A 350g tub of Irish butter costs 2.80$. Calculate the cost of Irish butter per 100g

Answer:

the answer to this question is b

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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The approximate distance between the two planes is 18 miles.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the calculations based on them. It is used to study the properties of triangles, including the lengths of sides and the measures of angles, and to understand the relationships between angles and circular functions, such as sine, cosine, and tangent. Trigonometry is used in many fields, such as engineering, physics, and navigation, and has many practical applications, such as finding the height of a building or the distance between two points.

To find the distance between the two planes, we can use the law of cosines. The law of cosines states that in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of these lengths and the cosine of the angle between them.

In this problem, we can treat the two planes as the two sides of the triangle and the distance between them as the third side. Let's call the distance between the two planes "d". Then, we have:

d² = 22² + 26² - 2(22)(26)cos(56)

Using the cosine formula and the value of cos(56) from a trigonometry table, we can simplify this expression:

d² = 22² + 26² - 2(22)(26)(0.624)

d² = 484 + 676 - (1352)(0.624)

d² = 1160 - 845.408

d² = 314.592

Taking the square root of both sides:

d = 17.7

Rounding to the nearest whole number, we get:

d = 18 miles

So, the approximate distance between the two planes is 18 miles.

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The value of the investment account after 16 years is $1,254.34.

The final value of the investment account is $1,254.34 after 16 years of earning an annual rate of 6.1%.After 16 years, the value of the investment account can be calculated using the formula: FV = PV × (1 + r)n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. Applying the values, we get:FV = $531 × (1 + 0.061)16FV = $1,254.34 . Thus, the value of the investment account after 16 years is $1,254.34.

Investment accounts are those that also contain cash and other assets like stocks, bonds, funds, and other securities. The value of the assets in an investment account might vary and even go down, which is a significant distinction between one and a bank account.

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Answer:

see details below

Step-by-step explanation:

a) week 1 :  #10" / (#10"+#12") = 509 / 736 =  69% (to nearest percent)

b) week 2 :  #10" / (#10"+#12") = 766 / 1076 = 383/538 = 71% (to nearest percent)

A).69% for week 1

B)71% for week 2

Considering the two similar triangles in the figure,  < K = 60° and < L = 95°. the other angles are

< E = 95°

< F = 60°

< G = 25°

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure since the corresponding angels in a similar triangles are congruent therefore

< K = < F = 60°

< L = < E = 95°

the remaining side is found by

180 - 60 - 95 = < G (sum of angles in a triangle)

< G = 25°

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Answer:

Step-by-step explanation:

Given on the diagram:

PQ is therefore a midsegment

Property of the midsegment:

The symmetric equations for the line passing through the point (4, -4, 9) and parallel to the vector (-1, 2, -3) are:

x = 4 - t

y = -4 + 2t

z = 9 - 3t

To find the symmetric equations for a line, we need a point on the line and a direction vector parallel to the line.

Given that the line is parallel to the vector (-1, 2, -3), we can write the direction vector as (-1, 2, -3)t, where t is a parameter.

Next, we use the point (4, -4, 9) on the line to set up the symmetric equations. For each coordinate, we have:

x-coordinate:

x - 4 = (-1)t

x = 4 - t

y-coordinate:

y + 4 = (2)t

y = -4 + 2t

z-coordinate:

z - 9 = (-3)t

z = 9 - 3t

Therefore, the symmetric equations for the line passing through the point (4, -4, 9) and parallel to the vector (-1, 2, -3) are x = 4 - t, y = -4 + 2t, and z = 9 - 3t.

In more detail, the equations x = 4 - t, y = -4 + 2t, and z = 9 - 3t represent the coordinates of any point (x, y, z) on the line. The parameter t allows us to obtain different points on the line as we vary its value. The direction vector (-1, 2, -3)t indicates the direction in which the line extends from the given point (4, -4, 9).

For example, if we set t = 0, we obtain the point (4, -4, 9), which lies on the line. As we increase or decrease the value of t, we move along the line parallel to the direction vector (-1, 2, -3), allowing us to find other points on the line.

Hence, the symmetric equations provide a concise way to express the relationship between the coordinates of points on the line and the parameter t.

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We can say with 99% confidence that the true proportion of all lawsuits that were later dropped or dismissed is between 0.273 and 0.331.

We are given: Number of lawsuits that were not dropped or dismissed (successes), x1 = 372

Total number of lawsuits (trials), n = 1228

Confidence level = 99% = 0.99 (in decimal form)

Alpha = 1 - Confidence level = 0.01

To find the confidence interval estimate for the true proportion of all lawsuits that were later dropped or dismissed, we can use the formula:

Cl = \((p\bar)\)± \(z(\alpha/2)\) * \(\sqrt{[(p\bar)}\) * \((q\bar)\) / n]

where p(bar) = x1/n is the sample proportion of lawsuits that were not dropped or dismissed, and q(bar) = 1 - p(bar) is the sample proportion of lawsuits that were dropped or dismissed.

We need to find z(alpha/2), the critical value of the standard normal distribution for the given confidence level.

Since the confidence level is 99%, the area in each tail of the distribution is (1 - 0.99) / 2 = 0.005.

Using a standard normal distribution table or calculator, we can find that z(0.005) = -2.576.

Now, we can substitute the given values into the formula:

\((p\bar)\)= x1/n = 372/1228 = 0.302

\((q\bar)\)= 1 - \((p\bar)\) = 1 - 0.302 = 0.698

\(z(\alpha/2)\)= -2.576

Cl = 0.302 ± (-2.576) * √[(0.302 * 0.698) / 1228]

Cl = 0.302 ± 0.029

Cl = (0.273, 0.331).

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Answer:

2 miles

Step-by-step explanation:

1/2 of 4 is 2

Mathematically

1/2 × 4/1

4/2

2

Answer:

36 minutes

Step-by-step explanation:

100 boxes in 3 hours is a rate. It is how fast you are working in boxes per hour 100/3 boxesperhour.

But 3 doesn't go into 100 very neatly and its going to make all kinds of ugly fractions or decimals. But lets look at minutes. 3 hours is 3 × 60 minutes (bc there's 60 minutes in an hour) So you loaded 100 boxes in 180 minutes. That's 100/180 boxes per minute.

100/180 = 10/18

10/18 means 10 boxes in 18 minutes.

So times 2 on the top and the bottom gives you 20/36.

20/36 means 20 boxes in 36 minutes.

This is your answer. It will take 36 minutes to load 20 more boxes.

The THEORETICAL probability of choosing a vowel is 3/8 and the experimental probability is 36/75

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

In the letters of the word, we have

Vowels = 3

Letters = 8

By calculation, the theoretical probability of choosing a vowel is

Theoretical probability = Vowels/Letters

So, we have

Theoretical probability = 3/8

Based on the experiment, we have

Vowels = 15+9+12 = 36

Letters = 8+15+7+5+20+20 = 75

So, we have

Experimental probability = 36/75

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Answer:

Slope-1/2

Y-intercept 4

Step-by-step explanation:

To find slope count the amount of squares but use rise over run

To find the y intercept, look where the line intercepts with the y intercept

Answer:

Options B, D and E

Step-by-step explanation:

Given equation is,

-4x + 5y - 12 = 8

-4x + 5y = 20

If a point given in the options lie on the line, point will satisfy the equation.

Option A.

For a point (5, 0),

-4(5) + 5(0) = 20

-20 = 20

False

Therefore, (5, 0) will not lie on the given line.

Option B

For (-2, 2.4)

-4(-2) + 5(2.4) = 20

8 + 12 = 20

20 = 20

True.

Therefore, (-2, 2.4) will lie on the given line

Option C

For (8, 5),

-4(8) + 5(5) = 20

-32 + 25 = 20

-7 = 20

False

Therefore, (8, 5) will not lie on the line.

Option D

For (10, 12)

-4(10) + 5(12) = 20

-40 + 60 = 20

20 = 20

True.

Therefore, (10, 12) will lie on the line.

Option E

For (0, 4)

-4(0) + 5(4) = 20

20 = 20

True.

Therefore, (0, 4) will lie on the line.

Options B, D and E are correct.

Answer:

you use division then add then you get the answer

Step-by-step explanation:

Answer:

The approximate number of gallons of water that flow over the waterfall in 1 day is:

Step-by-step explanation:

To obtain the answer to the question, you must multiply the number gallons of water flow over a waterfall each second (6.5 x 10^5 gal/s) by the number of seconds in a day (8.6 x 10^4 s), as I show you below:

Now, we must cancel the seconds, then:

How you can see, once you have multiplied these two values, the answer is the same to the option A.

Answer:

always true

Step-by-step explanation:

Given

2(x + 3) = 5x + 6 - 3x ← distribute left side

2x + 6 = 2x + 6

Since both sides are equal then any real value of x is a solution.

Thus the equation is always true

Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, 1 km has approximately 39,283.2 inches.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

From the problem, the conversion factors are given as

1 kilometer = 0.62 mile

36 inches = 1 yard

1 mile = 1760 yards

To convert 1 kilometer into inches, first, convert 1 kilometer to miles using the conversion factor, 1 kilometer = 0.62 mile

1 km = 0.62 miles

Then, convert miles to yards using the conversion factor, 1 mile = 1760 yards

1 km = 0.62 miles = 0.62 (1760 yards)

1 km = 0.62 miles = 1091.2 yards

Lastly, convert yards to inches using the conversion factor, 36 inches = 1 yard

1 km = 0.62 miles = 1091.2 yards = 1091.2 (36 inches)

1 km = 0.62 miles = 1091.2 yards = 39,283.2 inches

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Answer:

B. 22 AUD * ($1)/(1.2 AUD)

Step-by-step explanation:

Start with the equation of the conversion.

1.2 AUD = $1

Now divide both sides by 1.2 AUD.

(1.2 AUD)/(1.2 AUD) = ($1)/(1.2 AUD)

The left side equals 1 since you have a fraction in which the numerator and denominator are equal.

1 = ($1)/(1.2 AUD)

Notice that the line above shows that the fraction on the right equals 1. Since multiplying a number by 1 does not change the number, you can multiply a number of Australian dollars by ($1)/(1.2 AUD) without changing the amount.

Now start with 22 AUD.

We multiply it by the fraction ($1)/(1.2 AUD). This will nmot change the amount of ,money since this fraction equals 1.

22 AUD * ($1)/(1.2 AUD)

The expression above will give you a number in U.S. dollars since AUD cancels out.

Answer: B. 22 AUD * ($1)/(1.2 AUD)

Answer:

B

Step-by-step explanation:

Did the quiz

The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).

Now,

We are given the linear equation: \(4x + \frac{1}{2}(10x-4)=6\)

Hence, The third and fourth solutions are correct when using the division property of equality, i.e., The justifications are 1. Distributive Property 2. Combine like terms 3. Addition Property of Equality 4. Division Property of Equality (Option 3 and 4).

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The correct solutions to the equation 2x + 2 = 2(2)ˣ are (a) 0 and (b) 1

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

2x + 2 = 2(2)ˣ

Divide through by 2

So, we have

x + 1 = (2)ˣ

Set x = 0

So, we have

0 + 1 = 1

1 = 1

Set x = 1

So, we have

1 + 1 = 2

2 = 2

Hence, the correct solutions to the equation are (a) 0 and (b) 1

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Answer:

Step-by-step explanation:

Discussion

Where does that 682 come from? It cannot be the surface area of a cube with a side of 50 inches.

The edge length is 50 inches, so s = 50

SA = 6 * 50^2

SA = 15000 in^2

Answer: So at the very minimum, you need 15000 square inches of wrapping paper.

To find an equation of the plane passing through the three given points P, Q, and R, we can use the concept of cross products. By finding the vectors formed by two sides of the plane, we can calculate the normal vector, which will provide the coefficients of the equation of the plane in the form ax + by + cz = d.

Let's start by finding two vectors in the plane. We can take vectors formed by the points P and Q, and P and R, respectively. The vector formed by P and Q is given by v1 = Q - P = (6 - 5, 10 - 6, 16 - 6) = (1, 4, 10). The vector formed by P and R is given by v2 = R - P = (14 - 5, 12 - 6, 7 - 6) = (9, 6, 1).

Next, we calculate the cross product of v1 and v2 to obtain the normal vector of the plane. The cross product is given by n = v1 × v2 = (4*1 - 10*6, 10*9 - 1*1, 1*6 - 4*9) = (-56, 89, -30).

Now that we have the normal vector, we can write the equation of the plane using the point-normal form. Substituting the values from P into the equation, we have -56(x - 5) + 89(y - 6) - 30(z - 6) = 0. Simplifying further, we get -56x + 280 + 89y - 534 - 30z + 180 = 0. Combining like terms, we obtain -56x + 89y - 30z = 74.

Therefore, the equation of the plane passing through the points P, Q, and R is -56x + 89y - 30z = 74.

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If Ariana removes the $4,800 rent from the set, the mean and median of the remaining rents will decrease because $4,800 is a very high value compared to the other rents.

Before removing the $4,800 rent, the mean can be calculated by adding up all the rents and dividing by the total number of rents (5):

Mean = (1,000 + 1,200 + 1,300 + 1,400 + 4,800) / 5 = 2,540

The median is the middle value in the set, which is 1,300.

After removing the $4,800 rent, the new mean can be calculated by adding up the remaining rents and dividing by the new total number of rents (4):

New Mean = (1,000 + 1,200 + 1,300 + 1,400) / 4 = 1,225

The new median is still 1,300 because it is the middle value in the remaining set.

Therefore, removing the $4,800 rent will decrease both the mean and median of the remaining rents.

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Answer:#7 is 20%. #8 is 67.5 people

Step-by-step explanation: For #7 you would just divine 14/70 to get .20 converted to a percentage is 20%. For #8 you would convert 37.5% to a decimal of .375 and multiply that to 180 people to get the answer of 67.5 people.

False.

The Cp and Cpk statistics are both used to assess the capability of a process to meet specifications, but they have different purposes.

The Cp statistic is a measure of how well the process spread (variation) fits within the specification limits. It assumes that the process mean is centered on the target value. It is calculated as the ratio of the specification width to the process spread (six times the process standard deviation).

The Cpk statistic, on the other hand, takes into account both the process spread and the deviation of the process mean from the target value. It is calculated as the minimum of two values: the difference between the process mean and the closest specification limit divided by three times the process standard deviation (assuming the process is centered within the specification limits), or the Cp value adjusted for the deviation of the process mean from the target value.

Both statistics have their uses and limitations depending on the situation. If the process mean is not centered on the target value, the Cpk statistic may be more useful than the Cp statistic since it takes into account both the spread and centering of the process.

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