Mis directly proportional to r?
When r= 2, M= 14
a) Work out the value of M when r= 12.
b) Work out the value of r when M = 224.

Answer:

First, let's find how far away the pier is.

Using the distance formula, we can see that the pier is [tex]\sqrt{58}[/tex] units away.

So, the radius is sqrt 58.

Area = pi (r)^2

So,  the area is 182.82 square units.

Let me know if this helps!

We have that The area that the light covers is  is mathematically given as

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

From the Question we are told that

Revolving beam of light as far as the pier

Let distance to pier be x

Generally the revolving beam turns a complete angle of 360

Therefore

Its goes in a circle

The area that the light covers is  is mathematically given as

[tex]A=\pi r^2[/tex]

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

In conclusion

The area that the light covers is  is mathematically given as

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

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Answer:

Mean of sampling distribution = 50

Standard deviation of sampling distribution, = 0.625

Step-by-step explanation:

Given :

Mean, μ = 50

Standard deviation, σ = 5

Sample size, n = 64

The mean of sampling distribution, μxbar = population mean, μ

μxbar = μ

According to the central limit theorem, the sampling distribution converges to the population mean as the sample size increases, hence, , μxbar = μ = 50

Standard deviation of sampling distribution, σxbar = σ/√n

σxbar = 5/√64 = 5 / 8 = 0.625

Answer:

Commission Received refers to a percentage amount received by the company (or) an individual on the total sales incurred. It is an indirect income/revenue recorded on the credit side of profit and loss account.

Step-by-step explanation:

mark me brainliest if my answer is correct

Answer:

The intersection of plane R and plane P is line DB

Point H is not on plane P.

CE and DB intersect at point D

Explanation:

got it right on edge 2021 :)

Answer:

there right^

Step-by-step explanation:

edge 22

Answer:

3, 11, 35.

Step-by-step explanation:

The first 3 terms of the sequence can de written as:

n, 3n + 2, 3(3n + 2) + 2

So when n = 3 the first 3 terms are

3, 3(3) + 2,  3(3(3) + 2)) + 2

= 3 , 9 + 2, 33 + 2

= 3, 11, 35.

Answer:

good morning

Step-by-step explanation:

hope u have a nice day

Step-by-step explanation:

Ratio of height (large to small) = ratio of radii (large to small).

(h / 14) = (8 / 2)

h / 14 = 4

h = 56

The height of the larger cylinder is 56m.

Volume of cylinder is

V = πr2h

V = π(8)2(56)

V = 3584π

Answer:

Option C

Step-by-step explanation:

2 and 4 makes the figure look symmetrical

The required lines of symmetry are 2 and 4. option C is correct.

A given picture line of symmetry is to be determined from 1, 2, 3, and 4.

the line is a curve showing the shortest distance between 2 points.

A line of symmetry is defined as the line that draw across any curve or shape, The curve and shape have equal proportion across the line, that line is called the line of symmetry.

Clearly,  from observation, it is seen that line 1 and line 3 does not have the same proportion of area across it, so this is not a line of symmetry.
Line 2 and line 4, is lines of symmetry because it has equal proportion of the area across it.

Thus, the required lines of symmetry are 2 and 4. option C is correct.

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Answer:

Line of symmetry of f is x=2 and the line of symmetry for function g is x=1 as the graph starts repeating itself after x=1. Y intercept is the point at which x is 0, for f it is - 5 and for g it is - 6. Rate of change in interval [2,4] is given by (f(4)-f(2))/2=2 for f and for g it is, (g(4)-g(2))/2=-4

The true statements are:

This is the point where the function is divided into equal halves.

From the figure, the table and graph are divided at points x = 2, and x = 1.

So, the line of symmetry for function f is x = 2 and the line of symmetry for function g is x = 1

This is the point where the function has an x value of 0

From the figure, the y values when x = 0 are -5 and -6

So, the y-intercept of function f is -5 and the y-intercept of function g is -6

This is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

For function f, we have:

[tex]m = \frac{-5 + 9}{4-2}[/tex]

[tex]m = \frac{4}{2}[/tex]

[tex]m = 2[/tex]

For function g, we have:

[tex]m = \frac{2+ 6}{4-2}[/tex]

[tex]m = \frac{8}{2}[/tex]

[tex]m = 4[/tex]

By comparison,

[tex]m_f = 0.5 \times m_g[/tex]

Hence, over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.

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Answer:

C. [tex]5\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]1\frac{1}{2}[/tex] cups of milk makes 1 quart of yogurt.

x cups  of milk makes [tex]3\frac{1}{2}[/tex] quarts of yogurt.

[tex]\frac{milk}{yogurt}= \frac{1\frac{1}{2} }{1} =\frac{x}{3\frac{1}{2} }[/tex]

Cross multiply.

[tex]1\frac{1}{2}[/tex] × [tex]3\frac{1}{2}[/tex] = 1 × x

You get:

[tex]5\frac{1}{4} =x[/tex]

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

PW, BW,  GW, PY,  BY, GY

Step-by-step explanation:

We need to determine the sample space

pink(P), blue (B), and green (G) cards,   (W) and yellow (Y) envelopes

Each color card can match with each color envelope

Start with the white envelopes and each color card

and then the yellow envelopes with each color card

PW   BW  GW

PY  BY   GY

Answer:

[tex]y = 7 - 7x \\ y + 7x = 7 \\ 7x + y = 7[/tex]

Answer:

7x + y = 7

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = 7 - 7x ( add 7x to both sides )

7x + y = 7 ← in standard form

Answer in picture

….

Answer:

A is the correct answer :)

Answer:

A

Step-by-step explanation:

checking if A is correct, if we get x as 76 then it is correct

if 5miles = 8 kilometers

47.5 miles= x

that is

5=8

47.5=x

cross multiply

5x=380

x=380/5

x=76

there fore A is correct

checking if B is correct, if we get x as 86 then it is correct

if 5miles = 8 kilometers

52.5 miles= x

that is

5=8

52.5=x

cross multiply

5x=420

x=420/5

x=84

therefore B is incorrect

checking if C is correct, if we get x as 34 then it is correct

if 5miles = 8 kilometers

22.5 miles=x

that is

5=8

22.5=x

Cross multiply

5x=180

x=180/5

x=36

therefore C is incorrect

checking if D is correct, if we get x as 22 then it is correct

if 5miles = 8 kilometers

12.5miles = x

that is

5=8

12.5=x

5x=100

x=100/5

x= 20

Answer: [tex]12.333[/tex] or [tex]12\frac{1}{3}[/tex] or [tex]\frac{37}{3}[/tex]

Step-by-step explanation:

Replace every x with (3)

[tex]f(x) = 4x+3/x^2\\f(3) = 4(3)+3/3^2\\f(3) = 12+3/9\\f(3) = 12.333 or 12\frac{3}{9}or \frac{111}{9}\\f(3) = 12.333 or 12\frac{1}{3} or \frac{37}{3}[/tex]

Answer:

2.5+2.5+45+45

=95.0m

therefore area of the square= 95.0m

45m×0.5=45.5÷95=

Step-by-step explanation:

2.5m

2.5 m tiles are required

[tex]area = 2.5 \times 45 = 192.5 \: squared \: cenimetre \\ \\ no \: of \: tiles = 0.5 \times 0.5 = 0.25 \\ 192.5 \div 0.25 = 770tiles[/tex]

Answer:

[tex]Pr= \frac{1}{21}[/tex]

Step-by-step explanation:

Given

[tex]n(S) = 7[/tex] --- number of games

Required

Probability of bike and movie in consecutive order

This probability is represented as:

[tex]Pr = P(Bike\ and\ Movie) \ or\ P(Movie\ or\ Bike)[/tex]

So, we have:

[tex]Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)[/tex]

The probability is an illustration of selection without replacement;

So, we have:

[tex]P(Bike\ and\ Movie) = P(Bike) * P(Movie)[/tex]

[tex]P(Bike\ and\ Movie) = \frac{n(Bike)}{n(S)} * \frac{n(Movie)}{n(S) - 1}[/tex] ---- without replacement

Bike and Movie appear in the game list 1 time.

So, the equation becomes

[tex]P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{7 - 1}[/tex]

[tex]P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{6}[/tex]

[tex]P(Bike\ and\ Movie) = \frac{1}{42}[/tex]

Similarly,

[tex]P(Movie\ and\ Bike) = \frac{1}{42}[/tex]

So, we have:

[tex]Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)[/tex]

[tex]Pr= \frac{1}{42}+\frac{1}{42}[/tex]

Take LCM

[tex]Pr= \frac{1+1}{42}[/tex]

[tex]Pr= \frac{2}{42}[/tex]

[tex]Pr= \frac{1}{21}[/tex]

Answer:

Step-by-step explanation:

triangol BCD = triangle BDA

so

3x - 1 = 34 - 2x

5x = 35

x = 35 : 5

Answer:

x = 7

Step-by-step explanation:

BD is an angle bisector , so

∠ ABD = ∠ DBC , that is

3x - 1 = 34 - 2x ( add 2x to both sides )

5x - 1 = 34 ( add 1 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Answer:

Swimming pool

Step-by-step explanation:

Let's say that we invite x people. The cost of the bowling alley will be $15 for the room, and we add $5 dollars for each person. Therefore, we can represent the cost of the bowling alley as

5 * x + 15

Similarly, the cost of the swimming pool is

4 * x + 12

To find the maximum of the function, one thing we can do is set the expressions of the cost equal to 40. This will give us the amount of people we can invite for exactly 40 dollars. Because cost increases with amount of people, this will give us the maximum number of people we can invite with $40.

We thus have

5 * x+ 15  = 40

subtract 15 from both sides to isolate the x and its coefficient

25 = 5 * x

divide both sides by 5 to isolate x

25/5 = x = 5

We can therefore invite 5 people to the bowling alley

4 * x+ 12  = 40

subtract both sides by 12 to isolate the x and its coefficient

28 = 4 * x

divide both sides by 4 to isolate x

x = 7

Therefore, we can invite 7 people to the swimming pool. As 7 > 5, we can invite more people to the swimming pool.

A quicker way to solve this could be by looking at the cost of each location. Because the bowling alley costs more both per person and for the room, and there is no way to decrease the cost except by decreasing the amount of people, there is no way that the bowling alley could get as many people as the swimming pool with the same amount of money

Answer:

H0 : correlation is equal to 0

H1 : correlation is not equal to 0 ;

Pvalue < α ;

There is sufficient evidence

r = 0.945 ;

Pvalue = 0.01524

Step-by-step explanation:

Given the data :

Lemon_Imports_(x) Crash_Fatality_Rate_(y)

230 15.8

264 15.6

359 15.5

482 15.3

531 14.9

Using technology :

The regression equation obtained is :

y = 16.3363-0.002455X

Where, slope = - 0.002455 ; Intercept = 16.3363

The Correlation Coefficient, r = 0.945

H0 : correlation is equal to 0

H1 : correlation is not equal to 0 ;

The test statistic, T:

T = r / √(1 - r²) / (n - 2)

n = 5 ;

T = 0.945 / √(1 - 0.945²) / (5 - 2)

T = 0.945 / 0.1888341

T = 5.00439

The Pvalue = 0.01524

Since Pvalue < α ; Reject the Null and conclude that there is sufficient evidence to support the claim.

volume= a^2 * h

area= a^2+4ah

take the second equation, solve for h

4ah=1100-a^2

h=1100/4a -1/4 a now put that expression in volume equation for h.

YOu now have a volume expression as function of a.

take the derivative, set to zero, solve for a. Then put that value back into the volume equation, solve for Volume.

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Answer:

Approximately 68% of people have IQs between 84 and 116.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 100, standard deviation of 16.

Percentage of people with IQs between 84 and 116.

84 = 100 - 16

116 = 100 + 16

So within 1 standard deviation of the mean, which, by the Empirical Rule, is approximately 68%.

Answer:

at most

Step-by-step explanation:

The sample drawn from the population is a relative representation not the absolute representation. The box has 100 tickets in it and sample of tickets is selected to identify difference between sample sum and 252. The at most value for the sample sum can be 278.32 and value cannot exceed beyond this.

9514 1404 393

Answer:

  400 mL/h

Step-by-step explanation:

The required rate is ...

  (100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h

Answer:

probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)

=194/285 or 0.6807.

Step-by-step explanation:

The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.

The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.

Hence

|E'| = C(14,3)

= 14×13×12/3!.

Therefore probability P(E')

= |E'|/|S|

= (14×13×12)/(20×19×18)

= (14×13×2)/(20×19×3)

=(7×13)/(5×19×3)

= 91/285.

Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.

Answer:

(1) 16 x 14 x 10 Room: 2240 ft^3.

(2) How much greater the 18 x 16 x 10 Room is: 640 ft^3.

Step-by-step explanation:

To find the volume of a given space, all we need to do is multiply length*width*height. In this case, the values are 16*14*10, which equals 2240 ft^3.

The changed design would have a volume of 18*16*10, which would equal 2880 ft^3.

To find the difference in volume between the two rooms, all we have to do is subtract the smaller room from the bigger room. 2880 - 2240 = 640 ft^3.