State whether the equation is true, false, or an open sentence.

(50pts + brainliest) Which postulate can be used to prove that △BCA and △DAC are congruent?

kirza4 [7]

Not entirely sure if this is the right answer but angles BAC and ACD are the same because they are alternate angles. You can tell because of the parallel lines AB and CD they lie on. That could probably be how the triangles are congruent because they have the same angles... I’m just guessing

6 0

3 years ago

Read 2 more answers

A sample of 148 college students at a large university reports getting an average of 6.85 hours of sleep last night with a stand

nignag [31]

Answer:

70 students need to be surveyed.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

Assuming that the standard deviation of the above sample is a reasonable estimate of the standard deviation of sleep time at your university.

This means that $\sigma = 2.12$

How many students do you need to survey to estimate the mean sleep time of students at your university with 95% confidence and a margin of error of 0.5 hours?

n students need to be surveyed, and n is found when M = 0.5. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.5 = 1.96\frac{2.12}{\sqrt{n}}$

$0.5\sqrt{n} = 1.96*2.12$

Multiplying by 2 on both sides:

$\sqrt{n} = 1.96*4.24$

$(\sqrt{n})^2 = (1.96*4.24)^2$

$n = 69.1$

Rounding up

70 students need to be surveyed.

3 0

3 years ago

There are 620 students and 31 teachers at the Turner Middle School.There are 950 students and 38 teachers at the Green Middle Sc

kicyunya [14]

We begin with the Turner Middle School:
Ratio of students to teachers: $\frac{620}{31}$
Green Middle School:
Ratio of students to teachers: $\frac{950}{38}$
Let check that we cannot form a proportion:
$\frac{620}{31}=20\text{ and } \frac{950}{38}=25$
The two ratios are not equals so we cannot form a proportion.
Let x be the number of teachers that Green have to hire in order to make the two ratios equal. We get the equation:
 $\frac{950}{38+x}=\frac{620}{31}\text{ and we solve the equation like this:}\\38+x=\frac{950\times31}{620}=47.5 \text{ and then:}\\x=47.5-38=9.5$

The Green school need to hire 9 teachers.

Part-to-whole ratio:
Turner Middle School:
$\frac{620}{31+620}$
Green Middle School:
$\frac{950}{38+950}$

8 0

3 years ago

Read 2 more answers

Can someone please help me!

Irina18 [472]

A function WILL NOT have any repeating x values...they can have repeating y values, just not the x ones.

so ur function is { (1,2), (3,2), (5,7)}

7 0

3 years ago

30% of what number is 6

Hitman42 [59]

Answer:

20