A man had a square window with sides equal to 1 metre in his house. He decided that it lets in too much light, so he boarded up half of it and still had a square window 1 metre high and 1 metre wide. How did he do that? (6) Total: 40 marks​

Answer:

Round both numbers to 1 significant figure.

400+400=800

800 is the answer.

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.[tex][/tex]

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

[tex]\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}[/tex]

This distance for the cycling race can now be used to determine David's average speed:

[tex]\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}[/tex]

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

Answer:

Step-by-step explanation:

9 is dependent 6 is independent

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

[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 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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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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Answer:

It's the 3rd one down. 4,-12,6,42,18,0

Step-by-step explanation:

Answer:

[24  -12  6]

[42   18  0]

Step-by-step explanation:

Multiply each number in the brackets individually by 6.

Please mark me brainliest! Thanks!

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

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

Answer:

x = 6 , y = 4

Step-by-step explanation:

for the figure to be a parallelogram , the opposite sides must be congruent, that is

5y = 20 ( divide both sides by 5 )

y = 4

and

2(x + y - 1) = x + 3y ← distribute parenthesis on left side by 2

2x + 2y - 2 = x + 3y ← substitute y = 4

2x + 2(4) - 2 = x + 3(4)

2x + 8 - 2 = x + 12

2x + 6 = x + 12 ( subtract x from both sides )

x + 6 = 12 ( subtract 6 from both sides )

x = 6

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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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:

348 cm²

Step-by-step explanation:

In this problem, we are asked to find the surface area of the regular hexagonal prism. We can use the formula:

[tex]SA = 2A + (P \cdot h)[/tex]

where [tex]A[/tex] is the area of the prism's hexagonal faces, [tex]P[/tex] is the perimeter of the hexagonal faces, and [tex]h[/tex] is the prism's height.

We can solve for the area of the hexagonal faces by splitting it into 6 triangles and multiplying the area of each triangle by 6.

[tex]A = 6\left(\dfrac{1}{2} bh\right)[/tex]

where [tex]b[/tex] is the triangle's base and [tex]h[/tex] is the triangle's height.

[tex]A = 6\left(\dfrac{1}{2}\cdot 4 \cdot 3.5\right)[/tex]

[tex]A = 6\left(2 \cdot 3.5\right)[/tex]

[tex]A = 12 \cdot 3.5[/tex]

[tex]A = 42\text{ cm}^2[/tex]

We can solve for the perimeter by multiplying one side length by 6.

[tex]P = 6(4) = 24\text{ cm}[/tex]

We are given that the height of the prism is 11 cm.

[tex]h = 11\text{ cm}[/tex]

Finally, we can solve for the surface area of the prism by plugging these values into the above formula.

[tex]SA = 2A + (P \cdot h)[/tex]

[tex]SA = 2(42) + (24 \cdot 11)[/tex]

[tex]SA = 84 + 264[/tex]

[tex]\boxed{SA = 348 \text{ cm}^2}[/tex]

Reema should use 3 hooks. The distance between the hooks is approximately 4 inches, and the distances of each hook from the left edge of the wood are approximately 1.75 inches, 5.75 inches, and 9.75 inches.

Given:

Wall length: 4 feet

Wood length: 28 inches

Space between hooks: about 7 or 8 inches

Minimum distance from each end: 1 3/4 inches

To center the coat rack on the wall, we need to find the remaining space on either side of the wood after accounting for the minimum distances from each end.

Convert measurements to inches:

Wall length: 4 feet = 48 inches

Calculate the available space for the wood on the wall:

Available space on each side = (Wall length - Wood length) / 2

Available space on each side = (48 inches - 28 inches) / 2

Available space on each side = 20 inches / 2

Available space on each side = 10 inches

Determine the number of hooks and the space between them:

Space between hooks: about 7 or 8 inches

Let's assume we choose a space of 8 inches between hooks for this calculation.

Remaining space for hooks = Wood length - (Minimum distance from each end × 2)

Remaining space for hooks = 28 inches - (1 3/4 inches × 2)

Remaining space for hooks = 28 inches - (3 1/2 inches)

Remaining space for hooks = 28 inches - 7/2 inches

Remaining space for hooks = 28 inches - 3.5 inches

Remaining space for hooks = 24.5 inches

Number of hooks = Remaining space for hooks / Space between hooks

Number of hooks = 24.5 inches / 8 inches (approximately)

Number of hooks ≈ 3.06 (rounded to the nearest whole number)

Since we cannot have a fraction of a hook, we'll round down to 3 hooks.

Calculate the distance between hooks:

Distance between hooks = Space between hooks / (Number of hooks - 1)

Distance between hooks = 8 inches / (3 hooks - 1)

Distance between hooks = 8 inches / 2

Distance between hooks = 4 inches

Calculate the distance of each hook from the left edge of the wood:

Hook 1 distance from the left edge = Minimum distance from each end

Hook 2 distance from the left edge = Minimum distance from each end + Distance between hooks

Hook 3 distance from the left edge = Minimum distance from each end + (Distance between hooks × 2)

Using the given minimum distance from each end of 1 3/4 inches (or 1.75 inches), we can calculate the distances for each hook:

Hook 1 distance from the left edge = 1.75 inches

Hook 2 distance from the left edge = 1.75 inches + 4 inches

Hook 2 distance from the left edge = 5.75 inches

Hook 3 distance from the left edge = 1.75 inches + (4 inches × 2)

Hook 3 distance from the left edge = 9.75 inches

So, Reema should use 3 hooks. The distance between the hooks is approximately 4 inches, and the distances of each hook from the left edge of the wood are approximately 1.75 inches, 5.75 inches, and 9.75 inches.

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Question

a Reema wants to build a coat rack for the front hallway. The wall is 4 feet long, and the piece of wood she has for the rack is 28  Checklist Did You... inches long. She wants to center the coat rack on the wall. There Draw a detalled needs to be an equal amount of space, about 7 or 8 inches, diagram? between the coat hooks. The first and last hooks should be no Check all your less than 1 inches from either end of the wood. How many calculations? Complete all parts hooks should Reema use? What is the distance between the of the problem? hooks? What is the distance of each hook from the left edge of the wood? Draw and label a diagram of the coat rack on the wall. Mark all the measurements for - inches placing the wood on the wall, and for attaching the hooks on the wood. You can use either fractions or decimals to label and calculate the measurements. Reflect Reflect on Mathematical Practices After you complete the task, choose one of the following questions to answer. • Model What models helped you to solve this problem? How did they help? • Be Precise When was it easier to use fractions, and when was it easier to work with decimal numbers? 213 1.75 left 1.75 edge Right edge

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:

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:

  (d)  (0, 0), (0, 9), (9, 0)

Step-by-step explanation:

You want to know the vertices represented by the matrix 3T, where ...

  [tex]T=\left[\begin{array}{ccc}0&0&3\\0&3&0\end{array}\right][/tex]

The scaled matrix 3T is found by multiplying each element by the scale factor:

  [tex]3T=\left[\begin{array}{ccc}0&0&9\\0&9&0\end{array}\right][/tex]

Each column is an (x, y) pair representing a vertex. The vertices of the scaled triangle are ...

  (0, 0), (0, 9), (9, 0)

<95141404393>

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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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 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 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:

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:

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

Let d be the number of dimes and q be the number of quarters.

We can set up two equations based on the information given:

Use substitution here:

So he has 5 quarters.

We can plug that back into either equation to find the number of dimes:

So he has 9 dimes and 5 quarters.

Answer:

15.36

Step-by-step explanation:

192*0.02*4= 15.36

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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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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Use tracing paper for the rotation. Put a dot on the origin (0,0) and trace the shape. Then turn the paper 180 degrees and redraw the shape in its new position.

For the reflection, the line y = x + 2 would have an x interrcept of (-2,0) and y intercept of (0,2) so, draw a line through those coordinates and reflect the new shape you traced. That will be your final answer, you can rub out the rotated one as the question asked you to rotate AND reflect. Not just rotate.

Step-by-step explanation:

To simplify the expression √3 * √5 * √12, you can combine the square roots and simplify the numbers under the radicals.

Step 1: Simplify the numbers under the radicals:

√3 = √(3) (The square root of 3 cannot be simplified further because 3 is a prime number.)

√5 = √(5) (The square root of 5 cannot be simplified further because 5 is a prime number.)

√12 = √(4 * 3) (The number 12 can be expressed as the product of 4 and 3, and the square root of 4 simplifies to 2.)

√12 = 2√(3)

Step 2: Combine the simplified square roots:

√3 * √5 * √12 = √(3) * √(5) * 2√(3)

Step 3: Apply the rule of multiplying square roots:

√(3) * √(5) = √(3 * 5) = √15

Step 4: Substitute the simplified square roots back into the expression:

√3 * √5 * √12 = √15 * 2√(3)

Step 5: Simplify the expression further:

√15 * 2√(3) = 2√(15) * √(3) = 2√(15 * 3) = 2√(45)

Step 6: Simplify the number under the square root:

2√(45) = 2√(9 * 5) = 2√(9) * √(5) = 2 * 3 * √(5) = 6√(5)

Therefore, the simplified form of √3 * √5 * √12 is 6√5.

Answer: 6√5

√180 = 6√5