solve the system by elimination​

The standard deviation of the sampling distribution of sample means, when creating samples of the amounts of weight lost by 82 people on the latest fad diet, would be approximately 0.54 pounds.

The standard deviation of the sampling distribution of sample means can be calculated using the formula: standard deviation of the sampling distribution = standard deviation of the population / square root of the sample size.

In this case, the standard deviation of the population is given as 4.9 pounds, and the sample size is 82. Therefore, the standard deviation of the sampling distribution of sample means can be calculated as follows:

Standard deviation of the sampling distribution = 4.9 / √82 ≈ 0.541 pounds (rounded to two decimal places).

So, the standard deviation of the sampling distribution of sample means would be approximately 0.54 pounds.

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Answer:

4.5732 %

Step-by-step explanation:

Answer: slope is -4  y intercept is (0,-8)

Step-by-step explanation: you have to use the slope intercept form y = mx + b to find the slope and y intercept

If the family’s monthly income is $3,286, Wren family budgets for entertainment each month is $328.60.

Income, which is typically stated in the monetary terms, is the spending and saving opportunity acquired by an entity within a given duration. Conceptually, income is hard to define, and different fields may have the distinct definitions. For instance, a person's income may differ from their income as defined by law and in an economic sense.

Haig-Simons income, which defines income as Consumption + Change in Net Worth and is commonly applied in economics, is a very significant definition of income.

Income is a total that includes any wages, salaries, profits, interest payments, rent, or other forms of earnings received in a calendar year for families and individuals in the United States, as defined by tax law. Gross income less taxes and other deductions (such as required pension payments) is a common definition of discretionary income and is frequently used as a benchmark to assess the wellbeing of taxpayers.

The idea may include the accumulation of both monetary and non-monetary consumption capacity, with the former (monetary) serving as a stand-in for total income in the field of public economics.

Gross income for a business is the total revenue less the cost of items sold. Costs are subtracted from revenue by cost of goods sold, expenses, depreciation, interest, and taxes to arrive at net income.

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To find the critical numbers of the function f(x) = x^3e^(-9x), we need to find the values of x where the derivative of the function is equal to zero or does not exist. These values correspond to the relative maxima, minima, or inflection points of the function.

To find the derivative of the function, we can use the product rule and the chain rule of differentiation. The derivative of f(x) is given by:

f'(x) = 3x^2e^(-9x) - 9x^3e^(-9x)

To find the critical numbers, we need to set f'(x) equal to zero and solve for x:

3x^2e^(-9x) - 9x^3e^(-9x) = 0

Factorizing out e^(-9x), we get:

3x^2 - 9x^3 = 0

Simplifying further, we get:

x^2(3 - 9x) = 0

Thus, the critical numbers of the function are x = 0 and x = 1/3. At x = 0, the function has a relative minimum, while at x = 1/3, the function has a relative maximum. To determine the nature of these critical points, we can use the second derivative test or examine the sign of the derivative in the intervals around the critical points.

Overall, finding the critical numbers of a function is an important step in analyzing its behavior and determining its extrema or points of inflection. By setting the derivative equal to zero and solving for x, we can identify the critical points and then use additional tests or analysis to determine their nature and significance.

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Answer:

let the number be x.

hope it helps

Answer:

The lines beside the -3 on the left invert the negative/positive.

Step-by-step explanation:

See answer

Hence, the distance between Hawkes Meadow and Brunswick Street is roughly 11.1 kilometres (km).

Distance is a unit used to express the distances between two objects or positions. This is a scalar value that is typically stated in length units like feet, metres, kilometres, or miles. Distance between two things is a physical concept that specifies their separation; it is frequently used to estimate how much space there is between them. The shortest distance, also referred to as "as the crow flies," can be calculated either along a horizontal path or a curved path. Displacement, or the shift in an object's position from its original location to its end position, is a notion in physics that is closely connected to distance.

given

Using the data from the timetable and the calculation, we can determine how many kilometres the bus travels between Hawkes Meadow and Brunswick Street:

Distance is determined by multiplying time and speed.

According to the timetable, the bus travels from Hawkes Meadow to Othello Avenue in 15 minutes (from 14:25 to 14:32), and from Othello Avenue to Brunswick Street in 8 more minutes (i.e., from 14:32 to 14:40). Hence, it takes 15 + 8 = 23 minutes to get from Hawkes Meadow to Brunswick Street.

Also, we are informed that the bus travels at an average speed of 29 km/h between Hawkes Meadow and Brunswick Street.

To utilise the calculation, we must first divide the time in minutes by 60 to convert it to hours:

23, divided by 60 hours, or 0.3833 hours (rounded to 4 decimal places)

Hence, we can compute the distance using the following formula:

11.12 kilometres is equal to 29 km/h times 0.3833 hours (rounded to 2 decimal places)

Hence, the distance between Hawkes Meadow and Brunswick Street is roughly 11.1 kilometres (km).

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The algebraic expression that can be represented by the statement is -5x/2 = 10

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

The negation of the product of five times a number divided by two is ten

Represent the variable with y

So, we have the following representation

The negation of the product of five times x divided by two is ten

Express the product as an actual product

So, we have the following representation

The negation of 5x divided by two is ten

Express the quotient as an actual quotient

So, we have the following representation

The negation of the 5x/2 is ten

Lastly, we have

-5x/2 = 10

Hence, the expression is -5x/2 = 10

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A custom numbering format created at the "Define New Number Format" dialog box is automatically included in the "Numbering Library" section of the numbering button drop-down gallery.

The "Numbering Library" section of the numbering button drop-down gallery is where predefined and custom numbering formats are stored. When you create a custom numbering format using the "Define New Number Format" dialog box in a software application like Microsoft Word or Excel, the format is automatically added to the "Numbering Library" section.

This allows you to easily access and apply your custom numbering format in future documents or projects. By clicking on the numbering button drop-down gallery, you can select your custom numbering format from the "Numbering Library" section and apply it to your content.

The inclusion of custom numbering formats in the "Numbering Library" section provides a convenient and organized way to manage and reuse your custom formats, ensuring consistency and efficiency in your document formatting.

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The number of positive integers from 1 to 2000 that are multiples of 20 or 25 is 180.

To count the number of positive integers from 1 to 2000 that are multiples of 20 or 25 using the inclusion-exclusion principle, we need to consider the individual counts of multiples of 20 and multiples of 25 and then subtract the count of multiples of both 20 and 25 to avoid double-counting.

Multiples of 20:

The largest multiple of 20 less than or equal to 2000 is 2000.

The count of multiples of 20 from 1 to 2000 is given by 2000 / 20 = 100.

Multiples of 25:

The largest multiple of 25 less than or equal to 2000 is 2000.

The count of multiples of 25 from 1 to 2000 is given by 2000 / 25 = 80.

Multiples of both 20 and 25 (common multiples):

To determine the count of multiples of both 20 and 25, we need to find the least common multiple (LCM) of 20 and 25, which is 100.

The count of multiples of 100 from 1 to 2000 is given by 2000 / 100 = 20.

Now, using the inclusion-exclusion principle, we can calculate the total count:

Total count = Count of multiples of 20 + Count of multiples of 25 - Count of multiples of both 20 and 25

= 100 + 80 - 20

= 180.

Therefore, the number of positive integers from 1 to 2000 that are multiples of 20 or 25 is 180.

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The number of jobs that he could he do if the cost was $four thousand, one hundred twenty five will be 25.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

When a man does job at the rate of $165 per job, the number of jobs that he could he do if the cost was $four thousand, one hundred twenty five will be:

= Amount / Rate

= $4125 / $165

= 25

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A man does job at the rate of $165 per job. How many jobs could he do if the cost was $four thousand, one hundred twenty five?

The simplified expression is -4mv.

We have,

To simplify the expression:

-20(m²v)(-v³) / 5(-v²)(-m^4)

We can first cancel out common factors in the numerator and denominator.

-20(m²v)(-v³) / 5(-v²)(-m^4)

= -4m²v² / vm²

Next, we can simplify further by canceling out a factor of v in the numerator and denominator:

-4m²v² / vm² = -4mv

Therefore,

The simplified expression is -4mv.

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If the constraint Q1 + Q2 ≥ 30 is relaxed by one unit, the total cost will increase by λ = 4.

The given objective function is TC=4Q1²+5Q2²−Q1Q2, which we need to minimize subject to the constraint Q1+Q2≥30 using the Lagrangian method. Let's begin the Lagrangian method solution as follows;

L(Q1,Q2,λ)= TC + λ(30 - Q1 - Q2)

Where λ is the Lagrange multiplier

1: Calculate the partial derivatives of L with respect to Q1, Q2, and λ and set them equal to zero

∂L/∂Q1 = 8Q1 - Q2 - λ = 0 .......(1)

∂L/∂Q2 = 10Q2 - Q1 - λ = 0 .......(2)

∂L/∂λ = 30 - Q1 - Q2 = 0 .......(3)

2: Solve the above three equations for Q1, Q2, and λ using the elimination method. Eliminate λ by adding equations (1) and (2). Then substitute this λ value in the third equation. Simplify the equation and solve for Q1 and Q2.

Q1 = 6 and Q2 = 24

λ = 4

The optimal values of Q1 and Q2 are 6 and 24 respectively. The value of lambda is 4.

The value of λ represents the marginal cost of relaxing the constraint by one unit. Intuitively, lambda represents the shadow price of the constraint, i.e., the amount by which the objective function value will increase if the constraint is relaxed by one unit.

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The antiderivative of the function f(x) = e^(-x) - e^(4x) is given by -e^(-x) - (1/4)e^(4x)/4 + C, where C is the constant of integration. This represents the general solution to the indefinite integral of the function.

In simpler terms, the antiderivative of e^(-x) is -e^(-x), and the antiderivative of e^(4x) is (1/4)e^(4x)/4. By subtracting the antiderivative of e^(4x) from the antiderivative of e^(-x), we obtain the antiderivative of the given function.

To evaluate a definite integral of this function over a specific interval, we need to know the limits of integration. The indefinite integral provides a general formula for finding the antiderivative, but it does not give a specific numerical result without the limits of integration.

To compute the antiderivative of the function f(x) = e^(-x) - e^(4x), we can use basic integration formulas.

∫(e^(-x) - e^(4x))dx

Using the power rule of integration, the antiderivative of e^(-x) with respect to x is -e^(-x). For e^(4x), the antiderivative is (1/4)e^(4x) divided by the derivative of 4x, which is 4.

So, we have:

∫(e^(-x) - e^(4x))dx = -e^(-x) - (1/4)e^(4x) / 4 + C

where C is the constant of integration.

This gives us the indefinite integral of the function f(x) = e^(-x) - e^(4x).

If we want to compute the definite integral of f(x) over a specific interval, we need the limits of integration. Without the limits, we can only find the indefinite integral as shown above.

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Answer:

What you need to do is to find a multiple of 20 and 16 in other words a number that can multiply into 20 and 16. You have 2 and you have 4. So now this is how it looks like.

Either:

4(5+4) Or

2(10+8)

Step-by-step explanation:

Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Answer:

the answer is 6 u welcome

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Explanation:

The x intercepts (aka roots) are where the graph crosses or touches the x axis. These locations directly correspond to help set up the factors.

The root x = -6 shows that x+6 is a factor.

Effectively, we add 6 to both sides so that we go from x = -6 to x+6 = 0.

Answer:

20 foot.....................

Answer: 30

Step-by-step explanation:

1. You find the slope by picking 2 points and dividing the change in the y-axis by the change in the x-axis. (Time is ALWAYS x)

(50-40)/40-20

(10)/20)

1/2

SLOPE=1/2

2. You find the y-intercept by picking a point, and plugging them into your equation, and solving for b.

(I will be using the point (20,40) )

40=1/2(20)+b

40=10+b

b=30

Y-INTERCEPT=30

To compute the limit of the sequence bn = (n)^(5.6/n), we can use the fact that if a sequence cn has a limit k, then the sequence e^(cn) has a limit e^k. Additionally, we can apply L'Hôpital's rule to evaluate the limit.

Taking the natural logarithm of bn, we have:

ln(bn) = ln[(n)^(5.6/n)]

Using the property of logarithms, we can rewrite this expression as:

ln(bn) = (5.6/n) * ln(n)

Now, we can apply L'Hôpital's rule by taking the derivative of the numerator and denominator with respect to n:

ln(bn) = (5.6/n) * ln(n) = (5.6 * ln(n))/n

Applying L'Hôpital's rule once again, we differentiate the numerator and denominator:

ln(bn) = (5.6 * ln(n))/n = (5.6/n^2)

Now, we can take the exponential of both sides to find the limit of the sequence:

e^(ln(bn)) = e^((5.6/n^2))

bn = e^(5.6/n^2)

As n approaches infinity, the term 5.6/n^2 approaches 0, and therefore the limit of the sequence bn is e^0, which is equal to 1.

Hence, the limit of the sequence bn = (n)^(5.6/n) is 1.

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Answer:

There are 8 legs for every 4 ears.

There are 2 legs for every 1 ear.

Step-by-step explanation:

The pig and the mouse have a total of 4 ears.

We can count to see that there are 8 legs for every 4 ears.

We want to find a ratio of legs to ears that is equivalent to 8:4

1. The probability a randomly selected pregnancy is more than 265 days in length is 0.5793.

2. The length of pregnancy that separates the shortest and longest 10% from the rest is (247.4, 288.6).3.

3. The probability of pregnancy that lasts less than or equal to 290 days is 0.9292.

1. The probability a randomly selected pregnancy is more than 265 days in length The length of pregnancy follows a normal distribution with mean, μ = 268 days and standard deviation, σ = 15 days.The probability of pregnancy more than 265 days is:

P(X > 265)P(Z > (265 - 268) / 15)P(Z > -0.2) = 0.5793

2. The length of pregnancy that separates the shortest and longest 10% from the rest The length of pregnancy follows a normal distribution with mean, μ = 268 days and standard deviation, σ = 15 days.We need to find the length of pregnancy that separates the shortest and longest 10% from the rest.The length of pregnancy that separates the lowest 10% from the rest is the first decile.

The first decile is given by:

x1 = μ - 1.28σ x 1 = 268 - 1.28 (15) x 1 = 247.4 days

The length of pregnancy that separates the longest 10% from the rest is the ninth decile.The ninth decile is given by:

x9 = μ + 1.28σ x 9 = 268 + 1.28 (15) x 9 = 288.6 days

Yes, it would be unusual to select a pregnancy that lasts longer than 290 days. We can see from the calculation below:

P(X > 290)P(Z > (290 - 268) / 15)P(Z > 1.47) = 0.0708

The probability of pregnancy that lasts longer than 290 days is 0.0708.The probability of pregnancy that lasts less than or equal to 290 days is:

P(X ≤ 290) = 1 - P(X > 290) = 1 - 0.0708 = 0.9292

We know that if the probability of any event is less than 0.05 or 5%, it is considered unusual. As the probability of pregnancy that lasts longer than 290 days is only 0.0708, which is less than 0.05 or 5%, it is considered unusual. Hence, it is unusual to select a pregnancy that lasts longer than 290 days.

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Answer:

m=\(\frac{-1}{3}\)

Step-by-step explanation: