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lilavasa [31]
1 year ago
9

Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card. What is the probability that

he pulls out a 3 first and then pulls out a 2 without replacing them?
a. 1/64
b. 1/56
c. 3/32
d. 3/28
Mathematics
1 answer:
professor190 [17]1 year ago
7 0

Answer:

Therefore, the probability is P=3/32.

Step-by-step explanation:

We know that Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card.  

We calculate the probability that he pulls out a 3 first and then pulls out a 2 without replacing them.

The probability that he pulls out a 3 first is 3/8.

The probability of a second card being 2 is 2/8.

We get:

P=\frac{3}{8}\cdot \frac{2}{8}\\\\P=\frac{6}{64}\\\\P=\frac{3}{32}

Therefore, the probability is P=3/32.

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Answer:

To determine the number of real number solutions of as system of equations in which one equation is linear and the other is quadratic

1) Given that there are two variables, x and y as an example, we make y the subject of the equation of the linear equation and substitute the the expression for y in x into the quadratic equation

We simplify and check the number of real roots with the quadratic formula, x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a} for quadratic equations  the form 0 = a·x² - b·x + c

Where b² > 4·a·c there are two possible solutions and when b² = 4·a·c equation there is only one solution.

Step-by-step explanation:

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Given:

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Step-by-step explanation:

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Here is a flower made up of yellow hexagons, red trapezoids, and green triangles. How many copies of this flower pattern could y
olganol [36]

Answer:

Part a) You could build 5 copies of the flower pattern  

Part b) You would have 40 red trapezoids left over

Step-by-step explanation:

The complete question in the attached figure

Part a)

Let

x -----> the number of yellow hexagons

y ----> the number of red trapezoids

z ----> the number of green triangles

we know that

The flower pattern has the following ratios

\frac{x}{y}=\frac{6}{2} ---->\frac{x}{y}=3 ----> \text {equation A}

\frac{x}{z}=\frac{6}{9} -->\frac{x}{z}=\frac{2}{3} --> \text {equation B}

\frac{y}{z}=\frac{2}{9} ------> \text {equation C}

Find out how many copies of this flower pattern could you build if you had 30 yellow hexagons,50 red trapezoids, and 60 green triangles

1) For x=30

Divide 30 by 6 (remember that in one pattern there are 6 yellow hexagons)

30/6=5\ copies

Verify the quantity of y needed and the quantity of z needed

Find the value of y

\frac{30}{y}=3 ---->y=30/3=10\\

10 < 50 ----> is ok

Find the value of z

\frac{30}{z}=\frac{2}{3} ---> z=30*3/2=45

45<60 --->is ok

2) For y=50

Divide 50 by 2 (remember that in one pattern there are 2 red trapezoids)

50/2=25\ copies

Verify the quantity of x needed and the quantity of z needed

Find the value of x

\frac{x}{50}=3 ---->x=50*3=150

150 > 30 ----> is not ok

3) For z=60

Divide 60 by 9 (remember that in one pattern there are 9 green triangles)

60/9=6.7 copies

Round down

6 copies -----> 6(9)=54 green triangles

Verify the quantity of x needed and the quantity of y needed

Find the value of x

\frac{x}{54}=\frac{2}{3} ---> z=54*2/3=36

36> 30 --->is not ok

therefore

You could build 5 copies of the flower pattern

Part b)

we know that

x:y:z=6:2:9

If you build 5 copies

1) You would use 5*6=30 yellow hexagons and you would have 0 hexagons left over

2) You would use 5*2=10 red trapezoids and you would have (50-10=40) trapezoids left over

3) You would use 5*9=45 green triangles and you would have (60-45=15) triangles left over

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You would have 40 red trapezoids left over

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Answer:

B

Step-by-step explanation:

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  • Parabola opening downward has the form  y=-ax^2
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Where a is a constant

Now, looking at the graph given, it takes the form  x=-ay^2

Where a is 3 (matching the answer).

Hence, B is the correct answer choice.

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