find the product of (x-5)²-(x+5)(x-5)+10x​

Answer:

1/5 = q/p, or q:p

Step-by-step explanation:

You might want to rewrite 1/2p=2 1/2q as (1/2)p = (2 1/2)q.  

To remove the fractions, multiply both sides by 2:

p = 2(2 1/2)q  becomes p = 5q.

Dividing both sides by 5 yields p/5 = q.

Dividing both sides by p yields 1/5 = q/p, or q:p

This plot will provide a visual representation of how the purchased cost of the shell-and-tube heat exchanger changes over the specified range of surface areas.

To plot the purchased cost of the shell-and-tube heat exchanger as a function of the surface area, we need to consider the variation in the purchased cost capacity exponent.

The purchased cost of the heat exchanger can be expressed as:

C = C0 * (A)^b

where C is the purchased cost, C0 is the cost constant, A is the surface area, and b is the purchased cost capacity exponent.

Given that the purchased cost capacity exponent is not constant over the range of surface area requested (10 to 200 m²), we need to consider different values of b for different ranges of surface area.

Let's assume the following ranges and their corresponding purchased cost capacity exponents:

For 10 m² ≤ A ≤ 50 m², let b = 0.8

For 50 m² < A ≤ 100 m², let b = 0.7

For 100 m² < A ≤ 150 m², let b = 0.6

For 150 m² < A ≤ 200 m², let b = 0.5

Now, we can calculate the purchased cost for different values of surface area using the corresponding purchased cost capacity exponents.

For each range, substitute the given values of C0 and b into the cost equation to find the purchased cost for the corresponding surface area.

Once we have calculated the purchased costs for different surface areas, we can plot them on a graph with surface area (A) on the x-axis and purchased cost (C) on the y-axis.

The graph will show the variation in purchased cost as a function of surface area, considering the different purchased cost capacity exponents for different ranges.

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Answer:

         3-6= negative 3   9-6= 3

Step-by-step explanation:

One negative one positive

Hope it helped

Answer:

\(\boxed {a = 6}\)

Step-by-step explanation:

Solve for the value of \(a\):

\(3 - 6a = 9 - 6a\)

-Take \(-6a\) and add it to \(-6a\):

\(3 - 6a + 6a = 9 - 6a + 6a\)

\(3 - a = 9\)

-Subtract both sides by \(3\):

\(3 - 3 - a = 9 - 3\)

\(\boxed {a = 6}\)

Therefore, the value of \(a\) is \(6\).

Because we know one point and an axis of symmetry, we know that the point (2, -7) must lie on the graph.

If a function has a line of symmetry at x = x₀, then we know that:

f(x₀ + x) = f(x₀ - x).

So we have symmetry around that line.

Then, if the line of symmetry is at x = 5 and we know that:

f(8) = f(5 + 3) = -7

We also must have:

f(2) = f(5 - 3) = -7

Then the point (2, - 7) must be on the graph.

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Given the following polynomial:

You can follow the steps shown below in order to simplify it:

Step 1. Remember the Signs rules for multiplication:

Then, you can rewrite the expression as following:

Step 2. Now you must add the like terms (Remember that "like terms" are those terms whose variables are exponents are the same). Then, you get:

The answer is:

The series is absolutely convergent.

To determine the convergence of the series, we can compare it with the corresponding p-series. Let's consider the series:

\(\frac{\sum(-1)^n (arctan(n)}{ (n^{13})}\) where n starts from 1 and goes to infinity.

We know that \(|\frac{(-1)^n arctan(n) }{ n^{13}}| < \frac{1}{n^{13}}\) for all n.

Now, we compare it with the corresponding p-series:

\(\frac{\sum1}{n^{p}}\)

In our case, p = 13.

For a p-series, the series is absolutely convergent if p > 1, conditionally convergent if 0 < p ≤ 1, and divergent if p ≤ 0.

Since p = 13 > 1, the corresponding p-series \(\frac{\sum1}{n^{13}}\) converges absolutely.

Now, let's analyze the series \(\frac{\sum(-1)^n (arctan(n) }{ n^{13})}\):

We know that the terms of the series are bounded by the corresponding terms of the absolute value series, which is \(\frac{1}{n^{13}}\).

Since \(\frac{\sum1}{n^{13}}\) converges absolutely, by the comparison test, we can conclude that \(\frac{\sum(-1)^n (arctan(n)}{ n^{13})}\) also converges absolutely.

Therefore, the series \(\frac{\sum(-1)^n (arctan(n)}{ n^{13})}\) is absolutely convergent.

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The transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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

The functions f(x) and g(x)

Where, we have

f(x) = x²

The translation 6 units left and 4 units up means that

g(x) = f(x + 6) + 4

So, we have

g(x) = (x + 6)² + 4

This means that the transformation of f(x) to g(x) is g(x) = (x + 6)² + 4

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a. The MRS is constant (not diminishing) at 1/3.

U(x,y) = 3x + y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / 3

The MRS is constant (not diminishing) at 1/3.

b. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

The MRS is diminishing because as y increases, the MRS decreases.

c. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.

d. The MRS depends on the ratio of y to x and can vary.

U(x,y) = x^2 - y^2

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x

The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.

e. The MRS depends on the values of x and y and can vary.

U(x,y) = x + y / (x * y)

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)

The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.

Now let's move on to the second part of the question:

For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.

To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.

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Answer:

6120cm^3

Step-by-step explanation:

The formula for finding the volume of an object is the area of base times the height, in this case it can be shown as:

Length * width * height = volume

therefore we get the equation :

17*20*18=6120

Answer:

-1.714001255

Step-by-step explanation:

Well just plug it in your calculator.

\(\frac{3}{2} log(\frac{9}{125} )\)

Answer:

Step-by-step explanation:

100 + 20 = 120

Answer:

5(20+4)

Step-by-step explanation:

100+20=12

NoW

\(\\ \rm\Rrightarrow 5(20+4)\)

\(\\ \rm\Rrightarrow 100+20\)

\(\\ \rm\Rrightarrow 120\)

Hence verified

All logic connectives can be expressed in terms of ¬ and ∨.

The logic connectives ¬ (negation) and ∨ (disjunction) are sufficient to express all other logical connectives. Here is how each connective can be expressed:

Conjunction (∧): The conjunction of two propositions, p and q, can be expressed as ¬(p ∨ q), which means "not (p or q)." This is equivalent to saying "neither p nor q is true."

Implication (→): The implication of propositions p and q can be expressed as ¬p ∨ q, which means "not p or q." This states that if p is false or q is true, then the implication is true.

Biconditional (↔): The biconditional of propositions p and q can be expressed as (p ∧ q) ∨ (¬p ∧ ¬q), which means "either both p and q are true or both p and q are false." This captures the idea that p and q have the same truth value.

Exclusive OR (⊕): The exclusive OR of propositions p and q can be expressed as (p ∨ q) ∧ ¬(p ∧ q), which means "either p or q is true, but not both." This ensures that the propositions have different truth values.

By combining negation and disjunction, we can express all logic connectives. This shows the expressive power and versatility of these two fundamental connectives in logic.

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Assume that A and B are independent events. it means that the occurrence of event A does not affect the probability of event B and vice versa.

b. Assume that A and B are independent events. My response is Yes, P(A and B) can be defined as P(B) • P(A|B).

In the event that A and B are independent events, at that point the probability of A happening is one that is influenced by the event of B and vice versa. Hence, P(B) is comparable to P(B|A), showing that the probability of occasion B happening remains unaltered in any case of event A's event. Within the same vein, the likelihood of event A happening remains consistent whether event B has stay put or not, indicated as P(A) = P(A|B).

Therefore in response to question 2, The reason why independent events are not affected  by one another is that the likelihood of one event happening has no effect on the probability of the other event occurring.

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9514 1404 393

Answer:

  36

Step-by-step explanation:

The sum of the tangent segments shown is ...

  6 + 3 + 9 = 18

The unmarked tangent segments will have the same measure to the same vertex as the marked tangent segments. The perimeter is ...

  2 × 18 = 36 units

The category in the Excel Options dialog box that contains the option to change the user name is "General".

In the Excel Options dialog box, the category that contains the option to change the user name is the General category.

Excel graphing methods, Go to Insert > Line after selecting the data. The type of line chart you want may be chosen from a dropdown menu that appears when you click the icon.

We'll use the fourth 2-D line graph (Line with Markers) for this illustration. Your line graph for the chosen data series will be added by Excel.

What are the primary three graphs?

How to Use Graphs in Science

Bar, circle, and line graphs are the three most often utilized graph kinds. Each form of graph may be used to display a certain kind of data.

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It would take 3 minutes to copy 90 pages using the given digital copier.

To find the time required to copy z pages using a digital copier that copies in color at a rate of 30 pages per minute, we can use the concept of unitary method.

Since the copier can copy 30 pages per minute, we can set up a proportion to relate the number of pages and the time required:

30 pages / 1 minute = z pages / t minutes

Cross-multiplying the equation, we get:

30t = z

Now, we can solve for t by isolating it:

t = z / 30

Therefore, the time required to copy z pages is equal to z divided by 30.

For example, if we want to find the time required to copy 90 pages, we substitute z = 90 into the equation:

t = 90 / 30

t = 3 minutes

So, it would take 3 minutes to copy 90 pages using the given digital copier.

In general, the time required to copy z pages can be calculated by dividing the number of pages (z) by the copier's copying rate (30 pages per minute). This approach assumes a constant copying speed throughout the process.

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Answer:

I'm still in High School and planning on going to the military after going through and making money for the most part and for song recommendations I would say: Rob Zombie, Alice in Chains, and Guns N' Roses.

The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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Answer:16

Step-by-step explanation:

Answer:True
example:

89 and 84, 8 are equal, but next 9 is bigger than 4

Answer: 1,393 meters tall

Step-by-step explanation:

Plug in 1710 meters for the initial amount, 0.05 for the rate of decrease, and 4 millennia for the time elapsed.

y

= a(1–r)t

y

= 1,710(1–0.05)4 Plug in values

y

= 1,710(0.95)4 Subtract

y

= 1,710(0.81450…) Simplify

y

= 1,392.80568… Multiply

Round to the nearest whole number.

1,392.80568… → 1,393

To the nearest whole number, the mountain will be 1,393 meters tall.

Rotation is the rigid type of transformation which is equivalent to the two reflections across intersecting lines.

Therefore, the rigid type transformation which is equivalent to two reflection across the intersecting lines is called rotation.

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Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

A bee flies at 12 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 14 ​minutes, and then flies directly back to the hive at 8 feet per second. It is away from the hive for a total of 18 minutes. A. Write the equation. Let d be the distance of the flowerbed from the hive. B. how far away is the hive from the flower bed.

First we need to calculate the time taken by the bee to fly to a flowerbird to its hive using the formula;

Speed = Distance/Time

Time = Distance/Speed

If a bee flies at 12 feet per second directly to a flowerbed from its hive, then the time taken by the bee is expressed as;

t1 = d/12 ....... 1

If the bee then flies directly back to the hive at 8 feet per second, the time taken by the bird will be:

t2 = d/8 ....... 2

Total time taken by the bee to and fro will be the sum total of both times;

t1+t2 = d/12+d/8

t11+t2 = 2d+3d/24

t1+t2 = 5d/24 ........ 3

If the bee stays at the bee stays at the flowerbed for 14 ​minute and away from the hive for 18minutes, the total time used by the bird during the journey will be 18-14 = 4 minutes

converting 4 minutes to seconds

4 minutes = 4*60 = 240seconds

The equation that can be used to find the distance of the flowerbed from the​ hive is gotten by equating equation 3 to  the total time used by the bird during the journey i.e;

5d/24 = 240

5d = 24*240

5d = 5760

b) To know how far is the flowerbed from the​ hive, we will solve the resulting equation in a for the value of d as shown

Given 5d = 5760

Divide both sides by 5

5d/5 = 5760/5

d = 1152ft

Hence the distance of the flowerbed from the​ hive is 1152ft

The unit rate of the proportional relationship between the price and the number of buckets is 8.50 dollars/bucket.

One of the fundamental arithmetic procedures in math is division, which is the process of dividing a group of things into equal parts. Every day, we might use the division technique in various circumstances. Division by Zero: There is no defined result when dividing any number by zero.

We can use the given information to find the unit rate of the proportional relationship, which is the price per bucket of golf balls.

To find the unit rate, we divide the price by the number of buckets. For example, for the first row of the table, the unit rate is:

25.50 dollars / 3 buckets = 8.50 dollars/bucket

Similarly, we can find the unit rate for the other rows of the table:

42.50 dollars / 5 buckets = 8.50 dollars/bucket

59.50 dollars / 7 buckets = 8.50 dollars/bucket

We can see that the unit rate is the same for all rows of the table, which confirms that the relationship between the number of buckets and the price is proportional.

Therefore, the unit rate of the proportional relationship between the price and the number of buckets is 8.50 dollars/bucket.

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The approximate commission at the rate of 7% is $650.82

What is area of triangle?

The area occupied by a triangle is known as area of triangle. The area if computed as 1/2*base*height

We are given the, base of 1500 feet and a height of 600 feet

Hence the area of triangle can be given as

Area= 0.5*1500*600

Area= 450000 ft^2

Now 1 acre costs as 43560 sqft

Hence the area of triangle in acres is

Area in acres = \(\frac{450000}{43560}\)

Area in acres= 10.33

Hence total amount for which the piece of land is sold = 10.33*900

Total amount= $9297

Now we have to find the 7% of this amount

Hence

\(=\frac{9297*7}{100}\\=650.82\)

Hence the amount received as commission is $650.82

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The probability is 6.

Probability is the possibility of an event occurring. We can scale the probability of an event between 0 and 1. 0 refers to an improbable event, and one refers to an event with the highest possibility. The type of probability we will use to solve this problem is the geometric distribution.

The geometric distribution is defined as a discrete probability distribution representing the probability of consecutive failures before success in a Bernoulli trial. There could be only two possible outcomes; either True (1) or False (0).

Bernoulli's trial is an experiment in which we have only two possible outcomes, success or failure. In other words, the geometric distribution repeats Bernoulli trials until it succeeds, then stops. So, achieving success is the ultimate goal and is the point that stops Bernoulli's trials from happening further.

Geometric distribution, the class of probability distributions, is based on three key assumptions, and these assumptions are defined as:

Now for our given problem, we stand on a street corner and record the gender of the first twelve people who pass by. The condition here is the city is half male and half female. Now to find the probability, we will consider the possibility of each of the twelve events. Since half of the population is Female, the probability of one single event is;

p = 1/2 (50 %)

The overall probability is the sum of all the individual probabilities:

P ( ALL FEMALE)

= 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2

= 6

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Answer:

The fraction which would represent this question is \(\frac{3}{5}\)

Step-by-step explanation:

The way to represent a division problem as a fraction is to put the dividend (3) over the divisor (5).

Answer:

slope=4/5

y-intercept = -3

Step-by-step explanation:

first we need to rewrite the expression to

\(y=mx+b\)

were b is the y-intercept and m the slope

\(4x-5y=15\\\\4x-5y+5y=15+5y\\\\4x+0=15+5y\\\\4x=5(3)+5(y)\\\\4x=5(3+y)\\\\\frac{1}{5}*4x= \frac{1}{5}*5(3+y) \\\\\frac{4x}{5}=3+y\\\\\frac{4x}{5} -3=3+y-3\\\\\frac{4x}{5} -3=y+0\\\\y=\frac{4x}{5} -3\\\\y=\frac{4}{5}x-3\)

so there we have it

\(m=\frac{4}{5} \\\\b=-3\)