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Over [174]
1 year ago
7

You toss a coin (heads or tails), then spin a three-color spinner (red, yellow, or blue). Complete the tree diagram, and then us

e it to find a probability.
1. Label each column of rectangles with "Coin toss" or "Spinner."

2. Write the outcomes inside the rectangles. Use H for heads, T for tails, R for red, Y for yellow, and B for blue.




3. Write the sample space to the right of the tree diagram. For example, write "TY" next to the branch that represents "Toss a tails, spin yellow."


4. How many outcomes are in the event "Toss a tails, spin yellow"? (1 point)


5. What is the probability of tossing tails and spinning yellow? (1 point)
Mathematics
1 answer:
dolphi86 [110]1 year ago
3 0

The sample space in the tree diagram regarding the probability will be HR, HY, HB, TR, TY, TB.

<h3>What is probability?</h3>

It should be noted that probability simply means the likelihood of the occurence of an event.

In this case, the sample space in the tree diagram will be HR, HY, HB, TR, TY, TB where,

H= head

T = tail

B = blue

r = red

y = yellow

The number of outcomes are in the event "Toss a tails, spin yellow will be 1.

The probability of tossing tails and spinning yellow will be:

= 1/2 × 1/3

= 1/6

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

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2 years ago
In the expansion (ax+by)^7, the coefficients of the first two terms are 128 and -224, respectively. Find the values of a and b
madam [21]

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a = 2, b = 3.5

Step-by-step explanation:

Expanding (ax+by)^7 using Binomial expansion, we have that:

(ax+by)^7 =

(ax)^7(by)^0 + (ax)^6(by)^1 + (ax)^5(by)^2 + (ax)^4(by)^3 + (ax)^3(by)^4 + (ax)^2(by)^5 + (ax)^1(by)^6 + (ax)^0(by)^7

= (a)^7(x)^7+ (a)^6(x)^6(b)(y) + (a)^5(x)^5(b)^2(y)^2 + (a)^4(x)^4(b)^3(y)^3 + (a)^3(x)^3(b)^4(y)^4 + (a)^2(x)^2(b)^5(y)^5 + (a)(x)(b)^6(y)^6 + (b)^7(y)^7\\\\\\= (a)^7(x)^7+ (a)^6(b)(x)^6(y) + (a)^5(b)^2(x)^5(y)^2 + (a)^4(b)^3(x)^4(y)^3 + (a)^3(b)^4(x)^3(y)^4 + (a)^2(b)^5(x)^2(y)^5 + (a)(b)^6(x)(y)^6 + (b)^7(y)^7

We have that the coefficients of the first two terms are 128 and -224.

For the first term:

=> a^7 = 128

=> a = \sqrt[7]{128}\\ \\\\a = 2

For the second term:

a^6b = -224

b = \frac{-224}{a^6}

b = \frac{-224}{2^6} \\\\\\b = \frac{-224}{64} \\\\\\b = 3.5

Therefore, a = 2, b = 3.5

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