Atul gets a pocket money allowance of Rs. 120 per day. Thinking that this was rather less he asked his friends about their allowances and obtained the following data which includes his allowance also ( Amount I Rs. ) 120, 180, 100, 50, 250, 200,200,220, 150, 100,100,150,130,200,180, 100, 150, 100, 180, 150, 120, 150, 100, 150, 100, 120, 180, 200, 50. He presented this data to his father and asked for an increase in his allowance as he was getting less than average amount. His father, a statistician, countered pointing out that Atul's allowance was actually more than the average amount

sale price=$30

discount price=0.05

Taking it $30*0.05=600$

after applying 0.08

600*0.08=48$

, so 48$ is the final price of the wind chime.

In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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It took 15.03 seconds to fill the 67% larger than the 3-gallon bucket

Calculating the time required to fill the bucket:

To solve this problem, use the concept of proportionality to calculate the time required. Use the concept of percentage increase to find the volume of the larger bucket, which was 67% larger than the 3-gallon bucket.

Here we have

A hose fills a 3-gallon bucket in 9 seconds.

The volume of the bucket which is 167% more than 3 gallons

= 167% of 3 gallons = [167/100] × 3 = 5.01 gallons

It took 9 seconds to fill 3 gallons

The time required to fill 5.01 gallons = 9/3 × [5.01]

= 15.03 seconds

Therefore,

It took 15.03 seconds to fill the 67% larger than the 3-gallon bucket

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By speed fοrmula, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.

Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn.

Mathematically, speed is calculated as fοllοws:

speed = distance/time

Where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

We can use the fοrmula:

time = distance/speed

where distance is the distance frοm the star tο Earth, and speed is the speed οf light.

Putting the values, we get:

time = (3.9 x 10¹⁴ km) / (3.0 x 10⁵km/s)

Simplifying, we can divide the distances and divide the pοwers οf ten:

time = 1.3 x 10⁹ s

Therefοre, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.

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Based on the information provided in the question, The expected value of the sample mean is approximately 497.92 million dollars.

To calculate the expected value of the sample mean, first calculate the mean of the population ($10.82 million) and then multiply it by the sample size (46).
Mean of Population * Sample Size = Expected Value of Sample Mean
$10.82 million * 46 = $497.92 million
Expected Value of Sample Mean = $497.92 million

A sample mean is a statistical measurement that shows the mean value of the data in a sample. It is determined by summing all of the values in the sample and dividing the total by the number of observations.

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The best way to design a study to measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year and count the number of vehicles that pass a certain point, then calculate the average using the given formula.

The best way to accurately measure the amount of traffic during the morning rush hour along a city street is to make video recordings of the street during rush hour every day for a year. After recording the video, count the number of vehicles that pass a specific point in the video. Then, calculate the average number of vehicles that pass the point each day during one year by using the following formula: Average = (Number of vehicles per day1 + Number of vehicles per day2 + ... + Number of vehicles per dayn) / n, where n is the number of days the video recording was made. This method is the most reliable way to measure the amount of traffic during the morning rush hour since it provides an average based on the data collected over a full year.

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After spending 60% of his money Joseph has rs. 600., He has 1500 in the beginning.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Let the total amount be x

He spent 60% of his money

So, Money spent = 60% x=0.6x

Remaining amount = x- 0.6 x = 0.4x

We are given that Now he has Rs.600

[tex]0.4x=600\\\\x=\frac{600}{0.4}\\\\x=1500[/tex]

Hence He has Rs.1500 at the beginning

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Step-by-step explanation:

7. Cross multiply

14( 6x +1) = 7( 18x - 2)

Open the brackets

84x +14 = 126x - 14

Subract 84x from both sides

14 = 42x - 14

Add 14 to both sides

28 = 42x

Divide both sides by 42

X = 28/42

Write in simplest form

X=2/3

8. Add all the ratio 2+3+4= 9

Alana is ratio 3

3/9 x 63 candy = 21 candy

9. 3ab : 27ab

Divide both sides by 3, you have 1ab: 9ab

Divide both sides by ab, you have 1: 9

Answer:

the GCF of 270 & 360 is 90

exponent form: 3³x 2 x 5 = 270 & 3²x 2³x 5 = 360

Step-by-step explanation:

3 x 3 x 3 x 2 x 5 = 270

3 x 3 x 2 x 2 x 2 x 5 = 360

If the credit limit on the card is amount $1,000, then you should aim to keep the balance owing on the card at amount $300 or less.

It depends on the acceptable debt ratio. Generally, to maintain a good credit rating, it is recommended to keep a debt-to-credit ratio of 30% or less, meaning that you should have an amount owing on the card equal to or less than amount 30% of the credit limit.

If the credit limit on the card is $1,000, then you should aim to keep the balance owing on the card at $300 or less. So, if the balance owing at the end of the month is over $300, you would need to make a payment of at least the difference between the balance owing and the acceptable debt ratio.

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Answer:

x = -2

y = -4

Step-by-step explanation:

x - 3y = 10 --------------(1)

x + 5y = -22 -----------(2)

Taking Eq. (1)

x - 3y = 10

x = 10 + 3y ------------(3)

10 + 3y + 5y = -22

8y = -22 - 10

8y = -32

y = -32/8

x = 10 + 3(-4)

x = 10 - 12

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

To solve the given system, let's begin by solving for x in x- 3y=10:-

[tex]\tt x-3y=10[/tex]

Add 3y to both sides:-

[tex]\tt x-3y+3y=10+3y[/tex]

[tex]\tt x=10+3y[/tex]

Substitute x= 10+3y into x+5y=-22:-

[tex]\tt 10+3y+5y=-22[/tex]

Simplify:-

[tex]\tt 10+8y=-22[/tex]

Now, solve for y in 10+8y=-22:-

[tex]\tt 10+8y=-22[/tex]

Subtract 10 from both sides:-

[tex]\tt \tt 10+8y-10=-22-10[/tex]

[tex]\tt 8y=-32[/tex]

Divide both sides by -8:-

[tex]\boxed{\bf y=-4}[/tex]

Now, substitute y=-4 into x=10+3y:-

[tex]\tt x=10+3y[/tex]

[tex]\tt x=10+3\times-4[/tex]

Simplify:-

[tex]\boxed{\bf x=-2}[/tex]

Therefore, x=-2 and y=-4

_________________________

Hope this helps! :)

Answer : a ) Variance = (21 - 6.5)^2/12 = 13.7708, b) 1, 21 <= x, c) Probability = 0.5862, D) Probability = 0.8552

The uniform distribution on the interval (6.5, 21) can be represented as U(6.5, 21).
(a) The mean and variance of a uniform distribution can be calculated using the following formulas:
Mean = (a + b)/2
Variance = (b - a)^2/12
where a and b are the lower and upper bounds of the distribution, respectively.
For the given distribution, a = 6.5 and b = 21.
Therefore, the mean and variance of depth are:
Mean = (6.5 + 21)/2 = 13.75
Variance = (21 - 6.5)^2/12 = 13.7708

(b) The cdf of a uniform distribution can be calculated using the following formula:
F(x) = (x - a)/(b - a)
For the given distribution, F(x) = (x - 6.5)/(21 - 6.5) for 6.5 <= x < 21.
Therefore, the cdf of depth is:
F(x) = {
0, x < 6.5
(x - 6.5)/14.5, 6.5 <= x < 21
1, 21 <= x

(c) The probability that observed depth is at most 10 can be calculated using the cdf:
P(X <= 10) = F(10) = (10 - 6.5)/14.5 = 0.2414
The probability that observed depth is between 10 and 15 can be calculated using the cdf:
P(10 <= X <= 15) = F(15) - F(10) = (15 - 6.5)/14.5 - (10 - 6.5)/14.5 = 0.5862

(d) The standard deviation of a uniform distribution can be calculated using the following formula:
Standard deviation = sqrt(Variance)

For the given distribution, the standard deviation is:
Standard deviation = sqrt(13.7708) = 3.7118
The probability that the observed depth is within 1 standard deviation of the mean value can be calculated using the cdf:
P(13.75 - 3.7118 <= X <= 13.75 + 3.7118) = F(13.75 + 3.7118) - F(13.75 - 3.7118) = (13.75 + 3.7118 - 6.5)/14.5 - (13.75 - 3.7118 - 6.5)/14.5 = 0.5118
The probability that the observed depth is within 2 standard deviations of the mean value can be calculated using the cdf:
P(13.75 - 2*3.7118 <= X <= 13.75 + 2*3.7118) = F(13.75 + 2*3.7118) - F(13.75 - 2*3.7118) = (13.75 + 2*3.7118 - 6.5)/14.5 - (13.75 - 2*3.7118 - 6.5)/14.5 = 0.8552

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Therefore, DM = 0, which means that the plane is directly above point D. Pythagorean theorem The vertical distance from the plane to point D is simply the altitude of the plane.

The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides.

drawing a diagram

  A ------ 3 miles ------ D ----- x miles ------ C

  |                                               |

  |                                               |

  6 miles                                         6 miles

  |                                               |

  |                                               |

  B -----------------------------------------------

[tex]AC^2 = AD^2 + DC^2\\BC^2 = BD^2 + DC^2\\AD^2 + DC^2 = BD^2 + DC^2\\AD^2 = BD^2[/tex]

So, the plane must be directly above the midpoint of AB. Let's call this point M:

  A ------ 3 miles ------ D ----- x miles ------ C

  |                                               |

  |                                               |

  6 miles                           3 miles        6 miles

  |                                               |

  |                                               |

  B -----------------------------------------------

                     |

                     |

                     M

Now, let's use Pythagoras' theorem again to find the distance from the plane to point D:

[tex]DM^2 = AD^2 - AM^2\\DM^2 = AD^2 - 3^2\\DM^2 = 3^2 - 3^2\\DM^2 = 0[/tex]

Therefore, DM = 0, which means that the plane is directly above point D. The vertical distance from the plane to point D is simply the altitude of the plane.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]\stackrel{ y-intercept }{(\stackrel{x_1}{0}~,~\stackrel{y_1}{4})}\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{12}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ 8 }{ 4 } \implies 2[/tex]

Answer:

-180

Step-by-step explanation:

The measure of the angle on the attached figure is

There are two ways to measuring it

1. Counterclockwise: In this the sign is positive

So,

We can write

180°,

180°+360° = 540°,

180° + 2(360°) =180°+720° =900°,

2. Clockwise: In this, the sign is negative

So,

We can write

-180°,

-180° - 360° = -540°,

-180° - 2(360°) = -180° - 720° = -900°

the correct option is A.

The percentage of of the shaded region is 74.8%

A circle is simply a round shape that has no corners or line segments. It is a closed curve shape in geometry. The enclosed body of a circle is called the circumference.

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in squared units.

The area of a circle is expressed as :

πr²

The area of the shaded part = area of big circle - area of small circle

= 3.14(8.01²-4.02²)

= 3.14(64.16-16.16)

= 3.14( 48)

= 150.72in²

area of the big circle = 3.14 × 64.16 = 201.46

therefore the percentage of the shaded region of the point = 150.72/201.46 × 100

= 74.8% ( nearest tenth)

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diameter = 14cm

[tex]radius \: = \frac{d}{2} = \frac{14}{2} \\ = 7cm[/tex]

Area of circle ( A1 ) = [tex]\pi {r}^{2} [/tex]

[tex] = \frac{22}{7} \times 7 \times 7 \\ [/tex]

[tex] = 154 {cm}^{2} [/tex]

Area of Square ( A2 ) = l²

= ( 14 )²

= 196cm²

Area of shaded region = A2 - A1

= 196 - 154

= 42cm²

....Thank you !! :)

The probability of getting 2 kings out of 25 cards is approximately 0.044 or 4.4%.

Drawing cards from a standard deck of 52 cards is a random process, and the probability of getting 2 kings out of 25 cards depends on the total number of possible outcomes.

There are 4 kings in a deck of 52 cards,

So, The probability of drawing a king on the first draw = 4/52.

Since the deck is not replaced,

The probability of drawing another king on the second draw = 3/51.

Therefore,

The probability of getting 2 kings out of 25 cards can be calculated by combining these two probabilities.
The probability of drawing 2 kings = [tex](4/52) * (3/51) * (25C2)[/tex]

Where,

25C2 = The number of ways to select 2 cards out of 25.

After calculating this expression, the probability of getting 2 kings out of 25 cards is approximately 0.044 or 4.4%.

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According to proportionality, the virus will spread at a rate of 12475 students per day.

If five college students with the flu return to an isolated campus of 2500 students, and the rate at which the virus spreads is proportional to both the number of students infected and the number of students not infected, then we can use the following formula to find the rate of spread:

Rate of spread = (number of students infected) x (number of students not infected)

In this case, the number of students infected is 5 and the number of students not infected is 2500 - 5 = 2495. So, the rate of spread is:

Rate of spread = 5 x 2495 = 12475

This means that the virus will spread at a rate of 12475 students per day, assuming that the rate of spread is proportional to both the number of students infected and the number of students not infected.

It is important to note that this is a simplified model and does not take into account other factors that may affect the rate of spread, such as the effectiveness of quarantine measures or the individual immune systems of the students. However, it does give us an idea of how quickly the flu can spread in a population of 2500 students.

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The force exerted by the brick on the window is equal in magnitude but

opposite in direction to the force exerted by the window on the brick.

When a brick hits a window and smashes it, there are two forces

involved: the force exerted by the brick on the window and the force

exerted by the window on the brick.

According to Newton's third law of motion, for every action, there is an

equal and opposite reaction.

The magnitude of the forces involved depends on several factors,

including the mass of the brick, its velocity, the angle of incidence, and

the strength of the window. The force exerted by the brick on the

window will be the impact force, which is the force applied over a short

period of time during the collision.

The impact force will depend on the momentum of the brick, which is

the product of its mass and velocity.

It's not possible to say which force is larger because the two forces are

equal in magnitude but opposite in direction, according to Newton's third

law of motion.

The strength of the window will also play a role, as a stronger window

will be able to resist a higher impact force before breaking.

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Answer:

it depends

Step-by-step explanation:

it depends on the value of n

for instance if n was = to 7 then

2+2n = 2+2(7) = 2+14 = 16

Answer: 2+2n

Step-by-step explanation:

The expression 2 + 2n can be simplified as follows:

2 + 2n = 2(1 + n)

So the expression 2 + 2n is equivalent to 2 times the quantity 1 plus n, or simply 2(1 + n). It cannot be simplified any further unless there is additional information or context provided.

The factorized terms of the given expression  ax - a + x - 1 by grouping the terms in pairs is given by  (x - 1)(a + 1) .

Expression is equal to,

ax - a + x - 1

To factorize the expression ax-a+x-1 by grouping terms in pairs.

First group the first two terms and the last two terms together we get,

⇒ ax - a + x - 1 = ( ax - a ) + ( x - 1 )

Now factor out the common factor of 'a' from the first group.

And the common factor of '1' from the second group we get,

⇒ ax - a + x - 1 = a(x - 1) + 1(x - 1)

Both the groups have a common factor of (x - 1).

Take out  common factor we have,

⇒ ax - a + x - 1 = (x - 1)(a + 1)

Therefore, the factorized expression is equal to,

 ax - a + x - 1 = (x - 1)(a + 1)

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The value of tan (A-B) is -203/169, when angles A and B are in Quadrant 1.

In trigonometry, the Pythagorean identity is sin² + cos² = 1, where is an angle in a right triangle. The Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the legs of a right triangle, is the source of this identity. Trigonometric identities and formulae are derived from the Pythagorean identity, which is a basic idea in the subject.

The trigonometric identity is given as

tan(A-B) = (tan A - tan B) / (1 + tan A tan B)

The value of tan A and tan B is calculated as follows.

sin A = 7/25, we can use the Pythagorean identity: sin² A + cos² A = 1 to find cos A:

cos A = √(1 - sin² A) = √(1 - (7/25)²) = 24/25

Therefore, tan A = sin A / cos A = (7/25) / (24/25) = 7/24.

Similarly, since cos B = 12/37, we can use the Pythagorean identity cos² B + sin² B = 1 to find sin B:

sin B = √(1 - cos² B) = √(1 - (12/37)²) = 35/37

Therefore, tan B = sin B / cos B = (35/37) / (12/37) = 35/12.

Substituting the values:

tan(A-B) = (tan A - tan B) / (1 + tan A tan B)

= ((7/24) - (35/12)) / (1 + (7/24) x (35/12))

= (-203/288) / (169/288)

= -203/169

Therefore, the value of tan (A-B) is -203/169.

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The mean Depreciation of automobile for a random sample of 20 automobile models is 6626.

To find the mean of the Depreciation amounts in Car Depreciation, we can use the following formula:

mean = (sum of all values) / (number of values)

The resulting value of 6626 indicates the average depreciation amount in dollars of the 20 automobile models in the sample of standard deviation.

In statistics, the mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in the dataset and then dividing the sum by the number of values.

The mean is commonly used as a measure of the "typical" value in a dataset and is often used to compare the values of different datasets or to track changes in a single dataset over time.

Automobile Depreciation For a random sample of 20 automobile models, we record the value of the model as a new car and the value after the car has been purchased and driven 10 miles. 1 The difference between these two is a measure of the depreciation on the car just by driving it off the lot.

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The linear function that best fits the data is given as follows:

y = 60x.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

When x = 0, y = 0, hence the intercept b of the line is given as follows:

b = 0.

When x increases by 5, y increases by 300, hence the slope m of the line is given as follows:

m = 300/5

m = 60.

Hence the equation is:

y = 60x.

The points on the scatter plot are given as follows:

(0,0) and (5,300).

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Answer:

y = 2/3x + 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

We know

m = 2/3

Y-intercept is located at (0, 6)

So, our equation is y = 2/3x + 6

Option #1: point-slope form: y - y1 = m ( x - x1 )

y - 4 = 2/3 ( x - (-3) )     or     y - 4 = 2/3 ( x + 3 )

Option #2: slope-intercept form: y = mx + b

Take the point-slope and solve for y:

     y - 4 = 2/3 ( x + 3 )

     y - 4 = 2/3 x + 2

          y = 2/3 x + 6  

The probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.

Probability is an area of mathematics that deals with the study of chance events.

We have, A poll showed that 60.4% of Americans say they believe that some people see the future in their dreams.

Therefore, the probability of randomly selecting someone who does not believe that some people see the future in their dreams can be calculated as follows:

P(A) = 1 - P(B)

Where,

P(A) = Probability of selecting someone who does not believe that some people see the future in their dreams.

P(B) = Probability of selecting someone who believes that some people see the future in their dreams.

P(A) = 1 - P(B)

⇒ 1 - 60.4/100

⇒39.6/100

⇒ 0.396 or 39.6%

Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.

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The forecasted demand for Samsung TVs at X-store for the 4th year using seasonality indexing are as follows:

A seasonal index is a tool that compares a specific season during a cycle to the average season during that cycle. By deseasonalizing data, we can predict or approximate future data values by removing seasonal fluctuations or patterns in the data.

To use seasonality indexing to forecast the values of the 4th year, we first need to calculate the average indices for each season:

Average index for Spring:

= (1500 + 1650 + 1550) / 3

= 1567

Average index for Summer:

= (1000 + 900 + 850) / 3

= 917

Average index for Fall:

= (500 + 600 + 550) / 3

= 550

Average index for Winter:

= (200 + 150 + 220) / 3

= 190

Next, we need to calculate the seasonality index for each season by dividing the average index by 100:

Seasonality index for Spring = 1567 / 100 = 15.67

Seasonality index for Summer = 917 / 100 = 9.17

Seasonality index for Fall = 550 / 100 = 5.50

Seasonality index for Winter = 190 / 100 = 1.90

To forecast the demand for the 4th year, we can use the following formula "Seasonality index x Average demand for the season".

For Spring, the Forecasted demand for Spring in year 4:

= 15.67 x (3710/4)

= 5800.175

≈ 5800 TVs

For Summer, the Forecasted demand for Summer in year 4:

= 9.17 x (3710/4)

= 3372.925

≈ 3373 TVs

For Fall, the Forecasted demand for Fall in year 4:

= 5.50 x (3710/4)

= 2031.25

≈ 2031 TVs

For Winter, the Forecasted demand for Winter in year 4:

= 1.90 x (3710/4)

= 692.75

≈ 693 TVs

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x°=46

Step-by-step explanation:

There are two methods of solving this question

Method 1:

x°+90°=136° the theorem states that "the sum of two opposite interior is equal to the exterior"

x°=136°-90°

x°=46°

or

Method 2:

136° is on a straight line which is 180°

so, let the other side of the straight line be a.

therefore, 136°+a°=180° theorem {Angle on a straight line}

a°=180°-136°

a°=44°

so, in the triangle is the sum of 180°

a°+90°+x°=180° theorem {Sum of angles in a triangle}

44°+90°+x°=180°

x=180°-134°

x°=46°