What is the product?

total angles of the triangle = 180°

∠BAC + ∠ABC + ∠ACB = 180°

40° + 90° + ∠ACB = 180°

130° + ∠ACB = 180°

∠ACB = 180° - 130°

∠ACB = 50°

∠ACB and ∠ECD is opposite angles. So, that two angles are equal.

∠ACD = ∠ECD = 50° (B)

That's it :)

Step-by-step explanation:

50°

abc is right angle and

a is 40°

b is 90°

c is 50°

so angle acb is vertical opposite to angle ecd and it is equal

Answer:

please see answers below

Step-by-step explanation:

i) 5/8  X 320 = 200 people

ii) 0.75 X 200 = 150 (people in farming but also trade). only trade = 320 - 200 = 120.

number of people in trade = 150 + 120 = 270.

b) 0.75 X 5/8 = 3/4 X 5/8 = 15/32 = 150 people (both farm and trade).

c) only farming = 0.25 X 5/8 = 1/4 X 5/8 = 5/32 = 50.

only trade = 320 - 50 (only farm) - 150 (both farm and trade) = 120.

so, only do one activity = 50 + 120 = 170.

d) traders only = 120/320 = 3/8 = 37.5%

e) P(farmer only) = 50/320 = 0.15625

Answer:

Step-by-step explanation:

9 is dependent 6 is independent

The exact value of expression sin 9π/4 is,

⇒ sin 9π/4 = 1 / √2

We have to given that;

Expression to find exact value is,

⇒ sin 9π/4

Now, WE can change it into degree as,

⇒ 9π/4

⇒ 9 × 180 / 4

⇒ 9 × 45

⇒ 405 degree

Hence, We get;

⇒ sin 9π/4

⇒ sin 405°

⇒ sin (360 + 45°)

⇒ sin 45°

⇒ 1 / √2

Thus, The exact value of expression sin 9π/4 is,

⇒ sin 9π/4 = 1 / √2

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Ki traveled at an average speed of approximately 41.05 miles per hour without any stops.

To calculate the average speed at which Ki traveled from Memphis to Atlanta, we can use the formula:

Average Speed = Total Distance / Total Time

First, let's calculate the total time taken for the journey. Ki started from Memphis at 5:30 am and arrived in Atlanta at 3:00 pm, which is a total of 9.5 hours.

Next, we divide the total distance traveled, which is 391 miles, by the total time taken, which is 9.5 hours:

Average Speed = 391 miles / 9.5 hours

Calculating this, we find that Ki's average speed was approximately:

Average Speed ≈ 41.05 miles per hour

Therefore, Ki traveled at an average speed of approximately 41.05 miles per hour without any stops.

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Answer:

15.36

Step-by-step explanation:

192*0.02*4= 15.36

The slope of the line that passes through given points is -0.87. Option B is the correct answer.

In mathematics, slope is usually defined by the letter "m" and includes the change in y coordinate (vertical change) divided by the change in x coordinate (horizontal shift) between two points on a line.

We know that slope of a line that passes through two points is :

slope,   [tex]m = \frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]

The given points are (-3.9,4.1) and (5.5,-4.1).

y2 = -4.1

y1 = 4.1

x2 = 5.5

x1 = -3.9

Substituting all these values  in the above equation  we get,

slope,  [tex]m = \frac{-4.1 - (4.1)}{5.5 - (-3.9)}[/tex]

m = -8.2 / 9.4

m = -0.87

So, the slope of the line formed by given points is -0.87. Therefore , option B is correct answer.

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Answer: B 102

Step-by-step explanation: The perpendicular sides of the room tells us that it is a right triangle.

To find our the area of the triangle you use the formula [tex]\frac{base*height}{2}[/tex]base*height/2

We plug in 12feet and 17 feet for the base and height

We get [tex]\frac{12*17}{2}[/tex]

12 and 2 cancel out so our new equation is 6*17 squared feet

So our answer is 102 square feet

Yes, children, students, and senior citizens being eligible for discounted movie tickets is an example of price discrimination.

When a merchant charges different rates to various groups of clients based on their willingness to pay, this is referred to as price discrimination.

Price discrimination requires market strength, definable client segmentation, and the capacity to avoid arbitrage among various groups.

Price discrimination is a sales approach in which the seller charges varying rates for the same product or service based on what the vendor believes the consumer would agree to.

See graph attached.

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[tex]\theta =\cfrac{14}{3}\pi \implies \theta =\cfrac{14\pi }{3}\implies \theta =\cfrac{6\pi +6\pi +2\pi }{3} \\\\\\ \theta =\cfrac{6\pi }{3}+\cfrac{6\pi }{3}+\cfrac{2\pi }{3}\implies \theta =2\pi +2\pi +\cfrac{2\pi }{3}[/tex]

so if we take a look at that, we can say that the angle θ does two revolutions and then it lands on 2π/3, so the terminal point of it is the same as 2π/3's, and if you check your Unit Circle, as you should have one

[tex]\sin(\theta )=\cfrac{\sqrt{3}}{2}\hspace{5em}\cos(\theta )=-\cfrac{1}{2}[/tex]

Answer:

sin∅ = √3/2

cos∅ = -1/2

Step-by-step explanation:

Notice that 14π/3 is just under 3π, so the reference angle made with the negative x-axis is π/3. Since sin(π/3) = √3/2, then sin(14π/3) is also √3/2.

cos(14π/3) works somewhat similarly. Since cos(π/3) = 0.5, and cos(14π/3) would be located in Quadrant II where the negative axis is, then cos(14π/3) = -0.5

The number of jackets Meera will sell if she behaves like a monopolist is 3( option B).

To determine the number of jackets Meera will sell if she behaves like a monopolist, we need to compare the marginal revenue (MR) and marginal cost (MC) of producing and selling additional jackets. Meera can sell jackets at various price points depending on the quantity sold, but as she behaves like a monopolist, we consider the revenue and costs associated with a given production level.

From the pricing information given, we can determine her total revenue function, R(x), as follows:

- For 1 jacket, R(1) = 40

- For 2 jackets, R(2) = 70

- For 3 jackets, R(3) = 90

- For 4 jackets, R(4) = 100

- For 5 jackets, R(5) = 100

To determine her marginal revenue function, MR(x), we find the change in revenue from selling an additional jacket. From the data given, we can see that MR is not constant and decreases as the quantity sold increases. Specifically:

- For 1 jacket, MR(1) = 40 - 0 = 40

- For 2 jackets, MR(2) = 35 - 40 = -5

- For 3 jackets, MR(3) = 30 - 35 = -5

- For 4 jackets, MR(4) = 25 - 30 = -5

- For 5 jackets, MR(5) = 20 - 25 = -5

Meera's marginal cost of production is given as a constant $20 for each additional jacket produced, so MC(x) = 20 for all values of x.

To maximize her profits, Meera should produce and sell jackets up to the point where MR(x) = MC(x), which represents the level of production that equates the revenue from selling an additional jacket with the cost of producing that jacket. This happens at the output level of 3, where MR(3) = -5 = MC(3) = 20.(option-b)

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The minimum selling price on the special order to produce net income of 5.17 per basketball is $ 29.79 per ball.

Variable cost of goods sold for the special order = $ ( 3,582,000 - 960,000 ) / 120,000 * 10,000 = $ 218,500

Variable selling and administrative expenses for special order = $ [( 513,400 - 271,000) / 120,000 + 0.75] x 10,000 = $ 27,700

Fixed costs are not relevant, as they would remain unchanged.

c. Profit required = $ 5.17 x 10,000 = $ 51,700

Minimum selling price required = $ ( 51,700 + 218,500 + 27,700) / 10,000

= $ 29.79 per ball.

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ThreePoint Sports Inc. manufactures basketballs for the Women's National Basketball Association (WNBA). For the first 6 months of 2017, the company reported the following operating results while operating at 80% of plant capacity and producing 120,000 units.What is the minimum selling price on the special order to produce net income of 5.17 per basketball

Answer:

Step-by-step explanation:

Here are the probabilities for each event:

The probability of drawing a blue or green marble out of a bag containing three blue, two green, eight yellow, four red, and three orange marbles is 0.25.

The probability of choosing a card with a heart on it out of a standard deck of cards is 0.25.

The probability of getting an A or B on a paper if you could get in A,B,C, or F is 0.5.

The probability of getting a heads or tails on a flip of a coin is 0.5.

I hope this helps! Let me know if you have any other questions.

Answer:

Try contacting the Help center located at the bottom part of the home page of this site. It is recoverable as long as no violation committed

Answer: 99 in²

Step-by-step explanation:

We can use the given formula for a triangular prism. We will substitute our known values and solve.

       Surface Area = length * base perimeter + (2 × base area)

       Surface Area = length * (1.5 in + 2 in + 2.5 in) + (2 × [tex]\frac{bh}{2}[/tex])

       Surface Area = 16 * (6 in) + (2 × [tex]\frac{(2\;in)(1.5\;in)}{2}[/tex])

       Surface Area = 16 in * (6 in) + (3 in²)

       Surface Area = 96 in² + 3 in²

       Surface Area = 99 in²

The value of x for which the two lines are parallel is given as follows:

x = 60º.

We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.

Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of x can be found as follows:

x + 2x = 180

3x = 180º

x = 180º/3

x = 60º.

The figure is given by the image presented at the end of the answer.

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The angle formed is 91.84° which can be obtained using Cosine Rule since all the three sides are given.

CosC = (a²+b²-c²) /2(ab)

a = 31

b = 42

c = 53

Substituting the values into the relation

CosC = (31² + 42² - 53²) / 2(31×42)

CosC = - 84 / 2604

CosC = −0.032258

C =

[tex]C = {cos}^{ - 1} (- 0.03225)[/tex]

C = 91.84°

Hence, the angle formed is 91.84°

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In the ellipse shown below, each point marked with a dot is called a(n)  focus

In an ellipse, the focus (plural: foci) is a pair of special points that play a significant role in defining the shape of the ellipse. The focus points are located inside the ellipse along the major axis, which is the longer axis of the ellipse.

The defining property of an ellipse is that the sum of the distances from any point on the ellipse to the two foci is constant. This property is known as the "focus-directrix property."

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The graph of the function f(x) = x³- 2x² - 4x + 8​  is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = x³- 2x² - 4x + 8​

The above function is a polynomial function that has undergone for several transformations

Next, we plot the graph using a graphing tool by taking note of the transformations rules

The graph of the function is added as an attachment

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