15,10,20/3,... find the 9th term

The length of Elena's pencil is approximately 9.49 inches.

Let's break down the problem :

We are given that Elena's mini fish tank has a length of 4 inches, a width of 5 inches, and a volume of 140 cubic inches.

To find the height of the tank, we can use the formula for the volume of a rectangular prism: volume = length * width * height.

Plugging in the given values, we have[tex]140 =4 \times 5 \times height.[/tex]

Solving for height, we get height [tex]= 140 / (4 \times 5) = 7[/tex] inches.

Now, let's move on to finding the length of Elena's pencil.

We are told that the pencil fits diagonally in the tank.

The diagonal of a rectangular prism can be found using the formula: diagonal [tex]= \sqrt{(length^2 + width^2 + height^2) }[/tex]

Plugging in the values, we have diagonal [tex]= \sqrt{(4^2 + 5^2 + 7^2) }[/tex]

[tex]= \sqrt{(16 + 25 + 49) }[/tex]

= √90

= 9.49 inches (rounded to two decimal places).

Therefore, the length of Elena's pencil is approximately 9.49 inches.

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The area of the trapezoid in this problem is given as follows:

15 square feet.

The area of a trapezoid is given by half the multiplication of the height by the sum of the bases, hence:

A = 0.5 x h x (b1 + b2).

The dimensions for this problem are given as follows:

h = 3 ft, b1 = 4 ft and b2 = 6 ft.

Hence the area is given as follows:

A = 0.5 x 3 x (4 + 6)

A = 1.5 x 10

A = 15 square feet.

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Sure, happy to help! So, we have two furniture manufacturers producing chairs, and we'll call them Plant X and Plant Y. Let x represent the number of chairs produced daily at Plant X, and let y represent the number of chairs produced daily at Plant Y.

Now, we don't know what the actual numbers are, but we can use these variables to talk about them in a general way. For example, we could say that Plant X produces 100 chairs per day (so x = 100), and Plant Y produces 200 chairs per day (so y = 200).

Does that make sense? Let me know if you have any other questions!

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We know that the skier would have to go skiing for 5 days in order for both options to cost the same.

To find out how many days a skier would have to go skiing for both options to cost the same, we need to set up an equation. Let's use "d" to represent the number of days the skier goes skiing.

For the daily pass option:
Total cost = $48 x d

For the season pass option:
Total cost = $190 + ($10 x d)

Now we can set up the equation:

$48 x d = $190 + ($10 x d)

Simplifying this equation, we get:

$38 x d = $190

Solving for "d", we get:

d = 5

Therefore, the skier would have to go skiing for 5 days in order for both options to cost the same.

So the answer is A. 5 days.

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You're partially correct, as if x approaches ∞ it would approach 2, as eˣ is exponentially growing if x is positive.

If x is negative, which it is in this case, eˣ would get exponentially smaller. For example, e⁻² = 1/e².

So, in this case [tex]\frac{5}{e^x}[/tex] would get exponentially larger, as it is a number over an increasingly small number, like how [tex]\frac{1}{0.001}[/tex] is larger than [tex]\frac{1}{0.1}[/tex].

Therefore the limit would be equivalent to [tex]\frac{2}{\infty}[/tex], which is equal to 0

[tex] \Large{\boxed{\sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = 0}} [/tex]

[tex] \\ [/tex]

Explanation:

We are trying the find the limit of [tex] \: \sf \dfrac{2}{1 - \dfrac{5}{ {e}^{x} } } \: [/tex] when x tends to -∞.

[tex] \\ [/tex]

Given expression:

[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) [/tex]

[tex] \\ [/tex]

[tex]\blue{\begin{gathered}\begin{gathered} \\ \boxed { \begin{array}{c c} \\ \blue{ \star \: \sf{\boxed{ \sf Properties\text{:}}}} \\ \\ \sf{ \diamond \: \dfrac{c}{ + \infty} = 0^{ + } \: \: and \: \: \dfrac{c}{ - \infty} = 0^{ - } \: \: , \: where \: c \: is \: a \: positive \: number.} \\ \\ \\ \diamond \: \sf \dfrac{c}{ {0}^{ + } } = + \infty \: \: and \: \: \dfrac{c}{ {0}^{ - } } = - \infty \: \: , \: where \: c \: is \: a \: positive \: number.\\ \\ \\ \diamond \: \sf c - \infty = -\infty \: \: and \: \: c + \infty = \infty \: \: ,\: where \: c \: is \: a \: positive \: number. \\ \\ \\ \sf{ \diamond \: \green{e ^{ - \infty} = 0^{+} \: \: and \: \: e ^{ + \infty} = + \infty} } \\ \end{array}}\\\end{gathered} \end{gathered}}[/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \sf \left(\dfrac{2}{1-\frac{5}{e^{ - \infty}}}\right) [/tex]

[tex] \\ [/tex]

Simplify knowing that [tex] \sf e^{-\infty} \\ [/tex] approaches 0 but remains a positive number. This will be written as 0⁺.

[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \left(\dfrac{2}{1-\frac{5}{e^{ - \infty}}}\right) = \left(\dfrac{2}{1-\frac{5 \: \: }{0^{ + } }}\right)[/tex]

[tex] \\ [/tex]

Simplify again knowing that 5/0⁺ = +∞.

[tex] \\ [/tex]

[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \left(\dfrac{2}{1-\frac{5 \: \: }{0^{ + } }}\right) = \sf \left(\dfrac{2}{1 - \infty}\right) = \dfrac{2}{ - \infty} [/tex]

[tex] \\ [/tex]

[tex] \\ [/tex]

[tex] \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) = \dfrac{2}{ - \infty} = 0^{-} \\ \\ \\ \implies \boxed{ \boxed{ \sf \lim_{x\to-\infty}\left(\dfrac{2}{1-\frac{5}{e^x}}\right) =0}}[/tex]

[tex] \\ \\ \\ [/tex]

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To find out how much Casho would have to pay in a month in which she downloaded 30 songs, we need to consider both the monthly subscription cost and the cost per song for offline listening.

Step 1: Determine the cost of the monthly subscription, which is $7.

Step 2: Calculate the cost of downloading 30 songs for offline listening. To do this, multiply the cost per song ($1.50) by the number of songs (30).
1.50 * 30 = $45

Step 3: Add the monthly subscription cost ($7) to the cost of downloading 30 songs ($45).
7 + 45 = $52

So, Casho would have to pay $52 a month in which she downloaded 30 songs.

Now, let's find out how much Casho would have to pay if she downloaded ss songs.

Step 1: The cost of the monthly subscription remains the same at $7.

Step 2: Calculate the cost of downloading ss songs for offline listening. Multiply the cost per song ($1.50) by the number of songs (ss).
1.50 * ss = 1.50ss

Step 3: Add the monthly subscription cost ($7) to the cost of downloading ss songs (1.50ss).
7 + 1.50ss = 7 + 1.50ss

The total amount Casho would have to pay if she downloaded ss songs is 7 + 1.50ss.

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The equation that represents how much total interest Kera will pay towards the remaining balance of the loan at the end of each year is Total Interest Paid = (Remaining Balance) x (Annual Interest Rate) = $422.03.

The equation that represents how much total interest Kera will pay towards the remaining balance of the loan at the end of each year is:

Total Interest Paid = (Remaining Balance) x (Annual Interest Rate)

To calculate the remaining balance after m months, we can use the formula for the present value of an annuity:

Remaining Balance = (Payment per Month) x ((1 - (1 + r)^(-n)) / r)

where r is the monthly interest rate (0.0595 / 12 = 0.004958), n is the total number of months (24), and m is the number of months paid (12, 24, etc.).

Plugging in the given values, we get:

Remaining Balance = 450 x ((1 - (1 + 0.004958)^(-12)) / 0.004958) = $6,752.45

To calculate the annual interest rate, we can use the formula:

Annual Interest Rate = (1 + r)^12 - 1

Plugging in the monthly interest rate, we get:

Annual Interest Rate = (1 + 0.004958)^12 - 1 = 0.0625

Therefore, the equation that represents how much total interest Kera will pay towards the remaining balance of the loan at the end of each year is:

Total Interest Paid = $6,752.45 x 0.0625 = $422.03 (rounded to the nearest cent)

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The answer is (C) 67.20.

Charlie saved 30% off of the original price, which means he paid 70% of the original price.

Let x be the sale price of the skateboard.

We have:

0.7 * 96 = x

x = 67.20

Therefore, the sale price of the skateboard was $67.20.

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Answer:

0.48 = 48/100

48/100 ÷ 4/4 = 12/25

0.48 = 12/25 =A

To determine whether (x + 3) is a factor of the polynomial x^3 - x^2 - 12x, we can use polynomial division.

Step 1: Write the divisor, (x + 3), on the left side of a long division symbol and the dividend, x^3 - x^2 - 12x, on the right side.

x + 3 | x^3 - x^2 - 12x

Step 2: Divide the first term of the dividend, x^3, by the first term of the divisor, x, and write the result, x^2, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the dividend.

lua

       x^2 - 4x

  ___________________

x + 3 | x^3 - x^2 - 12x

      - (x^3 + 3x^2)

        ----------

         -4x^2

Step 3: Bring down the next term of the dividend, -12x, and write it next to the remainder, -4x^2.

lua

Copy code

       x^2 - 4x

  ___________________

x + 3 | x^3 - x^2 - 12x

      - (x^3 + 3x^2)

        ----------

         -4x^2 - 12x

Step 4: Divide the first term of the new dividend, -4x^2, by the first term of the divisor, x, and write the result, -4x, on top of the division symbol. Multiply the divisor by this quotient, and write the result under the previous subtraction.

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The price of one apple is $0.70, obtained by solving the system of equations 4x + 9y = 12.70 and 8x + 11y = 17.70 using elimination.

Let's use a system of equations caculation the problem.

Let x be the price of one apple and y be the price of one banana.

From the first sentence, we know that:

4x + 9y = 12.70

From the second sentence, we know that:

8x + 11y = 17.70

Now we can solve for x by using either substitution or elimination.

Let's use elimination.

We can multiply the first equation by 11 and the second equation by -9, then add them together:

44x + 99y = 139.70

-72x - 99y = -159.30

-28x = -19.60

Dividing both sides by -28, we get:

x = 0.70

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Answer:

y = (-2/5)x+b

Step-by-step explanation:

First plug these into the y=mx+b equation:

-5 = (-2/5)(10)+b.

Then solve for b:

-5 = -4+b

Add 4 to both sides:

-1 =b.

Therefore, the equation of the line is y = (-2/5)x+b. You can also double check this by plugging 10 into the equation we just obtained.

To find the maximum height of the object, we need to first determine when the object reaches that height. We can use the projectile motion model h(t) = -4.9t^2 + v0t + h0 to solve for the time it takes for the object to reach its maximum height.

Since the object is launched vertically, we know that its initial velocity is 41.65 m/s and its initial height is 7 meters. We can substitute these values into the projectile motion model and solve for when the object reaches its maximum height by finding the vertex of the resulting quadratic function.

h(t) = -4.9t^2 + 41.65t + 7

To find the time it takes for the object to reach its maximum height, we can use the formula t = -b/2a, where a = -4.9 and b = 41.65.
t = -(41.65)/(2(-4.9))
t = 4.25 seconds

Therefore, it takes 4.25 seconds for the object to reach its maximum height.
To find the maximum height, we can plug in this time value into the projectile motion model and solve for h(t).
h(4.25) = -4.9(4.25)^2 + 41.65(4.25) + 7

h(4.25) = 89.57 meters
The maximum height of the object is 89.57 meters.

In summary, the object launched vertically from a 7-meter-tall platform with an initial velocity of 41.65 m/s takes 4.25 seconds to reach its maximum height of 89.57 meters. This is found by using the projectile motion model h(t) = -4.9t^2 + v0t + h0 and finding the time it takes for the object to reach its maximum height, and then plugging in that time value to find the maximum height.

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The appropriate measures of center and variation are 13 and 4.

Measures of Center:

The appropriate measure of center for this data set is the median since there is no clear outlier present in the data. Hence, the value of median here is 13

Measures of Variation:

The appropriate measure of variation for this dataset is the range, which is the difference between the largest and smallest value in the dataset, Hence the value of range is 4

Since the data is small and there is no clear outlier present, the median is the appropriate measure of center. The range, which is the difference between the largest and smallest value in the dataset, is the appropriate measure of variation

Hence, the appropriate measures of center and variation are 13 and 4.

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Given points:

(u, v) = (24 + 0,u - 40, 8u): u = 3. V = 9 T, T, = n(u, v)

the equation of the tangent plane at the point (u, v) = (24, 9) is:-8x + z = -183T

Process of finding equation:

To start, let's find T..T,, which represents the magnitude of the tangent vector at the given point:

T..T, = ||n(u, v)|| = ||n(24, -31, 72)|| = ||<48, -62, 144>|| = sqrt(48^2 + (-62)^2 + 144^2) = sqrt(11668) ≈ 108.03

Next, let's find the normal vector n(u, v) at the given point:

n(u, v) =

where f_u and f_v are the partial derivatives of the surface equation with respect to u and v, respectively.

In this case, we have:

f(u, v) = (24 + 0,u - 40, 8u)
f_u = <0, 1, 8>
f_v = <1, 0, 0>

Therefore, at the point (u, v) = (24, 9), we have:

n(u, v) = <0, 1, 8> x <1, 0, 0> = <-8, 0, 1>

Finally, let's find the equation of the tangent plane at the point (u, v) = (24, 9). The equation of a plane can be written as:

Ax + By + Cz = D

where A, B, and C are the components of the normal vector, and D can be found by plugging in the coordinates of the point on the plane. In this case, we have:

A = -8
B = 0
C = 1
D = -8(24) + 1(9) = -183

Therefore, the equation of the tangent plane at the point (u, v) = (24, 9) is:

-8x + z = -183

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Both vertical angles measure 90 degrees, and the adjacent angles each measure 90 degrees as well.
When two lines intersect at a point, we can use the properties of vertical and adjacent angles to set up and solve equations relating to their measures. This can help us find missing angles or verify that two angles are congruent.

When two lines intersect at a point, they form two angles. These angles are called vertical angles, and they are always congruent. In addition, the two lines also form two pairs of adjacent angles, each pair of which adds up to 180 degrees.

Let's consider an example to understand this concept better. Suppose we have two lines AB and CD that intersect at point P. If angle APD measures x degrees, then angle BPC also measures x degrees because they are vertical angles. Similarly, angle APB and angle CPD are adjacent angles, and their sum is 180 degrees. If angle APB measures y degrees, then angle CPD also measures y degrees.

Therefore, we can set up the following equation:

x + y = 180

This equation relates the measures of the adjacent angles formed by the two lines. We can solve for one variable in terms of the other by rearranging the equation:

y = 180 - x

This equation gives us the measure of one angle in terms of the measure of the other. We can substitute this expression into the equation for the vertical angles to get:

2x = 180

Solving for x, we find that x = 90.

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Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.

To calculate the total amount Tabitha might pay for the SUV with a 7-year loan, we are able to use the compound interest formula for calculating the total amount of a loan, that is:

[tex]total amount = principal x (1 + interest charge)^{time}[/tex]

Wherein:

With a 7-year loan, the full amount Tabitha could pay is:

[tex]total amount = $29,000 x (1 + 0.043)^{7} = $37,501.76[/tex]

To calculate the overall amount she could pay with a 5-year loan and a 5% decrease interest rate, we first need to calculate the new interest price. A 5% discount inside the interest price of 4.3% is:

New interest price = 4.3% - 5% = 3.3%

Then we can use the equal formula as before to calculate the total amount with the 5-year mortgage:

[tex]total amount = $29,000 x (1 + 0.033)^{5} = $33,093.47[/tex]

The difference in the overall amount among the two loans is:

$37,501.76 - $33,093.47 = $4,408.29

Therefore, Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.

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The discount period for the bank to wait to receive its money is 37 days, and the discount rate is 3.5%.

To calculate the discount period, we need to find the difference between the date of the note and the date the note is discounted, and then find the corresponding discount period from a discount period table.

Date of note: April 3

Length of note: 82 days

Date note discounted: May 10

To find the number of days between April 3 and May 10, we can use a calendar or a date calculator, which gives us 37 days.

Using a discount period table, we can find that a 37-day discount period has a discount rate of 3.5%.

Therefore, the discount period for the bank to wait to receive its money is 37 days, and the discount rate is 3.5%.

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The area of the baby blanket with side length of 30 inches is equal to 900 square inches.

Let 'A' represents the area of the square.

And s represents the side length of the square.

The area of a square is given by the formula

A = s^2.

For Meg's baby blanket,

The side length of the baby blanket is equal to 30 inches,

Substitute the values in the area formula we get,

A = s^2

⇒ A = 30^2

⇒ A = 900 square inches

Therefore, the area of Meg's baby blanket is equal to 900 square inches.

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This means that there is a 50% chance that the outcome of a trial will be 17.

The given table represents the frequency distribution of a discrete random variable X, which has four possible outcomes: 15, 16, 17, and 18. The frequency of each outcome indicates the number of times that outcome occurs in 16 trials.

To calculate the probability of a specific outcome, we divide its frequency by the total number of trials. In this case, we want to find P(X=17), which is the probability that the outcome of a trial is 17. From the table, we see that the frequency of X=17 is 8, which means that 17 occurred 8 times out of 16 trials. Therefore,

P(X=17) = frequency of X=17 / total number of trials = 8 / 16 = 0.5

This means that there is a 50% chance that the outcome of a trial will be 17.

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Full Question: The Following Table Is Based On 16 Trials. X 15 16 17 18 Frequency 2 4 8 2 Based On The Table, What Is P(X=17)? Leave Your Answer In Decimal Form To Three Places.

The following table is based on 16 trials.

x 15 16 17 18

frequency 2 4 8 2

Based on the table, what is P(x=17)?

Leave your answer in decimal form to three places.

Orlando should consider using simple interest and the amount he will have to pay is $696, under the condition that he wants to borrow $3,000 for the purchase of a used car. He needs to clear the loan after 4 years.

Orlando should apply the simple interest method.

The amount of interest he will pay using simple interest is evaluated

I = P × r × t

Here

I = interest paid

P = borrowed principal amount

r =  rate of annual interest

t = time

In this case,

P = $3,000

r = 5.8%

t = 4 years

Therefore,

I = $3,000 × 0.058 × 4

= $696

So Orlando will pay $696 in interest using simple interest.

The amount of interest he will pay using compound interest is calculated as follows:

[tex]A = P * (1 + r/n)^{(n*t)}[/tex]

I = A - P

Here,

A = end term amount

n = count of interest that is compounded each year

In this case,

P = $3,000

r = 5.2%

t = 4 years

Interest is compounded annually so n=1

Therefore,

A = $3,000 × (1 + 0.052/1)⁴

= $3,697.47

I = $3,697.47 - $3,000

= $697.47

So Orlando will pay $697.47 in interest using compound interest.

Therefore, Orlando should choose simple interest method and he will owe $1.47 less using that method.

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A

Either divide each by one fourth or multiply each by 0.25. Then turn the answer to a fraction.

If A backyard is 40. 5 feet long and 25 feet wide then, the area of the reduced yard is approximately 450.09 ft².

The area of the original backyard is:

40.5 ft x 25 ft = 1012.5 ft²

To reduce the yard by a scale of one-third, we need to multiply the length and width by 2/3:

40.5 ft x 2/3 = 27 ft

25 ft x 2/3 = 16.67 ft (rounded to two decimal places)

The area of the reduced yard is:

27 ft x 16.67 ft = 450.09 ft² (rounded to two decimal places)

Therefore, the area of the reduced yard is approximately 450.09 ft².

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The expression that describes the length of one side of the rooftop is therefore: x - 9.

In mathematics, an expression is a combination of one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An expression can be as simple as a single variable or constant, or it can be a more complex combination of variables and operations.

Here,

The expression for the area of the rooftop is (x + 9)², where x is a variable representing the length of one side of the rectangle. To find the factors of this expression, we can expand it using the identity (a+b)² = a² + 2ab + b².

Expanding (x + 9)², we get:

(x + 9)² = x² + 18x + 81

Now, we need to find the factors of this expression that are also factors of the length of the sides of the rectangle. Since the sides of the rectangle must have a common factor of x, we can factor out x from the expression:

x² + 18x + 81 = x(x + 18) + 81

The factors of (x + 9)² are x(x + 18) + 81, (x + 9)(x + 9), (x - 9)(x - 9), and -(x + 9)(x + 9).

Since we are looking for factors that represent the length of one side of the rooftop, we can eliminate the negative factor and the factor (x + 9)(x + 9), since the sides of a rectangle must be positive.

That leaves us with x(x + 18) + 81 and (x - 9)(x - 9).

The expression describes the length of one side of the rooftop: x - 9

This is because the sides of a rectangle must be positive, and (x - 9) is a factor of (x + 9)² that represents a positive length.

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The type of study the sales director is conducting is an experiment to compare the number of orders secured by those who attended the training program and those who didn't attend.

The sales director conducted an experimented

The experiment is to do a test to see if something works or to try to improve it

Here the objective of the experiment was to see the effectiveness of the training by providing a one-month training program for employees. After that, the sales director collects the sales data for the first month. The sales director compared the number of orders secured by those who attended the training program and those who didn't attend. This experiment will help the company to determine the effectiveness of the training. If the experiment is effective or not.

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Answer:

Step-by-step explanation:

percentage is taken as out of 100 we have to do like this for finding any percentage for any given ratio.

add the given ration 7+3=10

now as ratio is given from red to blue so we have red=3 and blue=7.

now final step is that simply do this.....

if 10(total) is equal to 100 %

then 3(for red) is equal how many percentage?

so we know that it will be (3 x 100) / 10 = 30%

so 30 percent of marbles are red.

The value of the expression when x=8 is 56/9.

To find the value of an expression, follow these steps:

To find the value of the expression when x=8, we substitute 8 for x in the expression:

(8^2 - 8) / (8+1)

= (64 - 8) / 9

= 56/9

Therefore, the value of the expression when x=8 is 56/9.

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The probability that Mr Smith will have coffee on exactly 8 mornings out of the next 25 is 0.142, or 14.2%.

This scenario can be modeled by a binomial distribution, where:

The probability of success (having coffee) on any given morning is p = 0.35

The number of trials (mornings) is n = 25

The number of successes (mornings with coffee) we want to find the probability for is k = 8.

The probability mass function for a binomial distribution is given by:

[tex]P(X = k) = (n \: choose \: k) \times p^k \times (1-p)^{(n-k)},[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of n. It can be calculated as:

(n choose k) = n! / (k! × (n-k)!)

Using this formula and putting in the values we have,

[tex]P(X = 8) = (25 \: choose \: 8) \times 0.35^8 \times (1-0.35)^{(25-8)} [/tex]

[tex]P(X = 8) ≈ 0.142[/tex]

Therefore, the probability that Mr Smith will have coffee on exactly 8 mornings out of the next 25 is approximately 0.142, or 14.2%.

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Answer:

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We know the property of an absolute value: it is never negative.

Hence the given inequality is equivalent to below equation:

This is the only solution.

When we solve for K in the inequality, 0 ≥ |(3K + 1) / 74|, the result obtained is -1/3

We can solve the expression 0 ≥ |(3K + 1) / 74| as illustrated below:

0 ≥ |(3K + 1) / 74|

Remove the absolute sign

0 ≥ (3K + 1) / 74

Cross multiply

0 ≥ (3K + 1) / 74

0 × 74 ≥ 3K + 1

0 ≥ 3K + 1

Collect like terms

0 - 1 ≥ 3K

-1 ≥ 3K

Divide both sides by 3

-1/3 ≥ K

K = -1/3

Thus, we can conclude from the above calculation that the value of K in the inequality, 0 ≥ |(3K + 1) / 74| is -1/3

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