An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial cost of designing the airplane and setting up the factories in which to build it will be 740 million dollars. The additional cost of manufacturing each plane can be modeled by the function m(x) = 1,600x + 40x4/5 +0.2x2 where x is the number of aircraft produced and m is the manufacturing cost, in millions of dollars. The company estimates that if it charges a price p (in millions of dollars) for each plane, it will be able to sell x(p) = 390-5.8p. Find the cost function.

The width of Cade's picture is 7.09cm. The perimeter of Cade's picture is 101.58 inchs.

What is a rectangular object?

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with four equally long sides.

Given that Jens's picture is 36 centimeters long and 24 centimeters wide.

The area of a rectangular object is the product of length and width.

The area of Jens's picture is 36 × 24 cm² = 864 cm².

1 inches = 2.54 cm

The length of Cade's picture is 48 inches = 48× 24 cm = 121.92 cm

Assume that the width of Cade's picture is x.

The area of Cade's picture is 121.92x cm².

Given that the area of Cade's picture is the same as that of Jens's picture.

According to the question,

121.92x = 864

Divide both sides by 121.92:

x = 7.086

x = 7.09

The perimeter of a rectangular object is 2(l + w)

The perimeter of Cade's picture is 2(121.92 + 7.09) = 258.02 cm

Now convert it cm to inches:

=  258.02/2.54 inch

= 101.58 inchs

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Answer:

x=2.5

Step-by-step explanation:

Answer:

Three points determine a plane.

:)

Answer:

Three

Step-by-step explanation:

The maximum value of the objective function will be:50(100) + 50(20) = 5000 + 1000 = 6000

The given linear programming is:Max 50A + 50Bs.t.10A ≤ 100010B ≤ 80020A + 40B ≤ 4000A, B ≥ 0 To solve the linear programming using the solver follow these steps:Step 1: Open the Excel spreadsheet and go to Data, choose the solver and enable it.

Step 2: A Solver Parameters dialog box will appear. Input the necessary details as follows:Set Objective: 50A + 50BTo: Max Subject to constraints:

10A ≤ 100010B ≤ 80020A + 40B ≤ 4000

Select variables to change: A, BStep 3: Click Solve and the optimal value of A and B will be found.In this case, the optimal value of A is 100 and that of B is 20.

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Stanley will receive $27 and Emma will receive $9 amount of money.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that Mr. Tan gave $36 to Stanley and Emma. Stanley received 3 times as much money as Emma.

Let's assume Stanley would get x dollars and Emma would get y dollars

According to the given condition, we can write the equations as:

x = 3 y       .....(i)

x + y = 36  .....(ii)

Substitute the value of x = 3 y in equation (ii), and solve for y

3y + y = 36

4y = 36

y = 36 / 4

y = 9

Substitute the value of y = 9 y in equation (i), and solve for x

x = 3 × 9

x = 27

Therefore, Stanley will receive $27 and Emma will receive $9.

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The point (16, -99) is not a perfect fit in the linear model, and the slope-intercept equation for the remaining four data points (-8, 9), (-6, -9), (-2, -18), and (8, -63) is y = (-15/2)x + 3; the y-intercept (3) represents the net approval rating for the president when there is no change in the Dow Jones, and the slope (-15/2) indicates that for every 1-point increase in the Dow Jones, the net approval rating is expected to decrease by 7.5 percentage points.

To determine which point is not a perfect fit in the linear model, we need to compute the slopes for each pair of consecutive data points.

The slope of a linear model represents the rate of change between the two variables.

Using the given data points:

Points: -8, -6, -2, 8, 16

Percentage Points: 9, -9, -18, -63, -99

Let's compute the slopes:

Slope between (-8, 9) and (-6, -9):

slope = (change in percentage points) / (change in points)

slope = (-9 - 9) / (-6 - (-8))

slope = -18 / 2

slope = -9

Slope between (-6, -9) and (-2, -18):

slope = (-18 - (-9)) / (-2 - (-6))

slope = -9 / 4.0

slope = -2.25

Slope between (-2, -18) and (8, -63):

slope = (-63 - (-18)) / (8 - (-2))

slope = -45 / 10

slope = -4.5

Slope between (8, -63) and (16, -99):

slope = (-99 - (-63)) / (16 - 8)

slope = -36 / 8

slope = -4.5

The slopes for the first three pairs of points (-9, -2.25, -4.5) match, indicating a consistent linear relationship.

However, the slope between the last two points is -4.5, not -4.25 like the others.

Therefore, the point (16, -99) is not a perfect fit.

Removing the point (16, -99), we have four remaining data points:

(-8, 9), (-6, -9), (-2, -18), and (8, -63).

To find the slope-intercept equation for the linear model that passes through these four points, we can use the formula:

y = mx + b

Using the slope formula with two of the remaining points:

-9 = m(-6) + b

-18 = m(-2) + b

Solving these two equations simultaneously, we find:

m = -9/4

b = 9/2

So the slope-intercept equation for the linear model is:

y = (-9/4)x + 9/2

The practical meaning of the y-intercept (9/2) is that when the previous day's change in the Dow Jones is 0 points, the net approval rating for the president of the United States is expected to be 9/2 percentage points, or 4.5 percentage points.

The practical meaning of the slope (-9/4) is that for every 1-point increase in the previous day's change in the Dow Jones, the net approval rating for the president of the United States is expected to decrease by 9/4 percentage points, or 2.25 percentage points.

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The yellow mark is 1 foot above the water level.

This question can be answered using the concept of trigonometry.

According to the given question

radius of the waterwheel r= 4 feet

let OD is the part of the waterwheel that is submerged in the water and its value is to be determined.

From the figure we can see that

OA=OC=radius= 4 feet

Now

In triangle OAB

cos 60= \(\frac{OB}{OA}\)

\(\frac{1}{2}= \frac{OB}{OA}\)

OB= 2 feet

which means the length of the yellow mark above water is given by

OB-OD= 2-1= 1 feet.

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Answer:

1 +6 x + 12 x 2 + 8x 3

Explanation:

We must use our knowledge of the binomial expansion:

Method 1:

We can use:

(

x

+

1

)

n

=

1

+

n

x

+

n

(

n

−

1

)

2

!

x

2

+

n

(

n

−

1

)

(

n

−

2

)

3

!

x

3

+

...

Substituting  

n

=

3

and  

x

for  

2

x

⇒

(

2

x

+

1

)

3

=

1

+

(

3

⋅

2

x

)

+

3

⋅

2

2

!

⋅

(

2

x

)

2

+

3

⋅

2

⋅

1

3

!

⋅

(

2

x

)

3

=

1

+

6

x

+

12

x

2

+

8

x

3

Method 2:

We can use:

(

A

+

B

)

n

=

A

n

+

(

n

1

)

A

n

−

1

B

1

+

(

n

2

)

A

n

−

2

B

2

+

...

Letting  

A

=

2

x

and

B

=

1

for this circumstance:

(

2

x

+

1

)

3

=

(

2

x

)

3

+

(

3

1

)

(

2

x

)

2

(

1

)

+

(

3

2

)

(

2

x

)

1

(

1

)

2

+

(

3

3

)

(

2

x

)

0

(

1

)

3

=

8

x

3

+

12

x

2

+

6

x

+

1

Step-by-step explanation:

The pulse rates that are within 1 standard deviation of the mean represent approximately 68% of the total to the nearest 0.1 percent.

When working with a set of pulse rates that are normally distributed, we can use the Empirical Rule to determine the pulse rates that are within 1 standard deviation of the mean. According to the Empirical Rule, approximately 68% of the data falls within 1 standard deviation of the mean.

To find the pulse rates that are within 1 standard deviation of the mean, we need to first find the mean and standard deviation of the pulse rates. After we have these values, we can determine the range of pulse rates that fall within one standard deviation of the mean.

To calculate the percentage of the total that represents those rates, we can use the formula: Percentage = (Number of data points within 1 standard deviation / Total number of data points) x 100.

For example, let's say the mean pulse rate is 72 beats per minute and the standard deviation is 8 beats per minute. Using the Empirical Rule, we know that approximately 68% of the pulse rates fall within one standard deviation of the mean. This means that the pulse rates that fall within one standard deviation of the mean are between 64 and 80 beats per minute.

To find the percentage of the total that represents those rates, we need to count the number of data points within that range. If we assume that we have 1000 data points, then the number of data points within the range of 64 to 80 beats per minute is approximately 680. Therefore, the percentage of the total that represents those rates is:

Percentage = (680/1000) x 100

Percentage = 68%

Therefore, the pulse rates that are within 1 standard deviation of the mean represent approximately 68% of the total to the nearest 0.1 percent.

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Answer:

Step-by-step explanation:

One that has the next least in common with the rest.

The value of x + y in the given expression is determined as -21.

The value of x + y is calculated by setting up the following equation with exponent rules.

From the first function, we will have the following equation;

\(2^{3x} = 8^{y +3}\)

Simplify the equation as follows;

\(2^{3x} = 2^3^{(y +3)}\\\\\)

3x = 3(y + 3)

x = y + 3

From the second expression, we will have the following;

\(4^{x + 1} = \frac{16^{(y + 1)}}{8^{(y + 3)}}\)

Simplify as follows;

\(2^{2}^{(x + 1)} = \frac{2^4^{(y + 1)}}{2^3^{(y + 3)}}\)

\(2(x + 1) = \frac{4(y + 1)}{3(y + 3)}\)

2(x + 1) = 4(y + 1) - 3(y + 3)

2x + 1 = 4y + 4 - 3y - 9

2x = y - 6

Substitute the value of x;

2( y + 3) = y - 6

2y + 6 = y - 6

y = -6 - 6

y = -12

x = y + 3

x = -12 + 3

x = -9

The value of x + y = -9 - 12 = -21

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A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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v = -17

Step-by-step explanation:

Answer:

for 1 person: 188

for 2 people: 94

etc.

Step-by-step explanation:

divide 188 by the number of people

Answer:

Sequence A

Step-by-step explanation:

When arranging bands 6 and 7 with band 6 performing first and band 7 performing last, there are a total of 8080 different possible arrangements.

To understand why there are 8080 different ways to arrange the bands, we can break down the problem step by step. Since band 6 must perform first and band 7 must perform last, we have fixed positions for these two bands. This leaves us with the remaining bands, numbered from 1 to 5, and band 7 can be seen as the sixth band in this context.

Now, we have six available positions to fill with the remaining five bands (1 to 5) and the additional band 7. This can be represented as arranging the six bands in those six positions. We can think of this as a permutation problem, where we have 6 options for the first position, 5 options for the second position, and so on, until we have 2 options for the second-to-last position. Finally, band 7 takes the last position.

The total number of arrangements can be calculated by multiplying the number of options for each position: 6 × 5 × 4 × 3 × 2 = 720. However, since band 7 can be either the sixth or the last band, we need to double this number to account for both possibilities, resulting in 720 × 2 = 1440 arrangements.

However, there is one more factor to consider. The remaining bands (1 to 5) can be arranged among themselves in 5! (5 factorial) ways, which equals 120 arrangements. Multiplying this by the previously calculated 1440 arrangements gives us 1440 × 120 = 172,800 possible arrangements.

Since band 7 can be seen as the sixth band, we need to divide the total by the number of ways to arrange the remaining bands (1 to 5) in order to get the final answer. 172,800 ÷ 5! = 8080 different ways to arrange the bands when band 6 performs first and band 7 performs last.

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Answer:

d) 16 + 56

Step-by-step explanation:

The simplest way to get the sum is to distribute 8 into 2 and 7 which is the same thing as multiplying to the two numbers in the parentheses.  Your sum should be 16 + 56 when multiplied.

a) the probability of losing money is approximately 0.0228 or 2.28%.

b) the probability that the return is more than 12% is approximately 0.5 or 50%.

c) the value of the return for the 97.5th percentile is approximately 23.76%.

d) the value of the return for the 80th percentile is approximately 16.04%

a) To find the probability of losing money, we need to find the probability that the return (R) is less than 0.

Z = (0 - 12) / 6 = -2

Using the standard normal table or a calculator, we can find that the probability of Z being less than -2 is approximately 0.0228.

Therefore, the probability of losing money is approximately 0.0228 or 2.28%.

b) To find the probability that the return is more than 12%, we need to find the probability that R is greater than 12.

Z = (12 - 12) / 6 = 0

Using the standard normal table or a calculator, we can find that the probability of Z being greater than 0 is approximately 0.5.

Therefore, the probability that the return is more than 12% is approximately 0.5 or 50%.

c) To find the value of the return for the 97.5th percentile, we need to find the Z-score corresponding to the 97.5th percentile.

Using the standard normal table or a calculator, we can find that the Z-score corresponding to the 97.5th percentile is approximately 1.96.

Now we can use the Z-score formula to find the value of the return:

Z = (X - μ) / σ

1.96 = (X - 12) / 6

Solving for X, we get:

X = 1.96 * 6 + 12 = 23.76

Therefore, the value of the return for the 97.5th percentile is approximately 23.76%.

d) To find the value of the return for the 80th percentile, we need to find the Z-score corresponding to the 80th percentile.

Using the standard normal table or a calculator, we can find that the Z-score corresponding to the 80th percentile is approximately 0.84.

Now we can use the Z-score formula to find the value of the return:

Z = (X - μ) / σ

0.84 = (X - 12) / 6

Solving for X, we get:

X = 0.84 * 6 + 12 = 16.04

Therefore, the value of the return for the 80th percentile is approximately 16.04%

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In the JK Flip-Flop truth table, when both inputs of the JK Flip-Flop are set to 1 and the clock input is also set to "High," the circuit is toggled from the SET to the RESET state.

Similar in operation to the SR flip flop is the JK flip flop. The JK flip flop is marked with the letters "J" and "K" rather than "S" and "R." When both inputs are set to 1, SR flip flips yield incorrect states as outputs, while JK flip flops do not, even when both "J" and "K" flip flops are set to 1. The only distinction between JK and SR flip flops is this. The JK Flip Flop is an additional clock input circuitry-equipped gated SR flip-flop. The presence of a clock input circuit prevents the invalid or unlawful output situation from occurring when both inputs are set to 1. The JK flip-flop hence has four input combinations that are possible: 1, 0, "no change," "toggle," and With the exception of the clock input, the JK flip flop's symbol is identical to that of the SR bistable latch.

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Answer:

\(\frac{4}{6}\)

Step-by-step explanation:

The correct option is D)\(2+\sqrt{6z} /4-6z\) .The choice is equivalent to the given fraction when x is an appropriate value is \(2+\sqrt{6z} /4-6z\)

Let's rationalize the denominator of the given fraction as shown below:

\($4 - \sqrt{6z} = \frac{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})}{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})}$\)

Here, the denominator is of the form\($(a-b)(a+b)$\), which can be written as \($a^2 - b^2$\).

Therefore, the above expression can be simplified as:

\(\[\frac{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})}{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})} \\= \frac{(4^2 - \sqrt{(6z)^2})}{(4 - \sqrt{6z}) (\overline{4 + \sqrt{6z}})}\\\\= \frac{16 - 6z}{16 - (6z)}\\\\= \frac{16 - 6z}{10} = \frac{8-3z}{5}\]\)

Therefore, we can see that choice D) \(2+\sqrt{6z} /4-6z\) is equivalent to the given fraction when x is an appropriate value.

Thus, the correct option is D) \(2+\sqrt{6z} /4-6z\)

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Answer:Hi

Step-by-step explanation:

Answer:

6 months: 7200

8 months: 9600

Step-by-step explanation:

Given equations:

1200 * 6

1200 * 8

Solve 6 months:

1200 * 6

= 7200

Solve 8 months:

1200 * 8

= 9600.

Answer: angle BCD is 77°

Step-by-step explanation:

       BDC+CDA=119°

-5x+52°-2x+32°=119°

            -7x+84°=119°

                   -7x=35°

                      x=-5°

Then substitute x in the equation for BDC

-5(-5)+52°=BDC

   25+52°=BDC

       BDC=77°

Answer:

35

Step-by-step explanation:

5(3+4)

5x7=35

The difference between relative frequency and cumulative relative frequency is that relative frequency is the ratio of the frequency of a particular value in a dataset to the total number of values, expressed as a percentage. Cumulative relative frequency is the sum of all relative frequencies up to a certain point in the data set.

For example, if a data set has 8 values and 4 are the same, the relative frequency would be 50%. Cumulative relative frequency would be 50% at this point since it is the sum of all relative frequencies up to this point in the data set. If there were another 4 of the same values after this point, the relative frequency would remain at 50%, but the cumulative relative frequency would increase to 100% since it includes all previous relative frequencies.

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