MATHEMATICS MIDDLE SCHOOL

There are 105 lettered tiles in a board game. You choose thetiles shown (R, A, I, L, M, B, E). How many of the 105 tileswould you expect to be vowels?

Answers

Answer 1

Answer:

Answer: 45

Step-by-step explanation:

Given: The total number of lettered tiles in a board game =105

The number of tiles chosen (R, A, I, L, M, B, E) = 7

the number of vowels chosen (A,I,E)=3

Now, the fraction or probability of choosing of vowels out of 7 given letters is given by :-

$\text{P(vowels)}=(3)/(7)$

Now, the number of vowels we can expect to be vowels out of 105 letters is given by :-

$\text{P(vowels)}*\text{Total letters}=(3)/(7)*105=45$

Hence, the number of vowels we can expect to be vowels out of 105 letters is 45.

Answer 2

Answer: 105 ÷ 7 = 15 15 × 3 = 45 45 are vowels

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Answers

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A swimming pool 20 m long and 10 m wide is surrounded by a deck of uniform width. The total area of the swimming pool and the deck is 704 m^2. Find the width of the deck.

Answers

$S = 704 \ m^2 \nwidth \ of \ the \ deck - x \n \nS=a \cdot b \n \n (10+2x)(20+2x) = 704 \n \n 200+20x +40x+4x^2-704 =0\n \n4x^2 +60x -504=0\ \ /:4$

$x^2+15x -126=0\n \na=1, \ b=15 , \ c= - 126 \n \n\Delta =b^2-4ac = 15^2 -4\cdot1\cdot (-126) = 225 +504=729 \n \nx_(1)=(-b-√(\Delta) )/(2a)=(-15-√(729))/(2 )=( -15-27)/(2)=(-42)/(2)=-21 \ can \ not\ be \ negative \n \nx_(2)=(-b+√(\Delta) )/(2a)=(-15+√(729))/(2 )=( -15+27)/(2)= 6 \ m \n \n Answer : \ waist \ width \ is \ 6 \ m$

Let x = width of the deck.
Therefore total area of pool :
(10+2x)m*(20+2x)m = 704 m^2
( 200 + 20x + 40x + 4x^2 ) m^2 = 704 m^2
(200 + 60x + 4x^2) = 704
4x^2 + 60x = 704-200
4x^2 + 60x = 504
4x^2 + 60x - 504 = 0
4(x^2 + 15x - 126) = 0
(x+21) * (x-6) = 0
Therefore x, the deck's width is 6m (it can't be -21 as width is measured as a positive value)
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Please answer the 33 3/4 one i need answer

Answers

33.75
that's the answer I got let me know if you need more help(:

Jennifer got a box of chocolates. the box is a right triangular prism shaped box. it is 7 in long. and the triangular base measure 2in times 3in times 4in. what is the surface area of the box of chocolates?

Answers

Answer:

$A = 68.8 inches^(2)$

Step-by-step explanation:

Given : Jennifer got a box of chocolates. the box is a right triangular prism shaped box. it is 7 in long. and the triangular base measure 2in times 3in times 4in.

a = 2

b=3

c=4

To Find : what is the surface area of the box of chocolates?

Solution: The first thing we should know is the area of the triangular base.

Triangular base area:

$A1 =√((s * (s-a) * (s-b) * (s-c)) )$

Where, s is the semi-meter of the triangle:

$s =( (a + b + c) )/( 2)$

a, b, c: sides of the triangle.

Substituting:

s = (2 + 3 + 4) /2=4.5

$A1 = √( (4.5 * (4.5-2) * (4.5-3) * (4.5-4)))$

A1 = 2.90

Then, you must know the area of each rectangle associated with each side of the triangular base.

Rectangle area 1: Ar1 = (a) * (l)

Ar1 = (2) * (7)

Ar1 = 14

Rectangular area 2: Ar2 = (b) * (l)

Ar2 = (3) * (7)

Ar2 = 21

Rectangular area 3: Ar3 = (a) * (l)

Ar3 = (4) * (7)

Ar3 = 28

Finally the surface area is: A = Ar1 + Ar2 + Ar3 + 2 * A1

A = (14) + (21) + (28) + 2 * (2.90)

$A = 68.8 inches^(2)$

Hence the surface area of the box of chocolates is

$A = 68.8 inches^(2)$

The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation:2n + 1 = 157.

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