Find the area of the following figure if a line drawn from the side of length 8 to the side of length 2 is 8 units long.

48 square units, 46 square units, 50 square units, or 52 square units

The greatest distance to the boat consistent with my observations is 500 meters.

In my observations, I have noticed certain factors that limit the maximum distance to which I can see the boat clearly. These factors include atmospheric conditions, visibility, and the size of the boat itself. Based on these considerations, the greatest distance to the boat that is still consistent with my observations is 500 meters.

Atmospheric conditions play a crucial role in determining how far I can observe the boat. Factors like fog, haze, or heavy rain can significantly reduce visibility, making it difficult to see objects at a distance. Similarly, if the boat is small or located in a crowded area, it may be harder to spot from a greater distance. Additionally, my own visual acuity and the quality of optical devices I use, such as binoculars, can also influence the maximum distance at which I can observe the boat clearly.

Given these factors, the maximum distance of 500 meters is the greatest distance that aligns with my observations. At this distance, I can reasonably expect to see the boat clearly, taking into account the atmospheric conditions, visibility, and the size of the boat. It is important to note that this distance may vary for different individuals based on their own observational capabilities and the prevailing conditions at the time of observation.

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The graph of the inequality is attached below to represent the solution.

To solve this problem, we can simply plot the graph of the inequality using a graphing calculator. To do this, we can simply input the value of both inequalities and then plot the values.

In the graph below, the the red broken line represents the first equation which is "<" or less than and the second equation which is the straight blue line which represents the ">" or greater than sign.

Kindly find the attached image below.

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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

38

Step-by-step explanation:

$9/hour = 15 cents per minute. $5.70/0.15 = 38 minutes.

Answer:

38 minutes

Step-by-step explanation:

Answer:

0 = 8

5 = 23

14 = 50

Step-by-step explanation:

f(n)= 8+ 3n

when n=0

f(0)= 8+ 3(0)

f(0)= 8+0

f(0)= 8

when n=5

f(5)= 8+ 3(5)

f(5)= 8+ 15

f(5)= 23

f(n)= 50

f(n)= (50- 8)÷ 3

f(n)= 42÷3

f(n)=14

so n=14

According to the given information, (yn) is convergent.

What is the convergence and divergence of the sequence?

Convergence: A sequence approaches a fixed number as the number of terms increases.

Divergence: A sequence does not approach a fixed number as the number of terms increases.

Yes, (yn) is convergent.

Since (xn) is a convergent sequence, it has a limit L, which means that for any ε > 0, there exists an N such that |xn - L| < ε for all n ≥ N.

Now, let ε > 0 be given. Then, there exists an M such that |xn - yn| < ε for all n ≥ M.

Combining these two inequalities, we have:

|yn - L| = |yn - xn + xn - L|

≤ |yn - xn| + |xn - L|

< ε + ε (for all n ≥ M)

Therefore, we have shown that for any ε > 0, there exists an M such that |yn - L| < 2ε for all n ≥ M.

Since 2ε can be made arbitrarily small by choosing ε small enough, this implies that (yn) converges to L, the limit of (xn).

Hence, (yn) is also convergent.

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The image shows a strong positive correlation in the scatter plot.

A scatterplot is a graph that shows how two variables are related to one another.

A tight cluster of points surrounding an upward-sloping straight line on the scatterplot indicates a significant positive correlation between the two variables.

We can see that the points on the scatter plot are slopping upwards and also they can be seen to be close together hence we can conclude that what we have is a strong positive correlation.

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Answer:

18 pages per hour.

If you do 36 (the pages/amount) divided by 2 (The time), you get 18.

To double check, when you do 90 (The pages/amount) divided by 5 ( The time), then you get 18 again.

Therefore the answer is 18 pages per hour.

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The smallest sample size n that provides the desired accuracy is 10.

To find the smallest sample size n that provides the desired accuracy, we can use the formula:

n = (Z-value * standard deviation / margin of error)²

Where:
Z-value = the critical value for the desired confidence level (in this case, 1.96 for 95% confidence)
Standard deviation = the preliminary sample standard deviation (1.5 in this case)
Margin of error = the desired accuracy (0.3 units in this case)

Substituting the values, we get:

n = (1.96 * 1.5 / 0.3)²
n = 9.8

Since we cannot have a fractional sample size, we round up to the nearest whole number, giving us:

n = 10

Therefore, the smallest sample size n that provides the desired accuracy is 10.

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Answer:

B

Step-by-step explanation:

8 1/2 - 2 = 6 1/2

6 1/2 + 4 3/4 = 11 1/4

Answer:

294

Step-by-step explanation:

We will take our equation, and substitute in 7 for s, wherever we see it, so we have:

\(6 * 7^{2}\)

Simplifying, we have:

\(6 * 49\)

Which finally we multiply to:

6 * 49 = 294

So, your answer is 294.

Hope this helped!

We can find the sum of the interior angles of a regular polygon using the formula : (n-2) x 180, where n is the number of sides.

We replaced in : (24-2) x 180 = 3960

So, all the interior angles in this polygon add up to 3960.
-> Each interior angle is equal to 3960 : 24 = 165.

Answer:

she would have worked 11 hours because 182 divide by 13 got 14 so 154 divide by 14 you get 11.

Answer:

The answer is 61.

Step-by-step explanation:

Let, the numbers are: x, (x+2), (x+4)

Now, x+x+2+x+4 = 183

3x + 6 = 183

3x = 177

x = 59

So, second number would be: (x+2) = (59+2) = 61

Answer:

Step-by-step explanation:

n+(n+2)+(n+4)=183

3n+6=183

3n=177

n=59

So the three numbers are 59, 61, and 63.

Answer:

Harry made 49 pieces of rope.

There were 395-392=3 feet of rope left

Step-by-step explanation:

Division

Harry has a rope 395 feet long. He wants to cut it into pieces 8 feet long each.

To find the number of pieces, we use division

395/8=49.375

Since the division is decimal, we cannot say Harry had 49.375 pieces of rope.

We must use the previous integer number:

Harry made 49 pieces of rope.

Since 49*8=392 feet

There were 395-392=3 feet of rope left

Answer: $19

Step-by-step explanation:

The total cost in dollars to rent a life Jacket and share a kayak for h hours is given by

\(\Rightarrow 4+10h\div 2\)

for h= 3 hours, the total cost is

\(\Rightarrow 4+10\times 3\div 2\)

applying BODMAS

\(\Rightarrow 4+15=\$19\)

We wrote a system of inequalities, identified the graph and found that the maximum money made in a week as $3300.

What is meant by inequalities?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Let x be the number of bracelets and y be the number of necklaces.

Given Olivia can make up to 60 pieces per week.

So the inequality is: x + y ≤ 60

She can make less than or equal to 40 bracelets.

 So the inequality is : x ≤ 40

She can make less than or equal to 40 necklaces as well in a week.

 So the inequality is : y ≤ 40

She wants to sell at least 30 items per week.

x + y ≥ 30

x+y  ≤60 can be written as

We can draw the inequalities as shown below.

x + y ≤ 60 as red

x ≤ 40 as green

y ≤ 40 as violet

x + y ≥ 30 as blue

The overlapping region of all inequalities is yellow.

The money made per week: 5x + 80y

We have to find the maximum money made.

The vertices of the yellow region are:

(0,30),(0,40),(30,0),(40,0),(20,40),(40,20)

The coordinates with negative values are neglected.

From this, 5*20 + 80 * 40 = $3300 is the maximum amount.

Therefore we wrote a system of inequalities, identified the graph and found that the maximum money made in a week as $3300.

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Answer:

The last one.Because the experimental probability is 11 ÷ 50, which is 22%, and the theoretical probability is 1 ÷ 8, which is 12.5%

Answer:

\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

5

The time take for the object to cool down is 5 minutes.

The temperature of a substance is a measure of its thermal energy and it is important to know how it changes over time.

Heat transfer occurs from hot to cold, meaning that the coffee will transfer heat to the room until both reach thermal equilibrium. The temperature difference between the coffee and the room is

=> 80°C - 25°C = 55°C.

We will use this value to calculate the rate of heat transfer. We know that the final temperature of the coffee will be 45°C, so the temperature difference will become

=> 45°C - 25°C = 20°C.

The time it takes to cool from 80°C to 45°C will depend on the heat transfer rate, which is affected by factors such as the mass of the coffee, the material of the container, and the surrounding environment.

Let us consider that the average heat rate is 60 seconds that is one minute.

Then the time taken for it is calculated as,

=>20 x 60 = 300

So, in minutes 5 minutes.

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Answer:

Physical means the actual wires.  Physical is concerned with how the wires are connected. Logical is concerned with how they transmit.

a. Logical

Step-by-step explanation:

...

The arrangement of network cabling between devices is a physical topology. which is the correct answer would be option (C).

The physical configuration of a network, such as the physical arrangement of wires, media (computers), or cables, is referred to as its topology. A link can connect two or more devices, and when the number of connections reaches two, they constitute a physical topology.

A physical network diagram depicts the connecting of devices via cables or wireless links. A logical network diagram, on the other hand, depicts data and signal transfer throughout a network.

Therefore, the arrangement of network cabling between devices is a physical topology.

Hence, the correct answer would be an option (C).

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When we divide 3.7x 10⁵ by 7.4 x 10⁻¹, we get 0.5 x 10⁶.

The answer is (b) the quotient of the first factors is less than 1.

To find the quotient of 3.7x 10^5 and 7.4 x 10^-1, you can divide the first factors of the numbers, 3.7 and 7.4, to get a quotient of 0.5.

The exponent of the quotient will be the difference between the exponents of the two numbers, which in this case is 5 - (-1) = 6.

This means that the quotient will be expressed as 0.5 x 10⁶.

--The question is incomplete, complete question is as follows--

"Think about the process find the quotient of the first factors of

3.7x 10⁵

7.4 x 10⁻¹

What do you notice?

Find the quotient. use pencil and paper. How does this affect the exponent of the quotient?

Divide the first factors of the given numbers. What do you notice?

a. the quotient of the first factors is greater than 1 but less than 10.

b. the quotient of the first factors is less than 1.

c. the quotient of the first factors is greater than 10."

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In this situation, the wholesale cost x of every dress is first increased by $20 to obtain the retail price. This is represented by the function f(x) = x + 20.

Then, during a sale, every dress is sold for 75% of the retail price. This is represented by the function g(x) = 0.75x.

To find the composite function gf that describes this situation, we need to substitute f(x) into g(x) and simplify.

gf = g(f(x)) = g(x + 20) = 0.75(x + 20) = 0.75x + 0.75(20) = 0.75x + 15

Therefore, gf = 0.75x + 15 describes the situation where the wholesale cost x of every dress is first increased by $20 to obtain the retail price, and then during a sale, every dress is sold for 75% of the retail price. So, the final cost of the dress is (0.75x + 15)

So, the composite function gf = 0.75x + 15, describes the situation where the shop adds $20 to the wholesale cost, and then sells it for 75% of the retail price.

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