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mina
2 months ago
15

Sara’s little brother is getting ready to color the picture of a rainbow that Sara drew for him. To make the task easier for her

brother, Sara picks out crayons that match the colors of the rainbow and places them in a box. She asks her brother to randomly pick two crayons from the box, one after the other. The probability that the first color is violet and the second is orange, if the first crayon is replaced, is . The probability that the first color is violet and the second is orange, if the first crayon is not replaced, is .
Mathematics
2 answers:
tester [12.3K]2 months ago
8 0

Answer:

1/7 and 1/42

Step-by-step explanation:

Zina [12.3K]2 months ago
8 0
There are seven rainbow colors: red, orange, yellow, green, blue, indigo, and violet, so 7 possible choices. When two events occur in sequence, multiply their probabilities. With replacement: P(violet)=1/7 and P(orange)=1/7, so P(violet then orange)=1/7 * 1/7 = 1/49. Without replacement: after picking violet, P(orange)=1/6, so P(violet then orange)=1/7 * 1/6 = 1/42.
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One sphere has a radius of 5.10 cm; another has a radius of 5.00cm. What is the difference in volume (in cubic centimeters) betw
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\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\qquad 
\begin{cases}
r=radius\\
-----\\
r_1=5.10\\
r_2=5
\end{cases}\implies \cfrac{V_1}{V_2}\implies \cfrac{\frac{4\pi \cdot 5.10^3}{3}}{\frac{4\pi \cdot 5^3}{3}}
\\\\\\
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2 months ago
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The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding
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Answer:

Based on the findings, we infer that the average cost of a wedding is lower than the $30,000 that was initially suggested.

Step-by-step explanation:

The following data set is provided: (in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}

where x_i denotes data points, \bar{x} represents the mean, and n indicates the number of samples.

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{236100}{8} = 29512.5

The sum of squares of the differences equals 3408750

S.D = \sqrt{\frac{3408750}{7}} = 697.82

The population mean, μ = $30,000

The sample mean, \bar{x} = $29512.5

Sample size, n = 8

Alpha, α = 0.05

Sample standard deviation, s = $697.82

Initially, we formulate the null hypothesis and the alternative hypothesis.

H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars} A one-tailed t-test will be conducted for this analysis.

Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

<pinserting the="" values="" we="" derive="">

t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975

<pnow>

t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894

<pgiven the="" situation="">

t_{stat} < t_{critical}

<pwe do="" not="" accept="" the="" null="" hypothesis="" and="" reject="" it.="">

Thus, we conclude that the average wedding cost is indeed less than the advertised $30,000.

</pwe></pgiven></pnow></pinserting>
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Express 9 ten thousandths in Scientific notation
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