4.02 Lesson check ! (2)

The tangent function is defined as the ratio of the sine function to the cosine function. It is periodic with a period of pi and has vertical asymptotes at odd multiples of pi/2. An equation for a tangent function with a domain of all real numbers and n as an integer is given by the following equation:
y = tan(x + n(pi))


The tangent function is defined as the ratio of the sine function to the cosine function, and it is periodic with a period of pi. It has vertical asymptotes at odd multiples of pi/2.
The tangent function can be represented by the following equation:
y = tan(x)
Where x is the angle measured in radians.
If we want to shift the graph of the tangent function by a certain amount, n, in the horizontal direction, we can use the following equation:
y = tan(x + n(pi))
Where n is an integer.
For example, if n = 2, then the graph of the tangent function would be shifted 2pi units to the left, and the equation would be:
y = tan(x - 2pi)
If n = 3, then the graph of the tangent function would be shifted 3pi units to the left, and the equation would be:
y = tan(x - 3pi)
And so on for any integer value of n.

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from S^OH

sinθ=opp/hyp

sin38°=x/4

x=4sin38°

x=4×(0.61566147533)

x=(2.4626459013)

to 1dp

x=2.5cm

Answer: 22.4 cm

Step-by-step explanation:

Perimeter of sector is: P = 2r + 2πr(θ/360) P = 2*10 + 2(3.14) (135/360) = 22.4 cm (rounded)

The required number for given expression is a = -3/2

Mathematical expressions consist of at least two numbers or variables, at least one math procedure, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical procedure. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

We given that

Nine less than four times a number equals fithteen;'

Let the number is a.

So,

9 - 4a = 15

-4a = 6

a = 6/-4

a = -3/2

Thus, required number is a = -3/2

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Answer:

D is (3, -2)
Option D

Step-by-step explanation:

If E is the midpoint of DF then the x-distance between D and E must be the same as that between E and F and similarly for the y-distance

In addition, the x, y coordinates of D must be less than the x, y coordinates for E

x-distance from E to F = 5- 4 = 1

x-distance from D to E = 1 so x-coordinate of D = 4 - 1 = 3

y-distance from E to F = 8 - 3 =  5

y-distance from D to E = 3 - 5 = -2

So coordinate of D is(3, -2)

The direction angle of the vector Ū is approximately 16.26°.

A vector's direction angle is the angle, measured anticlockwise, between the positive x-axis and the vector in standard position.

Trigonometry can be used to determine the direction angle of the vector = (-7, 2).

The direction angle is determined by:

θ = tan^-1(y/x)

where y is the vector's vertical component and x is its horizontal component (in this example, -7). (in this case, 2).

θ = tan^-1(2/-7)

We can determine: Using a trigonometric table or a calculator

θ ≈ 16.26°

As a result, the vector's direction angle is roughly 16.26°.

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z = (x - np) / σ
z = (43 - 100(0.50)) / 0.05
z = -1.4
P(z > -1.4) = 0.9192

a) The number of working women in the sample is 100. The majority of women prefer a better 'work-life balance' to a higher salary, according to a global research study. The majority in percentage is 50% or greater, which implies that 50% of 100 working women or more prefer a better work-life balance to an increased salary. If we assume that the null hypothesis is correct and the number of women who say having a flexible work schedule is important is exactly 50, the standard error for the sample can be calculated as follows:

σ = sqrt(p(1-p)/n)
σ = sqrt(0.50(1-0.50)/100)
σ = 0.05

P(x<50) can be calculated as follows:

z = (x - np) / σ
z = (50 - 100(0.50)) / 0.05
z = -20
P(z < -20) = 0

Therefore, the probability that fewer than 50% of the sample say that having a flexible work schedule is either very important or extremely important to their career success is 0.

b) The proportion of women who said having a flexible work schedule is very important or extremely important to their career success is more than 43%. That implies the number of women in the sample who say having a flexible work schedule is important is greater than 43.

P(x > 43) can be calculated as follows:

z = (x - np) / σ
z = (43 - 100(0.50)) / 0.05
z = -1.4
P(z > -1.4) = 0.9192

Therefore, the probability that more than 43% of the sample says having a flexible work schedule is very important or extremely important to their career success is 0.9192.

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One bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

William uses 40 milliliters of liquid plant food per week, so to find out how much plant food he needs for 12 weeks, we can simply multiply the weekly usage by the number of weeks:

Amount of plant food needed for 12 weeks = 40 milliliters/week x 12 weeks = 480 milliliters

So, William needs 480 milliliters of liquid plant food for 12 weeks.

Since the bottle of liquid plant food, William purchased contains 0.5 liters or 500 milliliters of liquid plant food, we can see that one bottle is enough for 12 weeks since 480 milliliters is less than the total amount of liquid plant food in the bottle.

In fact, we can calculate how many weeks one bottle of liquid plant food will last William by dividing the total amount of liquid plant food in the bottle by the amount used per week:

Time to use up the liquid plant food = (Total amount of liquid plant food) / (Amount used per week) = 500 ml / 40 ml/week ≈ 12.5 weeks

So, we can say that one bottle of liquid plant food is enough for at least 12 weeks, and potentially a bit more.

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The correct question should be:

William bought a 0.5 -liter bottle of liquid plant food. He uses 40 milliliters each week? How much plant food does William need for 12 weeks? Is one bottle enough for 12 weeks?

Since, that the total interest that will be paid on a 40-year mortgage from a home loan of $100,000 is going to be $480,000. Then,  the payments each month if the payments are to pay off both the loan and the interest will be $1,504.

The 40-year loan has the lowest monthly payment at $1,504. But that only means "saving" $183 per month on the 30-year loan. When considering the total price of the house in this example, adding an additional 10 years to the term of the loan seems overkill, reducing the monthly payment by less than $200.

A 40-year loan doesn't sound like a good deal. But for homeowners struggling to meet their monthly payments and get a 40-year loan modification, the lower payments could have a big impact.

Comparing the 30-year and 15-year numbers is even more extreme. The monthly payment on the 15-year loan is an additional $700. Some buyers can afford higher payments. The advantage of the 15-year loan is that the total interest paid on the loan is $103,218, compared to $289,970 for the 30-year loan. Fifteen years seems to pass so quickly, and it's an exciting feeling to stop paying.

Objections to the 15-year loan could include a missed opportunity. With an interest rate of 4.67% on the 30-year loan, one can expect a higher rate of return in the long run by investing heavily in the stock market. But that raises the question of whether the $700 a month in cash freed up by the 30-year loan will be invested. It might be tempting to spend that money on a more expensive car than the one you would otherwise have purchased.

A family's needs, including space, savings and investment for retirement and education, as well as many household expenses should be considered when deciding which home to buy and the term of the loan. At a minimum, homebuyers need to understand how the different types of loans work.

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The equatiοn fοr the relatiοnship between the net prοfit and the number οf tickets sοld is y = 70x - 1500.

In mathematics, an equatiοn is a statement that shοws the equality between twο expressiοns. The equatiοns can cοntain variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, etc. In wοrd prοblems, the variables represent the unknοwn quantity οr unknοwn number

Here we have

A charity οrganizatiοn had tο sell a few tickets tο their fundraiser tο cοver necessary prοductiοn cοsts.  

Cοst οf each ticket =$70

Number οf tickets sοld = 10

Tοtal cοst οf 10 tickets = $ 70 × 10 = $ 700

Lοss after selling 10 tickets = $800    

Hence, tοtal cοst οf prοductiοn = $ 700 + $ 800 = $ 1500

Let's assume that they sοld 'x' tickets and gοt 'y' prοfit

=> Tοtal revenue gained by selling tickets = $ 70x  

Prοfit y = Tοtal revenue - Prοduct cοst  

=> y = 70x - 1500

Therefοre,

The equatiοn fοr the relatiοnship between the net prοfit and the number οf tickets sοld is y = 70x - 1500.

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Complete Question:

A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets, they were still at a net loss of $800 (due to the production costs). They sold each ticket for $70. Let y represent the net profit in dollars) when they have sold tickets. Complete the equation for the relationship between the net profit and the number of tickets sold.  

After just a reflection along the [tex]X-axis[/tex], a quadrilateral [tex]MNOP[/tex] of position [tex]P[/tex] is [tex](3, -4)[/tex].

Four closed sides are making up a quadrilateral. Quadrilaterals are the following figures: Designed by Raphael. a four-sided figure. There is just one pair of parallel sides to the form, and there are no right angles.

A closed form known as a quadrilateral is known to be have sides with various widths and lengths. It is a closed polygon in two dimensions with four vertices, four angles, and four sides. Some examples of a quadrilateral are a cohesion and coherence, parallelogram, rectangle, rhombus, square, and kite.

When a point is reflected across the [tex]X-axis[/tex], the [tex]X-[/tex]coordinate stays the same, but the [tex]Y-[/tex]coordinate is multiplied by [tex]-1[/tex].

So to find the image of point [tex]P[/tex] after a reflection across the [tex]X-axis[/tex], we keep the [tex]X-[/tex]coordinate of [tex]P[/tex] the same (which is 3) and multiply the [tex]Y-[/tex]coordinate by [tex]-1[/tex]

New [tex]Y-[/tex]coordinate of [tex]P = -1 * 4 = -4[/tex]

Therefore, the image of point [tex]P[/tex] after a reflection across the [tex]X-axis[/tex] is [tex](3, -4)[/tex].

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a) The probability of a randomly selected diner waits less than 8 minutes for a table is 0.4

b) The probability of a randomly selected diner waits more than 1.5 minutes is 0.925

Given, wait times of between 0 and 20 minutes at a local restaurant follow a uniform distribution.

The probability density function of a uniform distribution is given by

f(x) = {1/(b-a)} where a ≤ x ≤ b

where a = 0 and b = 20

Therefore, the probability density function of f(x) = 1/20 for 0 ≤ x ≤ 20

For the  probability that a randomly selected diner waits between 2 and 7.5 minutes for a table, we need to find the area under the curve from x = 2 to x = 7.5

∴ P(2 ≤ x ≤ 7.5) = ∫₂⁷.⁵(1/20) dx

= 5.5/20 ⇒ 0.275

a) We need to find the area under the curve from x = 0 to x = 8

∴ P(x < 8) = ∫₀⁸(1/20) dx

= 8/20 ⇒ 0.4

b) We need to find the area under the curve from x = 1.5 to x = 20

∴ P(x > 1.5) = ∫₁.₅²⁰(1/20) dx

= 18.5/20 ⇒ 0.925

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The required length of AD is equal to the length of BC.

A polygon with four edges, four angles, and four vertices is called a quadrilateral. The Latin terms quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above picture as an example.

First, we draw the quadrilateral ABCD and label the given angles:

[tex]$\begin{align*}\angle ABD &= 35^\circ \\angle BDC &= 25^\circ\end{align*}[/tex]

Since opposite sides of quadrilateral ABCD are equal, we have:

[tex]$\begin{align*}AB &= DC\end{align*}[/tex]

We can use this fact to draw diagonal BD and label its length as x:

[tex]$\begin{align*}AB &= DC \AD + DB &= BC + DB \AD &= BC\end{align*}[/tex]

Therefore, we can conclude that:

[tex]$\begin{align*}AD &= BC\end{align*}[/tex]

Thus, the length of AD is equal to the length of BC.

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The simplest form οf the expression (-5/2)+(4/5)x - 17x is (-5/2)-(81/5)x.

Mathematical expressions cοnsist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical οperation.

The term "like terms" in algebra refers tο terms that have the same variable raised tο the same power. Only the numerical coefficients can change in terms similar tο those of algebra. The algebraic expressions can be made simpler by cοmbining like terms, making it much simpler to determine the expressiοn's outcome.

The given expressiοn is

(-5/2)+(4/5)x - 17x

The like terms are (4/5)x and - 17x

Combine like terms:

= (-5/2)+(4 - 85/5)x

= (-5/2)+(- 81/5)x

=  (-5/2) - (81/5)x

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Deondra can purchase 2 amount outfits for $59.50 each within her budget of $420.

$420 - ($236.31 + $3.07 + $3.07 + $34.75) ≥ $59.50oo

$147.00 ≥ $59.50oo

$147.00 ÷ $59.50 ≥ oo

2.46 ≥ oo

Deondra can purchase 2 outfits.

Deondra has $420 to spend at a bicycle store for some new gear and biking outfits. She first buys a new bicycle for $236.31, then she buys two bicycle reflectors for $3.07 each and a pair of bike gloves for $34.75. In order to determine how many outfits she can purchase while staying within her budget, an inequality can be written and solved. The inequality is $420 - ($236.31 + $3.07 + $3.07 + $34.75) ≥ $59.50oo. This can be simplified to $147.00 ≥ $59.50oo. Dividing both sides of the inequality by $59.50, we get $147.00 ÷ $59.50 ≥ oo. After solving, this simplifies to 2.46 ≥ oo. Since Deondra can only purchase a whole outfit, the answer becomes 2 outfits. Therefore, Deondra can purchase 2 outfits while staying within her budget.

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A sample size οf 805 Flοrida panthers will give a standard deviatiοn οf 0.8 years.

It displays the average deviatiοn οf each scοre frοm the mean. In a nοrmal distributiοn, a high standard deviatiοn indicates that values are spread οut frοm the mean, whereas a lοw standard deviatiοn indicates that values are clustered clοse tο the mean.

We can use the fοllοwing fοrmula tο calculate the sample size that will result in a standard deviatiοn οf 0.8 years:

n = (z * σ / E)²

Where:

The sample size is denοted by n.

z is the desired cοnfidence level's z-scοre (we'll assume 95% cοnfidence, sο z = 1.96)

is the standard deviatiοn οf the pοpulatiοn (given as 14.3 years)

E represents the margin οf errοr (given as 0.8 years)

The fοllοwing results are οbtained when the given values are substituted:

[tex]n = (1.96 * 14.3 / 0.8)^2 \sn = 804.57[/tex]

We get the fοllοwing when we rοund up tο the nearest whοle number:

n = 805

A sample size οf 805 Flοrida panthers results in a standard deviatiοn οf 0.8 years.

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The improper fraction that is equivalent to 3 7/8 is 31/8.

A mixed number consists of a whole number and a proper fraction. In the case of 3 7/8, the whole number is 3 and the proper fraction is 7/8.

To convert a mixed number to an improper fraction, you need to first convert the whole number to a fraction by multiplying it by the denominator of the fraction in the mixed number. In this case, the denominator of the fraction is 8, so we multiply 3 by 8 to get 24.

Next, you add the numerator of the fraction to the result of the multiplication. In this case, the numerator is 7, so we add it to 24 to get 31.

3 7/8 = (3 x 8 + 7) / 8

= (24 + 7) / 8

= 31/8

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The given question is incomplete, the complete question is:

What is 3 7/8 as an improper fraction?

The number of ways to perform the task is 462.

In mathematics, a combination is a way of selecting items from a larger set in which the order of selection does not matter.

For example, if you are selecting a team of 3 people from a group of 10 people, the order in which you select the team members does not matter.

Here we have

Number of magazines = 11

Number of awards = 6

Using the combination formula,

No of ways to select 6 magazines out of 11 = C(11, 6)

= 11! / (6! × (11-6)!) = 11! / (6! × 5!) = 462  

Therefore,

The number of ways to perform the task is 462.

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In number 292,389 the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728.

What is a number?

A number is a mathematical value used for counting or measuring or labelling objects. Numbers are used to performing arithmetic calculations.

The value of a digit depends on its place value in a number. For example, the digit 3 in the number 143,728 has a value of 3 x 1,000 = 3,000 because it is in the thousands place.

Let's call the number we are looking for "x". We want to find a number where the value of the digit 3 is 10 times as great as the value of the digit 3 in 143,728.

The value of the digit 3 in x is 10 times the value of the digit 3 in 143,728, so we can set up the equation:

3 x place value of 3 in x = 10 x 3,000

Simplifying this equation, we get:

3 x place value of 3 in x = 30,000

Dividing both sides by 3, we get:

place value of 3 in x = 10,000

So the digit 3 in x must be in the ten thousands place. Now we can eliminate choices A and B, because they do not have a digit 3 in the ten thousands place.

Checking the remaining choices, we find that only choice C has a digit 3 in the ten thousands place, with a value of 3 x 10,000 = 30,000. Therefore, the answer is:

C. 292,389

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The expression 1/2(2a + 1)(a + 3) can be described as the product of two expressions as 1/2 and (2a + 1)(a + 3).

The entire expression is the product of two smaller expressions, namely 1/2 and (2a + 1)(a + 3).

The second expression, (2a + 1)(a + 3), is a product of two binomials. Each binomial contains two terms separated by a plus sign.

The first binomial, 2a + 1, has a coefficient of 2 in front of the variable a and a constant term of 1. The second binomial, a + 3, has a coefficient of 1 in front of the variable a and a constant term of 3.

To simplify the expression 1/2(2a + 1)(a + 3), we can distribute the 1/2 to both terms inside the parentheses, resulting in the expression (a+1/2)(a+3).

The expression can be further simplified by multiplying the two binomials together, resulting in the quadratic expression a² + 7/2a + 3/2.

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Complete Question:

Consider the expression 1/2(2a + 1)(a + 3)

Complete 2 descriptions of the parts of the expression.

Answer:

67.12

Step-by-step explanation:

Area of 1/2 circle = 1/2πr^2 = 1/2(3.14)(4^2) = 1/2(3.14)(16) = 25.12

Area of top rectangle = 8 x 3 = 24

Area of bottom rectangle = 3 x 6 = 18

Total area : 25.12 + 24 + 18 = 67.12

Answer:Hello how are you

Step-by-step explanation:

With this query, no effort is necessary. measure the tbsp. of all items.

A great source of both phosphorus and calcium, which are essential for the growth and upkeep of strong, strong teeth and bones, is milk. They lower the chance of developing osteoporosis and suffering broken bones later in life. Milk encourages strong bones.

1. Measure [tex]8[/tex] tbsp. chocolate sauce and add [tex]2\frac{1}{2}[/tex] cups of milk.

No work is required for this question. It is a simple instruction to measure out 8 tbsp. of chocolate sauce and add it to [tex]2\frac{1}{2}[/tex] cups of milk.

2. Start with [tex]1\frac{3}{4}[/tex] cups of milk and add [tex]2\frac{1}{2}[/tex] tbsp. chocolate sauce.

No work is required for this question. It is a simple instruction to start with [tex]1\frac{3}{4}[/tex] cups of milk and add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce.

3. Add [tex]3\frac{1}{3}[/tex] tbsp. chocolate sauce to [tex]1\frac{1}{4}[/tex] cups milk.

No work is required for this question. It is a simple instruction to add  [tex]3\frac{1}{3}[/tex]tbsp. of chocolate sauce to [tex]1\frac{1}{4}[/tex] cups of milk.

4. For every 1 cup of milk add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce.

No work is required for this question. It is a simple instruction to add [tex]2\frac{1}{2}[/tex] tbsp. of chocolate sauce for every [tex]1[/tex] cup of milk.

5. Stir [tex]1[/tex] tbsp. chocolate sauce into [tex]\frac{2}{3}[/tex] cup milk.

No work is required for this question. It is a simple instruction to stir 1 tbsp. of chocolate sauce into [tex]\frac{2}{3}[/tex] cup of milk.

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Using the definition of a straight angle, the measure of angle MON is calculated as: 130°.

A straight angle is an angle that measures exactly 180 degrees. It is a flat angle, which means it has no curvature and looks like a straight line.

Therefore, we have:

m∠LOM + m∠MON = 180 [straight angle is equal to 180 degrees]

Substitute:

4x + 30 + 8x + 90 = 180

Solve for x:

12x + 120 = 180

12x = 180 - 120

12x = 60

x = 60/12

x = 5

m∠MON = 8x + 90° = 8(5) + 90

m∠MON = 130°

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Complete Question:

Given

m∠LON is a straight angle.

m∠LOM = 4x + 30°

m∠MON = 8x + 90°

Find m∠MON

Answer:

A kite

Step-by-step explanation:

A kite shape is a quadrilateral in which two pairs of adjacent sides are of equal length. No pair of sides in a kite are parallel but one pair of opposite angles are equal

The diagonals bisect at right angles but all four sides are not equal, the sides are not parallel and there is only one line of symmetry

Answer:

------------

Step-by-step explanation:

Thanks...........

We find the following conclusions concerning the telegraph wire:

Case 1: The perimeter of the circle is equal to 20π centimeters.

Case 2: The extra length for the telegraph wire is equal to 10π meters.

In this problem we find two cases where the perimeter of a circle must be computed for a telegraph wire, this can be done by using the following formula:

s = 2π · r

Where:

Now we proceed to determine the perimeter for each case.

Case 1: (Please notice that diameter is twice the radius)

s = 2π · (20 / 2)

s = 20π cm

The circle has a perimeter of 20π centimeters.

Case 2: (The Earth has a radius of 6371000 meters)

Δs = 2π · (6371005 - 6371000)

Δs = 2π · 5

Δs = 10π m

An extra length of 10π meters is required for the telegraph wire.

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The forecast for week 7 is 309

Given time series data for the problem is; Week 1Week 2Week 3Week 4Week 5Week 6Week 7Observed value220254280276297309Naive forecast220254280276297309Where, the forecast for the next week is the most recent value. It means that the forecast for week 7 is 309.The formula to calculate mean absolute error (MAE) is;$$\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}|y_i-\hat{y}_i|$$Where, $n$ is the total number of observations, $y_i$ is the $i$th observed value, and $\hat{y}_i$ is the $i$th forecasted value by the naive method.MAE = $(1/7) \times (38+26+4+17+12+4+0)$ = 13.57Mean squared error (MSE) is given by;$$\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2$$MSE = $(1/7) \times (38^2+26^2+4^2+17^2+12^2+4^2+0^2)$ = 3004.29Mean absolute percentage error (MAPE) is given by;$$\text{MAPE}=\frac{1}{n}\sum_{i=1}^{n}\left(\frac{|y_i-\hat{y}_i|}{y_i}\right)\times 100$$MAPE = $(1/7) \times [(38/220) + (26/254) + (4/280) + (17/276) + (12/297) + (4/309) + (0/309)] \times 100$MAPE = 5.17%Thus, (a) mean absolute error (MAE) is 13.57, (b) mean squared error (MSE) is 3004.29, (c) mean absolute percentage error (MAPE) is 5.17% and (d) the forecast for week 7 is 309.

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Answer:

586 square inches

Step-by-step explanation:

[tex]2((11(7) + 12(7) + 12(11))[/tex]

[tex]2(77 + 84 + 132)[/tex]

[tex]2(293) = 586[/tex]

The probability of drawing 6 cards of the same suit is 0.002% while the probability of drawing a hand containing only one pair is 42.3%.

(a) The probability of drawing 6 cards of the same suit can be calculated as follows:

First, choose one of the four suits. There are 4 ways to do this.

Next, choose 6 cards from the chosen suit. There are 13 cards in each suit, so there are C(13,6) ways to do this.

Finally, choose any 6 cards from the deck. There are C(52,6) ways to do this.

Therefore, the probability of drawing 6 cards of the same suit is:

P(6 cards of the same suit) = (4 * C(13,6)) / C(52,6) ≈ 0.002%

(b) The probability of drawing a hand containing only one pair can be calculated as follows:

First, choose a rank for the pair. There are 13 ranks to choose from.

Next, choose 2 cards of the chosen rank. There are C(4,2) ways to do this.

Then, choose 4 cards from the remaining 48 cards. There are C(48,4) ways to do this.

Therefore, the probability of drawing a hand containing only one pair is:

P(only one pair) = (13 * C(4,2) * C(48,4)) / C(52,6) ≈ 42.3%

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