Given the triangles below what congruence theorem would prove that the two triangles were congruent.

The radius of a circle is 3 what is the circumference?

Alika [10]

Answer:

6π

Step-by-step explanation:

You have to use the formula for the circumference of a circe:

Circumference = π(diameter)

However, you do not have the diameter, you have the radius.

Diameter = radius * 2

Diameter = 3 * 2

D = 6

Now you can substitute this value back into the Circumference formula:

C = πd

C = 6π

4 0

4 years ago

If a = 7, b = 3, and c = 5, then 4a − 3c =

serious [3.7K]

4a-3c=4×a-3×c

=4×7-3×5

=28-15

=13 this is the correct answer

I hope this answer help you

8 0

3 years ago

The amount of money spent on textbooks per year for students is approximately normal.

Ostrovityanka [42]

Answer:a

a

$336.04 < \mu < 443.96$

b

The margin of error will increase

c

The margin of error will decreases

d

The 99% confidence interval is $0.4107 < p < 0.4293$

Step-by-step explanation:

From the question we are told that

The sample size $n = 19$

The sample mean is $\= x = \$\ 390$

The standard deviation is $\sigma = \$ \ 120$

Given that the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

So

$Z_{\frac{\alpha }{2} } = 1.96$

The margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }$

=> $E = 1.96 * \frac{120}{\sqrt{19} }$

=> $E = 53.96$

The 95% confidence interval is

$\= x - E < \mu < \= x + E$

=> $390 - 53.96 < \mu < 390 - 53.96$

=> $336.04 < \mu < 443.96$

When the confidence level increases the $Z_{\frac{\alpha }{2} }$ also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

$n \ \ \alpha \ \ \frac{1}{E^2 }$

So if the sample size increases the margin of error decrease

The sample proportion is mathematically represented as

$\r p = \frac{210}{500}$

$\r p = 0.42$

Given that the confidence level is 0.99 the level of significance is $\alpha = 0.01$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }$

=> $E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }$

=> $E = 0.0093$

The 99% confidence interval is

$\r p - E < p < \r p + E$

$0.42 - 0.0093 < p < 0.42 + 0.0093$

$0.4107 < p < 0.4293$

4 0

4 years ago

9. Alby says that the numbers in Pascal's Triangle are the values of the exponents on the variables in a binomial expansion. Is

Luba_88 [7]

Answer:

yes alby is correct

Step-by-step explanation:

4 0

4 years ago

Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are freshmen an

Georgia [21]

Answer: The probability is P = 0.1667 or 16.67%

Step-by-step explanation:

We have 2 slots and 4 possible options.

In the options, we have 2 freshmen and 2 sophomores, and we want to find the probability that the 2 slots are filled with freshmen.

The probability for a freshman to be randomly selected is:

p1 = (number of freshmen)/(number of options) = 2/4 = 1/2

now, for the second selection, we only have 1 freshman and 2 sophomores, so the probability now is:

p2 = 1/3

now, the joint probability of both events happening is equal to the product of the individual probabilities, this is:

P = p1*p2 = (1/3)*(1/2) = 1/6 = 0.1667

if we want the percentage, we must multiply this number by 100%:

P = 0.1667 or 16.67%

4 0

3 years ago

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