The cost of building a airplane with 200 seats is about 100million.if the cost of dollars,c, is proportional to the number of seats,s, what equation can be used to determine the cost,in millions of dollars to build an airplane with any number of seats

The arc length parametrization of the curve\(r(t) = 7e^t cos(t)i + 7e^t sin(t)j\), 0 ≤ t ≤ φ/2, with the same orientation and a reference point at t = 0, is given by s(t) = ∫[0,t] √(r'(u)·r'(u)) du, where r'(t) is the derivative of r(t) with respect to t.

To find the arc length parametrization, we need to calculate the integral of the magnitude of the derivative of r(t). Let's start by finding the derivative of r(t):

r'(t) =\((7e^t cos(t) - 7e^t sin(t))i + (7e^t sin(t) + 7e^t cos(t))j\)

|r'(t)| = \(\sqrt{((7e^t cos(t) - 7e^t sin(t))^2 + (7e^t sin(t) + 7e^t cos(t))^2)}\)

       = \(7e^t\)\(\sqrt{(cos^2(t) + sin^2(t))}\)

       = \(7e^t\)

Now, we integrate |r'(t)| from 0 to t to obtain the arc length parametrization:

s(t) =\(\int\limits^t_0 {} 7e^{u} \, du\)

     =\(7(e^t - e^0)\)

    = \(7(e^t - 1)\)

Therefore, the arc length parametrization of the curve\(r(t) = 7e^t cos(t)i + 7e^t sin(t)j\), 0 ≤ t ≤ φ/2, with the same orientation and a reference point at t = 0, is given by \(s(t) = 7(e^t - 1)\).

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The size of each section in a graph tells in relation to the portion of the data :

The magnitude of a graphic's segment indicates a specific attribute of the data being presented. In charts like pie charts or stacked bar graphs, each component's size denotes the relative frequency or proportion of data points in a particular category.

This implies that larger fragments reflect an increased number of data points for its associated categories whereas smaller ones represent categories with lesser data points.

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Given data: Jackson invests $2500 in an account that has a 6.7% annual growth rate.

We need to find when the investment will be worth $4200?

Let's assume that the time in which the investment becomes worth $4200 is x.

Now, using the formula for compound interest:Amount after time "t" = Principal * [ 1 + (rate/n) ]^(n*t)Where,Principal = $2500Rate = 6.7% = 0.067 [as a decimal]Time = xAmount after time "t" = $4200We will plug all the values in the above formula and solve for x:\(4200 = 2500 [1 + (0.067/1)]^{1x}\)\(\frac{4200}{2500} = (1.067)^x\)Now, taking the logarithm of both sides to solve for x:log(1.16^x) = log(1.68) => x = log(1.68) / log(1.067)x ≈ 7.54Therefore, the investment will be worth $4200 after 7.5 years (approximately).

Thus, the correct option is (C) 7.5 years.

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(a)The range of the given set of measurements is 4.

(b)The sample mean of the given set of measurements is approximately 5.625.

(c)The sample variance of the given set of measurements is approximately 2.337768, and the sample standard deviation is approximately 1.529.

(a) The range is the difference between the largest and smallest values in the set of measurements. In this case, the largest value is 8 and the smallest value is 4, so the range is 8 - 4 = 4.

To calculate the range, we subtract the smallest value from the largest value. In this case, the largest value is 8 and the smallest value is 4.

Range = Largest value - Smallest value

Range = 8 - 4

Range = 4

The range provides a simple measure of the spread or dispersion of the data. In this case, the range tells us that the values range from the smallest value of 4 to the largest value of 8, with a difference of 4 between them.

(b) The sample mean, denoted as x, is the sum of all the measurements divided by the total number of measurements.

To calculate the sample mean, we add up all the measurements and then divide by the total number of measurements. In this case, we have 8 measurements.

Sum of measurements = 4 + 4 + 7 + 6 + 4 + 6 + 6 + 8 = 45

Sample mean = Sum of measurements / Total number of measurements

Sample mean = 45 / 8

Sample mean ≈ 5.625

The sample mean represents the average value of the measurements and provides a measure of central tendency.

(c) The sample variance, denoted as s^2, measures the variability or dispersion of the data points around the sample mean. It is calculated as the average of the squared differences between each measurement and the sample mean.

To calculate the sample variance, we first calculate the squared difference between each measurement and the sample mean. Then, we average those squared differences.

Squared difference for each measurement:

(4 - 5.625)^2 = 2.890625

(4 - 5.625)^2 = 2.890625

(7 - 5.625)^2 = 1.890625

(6 - 5.625)^2 = 0.140625

(4 - 5.625)^2 = 2.890625

(6 - 5.625)^2 = 0.140625

(6 - 5.625)^2 = 0.140625

(8 - 5.625)^2 = 5.390625

Sum of squared differences = 2.890625 + 2.890625 + 1.890625 + 0.140625 + 2.890625 + 0.140625 + 0.140625 + 5.390625 = 16.364375

Sample variance = Sum of squared differences / (Total number of measurements - 1)

Sample variance = 16.364375 / (8 - 1)

Sample variance ≈ 2.337768

The standard deviation, denoted as s, is the square root of the sample variance.

Sample standard deviation = √(Sample variance)

Sample standard deviation = √(2.337768)

Sample standard deviation ≈ 1.529

These measures provide information about the dispersion or spread of the data points around the sample mean. A higher variance or standard deviation indicates greater variability in the measurements.

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Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Answer:

3

Step-by-step explanation:

13's function (the value of y corresponding to 13)is 16

16's function (the value of y corresponding to 16)is 32

Answer:

All except B.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

po keep on learning keep safe

The exponents expression of 9 x 9 x 9 x 9 is \(9^4.\)

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

9 x 9 x 9 x 9

There are four 9.

So,

= \(9^4\)

Thus,

The exponent's expression is \(9^4.\)

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Answer:

Question 1: 75 minutes

Question 2: 4:07

Question 3: 30 minutes

Question 4: 8:35

Step-by-step explanation:

An hour is sixty minutes; that's the key to solving these questions.

The time basketball was played is 75 minutes or 1 hour 15 minutes

The time I get home is at 4:07

The cook was cooked for 30 minutes.

The cheerleading was over at 8:35.

It is the conversion of one unit to another unit with its standard conversion.

We have,

Trey and Na Asia played basketball from 10:30 - 11:45.

From 10 to 11 we have 60 minutes.

= 60 minutes - 30 minutes [10:30] + 45 minutes [ 11:45]

= 105 minutes - 30 minutes

= 75 minutes

The time basketball was played.

= 75 minutes

= 1 hour 15 minutes

I left school at 3:15 on the bus. I got home 52 minutes later.

1 hour = 52 minutes

= 3:15 + 52 minutes

= 3  + 15 minutes + 52 minutes

= 3 + 67 minutes

= 3 + 1 hour +  7 minutes

= 4:07

The time I get home is at 4:07

Antavious makes Macaroni and cheese. He begins making it at 6:35 and finished at 7:05.

= 6:35 to 7:05

From 6 to 7 we have 60 minutes.

So,

= 60 minutes - 35 minutes [6:35] + 5 minutes [7:05]

=  65 minutes - 35 minutes

= 30 minutes

The cook was cooked for 30 minutes.

Makhiya and Madison went to cheerleading at 7:15. It was over 1 hour and 20 minutes later.

= 7:15 + 1 hour + 20 minutes

= 7 + 15 minutes + 1 hour + 20 minutes

= 8 + 35 minutes

= 8:35

The cheerleading was over at 8:35.

Thus,

The time basketball was played is 75 minutes or 1 hour 15 minutes

The time I get home is at 4:07

The cook was cooked for 30 minutes.

The cheerleading was over at 8:35.

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Answer:

88

Step-by-step explanation:

Given

x = 4y² - 12 ← substitute y = 5

x = 4(5)² - 12 = 4(25) - 12 = 100 - 12 = 88

Let's define the following variables :

We are told that the number of shoelaces produced is proportional to the time taken to produce them. This means that there is a constant of proportionality that relates N and t. Let's call this constant k.

Using the information that the machine produces 12 shoelaces in 3 minutes, we can set up the following equation:

12 = k * 3

We can solve for k by dividing both sides by 3:

k = 4

So the equation that represents the proportional relationship between the number of shoelaces produced and the time taken to produce them is:

N = kt

Substituting k = 4, we get:

N = 4t

This equation means that for every unit of time (in minutes) that passes, the machine produces 4 shoelaces.

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Answer:

2^-18

Step-by-step explanation:

\(v = \pi {r}^{2} h\)

\(v = 3.14 \times {2}^{2} \times 3\)

\(v = 37.68 \: {cm}^{3} \)

\(v = lwh\)

\(v = 6 \times 5 \times 7\)

\(v = 210 \: {cm}^{3} \)

\(v = 37.68 + 210\)

\(v = 247.68 \: {cm}^{3} \)

cylinder:

pi r^2 h

=3.14*2^2*3

=37.68 cm^3

prism:

whl

=6*5*7

=210 cm^3

all together:

=247.68 cm^3

Answer: 3months

Step-by-step explanation:

130 160 190 220 250 280 310 340 370 400

110 150 190 230 270 310 350 390 430 470 510

After 3 months they will both be at 190

Answer:

3 months until both costs are the same

Step-by-step explanation:

30x+100 = 40x+70

-30             -30

        100  = 10x+70

       -70              -70

        30 = 10x

     30/10   10x/10    

      30/10 = 3

Answer:

8.9k

Step-by-step explanation:

(1.8k+6.1k+k)+(-5+3.5+1.5)

8.9k +0

8.9k

1.8k+−5+3.5+6.1k+k+1.5  (combine like terms)(the ones i combined are in bold)

=0+1.8k+6.1k+k (combine like terms) (the ones I combined are in bold)

0+8.9k (add)

=8.9k

Answer:

Your question is Incomplete....

Answer:

4 \(\sqrt5\)

Step-by-step explanation:

Use Pythagorean theorem to get c^2 for the hypotenuse, which is equal to \(\sqrt80\). You then simplify to get the simplest radical form by \(\sqrt80\) = \(\sqrt{8*10} = \sqrt{4*2*5*2} = \sqrt{16*5} = 4\sqrt{5}\)

A large container can hold 8 liters of juice.

Let's define the variables and set up equations using the information provided:
Let L be the number of liters a large container can hold.
Let S be the number of liters a small container can hold.
From the given information, we can create two equations:
1) L + 3S = 11
2) L = 6 + 2S
Now, let's solve the system of equations using the substitution method:
Step 1: Since we know that L = 6 + 2S, we can substitute this expression into equation 1 in place of L:
(6 + 2S) + 3S = 11
Step 2: Simplify the equation and solve for S:
6 + 5S = 11
5S = 5
S = 1
Now that we have found the value for S, we can substitute it back into equation 2 to find the value of L:
L = 6 + 2(1)
L = 6 + 2
L = 8
So, a large container can hold 8 liters of juice.

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The equation for height on the wheel at any time t is

 h(t) =  394 - 197 cos(\(\frac{\pi }{15}\) t )

What are trigonometric functions?

The trigonometric functions are actual functions that relate a right-angled triangle's angle to side length ratios. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant and Cotangent.

Given,

 The diameter of the ferris wheel = 394 feet

  The height of the ferris wheel = 443 feet

Number of revolutions per hour = 2

we know 1 revolution = 2\(\pi\) radians

In one hour = 2 revolutions =  4\(\pi\) radians covered

So, in one minute = \(\frac{4\pi }{60}\) = \(\frac{\pi }{15}\) radians covered

At t minutes, angle Ф covered = \(\frac{\pi }{15}\) t radians

From the right angled triangle ΔABC,

cos Ф = \(\frac{k}{197}\)

k = 197 cosФ

From diagram,

h = 394 - k

   = 394 - 197 cosФ

From diagram, Ф =  \(\frac{\pi }{15}\) t

Therefore for any time t, the equation for height on the wheel is

 h(t) =  394 - 197 cos(\(\frac{\pi }{15}\) t )

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Answer:

D. \(a^{2} + b^{2} = c^{2}\)

Step-by-step explanation:

Pythagorean Theorem

Answer:

1. 26.4

2. 23

3. 20.3

4. 15

5. 114.75

Step-by-step explanation:

1. 19.20/8= 2.4

   2.4 *11= 26.4

2. 270/15=18

   414/18=23

3. 34.80/12= 2.9

    2.9*7=20.3

4. 9/5=1.8

      27/1.8=15

5. 51.00/4= 12.75

    12.75*9=114.75

Answer:

Triangle ISK

Step-by-step explanation:

Answer:

Triangle ISK

Step-by-step explanation:

if the angles and sides of one triangle are equal to the corresponding sides and angles of the other triangle, they are congruent.

∠Q = ∠I

∠R = ∠S

∠S = ∠K

Answer:

X=1

Step-by-step explanation:

-10x-2=-3x-9

-10x-2+2=-3x-9+2

-10x=-3x-7

-10x+3x=-3x-7+3x

-7x=-7

Then divide both sides by -7

x=1

Answer:

\(f(x) = - 3x + 10 \\ f( - 5) = - 3( - 5) + 10 \\ = 15 + 10 = 25\)

\(g(x) = x ^{2} - 7x \\ g(2) = {2}^{2} - 7 \times 2 \\ = 4 - 14 \\ = - 10\)

Solving the given functions for the asked value, we get

f(-5) = 25, g(2) = -10

A function is a rule defining the relationship between two variables, one is dependent and the other independent.

To solve the given functions for asked values, we put in the value asked for in place of the variable determining the function.

Two given functions are:

f(x) = -3x + 10

g(x) = x² - 7x.

We are asked for values of f(-5) and g(2).

To calculate the value of f(-5), we substitute x with (-5) in the function f(x), that is,

f(-5) = -3(-5) + 10 = 15 + 10 = 25.

To calculate the value of g(2), we substitute x with (2) in the function g(x), that is,

g(2) = (2)² - 7(2) = 4 - 14 = -10.

∴ f(-5) = 25, g(2) = -10

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Answer:

hey here is ur answer

the perimeter of a square = 4* side

4*s=14

S = 14/4

s= 7/2 or 3.5

area = side * side

area = (7/2) sq

area = 12.25sq m

Step-by-step explanation:

We know that:

In this case, by convention:

Then,

For real gas,the equation can be written as μn = n! * ∑(α) ∏l=0[∞] αl! * λlαl​​​.

The coefficient μn in the equation of state for a real gas can be expressed in terms of the parameters αl and λl as follows:

In the given equation PV = ∑n=0[∞] λnPn or PV = ∑n=0[∞] μnV^(-n) (equation 2), the coefficients λn and μn represent the contributions of the different powers of the pressure (P) and volume (V), respectively. To express μn in terms of αl and λl, we need to consider the following steps:

Step 1: Express μn as a product of factorials and summations.

μn = n! * ∑(α) ∏l=0[∞] αl! * λlαl​​​

Step 2: Define the parameters αl and λl.

Here, ∑l=0[∞] lαl = n, and ∑l=0[∞] αl = n + 1.

Step 3: Substitute the values of αl and λl in the expression for μn.

By substituting the given values, we have:

μn = n! * ∑(n) ∏l=0[∞] αl! * λlαl​​​

In summary, the coefficient μn in the equation of state for a real gas can be expressed as n! times the product of the factorials of αl and the summation of αl raised to the power of λl, where the parameters αl satisfy ∑l=0[∞] lαl = n and ∑l=0[∞] αl = n + 1.

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