Which theorem can be used to show that AJKL - AMNP?

Answer:

(a) [tex]Area = 14.7824cm^2[/tex]

(b) [tex]Area = 118.2592cm^2[/tex]

(c) [tex]Area = 4nh[/tex]

Step-by-step explanation:

Given

[tex]\theta = 67.5[/tex]

[tex]b= 8cm[/tex] --- base

[tex]n = 8[/tex] --- triangles

Solving (a) The area of each triangle

First, calculate the height (h) of each triangle using:

[tex]\sin(67.5) = \frac{h}{b/2}[/tex] --- i.e. we consider half of the triangle

[tex]\sin(67.5) = \frac{h}{8/2}[/tex]

[tex]\sin(67.5) = \frac{h}{4}[/tex]

Solve for h

[tex]h =4*\sin(67.5)[/tex]

[tex]h =4*0.9239[/tex]

[tex]h =3.6956[/tex]

The area of each triangle is:

[tex]Area = \frac{1}{2} *b * h[/tex]

[tex]Area = \frac{1}{2} *3.6956 * 8[/tex]

[tex]Area = 14.7824cm^2[/tex]

Solving (b): Area of the octagon

This is calculated as:

Area = 8 * area of 1 triangle

[tex]Area = 8 * 14.7824cm^2[/tex]

[tex]Area = 118.2592cm^2[/tex]

Solving (c): Area of octagon of side length n

In (a), we have:

[tex]Area = \frac{1}{2} *b * h[/tex]

Replace b with n

[tex]Area = \frac{1}{2} *n * h[/tex]

Multiply by 8 (the sides) to get the area of the octagon

[tex]Area = 8 * \frac{1}{2} *n * h[/tex]

[tex]Area = 4nh[/tex]

Answer:

The expected winnings of the player in one game = 2.55

Step-by-step explanation:

Given - A blue die and a red die are thrown in a game. If the sum of the two numbers is 7 or 11, the player wins $10. If the sum of the two numbers is 12, then the player wins $20. In all other cases, the player loses a dollar.

To find - What are the expected winnings of the player in one game ?

Solution -

Given that,

A blue die and a red die are thrown in a game.

The Sample Space becomes -

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

       (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

       (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

       (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

       (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

       (6, 1), (6, 2), (6, 3), (4, 4), (6, 5), (6, 6) }

So,

n(S) = 36

Now,

Let A be the outcome that, the sum of the two numbers is 7 or 11

A = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2),  (6, 1)

       (6, 5), (5, 6) }

So,

n(A) = 8

So,

P(A) = n(A)/ n(S)

       = 8/ 36

       = 2/9

⇒P(A) = 2/9

Now,

Let B be the outcome that, the sum of the two numbers is 12

B = {(6, 6)}

So,

n(B) = 1

So,

P(B) = n(B)/ n(S)

       = 1/ 36

⇒P(B) = 1/36

Now,

Expected value, E(x) = ∑ x P(x)

                                  = 10 × P(A) + 12 × P(B)

                                  = 10 × 2/9 + 12 × 1/36

                                  = 20/9 + 12/36

                                  = (20×4 + 12)/36

                                  = (80 + 12)/36

                                  = 92/36

                                  = 2.55

⇒Expected value, E(x) = 2.55

∴ we get

The expected winnings of the player in one game = 2.55

Answer:

2.5, 2 and 1 half stars

Step-by-step explanation:

0.5=1/2, so 5/2= 2.5

Answer:

5

Step-by-step explanation:

it is asking for .5 of the stars, which in percentage is 50%. if the total is 10 because 5 stars in each row and there are 2 rows. you add the numbers of stars per row, then divide it by 2, and you would get 5; so you would circle 5 stars.

Answer: [tex]\dfrac{2}{65}[/tex]

Step-by-step explanation:

Given

There is a six letter word with no repeated letters

Number of ways of arranging 6 letters out of 26 letters is [tex]^{26}P_6[/tex]

For the 6 letter word with vowels in the beginning and the end can be formed by selecting 2 vowels out of 5 available.

First place has 5 choices to fill and the last place left with 4 choices to fill

Remaining 4 places can be filled by [tex]^{24}P_4[/tex] ways

So, the required probability is given by

[tex]\Rightarrow \dfrac{5\times ^{24}P_4\times 4}{^{26}P_6}=\dfrac{2}{65}[/tex]

Answer:

Hey there I think the answer is 0.06 hopefully that helps

Step-by-step explanation:

Answer:

-5+(-7)+9+(-3) = -6

Step-by-step explanation:

We need to add the following i.e.

-5+(-7)+9+(-3)

We know that, +(-) = - (minus)

So,

-5-7+9-3 = -12+6

= -6

So, the value of the given expression is equal to -6.

Answer:

B. 36 yd

Step-by-step explanation:

I calculated it logically

Answer: 7

Step-by-step explanation: 7+7=14

Answer:

This is decay. The exponent has a negative sign. The reciprocal of 2 is 0.5. So N(t) can be rewritten as 0.5^(t/8). The base is fraction less than 1, which is decay.

Step-by-step explanation:

sample response on edgen 2022

Answer:

18x^3sqrt(7)

Step-by-step explanation:

14x^3sqrt(7)+4x^3sqrt(7); factor our 4 in the first radical and factor out x^6 in both radicals

Add like terms;

18x^3sqrt(7).

Answer:

72ft^3

Step-by-step explanation:

I first took a single slice off the box and counted how many cubes there were. By looking at the blue side, I counted 12 cubes in that slice. I then counted how many slices were in the box, which were 6.

12* 6 = 72ft^3

Answer:

(8, 11π/6)

Step-by-step explanation:

r= √(4√3)²+(-4)² = √48+16=√64=8

0 = tan~¹ -4/(4√3)

= tan~¹ -⅓√3 = 330° = 11π/6

the polar coord. => (8, 11π/6)

9514 1404 393

Answer:

  8∠11π/6

Step-by-step explanation:

To simplify the way we talk of this number, we will refer to it as a vector. We'll assume its head is at the given coordinates, and its tail is at the origin. The magnitude of the vector is the root of the sum of the squares of its components:

  [tex]\displaystyle r=\sqrt{x^2+y^2}=\sqrt{(4\sqrt{3})^2+(-4)^2}=\sqrt{48+16}=\sqrt{64}\\\\r=8[/tex]

The angle of the vector with respect to the +x axis is ...

  [tex]\theta=\arctan{\dfrac{y}{x}}\qquad\text{a 4-quadrant arctangent}\\\\\theta=\arctan{\dfrac{-4}{4\sqrt{3}}}=-\arctan{\dfrac{1}{\sqrt{3}}}\qquad\text{a 4th-quadrant angle}\\\\\theta=\dfrac{11\pi}{6}[/tex]

In magnitude∠angle notation, the polar coordinates are ...

  (4√3, -4)  ⇔  8∠(11π/6) . . . . . θ in radians

_____

Additional comment

Spreadsheets generally have an ATAN2(x, y) function that will return a 4-quadrant version of the angle. The usual ATAN( ) function will give the angle only in quadrants I or IV.

Some graphing calculators may also have the ATAN2 function. Some will simply do the entire conversion for you, without any need to deal separately with magnitude and angle. (You may need to write the number as a complex number, x +iy.)

Answer:

1.

In triangle ∆AFD ,∆BGD ,∆CHD

<AFD=<BGD=<CHD

[being corresponding angle]

<DAF=<DBG=<DCH

[being corresponding angle]

<D is common for all.

So

∆AFD ~∆BGD ~∆CHD

[By A .A .A. axiom]

look

again

at picture pasted

By AAA axiom ∆AFD , ∆BGD , ∆CHD are similar with each other.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

a). In ΔAFD, ΔBGD, ΔCHD

∠AFD = ∠BGD = ∠CHD [being corresponding angle]

∠DAF = ∠DBG = ∠DCH  [being corresponding angle]

∠D is common for all.

So ∆AFD ~∆BGD ~∆CHD   [By A .A .A. axiom]

Learn more about similarity of triangle from:

https://brainly.com/question/25882965

#SPJ2

Answer:

can you provide a picture of the question plz

Step-by-step explanation:

9514 1404 393

Answer:

  equation: y = 4x

  graph is attached

Step-by-step explanation:

Let y represent the cost of the peaches in dollars. Let x represent their weight in pounds. Then the relation between the two variables is ...

  cost = (cost per pound) × (pounds)

  y = 4x

__

This graphs as a line through the origin with a slope of 4. In the attached, the x- and y-axes have different scales so more of the graph can be seen.

Answer:

Number of biscuit needs = 28 packets

Number of Pemmican needs = 18 packets

Number of Butter cocoa needs = 4 packets

Step-by-step explanation:

GIven:

Total calorie required = 5,600 calories

Biscuits 80 (Calorie per packet) 40% of total diet

Pemmican 140 (Calorie per packet) 45% of total diet

Butter cocoa 210 (Calorie per packet) 15% of total diet

Find:

Number of biscuit, Pemmican and butter cocoa need

Computation:

Number of biscuit needs = [5,600(40%)]/80

Number of biscuit needs = [2,240]/80

Number of biscuit needs = 28 packets

Number of Pemmican needs = [5,600(45%)]/140

Number of Pemmican needs = [2,520]/140

Number of Pemmican needs = 18 packets

Number of Butter cocoa needs = [5,600(15%)]/210

Number of Butter cocoa needs = [840]/210

Number of Butter cocoa needs = 4 packets

Answer:

The correct approach will be "0.612580".

Step-by-step explanation:

Given:

Randomly selected customers,

n = 10

Probability of recognition,

p = 90%

or,

  = 0.9

q = 1 - p

  = 1 - 0.9

  = 0.1

Now,

The probability that 9 out of 10 clients are likely to be familiar with the brand will be:

⇒ [tex]P(X=r)=nCr\times (p)^r\times (q)^{(n-r)}[/tex]

⇒ [tex]P(X=9)=10C_9\times (0.9)^9\times (0.1)^{(10-9)}[/tex]

                    [tex]=10C_9\times (0.9)^9\times (0.1)^1[/tex]

                    [tex]=10\times (0.9)^9\times 0.1[/tex]

                    [tex]=0.387420[/tex]

hence,

The probability that not nine seem to be the numbers recognizing her brand name will be:

⇒ [tex]P(X=not \ 9)=1-P(X=9)[/tex]

                          [tex]=1-0.387420[/tex]

                          [tex]=0.612580[/tex]

Answer:

(x+10)^2

Step-by-step explanation:

x^2+20x+ 100

What 2 numbers multiply to 100 and add to 20

10*10 =100

10+10=20

(x+10) (x+10)

(x+10)^2

Answer:

circle

Step-by-step explanation:

Answer:

49/5 mm

Step-by-step explanation:

7/2×14/5

multiply the numerator and denominator

98/10

simplify

49/5 or

9 4/5 mm

Answer:

9 ft by 9 ft

Step-by-step explanation:

Answer:

length of 9 ft; width of 9 ft

Step-by-step explanation:

It is because you see it says it is square storage, which means its length and width have to be the same, and when you do 607.5 divided by 7.5, you get 81 which you can guess is a length of 9 ft; width of 9 ft because 9 x 9 equals to 81. I hope it helps! :)

Answer:

5

Step-by-step explanation:

Given :

Observed values = 5, 10, 15

Expected freqencies = 10

χ² = Σ(observed - Expected)² / Expected

χ² = (5-10)²/10 + (10-10)²/10 + (15-10)²/10

χ² = 25/10 + 0/10 + 25/10

χ² = 2.5 + 0 + 2.5

χ² = 5

Answer: [tex]\$10,\ \$5[/tex]

Step-by-step explanation:

(a) Given

Sam charge $5 for each dog for a thirty minute walk

For an hour which is double the thirty minutes, it must be double of the same charge.

[tex]\Rightarrow 2\times 5=\$10[/tex]

(b)Given

With $20, Christie sells 100 cups of lemonade with a quarter per cup charge

For 100 cup, she generate a revenue of

[tex]\Rightarrow \dfrac{1}{4}\times 100\\\\\Rightarrow \$25[/tex]

So, she earns [tex]25-20=\$5[/tex] that is , her profit is [tex]\$5[/tex]

Answer:

1/4

Step-by-step explanation:

Step-by-step explanation:

We can set up the ration of the radian angle θ in your problem in terms of degrees given as the ratio: (Θ/2·pi) = (72/360), solving for Θ we get Θ = 1.26 radians. Then for the arc length s = Θ·r using this value gives s = 1.26·4 = 5.04

Answer:

B.

Step-by-step explanation:

The street sign is composed of two rectangles and 1 triangle.

Painted area = area of triangle + area of rectangle 1 + area of square

✔️Area of triangle = ½bh

b = 15 in.

h = 8 in.

Area of triangle = ½*15*8 = 60 in.²

✔️Area of rectangle 1 = L*W

L = 50 in.

W = 6 in.

Area = 50*6 = 300 in.²

✔️Area of Square = s²

s = 15 in.

Area = 15² = 255 in.²

✅Painted area = 60 + 300 + 225 = 585 in.²

Answer:

B. 585 square inches :)

Step-by-step explanation: