Enter the equation of the circle with the given center and radius.

CAN SOMEONE HELP ME WITH THESE QUESTIONS PLEASE

Lady_Fox [76]

Answer:

17. A

18. B

Step-by-step explanation:

<u>17.</u> We need to find the longest side length. Remember that in a triangle, the smallest angle corresponds to the shortest side length and the largest angle corresponds to the longest side length.

Here, we already know two angles are 75 and 60, which means that the third angle is 180 - 75 - 60 = 45 (because all angles of a triangle add up to 180). Since 45 is the smallest angle, it corresponds to the shortest side, which we know is 10 units. Since 75 is the largest angle, it corresponds to the longest side, which we want to find.

We now use the Law of Sines, which states that for a triangle with side lengths a, b, and c and angles A, B, and C:

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

Here, let's say that a = 10, A = 45, and B = 75. Then:

$\frac{a}{sinA} =\frac{b}{sinB}$

$\frac{10}{sin(45)} =\frac{b}{sin(75)}$

Remember that sin(45) = √2/2 and sin(75) = (√2 + √6) / 4. Plug these in and solve for b, which is the longest side we want to find:

b = [(√2 + √6) / 4] * [10 / (√2/2)] = 5 + 5√3 = 5(1 + √3)

The answer is thus A.

<u>18.</u> We need to use trigonometry for this. Notice that in triangle ABC, we can write the tangent (which is opposite divided by adjacent) expression:

tan(30) = BC / AB = h / (4 + x)

Remember that tan(30) = √3/3. So:

h/(4 + x) = √3/3

Now we can also write a tangent expression for triangle BDC:

tan(60) = BC / DB = h/x

Remember that tan(60) = √3, so:

h/x = √3

We're looking for x, so write h in terms of x from the second equation:

h/x = √3

h = x√3

Plug this in for h in the first equation:

h/(4 + x) = √3/3

(x√3) / (4 + x) = √3/3

x√3 = (4√3 / 3) + x√3/3

x√3 - x√3/3 = 4√3/3

2x√3/3 = 4√3/3

x = 2

The answer is thus B.

7 0

3 years ago

Which lines are parallel? Justify your answer.

svlad2 [7]

Answer:

It's C

Step-by-step explanation:

I just took the test :)

7 0

3 years ago

Read 2 more answers

ANSWER ASAP WILL GIVE BRAINLIEST PLS HELP

jeka57 [31]

Answer:

Step-by-step explanation:

11) Probability of Black is 1/4

12) P of not orange is 3/4

13) P of blue or black is 1/2

this should be pretty easy for you, why is it tough? don't say .. " it just is" say what makes it tough. I'm curious why this is difficult. :?

3 0

3 years ago

Ms Feheley buys 9 bottles of eye of Newt for the same price, and also a new couldron for $9.45. She spent $118.89. How much did

scoundrel [369]

See picture for answer and solution steps.

4 0

3 years ago

Read 2 more answers

Some scientists believe alcoholism is linked to social isolation. One measure of social isolation is marital status. A study of

frez [133]

Answer:

1) H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

2) The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

3) $\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72$

4) $df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.72,2,TRUE)"

Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total

Married 21 37 58 116

Not Married 59 63 42 164

Total 80 100 100 280

Part 1

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

The level os significance assumed for this case is $\alpha=0.05$

Part 2

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

Part 3

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{80*116}{280}=33.143$

$E_{2} =\frac{100*116}{280}=41.429$

$E_{3} =\frac{100*116}{280}=41.429$

$E_{4} =\frac{80*164}{280}=46.857$

$E_{5} =\frac{100*164}{280}=58.571$

$E_{6} =\frac{100*164}{280}=58.571$

And the expected values are given by:

Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total

Married 33.143 41.429 41.429 116

Not Married 46.857 58.571 58.571 164

Total 80 100 100 280

And now we can calculate the statistic:

$\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72$

Part 4

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(19.72,2,TRUE)"

Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.

7 0

4 years ago