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2 years ago

NEED HELP ASAP!!! thank you.

Mathematics

1 answer:

Alex17521 [72]2 years ago

7 0

Answer:

See explanation

Step-by-step explanation:

Consider triangles ACM and BCM. In these triangles,

$m\angle 3=m\angle 4$ - given;
$m\angle 1=m\angle 2=90^{\circ}$ - definition of perpendicular lines CM and AB;
$\overline{CM}\cong \overline{CM}$ - reflexive property.

So,

$\triangle ACM\cong \triangle BCM$ by ASA postulate (if one side and two angles adjacent to this side of one triangle are congruent to one side and two angles adjacent to this side of another triangle, then two triangles are congruent).

Two-column proof:

Statement Reason

1. $m\angle 3=m\angle 4$ Given

2. $CM\perp AB$ Given

3. $m\angle 1=m\angle 2=90^{\circ}$ Definition of perpendicular lines CM and AB

4. $\overline{CM}\cong \overline{CM}$ Reflexive property

5. $\triangle ACM\cong \triangle BCM$ ASA postulate

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Step-by-step explanation:

This explanation uses a z-score table where each $z$ entry has two decimal places.

Let $\mu$ represent the mean of a normal distribution of variable $X$ . Let $\sigma$ be the standard deviation of the distribution. The z-score for the observation $x$ would be:

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The question is asking for the probability $P(225 \le X \le 245)$ (where $X$ is between two values.) In this case, that's the same as $P(-1.61 \le Z \le 0.54)$ .

Keep in mind that the probabilities on many z-table correspond to probability of $P(Z \le z)$ (where $Z$ is no greater than one value.) Therefore, apply the identity $P(z_1 \le Z \le z_2) = P(Z \le z_2) - P(Z \le z_1)$ to rewrite $P(-1.61 \le Z \le 0.54)$ as the difference between two probabilities:

$P(-1.61 \le Z \le 0.54) = P(Z \le 0.54) - P(Z \le -1.61)$ .

Look up the z-table for $P(Z \le 0.54)$ and $P(Z \le -1.61)$ :

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$P(Z \le -1.61) \approx 0.05370$ .

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