Write an explicit formula for an, the nth term of the sequence 15, 12,9,....

Answer:

5 Neon tetras

6 Zebra Fish

Step-by-step explanation:

21.60/2=10.80

Neon Tetras: 2.10*5=10.50

Zebra fish: 1.85*6=11.10

10.50+11.10= 21.60

To find the partial fraction expansion of the rational function:

f(s) = (6s^3 + 120s^2 + 806s + 1884) / (s^2 + 10s + 29)^2

We start by factoring in the denominator:

s^2 + 10s + 29 = (s + 5 - 2i)(s + 5 + 2i)

Since we have a quadratic factor repeated twice, we will have two partial fractions of the form:

A / (s + 5 - 2i) + B / (s + 5 + 2i) + C / (s + 5 - 2i)^2 + D / (s + 5 + 2i)^2

where A, B, C, and D are constants to be determined.

To find A and B, we can multiply both sides of the equation by (s + 5 - 2i)(s + 5 + 2i) and then set s = -5 + 2i and s = -5 - 2i, respectively. This gives us the equations:

A(s + 5 + 2i) + B(s + 5 - 2i) + C(s + 5 - 2i)^2 + D(s + 5 + 2i)^2 = 6s^3 + 120s^2 + 806s + 1884

Substituting s = -5 + 2i, we get:

A(3 + 2i) = -204 + 856i

Substituting s = -5 - 2i, we get:

B(3 - 2i) = -204 - 856i

Solving these equations for A and B, we get:

A = (356 + 144i) / 29

B = (-560 + 144i) / 29

To find C and D, we differentiate both sides of the equation with respect to s and then set s = -5 + 2i and s = -5 - 2i, respectively. This gives us the equations:

A + B + 2C(s + 5 - 2i) + 2D(s + 5 + 2i) = 6s^2 + 240s + 806

2C + 2D = 0

Substituting s = -5 + 2i, we get:

A + B + 4C = -176 - 264i

Substituting s = -5 - 2i, we get:

A + B + 4D = -176 + 264i

Solving these equations for C and D, we get:

C = (16 + 3i) / 58

D = (16 - 3i) / 58

Therefore, the partial fraction expansion of f(s) is:

f(s) = [(356 + 144i) / 29] / (s + 5 - 2i) + [(-560 + 144i) / 29] / (s + 5 + 2i) + [(16 + 3i) / 58] / (s + 5 - 2i)^2 + [(16 - 3i) / 58] / (s + 5 + 2i)^2

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Answer:

The five rational numbers between -3 and -2 are : - -13/6, -14/6, -15/6, -16/6, -17/6. so, the rational numbers between -2 & -3 are -13/6, -14/6, -15/6, -16/6, -17/6.

Step-by-step explanation:

if it helped uh please mark me a BRAINLIEST :)

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1. Difference: \(\displaystyle\sf (-2) - (-3) = -2 + 3 = 1\).

2. Interval: \(\displaystyle\sf \frac{1}{6}\).

3. Rational Numbers:

a. \(\displaystyle\sf -3 + \text{Interval} = -3 + \left(\frac{1}{6}\right) = -\frac{17}{6}\).

b. \(\displaystyle\sf -3 + 2 \times \text{Interval} = -3 + 2 \times \left(\frac{1}{6}\right) = -\frac{16}{6}\).

c. \(\displaystyle\sf -3 + 3 \times \text{Interval} = -3 + 3 \times \left(\frac{1}{6}\right) = -\frac{15}{6} = -\frac{5}{2}\).

d. \(\displaystyle\sf -3 + 4 \times \text{Interval} = -3 + 4 \times \left(\frac{1}{6}\right) = -\frac{14}{6} = -\frac{7}{3}\).

e. \(\displaystyle\sf -3 + 5 \times \text{Interval} = -3 + 5 \times \left(\frac{1}{6}\right) = -\frac{13}{6}\).

Therefore, the five rational numbers between -3 and -2 are:

\(\displaystyle\sf -\frac{17}{6}, -\frac{16}{6}, -\frac{5}{2}, -\frac{7}{3}, \text{ and } -\frac{13}{6}\).

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Answer:

7.3units

Step-by-step explanation:

\( \sqrt{(x2 - x1) {}^{2} + (y2 -y1) {}^{2} } \)

\( \sqrt{ (- 1 - 6) { \\ }^{2} + (14 - 16) {}^{2} } \)

\( = 7.3\)

The answer are:

a. The random variable X is car battery

b. X is a continuous random variable

c. X ~ Exponential(0.025)

d. battery lasts (1/0.025)

e. 9 times 40 months, which is 360 months

f.the probability that a car battery lasts more than 36 months is approximately  30.33%.

g.seventy percent of the batteries last at least approximately  78.40 months.

a. The random variable X is defined as the useful life of a particular car battery, measured in months. In other words, X represents the duration, in months, that a car battery will last before it needs to be replaced.

b. X is a continuous random variable because the useful life of a car battery can take on any positive real value within a certain range (e.g., 0 months, 1 month, 2 months, etc.) without any gaps or jumps.

c. X ~ Exponential(0.025) means that X follows an exponential distribution with a decay parameter of 0.025. The exponential distribution is commonly used to model the time between events in a Poisson process, such as the failure or replacement of car batteries in this case. The decay parameter (λ) determines the rate at which the battery's useful life decays. In this scenario, a higher decay parameter value (0.025) implies a faster decay or shorter average life for the battery.

d. The average or expected value of an exponential distribution is given by the reciprocal of the parameter. Therefore, the average useful life of one car battery would be:

Expected value of X = 1 / 0.025 = 40 months

On average, one car battery would be expected to last 40 months,

e. The expected value of a sum of independent random variables is equal to the sum of their individual expected values. Therefore, if you use nine car batteries one after another, the expected total useful life would be:

Expected value of 9X = 9 * Expected value of X = 9 * 40 = 360 months

On average, you would expect nine car batteries to last for a total of 360 months.

f.To find the probability that a car battery lasts more than 36 months, we can use the cumulative distribution function (CDF) of the exponential distribution:

P(X > 36) = 1 - P(X ≤ 36)

The CDF of an exponential distribution with parameter λ is given by:

F(x) = 1 - \(e^{-\lambda x}\)

In this case, λ = 0.025. Substituting the values:

P(X > 36) =\(1 - e^{-0.025 * 36}\)

Calculate the probability using the formula:

P(X > 36) ≈ 0.3033

Therefore, the probability that a car battery lasts more than 36 months is approximately 0.3033, or 30.33%.

g.  To find the value of x at which 70% of the batteries last at least that long, we can use the quantile function (inverse of the CDF) of the exponential distribution.

Let's denote the value we are looking for as\(x_0.\)

P(X ≥ \(x_0\)) = 0.70

Using the CDF of the exponential distribution:

\(1 - e^{-0.025 * x_0} = 0.70\)

Solving for x_0:

\(e^{-0.025 * x_0}= 0.30\)

Taking the natural logarithm of both sides:

\(-0.025 * x_0 = ln(0.30\))

Solving for \(x_0:\)

\(x_0 = ln(0.30) / (-0.025)\)

Calculate the value:

\(x_0 =\) 78.40

Therefore, seventy percent of the batteries last at least approximately 78.40 months.

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Answer:

POR LAS DIFICULTADES ENCONTRADAS VAMOS A SEGUIR EN EL MISMO TEMA

Pero para ello veremos primero una regla de tres compuesta inversa y haremos el respectivo análisis.

Ejemplo:

4 obreros trabajando 7 horas diarias construyen un muro en 3 días ¿cuántos días tardarán 2 obreros trabajando 6 horas diarias en construir el mismo muro?

Ahora usamos la ley de los signos arriba tenemos más obreros, más horas, abajo en cambio lo contrario

+x-=-

por lo tanto es una regla de tres inversa

realizamos el proceso :Multiplicamos todo lo que está arriba o como haciamos los ejemplos:

X=3x4x7/2x6

X=84/12

X=7

Dos obreros trabajando 6 horas diarias contruyen el muro en 7 días.

Ahora esperemos que este más claro y vamos a realizar la regla de tres inversa en otros problemas .

1.Cuatro tractores pueden remover 400 m3 de tierra en 6 horas. ¿Cuánto demorarán seis tractores en remover 800 m3 de tierra?

2.Un grupo de 24 pintores demoran 5 días en pintar una fachada de 100 m2, trabajando 12 horas diarias. ¿Cuánto demorarían 18 pintores en una fachada de 150 m2, trabajando 8 horas diarias?

3. Una tripulación de 20 marineros tiene víveres para 40 días. Al cabo del octavo día, 4 de los marineros son desembarcados por enfermedad. ¿Cuántos días podrán alimentarse los marineros restantes con lo que queda?

4. Una cuadrilla de 40 trabajadores puede realizar una obra en 30 días. Al cabo de 2 días se retiran 5 trabajadores. ¿En cuántos días se terminará lo que falta de la obra?

Step-by-step explanation

:

k

Hence proved ,the series for j 0(x) converges for all x .

A series in mathematics is the process of adding an unbounded number of quantities, after the one  other, to a specified initial amount. A significant component of calculus and its generalization, mathematical analysis, is the study of series.

Then we call that the series has converged and  in that case we define the total of the series as the limit of the partial sums,When the sequence of partial sums in a series are converges.

J 0(x) is called the Bessel function of the first kind of order zero,

we know that , \(J0(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ...\)is called JO(x) series,

We use the ratio test to determine that this series converges for all values of x.

According to the ratio test, the series of the form \(\frac{a_(n+1)}{a_n}\) also converges if the series JO(x) converges. The series converges if it is less than 1.  and diverges if the limit of the ratio test is greater than 1,

Let a use the ratio test for the J0(x) series:

let a consider term  is  R=\(((a_(n+1))/a_n) = (x^2_(n+2)) / [(2n+2)(2n+1)] / (x^2n) / [(2n)(2n-1)] | = | x^2 / [(2n+2)(2n+1)] |\)

Considering the limit as n tends to infinity:

\(\lim_{n \to \infty} |a_(n+1) / a_n) |=\lim_{n \to \infty} | x^2 / [(2n+2)(2n+1)] = 0\)

For all values of x, the series converges  since the limit is less than 1.

therefore the J 0(x) series converges for all x.

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The volume of water in the tank is 35,100 cubic feet.

Volume = length × width × height

We have the following parameters based on the information provided;

Length = 20 meters

Width = 13 meters

Height = 5 meters

Substitute the values into the formula to get

Volume = 20 × 13 × 5

Volume = 1300 cubic meters

Convert the cubic yard into cubic feet

1 cubic yard = 27 cubic foot

⇒ 1300 yards = x

⇒ x = 27 × 1300

⇒ x = 35,100 cubic feet

Therefore, the amount of water a bag of salt can treat is 35,100 cubic feet

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The question seems to be incomplete the correct question would be

The new dolphin tank at the city aquarium is in the shape of a rectangular prism. It is 20 yds long by 13 yds wide 5yds by deep. To make the tank livable for the dolphins, the aquarium workers treat the water using bags of salt. The amount of water a bag of salt can treat is known in cubic feet.

Find the volume of water in the tank in cubic feet.

Part A: The height of the container is 5cm.

Part B: The cost of the coffee is $2.83.

Part C: The height of the container is 9cm.

Part D: The cost of the hot chocolate powder is $49.35.

What is volume of cylinder ?

The volume of a cylinder is the amount of space occupied by a cylindrical shape. It is given by the formula:

V = πr²h

where V is the volume, r is the radius of the circular base of the cylinder, and h is the height of the cylinder. The formula is derived by multiplying the area of the circular base (πr²) by the height (h) of the cylinder.

According to the question:
Part A:

Given that the container is a cylinder with a radius of 3cm, we can use the formula for the volume of a cylinder to find the height of the container. The formula for the volume of a cylinder is:

V = πr²h

where V is the volume of the cylinder, r is the radius of the cylinder, and h is the height of the cylinder.

Substituting the given values, we get:

45π = π(3)²h

Simplifying and solving for h, we get:

h = 5

Therefore, the height of the container is 5cm.

Part B:

The volume of the container is 45π cm³ and the cost of coffee is $0.02 per cubic centimeter. Therefore, the total cost of the coffee is:

Total cost = Volume x Cost per unit volume

Total cost = 45π x $0.02

Total cost = $0.90π

Rounding to two decimal places, we get:

Total cost = $2.83

Therefore, the cost of the coffee is $2.83.

Part C:

Given that the container is a cylinder with a radius of 5cm, we can use the same formula for the volume of a cylinder to find the height of the container. Substituting the given values, we get:

225π = π(5)²h

Simplifying and solving for h, we get:

h = 9

Therefore, the height of the container is 9cm.

Part D:

The volume of the container is 225π cm³ and the cost of hot chocolate powder is $0.07 per cubic centimeter. Therefore, the total cost of the hot chocolate powder is:

Total cost = Volume x Cost per unit volume

Total cost = 225π x $0.07

Total cost = $15.75π

Rounding to two decimal places, we get:

Total cost = $49.35

Therefore, the cost of the hot chocolate powder is $49.35.

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Solution

Given that;

42, 10, 36, 51, 70, 28

max = 70

min = 10

range = 70 - 10 = 60

midrange = (max + min)/2

= (70 + 10)/2

= 80/2

= 40

Therefore, The range is larger than the midrange.

The formula used to calculate the likely size of the chance error is SE = s/√n where SE is the standard error, s is the standard deviation, and n is the sample size. In this problem, there are eight students, so n = 8.

The standard deviation can be calculated using the formula σ = √(Σ(x - µ)² / n), where σ is the standard deviation, x is each data point, µ is the mean, and n is the sample size. Using the given data, the mean can be calculated as follows:

Mean = (9.93 + 9.96 + 10.10 + 10.02 + 10.02 + 9.90 + 9.93 + 9.92) / 8 = 9.985Next, calculate the sum of the squared deviations from the mean:Σ(x - µ)² = (9.93 - 9.985)² + (9.96 - 9.985)² + (10.10 - 9.985)² + (10.02 - 9.985)² + (10.02 - 9.985)² + (9.90 - 9.985)² + (9.93 - 9.985)² + (9.92 - 9.985)²Σ(x - µ)² = 0.0211.

Then, calculate the variance by dividing the sum of squared deviations by the sample size:

Variance = Σ(x - µ)² / n

Variance = 0.0211 / 8Variance = 0.00264Finally, calculate the standard deviation by taking the square root of the variance:

Standard deviation = √(Σ(x - µ)² / n)Standard deviation = √(0.00264)Standard deviation = 0.05134The standard error can now be calculated by dividing the standard deviation by the square root of the sample size:

Standard error = s/√nStandard error = 0.05134/√8Standard error = 0.01813

Given the measurements of eight students to determine the correct length of a ruler in a laboratory, we can calculate the size of the chance error using the formula SE = s/√n. This formula calculates the standard error, where s is the standard deviation and n is the sample size. To find the standard deviation, we use the formula σ = √(Σ(x - µ)² / n), where x is each data point, µ is the mean, and n is the sample size. Using the given measurements, the mean of the data is calculated to be 9.985. Using this mean, we can calculate the sum of the squared deviations from the mean, which is equal to 0.0211. Then, we can calculate the variance by dividing the sum of squared deviations by the sample size, which is equal to 0.00264. Finally, the standard deviation can be calculated by taking the square root of the variance, which is equal to 0.05134. By dividing the standard deviation by the square root of the sample size, we can find the standard error, which is equal to 0.01813. Therefore, we would expect the likely size of the chance error to be about 0.018 inches or so.

Given the measurements of eight students, we used the formulas SE = s/√n and σ = √(Σ(x - µ)² / n) to calculate the size of the chance error. The mean of the data was found to be 9.985, and the sum of the squared deviations from the mean was equal to 0.0211. We used these values to calculate the variance, which was equal to 0.00264, and the standard deviation, which was equal to 0.05134. Finally, we found the standard error to be equal to 0.01813. Therefore, we would expect the likely size of the chance error to be about 0.018 inches or so.

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Step-by-step explanation:

5/9×3/10= 15/90 simplification is 1/6

the correct is 1/6

Answer:

The 4th answer is correct

Step-by-step explanation:

\(\frac{5}{9} *\frac{3}{10} \\\\\)

\(\frac{5*3}{9*10}\)

\(\frac{15}{90}\)

Now you can make the answer as the simplest form divide both sides by 15

\(\frac{15}{90} =\frac{1}{6}\)

ANSWER IS,

\(\frac{1}{6}\)

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

dark blue

Step-by-step explanation:

The farmer needs at least 25 tomatos

He needs to pick at least 11 more

therefore

it's the dark blue

t>11

Answer:

answer choice A

Step-by-step explanation:

you make two equations.

Answer:

It's b, 54, because that makes the sum.

Answer:

43

Step-by-step explanation:

how

\(2x - \frac{3}{4} = \frac{1}{3} x + \frac{5}{6} \\ = > 2x - \frac{1}{3} x = \frac{5}{6} + \frac{3}{4} \\ = > \frac{6x - x}{3} = \frac{10 + 9}{12} \\ = > \frac{5x}{3} = \frac{19}{12} \\ = > x = \frac{19}{12} \times \frac{3}{5} \\ = > \frac{19}{20} \\ \)

Therefore,

\(x = \frac{19}{20} \)

verified.

Hope you could get an idea from here.

Doubt clarification - use comment section.

In summary, using Z scores and a Z table, we can find that approximately 51% of respondents were married for the first time between the ages of 20 and 30, and an individual married for the first time at the age of 35 is in approximately the 97th percentile.

(a) To calculate the Z score for an observed age of 25.50, we use the formula Z = (X - μ) / σ, where X is the observed value, μ is the mean, and σ is the standard deviation. Substituting the given values, we get Z = (25.50 - 23.33) / 6.13 ≈ 0.36. The Z score tells us that the observed age is approximately 0.36 standard deviations above the mean. (b) To find the observed age associated with a Z score of -0.72, we rearrange the formula and solve for X: X = Z * σ + μ. Substituting the values, we get X = -0.72 * 6.13 + 23.33 ≈ 20.95. Thus, an observed age of approximately 20.95 corresponds to a Z score of -0.72.

(c) To calculate the proportion of respondents married between the ages of 20 and 30, we need to convert the age range to Z scores. The Z score for 20 is (20 - 23.33) / 6.13 ≈ -0.54, and the Z score for 30 is (30 - 23.33) / 6.13 ≈ 1.09. We then calculate the area under the normal distribution curve between these Z scores using a Z-table or a statistical software. This proportion represents the proportion of respondents married for the first time between the ages of 20 and 30.

(d) To determine the percentile rank for an individual married at the age of 35, we need to calculate the area under the normal distribution curve to the left of the corresponding Z score. The Z score for 35 is (35 - 23.33) / 6.13 ≈ 1.90. We then look up the corresponding percentile in a Z-table or use statistical software to find the percentage of the population with a Z score less than 1.90. This percentage represents the percentile rank for an individual married at the age of 35.

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Answer:

576

Step-by-step explanation:

18 x 32 = 576

Answer:

E)

Step-by-step explanation:

Because its gonna be a negative number and while using letters you should not use negative numbers you should use positive numbers or decimals

:) good luck

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

Step-by-step explanation:

1  1/4  = 5/4

5/4 ÷ 5/7   =   5/4 * 7/5  =  35 / 20  =  7/4  =   1  3/4

Answer:1 whole +  1/4÷5/7 = -0.5617339+0.4107813i

There are 150 different ways can 30 books be placed on these shelves if the books are all different.

The number of shelves on a bookshelf is 5.

The number of books on one shelf is 30.

The number of books on 5 shelves= The number of books on one shelf *The number of shelves.

which implies that, the total number of books =30*5

By multiplying 30 by 5 we get 150

total number of books =150.

hence, bookshelves have 150 books if books are placed differently.

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We have proven that no two events a and b can be independent unless either a or b is the whole sample space or the empty set below.

A sample space can be defined as the set of all possible outcomes of any experiment.

We are already aware that the outcomes of this die are going to be (1,2,3,..p). If we have a pair of proper events A, B which are independent, this would mean that = A∩B={∅}  (i)

This is a contradiction. So, now we suppose that = A∩B=C, for some proper event C (ii)

Using the values of (i) and (ii), we get -

= |C|p=P(A∩B)=P(A)P(B)=|A||B|p2.

= p|C|=|A||B|.

From this, we understand that neither A nor B are going to be full spaces and hence, no two events a and b are independent and 0<|A|<p and 0<|B|<p. Since |C| is also going to be less than 0 and p is prime, p divides either |A| or |B|.  if p was not prime (say, p=4), then you would only need the factors of p to divide either |A|,|B|, so, it becomes necessary for p to be a prime number. Hence, proved.

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Answer:

Border City is 1488 Miles

Step-by-step explanation:

Do 248*6

The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:

SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case, we have the following values:

X1 = 24 (number of successes in sample 1)

n1 = 200 (sample size 1)

X2 = 17 (number of successes in sample 2)

n2 = 150 (sample size 2)

To calculate the sample proportions, we divide the number of successes by the respective sample sizes:

p1 = X1 / n1 = 24 / 200 = 0.12

p2 = X2 / n2 = 17 / 150 = 0.1133

Now, we can plug these values into the formula to calculate the standard error:

SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]

SE ≈ 0.0319

Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:

Z = (p1 - p2) / SE

Z = (0.12 - 0.1133) / 0.0319

Z ≈ 0.2103

Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

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a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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Answer:

g = x2 + 4/x

Step-by-step explanation:

Step 1: Divide both sides by x.

gx/x = x2 + 4/x

g = x2 + 4/x