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3 years ago

Are the two triangles similar? How do you know?

Mathematics

2 answers:

Readme [11.4K]3 years ago

7 0

Answer. C (yes; by SAS)

We know that opposite angles formed by the intersection of two lines are congruent:
Therefore, Angle HMG ≅ Angle JMK

Line HM : Line MK
= 8:12
= 2:3

Line GM : Line MJ
= 6:9
= 2:3

Therefore,
HM ≅ MK
GM ≅ MJ

Therefore, we have one pair of congruent angles, and a pair of congruent sides.
⇒ The two triangles are congruent by SAS theorem.

dedylja [7]3 years ago

5 0

Answer

nvmd I'm on the wrong question

SAS should be right

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A tobacco company claims that the amount of nicotene in its cigarettes is a random variable with mean 2.2 and standard deviation

Aleksandr-060686 [28]

Answer:

0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.

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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 2.2, \sigma = 0.3, n = 100, s = \frac{0.3}{\sqrt{100}} = 0.03$

What is the approximate probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true?

This is 1 subtracted by the pvalue of Z when X = 3.1. So

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

By the Central Limit Theorem

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

$Z = \frac{3.1 - 2.2}{0.03}$

$Z = 30$

$Z = 30$ has a pvalue of 1.

1 - 1 = 0

0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.

4 0

3 years ago

Assume you have such a watch. if a minimum of 18.0% of the original tritium is needed to read the dial in dark places, for how m

laila [671]

Given that the half life of 3H is 12.3 years.

The amount of substance left of a radioactive substance with half life of $t_{ \frac{1}{2} }$ after t years is given by

$N(t)=N_0\left(\frac{1}{2} \right)^{ \frac{t}{t_{\frac{1}{2}} }$

Therefore, the number of years it will take for 18% of the original tritinum to remain is given by

$18 \% = 100 \% \left(\frac{1}{2} \right)^{ \frac{t}{12.3}} \\ \\ \Rightarrow\left(\frac{1}{2} \right)^{ \frac{t}{12.3}} =0.18 \\ \\ \Rightarrow\frac{t}{12.3}\ln\left(\frac{1}{2} \right)=\ln0.18 \\ \\ \Rightarrow\frac{t}{12.3}= \frac{\ln0.18}{\ln\left(\frac{1}{2} \right)} = \frac{-1.715}{-0.6931} =2.474\\ \\ \Rightarrow t=2.474(12.3)=30.4$

Therefore, the number of <span>years that the time could be read at night is 30.4 years.</span>

5 0

3 years ago

In 2009, a town's population was about 9,000 residents. In 2014, the population was about 12,500 residents. Which linear model r

jek_recluse [69]

Answer:

The linear function that discribes the size of the population in function of the t in years is p = 700t - 1,397,300

Step-by-step explanation:

A linear function is defined by a line, so in order to determine the linear function we can use the two points that were given to us to create a line equation and use that as our linear function. The points given to us were (2009; 9000) and (2014; 12500), in this case the year is our value of "x" and the size of the population is our value of "y". The first step is to find the slope of the line which is given by:

m = (y2 - y1)/(x2 - x1)

m = (12500 -9000)/(2014 - 2009) = 3500/5 = 700

Then we can use the slope and the first point to build the equation:

p - 9000 = 700*(t - 2009)

p = 700t - 1406300 + 9000

p = 700t - 1397300

5 0

3 years ago

Carl has 9 1/2 cups of juice for a party. If each party goer gets exactly 3/5 cup of juice each, how many party goers will get t

topjm [15]

Answer: 158

Step-by-step explanation:

Okay so the total is 9 5/10.

Each party goer needs 6/10

So 95/10 / 6/0=. 95/10x10/6

=950/6 = 158.

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2 years ago

A map has a scale of 1 cm : 5 km. Determine how far apart two cities are if they are 4 cm apart on the map?

Kay [80]

Answer:

he is right its A

Step-by-step explanation:

5 0

3 years ago