find the equation of the line y = c0 c1x coming closest to passing through the points (0, 1), (1, −2) and (2, 4), i.e., find the least squares line for these data points.

The solution of the given expression is \([p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}\)

Given \(p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}\)

We have to solve the above expression.

We know that expression is a combination of numbers, symbols, variables and coefficients, indeterminants. Expression shows relationship between variables. LCM is the smallest number that is divisible by both the numbers whose LCM has been taken. Coefficients are present in the beginning of variables. Symbols are arithmetic signs like addition, subtraction, multiplication and division, etc.

We have to take LCM of the expression and solve accordingly so that the expression can be solved =

\(p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}\)=  \([p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}\)

Hence the expression  \(p^{2} /(p-y)^{y} -2p/(p-y)^{y-1} +7/(p-y)^{y-2}\) is equal to = \([p^{2}(p-y)^{y-1} (p-y)^{y-2} -2p(p-y)^{y} (p-y)^{y-2} +7(p-y)^{y} (p-y)^{y-1}]/ (p-y)^{y} (p-y)^{y-1}(p-y)^{y-2}\)

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The yy-component of vector a a is -y-direction, which is equal to 0 m/s2.the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.

Given a vector, a⃗ a→ = (5.0 m/s2, −y−direction)Find the yy -component of the given vector a⃗ a→.Solution: The yy-component of the given vector a⃗ a→ = -y-directionTo find the yy-component of the given vector a⃗ a→, we have to take the product of the second term of the vector with unit vector j^j^, which is in the direction of the y-axis.Therefore, the yy-component of vector a⃗ a→ is :a_yy = -y-direction = (-1)(0) = 0 m/s²  Answer: 0 m/s².

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The yy-component of vector a⃗ a→ is -y-direction.

The yy-component of a vector represents the magnitude of the vector in the y-direction.

In this case, the vector a⃗ a→ is given as (5.0 m/s2, −y-direction).

Since the yy-component is the magnitude in the y-direction, the yy-component of the vector a⃗ a→ is -y-direction.

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Answer:x = 75

Step-by-step explanation:y=105 - 5 = 100 ft

z=125 ft

dz/dt=2 ft/sec

by using Pythagorean Theorem, we find x

x^2 + 100^2 = 125^2

x = 75

Answer:

A: 19.3 and 19.25

Step-by-step explanation:

When rounding decimals if the number in the decimal place to the right is higher than 5 you round up. If not keep keep the same.

The rounding off 19.254 to the nearest tenth and the nearest hundredth will be 19.3 and 19.25 respectively.

What is rounding off ?

Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.

To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.

here, The number 19.254 at tenth place is 5 so round up the hundredths place digit, hence the rounded off to the nearest tenth will be 19.3.

and also,

To round off the number to the nearest hundredth we need to look at the thousandth place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.

here, The number 19.254 at hundredth place is 4 so round up the thousandth place digit, hence the rounded off to the nearest hundredth will be 19.25.

Therefore, the rounding off 19.254 to the nearest tenth and the nearest hundredth will be 19.3 and 19.25 respectively.

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The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

  22

Step-by-step explanation:

The least common multiple of 6 and 9 is 18. Consider a group of 18 numbers, 1–18, for example. The multiples of 6 are 6, 12, and 18, of which two are not multiples of 9.

There are 11 groups of 18 numbers in 1–200, with 2 left over. That means there will be 11×2 = 22 numbers that are multiples of 6 but not 9.

__

200/18 = 11 remainder 2

Answer:

-1/2

Step-by-step explanation:

Make these mixed fractions:

-2 1/3 = -7/3

-1 5/6 = 11/6

Make these have common denominators:

-7/3 - (-11/6)

-14/6 - (-11/6)

-14/6 + 11/6

-3/6

-1/2

Answer:-0.5

Step-by-step explanation: have a good day!

Answer:

2 miles = 3218.6m

3km = 3000m

ATQ, 2 miles - 3km = 3218.6m - 3000m =

218.6m

The value of n is 25  according to standard deviation in the question.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

s = 30 minutes

C.I. = 99%

mean = 15 minutes

z value for 99% = 2.58

mean = z*s/√n

15  = 2.58 * 30 / √n

√n = 5.06

n = 25

Hence the value of n is 25 .

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The number of ways there for the 125 pages to be assigned to the four printers = 5^125 ways.

As per the question,

A 125-page document is being printed by four printers.

Each page will be printed exactly once.

There are no restrictions on how many pages a printer can print.

One of the possible combinations is that printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer C prints out 61-80 and 86-90 and printer D prints out pages 81-85 and 91-100.

Since, there are no restrictions in printing the pages any printer cannot print even a single page and any printer can print all 125 pages. To print 100 pages we have four printers.

⇒ Number of possible ways a single paper can be assigned to the four printers = 4 ways

⇒ Number of possible ways 125 pages can be assigned to the four printers

=  5 × 5 × 5 × 5 .................... 5 ( a total of 125 terms )

=     ways.

Therefore, In   ways we can assign 125 pages to four printers with no restrictions.

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Answer:  Choice A

f(x) is continuous for all real numbers

=============================================================

Explanation:

The piecewise function given to us basically breaks down into these two cases:

So if we plug in x = 1, then we go for the top line and say

f(x) = x^2+4

f(1) = 1^2+4

f(1) = 5

Showing that f(1) is indeed defined. We rule out choice D because of this.

----------------

Let's see what happens when we plug x = 1 into the bottom equation

f(x) = x+4

f(1) = 1+4

f(1) = 5

Both pieces produce the same output. This tells us that as x approaches 1 from either the left or right sides, the y value approaches y = 5. Therefore, the limit at x = 1 exists. We rule out choice B because of this.

We rule out choice C as well because f(1) does equal the limiting value mentioned earlier.

----------------

The answer is choice A because no matter what x value we plug in, it's not only defined but also it's connected to the rest of the function curve as shown below.

Answer: A; f(x) is continuous for all real numbers

There are several incentives for saving that are mentioned below.

Savings refers to the money that is not spent and is set aside for future use, such as emergencies, investments, or long-term goals. It is the difference between income earned and expenses incurred.

Interest earnings: When you save money in a bank account, you may earn interest on your balance.

Tax benefits: Some types of savings accounts, such as individual retirement accounts (IRAs) and 401(k) plans, offer tax benefits. Contributions to these accounts may be tax-deductible, and the money grows tax-free until you withdraw it.

Emergency fund: Saving money in an emergency fund can give you peace of mind and help you avoid going into debt if unexpected expenses arise, such as a medical emergency or a car repair.

Financial security: Saving money can help you achieve your long-term financial goals, such as buying a home, starting a business, or retiring comfortably.

Flexibility: Having savings can give you more flexibility and freedom in your life. You can use your savings to travel, start a new hobby, or take time off work to care for a loved one.

Overall, saving money can provide numerous benefits and incentives, both in the short-term and the long-term.

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Complete question:

What are the different types of incentives for saving ?

Answer:

0.70p

Step-by-step explanation:

"30% off" means paying only 70% of the original sales price (subtracting 30% from 100% yields 70%).  Next, find the decimal equivalent of 70%:

It is 0.70.  Finally, multiply the price p by 0.70:  0.70p (Answer b)

Answer:

d

Step-by-step explanation:

what are the pair of solutions?

To determine whether a triangle is an SSS, SAS, or AA triangle, you need to compare the sides and angles of the triangle to those of another triangle.

What are congruent triangles?

Congruent triangles are triangles that have the same size and shape. In other words, if you were to superimpose one triangle on top of the other, the two triangles would fit perfectly together, with all of the sides and angles being equal in measure.

To determine whether a triangle is an SSS, SAS, or AA triangle, you need to compare the sides and angles of the triangle to those of another triangle. Here's how you can do this

Side-Side-Side (SSS) Congruence: If three sides of one triangle are congruent to three sides of another triangle, then the triangles are SSS congruent.

Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are SAS congruent.

Angle-Angle (AA) Congruence: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are AA congruent.

Hence, To determine whether a triangle is an SSS, SAS, or AA triangle, you need to compare the sides and angles of the triangle to those of another triangle.

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Answer:1/5 is the answer

Step-by-step explanation:

Answer:

It has negative run, between two points so the slope is negative. the y intercept if 4. y=-2x+4

Answer:

A.

Step-by-step explanation:

Get the two points first.

(2, 0) and (0, 4)

The slope is -2

y = -2x + b

y = -2x + 4

Answer:

$324

Step-by-step explanation:

Melissa sold 18 tickets.

Jona sold 1/2 * 18 = 9 tickets

Shona sold 1 1/2 * 18 = 1.5 * 18 = 27 tickets

Total number of tickets sold:

18 + 9 + 27 = 54

Total money from sales: 54 * $6 = $324

CS responding of 81 refers to the response to a conditioned stimulus. A suppression ratio of zero means no fear response is observed, indicating no learned association between the conditioned stimulus and the aversive outcome.


“CS responding” refers to the response elicited by a conditioned stimulus (CS). A conditioned stimulus is a neutral stimulus that, through repeated pairing with an unconditioned stimulus (UCS), acquires the ability to elicit a conditioned response (CR). The CS responding value represents the level or frequency of the conditioned response.
Now, let’s address the concept of a suppression ratio. In fear conditioning experiments, a common way to measure fear is through a suppression ratio, which is calculated by dividing the number of responses emitted during the CS presentation by the total number of responses emitted during a specific period, usually including both the CS and a baseline period.

A suppression ratio of zero indicates that no suppression of responding occurs during the presentation of the conditioned stimulus. This means that the individual is not showing any reduction in their responding when the CS is presented compared to the baseline period.
In terms of both responding and fear, a suppression ratio of zero suggests that the individual is not associating the CS with the aversive outcome (UCS) and does not exhibit any fear response. Essentially, there is no behavioral evidence of conditioned fear or a learned association between the CS and the aversive stimulus.

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Answer:

Hope this helps. x

Step-by-step explanation:

5(x+5x)

=5x+25

Hope it helps

Answer:

30x

Step-by-step explanation:

Roadway offers the best deal for renting a truck, and it becomes the best deal when you need to drive more than 98 miles a day.

To determine which company offers the best deal for renting a truck, we need to compare the costs based on the daily rate and the cost per mile. Roadway charges $50.70 per day and an additional $0.25 for each mile driven, while UK-Plug-It charges $55.60 per day and an additional $0.20 per mile.

To find out when Roadway becomes the best deal, we need to calculate the point at which the total cost for Roadway is lower than that of UK-Plug-It. Let's assume the number of miles driven in a day is represented by 'm.'

For Roadway, the total cost can be calculated as:

Total cost for Roadway = $50.70 (daily rate) + $0.25 (cost per mile) * m (miles driven)

For UK-Plug-It, the total cost can be calculated as:

Total cost for UK-Plug-It = $55.60 (daily rate) + $0.20 (cost per mile) * m (miles driven)

To find the point at which Roadway becomes the best deal, we need to equate the total costs of Roadway and UK-Plug-It:

$50.70 + $0.25m = $55.60 + $0.20m

Simplifying the equation, we get:

$0.05m = $4.90

Dividing both sides by $0.05, we find:

m = 98

Therefore, if you need to drive more than 98 miles in a day, Roadway offers the best deal for renting a truck.

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An equation of the line passing through the pair of points (-5,2) and (-6,-8) in the form Ax + By = C is 5x + 7y = -36.

We can find the equation of the line passing through the pair of points (-5,2) and (-6,-8) using the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1,y1) and (x,y) are points on the line, and m is the slope of the line. To find the slope, we use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1,y1) and (x2,y2) are the given points.

Substituting the values:

m = (-8 - 2)/(-6 - (-5)) = -10/-1 = 10

Now, we can use either point and the slope to find the equation of the line in point-slope form:

y - 2 = 10(x + 5)

Simplifying:

y - 2 = 10x + 50

y = 10x + 52

To write the equation in the form Ax + By = C, we rearrange the terms:

-10x + y = 52

Multiplying both sides by -1:

10x - y = -52

Multiplying both sides by -1 again to make the coefficient of x positive, we get:

-10x + y = 52

Thus, the equation of the line passing through (-5,2) and (-6,-8) in the form Ax + By = C is 5x + 7y = -36.

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Answer:

-3/2

Step-by-step explanation:

Answer:

( -3 , 2 )

Step-by-step explanation:

Answer:

f⁻¹(x) = \(\frac{\sqrt{x}}{2}\) , -\(\frac{\sqrt{x} }{2}\)

Step-by-step explanation:

f(x) = 4x²

rewrite as:

y = 4x²

Interchange the variables, then solve for y:

x = 4y²

y² = x/4

y = √x/2, -√x/2

Answer:

f⁻¹(x) = \(\frac{\sqrt{x}}{2}\) , -\(\frac{\sqrt{x} }{2}\)

The total volume of the pool is 156 yd³. Option D

First, to determine the volume, we need to note the properties of a rectangular prism.

The formula for volume of a rectangular prism is;

Volume = lwh

Given that;

Now, substitute the value

Volume = 8 × 3 × 13/2

Volume = 312/2

Volume = 156 yd³

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Among the given models, only model d is stable. The steady-state response for model d can be obtained. Models a, b, and c are not stable.

In control systems, stability refers to the behavior of a system over time. A stable system produces a bounded response that eventually settles to a steady-state value. On the other hand, an unstable system results in an unbounded or divergent response.

Model a has a transfer function of Y(s)/F(s) = 14/(7s+3). The denominator of the transfer function has a positive coefficient for the s term, indicating a positive power of s. This implies that the system is unstable, as it will have exponential growth or decay in its response. Therefore, model a is not stable.

Model b has a transfer function of Y(s)/F(s) = 5/(1082s+68+9). Similar to model a, the denominator has a positive coefficient for the s term, indicating instability. Hence, model b is not stable.

Model c has a transfer function of Y(s)/F(s) = 12/(s^2-9). The denominator of the transfer function has roots at s = 3 and s = -3, indicating poles on the imaginary axis. This type of system is marginally stable but not strictly stable. Therefore, model c is not stable.

Model d has a transfer function of Y(s)/F(s) = 8/(s^2+25-7). The denominator of the transfer function has roots at s = 3j and s = -3j, where j represents the imaginary unit. These roots have negative real parts, indicating stability. Thus, model d is stable. The steady-state response for model d can be obtained by substituting s = jw into the transfer function, where w is the frequency. However, the given input f(t) does not provide information on the frequency or initial conditions needed to compute the steady-state response in this case.

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48630 is large should the sample be if the margin of error is to be less than $4 .

What does the term "margin of error" mean?

Margin of Error  = Z*Stdev/sqrt(n)

4 <= 0.90* 33/sqrt(n)

n >= (0.90* 33/2)^4 = 48630.17 OR 48630

So, n should be atleast 48630 so that margin of error is within $4

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The shaded area is 239.4 ft²

Answer:

-0.9a - 2.8b

Step-by-step explanation:

You subtract 0.7a and 1.6a

You subtract 0.4b and 3.2b

The probability of hitting the shaded area is 0.64

The diameters are given as:

D = 10

d = 6

The shaded area is calculated as:

Shaded = π((D/2)² - (d/2)²)

So, we have:

Shaded = π((10/2)² - (6/2)²)

Evaluate the exponents

Shaded = 16π

The area of the big circle is calculated as:

Area = π(D/2)²

So, we have:

Area = π(10/2)²

Evaluate the exponents

Area = 25π

The probability of hitting the shaded area is:

P = 16π/25π

Evaluate

P = 0.64

Hence, the probability of hitting the shaded area is 0.64

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