What is the mean of the following set of data? {1, 4, 7, 5, 3, 3, 5}

Answer:

  (a)  north: 172.5 mph; west: 298.8 mph

  (b)  363.9 mph at 298.9°

Step-by-step explanation:

The components of velocity are found using the formula for polar to rectangular coordinate conversion. The actual ground speed will be the result of adding the velocity vectors of the airplane and wind.

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The usual formula for converting polar coordinates (r; θ) to rectangular coordinates (x, y) is ...

  (x, y) = r(cos(θ), sin(θ))

When this formula is used with bearing angles, the resulting components are (north, east).

The airplane velocity components are ...

  north: 345·cos(300°) = 172.5 . . . . mph

  east: 345·sin(300°) ≈ -298.8 . . . . mph (or 298.8 mph to the west)

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The sum of the two velocity vectors is found by a calculator to be ...

  345∠300° +20∠280° = 363.9∠298.9°

If you wanted to calculate this by hand, you would find the components of the wind speed, add them to the components of the plane speed, and convert the rectangular components back to polar coordinates. The usual way that is done is using the formula ...

  r = √(x² +y²)

  θ = arctan(y/x) . . . . paying attention to quadrant

If you use x=northerly component, y=easterly component, then the resulting angle is the bearing angle.

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Additional comment

Some calculators are able to convert directly between (x, y) coordinates and (r; θ) coordinates. The calculator shown in the attachment converts (r; θ) coordinates to/from complex numbers. For the purpose here, the real part of the number is the northerly component, and the imaginary part is the easterly component.

The conversion to a complex number is x +iy = r(cos(θ) +i·sin(θ)), sometimes abbreviated r·cis(θ). The notation used here is even more compact: r∠θ. Conveniently, the calculator we used is able to employ this notation.

Problem 9

a = 500 = initial amount

b = 1+r/n = 1 + 0.034/52 = 1.000654 = approximate growth factor

The equation goes from [tex]y = a*b^x[/tex] to [tex]y = 500*1.000654^x[/tex] where x is the number of weeks and y is the account balance in dollars.

Plug in y = 700 and isolate x by using logarithms.

[tex]y = a*b^x\\\\y = 500*1.000654^x\\\\700 = 500*1.000654^x\\\\700/500 = 1.000654^x\\\\1.4 = 1.000654^x\\\\1.000654^x = 1.4\\\\\log(1.000654^x) = \log(1.4)\\\\x\log(1.000654) = \log(1.4)\\\\x = \log(1.4)/\log(1.000654)\\\\x = 514.652\\\\x = 515\\\\[/tex]

It takes about 515 weeks for the account balance to reach $700

This is equivalent to roughly 515/52 = 9.904 years

===========================================================

Problem 10

The formula to calculate the monthly payment is not a simple exponential growth or decay function. I'm not sure how your teacher wanted you to answer this question. You'll have to get clarification on it.

If your teacher is asking something along the lines of "$240,000 is invested at a rate of 1.2% compounded bimonthly. How many years does it take to have the investment reach $300,000?" then you could follow these steps below.

a = 240,000 = initial amount

b = 1 + r/n = 1 + 0.012/24 = 1.0005 = growth factor

[tex]y = a*b^x\\\\y = 240000*1.0005^x\\\\300000 = 240000*1.0005^x\\\\240000*1.0005^x = 300000\\\\1.0005^x = 300000/240000\\\\[/tex]

[tex]1.0005^x = 1.25\\\\\log(1.0005^x) = \log(1.25)\\\\x\log(1.0005) = \log(1.25)\\\\x = \log(1.25)/\log(1.0005)\\\\x = 446.3987\\\\x = 446\\\\[/tex]

The x represents the number of bimonthly periods. There are 24 bimonthly periods in a year, which means it takes roughly 446/24 = 18.58 years for the starting balance of $240,000 to reach $300,000.

Keep in mind that the steps above are based on the assumption I made at the top of the problem. If that assumption is incorrect, then ignore the steps and answer entirely.

#9

[tex]\\ \rm\Rrightarrow P=P_o(1+r/n)^t[/tex]

we need t

[tex]\\ \rm\Rrightarrow P=500(1+0.034/52)^t[/tex]

[tex]\\ \rm\Rrightarrow 700=500(1+0.000654)^t[/tex]

[tex]\\ \rm\Rrightarrow 700=500(1.000654)^t[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{7}{5}=(1.000654)^t[/tex]

[tex]\\ \rm\Rrightarrow 1.4=1.000654^t[/tex]

[tex]\\ \rm\Rrightarrow log1.4=log1.000654^t[/tex]

[tex]\\ \rm\Rrightarrow log1.4=tlog1.000654[/tex]

[tex]\\ \rm\Rrightarrow t=\dfrac{log1.4}{1.000654}[/tex]

[tex]\\ \rm\Rrightarrow t\approx 514.6\approx 515weeks[/tex]

#2

[tex]\\ \rm\Rrightarrow P=240000(1+0.012/25)^t[/tex]

[tex]\\ \rm\Rrightarrow 300000=240000(1.0005)^t[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{5}{4}=(1.0005)^t[/tex]

[tex]\\ \rm\Rrightarrow 1.25=(1.0005)^t[/tex]

[tex]\\ \rm\Rrightarrow log1.25=log1.0005^t[/tex]

[tex]\\ \rm\Rrightarrow log1.25=tlog1.0005[/tex]

[tex]\\ \rm\Rrightarrow t=\dfrac{log1.25}{1.0005}[/tex]

[tex]\\ \rm\Rrightarrow t=446.4\approx 446[/tex]

Question is bit unclear to assume final units of time

The distance the brake anchor has to be placed away from the base of the ending tree so the just reach the tree is 40.31 feet.

From the information given, the height of the tree is given as 20ft. The brake anchor 35 feet from the base of the ending tree.

Therefore, the distance the brake anchor has to be placed away from the base of the ending tree so the just reach the tree will be:

d² = ✓20² + ✓35²

d² = ✓400 + 1225

d² = ✓1625

d = 40.31 feet.

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Answer:

I think the answer is 43.8

Answer:

198.4

Step-by-step explanation:

Right side is a rectangle   12.8 * 12.8 = 163.84 cm^2

Left side is triangle   area = 1/2 Base * height = 1/2 * 12.8 * (18.2-12.8) =

         34.56 cm^2

summed = 198.4  cm^2

The difference, in euros, between the cost of the newspaper in France and the cost of the newspaper in England is 2.10 euros.

Exchange rate is the rate at which one currency is exchanged for another currency.

Cost of the newspaper in England in euros = 2.50 x 1.16 = 2.90

Difference in costs = 5 euros - 2.90 euros = 2.10 euros

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Answer:

240 cm

Step-by-step explanation:

18*12= 216

+

4*3*2= 24

216*24= 240

Answer:

I think it b

Step-by-step explanation:

I had the same question

Answer:

C: strong

Step-by-step explanation:

Its basically asking if the line going through the points fits them. Parabolic would mean the trend line is a parabola, which its not. a parabola is a curved line. weak would mean it doesnt follow most of the points. strong would mean it does follow most of the points, which it does. negative, im guessing would mean it follows none and is completely separate from the points. hope this helps.

Answer:

11.405

Step-by-step explanation:

When rounding numbers, check the digit to the right of the one you're rounding to:

If a = 14.6 is rounded to 1 decimal place then:

If b = 3.25 is rounded to 2 decimal places then:

Therefore, to find the maximum value of a - b, subtract the smallest value of b from the largest value of a:

[tex]\implies \sf a_{max}-b_{min}=14.649999...-3.245=11.405[/tex]

Answer:

$45.5

Step-by-step explanation:

Assuming that there is no tax or change in rate its simply $91 divided by two. We know that 45 is half of 91, 45.5 x 2 = 91

Answer:

The accounting equation is a formula that shows the sum of a company’s liabilities and shareholders’ equity are equal to its total assets (Assets = Liabilities + Equity). The clear-cut relationship between a company’s liabilities, assets and equity are the backbone to double-entry bookkeeping. The source of a company’s accounting equation numbers is its balance sheet. Equity can be Shareholders’ Equity, Stockholders’ Equity, or Owner’s Equity.

Like other equations, if two terms of the basic accounting equation are known, you can solve for the third term. For example, Total Assets – Total Liabilities = Total Equity, or Total Assets – Total Equity = Total Liabilities. You move a term from the right side to the left side of the accounting equation by using a minus sign. 

Names meaning the same as Balance Sheet are Statement of Financial Position or Statement of Financial Condition. 

Answer:

555.94

Step-by-step explanation:

16 x 11 = 176/2

88

since there are two of the same triangle

88 x 2

176

11 is the radius

A = [tex]\pi[/tex][tex]x^{2}[/tex]

A = 3.14 ( pie is 3.14, if not then pi) x (11x11)

A = 3.14 x 121 (or 121[tex]\pi[/tex])

A = 379.94

379.94 + 176 (or 121pi + 176)

555.94

The number of rows of beans that are in the garden is 24 rows.

The first step is to convert feet to inches.

1 feet = 12 inches

30 x 12 = 360 inches

The second step is to divide 360 inches by 15 inches: 360 / 15 = 24 rows

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Answer:24

Step-by-step explanation:

Answer:

-35, 1493

Step-by-step explanation:

p(x) = 2x⁴ + 3x³ - 9x² + 16x + 13

p(-3) = 2(-3⁴) + 3(-3³) - 9(-3²) + 16(-3) + 13

-3² = 9

-3³ = -27

-3⁴ = 81

p(-3) = 2(81) + 3(-27) -9(9) - 48 + 13

p(-3) = 162 - 81 - 81 -48 + 13

81 + 81 = 162 therefore 162 - 81 - 81 cancels

-48 + 13 = -35

p(5) = 2(5⁴) + 3(5³) - 9(5²) + 16(5) + 13

5² = 25

5³ = 125

5⁴ = 625

p(5) = 2(625) + 3(125) - 9(25) + 80 + 13

p(5) = 1250 + 375 - 225 + 93

p(5) = 1250 + 150 + 93

p(5) = 1493

Answer:

24

Step-by-step explanation:

you have to add them

Answer:

3/4

Step-by-step explanation:

(36÷12)/(48÷12).

g

7293.16

Step-by-step explanation

42.7 x 2= 85.4, 85.4 ft to cubic feet = 7293.16

Answer:

>

Step-by-step explanation:

π / 3 is in radians.

Radian need to be converted into

degree ( ° ).

The value of in degree is 180°

π / 3 = 180 / 3 = 60°

60° > 30°

So,

( π / 3 ) > 30°

Answer:

$1890.57

Step-by-step explanation:

First we put the 70% on the original 1011, we can do this by multiplying 1011 by 1.7, now we have 1718.7

Now we put on the 10% tax on the new price, we can do this by multiplying 1718.7 by 1.1, now we get 1890.57

Therefore, the final retail price of the mower is $1890.57, respectively

Answer:

4001

Step-by-step explanation:

here you go hopw it helps you

Answer :

It is D because you have to subtract 4.73 from both sides in order to isolate the y by itself and get the answer which is 3.27

Step-by-step explanation:

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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

What is the solution to the equation below?

y+4.73=8.0

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer and how to Solve:-}}}}[/tex]

To solve it, simply subtract 4.73 from both sides:-

y=3.27 (Option D)

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Answer:

expand the equation

then make q the subject of the formal

well, since we know the endpoints for the diameter, its midpoint will be where the center of the circle is located, so

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -4 -10}{2}~~~ ,~~~ \cfrac{ 11 + 5}{2} \right)\implies \left(\cfrac{-14}{2}~~,~~\cfrac{16}{2} \right)\implies \stackrel{center}{(-7~~,~~8)}[/tex]

and if we get the distance between those endpoints, and take half of that, that'd be the radius of it.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{11})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-4 - (-10)]^2 + [11 - 5]^2}\implies d=\sqrt{(-4+10)^2+6^2} \\\\\\ d=\sqrt{6^2+6^2}\implies d=\sqrt{72}~\hfill \stackrel{radius=half~that}{\cfrac{\sqrt{72}}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-7}{ h},\stackrel{8}{ k})\qquad \qquad radius=\stackrel{\frac{\sqrt{72}}{2}}{ r} \\\\\\\ [x-(-7)]^2~~ + ~~[y-8]^2~~ = ~~\left( \frac{\sqrt{72}}{2} \right)^2\implies (x+7)^2~~ + ~~(y-8)^2~~ = ~~18[/tex]

Answer:

The inverse of f exists

Step-by-step explanation:

Because f  is a function, then the function f  has an inverse

Answer No Can not help in I-Ready Diagnostic That really counts as cheating and its state law to help with Diagnostics.

Step-by-step explanation:

Answer: 766,000

Step-by-step explanation:

* To find the number rounded to the 100th place you would need a decimal. I am going to assume you meant the 100s place instead and answer based off that.

The force vector F in terms of i and j, considering it's magnitude and angle, is represented by:

[tex]V = 11\sqrt{2}i + 11\sqrt{2}j[/tex]

Given a magnitude M and angle [tex]\theta[/tex], the a vector V can be represented as follows:

[tex]V = M\sin{\theta}i + M\cos{\theta}j[/tex]

In this problem, we have that the parameters are as follows:

[tex]M = 22, \theta = 45^\circ[/tex]

Hence:

[tex]V = 22\sin{45^\circ}i + 22\cos{45^\circ}j[/tex]

[tex]V = 22\frac{\sqrt{2}}{2}i + 22\frac{\sqrt{2}}{2}j[/tex]

[tex]V = 11\sqrt{2}i + 11\sqrt{2}j[/tex]

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