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3 years ago

What is the measure of ∠ABC ?

Mathematics

2 answers:

PtichkaEL [24]3 years ago

7 0

Answer:

m∠ACB = 32°

Step-by-step explanation:

It is given in the question that AC is tangent on a circle at A.

m∠ACB = 58° then we have to tell the measurement of ∠ABC.

In ΔABC, ∠BAC = 90° (since radius of a circle is always ⊥ to the tangent drawn)

Therefore in ΔABC

∠ABC + ∠BAC + ∠ACB = 180°

∠ACB + 90 + 58 = 180

∠ACB = 180 - (90 + 58) = 180 - 148 = 32°

Finally m∠ ACB = 32° is the answer.

il63 [147K]3 years ago

5 0

I think the answer is 32 degrees but i am not 100% sure

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2 years ago

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2 years ago

If we wanted to create a new 90% confidence interval from a different sample for the proportion of those with a two on one date

slava [35]

Answer: 271

Step-by-step explanation:

The formula we use to find the sample size is given by :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

, where $z_{\alpha/2}$ is the two-tailed z-value for significance level of $(\alpha)$

p = prior estimation of the proportion

E = Margin of error.

If prior estimation of the proportion is unknown, then we take p= 0.5 , the formula becomes

$n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2$

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2$

Given : Margin of error : E= 0.05

Confidence level = 90%

Significance level $\alpha=1-0.90=0.10$

Using z-value table , Two-tailed z-value for significance level of $0.10$

$z_{\alpha/2}=1.645$

Then, the required sample size would be :

$n=0.25(\dfrac{1.645}{0.05})^2$

Simplify,

$n=270.6025\approx271$

Hence, the required minimum sample size =271

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3 years ago