how much weight has my dog lost if he was 4.25 kg now is 4.117

The function is f(x) = -2x + 5, and the constants m and b are -2 and 5, respectively.

Given the function f(x) = mx + b, where m and b are constants, we know that:

limx→2 f(x) = 1

limx→3 f(x) = -1

Using the definition of a limit, we can rewrite these statements as:

For any ε > 0, there exists δ1 > 0 such that if 0 < |x - 2| < δ1, then |f(x) - 1| < ε.

For any ε > 0, there exists δ2 > 0 such that if 0 < |x - 3| < δ2, then |f(x) + 1| < ε.

We want to determine the values of m and b that satisfy these conditions. To do so, we will use the fact that if a function has a limit as x approaches a point, then the left-hand and right-hand limits must exist and be equal to each other. In other words, we need to ensure that the left-hand and right-hand limits of f(x) exist and are equal to the given limits.

Let's start by finding the left-hand limit of f(x) as x approaches 2. We have:

limx→2- f(x) = limx→2- (mx + b) = 2m + b

Next, we find the right-hand limit of f(x) as x approaches 2:

limx→2+ f(x) = limx→2+ (mx + b) = 2m + b

Since the limit as x approaches 2 exists, we know that the left-hand and right-hand limits must be equal. Thus, we have:

2m + b = 1

Similarly, we can find the left-hand and right-hand limits of f(x) as x approaches 3:

limx→3- f(x) = limx→3- (mx + b) = 3m + b

limx→3+ f(x) = limx→3+ (mx + b) = 3m + b

Since the limit as x approaches 3 exists, we know that the left-hand and right-hand limits must be equal. Thus, we have:

3m + b = -1

We now have two equations:

2m + b = 1

3m + b = -1

We can solve for m and b by subtracting the first equation from the second:

m = -2

Substituting this value of m into one of the equations above, we can solve for b:

2(-2) + b = 1

b = 5

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Answer:

(3, -1)

Step-by-step explanation:

The point (3, -1) is the intersection of both the two functions, its also considered the system of equations.

Answer:

1. x=6 y=7

hope that helps!

Answer:

Step-by-step explanation:

(a) To find the height that represents the 90th percentile, we would need to use a standard normal distribution table and a Z-score. We need to first find the Z-score corresponding to the 90th percentile by solving for Z using the formula:

Z = (x - μ) / σ

Where x is the height at the 90th percentile, μ is the mean height (64.7 inches), and σ is the standard deviation (2.9 inches).

Z = (x - 64.7) / 2.9

Since the 90th percentile corresponds to a Z-score of 1.28, we can use the above formula to find x:

x = μ + Zσ

x = 64.7 + (1.28)(2.9)

x = 68.9 inches

So, the height that represents the 90th percentile is 68.9 inches.

(b) To find the first quartile (25th percentile), we would use a Z-score of -0.67.

x = μ + Zσ

x = 64.7 + (-0.67)(2.9)

x = 62.3 inches

So, the height that represents the first quartile is 62.3 inches.

Answer:

Step-by-step explanation:

The answer is 16 3/10

That's about as mixed as you can get it.

Answer:

5 1/3

Step-by-step explanation:

hope this works.

C) 6

Solution: 6.

Because the segments in the triangle are parallel, we can set up a proportion to solve for MN.

\(\frac{4}{10}=\frac{x}{15}\)

The personal banker given lending arrangement, the APR for your cousin's buddies who borrowed $20 and repaid $40 at the end of the month would be 120%

The annual percentage rate (APR) for your cousin's lending arrangement,  to make a few assumptions. That each lending transaction occurs on the first day of the month and is repaid on the last day of the same month. Based on these assumptions, calculate the effective APR as follows:

Calculate the interest charged for a $20 loan over one month:

Interest = $40 (repaid amount) - $20 (loaned amount) = $20

Divide the interest by the loan amount and multiply by 100 to get the monthly interest rate:

Monthly Interest Rate = (Interest / Loan Amount) ×100 = ($20 / $20) ×100 = 100%

Multiply the monthly interest rate by 12 to obtain the annual interest rate:

APR = Monthly Interest Rate ×12 = 100% ×12 = 120%

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Answer:

x value=1

Step-by-step explanation:

Look where the two lines meet. That point is called the solution. The solution is (1,-4)

The probability of contracting an illness is 0.0475.

According to our question-

D: The patient has the illness

ND: the individual without the disease

TD: The results of the test show the patient has the illness.

P(D) will therefore equal 0.001 since only 0.001 of the population is affected by the disease.

P(ND) = 0.991

Because the test successfully identifies a patient with the condition 99% of the time, P(TD/D) = 0.99.

P(TD/ND) = 0.02 because the test indicates that a healthy person contracts the disease 2% of the time.

We are seeking for P(D|TD) and P(ND|TD), respectively.

According to the Bayes formula, 0.00099/0.00099+0.01982 = 0.00099/0.02081 = 0.0475 = (0.99*0.001)/(0.99*0.001)+(0.02*0.991)

And, \s = 1 - \s = 1 - 0.0475 \s = 0.9525

Therefore,

The likelihood of having an illness is 0.0475.

The likelihood of not having any sick people is 0.9525.

Hence, The probability of contracting an illness is 0.0475.

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James has 60 cars

john has 20 cars

this statement implies that James has 3 times has the number of cars jokhn hax

= 60/ 20

= 3

Answer:

40% is bigger

Step-by-step explanation:

40% ⇒ 40/100

1/4 ⇒ 25/100

40>25

∴ 40% is bigger

Answer:

Your answer should be x = \(\frac{48}{7}\).

Hope this helps.

Answer:

x is about 6.857 or 48/7

Step-by-step explanation:

to do this we cross multiply

42/18=16/x

42x=18(16)

42x=288

x=6.857

Hopes this helps please mark brainliest

The solution to this system of equations is x = -6, y = 9, and z = 5.

To solve this system of equations using row operations or elementary matrices, we can first start by subtracting 4x from both sides of the first equation. This leaves us with 3x - 3x = -6. Since the x terms cancel out, this equation is now true for any value of x. We can then use this equation to substitute -6 for the x terms in the other two equations. In the second equation, we have 5y - 2y - 6 = -16. We can then subtract 5y from both sides of the equation to get -2y - 6 = -16. Dividing both sides by -2 gives us y = 9. The third equation is now 3y - 3z - 4z - 4z = -6. We can then subtract 3y from both sides of the equation to get -3z - 4z = -15. We can then divide both sides of the equation by -3 to get z = 5. Therefore, the solution to this  system of equations  is x = -6, y = 9, and z = 5.

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Answer:

To mow the lawn once, it takes 1/12 gallon.

She can mow the lawn 12 times with 1 gallon.

Step-by-step explanation:

Kevin completed 1 assignment in total.

To find the total number of assignments Kevin completed, we need to add the fractions (1/2) and (5/6) together.

To add fractions with unlike denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 2 and 6 is 6. Let's rewrite both fractions with the common denominator of 6:

(1/2) = (3/6) (reducing the fraction to simplify it)

(5/6) = (5/6) (already in terms of 6 as the denominator)

(3/6) + (5/6) = 8/6

The sum of the fractions is 8/6. Now we have to reduce it again for having the least and simplified fraction by dividing by factor 2.

(8/2) / (6/2) = 4/3

So, Kevin completed a total of 4/3 of the assignment.

The number of assignments completed cant be a fractional number it should be a complete real number hence we approximate the given fraction as a whole number 1.

Therefore, Kevin completed 1 assignment in total.

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The required missing terms are sequential as 3, -8, -10, 1, -9, -7, 5, 10, 6, -9, 1, -1, 1,  and -7.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
What we do is, lets fill the blank space be x,
Now for 1,
[-1] + [-1] + x = 1
-2 + x = 1
x = 1 + 2
x = 3
Similarly, all the blank spaces can be determined as, -8, -10, 1, -9, -7, 5, 10, 6, -9, 1, -1, 1,  and -7.

Thus, the required missing terms are sequential as 3, -8, -10, 1, -9, -7, 5, 10, 6, -9, 1, -1, 1,  and -7.

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Answer:

0.7??

Step-by-step explanation:

I think. Sorry If i'm wrong. :)

Answer:

3.9%

Step-by-step explanation:

Let the digit in one's place be y and digit at ten's place be x.

Sum of the digits = 11

⟶ x + y = 11

⟶ x = 11 - y -- equation (1).

And,

The number formed by reversing the digits is 27 more than the original number.

⟶ Reversed number = Original number + 27

reversed number = 10y + x.

⟶ 10y + x = 10x + y + 27

⟶ 10y + x - 10x - y = 27

⟶ 9y - 9x = 27

Substitute the value x from equation (1).

⟶ 9y - 9(11 - y) = 27

⟶ 9y - 99 + 9y = 27

⟶ 18y = 27 + 99

⟶ 18y = 126

⟶ y = 126/18

⟶ y = 7

Substitute the value of y in equation (1).

⟶ x = 11 - 7

⟶ x = 4

The number = 10(4) + 7 = 40 + 7 = 47.

∴ The required two digit number is 47.

I hope it will help you.

Regards.

If Janice pays interest only until the final payment when the principal is paid off then it is a short-term loan in which the borrower only pays the interest on the loan during the term of the loan, and pays the principal in full at the final payment.

If Janice pays interest only until the final payment when the principal is paid off, the type of loan she is paying off is called an interest-only balloon loan. An interest-only balloon loan is a loan in which the borrower only pays the interest, without paying off the principal until the final payment. It is usually a short-term loan, in which the borrower pays only the interest on the loan during the term of the loan, usually three to ten years. After the term of the loan, the final payment includes the principal balance. This means the borrower will have a significant payment at the end of the loan term. In conclusion, the type of loan Janice is paying off is an interest-only balloon loan. It is a short-term loan in which the borrower only pays the interest on the loan during the term of the loan, and pays the principal in full at the final payment.

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(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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The economic and political circumstances that President Obama thinks might make terrorist groups attractive to many people in the world are the economic disparity between the rich and the poor, the political instability in many regions of the world, and dissatisfaction with the current political circumstances.

According to President Obama, there are several economic and political circumstances that might make terrorist groups attractive to many people in the world. The first circumstance is the economic disparity between the rich and the poor. Many people who are attracted to terrorist groups come from poor and underdeveloped countries where there is a lack of economic opportunities. These individuals may be drawn to terrorist groups because they see it as a way to achieve financial stability and gain power.

Another circumstance is the political instability in many regions of the world. Many terrorist groups take advantage of the instability and lack of government control in certain areas to gain support and recruit new members. Additionally, many people who are dissatisfied with their current political circumstances may be drawn to terrorist groups because they believe it is a way to bring about change and fight against perceived injustices.

Overall, the economic and political circumstances that President Obama believes might make terrorist groups attractive to many people in the world are the economic disparity between the rich and the poor, political instability, and dissatisfaction with the current political circumstances.

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Answer:

To solve this question, you simply apply algebraic formulas to geometric relationships.

The perimeter is simply the sum of the lengths of the sides of a shape. However, in this case, there is an "x" involved, so you must add algebraically.

Simply add the length of the sides up.

[3x] + [6x-2] + [x+3] + [4x+1] + [5x-2] = Perimeter

Now, simplify. Since adding is commutative, you can simply put all the variables first and constants next, no matter where they come from within the expression.

3x + 6x + x + 4x + 5x + -2 + 3 + 1 + -2

19x + 0 (-2-2 + 3+1 cancel out)

The perimeter of this pentagon is 19x.

Step-by-step explanation:

Answer: it's around 40

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

okay.. so basically you have 2x+6=34 right? so basically i’m gonna tell you the easiest way to do this

so you’re gonna start off by separating the 2x from the 6=34.

now that you’ve done that, let’s focus on the 6=34. so to get your answer, start by subtracting 6 from 34 so (34 - 6 = 28)

now that you’ve got that, keep the number 28 in mind. youre gonna want to take 2 and multiply by x. but 2x = 28, so what do you multiply by 2 to make 28? 14. so x is 14. to check your work, let’s see.

2 x 14 + 6 = 34?

2 x 14 = 28 + 6 = 34.

34 = 34

so, x is 14. hope this helped!

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

We have,

a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:

P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))

Where:

P(t) = Pressure at time t

Pi = Initial reservoir pressure

Q = Flow rate

K = Permeability

h = Reservoir thickness

ϕ = Porosity

μ = Viscosity

Ct = Total compressibility

t = Shut-in time (12 hours)

Δt = Time since the start of the flow period

Bo = Oil formation volume factor

ΔP = Pressure drop during the flow period

Given:

Pi = 3100 psi

Q = 200 STB/day

K = 45 md

h = 60 ft

ϕ = 15%

μ = 1.2 cp

Ct = 15x10^-6 psi^-1

Bo = 1.3 bbl/STB

t = 12 hours

Δt = 48 hours

ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))

Substituting the given values into the equation:

ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x\(10^{-6}\) * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x \(10^{-6}\) * (48 + 48)) / (1.3 * (0 + 48))))))

After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.

b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.

It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.

The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.

Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.

It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.

Thus,

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

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On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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Answer:

1/2

Step-by-step explanation:

KEEP 1/4 CHANGE the sign to multiplication FLIP 1/2 to 2/1

new equation: 1/4 x 2/1

now we can solve

we do: 1 x 2= 2

so 2 is our nominator

then we do: 4 x 1= 4

so 4 is our denominator

combine the nominator and denominator and we get

1/2 which in decimal form is 0.5

Answer:

f(-2) means that x = -2

f(-2) = 65

Step-by-step explanation:

f(x) = 6(8 - x) + 5

f(-2) = 6(8 + 2) + 5

f(-2) = 6(10) +5

f(-2) = 60 + 5

f(-2) = 65

If the customer source has an arrival rate of 10 customers per hour , then

(a) the number of customers arrivals follows a Poisson Distribution .

(b) The probability formula is P(n) = \(e^{-\lambda t} \times \frac{(\lambda t)^{n} }{n!}\) .

(c) 80 customers are expected .

(d) Probability of at least 3 customers is 0.9972 .

(e) The probability function follows exponential distribution .

(f) The probability density function is f(x) = λ\(e^{\lambda x}\) .

(g) The 8th customer will be welcomed in 48th minute .

(h) probability of 8th customer arriving is 0.113 .

(i) probability distribution follows exponential distribution .

(j) expected inter arrival time in 1/6 .

Part (a) : If the customer source has an arrival rate of 10 customers per hour , then the number of customers arrivals follows a Poisson Distribution .

Part(b) : Probability of n customers arrivals at time t, can be calculated by the formula : P(n) = \(e^{-\lambda t} \times \frac{(\lambda t)^{n} }{n!}\)

Part (c) : substituting the value of lambda = 10 and t = 8 ,

We get , Number of customers expected during 8 hr day =10×8=80 .

Part (d) : Probability of having at least 3 customers within one hour

⇒ P(n≥3) = 1 - P(n≤2)

= 1 - e⁻¹⁰ × {(10⁰/0!) + (10¹/1!) + (10²/2!)}

= 1 - e⁻¹⁰ × {1 + 10 + 50}

= 1 - 0.0028

= 0.9972

Part (e) : The probability function that the nth customer follows is the exponential function.

Part (f) : The Probability density function (pdf) of this exponential function is as follow:

f(x) = λ\(e^{\lambda x}\) ,

Part (g) : The time at which we expect the 8th customer to arrive is :

⇒ 10 customers arrive in One hour, which means 1st customer arrive at 1/10th of an hour.

So,  by unitary method, we say that 8th customer arrives at 8/10th of an hour which is  48th minute.

Part (h) : The probability of 8th customer arriving in one hour is calculated by the formula :

⇒ P(X=x) = {λˣ \(e^{-\lambda}\)}/x! ,

⇒ P(X=8) = (10)⁸ e⁻¹⁰/8! = 0.113 .

Part (i) : The probability distribution for the inter-arrival time follows an exponential distribution.

Part (j) : The expected inter arrival time between the nth and (n + 1)th customer is calculated as :

⇒ (no. of customers per hour)/(no. of mins in 1hour ) = 10/60 =1/6 .

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The given question is incomplete , the complete question is

Suppose that we have a Poisson customer source, which has an arrival rate of 10 customers per hour.

(a) What probability distribution does the number of customer arrivals follow at time t?

(b) Write out the probability when we have n customer arrivals at time t.

(c) How many customers are expected during an 8-hour day?

(d) What is the probability of having at least 3 customers within one hour?

(e) What probability distribution does the nth customer arrival time follow?

(f) Write out is probability density function.

(g) What time do you expect to welcome the 8th customer?

(h) What is the probability you have 8 customers in one hour?

(i) What probability distribution does the inter-arrival time follow?

(j) What is the expected inter-arrival time between nth and (n+1)th customer?

Answer: 24

Step-by-step explanation:

Amount of bushels of peas collected = 42

Fraction that'll be sent to market = 3/7

Fraction that'll be kept = 1 - 3/7 = 7/7 - 3/7 = 4/7

The number of bushels that'll be kept will be:

= Fraction that'll be kept × Total number of bushels collected

= 4/7 × 42

= 24