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Ghella [55]
3 years ago
14

Henry is going to color a spinner with 8 equal-sized sections.Three of the sections will be blue and 5 of the sections will be p

urple. Is this spinner fair? If so explain why. If not explain how to make it a fair spinner
Mathematics
1 answer:
antoniya [11.8K]3 years ago
8 0

Answer:

The spinner is not fair

Step-by-step explanation:

Given

Sections = 8

Blue = 3

Purple = 5

Solving(a): Is it fair?

The spinner is not fair because the probability of an outcome of Blue does not equal the probability of obtaining Purple.

i.e.

P(Blue) = \frac{3}{8}

P(Purple) = \frac{5}{8}

\frac{3}{8} \ne \frac{5}{8}

Solving (b):

To make it fair, the blue sections and the purple sections must be made equal (4 each)

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What are the roots of the equation? x^2+24=14×
defon
\begin{gathered} x^2+24=14x \\ x^2-14x+24=0 \end{gathered}

Therefore,

\begin{gathered} x^2-14x+24=0 \\ x^2-2x-12x+24=0 \\ x(x-2)-12(x-2)=0 \\ (x-2)(x-12)=0 \\ x=2 \\ or\text{ } \\ x=12 \end{gathered}

6 0
1 year ago
I’ve been having trouble with these all week!
Kobotan [32]

Answer:


Step-by-step explanation:

so you will move constant to the right side and change the sign. 72x=223-7

then you will subtract the numbers 72x=223-7 and that will give you 72=216

then you will divide both sides by 72  and that will give you

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7 0
3 years ago
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Ellen divides a piece of fabric into 8 equal sections by drawing chalk lines. Then she cuts off 5 of the sections to make into p
zaharov [31]

Answer:

3/8

Step-by-step explanation:

Let us represent the total fabric as an integer = 1

Ellen divides a piece of fabric into 8 equal sections by drawing chalk lines.

= 1/8, hence each section = 1/8

Then she cuts off 5 of the sections to make into placemats.

This is written as: 5 sections × 1/8 = 5/8

The fraction of the fabric that is left is calculated as:

1 - 5/8

Lowest Common Denominator = 8

Hence: 8 - 5/8 = 3/8

The fraction of the fabric that is left is 3/8

8 0
3 years ago
Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ti
spayn [35]

Answer:

(a)D(x)=-2,500x+60,000

(b)R(x)=60,000x-2500x^2

(c) x=12

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500

Therefore, we have:

y=-2500x+b

At point (12,30000)

30000=-2500(12)+b\\b=30000+30000\\b=60000

Therefore:

D(x)=-2,500x+60,000

(b)Revenue

R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0

Therefore:

  • Optimal ticket price:$12
  • Maximum Revenue:$360,000

3 0
3 years ago
5000 is 1/10 of what
KatRina [158]
<span>The correct answer is 50,000.

Explanation<span>:
We can set up the equation 5000=1/10x to represent this situation.

To solve, we will divide both sides by 1/10:
5000</span></span>÷<span><span>(1/10) = (1/10x)</span></span>÷<span><span>(1/10)
5000</span></span>÷<span><span>(1/10) = x.

To divide fractions, flip the second one and multiply; this gives us
5000*(10/1) = x
50000 = x.</span></span>
8 0
3 years ago
Read 2 more answers
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