Write the equation in slope-intercept form (y = mx + b).
-6x + 3y = 18

The value of x in the series given the first three terms x + 5, x + 1 and x is 1/3

Given that, we have

x + 5, x + 1 and x

Using the common ratio, we have

(x + 5)/(x + 1) = (x + 1)/x

So, we have

x² + 5x = x² + 2x + 1

Evaluating the like terms, we have

3x = 1

Divide by 3

x = 1/3

Hence, the value of x is 1/3

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On average, someone who buys a ticket can expect to make a profit of $2.43 as the expected value for someone who buys a ticket is $2.43.

It is the average amount of money that an individual can expect to win or lose on an investment. It is calculated by multiplying the probability of each outcome by its payoff and then adding the expected values of all outcomes.

In this case, the probability of winning= 1/737

and the payoff = $1800 - $8

= $1792.

The expected value (EV) is calculated by multiplying the probability of each outcome by its payoff.

EV = (1/737) x (1792)

EV = $2.43

Therefore, the expected value for someone who buys a ticket is $2.43. This means that, on average, someone who buys a ticket can expect to make a profit of $2.43.

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The true total distance chained if the measured distance on the ground is 6000 m would be 6001.8 m.

The measured distance on the ground is 6000 m. However, due to the increase in temperature during the surveying, the chain would have expanded, leading to an increase in the measured length.

The coefficient of linear expansion of steel is 8 x 10^-6 per oC. Therefore, for a temperature increase of 45 - 20 = 25 oC, the increase in length of the chain can be calculated as follows:

ΔL/L = αΔT

Substituting the given values, we get:

ΔL/30.00 = (8 x 10^-6) x 25

ΔL = 0.006 m

This means that the actual length of the chain during the surveying was 30.006 m.

To find the true total distance chained, we need to correct the measured distance on the ground for the increase in chain length. Let D be the true total distance chained. Then we have:

D/30.006 = 6000/30.00

Solving for D, we get:

D = 6000 x 30.006 / 30.00

D = 6001.8 m

Therefore, the true total distance chained is 6001.8 m.

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We can see that the roots are:

α = 1 + 1.5i

β = 1 - 1.5i

Then the expression is:

1/(2α + β) + 1/(α + 2β) =  0.53

Here we first need to find the roots of the quadratic equation:

2x²-4x+5=0

Using the quadratic formula we will get:

[tex]x = \frac{4 \pm \sqrt{(-4)^2 - 4*2*5} }{2*2} \\\\x = \frac{4 \pm \sqrt{-24} }{4} \\\\x = 1 \pm 1.5i[/tex]

So the two solutions are:

α = 1 + 1.5i

β = 1 - 1.5i

Then the expression becomes:

1/(2α + β) + 1/(α + 2β)

1/(2 + 3i + 1 - 1.5i) + 1/(1 + 1.5i + 2 - 3i)

1/(3 + 1.5i) + 1/(3 - 1.5i)

To remove the complex part for the denominators we need to multiply and divide by the complements in each fraction, so we will get:

(3 - 1.5i)/(​3 + 1.5i)*(3 - 1.5i) + (3 + 1.5i)/(3 - 1.5i)*(3 + 1.5i)

[(3 - 1.5i) + (3 + 1.5i)]/(3² + 1.5²)

6/11.25 = 0.53

That is the solution.

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which gives us a rate of "4 airplanes per 5 minutes" or "4/5 airplanes per minute."

To change minutes into hours, you can use simple mathematical operations.

There are 60 minutes in one hour. Therefore, to convert minutes into hours, you can divide the number of minutes by 60.

For example, if you have 120 minutes, you can divide 120 by 60 to get 2 hours (120 ÷ 60 = 2). Similarly, if you have 90 minutes, you can divide 90 by 60 to get 1.5 hours (90 ÷ 60 = 1.5).

Here's the formula you can use:

Hours = Minutes ÷ 60

So, to change any number of minutes into hours, divide that number by 60

by the question.

On a normal day, 12 airplanes arrive at an airport every 15 minutes. Write a rate that represents this situation.

The rate of airplanes arriving at the airport can be expressed as "12 airplanes per 15 minutes" or "12/15 airplanes per minute."

We can simplify this fraction by dividing the numerator and denominator by 3,

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The values of k that would make the product of ᵏ⁄3 × 12 be greater than 12 is: D. for any value of k greater than 3.

The product of two numbers is the result obtained when one number is multiplied by another.

A. For values of k that are less than 1 but greater than 0, i.e 1.5, we have:

0.5/3 * 12 > 12

2 > 12 [false]

B. For values of k that are less than 3 but greater than 1, i.e 2, we have:

2/3 * 12 > 12

8 > 12 [false]

C. For any value of k that is equal to 3, i.e. 3, we have:

3/3 * 12 > 12

12 > 12 [false]

D. For values of k that are greater than 3, i.e 6, we have:

6/3 * 12 > 12

24 > 12 [true]

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Answer:

Commutative Property.

Associative Property.

Distributive Property.

Identity Property.

Answer:

1 hot dog = $1.45

1 juice drink = $1.05

Step-by-step explanation:

let x rep hot dog

y rep juice drink

Baxter= 6x+4y=12.9

Farley=3x+4y=8.55

6x+4y=12.9

-3x+4y=8.55

3x+0=4.35

x=4.35/3=1.45

y=1.05

The number of vacation packages offered by Peaceful Travel Agency is 10

To determine the number of different vacation packages offered by Peaceful Travel Agency, we need to use the multiplication principle of combination and counting.

Since the agency has 2 cities, 5 months, and 1 airline to choose from, we can multiply the number of options for each category to get the total number of vacation packages:

So, we have

vacation packages = 2 cities x 5 months x 1 airline

vacation packages = 10

Therefore, Peaceful Travel Agency offers 10 different vacation packages.

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Answer:

650

Step-by-step explanation:

It's simple

The answer would probaly be 1

Answer: i believe its 10 if there no multiplication

Step-by-step explanation:

:o

(a) Positive derivative interval: From x = -∞ to x = -4, and from x = 0 to x = 3.

(b) Negative derivative interval: From x = -4 to x = 0, and from x = 3 to x = ∞.

(c) x-value(s) where derivative equals zero: At x = -3 and x = 2.

(d) x-value(s) where derivative does not exist: At x = -4 and x = 3.

To find the intervals where the derivative of the function is positive, negative, or equals zero, we first need to find the critical points by setting the derivative equal to zero and solving for x. We can see from the graph that there is only one critical point at x = -2. We then test each interval between the critical points and endpoints to determine if the derivative is positive or negative.

From x = -infinity to x = -2, the derivative is negative. From x = -2 to x = 3, the derivative is positive. From x = 3 to x = infinity, the derivative is negative. Therefore, the answer is (a) the derivative is positive on (-2, 3); (b) the derivative is negative on (-infinity, -2) and (3, infinity); (c) the derivative equals zero at x = -2; (d) the derivative exists for all x.

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Answer : 0.99

Explanation :  15 * 6.6/100 For The Tax.

Total : 15.99

now, we're making an assumption that's a rectangular prism pool, so the volume is simple the product of length and widh and height, which we have, let's convert them all to improper fractions.

[tex]\stackrel{mixed}{14\frac{1}{2}}\implies \cfrac{14\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{29}{2}}~\hfill \stackrel{mixed}{6\frac{1}{2}} \implies \cfrac{6\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{13}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{length}{\cfrac{29}{2}}\cdot \stackrel{width}{\cfrac{13}{2}}\cdot \stackrel{depth}{\cfrac{13}{2}}\implies \cfrac{4901}{8} \\\\\\ \cfrac{4896+5}{8}\implies \cfrac{4896}{8}+\cfrac{5}{8}\implies 612+\cfrac{5}{8}\implies 612\frac{5}{8}[/tex]

The probability of choosing a red marble and a green marble is 21/136 or approximately 0.154.

We must combine the probability of each occurrence occurring in order to determine the likelihood of selecting a red or an even-numbered green marble. Given that there are 14 red marbles in total among the total of 17 marbles, the chance of selecting a red marble is 14/17. Given that there is only one even-numbered green marble among the other 17 marbles, the probability of selecting one is 1/17. The likelihood of selecting a red or an even-numbered green marble is therefore: 14/17 + 1/17 = 15/17.

The likelihood of selecting a red or an even-numbered green marble is therefore 15/17, or roughly 0.882.

We must multiply the likelihood of selecting a red marble by the likelihood of selecting a green marble in order to determine the likelihood of selecting both red and green marbles. There are 16 marbles left after selecting one, including 2 green marbles. The odds of selecting a red stone during the initial draw are 14/17. After a red marble has been selected and is not being changed, the likelihood of selecting a green marble on the subsequent draw is 3/16. The odds of selecting a red marble and a green marble are as follows: (14/17) x (3/16) = 21/136 = 0.154

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The probability that an adult resident has 3 or more vehicles 0.54.

The probability of an adult resident having 3 or more vehicles is the sum of the probabilities associated with owning 3, 4, or 5 or more vehicles:

P(3 or more vehicles) = P(3) + P(4) + P(5 or more)

P(3 or more vehicles) = 0.38 + 0.13 + 0.03

P(3 or more vehicles) = 0.54

Therefore, the probability that an adult resident has 3 or more vehicles is 0.54.

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Answer:2.75 gallons of water

Step-by-step explanation:

Answer:

One gallon is equal to 16 cups of water.

To find out how many gallons are in 44 cups of water, we can divide 44 by 16:

44 cups ÷ 16 cups/gallon = 2.75 gallons

Therefore, 44 cups of water is equal to 2 and 3/4 gallons.

Step-by-step explanation:

1. Recall that 1 gallon is equal to 16 cups of water. Therefore, to find how many gallons are in 44 cups of water, we can set up a proportion:

1 gallon / 16 cups = x gallons / 44 cups

2. To solve for x, we can cross-multiply and simplify:

16x = 1 * 44

16x = 44

x = 44 / 16

x = 2.75

3. The result of 2.75 gallons represents the equivalent amount of water in gallons. To express this answer as a whole number or mixed number, we can observe that 2.75 is equal to 2 and 3/4:

2.75 = 2 + 0.75

2.75 = 2 + 3/4

Therefore, 44 cups of water is equal to 2 and 3/4 gallons.

Monte Carlo simulation can done by generating a large number of random points within the quarter circle and the square, we can obtain an accurate estimate of pi using the formula pi/4 = area Q/area S.

Monte Carlo simulation is a statistical method that involves generating random numbers to simulate real-life scenarios. In this case, we will use the method to approximate the value of pi by generating random points inside the quarter circle Q and the square S.

The algorithm for this simulation is as follows:

1. Set the number of random points (n) to be generated.

2. Initialize two counters: count_Q and count_S to zero.

3. Generate n random points within the square S. Each point is represented by a pair of random numbers (x,y) such that 0 <= x <= 1 and 0 <= y <= 1.

4. For each point generated, determine if it falls within the quarter circle Q by checking if x^2 + y^2 <= 1. If it does, increment the count_Q by 1.

5. Increment the count_S by 1 for every point generated.

6. Calculate the ratio of count_Q to count_S, which represents the ratio of the area of Q to the area of S.

7. Multiply the ratio obtained in step 6 by 4 to get an approximation of pi.

The logic behind this algorithm is that the ratio of the areas of the quarter circle Q to the square S is pi/4. Thus, by generating random points within the square S and determining the number of points that fall inside the quarter circle Q, we can estimate the value of pi.

To implement this algorithm in Excel, we can use the RAND() function to generate random numbers for the x and y coordinates of each point. We can then use an IF statement to determine if each point falls within the quarter circle. We can use a loop to generate a large number of random points, such as 10,000 or 100,000, to obtain a more accurate estimate of pi.

In summary, Monte Carlo simulation is a powerful tool for approximating the value of pi using random numbers and the properties of geometric shapes. By generating a large number of random points within the quarter circle and the square, we can obtain an accurate estimate of pi using the formula pi/4 = area Q/area S.

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Answer: the total direct cost of one item is $0.47.

Step-by-step explanation:

If the packaging employee makes $14 per hour and can package 200 items in one hour, the direct labor cost per item would be:

Direct labor cost per item = Hourly wage rate / Number of items packaged per hour

Direct labor cost per item = $14 / 200

Direct labor cost per item = $0.07

The direct material cost per item is given as $0.40.

Now we can calculate the total direct cost per item:

Total direct cost per item = Direct labor cost per item + Direct material cost per item

Total direct cost per item = $0.07 + $0.40

Total direct cost per item = $0.47

The probability of selecting at random, without replacement, two blue marbles is 5/12 i.e. A.

What exactly is probability?

Probability is a measure of the possibility or chance of an event to be occurred. It is a mathematical concept that is used to describe the degree of uncertainty or randomness associated with an event.

The probability of an event is represented by a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. For example, the probability of rolling a 6 on a fair six-sided die is 1/6, because there is only one way to roll a 6 out of the six possible outcomes.

Now,

Using formula for probability:

P(A and B) = P(A) × P(B|A)

where P(A and B) is the probability of events A and B occurring together, P(A) is the probability of event A occurring, and P(B|A) is the probability of event B occurring given that event A has occurred.

In this case, we want to find the probability of selecting two blue marbles without replacement. Let's break this down into two events:

Event A: Selecting a blue marble on the first draw

Event B: Selecting a second blue marble on the second draw (without replacement)

For Event A, the probability of selecting a blue marble on the first draw is 6/9, since there are 6 blue marbles out of a total of 9 marbles.

For Event B, the probability of selecting a blue marble on the second draw given that a blue marble was selected on the first draw is 5/8, since there are 5 blue marbles remaining out of a total of 8 marbles.

So, using the formula for probability, we have:

P(Event A and Event B) = P(Event A) × P(Event B|Event A)

= (6/9) × (5/8)

= 30/72

= 5/12

Therefore, the probability of selecting at random, without replacement, two blue marbles is 5/12.

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Answer:

Step-by-step explanation: b) 10

Area of sector is 177.8cm².

In geometry, a sector is a region of a circle that is bounded by two radii and an arc, where the radii intersect at the center of the circle. The area of a sector is the fraction of the circle's total area that is enclosed by the sector.

where A is the area of the sector, θ is the central angle of the sector (measured in degrees), r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159.

The formula for the area of a sector is:

A = (θ/360) x πr²

Angle made by sector=360-256=104

Radius of circle=14cm

Area of the sector DFE=∅/360×πr²

=104/360×π×14²

=177.8cm²

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In physics, work is energy transferred to or from an object by applying a force along a displacement and the work done in the given situation is 120J.

In physics, work is energy transferred to or from an object by applying a force along a displacement.

In its simplest form, work done with a constant force in the direction of motion is equal to the product of the force and the distance traveled.

Expressing this concept mathematically, the work W is equal to the force f multiplied by the distance d, or W = fd.

If the force is applied at an angle θ to the displacement, the work done is W = fd cos θ.

So, the work done is calculated as follows:

W = 40lb*3ft

W = 120 J

Therefore, the work done in the given situation is 120 J.

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The expression for the difference quotient is option C and the simplified form of the function f(x) when evaluated at x and x + h is 2x + 4 + 2h.

We are asked to find the expression for the difference quotient of the function f(x) when evaluated at x and x + h. The difference quotient is given by:

[tex]$\frac{f(x+h) - f(x)}{h}$[/tex]

where h is a small nonzero number representing the change in the input.

Substituting f(x) with its expression, we get:

[tex]$\frac{(2(x+h)^2 + 4(x+h) - 3) - (2x^2 + 4x - 3)}{h}$[/tex]

Expanding and simplifying the numerator, we get:

[tex]$\frac{2x^2 + 4xh + 2h^2 + 4x + 4h - 3 - 2x^2 - 4x + 3}{h}$[/tex]

Simplifying further, we get:

[tex]$\frac{2x^2 + 4xh + 2h^2 + 4h}{h}$[/tex]

Canceling the common factors of h, we get:

[tex]$2x + 4 + 2h$[/tex]

Therefore, the expression for the difference quotient of the function f(x) when evaluated at x and x + h is 2x + 4 + 2h.

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Answer:

≈24,57°

Step-by-step explanation:

Use trigonometry:

[tex] \tan(x°) = \frac{16}{35} [/tex]

[tex]x≈24.57°[/tex]

Use the reverse (SHIFT, tg (16/35)) to find x

I think this is the right answer

Answer:

x ≈ 24.57°

Step-by-step explanation:

using the tangent ratio in the right triangle

tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{16}{35}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{16}{35}[/tex] ) ≈ 24.57° ( to 2 decimal places )

The x-values of the points of intersection are x = 0, x = 3, and x = -2.

A point of intersection is a point where two or more lines, curves, or surfaces intersect or cross each other. In other words, it is the point where two or more objects coincide. For example, in a two-dimensional plane, the point of intersection of two lines is the point where the two lines cross each other.

In the given question,

To find the x-values of the points of intersection, we need to solve the equation 2x³ - x² - 7x = x² + 5x.

Simplifying this equation, we get:

2x³ - 2x² - 12x = 0

2x(x² - x - 6) = 0

2x(x - 3)(x + 2) = 0

So, the x-values of the points of intersection are x = 0, x = 3, and x = -2.

a. A = -2, B = 0, C = 3

b. To set up integrals to find the area of the regions, we need to determine which function is on top in each region. The boundary points give us the values of x for which the functions intersect and change positions.

The region between A and B is bounded by y = x² + 5x on top and y = 2x³ - x² - 7x on the bottom, so the integral for this region is:

∫ from A to B of [x² + 5x - (2x³ - x² - 7x)] dx

The region between B and C is bounded by y = 2x³ - x² - 7x on top and y = x² + 5x on the bottom, so the integral for this region is:

∫ from B to C of [(2x³ - x² - 7x) - (x² + 5x)] dx

Note that the limits of integration are the x-values of the points of intersection.

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Answer:

m = 4 + 0.18b

Step-by-step explanation:

So, we are looking to find the total amount of money that Ariella earns.

$4.00 is what she initially gets paid.

plus 18%, 18 / 100 = 0.18

then b is the amount of total bill

so, we multiply the amount of percentage which is 18% to the amount of total bill which is b to get what she additionally earns after the customers paid the bill.

so initial pay is $4 + 18% which is 0.18 multiply to b, b represents the total bill.

$4 + 0.18b = m