The lifting force, F, exerted on an airplane wing varies jointly as the area, A, of the wing's surface and the square of the plane's velocity, v. The lift of a wing with an area of 300 square feet is 12,000 pounds when the plane is going 110 miles per hour. Find the lifting force on the wing if the plane slows down to 100 miles per hour. (Leave the variation constant in fraction form or round to at least 5 decimal places. Round off your final answer to the nearest pound.)

Answer:

2x-7=3

2x=3+7

{2x=10}÷2

x=5

꧁꧁꧂꧂

3x+1=

{3x=1}÷3

x=1/3

Answer:

Proved

Step-by-step explanation:

Given

\(UPC = 0-58200-48826-5\)

Required

Show that it is valid

Add up the elements at odd positions

\(Odd = 0 + 8 + 0 + 4+8+6\)

\(Odd = 26\)

Multiply by 3

\(Product = 26 * 3\)

\(Product = 78\)

Add up the elements at even positions

\(Even = 5 + 2 + 0 + 8 + 2 + 5\)

\(Even = 22\)

Add up both results

\(Result = 78 +22\)

\(Result = 100\)

Take modulus of 10

\(Result \% 10 = 100 \% 10\)

\(Result \% 10 = 0\)

Since the result of the modulus is 0, then the number is valid

Answer:

Step-by-step explanation:

\( \frac{5(x + 6) - 15(2 - x)}{3x - 1} = 10 \\ \)

\( = > 5(x + 6) - 15(2 - x) = 10(3x - 1)\)

\(5x + 30 - 30 + 15x = 30x - 10\)

\( = > 20x = 30x - 10 \\ = > 20x - 30x = - 10 \\ = > - 10x = - 10 \\ = > x = 1\)

hope it helps:)

The pattern for the 6th term of the sequence is A₆ = 36

Given data ,

The first term has one dot (1² = 1)

The second term has four dots (2² = 4)

The third term has nine dots (3² = 9)

The fourth term has sixteen dots (4² = 16)

So , the fifth term A₅ = 25

And , from the pattern , the 6th term A₆ = 36

Hence , the 6th term is A₆ = 36

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Precession is a phenomenon that refers to the gradual and continuous change in the orientation of the Earth's rotational axis over long periods of time.

This shift in the orientation of the axis of rotation results in changes in the position of the celestial pole with respect to the stars, which causes a shift in the apparent position of stars over time. The precession of the Earth's axis is caused by the gravitational forces of the Sun, Moon, and other planets in the solar system.
Precession is characterized by changes in the magnitude of the angle of tilt, which causes changes in the rate of the Earth's spin. As the axis of rotation moves, it causes the length of the day to change over time. Additionally, deviations in the circularity of the orbit also affect the precession of the Earth's axis.
Precession is a significant phenomenon in astronomy and has been observed for thousands of years. It has important implications for studies of astronomy, geology, and climate change. For instance, precession affects the timing of the seasons and has a significant impact on the Earth's climate. It also affects the orientation of the Earth's magnetic field, which has important implications for navigation and communication systems.
In conclusion, precession is the gradual change in the orientation of the Earth's rotational axis, caused by the gravitational forces of the Sun, Moon, and other planets. It results in changes in the magnitude of the angle of tilt, changes in the rate of Earth's spin, and deviations in the circularity of the orbit. Precession has significant implications for various fields of study, including astronomy, geology, and climate change.

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TRUE. If two individuals in the same population have identical X scores, they also will have identical z-scores.

The z-score of an individual in a population is calculated using the formula:

z = (X - μ) / σ

where X is the individual's score, μ is the population mean, and σ is the population standard deviation.

If two individuals in the same population have identical X scores, it means they have the same value for X. Therefore, when calculating the z-score for each individual using the same population mean and standard deviation, the numerator (X - μ) will be the same for both individuals.

Since the numerator is the same, the z-score for both individuals will also be the same. Therefore, if two individuals have identical X scores in a population, they will have identical z-scores. Hence, the statement is TRUE.

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The followings A, C, D, and F subsets of P₂ are subspace of P₂.

The subsets of P₂ that are subspace of P₂ are A, C, D, and F.

A.{p(t) | p'(t)+1p(t)+6=0} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

B.{p(t) | p('t)='p(t) for all t} is not a subspace of P₂ because the derivative of p(0) does not equal p(4).

C. {p(t) | p(4)=7} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

\({p(t) | \int_{-1}^{7}p(t)dt=0\) is constant } is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

E. {p(t) | '(8) = p(0)} is not a subspace of P₂ because the derivative of p(8) does not equal 0.

F. {p(t) | p(3)=0} for all t} is a subspace of P₂ because it satisfies the criteria of being closed under addition and scalar multiplication.

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Answer:

a=90°

c=45°

b=45°

Step-by-step explanation:

this triangle is a right triangle. (shown by the box in angle a) this means a must equal 90°

and by extension means the other two angles have to equal 45° each because right angles always have two angles of the same degree and the angles of a triangle always Equal 180°

Answer:

$216

Step by step

Explanation:

First we subtract  $ 20 from  $ 84  giving us a total of  $ 64 and when we add that to  $ 152  we get  $ 216

.

Answer:

-60

Step-by-step explanation:

Answer:

X³ – 3x² – 9x – 5

= x³ + x² – 4x² – 4x – 5x – 5

= x²( x + 1) – 4x ( x + 1) – 5(x + 1)

= (x + 1)(x² – 4x – 5)

= (x + 1)(x² -5x + x – 5)

= (x + 1)(x – 5) (x + 1)

hence, (x +1), (x -5) and (x +1) are the factors of given polynomial .

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Answer:

a) Josef jogging from A to B;

i. speed = 2 m/s

ii. velocity = 2m/s

a) a) Josef jogging from A to C;

speed = 1.9 m/s

ii. velocity = 2.2 m/s

Step-by-step explanation:

One major difference between speed and velocity is that speed is a scalar quantity, while velocity is a vector quantity.

a) Josef jogging from A to B;

distance = 300 m

time = 2.5 seconds = 150 seconds

i. his average speed = \(\frac{distance}{time}\)

                               = \(\frac{300}{150}\)

                               = 2 m/s

ii. his average velocity = \(\frac{displacement}{time}\)

                               = \(\frac{300}{150}\)

                               = 2 m/s

b) Josef jogging from A to C,

distance = 300 + 100 = 400 m

time = 2.5 + 1 = 3.5 minutes

        = 210 seconds

i. his average speed = \(\frac{distance}{time}\)

                                  = \(\frac{400}{210}\)

                                  = 1.9 m/s

ii. his average velocity = \(\frac{\sqrt{V_{1} ^{2} + V_{2} ^{2} } }{2}\)

\(V_{1} ^{2}\) = 4 m/s

\(V_{2} ^{2}\) = 1.9 m/s

his average velocity = \(\frac{\sqrt{4^{2} + 1.9^{2} } }{2}\)

                                  = 2.2 m/s

Answer:

y = 5x - 3, so M = 5 and C = -3.

\(f(x)=\frac{1}{9}x-2\\ take:\\x=f(x)^{-1}\\\\f(x)=X\\\\X=\frac{1}{9}f(x)^{-1}-2\\\\(X+2)9 =f(x)^{-1} \\\\f(x)^{-1}=9X+18\\\)

Answer:

22

Step-by-step explanation:

ftrrrrgd fff fftttr fddd

Answer: 6x

Step-by-step explanation:

Factor each term and see what they have in common.

12x²:   2 · 2 · 3 · x · x

18x:     2 · 3 · 3 · x

The common factors are:      2 · 3 · x   = 6x

The actual cost to see the game is $150, as that is the amount you paid for the ticket. The cost in this scenario can be considered an opportunity cost. By choosing to attend the game instead of selling the ticket for $400, you forgo the opportunity to earn that additional $400.

In this scenario, the cost of attending the game refers to the actual amount of money you spent on the ticket, which is $150. This is the out-of-pocket expense that directly affects your financial resources.

On the other hand, the opportunity cost is the potential benefit or value that you give up by choosing one option over another. In this case, if you had sold the ticket for $400, you would have received a higher amount of money, which represents the opportunity cost of attending the game. By deciding to go to the game, you forego the opportunity to earn that additional $400.

Opportunity cost is a concept in economics that emphasizes the value of the next best alternative forgone when making a decision. It helps assess the trade-offs involved in different choices and helps in evaluating the true cost of a decision beyond the immediate financial expenses.

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a) Where the above condition exists, it is correct to state that, yes, Package C represents a function, specifically a step function.

b) We know that Package A and Package B represent linear functions because they have a constant rate of change, or slope.

A step function is a function that has a constant value over a series of intervals, and the value changes abruptly from one interval to the next.

A) With regards to the Benjamin's conditions, Package C represents a function, specifically a step function. It relates the cost of a birthday package to the number of people attending the party. The function takes on different constant values for different intervals of the number of people. For example, if x represents the number of people attending the party, then:

C(x) = 15, if 1 ≤ x ≤ 15

C(x) = 12, if 16 ≤ x ≤ 30

C(x) = 9, if x > 30

So, if Benjamin is expecting 25 guests, his birthday package cost would be $12 per person, or a total of $300.

B)
We know that Package A and Package B represent linear functions because they have a constant rate of change, or slope. In Package A, the cost is determined by multiplying the number of people by a fixed rate of $8, and then adding a constant value of $12. This can be written as:

C(p) = 8p + 12

where p is the number of people attending the party.

The slope of this function is 8, indicating that for each additional person, the cost of the package increases by $8.

Similarly, in Package B, the cost is determined by the total number of people attending the party, and the cost varies linearly with the number of people. This can be represented as:

C(x) = mx + b

where x is the number of people, m is the slope (rate of change), and b is the y-intercept (constant term).

Since the cost varies linearly with the number of people, we know that the slope is constant, indicating that the function represents a linear relationship between the number of people and the cost of the package.

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Answer: 624 ft^3

work is in the image i attached

Answer:

Step-by-step explanation: There are 6 equilateral triangles in a regular hexagon by connecting the opposite vertices of a regular hexagon.

Answer:

y = 5x + 6

Step-by-step explanation:

Remember:

Parallel: The slope is the same

Perpendicular: The slope is the opposite reciprocal

If we look at the equation \(y=-\frac{1}{5}x+6\), it is in slope intercept form and its slope is -1/5. Now, we will first need to flip the fraction and get rid of the negative sign.

\(y=5x+6\)

And we are done!

Yes, I can help them determine how they did within their respective groups. A higher Z-score indicates a faster time compared to the average for their group, while a lower Z-score indicates a slower time.

To do this, we will calculate the standard score or Z-score for each of them, which measures how many standard deviations above or below the mean their finishing time was. Calculation is as follows:

For Leo:

Z = (4948 - 4313) / 583 = 1.01

For Mary:

Z = (5513 - 5261) / 807 = 0.33

So, Leo finished 1.01 standard deviations above the mean for the Men, Ages 30 - 34 group, while Mary finished 0.33 standard deviations below the mean for the Women, Ages 25 - 29 group.

As for your second question, if the distributions of finishing times were not nearly normal, then the values of the standard score would change. This is because the standard score is calculated using the mean and standard deviation, which are important parameters of a normal distribution, these parameters may not accurately represent the data, and therefore the standard score would not be an accurate measure of relative performance.

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9514 1404 393

Answer:

  KM = 4

Step-by-step explanation:

The point of the segment addition postulate is that the combined length of segments laid end-to-end is the sum of their individual lengths.*

  KL +LM = KM

  (5x +1) +(3x +3) = 5x +4

  8x +4 = 5x +4 . . . .simplify

  3x = 0 . . . . . . . . . . subtract 5x+4

  x = 0 . . . . . . . . . . . divide by 3

Then the length of KM is ...

  KM = 5x +4 = 5·0 +4 = 0 +4

  KM = 4

_____

* Sometimes it seems that geometrical theorems simply state the obvious. Some interesting math arises from systems of geometry in which this is not true. We usually don't study those in high school.

Answer:

At the end of ten days, the size of population B is 256 times that of population A

Step-by-step explanation:

We work under the premise that population A and B start both with the same number of individuals. Let's call such initial population \(N_0\)

Now, we write the exponential expression that describes population A as a function of days (t) for the first 6 days:

\(N_A=N_0\,(2)^t\)

which represents the starting point with \(N_0\) individuals on day zero, doubling after one day (t= 1), and keeping on doubling the following days for 6 days.

So at the end of 6 days, population A would have the following number of individuals:

\(N_A=N_0\,(2)^6\\N_A=N_0\,(64)\\N_A=64\,N_0\)

That is 64 times the starting number of individuals.

After this, the population stops growing and starts reducing to one-half each day. This behavior can be represented by:

\(N_A=64\,N_0\,(\frac{1}{2} )^t\)

therefore after 4 days in this pattern, this culture has the following number of organisms:

\(N_A=64\,N_0\,(\frac{1}{2} )^4\\N_A=64\,N_0\,(\frac{1}{16} )\\N_A=4\,N_0\)

which is now just four times what the culture started with.

Now, on the other hand, population B grows doubling each day without interruption, so at the end of 10 days its size is given by:

\(N_B=N_0\,(2)^t\\N_B=N_0\,(2)^10\\N_B=N_0\1024\\N_B=1024\,N_0\)

that is it has 1024 times the initial number of organisms.

So if we compare both populations at day 10:

\(\frac{N_B}{N_A} =\frac{1024\/N_0}{4\,N_0} =256\)

Therefore, at the end of ten days, population B is 256 times the size of population A

Answer:

After 10 days, population B has grown to be 256 times the size of population A.

Step-by-step explanation:

Answer:

I dont see a

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

1/4*3

Answer:

f(-1)=-2

Step-by-step explanation:

f(x)=-3x-5x^2

f(-1)=-3(-1)-5(-1)^2

f(-1)=-3(-1)-5(1)

f(-1)=3-5

f(-1)=-2

Answer:

Step-by-step explanation:

Exponential growth or decay can be modeled by the exponential function ...

  f(n) = a×b^n

where 'a' is the initial value, and 'b' is the growth factor. The growth factor is ...

  b = 1 +r

where r is the growth rate. If decay is involved, the sign of r will be negative.

__

If 40% of the participants are eliminated each round, then the growth rate per round is -40% = -0.40, and the growth factor is ...

  b = 1 -0.40 = 0.60

The initial number of participants is 150, so the number remaining after n rounds is ...

  f(n) = 150×0.60^n . . . . . . matches the 3rd choice

__

The growth rate of 11% per hour means the growth factor is ...

  b = 1 +11% = 1.11

The initial population is 2500, so the population after n hours is ...

  f(n) = 2500×1.11^n . . . . . . matches the 2nd choice

Answer:

Step-by-step explanation:

EF = FG

9x + 114 = 15x

114 = 15x - 9x

x = 114 / 6

x = 19

Solve EF: substitute x into the equation

EF = 9x + 114

    = 9(19) + 114

    = 285

m∠EDG = 32°

-2\(\sqrt{6x^{8}y^{3}}\) * 4\(\sqrt{10xy^{8}}\)

You can move \(x^{8}\), \(y^{3}\) and \(y^{8}\) out of the square root to get

-2\(x^{4}\)\(y\)\(\sqrt{6y}\) * 4\(y^{4}\)\(\sqrt{10x}\)

Multiply them

-8\(x^{4}y^{5}\sqrt{60xy}\)

You can take 4 out of 60 to get 2

-16\(x^{4}y^{5}\sqrt{15xy}\)

Answer:

5/8

Step-by-step explanation:

If 3/8 IS raining, then the remaining 8ths is NOT raining. 8 - 3 = 5. So, 5/8 is NOT raining.

I hope this helps!

Answer:

5/8

Step-by-step explanation:

To find the probability of it not raining, subtract 3/8 from 1.

1 - 3/8

= 5/8

Since the probability of it raining is 3/8, this must mean that during the rest of the time, it will not rain.

So, the probability of it not raining is 5/8