I Need to know a or b is the answer to this question

The number A(t) of grams of salt in the tank at time is: \(200 - 180e^{-1/40t}\)

To determine the number of grams of salt in the tank at time t, we would apply the equation of state to have:

dA/dt = R(in) - R(out)

For R(out), we would have:

R(in) = 5g/min

R (out) = A/40 g/min

We would substitute these in the equation and apply a differential limit where A = 20 and t = 0

So,

20 = 200 + C

c = -180

Thus, the equation that expresses the rate = \(200 - 180e ^{-1/40t}\)

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Complete Question:

1. A tank contains 200 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

A(t) = ____ g

Answer:

x = - 2, x = 12

Step-by-step explanation:

Given

x² - 9x = x + 24 ( subtract x + 24 from both sides )

x² - 10x - 24 = 0 ← in standard form

(x + 2)(x - 12) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 12 = 0 ⇒ x = 12

Answer:

A

Step-by-step explanation:

Surface area of sphere is 4 pi r^2

                     144 pi   = 4 pi r^2

                          144 pi / (4 pi) = r^2

                             36 = r^2

                               r = 6 ft

We need a minimum of 12 terms in order to guarantee this level of accuracy.

Now, According to the Simpson rule approximation :
\(\int\limits^1_0 {15e^x^2} \, dx\)

So, a = 0 , b = 1 and \(f(x) = 15e^x^2\) . We need the fourth derivative of f:

\(f'(x) = 30xe^x^2\)

\(f''(x) = 30e^x^2+60x^2e^x^2=(30x+60x^2)e^x^2\)

\(f'''(x)=120xe^x^2+2x(30+60x^2)e^x^2=(180x+120x^3)e^x^2\)

\(f''''(x)=(180+360x^2)e^x^2+2x(180x+120x^3)e^x^2=(180+720x^{2} +240x^{4} )e^x^{2}\)

The maximum value of the fourth derivative on the interval [0,1] is \(f^i^v(1)=1140e\) so the error is bounded by:

\(|\frac{f^i^v(1)(1-0)^5}{180n^4} |=\frac{1140e}{180n^4} =\frac{19e}{30n^4}\)

We wish the error to be less than 0.0001, so

\(\frac{19e}{30n^4} < .0001\\ \\19e < .003n^4\\\\n^4 > \frac{19e}{0.003}\\ \\n > \sqrt[4]{\frac{19e}{0.003} }\)

   ≈ 11.454

Therefore we need a minimum of 12 terms in order to guarantee this level of accuracy.

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The given question is incomplete, complete question:

How large should n be to guarantee that the Simpson's Rule approximation to \(\int\limits^1_0 {15e^x^2} \, dx\) is accurate to within 0.0001?

To approximate the solution and maximize the given objective function we need to find the steepest ascent direction and iteratively update the values of x₁ and x₂ to approach the maximum value of z.

The method of steepest ascent involves finding the direction that leads to the maximum increase in the objective function and updating the values of the decision variables accordingly. In this case, we aim to maximize the objective function z = -(x₁ - 3)² - (x₂ - 2)².

To find the steepest ascent direction, we can take the gradient of the objective function with respect to x₁ and x₂. The gradient represents the direction of the steepest increase in the objective function. In this case, the gradient is given by (∂z/∂x₁, ∂z/∂x₂) = (-2(x₁ - 3), -2(x₂ - 2)).

Starting with initial values for x₁ and x₂, we can update their values iteratively by adding a fraction of the gradient to each variable. The fraction determines the step size or learning rate and should be chosen carefully to ensure convergence to the maximum value of z.

By repeatedly updating the values of x₁ and x₂ in the direction of steepest ascent, we can approach the solution that maximizes the objective function z. The process continues until convergence is achieved or a predefined stopping criterion is met.

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Answer:

The correct answer is B. Jonas is correct because an equilateral triangle has 3 acute angles and all sides the same lenght

Answer:

So first add the perimeter lengths together.

65+45=110

Then do 110 because there are 2 backyards.

110x2= 220

Then we need to see how many 8ft panels of fencing we need for that much perimeter length so do 220/8.

220/8=27.5

You need 27 and 1/2 panels to enclose the yards.

Geometric averages are usually smaller than arithmetic averages.

The geometric average is a type of average that is calculated by taking the nth root of the product of n numbers. It is commonly used when dealing with growth rates, ratios, and exponential functions. On the other hand, the arithmetic average, also known as the mean, is calculated by summing up a set of numbers and dividing it by the count of those numbers.

The relationship between the geometric average and the arithmetic average can be understood by considering the behavior of the numbers being averaged. When the numbers being averaged have a wide range or vary significantly, the geometric average tends to be smaller than the arithmetic average. This is because the geometric average gives more weight to smaller values, which can pull down the average.

For example, if we have a set of numbers that includes both very small values and very large values, the geometric average will be more influenced by the small values, resulting in a smaller average compared to the arithmetic average. This is because the geometric average emphasizes the impact of each individual value's proportionate contribution to the overall average.

In summary, geometric averages are usually smaller than arithmetic averages when dealing with sets of numbers that have a wide range or significant variation. However, it is important to note that the relationship between these averages can vary depending on the specific dataset and its characteristics.

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yes here x and y are directly proportional when looking at the x-coordinate

Step-by-step explanation:

here,

x1=7, y1=14

x/y=7/14

=1/2.

when considering the second coordinates,

=we will get the answer again

1/2.

all the coordinates is proportional in this form it is all will get the answer one by two so this x -axis and y-axis are directly proportional

The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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A) The area οf the pizza frοm Lοs Angeles is 153.94 square inches

B) The area οf the pizza frοm Lοndοn is 78.5 square inches

C) Cοmparing the twο areas, we can see that the pizza frοm Lοs Angeles has a larger area than the pizza frοm Lοndοn.

Part A:

Tο find the area οf the pizza frοm Lοs Angeles, we need tο use the fοrmula fοr the area οf a circle:

A = πr²

where r is the radius οf the circle, which is half the diameter.

d = 14 inches

r = d/2 = 7 inches

Substituting the value οf r intο the fοrmula, we get:

A = π(7)²

A = 49π

Using a calculatοr οr apprοximating π tο 3.14, we get:

A ≈ 153.94 square inches

Part B:

Tο find the area οf the pizza frοm Lοndοn, we use the same fοrmula fοr the area οf a circle, but we need tο cοnvert the diameter frοm centimeters tο inches first.

d = 25.4 centimeters = 25.4/2.54 inches

d ≈ 10 inches

r = d/2 ≈ 5 inches

A = π(5)²

A = 25π

Using a calculatοr οr apprοximating π tο 3.14, we get:

A ≈ 78.5 square inches

Part C:

Tο cοmpare the areas οf the twο pizzas, we need tο cοnvert the area οf the pizza frοm Lοs Angeles tο square centimeters, since the area οf the pizza frοm Lοndοn is given in square centimeters.

1 inch = 2.54 centimeters

1 square inch = (2.54)² square centimeters

1 square inch ≈ 6.45 square centimeters

Area οf pizza frοm Lοs Angeles ≈ 153.94 square inches

Area οf pizza frοm Lοs Angeles in square centimeters ≈ 153.94 x 6.45 ≈ 992.52 square centimeters

Area οf pizza frοm Lοndοn ≈ 78.5 square inches

Cοmparing the twο areas, we can see that the pizza frοm Lοs Angeles has a larger area than the pizza frοm Lοndοn.

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Complete question:

A pizza parlοr in Lοs Angeles sells a pizza with a 14-inch diameter. A pizza parlοr in Lοndοn sells a pizza with a 25.4-centimeter diameter.

Part A: Hοw many square inches οf pizza is the pizza frοm Lοs Angeles? Shοw every step οf yοur wοrk. (1 pοint)

Part B: Hοw many square centimeters οf pizza is the pizza frοm Lοndοn? Shοw every step οf yοur wοrk. (1 pοint)

Part C: If 1 in. = 2.54 cm, which pizza has the larger area? Shοw every step οf yοur wοrk. (1 pοint)

The level of measurement of the data "restaurant rating (superior, good, average, poor, inferior)" is ordinal.

Ordinal level of measurement refers to data that has a natural order or ranking, but the difference between each category is not necessarily equal. In this case, the restaurant ratings have a clear order, with superior being the highest and inferior being the lowest, but the difference between each category is not specified or quantifiable.

An ordinal scale allows for the ranking or ordering of data but not for mathematical operations such as addition, subtraction, or division. This is because the intervals between categories are not equal and cannot be assumed to be so.

In summary, the restaurant rating data is an example of ordinal level of measurement as it has a clear order or ranking, but the intervals between categories are not equal and cannot be used for mathematical operations.

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Answer:

-7

-48

Step-by-step explanation:

-2*2 = -4. -4-3=-7

-3*-3*-3=-27    -27*2=-54. -54+6=-48

Answer:

\(x= \frac{16}{3}\)

Step-by-step explanation: Can i get brain plz!

Answer:

29.5 or 30 (rounded)  

Step-by-step explanation:

Add 12 and 47 together and divide by 2 because there are 2 numbers.

Answer:

the geometric mean is 23.7 or 23.74868

Step-by-step explanation:

take your numbers

12 and 47. you have 2 numbers so n=2

find 1/n=0.5

(12*47)^0.5

(564)^0.5=23.74868

round 23.74868 to the nearest 10

23.7

When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

So, the equations are graphs are:

Now, graph both equations as follows:

Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

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Answer:

The answer is C

Step-by-step explanation:

The variable is the same so they are like terms

There is no graph provided for reference, but if the graph shows a probability distribution, then the probabilities that are equal to 0.3 would depend on the specific shape and values displayed on the graph.

Without this information, it is impossible to determine which probabilities are equal to 0.3. Based on the given information, the graph represents a probability distribution. To determine which probabilities are equal to 0.3, you would need to analyze the graph (which is not provided). However, I can explain each term:
1. p(5≤x≤8): This represents the probability that x falls between 5 and 8, inclusive.
2. p(x≤3): This denotes the probability that x is less than or equal to 3.
3. p(x≥3): This signifies the probability that x is greater than or equal to 3.
4. p(3≤x≤5): This indicates the probability that x falls between 3 and 5, inclusive.

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Answer:   Therefore, the answer is:

a) ONE TRIANGLE

b) The sides 4 cm, 6 cm, and 9 cm can form a single triangle.

Step-by-step explanation:

a) There is exactly ONE TRIANGLE that can be constructed with sides measuring 4 cm, 6 cm, and 9 cm.

b) To determine the number of triangles that can be formed from three given sides, we can use the triangle inequality theorem which states that the sum of any two sides of a triangle must be greater than the third side.

Let's check if the given sides satisfy this inequality:

4 cm + 6 cm > 9 cm (True)

4 cm + 9 cm > 6 cm (True)

6 cm + 9 cm > 4 cm (True)

Since all three inequalities are true, we can conclude that a triangle can be formed using these three sides.

Now, let's determine if there is only one possible triangle that can be formed or if there are more than one. To do this, we can use the fact that the largest side of a triangle must be smaller than the sum of the other two sides. If this is not the case, then it's not possible to form a triangle.

In this case, the largest side is 9 cm. Let's check if it's smaller than the sum of the other two sides:

4 cm + 6 cm = 10 cm (True)

Since 9 cm is smaller than the sum of the other two sides, we can conclude that it's possible to form a triangle, but there is only one possible triangle that can be formed.

The set that contains all the roots of the polynomial is given by:

C. {-3/2, 0,1}

They are the values of x for which F(x) = 0.

In this problem, the polynomial is given by:

F(x) = 2x³ + x² - 3x.

Hence:

2x³ + x² - 3x = 0.

2x(x² + 0.5x - 1.5) = 0.

2x = 0 -> x = 0.

x² + 0.5x - 1.5 = 0 -> (x + 1.5)(x - 1) = 0.

Then, this means that the other two roots are:

Hence the correct option is:

C. {-3/2, 0,1}

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The function, g(x), has a constant rate of change and will increase at a faster rate than the function f(x) for all the values of x.  

Given:

g(x) = 5/2 x -3 ..... (1)

f(x) = - 3.5 at x = 0

So, putting the value of x=0 in equation (1) for comparison. We get,

g(x) at x = 0

=> g(x) = 5/2 x (0) - 3

=> g(x) = -3

In this value of x function g(x) is faster than function f(x) having a value equal to -3.5.

Similarly, put x = 1 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (1) - 3

=> g(x) = (5-6)/2

=> g(x) = -1/2

In this value of x function g(x) is faster than function f(x) having a value equal to -1.

Similarly, put x = 2 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (2) - 3

=> g(x) = (5-3)

=> g(x) = 2

In this value of x function g(x) is faster than function f(x) having a value equal to 1.5.

Similarly, put x = 3 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (3) - 3

=> g(x) = (15/2 - 3)

=> g(x) = 7.5 - 3

=> g(x) = 4.5

In this value of x function g(x) is faster than function f(x) having a value equal to 4.

Therefore, for all values of x function g(x) is faster than function f(x).

function f(x).

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The value of an excel formula that will square this number is,

⇒ N²

We have to given that;

A number is stored in cell a1.

Hence, We can formulate;

Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.

And, We also get;

To display the square of the value in cell A1 into cell B1,

We can type = A1² into cell B1.

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To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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The total distance covered by Zachary is found using Pythagoras Theorem, which is 17.39 miles.

What is Pythagoras Theorem?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

To find the total distance Zachary walked, we need to add up the distance from his home to Ian's house, the distance from Dustin's house back to his home, and the distance they walked through the field. We can use the Pythagorean theorem to find the distance they walked through the field, since they cut directly through it.

Let's call the distance they walked through the field d.

Then we have the equation -

d² = (5 miles)² + (2 miles)²

d² = 25 + 4

d² = 29

d ≈ 5.39 miles

So, Zachary walked a total distance of -

2 miles (from home to Dustin's) + 5 miles (from home to Ian's) + 5.39 miles (through the field) + 5 miles (from Dustin's back home) = 17.39 miles

Therefore, Zachary walked a total distance of approximately 17.39 miles.

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We cannot say that the two events are independent since the probability of eating pizza and sushi together is not known. If the probability of eating both together is 0, then the events are mutually exclusive, and if the probability is greater than 0, then the events are dependent.

We cannot say that the events of Marco eating sushi and pizza are independent. Two events are independent if the occurrence of one does not affect the probability of the other. However, in this case, if Marco eats sushi for dinner, it reduces the probability that he will eat pizza for dinner since he never eats both together.

Similarly, if Marco eats pizza for dinner, it reduces the probability that he will eat sushi for dinner. Therefore, the events are not independent, and the occurrence of one event affects the probability of the other. In other words, the events are dependent.

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An equation for this statement "The sum of seven times a number and 16 is 163," is 7n + 16 = 163.

The solution is 21.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The sum of seven times a number and 16 is 163," we can logically deduce the following algebraic equation;

7n + 16 = 163

7n = 163 - 16

7n = 147

n = 147/7

n = 21.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

170

Step-by-step explanation:

don't know if its right

i calculate it...hope it help a little

The equation that describes the given situation and the number of packs required are; 25x = (17 * 10) and x = 7 packs

We are told that;

Each sticker comes in a pack of 25

Now, she wants to give each of the 17 guests at least 10 stickers.

Let the number of packs she will require be x. Thus, the expression to describe this situation is;

25x = (17 * 10)

x = (17 * 10)/25

x = 6.8 packs

Approximating to a whole number gives us 7 packs of stickers required.

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Answer:

They wanted to spread Christianity. They also hoped to gain new lands and wealth for their countries. Finally, you read about the valuable cargo of New World plants that explorers brought back to Europe.

1. True.

2. False.

3. False.

4. True.

1. True. The probability of a Type I error, denoted by α, is the significance level of a hypothesis test. It represents the probability of rejecting a null hypothesis when it is actually true. In other words, it is the probability of falsely concluding that there is a significant effect or relationship.

2. False. The p-value of a test is not the smallest α for which the null hypothesis can be rejected. The p-value is the probability of obtaining the observed data, or more extreme results, assuming that the null hypothesis is true. It is compared to the significance level (α) to make a decision regarding the rejection or acceptance of the null hypothesis.

3. False. Rejecting the null hypothesis does not necessarily mean that the alternative hypothesis is true. It indicates that there is enough statistical evidence to suggest that the null hypothesis is unlikely, but it does not provide direct evidence for the alternative hypothesis. Additional analysis and evidence are required to draw conclusions about the alternative hypothesis.

4. True. Increasing the probability of a Type I error (α) generally leads to a decrease in the probability of a Type II error (β). These two types of errors are inversely related. By setting a higher significance level (α) and making it easier to reject the null hypothesis, the chances of accepting the alternative hypothesis when it is true increase. Consequently, the likelihood of failing to reject the null hypothesis when it is false (Type II error) decreases. However, it is important to note that there is a trade-off between Type I and Type II errors, and adjusting the significance level should be done cautiously, considering the specific context and consequences of each type of error.

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