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creativ13 [48]
2 years ago
11

Triangle ABC

Mathematics
2 answers:
Stolb23 [73]2 years ago
8 0

▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪

Let's solve for value of values of x and y ~

According to Angle sum property of triangles :

\qquad \sf  \dashrightarrow \: 70 \degree + 58\degree + x = 180\degree

\qquad \sf  \dashrightarrow \: x\degree + 128\degree = 180\degree

\qquad \sf  \dashrightarrow \:x =  180\degree - 128\degree

\qquad \sf  \dashrightarrow \: x = 52\degree

Now, solve for y ~

\qquad \sf  \dashrightarrow \: 70\degree + 49\degree + y = 180\degree

\qquad \sf  \dashrightarrow \:  y + 119 = 180\degree

\qquad \sf  \dashrightarrow \:  y =  180  -  119\degree

\qquad \sf  \dashrightarrow \:  y = 61 \degree

Now, by the results we got, we can conclude that :

The two triangles are not similar because 70 + 58 + x = 180 means x = 52° and 70 + 49 + y=180 means y = 61°

Vlad [161]2 years ago
7 0

» Let's solve for value of values of x and y

⛥Solve for x :

⟿70° +58° + x = 180°

⟿x + 128° = 180°

⟿x = 180° - 128°

⟿x = 52°

⛥Solve for y :

⟿70° +49° + y = 180°

⟿y+119 = 180°

⟿y = 180 - 119°

⟿y = 61°

The two triangles are not similar because

70 +58 + x = 180 means x = 52°

70 + 49 + y = 180° means y = 61°

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Answer:

\mu_p -\sigma_p = 0.74-0.0219=0.718

\mu_p +\sigma_p = 0.74+0.0219=0.762

68% of the rates are expected to be betwen 0.718 and 0.762

\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696

\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784

95% of the rates are expected to be betwen 0.696 and 0.784

\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674

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Step-by-step explanation:

Check for conditions

For this case in order to use the normal distribution for this case or the 68-95-99.7% rule we need to satisfy 3 conditions:

a) Independence : we assume that the random sample of 400 students each student is independent from the other.

b) 10% condition: We assume that the sample size on this case 400 is less than 10% of the real population size.

c) np= 400*0.74= 296>10

n(1-p) = 400*(1-0.74)=104>10

So then we have all the conditions satisfied.

Solution to the problem

For this case we know that the distribution for the population proportion is given by:

p \sim N(p, \sqrt{\frac{p(1-p)}{n}})

So then:

\mu_p = 0.74

\sigma_p =\sqrt{\frac{0.74(1-0.74)}{400}}=0.0219

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

\mu_p -\sigma_p = 0.74-0.0219=0.718

\mu_p +\sigma_p = 0.74+0.0219=0.762

68% of the rates are expected to be betwen 0.718 and 0.762

\mu_p -2*\sigma_p = 0.74-2*0.0219=0.696

\mu_p +2*\sigma_p = 0.74+2*0.0219=0.784

95% of the rates are expected to be betwen 0.696 and 0.784

\mu_p -3*\sigma_p = 0.74-3*0.0219=0.674

\mu_p +3*\sigma_p = 0.74+3*0.0219=0.806

99.7% of the rates are expected to be betwen 0.674 and 0.806

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