)) < 0.0399

To solve for n, we need to use a numerical method such as trial and error, or a graphing calculator. We can also use a table of values for n! and (b-a)^n to simplify the inequality.

For example, if we assume that K = 1 (which is a reasonable assumption for many functions), and let b-a = 1 (i.e. we are integrating over the interval [0,1]), we can create a table of values for n! and (b-a)^n:

n | n! | (b-a)^n
--|----|---------
1 | 1  | 1
2 | 2  | 1
3 | 6  | 1
4 | 24 | 1
5 | 120| 1
6 | 720| 1

Using these values, we can rewrite the inequality as:

(K/n!) < (0.0399/(b-a)^n)

Plugging in our values, we get:

1/n! < 0.0399

Solving for n using trial and error or a graphing calculator, we find that n = 4 is the minimum number of terms required for the sum sn to have an error less than 0.0399, assuming K = 1 and b-a = 1. However, keep in mind that this value may change depending on the specific function and limits of integration.

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Answer: I cant understand what you want think you could put it in English?

Step-by-step explanation:

Therefore, the correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

Based on the given information, D represents the null hypothesis (H₀) and E represents the alternative hypothesis (Hₐ).

The null hypothesis (H₀) is a statement that there is no significant difference between the observed data and the expected results. In this case, the null hypothesis is that the population mean (μ) is greater than or equal to 1000.

The alternative hypothesis (Hₐ) is a statement that there is a significant difference between the observed data and the expected results. In this case, the alternative hypothesis is that the population mean (μ) is less than 1000.

Correct answer is (b) H(0) and H(a), where H(0) represents the null hypothesis and H(a) represents the alternative hypothesis.

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1. The base of the trapezoid is a rectangle, thus its area is 96 sq. units. 2. The volume of the trapezoid prism is 312 cubic units. 2. We cannot draw different triangle with same condition.

A trapezoidal prism's volume determines its capacity. It is also known as the area contained by a trapezoidal prism. The top and bottom faces of a prism have cogruent polygons, and its bases are the same. The lateral faces, or side faces, of a prism are parallelograms. The forms of the two identical faces at a prism's end can be used to identify it. A three-dimensional solid with two trapezoid/trapezium bases at the bottom and top is called a trapezoidal prism. A trapezoidal prism's lateral faces and side faces have a parallelogram form.

1. The base of the trapezoid is a rectangle, thus its area is given as:

A = lw

A = (8)(12) = 96 sq. units.

2. The volume of the trapezoid prism is given as:

V = 1/2(a + b) h(l)

Here, a = 5, b = 8, h = 4, and l = 12.

Substituting the values we have:

V = 1/2(5 + 8)(4)(12)

V = 24(13)

V = 312 cubic units.

2. The triangles with the conditions, 50° angle, a 40° angle, and a side of length 4 cm has the third angle as 90 degrees according to the internal angle of triangle theorem.

Also, the sides corresponding to the triangle remain same, and hence we cannot draw different triangle with same condition.

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Answer:

figure it out

Step-by-step explanation:

Answer:

1Kilogram=1000

5820/1000= 5.82 kilograms

Step-by-step explanation:

please mark me as brainliest if im correct

Answer:

C

Step-by-step explanation:

Here in this question , we are interested in calculating the total distance covered by the train in the 10 minutes that it ran.

From the first part of the question, we already know the distances in the first 5 minutes.

Now, to calculate the total distance in the second 5 minutes, we use the distance formula since we have the average speed and the time;

Mathematically; Total distance = average speed * time

From the question, average speed is 33km/h, while time is 5 minutes. To achieve a consistent unit, we convert 5 minutes to hours.

That would be 5/60 = 1/12 hours

So the total distance in the second 5 minutes is;

33 * 1/12 = 2.75 km

Now, to calculate the total distance traveled, let’s add up the distances in the first 5 minutes and convert to kilometers;

That would be;

68 + 127 + 208 + 312 + 535 = 1,250 m

Let’s convert this to km.

We simply divide by 1000 = 1250/1000 = 1.25 km

The total distance is thus ;

1.25 + 2.75 = 4 km

Center point of dilation is a fixed point in a plane about which all the points of the figure expanded or contract. And scale factor of a dilation is the ratio of new formed image to the old given image.

Explanation:

Therefore, the center of the dilation can be find using the translation and scale factor can be calculated using the ratio of the new to the old images.

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Answer:

a. 0.81

b. 0.81

Step-by-step explanation:

Let's assume that the player makes x% of his free throws. Then, the probability that he will make both free throws is (x/100)^2, and he will make at least one free throw is 1 - (1 - x/100)^2.

So if he makes 90% of his free throws, then:

a. The probability that he will make both free throws is (90/100)^2 = 0.81.

b. The probability that he will make at least one free throw is 1 - (1 - 90/100)^2 = 1 - (1 - 0.9)^2 = 1 - 0.19 = 0.81.

The answers to the questions rounded to 4 decimal places are:

a. 0.81

b. 0.81

The monthly payment for the car loan is approximately 16,216.38 pesos. The outstanding balance after 2 years is approximately 650,577.85 pesos.

To find the monthly payment for the car loan, we can use the formula for the monthly payment on a loan:

P = (r * PV) / (1 - (1 + r)^(-n))

Where:

P is the monthly payment

r is the monthly interest rate

PV is the loan amount (present value)

n is the total number of payments

In this case, the loan amount PV is 800,000 pesos, the monthly interest rate r is 7% / 12 (since the interest is compounded monthly), and the total number of payments n is 5 years * 12 months/year = 60 months.

Substituting these values into the formula, we have:

P = (0.07/12 * 800,000) / (1 - (1 + 0.07/12)^(-60))

Calculating this expression, we find that P ≈ 16,216.38 pesos.

So, the monthly payment for the car loan is approximately 16,216.38 pesos.

To find the outstanding balance after 2 years, we need to calculate the remaining balance after making monthly payments for 2 years. We can use the formula for the remaining balance on a loan:

Remaining Balance = PV * (1 + r)^n - P * ((1 + r)^n - 1) / r

Where:

PV is the loan amount (present value)

r is the monthly interest rate

n is the number of payments made

Substituting the given values into the formula, we have:

Remaining Balance = 800,000 * (1 + 0.07/12)^24 - 16,216.38 * ((1 + 0.07/12)^24 - 1) / (0.07/12)

Calculating this expression, we find that the outstanding balance after 2 years is approximately 650,577.85 pesos.

So, the outstanding balance after 2 years is approximately 650,577.85 pesos.

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The correct expression to find the volume of a rectangular prism is D. (3 × 6) × 15 = 270 in.3.

Expression is a word, phrase, or gesture that conveys an idea, thought, or feeling. It is an outward representation of an emotion, attitude, or opinion. Expressions can be verbal, physical, or written. They can also take the form of art, music, or dance. Expression is used to communicate and express emotions, thoughts, and ideas. It can be a powerful tool to create a connection with others and build relationships.

The correct expression to find the volume of a rectangular prism is D. (3 × 6) × 15 = 270 in.3. This expression involves multiplying the length, width, and height of the rectangular prism in order to calculate the total volume. In this case, the length is 3, the width is 6, and the height is 15. If these values are multiplied together, the result is 270 in.3, which is the total volume of the rectangular prism.

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AB=AOB×r

6π=9AOB

AOB=3π/2

The area of the circular sector is given by;

\(a = \frac{ \frac{3\pi}{2} }{2\pi} \times (\pi \: r {}^{2} )\)

\(a = \frac{3\pi}{4} \times 81\pi\)

\(a = 60.75\pi\)

\(a = 190.85 \: cm {}^{2} \)

For a closed curve encircles several conductors. If the line integral around this curve is then the net current in the conductors is equals to the 334 Ampere.

Ampere’s Law is stated as ‘the line integral of a Magnetic field \(\vec B\) along a closed path is equals to the \( \mu_0\) (permeability of free space) times the total current 'I' enclosed by closed path or curve, mathematically form, we can say that \(\int \vec B. \vec dl = \mu_0 I\)

where, I --> total or net current.

It is used to describe a relationship between the current and the Magnetic field that it generates around itself. Now, we have the line integral around closed curve, \(\int \vec B.\vec dl \)

= 4.20×10⁻⁴ T-m

We have to determine value of the net current in the conductors. Using the ampere's law, for a closed loop carrying current, \( 4.20 × 10^{-4} = \mu_0 I\).

plug the value of constant of permeability of free space, \(\mu_0\) = 4π× 10⁻⁷ T-m/A

=> I × 4π× 10⁻⁷ T-m/A = 4.20 × 10⁻⁴ T-m

=> I = ( 4.20/4π) 10⁻⁴⁺⁷ A

=> I = 0.334× 10³ A

=> I = 334 A

Hence, required value is 334 A.

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Complete question:

a closed curve encircles several conductors. the line integral around this curve is int B.dl = 4.20×10-4 T-m. What is the net current in the conductors?

To find the value of x, we calculate the average of the sample observations. Summing up the observations and dividing by the total number of observations, we get:

x = (125 + 122 + 126 + 100 + 155 + 132 + 121 + 118 + 114 + 125 + 142 + 2 + 130 + 110 + 140 + 129 + 3) / 17 = 114.118 seconds (rounded to three decimal places).b) To find the value of R, we calculate the range of each sample by subtracting the minimum observation from the maximum observation. Then we find the average range across all samples:R = (155 - 100 + 142 - 2 + 140 - 110 + 132 - 114 + 142 - 3) / 5 = 109.2 seconds (rounded to three decimal places).

c) The Upper Control Limit (UCL) and Lower Control Limit (LCL) using 3-sigma can be calculated by adding and subtracting three times the standard deviation from the average:UCL = x + (3 * R / d2) = 114.118 + (3 * 109.2 / 1.693) = 348.351 seconds (rounded to three decimal places).LCL = x - (3 * R / d2) = 114.118 - (3 * 109.2 / 1.693) = -120.115 seconds (rounded to three decimal places).

d) The Upper Control Limit Range (UCLR) and Lower Control Limit Range (LCLR) using 3-sigma can be calculated by multiplying the average range by the appropriate factor:UCLR = R * D4 = 109.2 * 2.115 = 231.108 seconds (rounded to three decimal places).LCLR = R * D3 = 109.2 * 0 = 0 seconds.

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infinetly many because

for example if 5=5 on a graph. both lines would always touch

a) Causal, memoryless, linear, time-invariant.

b) Causal, memoryless, linear, time-invariant.

c) Causal, memoryless, nonlinear, time-invariant.

d) Causal, has memory, nonlinear, time-invariant.

a) The system described by y[n] = x[n] + 2x[n+1] is causal because the output value at any time index n only depends on the current and past input values. It is memoryless since the output at a given time index n does not depend on any past or future inputs. The system is linear because the output is a linear combination of the input values. It is also time-invariant because the system's behavior remains unchanged over time.

b) The system y[n] = u[n]x[n] is causal since the output at any time index n only depends on the current and past input values. It is memoryless because the output at a given time index n does not depend on any past or future inputs. The system is linear because the output is a product of the input signal and a constant. It is also time-invariant because the system's behavior remains unchanged over time.

c) The system y[n] = |x[n]| is causal since the output at any time index n only depends on the current and past input values. It is memoryless because the output at a given time index n does not depend on any past or future inputs. The system is nonlinear because the absolute value operation is a nonlinear operation. It is time-invariant because the system's behavior remains unchanged over time.

d) The system y[n] = ∑(0.5)^n x[i] for i=0 to n is causal since the output at any time index n only depends on the current and past input values. It has memory because the output at a given time index n depends on all past input values up to the current time index. The system is nonlinear because the output is a sum of terms raised to a power, which is a nonlinear operation. It is time-invariant because the system's behavior remains unchanged over time.

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Answer:

x = 40

Step-by-step explanation:

\((3x - 10) \degree = (2x + 30) \degree \\ (vertical \: \angle s) \\ \\ \\ 3x - 10 = 2x + 30 \\ \\ 3x - 2x = 30 + 10 \\ \\ x = 40\)

Alana and Eli will each have passed 42 tests in 8 weeks.

In order to write a a system of linear equations to describe this situation, we would a assign variable to the number of weeks and the total number of test passed respectively, and then translate the word problem into a linear equation as follows:

Since Alana has passed 2 tests so far and plans to take and pass 5 tests per week, a linear equation to model this situation is given by:

y = 5x + 2    ......equation 1.

Additionally, Eli, has passed 10 tests and plans to do 4 per week:

y = 4x + 10     ......equation 2.

By equating equation 1 and equation 2, we have the following:

5x + 2 = 4x + 10

5x - 4x = 10 - 2

x = 8 weeks.

For the number of test, we have;

Alan ⇒ y = 5x + 2 = 5(8) + 2 = 42 tests.

Eli ⇒ y = 4x + 10 = 4(8) + 10 = 42 tests.

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In linear equation, 60 hours does she spend on running in 30 days .

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

                              The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

she runs =  12 miles

she take time to runs a mile  = 10 min.

 total time she take = 12 *   10  = 120 min.

  if she spend on running in 30 days =  120 * 30

                                                 = 3600 min

                                        1 hours = 60 min.

                                       3600 min  =  3600/60 ⇒ 60 hours

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The value of the piecewise function for f(3) is 4

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

f(x) = 2x if x < 1

f(x) = 1/2x + 5/2 if x >= 1

The function f(3) implies that we make use of the function

f(x) = 1/2x + 5/2

This is because it is valid for x >= 1

substitute the known values in the above equation, so, we have the following representation

f(3) = 1/2 * 3 + 5/2

Evaluate

f(3) = 4

Hence, the piecewise function for f(3) is 4

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Answer:

v=53 degrees

Step-by-step explanation:

So since 180 degrees in tri, v-23+2v+v-9=180

Plus 23 and 9: 4v=212

v=53 degrees

Answer:

\(\frac{6}{5}\)

Step-by-step explanation:

1.Turn the 9 into a fraction

\(\frac{2}{15} *\frac{9}{1}\)

2.factor the bigger numbers.

\(\frac{2}{3*5} *\frac{3*3}{1}\)

3.Cancel out the common factor(3)

\(\frac{2}{5} * \frac{3}{1}\)

4.multiply across

\(\frac{2}{5} *\frac{3}{1} =\frac{6}{5}\)

The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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The derivative of the function  f(x) = 2cosh(x) + 9sinh(x) is given as is f'(x) = 2sinh(x) + 9cosh(x).

To find its derivative, we can use the derivative rules for hyperbolic functions. The derivative of cosh(x) with respect to x is sinh(x), and the derivative of sinh(x) with respect to x is cosh(x). Applying these rules, we can find that the derivative of f(x) is f'(x) = 2sinh(x) + 9cosh(x).

In the first paragraph, we state the problem of finding the derivative of the given function f(x) = 2cosh(x) + 9sinh(x). The derivative is found using the derivative rules for hyperbolic functions. In the second paragraph, we provide a step-by-step explanation of how the derivative is calculated. We apply the derivative rules to each term of the function separately and obtain the derivative f'(x) = 2sinh(x) + 9cosh(x). This represents the rate of change of the function f(x) with respect to x at any given point.

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Answer:

\(\huge\boxed{\text{(C), (D), and (E)}}\)

Step-by-step explanation:

We can use basic angle relationships to find which statements are true.

Since we know that the horizontal line is being intersected by two vertical lines that are parallel, we know the corresponding angles are equivalent.

A can’t be true because alternate exterior angles come from the same line. 4 and 7 are from two different lines.

B can’t be true because the 50° angle and 1 and 2 are supplementary. In order for 1 and two to be complementary, the 50° angle would have to be 90°. So this isn’t true.

C must be true because angles 8 and 5 come together to form one of the parallel lines that intersects the horizontal line. Since it’s a line intersection, the two angles must be supplementary.

D must be true because we have two angles that are formed by parallel lines intersecting the same line. Since the lines are parallel, the angles on either side are equivalent. These are called corresponding angles.

E must be true because the angles are equivalent to each other. 5 and 7 are equivalent, and so are 8 and 6. Therefore, these are vertical angles.

Hope this helped!

Answer:

Table c mate

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

3:12 is the amount of shaded circles to all circles, 8:2 is basically the same thing as 3:12 and 9:3 is the amount of shaded circles to the amount of non-shaded circles.  1:3 wouldn't work because it is not the right ratio.