x^2+3 divided by x-2

Answer:

I don't know sorry the question is not clear

Answer:

\(\text{h}^{-1}(x)=\sqrt{1+x}-2\)

Step-by-step explanation:

Given functions:

\(\begin{cases}\text{f}(x)=x^2-2x\\\text{g}(x)=x+3\end{cases}\)

Function composition is an operation that takes two functions and produces a third function.

The composite function of fg(x) means to substitute the function g(x) in place of the x in function f(x).

\(\begin{aligned}\implies\text{h}(x) & = \text{fg}(x)\\& = \text{f}(x+3)\\& = (x+3)^2-2(x+3)\\& = (x+3)(x+3)-2x-6\\& = x^2+6x+9-2x-6\\& = x^2+4x+3\end{aligned}\)

Therefore:

\(\text{h}(x)=x^2+4x+3, \quad x\geq -2\)

h⁻¹(x) is the notation for the inverse of a function.  

The inverse of a function is a reflection of the function in the line y = x.

To find the inverse of function h(x), first swap h(x) for y:

\(\implies y=x^2+4x+3\)

Replace x with y:

\(\implies x =y^2+4y+3\)

Subtract x from both sides:

\(\implies y^2+4y+(3-x)=0\)

Using the quadratic formula to solve for y:

Quadratic Formula

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0\)

Therefore:

\(\implies y=\dfrac{-4 \pm \sqrt{4^2-4(1)(3-x)}}{2(1)}\)

\(\implies y=\dfrac{-4 \pm \sqrt{4+4x}}{2}\)

\(\implies y=\dfrac{-4 \pm \sqrt{4(1+x)}}{2}\)

\(\implies y=\dfrac{-4 \pm \sqrt{4}\sqrt{1+x}}{2}\)

\(\implies y=\dfrac{-4 \pm 2\sqrt{1+x}}{2}\)

\(\implies y=-2 \pm \sqrt{1+x}\)

The domain of the function is the range of the inverse function.

The range of the function is the domain of the inverse function.

Therefore, as the domain of function h(x) is restricted to x ≥ -2, the range of the inverse function is also restricted to h⁻¹(x) ≥ -2.

Therefore, from the two options found for the inverse function, the only option that satisfies the restricted range of h⁻¹(x) ≥ -2 is:

\(\text{h}^{-1}(x)=\sqrt{1+x}-2\)

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GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

Okay in this question, we're looking at the g mat and g p, a looking at like students who are applying to be in an m b a program. You can see that our answers are down here and we're going to be looking at the g mat and the g p a so like. Let'S keep track of how many people have good, just only good g p, only a good g mat and not a good g p, both good, so i'm just going to put a check for a good bath good or both bad. Those are our categories, so i'm going to put an x both bad, so we're just going to count up these people. We know a total there's going to be 10 in the sample, so a good g p. A! U was just refreshed. I think a good g p, a was 9.0 and a good g mat was 600 point, so first person, 599 and 9.6, not a good g mat, even though its really close had to be above 600 but g p, a 9.6. That'S a good g p. So we have 1 person in this category of good g p, but not a good g mat then 689 and 8.8. That is a good g mat, but not a good g p. So then, 58410 good g p now to go at 6317.4. Good g mat bad g, p, 5949.8, good g p, a bad g mat 6439.2 that is going to be both good 6569.6, both good 594 poi 8.4. That'S both bad 71011.2, both good and 611 point okay. So that's a good g, math, 7.6 bad g p. So, just a good g mat now to calculate the relative frequency which, since you see decimals here, we know that's what that means. You just take the number and divide by 10 because 10 is your total sample size you're, trying to figure out like relative to the whole group? What percent had each of these 3 divided by 10? Point? That'S a .33 divided by 10.3 .3. These should always add up to 1 and .1. So, let's see what matches with that its going to be option d down here : (values from 0 to 12) and their gmat score (values range from 200 to 800) are listed below: gmat gpa 5999.6 6898.8 58410.0 6317.4 5947.8 6439.2 6569.6 5948.4 71011.2 6117.6

GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

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GMAT greater than 600, less than or equal to 600, GPA greater than 9.0, 0.2, and 0.3, and less than or equal to 9.0, 0.4, and 0.1 Hence the correct table is Table 4.

In this question, we're going to be looking at the GMAT and the GPA, as well as people who are applying to be in an MBA school. We'll be looking at the GMAT and the GPA, as you can see from our answers, which are located down below. To keep track of how many people have good, just a good GMAT and not a good GPA, both good, and only a good GMAT, I'm just going to write a check for a good bath good or both horrible. These are our categories, so I'm going to mark both with an x, and we'll just add up these folks . The sample will have a total of 10, therefore that is a good general probability. A! You had just refilled. A good g mat, in my opinion, had to be above 600 points, so first person, 599 and 9.6, even though it's pretty near, isn't a good g mat. However, a good GPS 9.6 was. That's a decent g p. In this category of good GPA there is only one person who is not a good GMAT, followed by 689 and 8.8. That is an excellent g mat, but a poor GPA. 58410 nice GPA is now ready to depart at 6317.4, so. 5949.8, excellent g mat terrible g, p, good g p,  a bad g mat 6439.2 that is going to be both good 6569.6, both good 594 poi 8.4.

Both are awful. 71011.2, good and 611 points are acceptable. So, 7.6 terrible g p, decent g in math. Simply use a decent g mat to determine the relative frequency, which is what that indicates since decimals are included. You just divide the number by 10, since that is the overall sample size you are attempting to determine relative to the entire group. How much of each of these three when multiplied by ten? Point? 10.3 divided by.33 equals a. The sum should always be 1 plus.1. Let's see whether this matches option d down here, then: Below is a list of the applicants' (ranging from 0 to 12) and GMAT scores (200 to 800): GMAT GPA: 5999.6, 6898.8, 58410.0, 6317.4, 5947.8, 6439.2, 6569.6, 5948, and 71011.2, respectively.

GMAT higher than 600 GMAT lower than or equal to 600 GPA higher than 9.0 0.2 0.3 GPA lower than or equal to 9.0 0.4 0.1

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The complete question is:

Graduate Management Admission Test is required of students applying to MBA schools (GMAT). One of the most important indicators of how well a student would likely perform in the MBA program is the GMAT score, which is used by university admissions committees. A sample of 10 graduates was chosen to assess how well the GMAT score predicts MBA achievement. Below are their GMAT scores (which range from 200 to 800) and grade point averages (ranging from 0 to 12) for the MBA program (See Picture).

Suppose that university admissions committees consider a GMAT score higher than 600 as an indicator of a good candidate, and a GPA higher than 9.0 as a good performance. find the probability distribution table that correctly summarizes the data.

The initial flounder population in millions is 1 million. The derivative of the population function at t = 10 is 1.4000 million flounder per year.

(a) To find the initial flounder population, we substitute t = 0 into the population function P(t). Given that t is measured in years, we have:

P(0) = 7(0) + 5 - 0.2(0^2) + 1 = 0 + 5 - 0 + 1 = 6 million flounder.

Therefore, the initial flounder population is 6 million.

(b) To determine P'(10), we need to find the derivative of the population function P(t) and evaluate it at t = 10. Taking the derivative of P(t) with respect to t, we have:

P'(t) = 7 + 0.4t.

Now, substituting t = 10 into the derivative equation:

P'(10) = 7 + 0.4(10) = 7 + 4 = 11 million flounder per year.

Rounded to four decimal places, P'(10) is approximately 11.0000 million flounder per year.

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The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

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Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.

Answer:

-3xy^3 (7xy^2z-4y-12)

Step-by-step explanation:

Simply factor out "-3xy^3." GL!

Answer:

so in both you can see that 7xy is common . Thus it is a common factor.Step-by-step explanation:

The expression represents the time she spent driving is       \(\frac{228.95}{x}\)

The expression represent the time she spent driving can be calculated as follows:

We know that

Time = \(\frac{distance}{ speed}\)

Let x be her speed on the first half of the trip.

Then for first half , the tiime she takes is

T1= \(\frac{150}{x}\)

while in a second half the time taken by her is

T2= \(\frac{150}{1.9x}\)

T2= \(\frac{78.95}{x}\)

the total time she spent on driving is

T1 + T2 =    \(\frac{150}{x}\) + \(\frac{78.95}{x}\) =    \(\frac{228.95}{x}\)

Hence, the expression represents the time she spent driving is       \(\frac{228.95}{x}\)

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Answer:

3

Step-by-step explanation:

add them all to get 18 then divide by 6 which is a total number of numbers there

Answer:

3

Step-by-step explanation:

In this situation, interval measurement is being employed as the measurement level.

As the height of each student can be measured on a continuous scale with equal intervals between the values. It's important to note that the teacher may have rounded the measurements to the nearest unit, which would make it a discrete measurement.

Interval measurement is a level of measurement in which the values are measured on a continuous scale and have equal intervals between them, but there is no true zero point. This means that the difference between any two values on the scale is meaningful and consistent, but it is not possible to say that one value is "zero" or has no quantity of the measured attribute.

For example, measuring temperature in degrees Celsius or Fahrenheit is an example of interval measurement. In this case, the difference between 10 and 20 degrees is the same as the difference between 20 and 30 degrees, but there is no true zero temperature - a temperature of 0 degrees does not mean the absence of heat.

Another example of interval measurement is measuring time in minutes or hours. The difference between 10 minutes and 20 minutes is the same as the difference between 20 minutes and 30 minutes, but there is no "zero" point in time - even if nothing is happening, time continues to pass.

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The statements that is true about the similarity of the two triangles the option D

D. ΔMNO and ΔJKL are not similar triangles

Similar triangles are triangles which have proportional corresponding sides

The parameters in the question are;

The length of segment MN = 20

Length of segment NO = 12

Length of segment OM = 25

Measure of angle ∠O = 56°

Length of segment LJ =- 15

Length of segment JK = 12

Length of segment KL = 9

Measure of angle ∠L = 56°

Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included  angle between the two sides are congruent

The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL

However, the ratio of the sides  LK to ON and JL to MO are;

9/12 ≠ 15/25

Therefore, the triangles are not similar

The correct option is option D

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Answer: 3/4

Step-by-step explanation:

The absolute value is the distance away from zero. -3/4 is 3/4 away from zero.

Answer:

The measure of the angle is 150°, the measure of its supplementary is 30°

Step-by-step explanation:

The given parameters are;

The measure of the given angle = 5 × The measure of its supplementary angle

Let "x" represent the given angle, and let "y" represent its supplementary angle, we have;

x = 5 × y...(1)

x + y = 180°...(2)

By substituting the value of x = 5 × y, from the first equation into the second equation, we have;

x + y = 180°

x + y = 5 × y + y = 5·y +  y = 6·y = 180°

y = 180°/6 = 30°

y = 30°

x = 5 × y = 5 × 30° = 150°

x = 150°

The measure of the angle = x = 150°, the measure of its supplementary = y = 30°.

Answer:hi

Step-by-step explanation:hi

Because, in reverse it's basically asking what is 12 minus 5. So, 12 minus 5 is 3!

Hopefully, this helps! :D

Ask your question below.

Answer:

x=9/7

Step-by-step explanation:

14x+3=21

14x=21-3

14x=18

14x/14=18/14

x=9/7

14(9/7)+3=21

2*9+3=21

18+3=21

21=21

if you have any question about this you can ask me

Answer: What the pic tell you what upload a new question with a pic and ill help

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Have the cookies as x and the cupcakes as y. From there, we know that she bought a total of 42 goodies, meaning that x + y=42. From there we know the cost of 1 cookie, and 1 cupcake. Being that a cookie costs .50, and a cupcake .85, we can conclude that the next equation is .5x+.85y= 27.30 because that is the total she spent BEOFRE tax.

The student's final average, based on the given weights and grades, is 90.2.

To calculate the student's final average using the weighted mean, we need to multiply each grade by its corresponding weight (percentage), and then sum up these weighted values.

Given:

Exam grade: 75 (weight: 30%)

Term paper grade: 89 (weight: 10%)

Final exam grade: 98 (weight: 60%)

Calculating the weighted values:

Exam weighted value = 75 * 0.30 = 22.5

Term paper weighted value = 89 * 0.10 = 8.9

Final exam weighted value = 98 * 0.60 = 58.8

Summing up the weighted values:

Final average = Exam weighted value + Term paper weighted value + Final exam weighted value

Final average = 22.5 + 8.9 + 58.8

Final average = 90.2

Therefore, the student's final average, based on the given weights and grades, is 90.2.

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Answer:

5

Step-by-step explanation:

10 - 2 + 3- 7 = 5

Answer:

5........................

Answer: Always negative

Answer:

8

Step-by-step explanation:

take 16 and divide by two and you get 8

:D

Answer:

21 is answer

Step-by-step explanation:

Find the value of expression the a3−3a2+5a−7 by substituting a=3.

Using the given description < NOP is found to be 46 degrees

given data]

< OPQ = ( 9x - 19 ) degrees

< PNO = ( 2x + 5 ) degrees

< NOP = ( 3x + 16 ) degrees

From the figure described

let < NPO = y

< PNO + < NOP + y = 180 degrees ( sum of angles of triangle )

< OPQ + y = 180 degrees ( linear pair theorem )

Hence we equate both

< PNO + < NOP + y = < OPQ + y

< PNO + < NOP  = < OPQ + y - y

< PNO + < NOP  = < OPQ

( 2x + 5 ) + ( 3x + 16 ) =  ( 9x - 19 )

2x + 3x + 5 + 16 = 9x - 19

5x + 21 = 9x - 19

21 + 19 = 9x - 5x

40 = 4x

x = 40 / 4

x = 10

< NOP = ( 3x + 16 ) degrees

< NOP = ( 3 * 10 + 16 ) degrees

< NOP = ( 30 + 16 ) degrees

< NOP = 46 degrees

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Answer:

(a) \(\dfrac{foot \ print \ length }{dinosaurs \ length }= \dfrac{2}{35}\)

(b)The body length of the dinosaur is 525 cm

Step-by-step explanation:

Question

(a) What is the ratio of the length of the footprints in the dinosaur length?

(b) Iris found a new track she believes was made by the same species of dinosaur. If the footprint was 30 cm long and if the same ratio of foot length to body length holds, how long is the dinosaur?

(a)

Given that:

The length of footprint = 40 cm

the thigh bone = 100 cm

the body length = 700 cm

∴

\(\dfrac{foot \ print \ length }{dinosaurs \ length }= \dfrac{40}{700}\)

\(\dfrac{foot \ print \ length }{dinosaurs \ length }= \dfrac{4}{70}\)

\(\dfrac{foot \ print \ length }{dinosaurs \ length }= \dfrac{2}{35}\)

(b)

suppose p,q,r,s are real numbers, where q ≠ 0 & s ≠ 0.

Then:

\(\dfrac{p}{q}=\dfrac{r}{s}\) is a proportion if and only if ps = qr

Given that:

length of footprint = 30 cm

If possible the body length of the dinosaur is q (cm)

The length of how long the dinosaur is can be computed as:

\(\dfrac{30}{q}=\dfrac{2}{35}\)

2q = 30 * 35

q = (30 * 35)/2

q = 525 cm

The radius of convergence, R, is 1. The interval of convergence, I, is -1 ≤ x ≤ 1. To find the radius of convergence, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms of a series is L, then the series converges if L < 1 and diverges if L > 1.

Let's apply the ratio test to the given series:

lim(n→∞) |(x^(n+9) / sqrt(n+1)) / (x^(n+8) / sqrt(n))|

Taking the absolute value and simplifying, we get:

lim(n→∞) |x| * sqrt(n) / sqrt(n+1)

To find the limit, we can simplify the expression further:

lim(n→∞) sqrt(n) / sqrt(n+1)

To evaluate this limit, we can multiply the expression by the conjugate:

lim(n→∞) (sqrt(n) / sqrt(n+1)) * (sqrt(n+1) / sqrt(n+1))

Simplifying, we have:

lim(n→∞) sqrt(n(n+1)) / sqrt(n(n+1))

The square root terms cancel out, and we are left with:

lim(n→∞) 1

Therefore, the limit is 1. Since the limit is equal to 1, we need to check the boundary values separately to determine the convergence. When L = 1, the series may converge or diverge.

For x = 1, the series becomes:

∑(n=2 to ∞) (1^(n+8) / sqrt(n))

Simplifying, we have:

∑(n=2 to ∞) 1 / sqrt(n)

This is a p-series with p = 1/2, which converges.

For x = -1, the series becomes:

∑(n=2 to ∞) ((-1)^(n+8) / sqrt(n))

Simplifying, we have:

∑(n=2 to ∞) (-1)^n / sqrt(n)

This is an alternating series, and we can apply the alternating series test. The terms are decreasing in magnitude and approach zero, so the series converges.

Therefore, the series converges for -1 ≤ x ≤ 1. Since the series converges for all x within this interval, the radius of convergence, R, is 1. The interval of convergence, I, is -1 ≤ x ≤ 1.

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The probability of exactly five out of eight observed drivers coming to a complete stop is approximately 0.278.

To calculate the probability that exactly five out of eight randomly observed drivers will come to a complete stop at an intersection with flashing red lights, we can use the binomial probability formula.

Probability of success (p) = 0.40 (drivers coming to a complete stop)

Number of trials (n) = 8 (observed drivers)

Number of successes (k) = 5 (drivers coming to a complete stop)

The binomial probability formula is : P(X = k) = nCk * p^k * (1 - p)^(n - k)

By using this formula, we can calculate the probability of achieving a specific number of successes in a given number of trials or observations, assuming the trials are independent and the probability of success remains constant for each trial.

nCk represents the number of combinations of n items taken k at a time.

Plugging in the values:

P(X = 5) = 8C5 * 0.40^5 * (1 - 0.40)^(8 - 5)

By evaluating this expression, we find that the probability of exactly five out of eight observed drivers coming to a complete stop is approximately 0.278.

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Answer:

In Q39, the value 3x should be positive and in Q40, the final answer is missing 8x and the fact that 4x^2 is negative (-4x^2)

Step-by-step explanation:

39:

1. \(-(-3x)\) is presented as \(-3x\) when it should be \(+3x\), as 2 negatives make a positive.

2. Again, \(-3x\) is shown instead of \(+3x\)

3. The answer \(-x^2-2x\) should instead be \(-x^2+4x\), as \(-3x\) is used to reach this incorrect answer instead of the correct \(+3x\)

40:

1. \((x^3-4x^2+3)+(-3x^3+8x-2)=(x^3-3x^3)-4x^2+8x+(3-2)=-2^3-4x^2+8x+1\),

The final answer is wrong as it is missing the 8x and the fact that it is \(-4x^2\)and not \(+4x^2\)

Solving the equation x²+2x+7 using the quadratic formula, the resultant answer is x = -1 ± 2.44949i.

Any quadratic problem can be solved using the quadratic formula.

The equation is first changed to have the form ax²+bx+c=0, where a, b, and c are coefficients.

After that, we enter these coefficients into the following formula:

(-b±√(b²-4ac))/(2a)

Quadratic equations can be solved using one of three main strategies: factoring, the quadratic formula, or completing the square.

So, solving x²+2x+7 using the quadratic formula as follows:

Quadratic formula: (-b±√(b²-4ac))/(2a)

Substitute values and caluclate:

x = (-b±√(b²-4ac))/(2a)

x = (-2±√(2²-4(1)(7))/(2*1)

x = (-2±√4-28)/(2)

x = (-2±√-24)/(2)

Complex roots:
x = (-2±2√6i)/(2)

x = -2/2 ± 2√6i/2

Simplifying fractions:
x = -1 ± √6i

So, we have:
x = -1 ± 2.44949i

Therefore, solving the equation x²+2x+7 using the quadratic formula, the resultant answer is x = -1 ± 2.44949i.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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Answer:

-16

Step-by-step explanation:

\(28-(\sqrt{44} )^2\\28 - (44)\\-16\)

When you square a square root, the number inside is the answer.

Answer:

D. (z) = (x − 3)¹ – 2​

Step-by-step explanation:

To determine which transformation of the parent square root function will result in the given domain and range, we need to consider the effects of the transformations on the function.

The parent square root function is given by f(x) = √x.

Let's analyze each option and see if it satisfies the given conditions:

A. j(x) = (x + 2)³ + 3

This transformation involves shifting the graph 2 units to the left and 3 units up. However, this does not change the domain of the function, so it does not satisfy the given domain condition.

B. k(x) = (z + 3) – 2

This transformation involves shifting the graph 3 units to the left and 2 units down. Again, this does not change the domain of the function, so it does not satisfy the given domain condition.

C. g(x) = (x − 2)³ + 3

This transformation involves shifting the graph 2 units to the right and 3 units up. However, this does not change the range of the function, so it does not satisfy the given range condition.

D. z(x) = (x − 3)¹ – 2

This transformation involves shifting the graph 3 units to the right and 2 units down. This shift does not affect the domain of the function, but it affects the range. The function z(x) = (x − 3)¹ – 2 starts at y = -2 when x = 3, and it increases as x goes to infinity. Therefore, it satisfies both the given domain and range conditions.

Based on the analysis, the correct transformation that satisfies the given domain and range is option D:

z(x) = (x − 3)¹ – 2

chatgpt

The process is wide sense stationary. The process \(X(t)\) has finite second-order statistics because its mean is finite and its autocorrelation function (as determined in part c, if available) would also be finite. the mean of the process \(X(t)\) is \(\frac{1}{2}\).

a) The given random process \(X(t)\) is **continuous**. This is because it is described by a continuous random variable \(A\) that is uniformly distributed from 0 to 1.

b) The given random process \(X(t)\) is **non-deterministic**. This is because it is determined by the random variable \(A\), which introduces randomness and variability into the process.

c) To find the autocorrelation function of the process, we need more information about the relationship between different instances of the random variable \(A\) at different time points. Without that information, we cannot determine the autocorrelation function.

d) Since the process is defined as \(X(t) = A\) where \(A\) is uniformly distributed from 0 to 1, the mean of the process can be calculated by taking the mean of the random variable \(A\). In this case, the mean of \(A\) is \(\frac{1}{2}\). Therefore, the mean of the process \(X(t)\) is \(\frac{1}{2}\).

e) The given process is **wide sense stationary**. To be considered wide sense stationary, a process must satisfy two conditions: time-invariance and finite second-order statistics.

- Time-invariance: The given process \(X(t) = A\) is time-invariant because the statistical properties of \(X(t)\) are not dependent on the specific time at which it is observed. The distribution of \(A\) remains the same regardless of the time.

- Finite second-order statistics: The process \(X(t)\) has finite second-order statistics because its mean is finite (as determined in part d), and its autocorrelation function (as determined in part c, if available) would also be finite.

Therefore, the process is wide sense stationary.

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