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3 years ago

Identify which triangles are congruent, and explain your answer.

Mathematics

2 answers:

Paha777 [63]3 years ago

7 0

I believe that A and D would be the correct answer. Because both are 30,60,90 triangles and would be congruent. The other 2 triangles only have 1 angle and their side measures are at two different places meaning they cannot be congruent.

Marina86 [1]3 years ago

6 0

This is a 30-60-90 triangle. Following the pattern of x, $x \sqrt{3}$ , and 2x. So lets us look for that pattern in these triagles.
Judging from what I know, the answer is A and C.
They hypotenuse is 2 times the shorter leg, which is evident here. B and D are incorrect, since if the longer leg is 18, then the smaller leg would be a large square root , possibly a number in the mid 500s being squared.
Hope this helps

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Answer:

We conclude that the machine is under filling the bags.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 436.0 gram

Sample mean, $\bar{x}$ = 429.0 grams

Sample size, n = 40

Alpha, α = 0.05

Population standard deviation, σ = 23.0 grams

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 436.0\text{ grams}\\H_A: \mu < 436.0\text{ grams}$

We use one-tailed(left) z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{429 - 436}{\frac{23}{\sqrt{40}} } = -1.92$

Now, $z_{critical} \text{ at 0.05 level of significance } = -1.64$

Since,

$z_{stat} < z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that the machine is under filling the bags.

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3 years ago

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2 years ago

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Answer:

I believe there are 70 students in the theater!

Step-by-step explanation:

In the ratio 2:3 going to 28:? there is a pattern. You multiply 2 by 14 to get to 28, so if you multiply 3 by 14 you get 42. Add 42 to 28 for the total amount of students in class!

Have a nice night!

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2 years ago

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