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2 years ago

Pls help. What is the appropriate congruent for these triangles

Mathematics

1 answer:

Leviafan [203]2 years ago

5 0

Answer:

C. HL

Step-by-step explanation:

The diagram given shows that the hypotenuse length and the length of a leg of one right triangle is congruent to the hypotenuse and corresponding leg length of the other. Based on Hypotenus-Leg criterion, the two right triangles is proved to be congruent because it meets the criterion of HL.

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There are 31 motor scooters on a used car lot, along with 67 other vehicles.

just olya [345]

Answer:

31/98

Step-by-step explanation:

31 motor scooters

67 other vehicles

31 + 67 total vehicles

31 + 67 = 98

The probability is motor scooters/total vehicles

31/98 is the answer.

4 0

3 years ago

Which diagonal (IE or KT) is the line of symmetry for kite KITE below? Explain.

Leviafan [203]

Answer:

Step-by-step explanation:

KT because triangles KIT and KET are congruent ( mirror images).

6 0

2 years ago

Prove or disprove that the circle with equation x^2-4x+y^2=-3 intersects the y axis

wel

The general equation given is x^2 - 4x + y^2 = -3. Transform this to an equation of a circle of the form x^2 + y^2 = r^2.

Use completing the square method:

x^2 - 4x + 4 + y^2 = -3 + 4
(x - 2)^2 + y^2 = 1

the center of the circle is (2,0) and r = 1

To check if it intersects the y axis, find the value of the x-intercept.

7 0

3 years ago

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.8. (Round your ans

Alenkinab [10]

Answer:

a) 0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51

b) 0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 50, \sigma = 1.8$

(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 17 pins is at least 51?

Here $n = 17, s = \frac{1.8}{\sqrt{17}} = 0.4366$

This probability is 1 subtracted by the pvalue of Z when X = 51. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{51 - 50}{0.4366}$

$Z = 2.29$

$Z = 2.29$ has a pvalue of 0.9890

1 - 0.989 = 0.011

0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 45 pins is at least 51?

Here $n = 17, s = \frac{1.8}{\sqrt{45}} = 0.2683$

$Z = \frac{X - \mu}{s}$

$Z = \frac{51 - 50}{0.0.2683}$

$Z = 3.73$

$Z = 3.73$ has a pvalue of 0.9999

1 - 0.9999 = 0.0001

0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51

8 0

3 years ago

What is the measure of Zc<br>

maks197457 [2]

Answer: 56 degrees

Step-by-step explanation:

We know that angle between b and c is 90 degrees. Because there is a line dividing angles a and b from 124 and c, we also know that each side is 180 degrees (a and b add to 180, and 124 and c add to 180).

124 and c are supplementary angles. We can represent this in an equation to solve for c:

$124 + c = 180\\\\c = 56$

3 0

3 years ago