The lifeguards at the beach post information of surfers by placing 3 flags, one above the other, on a flag pole. If there are 8 different flags available, how many possible signals can be flown?

Answer:

The answer is A. V=pi r³

Step-by-step explanation:

:)

The expression for the volume of the pyramid in terms of the radius r of the cone is [tex]\pi r^3[/tex]. So, option A is correct.

The cone is a three-dimensional figure with a vertex and a flat base.

The volume of a pyramid is given by the formula:

[tex]V = \dfrac{1}{3} \times base\ area \times height.[/tex]

Given that:

The base area of the pyramid = B

The height is 3r

The base area of the pyramid is the same as that of the cone.

The base of the cone = [tex]\pi r^2[/tex]

The volume of the pyramid is calculated as:

[tex]V = \dfrac{1}{3} \times \pi r^2 \times 3r[/tex]

V =[tex]\pi r^3[/tex]

Therefore, the volume of the pyramid is [tex]\pi r^3[/tex]. So, option A is correct.

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The results of subtraction of functions are listed below:

There three fundamental binary operators (addition, multiplication, composition) and two secondary binary operators (subtraction, division) for functions. The subtraction is operation derived from addition, defined by the following expression:

(h - f) (x) = h(x) - f(x)       (1)

Now we proceed to develop each expression:

i) (h - f) (x):

ii) m(x) = (g - j) (x):

iii) m(3):

m(3) = 3² + 10 · 3 + 5

m(3) = 9 + 30 + 5

m(3) = 44

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Answer:

0.213

Step-by-step explanation:

→ Convert into binomial information

x ~ B ( 12 , 0.4 )

→ Write down probability required

p ( x = 4 )

→ Evaluate

0.2128

Step-by-step explanation:

There is 31 days in May so the probability is

[tex]p(bday \: in \: may) = \frac{2}{31} [/tex]

Answer:

A

Step-by-step explanation:

The factored form of the expression is (2x-1)(2x+5) and the x-intercept of the function is 1/4 and -5/2 respectively

Quadratic equations are equations that has a leading degree of 2. Given the quadratic equation below;

y = 4x^2 + 8x -5

The x-intercept is the point where the value of y is zero.

Factorize the resulting expression

y = 4x^2 + 8x -5

y = 4x^2 - 2x + 10x -5

y = 2x(2x-1)+5(2x -1)

y = (2x-1)(2x+5)

The factored form of the expression is (2x-1)(2x+5)

Equate the given factors to zero

(2x-1)(2x+5) = 0

Equate the factors to zero

2x - 1 = 0

2x = 1

x = 1/4

Similarly

2x + 5 = 0

2x = -5

x = -5/2

Hence the x-intercept of the function is 1/4 and -5/2 respectively

C) For the end behavior, as the value of x tends to infinity, hence the y-values tends to infinity

D) In order to plot the graph, the x-intercepts of the will be plotted on the graph and then curve will be created.

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The area of the shaded region shown in the image is 14π unit²

An equation is an expression that shows the relationship between two or more numbers and variables.

Area of semicircle = π*diameter² / 4

The area of the shaded region is the sum of the area of the individual semi circles shown in the diagram.

Area of shaded region = area of SR + area of QR + area of PQ

Area of shaded region = (1/2) * π(4²/4) +  (1/2) * π(2*4²/4) + (1/2) * π(2 * 2 * 4²/4) = 14π

The area of the shaded region shown in the image is 14π unit²

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Answer:

green=100 jellybeans

Step-by-step explanation:

let the bag be (B)

red jellybeans (R)

yellow jellybeans (Y)

green jellybeans (G)

R=25

Y=3R............(1)

½ of B=G ..........(2)

from equation (1)

Y=3(25)

Y=75

since 1/2 0f the bag are G that means R+Y is equal to the remaining bag

R+Y=75+25=100 which is half of the bag

G that's half of the bag =100

Step-by-step explanation:

4)

the surface area is

top and bottom : 2× pentagon (5 sides)

sides : 5× rectangle 14×8 ft²

let's start with the easiest : the rectangles.

5 × 14×8 = 560 ft²

the area of a pentagon is similar to any regular polygon :

n × triangle of side×height (to middle of pentagon) / 2

n = number of sides (5 in our case).

the middle or center of the pentagon is the top vertex of each triangle.

so,

5 × 14×9.63 / 2 = 5 × 7 × 9.63 = 337.05 ft²

and we have 2 of them (top and bottom), so

2×337.05 = 674.1 ft³

in total the surface area is

560 + 674.1 = 1,234.1 ft²

5)

6 sides :

top and bottom : 7×14 rectangle

left and right : 7×8 rectangle

front and back : 8×14 rectangle

so, we have

2× 7×14 = 196 mm²

2× 7×8 = 112 mm²

2× 8×14 = 224 mm²

in total that is : 532 mm²

Answer:

  (a) 48, 52, 54

  (b) 6

  (c) b, c

Step-by-step explanation:

The sample mean is the mean of the sample. The range of sample means is the difference between the largest and smallest. As with all sampling processes, more data gives a better estimate.

The sample means are calculated in the attachment. For the different samples, they are ...

The range of the sample means is the difference between the largest and the smallest:

  range = 54 -48 = 6

More data is better, and the closer the estimates are to each other, the better confidence they offer. The true statements are ...

Angles are said to be produced whenever two or more straight lines intersect. Some types of angles are right angle, obtuse angle, acute angle, etc. Thus, the required proof is stated below:

Prove: <A > <C

           <B > <D

An obtuse angle is a given angle that is greater than [tex]90^{o}[/tex] but less than [tex]180^{o}[/tex]. While an acute angle is a given angle that is less than [tex]90^{o}[/tex].

Thus extend AB to F, such that BF = CD.

Draw a perpendicular from a to intersect CD at point E.

So that;

<BAD = <BAE + <DAE (addition property of an angle)

Such that;

<A is an obtuse angle, while <C is an acute angle. Thu,

<A > <C (different types of angles)

Also,

<ADC = <CDF - <ADF (subtraction property of angles)

But both angles B and D are acute angles.

So that;

<B > <C (comparison of measures of two angles)

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Answer:

61.9°

Step-by-step explanation:

The angles of a triangle always add up to 180°. Using this information along with the values of two of the three angles, we can set up an equation to find the measure of the third angle.

Let the measure of the third angle be represented as "x". The first angle + the second angle + the third angle must equal 180 therefore...

[tex]35.5+82.6+x=180[/tex]

Start by adding the like terms on the left side of the equation:

[tex]118.1+x=180[/tex]

Then, subtract both sides by 118.1:

[tex]x=61.9[/tex]

Therefore the measure of the third angle of the triangle is 61.9°.

The distance between the two schools on the map is (C) 4.2 inches.

To find the distance:

On the map,2 inches represents 5 miles.

Thus, we can write:

Since the actual distance between the two schools is 10.6 miles.

Multiplying both sides by 10.6 in equation (1).

Therefore, the distance between the two schools on the map is (C) 4.2 inches.

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The complete question is given below:
Kim is drawing a map of the different schools in her school district. she knows that her middle school is 10.6 miles away from the middle school that her best friend attends. if every 2 inches on the map represents 5 miles, how far apart will the two schools be on the map, to the nearest tenth of an inch?

(A) 0.2 inch

(B) 0.9 inch

(C) 4.2 inches

(D) 26.5 inches

[tex]\boldsymbol{\sf{3n\left(\dfrac{1}{4}\right)=16\dfrac{1}{2} } }[/tex]

Multiply both sides of the equation by 4, the lowest common denominator of 4.2.

[tex]\boldsymbol{\sf{ 12n\times\left(\dfrac{1 }{4}\right)=2(16\times2+1) }}[/tex]

Multiply 12 and 1/4, because once multiplied, we get the following 12/4.

[tex]\boldsymbol{\sf{\dfrac{12}{4}n=2(16\times2+1) \ \ \longmapsto \ \ [Divide \ 12 \div 4.] }}[/tex]

[tex]\boldsymbol{\sf{3n=2(16\times2+1) \ \ \longmapsto \ \ [ Multiply \ 16\times 2] }}[/tex]

[tex]\boldsymbol{\sf{3n=2(32+1) \ \longmapsto \ \ [Add] }}[/tex]

[tex]\boldsymbol{\sf{3n=2\times33 \ \ \longmapsto \ \ [Multiply] }}[/tex]

[tex]\boldsymbol{\sf{3n=66}}[/tex]

Divide both sides by 3.

[tex]\boldsymbol{\sf{n=\dfrac{66}{3} \ \longmapsto \ \ [Split] } }[/tex]

[tex]\boxed{\boldsymbol{\sf{n=22}}}[/tex]

Once the exercise is solved, we find that the value of n is 22.

The number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16

The equation is given as:

a+b+c+d+e+f = 2006

In the above equation, we have:

Result = 2006

Variables = 6

This means that

n = 2006

r = 6

The number of solutions is then calculated as:

(n + r - 1)Cr

This gives

(2006 + 6 - 1)C6

Evaluate the sum and difference

2011C6

Apply the combination formula:

2011C6 = 2011!/((2011-6)! * 6!)

Evaluate the difference

2011C6 = 2011!/(2005! * 6!)

Expand the expression

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006 * 2005!/(2005! * 6!)

Cancel out the common factors

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/6!

Expand the denominator

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/720

Evaluate the quotient

2011C6 = 9.12 * 10^16

Hence, the number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16

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Question 17: B. A’ (1,2), B’ (3,2), C’ (3,5)

Translating 4 to the right means that you should add 4 to the x value of your coordinate point.

Question 18: C. (3,-5)

This is because reflecting over the x-axis would mean to move down the same amount of units above the x-axis the original point is (the original point is five units above the x-axis so you just move down five units). Look at the attached picture for more help.

Question 19: A. C’ (0,-2)

We can see that the triangle has been translated 1 unit to the right and 2 units up. This would mean you add 1 to the x-value of the coordinate and add 2 to the y-value of the coordinate. I can’t see point C clearly, but I’m guessing that it’s at (-1,-4). This would give point C’ as (0,-2)

Hope this helps! Let me know if you need more help! Have a fantastic day!

By 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d. This can be obtained by using the function representing the exponential decay.

Number of weeds is represented by the function,

W(d)=1650(0.85)^d

⇒ W(d)=1650(1 - 0.15)^d

Here, d = number of days since application

Function representing the exponential decay is,

⇒ A(r) = A(1 - r)^t

where,

A = Initial value

r = Percentage decay

t = duration

By comparing the given function and function representing the exponential decay,

r = 0.15 ≈ 15/100

Or r = 15%    

Therefore, population of weeds will decrease 15% each day.

Hence by 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d.

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Answer:

5x^2-x+6

Step-by-step explanation:

That should work

Answer: 96

Step-by-step explanation:

A palindrome is a number that is the same when reading in both ways (right to left, and left to right), for example, 121

Then, we have 9 digits, and all the digits need to be even.

the options are: 0, 2, 4, 6, 8.

Now, we can think of a 9-digit number as 9 empty slots, and in each slot, we can put a number.

But because this is a palindrome, the first digit must be equal to the ninth, and the second digit must be equal to the eight, and so on.

So, we can think it as actually only 5 slots, where in each slot, we can put an even number, now let's count the options that we have in each selection.

For the first digit we have 4 options: 2, 4, 6 and 8 (0 is not counted here because if the first digit was a 0, then this would not be a 9-digit number).

for the second digit, we have also 4 options (because we already toked one, but now the 0 can be chosen)

for the third digit, we have 3 options

for the fourth digit, we have 2 options

for the fifth digit, we have only one option.

The total number of combinations is equal to the product of the number of options for each selection:

C = 4*4*3*2*1 = 96

The given statement simpson’s paradox occurs whenever including a lurking variable causes you to rethink the direction of an association is true.

Since, we know that

A variable that we did not include in our analysis, that could susbtantially change our intepretation of the data if we did include it, is called a lurking variable.

Including a lurking variable may

And,

When including a lurking variable causes you to re-think the direction of an association, this is called Simpson's paradox.

Hence, the given statement simpson’s paradox occurs whenever including a lurking variable causes you to rethink the direction of an association is true.

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Answer:

11.3 miles more than

Step-by-step explanation:

Looking at the graph, when x is 10 the y is 308. For the equation, if you make x 10, then y is 421. 421 is 113 more than 308. Jace travels 113 more than Jeriel on 10 gallons of gas. If you divide 113 by 10 (to get 1 gallon of gas), you would end up with 11.3 miles more than :)

The minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls is 4

The total number of balls is

Total = 50

Let k represent the minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls

Using the pigeonhole principle, we have

n + 1 = k

Where n = 3

So, we have

3 + 1 = k

Evaluate the sum

4 = k

Rewrite the equation as

k = 3

Hence, the minimum number of balls that we need to draw to ensure that we get at least 3 even labeled balls is 4

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The definition of the given piecewise function is:

A piecewise function is a function that has different definitions, depending on the input.

In this problem, for x until 2, the function is the cube function shifted down 3 units, hence the definition is:

[tex]y = x^3  - 3, x \leq 2[/tex]

For x greater than 2, the function is the square function shifted up 6 units, hence the definition is:

[tex]y = x^2 + 6, x > 2[/tex]

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Answer:

$528
If not then it might be $385

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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Answer:

heat map is the answer

When calculating a nation’s digital power, the term that is used to refer to the demonstrated capabilities of a nation-state in cyber offense or defense is Cyberwarfare.

Cyberwarfare  can be regarded as the use of cyber attacks against a nation-state so as to produce significant harm.

It should be noted that Cyber Warfare is set of actions  which is been carried out by  nation or organization so as to be able to launch an attack on institutions' computer network systems.

The interests or reasons for cyberwarfares based on the Cybersecurity as well as Infrastructure Security Agency are;

In order to achieve the goals behind the cyberwarfare programs, it is usually designed to focus on spectrum of objectives which will bring harm to national interests.

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Answer:

[0,+♾)

Step-by-step explanation:

|x| function is kinda like a half opened book from (0, 0) and |x+5| is from (–5, 0)

So we can't find any changes for y

so the domain is

[0, +♾)

The unit rate of the proportional relationship y = 3x is 3

The proportional relationship is given as:

y = 3x

Divide both sides by x

y/x = 3

For a proportional relationship y/x = k;

The unit rate is 3

This means that the unit rate of the proportional relationship y = 3x is 3

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