Larry has 25 goldfish and 15 minnows. He wants to put them in tanks so that there is the same number of goldfish and the same number of minnows in each tank. He wants to have the greatest amount of tanks possible. How many goldfish and how many willows will be in each tank?

The measure of secant WZ = 5 units

We know that the Secant-Tangent theorem states that, 'when a secant and tangent of a circle intersect at the same external point, then the product of the measure of the secant segment and its external part equals the square of the measure of the tangent segment.'

Here, VW is a tanget to a circle at point V and ZW is a secant of a circle.

From  Secant-Tangent theorem,

ZY × YW = VW²

(x + 3) × (x) = (x + 1)²

We solve this equation for x.

x² + 3x = x² + 2x + 1

3x - 2x = 1

x = 1

So, the length of WY = 1 unit

So, the length of ZY would be,

x + 3

= 1 + 3

= 4

and the length of WZ = WY + YZ

                                    = 1 + 4

                                    = 5 units

This is the required length of WZ  

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Answer:

x = 10.1, AXY = 71.7 degrees

Step-by-step explanation:

There are two ways to solve this problem. You could either do 7x+1+108.3=180 or 180-108.3, then take that number and set it equal to 7x+1.

I will be using the latter. (You can do this because angle YXB is a linear pair with angle AXY. This means they add up to 180. So to find angle AXY, you subtract 180 from 108.3)

[tex]180-108.3=71.7\\\\7x+1=71.7\\\\[/tex]

Subtract one from each side to move variables to the left and constants to the right.

[tex]7x+1-1=71.7-1\\\\7x=70.7[/tex]

Divide seven by both sides to isolate the variable.

[tex]\frac{7x}{7}=\frac{70.7}{7} \\\\x=10.1[/tex]

So now we know what x is. So to find AXY, you substitute it back into the equation.

[tex]7(10.1)+1=71.7\\\\70.1+1=71.7?\\\\71.1=71.7?[/tex]

The probability of the first 2 participants preferring Simply Significant and the remaining 13 participants preferring one of the other coffee brands is approximately 0.0392.

Assuming that each participant has an equal chance of preferring any of the four coffee brands and that their preferences are independent of each other, we can model the preference of each participant as a Bernoulli random variable with probability p of preferring Simply Significant Coffee.

Then, the probability of the first 2 participants preferring Simply Significant Coffee and the remaining 13 participants preferring one of the other coffee brands can be calculated as follows:

P(2 participants prefer Simply Significant and 13 prefer other brands) = P(Simply Significant)^2 * P(other brands)^13

where P(Simply Significant) is the probability of a participant preferring Simply Significant Coffee and P(other brands) is the probability of a participant preferring one of the other brands, which is 1/3 since there are three other brands besides Simply Significant.

Using the binomial probability formula, we can calculate P(Simply Significant) as follows:

P(Simply Significant) = C(15,2) * (1/4)^2 * (3/4)^13

where C(15,2) is the number of ways to choose 2 participants out of 15.

Plugging in the values, we get:

P(Simply Significant) = 105 * (1/16) * (0.3164) ≈ 0.0392

Therefore, the probability of the first 2 participants preferring Simply Significant and the remaining 13 participants preferring one of the other coffee brands is approximately 0.0392.

Note that this assumes that participants are choosing at random and are not influenced by factors such as the order in which the coffees are presented or any other external factors that could affect their preferences.

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The probability of receiving more than 5 calls during the next 15 minutes is approximately 0.0322.

To solve this problem, we will use the Poisson probability distribution formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where:

P(X = k) is the probability of getting k events in a specific time interval

e is Euler's number (approximately equal to 2.71828)

λ is the average rate of events per interval (also known as the Poisson parameter)

k is the number of events we want to calculate the probability for

k! is the factorial of k (i.e., k! = k x (k-1) x (k-2) x ... x 2 x 1)

In this problem, we are given that the rate of calls to a customer service center follows a Poisson process with a rate of 1 call every 3 minutes. Therefore, the average rate of calls per minute (i.e., λ) is:

λ = 1 call / 3 minutes = 1/3 calls per minute

Now, we want to find the probability of receiving more than 5 calls during the next 15 minutes. We can use the Poisson formula to calculate this probability as follows:

P(X > 5) = 1 - P(X ≤ 5)

= 1 - ∑(k=0 to 5) [e^(-λ) * λ^k / k!]

= 1 - [(e^(-λ) * λ^0 / 0!) + (e^(-λ) * λ^1 / 1!) + ... + (e^(-λ) * λ^5 / 5!)]

Substituting λ = 1/3 and simplifying the equation, we get:

P(X > 5) = 1 - [(e^(-1/3) * 1^0 / 0!) + (e^(-1/3) * 1^1 / 1!) + ... + (e^(-1/3) * 1^5 / 5!)]

≈ 0.0322

Therefore, the probability of receiving more than 5 calls during the next 15 minutes is approximately 0.0322.

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We may draw a scatterplot of the data and compute the correlation coefficient to see whether there is a relationship between Nadeem's visits to the library and the number of books he checks out. Linear Equation = Y =mx+c. Option A is Correct.

The degree and direction of the linear link between two variables are measured by the correlation coefficient. If the correlation is positive, it suggests that if one variable rises, the other variable rises as well.

If there is a correlation, linear regression may be used to describe the data with a linear equation.

Y= mx+c

Based on how frequently Nadeem visits the library, we may use this equation to anticipate how many books he will borrow. Correlation does not always indicate cause, though. Option A is Correct.

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Correct Question:

Each month, Nadeem keeps track of the number of times he visits the library and the number of books he checks out Is there a correlation. you model his data with a linear equation? Is there a causal relationship?

A. There is a positive correlation and no causal relationship.

B. There is a negative correlation and no casual relationship.

C. There is a casual relationship but no positive correlation.

D. There is neither a correlation nor a casual relationship.

The equation of the blue graph include the following: B. g(x) = (x - 2)² + 1.

In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.

Where:

In order to write an expression that models g(x), we would have to apply a vertical translation to f(x) by 1 units up and a horizontal translation by 2 units right;

f(x)=x²

g(x) = (x - 2)² + 1.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The equation of the graph is determined as y - 1 = 5x/3.

The equation of the graph is calculated by applying the general equation of a line form.

y = mx + c

where;

The slope of the graph is calculated as follows;

m = Δy/Δx

m = (y₂ - y₁ ) / (x₂ - x₁ )

m = ( -4 - 1 ) / (3 - 0)

m = -5/3

y = -5x/3 + 1

y - 1 = 5x/3

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The domain of the function is all real numbers and  range is  y ≥ -1.

Since the vertex is at (1,-1), the axis of symmetry is x = 1.

This means that the domain of the function is all real numbers.

To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.

However, since the parabola opens upwards, there is no upper bound on the y-values.

Therefore, the range is given by y ≥ -1.

Hence, the domain of the function is all real numbers and  range is  y ≥ -1.

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We first need to clarify a few terms and the question itself. It seems like you are asking about a codeword in polynomial form and finding the third circular shift of the codeword. Let's express the codeword in polynomial form:

Let u(x) be the original polynomial codeword, and let n = 4. Based on the information provided, assuming that q(x) = u(x)n(x) = u(x)(1 + x^4).

To find the third circular shift of the codeword, follow these steps:

1. Express the original codeword u(x) in polynomial form, for example, u(x) = a_0 + a_1x + a_2x^2 + a_3x^3 (where a_i are coefficients).
2. Perform the first circular shift by moving the last term to the front: a_3x^3 + a_0 + a_1x + a_2x^2.
3. Perform the second circular shift: a_2x^2 + a_3x^3 + a_0 + a_1x.
4. Perform the third circular shift: a_1x + a_2x^2 + a_3x^3 + a_0.

The third circular shift of the codeword u(x) is given by the polynomial a_1x + a_2x^2 + a_3x^3 + a_0.

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All Trigonometric Expressions:

a. ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx = ∫2sin³θ cos²θ dθ

b. ∫[tex]x^{2} dx/(4x^{2} + 6)[/tex]= ∫tan²θ sec²θ dθ

c. ∫x√(5x + 50)/(x + 118)dx = ∫(5tan²θ – 25)tanθ sec³θ dθ

d. ∫(19 – 50x)/(119 – 5x² + 50x)dx = -2∫dθ/(25tan²θ + 94)

a. The integral ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx, we can use the substitution x = (2/5)sinθ. This gives dx = (2/5)cosθ dθ and 5x² – 2 = 5(2/5 sinθ)² – 2 = 2cos²θ. Substituting these expressions into the integral, we get:

∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx  

= ∫2sin³θ cos²θ dθ

b. For the integral ∫x²dx/(4x² + 6), we can use the substitution x = tanθ. This gives dx = sec²θ dθ and 4x² + 6 = 4tan²θ + 6 = 2sec²θ. Substituting these expressions into the integral, we get:

∫x²dx/(4x² + 6) = ∫tan²θ sec²θ dθ

c. For the integral ∫x√(5x + 50)/(x + 118)dx, we can use the substitution

x + 25 = 5tan²θ.

This gives x = 5tan²θ – 25 and dx = 10tanθ sec²θ dθ, and

5x + 50 = 25sec²θ. Substituting these expressions into the integral, we get:

∫x√(5x + 50)/(x + 118)dx

= ∫(5tan²θ – 25)tanθ sec³θ dθ

d. For the integral:

∫(19 – 50x)/(119 – 5x² + 50x)dx,

we can use the substitution

5x – 5 = √(50x – 5)tanθ.

This gives x = (1/10)[(tanθ)² + 1] and

dx = (1/5)(tanθ sec²θ) dθ, and 119 – 5x² + 50x

= (25tan²θ + 94)².

Substituting these expressions into the integral, we get:

∫(19 – 50x)/(119 – 5x² + 50x)dx

= -2∫dθ/(25tan²θ + 94)

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Correct Question:

For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral.

a. ∫5x * ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx

b. ∫[tex]x^{2} dx/(4x^{2} + 6)[/tex]

c. ∫x√(5x + 50)/(x + 118)dx

d. ∫(19 – 50x)/(119 – 5x² + 50x)dx

The distance form point A to point B is 333 feet.

An angle of depression is the measure of an angle formed when an object is viewed below the horizontal plane by an observer.

In the given question, let the distance from point A to the base of the lighthouse be represented by x, and that of B to the base of the lighthouse as y.

So that to determine x, we have;

Tan θ = opposite/ adjacent

Tan 15 = 115/ x

x = 115/ 0.2680

  = 429.1045

x = 429.1045 feet

To determine y, we have;

Tan θ = opposite/ adjacent

Tan 50 = 115/ y

y = 115/ 1.1918

  = 96.492y

y =  96.4927 feet

The distance from point A to point B = x - y

                             = 429.1045 - 96.4927

                             = 332.6118

The distance from point A to point B is 333 feet.

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A regular octagon has a rotation about its centre that has A regular octagon possesses rotational symmetry in addition to other types of symmetry. Reflective lines 6 and 6. Option d is Correct.

A regular pentagon has five rotational symmetries when it is rotated around its centre. A regular pentagon has _5_ lines of reflectional symmetry in addition to rotational symmetry.

Regular pentagons are regular polygons that have five sides. If a figure has the exact same shape after being rotated by a certain angle with regard to a fixed point in the figure, then that figure exhibits rotational symmetry for that angle.

The figure is considered to have reflectional symmetry if it is the same as the preceding figure when we reflect it with respect to a fixed line. Finding the amount of rotational and reflectional symmetries in a regular pentagon using the aforementioned definitions

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Correct Question:

When rotated about its center, a regular octagon has In addition to rotational symmetry, a regular octagon has symmetry rotational symmetries. Lines of reflectional

a. 6 and 8

b. 8 and 6

c. 8 and 8

d. 6 and 6​

The perimeter of the L shape is: AB + BC + CD + AC = x + x + x √2 + x = 2x + x √2

To find the perimeter of the L shape, we need to add up the lengths of all the sides.

Starting from the top left corner, we can label the four vertices of the L shape as A, B, C, and D, as shown in the diagram below.

The length of side AB is simply x, and the length of side BC is also x.

To find the length of side AC, we can use the Pythagorean theorem. Since triangle ABC is a right triangle, we have:

[tex]AC^2 = AB^2 + BC^2[/tex]

[tex]AC^2 = x^2 + x^2\\AC^2 = 2x^2\\\\AC = sqrt(2x^2) = x sqrt(2)\\\\[/tex]

Finally, to find the length of side CD, we can use the fact that it is parallel to AB and has the same length as BC, which is x.

Therefore, the perimeter of the L shape is:

AB + BC + CD + AC = x + x + x √2 + x = 2x + x √2

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What is an expression in terms of x for the greatest perimeter for a shape made of L regular hexagons?

Answer:

64

Step-by-step explanation:

the total must be 60×4 =240

subtract the miles already given and that us your answer. You could also make an equation. (64+53+59+x)/4=

The slope of the line is 4/5.

Option C is the correct answer.

We have,

The slope of the line that passes through the points (3, -1) and (-2, -5) can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the coordinates, we get:

slope = (-5 - (-1)) / (-2 - 3) = -4 / (-5) = 4/5

Therefore,

The slope of the line is 4/5.

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The surface area of the figure is 132 square units.

Option D is the correct answer.

We have,

The figure has two types of shapes.

- 3 rectangles

- 2 triangles

Now,

Area of the 3 rectangles.

= 5 x 10 + 4 x 10 + 3 x 10

= 50 + 40 + 30

= 120 square units

Area of 2 triangles.

= 1/2 x 4 x 3 + 1/2 x 4 x 3

= 1/2 x 12 + 1/2 x 12

= 6 + 6

= 12 square units

Now,

Total surface area.

= 120 + 12

= 132 square units.

Thus,

The surface area of the figure is 132 square units.

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The probability that at most 2 columns will fail is 0.98.

This is a binomial distribution problem, where the number of trials n = 16, the probability of success (a column failing) p = 0.05, and we want to find the probability of at most 2 columns failing.

To solve this, we need to calculate the probability of 0, 1, or 2 columns failing and add them up.

P(at most 2 columns failing) = P(0 columns failing) + P(1 column failing) + P(2 columns failing)

P(0 columns failing) = (n choose 0) * p^0 * (1-p)^(n-0) = (16 choose 0) * 0.05^0 * 0.95^16 = 0.45

P(1 column failing) = (n choose 1) * p^1 * (1-p)^(n-1) = (16 choose 1) * 0.05^1 * 0.95^15 = 0.38

P(2 columns failing) = (n choose 2) * p^2 * (1-p)^(n-2) = (16 choose 2) * 0.05^2 * 0.95^14 = 0.15

P(at most 2 columns failing) = 0.45 + 0.38 + 0.15 = 0.98

Therefore, the probability that at most 2 columns will fail is 0.98.

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The probability of at least two failures is 1 minus the probability of 0 or 1 failure, which is 1 - [p^n + nqp^(n-1)].

The probability of a success in one Bernoulli trial is given by p, and the probability of a failure is q = 1 - p.

(a) The probability of no successes is (1-p)^n.

(b) The probability of at least one success is 1 minus the probability of no successes, which is 1 - (1-p)^n.

(c) The probability of at most one success is the sum of the probabilities of 0 and 1 successes, which is (1-p)^n + np(1-p)^(n-1).

(d) The probability of at least two successes is 1 minus the probability of 0 or 1 success, which is 1 - [(1-p)^n + np(1-p)^(n-1)].

(e) The probability of no failures is the same as the probability of n successes, which is p^n.

(f) The probability of at least one failure is 1 minus the probability of no failures, which is 1 - p^n.

(g) The probability of at most one failure is the sum of the probabilities of 0 and 1 failures, which is p^n + nqp^(n-1).

(h) The probability of at least two failures is 1 minus the probability of 0 or 1 failure, which is 1 - [p^n + nqp^(n-1)].

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To find the rate of depreciation after 2 years, we need to find the derivative of this function at t = 2.
V(t) = 23,351(0.783)^t
V'(t) = 23,351(0.783)^t * ln(0.783)  [Using the chain rule]

V'(2) = 23,351(0.783)^2 * ln(0.783) ≈ -2,346.29

Since we are interested in the absolute value of the rate of depreciation, we can ignore the negative sign. Therefore, the car is depreciating at $2,346.29 per year (rounded to the nearest cent).

Note that this is the instantaneous rate of depreciation at t = 2. The average rate of depreciation over the first two years would be the difference in resale value divided by the number of years, which would be:

[(23,351(0.783)^2) - 23,351] / 2 ≈ $2,336.67 per year
Hi! To find the rate of depreciation after 2 years, we need to first determine the resale value of the car after 2 years and then find the difference in value per year. Here's a step-by-step explanation:

1. Plug in the given years (t=2) into the formula for the estimated resale value: V(t) = 23,351(0.783^t)
2. Calculate the resale value after 2 years: V(2) = 23,351(0.783^2) ≈ 14,342.76 (rounded to the nearest cent)
3. Find the depreciation value by subtracting the resale value from the initial value: Depreciation = Initial Value - Resale Value = 23,351 - 14,342.76 ≈ 9,008.24
4. Calculate the rate of depreciation per year: Rate of Depreciation = Depreciation / Years = 9,008.24 / 2 ≈ 4,504.12

The car is depreciating at approximately $4,504.12 per year after 2 years, rounded to the nearest cent.

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To calculate the percentage of the 250 ha paddock that can be sowed with 12.560 kg of wheat seed, we first need to determine how much seed is needed per hectare and this will give the answer 0.063%.

Given that the showing rate is 79.62 kg/ha, we can divide the total seed amount by the showing rate to get the number of hectares that can be sown with the given amount of seed:

12.560 kg / 79.62 kg/ha = 0.1576 ha

This means that 0.1576 hectares of land can be sown with 12.560 kg of wheat seed.

To calculate the percentage of the 250 ha paddock that can be sown, we can divide the sown land area by the total paddock area and then multiply by 100:

0.1576 ha / 250 ha x 100% = 0.063%

Therefore, you can sow approximately 0.063% of the 250 ha paddock with 12.560 kg of wheat seed, assuming a showing rate of 79.62 kg/ha.

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The correct statement is: the center of the graph of class 1 is best measured by the mean, and the center of the graph of class 2 is best measured by the median.

Given is a dot plots show the distribution of heights, in inches, for third grade girls in two classrooms.

The dot plot of class 1 is uneven and that of class 2 is even.

So, the center of the graph will be calculated by mean and that of class 2 by median.

Hence. the correct statement is: the center of the graph of class 1 is best measured by the mean, and the center of the graph of class 2 is best measured by the median.

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The differential equation solution is y(x) = [tex]-9e^_{(-0.6x)[/tex] for the initial condition y(0) = -9.

The given differential condition is dy/dx = -0.6y. To address this condition, we can isolate the factors by partitioning the two sides by y and duplicating the two sides by dx:

dy/y = -0.6dx

Then, we can incorporate the two sides. On the left side, we get ln|y|, and on the right side, we get -0.6x+C, where C is an inconsistent steady of joining:

ln|y| = -0.6x+C

To find the specific arrangement that fulfills the underlying condition y(0) = -9, we can substitute x = 0 and y = -9 into the situation:

ln|-9| = -0.6(0)+C

Rearranging, we get:

C = ln(9)

In this manner, the specific arrangement that fulfills the underlying condition is:

y(x) = [tex]-9e^_{(-0.6x)[/tex]

This is the last response.

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The complete question is:

Solve the separable differential equation dy/dx = 0.9y, and find the particular solution satisfying the initial condition y(0) = -9. y(x) = e^((0.9/2)x^2-ln(9)).

Answer:

Step-by-step explanation:

(x - 2)²/16 - (y - 1)²/4 = 1

(x - 2)² - 4(y - 1)² = 16

x² + 4 - 4x - 4(y² + 1 - 2y) = 16

x² + 4 - 4x - 4y² - 4 + 8y = 16

x² - 4x + 8y - 4y² = 16

x² - 4x = 16  ,  -4y² + 8y = 16

x(x - 4) = 16  ,  4y(-y + 2) = 16

x = 16, x = 20,  y = 4, y = -14

False. An intrinsic reward is enjoying what one does for its own sake, while an extrinsic reward is an inducement such as money, grades, or recognition.

Intrinsic and extrinsic rewards are two different types of motivational factors that can influence behavior.

Intrinsic rewards are those that come from within oneself, such as the enjoyment of doing a task or the sense of accomplishment that comes from completing it. These rewards are inherently satisfying and enjoyable, and they motivate people to continue doing the task or activity because of the pleasure they derive from it. For example, a person may engage in a hobby like playing music, painting, or playing a sport simply because they find it enjoyable and rewarding in itself.

On the other hand, extrinsic rewards are external motivators that are used to induce or encourage behavior. These rewards are typically tangible, such as money, grades, or recognition, and are given as a result of completing a task or activity. They are designed to incentivize individuals to perform specific actions, often with the aim of achieving a specific goal or outcome. For example, a person may work hard at their job in order to earn a promotion or raise, or may study hard in school to earn good grades.

Intrinsic and extrinsic rewards can both be effective motivators, but they operate in different ways. Intrinsic rewards are powerful because they come from within the individual and are based on personal enjoyment and satisfaction. Extrinsic rewards, on the other hand, are often seen as less powerful and may only work in the short term, because they are not inherently satisfying and may not motivate people to continue performing the task or activity once the reward is removed. However, when used effectively, extrinsic rewards can be a useful tool for motivating people and achieving specific outcomes.

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Answer:

To find the height of the box, we need to use the formula for volume of a box: Volume = length x breadth x height

Given the values for length and breadth, we can substitute them into the formula and solve for height: 140 = 7 x 5 x height

Simplifying the equation, we get: 140 = 35 x height

Dividing both sides by 35, we get: height = 4

Therefore, the height of the box is 4 cm

Answer:

(12, 28 )

Step-by-step explanation:

y = 2x + 4 → (1)

y = 3x - 8 → (2)

substitute y = 3x - 8 into (1)

3x - 8 = 2x + 4 ( subtract 2x from both sides )

x - 8 = 4 ( add 8 to both sides )

x = 12

substitute x = 12 into either of the 2 equations

substituting into (1)

y = 2(12) + 4 = 24 + 4 = 28

solution is (12, 28 )

The difference in minutes between 55 minutes and 1 3/4 hours is 50 minutes.

We have,

To convert 1 3/4 hours to minutes, we can multiply it by 60 (since there are 60 minutes in an hour):

So,

1 3/4 hours

= (1 x 60) + (3/4 x 60)

= 60 + 45

= 105 minutes

Now we can find the difference between 105 minutes and 55 minutes:

= 105 minutes - 55 minutes

= 50 minutes

Therefore,

The difference in minutes between 55 minutes and 1 3/4 hours is 50 minutes.

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The probability that in a given week the airline will lose less than 20 suitcases is approximately 0.8186 or 81.86%.

We are given that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with a mean of [tex]$\mu = 16.9$[/tex] and standard deviation of [tex]$\sigma = 3.3$[/tex]. We need to find the probability that in a given week the airline will lose less than 20 suitcases.

Let X be the number of suitcases lost in a week. Then we need to find P(X < 20).

Using the Z-score formula, we can standardize the variable X as:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Substituting the given values, we get:

[tex]Z=\frac{20-16.9}{3.3}=0.91[/tex]

Now, we need to find the probability that Z is less than 0.91. We can use a standard normal distribution table or calculator to find this probability, which is approximately 0.8186.

Therefore, the probability that in a given week the airline will lose less than 20 suitcases is approximately 0.8186 or 81.86%.

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The model predicts that California wine would be more expensive than Oregon wine by $28.00.

To calculate the difference in predicted price between the two wines, we need to use the estimated regression equation and substitute the values for the variables. Let's say our estimated regression equation is:

Price = 50 + 2.5(Rating) + 10(California) - 8(Oregon)

Both wines have a rating of 90, so we can substitute that value in:

Price of California wine = 50 + 2.5(90) + 10(1) - 8(0) = 295

Price of Oregon wine = 50 + 2.5(90) + 10(0) - 8(1) = 267

Therefore, the predicted price of California wine is $295 and the predicted price of Oregon wine is $267. The difference between the two is $28.00.

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Amani would need to pay $66.15 for the scooter with the discount and sales tax included.

If the regular price of the scooter is $70, and it is on sale for 10% off, the sale price would be:

Sale price = Regular price - 10% of Regular price

Sale price = $70 - 0.1*$70

Sale price = $63

So the sale price of the scooter is $63.

Next, we need to add the 5% sales tax to the sale price to get the total price of the scooter. To do this, we can calculate the amount of sales tax as:

Sales tax = 5% of the Sale price

Sales tax = 0.05*$63

Sales tax = $3.15

Therefore, the total price of the scooter, including the 10% discount and 5% sales tax, would be:

Total price = Sale price + Sales tax

Total price = $63 + $3.15

Total price = $66.15

So Amani would need to pay $66.15 for the scooter with the discount and sales tax included.

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