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3 years ago

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June made a design with 6 equal tiles. One tile is yellow, 2 tiles are blue,and three tiles are purple. What fraction of the til

es are yellow or purple?

1 answer:

Amiraneli [1.4K]3 years ago

4 0

total number of tiles is 6. the number of yellow or purple tiles i 1+3 = 4.

So the probability of a yellow or purple tile is 4/6=2/3

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Simplify the equation, please show steps. Thank you so much!

Sedaia [141]

I'll assume they are. This will give
4(x + 3)(x - 1)
-----------------
(x + 3)(x^2 + 3x)

Th (x + 3) ' s cancel ou so we are left with:_
4x - 4
--------
x^2 + 3x

- which is A.

4 0

3 years ago

Solve for y, z, x or t:

Andrews [41]

Problem 1

y + (y/a) = b

a*( y + (y/a) ) = a*b ... multiply both sides by 'a'

ay + a(y/a) = ab ... distribute

ay + y = ab

(a+1)y = ab .... factor

y(a+1) = ab

y = ab/(a+1) ... divide both sides by (a+1)

<h3>Answer: y = ab/(a+1)</h3>

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

Problem 2

z - a = z/b

b(z - a) = b(z/b) .... multiply both sides by b

b(z - a) = z

bz - ab = z ... distribute

bz - ab+ab = z+ab ... add ab to both sides

bz = z+ab

bz-z = z+ab-z ... subtract z from both sides

bz-z = ab

z(b-1) = ab .... factor

z = ab/(b-1) .... divide both sides by (b-1)

<h3>Answer: z = ab/(b-1) </h3>

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

Notes:

To clear out the fractions, I multiplied both sides by the denominator value.

The restriction that 'a' cannot equal -1, back in problem 1, is to avoid having the denominator (a+1) be equal to zero. We cannot divide by zero. A similar situation happens with problem 2 as well.

4 0

3 years ago

A fisherman yanks a fish vertically out of the water with an acceleration of 2.5! !! using very light fishing line that has a br

Artyom0805 [142]

Two forces act on the fish, and these are:

1) Its weight mg, downwards and

2) pressure in the string, T, upwards which is 22 N when the string breaks.
In the result of these two forces, the fish had an acceleration of 2.5 m/s^2 in the upward way.

So, T - mg = m*2.5

=> m = T / (2.5 + g)

=> m > 22 / (2.5 + 9.8) ( when the string snaps )

=> m > 1.79 kg.

As a result, the mass of the fish is more than 1.79 kg as the line has been broken.

6 0

3 years ago

Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. Here are th

Vesnalui [34]

Answer:

Part a:

"The unit has 7 or more rooms" in terms of X is given by the unit which has 7, 8, 9 or 10 rooms.

P{ X≥7}= 0.424

Part b:

The event {X > 7} in words is that the unit has more than 7 rooms. .

Part C:

A continuous random variable is given by intervals of numbers

A discrete random variable is the variable that is obtained by counting.

Step-by-step explanation:

Part a:

"The unit has 7 or more rooms" in terms of X is given by

{ X≥7} = {x=7} + {x=8} + {x=9} + {x=10}

the unit which has 7, 8, 9 or 10 rooms.

The probability of this event is given by

P{ X≥7} =P {x=7} + P {x=8} + P {x=9} + P {x=10}

P{ X≥7} = 0.198 + 0.149+ 0.053 + 0.024

P{ X≥7}= 0.424

Part b:

The event {X > 7} in words is that the unit has more than 7 rooms. This does not include the unit having 7 rooms.

Part C:

A continuous random variable takes all the values in the given interval as in part a.The random variable X takes the values between 7 and 10 inclusive of 7.

A discrete random variable is the variable that is obtained by counting as in part b. The variable X takes the values of the units with 8 , 9 or 10 rooms.

8 0

2 years ago

F(x)=2x^2-x-6 g(x)=4-x (f+g)(x)

Semenov [28]

$\large \boxed{(f + g)(x) = f(x) + g(x)}$

The property above is distribution property where we distribute x-term in the function.

Substitute both f(x) and g(x) in.

$\large{ \begin{cases} f(x) = 2 {x}^{2} - x - 6 \\ g(x) = 4 - x \end{cases}} \\ \large{f(x) + g(x) = (2 {x}^{2} - x - 6) + (4 - x)} \\ \large{f(x) + g(x) = 2 {x}^{2} - x - 6 + 4 - x}$

Évaluate/Combine like terms.

$\large{f(x) + g(x) = 2 {x}^{2} - 2x - 2}$

The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)

$\large{(f + g)(x) = 2 {x}^{2} -2x -2}$

<u>Alternative</u>

$\large{(f + g)(x) = 2({x}^{2} -x - 1)}$

<u>Answer</u>

(f+g)(x) = 2x²-2x-2
(f+g)(x) = 2(x²-x-1)

Both answers work. The second answer is in factored form.

Let me know if you have any doubts!

8 0

2 years ago