URGENT PLEASE HELP !!

If workers note that for every "3 m" of rope pulled down-ward, the piano rises 0.3 m, then we have shown that 700 N is required force to lift the motorcycle.

The term "Mechanical advantage" (MA) is defined as ratio of "output-force" to "input-force" in a machine.

In this case, the output force is the weight of the motorcycle (7000 N) and the input force is the force applied to pull the rope downward.

We use the formula for mechanical advantage in a pulley system, which is given by:

⇒ MA = (distance moved by the effort) / (distance moved by the load),

In this case, the distance moved by the effort is 3 m, and

The distance moved by the load is 0.3 m,

Substituting the values,

We get,

⇒ MA = 3/0.3,

⇒ MA = 10,

So, mechanical advantage of "pulley-system" is 10.

Now, we use mechanical advantage to calculate the required force to lift the motorcycle.

Since mechanical advantage is defined as the ratio of output force to input force, we can rearrange the formula as:

⇒ Input force = (Output force)/(Mechanical advantage),

Substituting values for "output-force" as 7000 N and "mechanical-advantage" as 10,

We get,

⇒ Input force = 7000/10,

⇒ 700 N,

Therefore, the required force to lift motorcycle is 700 N.

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The density of a sample of an unknown substance with a mass of 6 grams and a volume of 12 cm³ is 0.5 grams.

Density is a fundamental physical property that measures the amount of matter (mass) packed into a particular space (volume). The mathematical definition of density is simply the mass of an object divided by its volume. Density is typically measured in units of mass per unit volume, such as grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). One crucial aspect of density is that it is an intrinsic property of a substance, meaning it is a characteristic that depends solely on the material and is not affected by the amount of the substance. By using density, we can identify the material a particular object is made of. For example, a piece of gold will have a higher density than a piece of silver because gold is a more dense metal. Additionally, the density of an object can be used to determine its buoyancy in a fluid. Objects with a higher density will sink in a fluid with a lower density, while objects with a lower density will float.

Density is defined as the amount of mass per unit of volume. Mathematically, it can be represented as:

Density = Mass/Volume

Substituting the given values, we get:

Density = 6 grams/12 cm³

Density = 0.5 grams/cm³

Therefore, the density of the sample is 0.5 grams/cm³.

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Therefore , the solution of the given problem of equation comes out to be 2.61, -6.61 is the answer's numerical component.

Regression modelling uses the polynomial solution, which is x = ax2 + b + c=0, to solve problems with a single variable. The First Principle of Algebra states that there can only be one solution because it contains an additional order. There are both simple and complex solutions available. As the name suggests, a "non-linear algorithm" comprises four variables.

Here,

The equation y = x² + 4x - 12 has a parabola as its graph. To graph the solution to the equation x² + 4x = 12,

Rewrite the equation in the following format: y = x² + 4x - 12

Locate the x-values where the graph and x-axis overlap.

These x-values, which stand in for the equation's solutions, are those when y = 0.

Read off the graph's x-values and write them down as the equation's answers.

The solutions to the equation x² + 4x = 12 are about x = 2.61

and x = -6.61 (rounded to two decimal places), according to the graph of the equation y = x² + 4x - 12.

As a result, "2.61, -6.61" is the answer's numerical component.

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Answer:

40.50 + 5g < 60.00

5g < 19.50

g < 3.9 gigabytes

Answer:

A = 40 in²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the height between the bases b₁ and b₂

here h = 8 , b₁ = 4 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 8 × (4 + 6)

   = 4 × 10

   = 40 in²

We have confirmed that the sum of the series is 28/3. Therefore, the correct answer is option (b) 28/3.

A geometric series is a series of numbers where each term is a fixed multiple of the preceding term. Specifically, a geometric series has the form:

a+ar+ar²+ar³+.....

The given series is a geometric series with first term (a) = 14 and common ratio (r) = -1/2.

Consider sum of series be S, So-

S = a/(1 - r) = 14/(1 - (-1/2)) = 28/3

To see why this is the correct answer, we can also write out the first few terms of the series:

14-7+7/2-7/4+7/8-.....

It is evident that each term is produced by multiplying the one before it by -1/2.

So, the second term is obtained by multiplying the first term by -1/2, the third term is obtained by multiplying the second term by -1/2, and so on.

We can also notice that the sum of the first two terms is 7, the sum of the first three terms is 21/2, and the sum of the first four terms is 28/3. This suggests that the sum of the first n terms of the series might be given by the formula Sn = a(1 - rⁿ)/(1 - r).

We can verify that this is true by using the formula to find the sum of the first four terms:

S4 = 14(1 - (-1/2)⁴)/(1 - (-1/2)) = 28/3

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The value of 'x' evaluated on the basis of angle sum property is 31 & arranged length of sides of given triangle ΔEBD from longest to shortest is DE > BD > BE

What is a triangle?

A triangle is a three-sided polygon with three vertices that is constructed using segments of straight lines. The triangle's angles are created by connecting the three line segments that make up its sides end to end at a single point. Angle sum attribute states that the sum of the triangle's three angles is 180 degrees. Triangle inequality asserts that the third side is greater than or equal to the sum of any two triangle sides.

Given that

∠ABC=(4x)°

∠BED=(5+x)°

∠BDF=160°

a)Find 'x'

consider ΔBED,

∠ABC=∠EBD {vertically opposite angles}

∴∠EBD=(4x)°

∠BDF+∠BDE=180° {angles on straight line}

∠BDE=180-160

∠BDE=20°

We know that ∠EBD+∠BDE+∠DEB=180° {angle sum property}

4x + 20 + (5+x)=180°

4x + 20 + 5 + x = 180°

5x + 25 = 180°

5x = 180 - 25

5x = 155

x = 31

b)Arrangement of sides from the longest to the shortest:

Based on the value of 'x', the angles of triangle ΔEBD:

∠EBD=4x=4 . 31 = 124°

∠BED=5 + x= 5 + 31 = 36°

∠BDE=20°

We know that the side opposite to the larger angle is the longest and that of the  least angle is the shortest.

∴Side opposite to the largest angle ∠EBD=124° is DE

side opposite to the least angle ∠BDE=20° is BE

∴Descending order of sides of ΔEBD is DE > BD > BE

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The equation to model the situation given in the question is (x+3)(x+6) = 148.

Let's assume that the original length and width of the square flower garden were "x". When Harrison expanded the garden, the new length became "x+3" and the new width became "x+6".

The area of a rectangle is given by the formula A = L × W, where A is the area, L is the length, and W is the width. Therefore, the area of the expanded rectangular flower garden is:

A = (x+3)(x+6)

We know that the area of the expanded rectangular flower garden is 148 square feet. So we can set up an equation:

(x+3)(x+6) = 148

{When we solve this equation using the quadratic formula we get x values:

x ≈ 8.2 and x ≈ -17.2 but we know x is the side of the garden so it cannot be negative, therefore, x = 8.2 unit}

This is the equation that models the situation described in the problem.

Therefore, the equation to model this situation is (x+3)(x+6) = 148.

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Therefore , the solution of the given problem of expressions comes out to be 4xy³ is the fourth term in the binomial expansion of (x - y)⁴.

Instead of using random estimates, shifting equation numbers should be employed instead, which could be growing, reducing, or blocking. They could only help one another by exchanging resources like tools, knowledge, or solutions to issues. The arguments, components, or quantitative statements for strategies like more debate, fabrication, and blending may be included in the explanation of the reality equation.

Here,

The expansion of (x + y)ⁿ is provided by the following for any positive integer n, according to the binomial theorem:

=>  (x + y)ⁿ = nC0 * xⁿ * y⁰ + nC1 * xⁿ⁻¹ * y¹+ nC2 * xⁿ⁻² * y² + ... + nCr * xⁿ⁻ˣ * yˣ + ... + nCn * x⁰ * yⁿ

where nCr stands for the "n choose r" or binomial coefficient, which is defined as:

=> nCr = n! / (r! * (n - r)!)

Since the term with r = 4 would be the final term in the expansion, the term with r = 3 must be taken into consideration in order to find the fourth term in the binomial expansion of (x - y)⁴.

The fourth term in the expansion of (x - y)4 using the binomial theorem is:

=> 4C3 * x⁴⁻³ * y³ = 4 * x * y³

As a result, 4xy³ is the fourth term in the binomial expansion of (x - y)⁴.

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Step-by-step explanation:

this is to calculate the area of a rectangle. you really need help with that ?

the area is

8 × 22 = 176 ft²

the wallpaper costs $3 per ft².

so, the total costs will be

176 × 3 = $528.-

The wallpaper will cost Jacob $528 to cover his entire wall.

This is a simple mathematics problem that can be solved using mensuration.

Firstly we need to find the area of the wall. Since the wall is rectangular in shape, we will use the formula of the area of a rectangle to find the area of the wall.

Area of the wall (rectangle) = length x breadth

Area of the wall (rectangle) = 22 x 8

Area of the wall (rectangle) = 176 square feet

Now we have been given that the rate per square foot of wallpaper is $3. So we need to multiply the area of the wall by the rate per square foot of the wallpaper to get our answer.

Cost of wallpaper = Area of wall x Rate per square foot of wallpaper

Cost of wallpaper = 176 x 3

Cost of wallpaper = 528

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Answer:  7/24 ≅ 0.2916667

Step-by-step explanation: QUICK MATH

Answer: False

Step-by-step explanation:

1/7 x 1/7 = 1/49 x 1/7 = 1/343

The answer is D. 5+3 > 5, 3+5 > 5, 5+5 > 3 the first two sides satisfy the triangle inequality theorem, but the third side does not.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side.

Let's check if each set of side lengths satisfies this theorem:

A. 3 in., 4in., 5 in

3+4 > 5, 4+5 > 3, 3+5 > 4

These side lengths satisfy the triangle inequality theorem.

B. 6 in., 9in., 5in.

6+9 > 5, 9+5 > 6, 6+5 > 9

These side lengths satisfy the triangle inequality theorem.

C. 7 in., 9 in., 10 in.

7+9 > 10, 9+10 > 7, 7+10 > 9

These side lengths satisfy the triangle inequality theorem.

D. 5 in., 3 in., 5 in.

5+3 > 5, 3+5 > 5, 5+5 > 3

The first two sides satisfy the triangle inequality theorem, but the third side does not. Therefore, this set of side lengths could not be the lengths of a triangle.

Therefore, the answer is D.

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a. The distribution of x1 x2 is z1z2 ~ Cauchy(0,1). (b) The probability that x1 x2 is greater than 16 is 0.1056. (c) The distribution of 3x1 + 2x2 + x3, is given as N(38, 29).

A probability density function (PDF) expresses the likelihood that a continuous random variable will take a specified value or fall within a predetermined range of values. It is a derivative of the cumulative distribution function (CDF), which is the likelihood that a random variable will have a value that is less than or equal to a certain value.

The CDF is a function that converts every potential value of the random variable to a probability between 0 and 1, and it is defined for both discrete and continuous random variables.

a. Covert the x1 and x3 into standard normal variables by subtracting their means and dividing by their standard deviations:

z1 = (x1 - 4) / 2 ~ N(0,1)

z2 = (x2 - 8) / 3 ~ N(0,1)

The product is thus:

z1z2 ~ Cauchy(0,1)

b. The probability that x1 x2 is greater than 16:

Y / z1 ~ Cauchy(0,1)

Now,

z1 = Y / (z1z2) ~ Cauchy(0,1)

Here, the probability that x1 x2 > 16 is:

P(x1 x2 > 16) = P(Y / z1 > 16 / z1) = P(z1 < -Y / 16) + P(z1 > Y / 16)

= 2 * P(z1 < -Y / 16)

Substituting the value of z1 and Y we have:

P(x1 x2 > 16) = 2 * P(z1 < -16z1z2 / (9)) = 2 * Φ(-16z2 / 3) ≈ 0.1056

Hence, the probability that x1 x2 is greater than 16 is 0.1056.

c) The distribution of 3x1 + 2x2 + x3, is given as:

[tex]3x1 + 2x2 + x3 \~ N(34 + 28 + 12, 3^22^2 + 2^23^2 + 4^2) = N(38, 29)[/tex]

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As the number of degrees of freedom become large, the t distribution actually approaches the normal distribution, not

the binomial distribution. The correct answer is false.

The t distribution is used when the sample size is small and the population standard deviation is unknown, while the

binomial distribution is used for discrete data where there are only two possible outcomes.

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of

independent trials with a constant probability of success, whereas the t distribution is a continuous probability

distribution that models the variability of sample means from a normal population.

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Step-by-step explanation:

Its the third one

Because in the bracket

so that's your answer

The surface area of the pyramid is 44.2 square inches, which is closest to option (C) 44.2.

To solve the problem, we can start by using the formula for the area of an equilateral triangle to find the length of one side of the base. Let s be the length of one side of the base, then we have:

Area of the base = (sqrt(3)/4) * s^2 = 13

Solving for s, we get:

s^2 = (4 * 13) / sqrt(3)

s = 8.0

Therefore, the perimeter of the base is 3 * s = 24 inches

Next, we can use the formula for the surface area of a pyramid to find the surface area of the entire pyramid. Let B be the area of the base, then we have:

Surface area = B + (1/2) * P * h

where P is the perimeter of the base and h is the height of the pyramid.

Substituting the given values, we get:

Surface area = 13 + (1/2) * 4.8 * 13

Surface area = 13 + 31.2

Surface area = 44.2 square inches

Therefore, the surface area of the pyramid is 44.2 square inches, which is closest to option (C) 44.2.

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In the equation, y=β_0+β_1 x_1+β_2 x_2+u, β_2 is a(n) slope parameter. Option B is the correct answer.

In the given equation, y is the dependent variable, x1, and x2 are independent variables, β0 is the intercept parameter, β1 is the slope parameter for x1, β2 is the slope parameter for x2, and u is the error term. Therefore, β2 represents the effect or impact of the independent variable x2 on the dependent variable y, holding other independent variables constant.

Understanding the role and significance of each parameter is essential for interpreting the results of statistical models and drawing meaningful conclusions from the data.

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The question is -

In the equation, y=β_0+β_1 x_1+β_2 x_2+u, β_2 is a(n) _____.

a. independent variable

b. dependent variable

c. slope parameter

d. intercept parameter

Therefore, gross pay will be deducted for the Social Security tax. The answer is option B, $97.22.

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". For example, if you say "20%", it means 20 out of 100, or 0.2 as a decimal.

Percentages are commonly used in many areas, such as finance, statistics, and everyday life. They can be used to represent changes in value over time, compare different values, and calculate discounts or interest rates.

To calculate a percentage, you can divide the part (the value you want to express as a percentage) by the whole (the total value) and then multiply the result by 100. For example, if you want to find out what percentage of 50 is 20, you will do:

20 ÷ 50 × 100 = 40%

So, 20 is 40% of 50.

To calculate the amount of Tim's gross pay that will be deducted for the Social Security tax, we need to multiply his gross pay by the percentage of the tax.

6.2% of $1568 can be calculated as:

(6.2/100) * $1568 = $97.216

Rounding to the nearest cent, we get $97.22 as the amount of Tim's gross pay that will be deducted for the Social Security tax.

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The probability that the golfer will hit at least 6 times in his next 10 attempts is A. 20 %

To estimate the probability of the golfer hitting at least 6 times in his next 10 attempts using a table of random numbers, we can perform a simulation.

Let's use the given table of random numbers to simulate 10 attempts for each trial. We can consider each pair of digits as one attempt. We will perform 10 trials and count how many times the golfer hits at least 6 times in 10 attempts.

Now count the number of trials with at least 6 hits:

Trial 2, Trial 5, and Trial 9 have at least 6 hits. That's 3 out of 10 trials.

To estimate the probability, divide the number of successful trials (at least 6 hits) by the total number of trials:

Probability = (Number of successful trials) / (Total number of trials)

Probability = 3 / 10 = 0.3

The estimated probability that the golfer will hit at least 6 times in his next 10 attempts is 30%. There is no exact match among the possible answers, but the closest one is 20%.

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One plate costs $3.20, and one cup costs $1.30.

Let's use the letters "p" and "c" to stand for the price of a plate and a cup, respectively.

We can infer the following from the first piece of knowledge:

5p + 4c = 21.20

We learn the following from the second piece of information:

6p + 5c = 25.70

These two equations can be used to find the values of p and c.

Here's one approach:

Let's start by removing one of the variables from the equations by multiplying them by integers that will make this possible.

The first equation can be multiplied by 5 and the second equation by -4 to achieve this:

25p + 20c = 106

-24p - 20c = -102.80

The "c" variable is removed by combining these two equations:

p = 3.20

Knowing the price of a single plate, we can:

We can use one of the initial equations to find the price of a cup now that we know the price of a plate.

Let's employ the first equation:

5p + 4c = 21.20

When we replace p with our value, we obtain:

5(3.20) + 4c = 21.20

Simplifying:

16 + 4c = 21.20

4c = 5.20

c = 1.30.

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The center-radius form equation and the key features are listed below

The first equation, x^2 + y^2 - 9 = 0, is already in center-radius form, where the center is (0, 0) and the radius is 3.

The domain and range of this equation are:

Domain: -3 ≤ x ≤ 3

Range: -3 ≤ y ≤ 3

For the second equation, we can simplify it by completing the square:

x^2 - 10x + y^2 + 9 = 0

(x^2 - 10x + 25) + y^2 = 16

(x - 5)^2 + y^2 = 4^2

This equation is now in center-radius form, where the center is (5, 0) and the radius is 4.

The domain and range of this equation are:

Domain: 1 ≤ x ≤ 9

Range: -4 ≤ y ≤ 4

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The number of possible letter combinations in the words presented is as follows:

CANNON: 2520

BANANA: 120

TOMORROW: 2520

REFERENCE: 20160

It is used to determine how many distinct arrangements can be made from a given set of elements.

1) CANNON: CANNON is made up of seven letters, two of which are identical 'N's. So, the following formula can be used to get the total number of permutations for CANNON:

Total number of permutations = 7! / 2!

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 2520

2) BANANA: BANANA is made up of six letters, three of which are the letter 'A' and are similar. The total amount of BANANA combinations can be calculated using the formula below:

Total number of permutations = 6! / 3!

= (6 x 5 x 4 x 3 x 2 x 1) / 3!

= 120

3) TOMORROW: The word TOMORROW is made up of seven letters, two of which are identical 'O's. Thus, the sum of TOMORROW's permutations can be determined as follows:

Total number of permutations = 7! / 2!

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 2520

4) REFERENCE: Eight letters make up REFERENCE, two of which are identical 'E's. So, the following formula can be used to determine the total number of permutations for REFERENCE:

Total number of permutations = 8! / 2!

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 20160

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The area of the rectangle is 104 m², area of the triangle is 15 m², and area of the shaded region is equal to 74 m².

The shaded region is the remaining area in the rectangle which is outside the triangle, so it is derived by subtracting the area of the triangle from the area of the rectangle as follows:

area of the rectangle = 13 m × 8 m

area of the rectangle = 104 m²

area of the triangle = 1/2 × 5 m × 6 m

area of the triangle = 15 m²

area of the shaded region = 104 m² - 15 m²

area of the shaded region = 89 m²

Therefore, the area of the rectangle is 104 m², area of the triangle is 15 m², and area of the shaded region is equal to 74 m².

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Answer:

The two data sets that have equal standard deviations are:

Data set A: 40, 50, 60, 60, 70, 80

Data set C: 50, 55, 60, 65, 70

To see this, we can calculate the standard deviation for each data set using a formula or a calculator. Alternatively, we can observe that data sets A and C have similar ranges and distributions, which suggests that they may have similar standard deviations. In contrast, data sets B and D have different ranges and distributions, which suggests that their standard deviations may be different.

The probability that Sam catches a bluegill, then a carp is 1/40.

The probability of catching a bluegill on the first try is 3/16, since there are 3 bluegills in the pond out of a total of 16 fish. Once Sam releases the first fish, there are 15 fish left, and 2 of them are carp. Therefore, the probability of catching a carp on the second try is 2/15.

To find the probability of both events occurring together (catching a bluegill and then a carp), we need to multiply the probabilities of each event. So the probability of catching a bluegill, then a carp is

P(bluegill and then carp) = P(bluegill) x P(carp | bluegill not caught)

We use "bluegill not caught" in the second event to indicate that the pond has one less fish after the first event, and we can't assume that the first fish is still in the pond.

P(bluegill and then carp) = (3/16) x (2/15)

P(bluegill and then carp) = 1/40

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Answer:

(6, 8)

Step-by-step explanation:

A dilation scales an object on the coordinate plane using the scale factor, causing it to get bigger or smaller.

We are given that the point (3, 4) is dilated by 2; since 2 is greater than 1, this is an enlargement (in which the figure gets bigger).

So, all we need to do is multiply each of the coordinates by 2, like so:

[tex]3*2=6\\4*2=8[/tex]

Thus, the image of the point (3, 4), after being dilated by 2, is (6, 8).

A) The expected value of the sampling distribution is 0.40.

B) The standard error is 0.05.

C) The sampling distribution will be centered around the population proportion of 0.40, with a spread given by the standard error of 0.05.

D) By examining the sampling distribution, we can see how likely it is to obtain a certain sample proportion by chance alone, and therefore make conclusions about the population based on the sample.

A) The expected value (also called the mean) of a sampling distribution is equal to the population parameter being estimated. In this case, the population parameter is the proportion, p, which is 0.40.

B) The standard error is the standard deviation of the sampling distribution. For a proportion, the formula for the standard error is √((p(1-p))/n), where p is the population proportion and n is the sample size. Plugging in the values given, we get √((0.40(1-0.40))/100) = 0.049.

C) The sampling distribution of a proportion is approximately normal if both np and n(1-p) are greater than or equal to 10. In this case, np = 1000.40 = 40 and n(1-p) = 100*0.60 = 60, so the conditions for normality are met.

D) The sampling distribution of a proportion shows the distribution of all possible sample proportions of a given size that could be drawn from a population with a known proportion.

The sampling distribution allows us to make inferences about the population proportion, such as constructing confidence intervals or conducting hypothesis tests.

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Complete Question:

A random sample of size 100 is selected from a population with p =0 .40.

A. What is the expected value (to 2 decimals)?

B. What is the standard error (to 2 decimals)?

C. Show the sampling distribution (to 2 decimals).

D. What does the sampling distribution of show?

(a) The concentration of the solution in the tank will be changing over time.

(b) The amount of salt in the tank after 3.5 hours is 63.292 kg.

(c) When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.

(a) To find the concentration of the solution in the tank initially, we can use the formula:

concentration = mass of salt / volume of solution

The mass of salt in the tank initially is 60 kg, and the volume of solution is 2000 liters.

Therefore, the initial concentration is:

concentration = 60 kg / 2000 L

concentration = 0.03 kg/L

However, we know that a solution with a concentration of 0.015 kg/L is entering the tank at a rate of 9 L/min.

Therefore, the concentration of the solution in the tank will be changing over time.

(b) To find the amount of salt in the tank after 3.5 hours, we can use the formula:

amount of salt = initial amount of salt + (concentration of incoming solution - concentration of solution in tank) x rate x time

The initial amount of salt is 60 kg, and the concentration of the incoming solution is 0.015 kg/L.

We need to find the concentration of the solution in the tank after 3.5 hours.

The rate of flow is 9 L/min, so the total volume of solution that has entered the tank after 3.5 hours is:

volume of solution = rate x time

volume of solution = 9 L/min x 210 min

volume of solution = 1890 L

The total volume of solution in the tank after 3.5 hours is:

total volume = initial volume + volume of incoming solution - volume of drained solution

total volume = 2000 L + 9 L/min x 210 min - 9 L/min x 210 min

total volume = 2000 L

Therefore, the concentration of salt in the tank after 3.5 hours is:

amount of salt = 60 kg + (0.015 kg/L - concentration of solution in tank) x 9 L/min x 210 min

amount of salt - 60 kg = (0.015 kg/L - concentration of solution in tank) x 1890 L

concentration of solution in tank = 0.015 kg/L - (amount of salt - 60 kg) / 1890 L

Now we can substitute the concentration of the solution in the tank into the formula and solve for the amount of salt:

amount of salt = 60 kg + (0.015 kg/L - (0.015 kg/L - (amount of salt - 60 kg) / 1890 L)) x 9 L/min x 210 min

amount of salt = 63.292 kg

Therefore, the amount of salt in the tank after 3.5 hours is 63.292 kg.

(c) To find the concentration of salt in the solution in the tank as time approaches infinity, we need to find the concentration that the solution will reach when the inflow and outflow rates of solution are equal.

At this point, the amount of salt in the tank will remain constant.

Let's denote the concentration of salt in the solution in the tank as c.

We know that the volume of solution in the tank remains constant at 2000 L, and that the inflow and outflow rates are both 9 L/min. Therefore, the amount of salt that enters the tank per minute is 0.015 kg/L x 9 L/min = 0.135 kg/min, and the amount of salt that leaves the tank per minute is c x 9 L/min.

When the inflow and outflow rates are equal, the amount of salt in the tank will remain constant.

Therefore, we can set the rate of inflow equal to the rate of outflow and solve for c:

0.015 kg/L x 9.

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