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dem82 [27]
3 years ago
12

Janelle was trying to find the distance between (3,7) and (9,6) in the coordinate plane. She knew the formula was D=√(9 - 3)^2 +

(6 - 7)^2. So she took the square root and got (9-3)+(6-7)=5. Did she get the correct answer? Explain.
Mathematics
1 answer:
s2008m [1.1K]3 years ago
5 0
Hello : 
incorrect  answer because : 
\sqrt{ a^{2} + b^{2} }  \neq   \sqrt{ a^{2} } + \sqrt{ b^{2}}  \neq a+b
but : 
\sqrt{ (a+b)^{2} } = a+b........a+b <span>≥ 0</span>
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According to a survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the populati
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Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: number of daily text messages a high school girl sends.

This variable has a population standard deviation of 20 text messages.

A sample of 50 high school girls is taken.

The is no information about the variable distribution, but since the sample is large enough, n ≥ 30, you can apply the Central Limit Theorem and approximate the distribution of the sample mean to normal:

X[bar]≈N(μ;δ²/n)

This way you can use an approximation of the standard normal to calculate the asked probabilities of the sample mean of daily text messages of high school girls:

Z=(X[bar]-μ)/(δ/√n)≈ N(0;1)

a.

P(X[bar]<95) = P(Z<(95-100)/(20/√50))= P(Z<-1.77)= 0.03836

b.

P(95≤X[bar]≤105)= P(X[bar]≤105)-P(X[bar]≤95)

P(Z≤(105-100)/(20/√50))-P(Z≤(95-100)/(20/√50))= P(Z≤1.77)-P(Z≤-1.77)= 0.96164-0.03836= 0.92328

I hope you have a SUPER day!

3 0
3 years ago
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