Z=25/5 what is the next step in the equation solving sequence.

Triangle A B C is reflected over side A C and then is dilated to form smaller triangle D E C. Angles B C A and D C E are right a

andreyandreev [35.5K]

Answer:

A. △ABC ~ △DEC

B. ∠B ≅ ∠E

D. 3DE = 2AB

Step-by-step explanation:

Transformation involves the reshaping or resizing of a given figure. The types are: reflection, dilation, rotation and translation.

In the given question, the two operations performed on triangle ABC are reflection and dilation to form triangle DEC. The length of each side of triangle DEC is two-third of that of ABC. Therefore, the correct statements about the two triangles are:

i. △ABC ~ △DEC

ii. ∠B ≅ ∠E

iii. 3DE = 2AB

4 0

2 years ago

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 265 minu

pochemuha

Answer:

a) 0.691 = 69.1% probability that a battery lasts more than four hours

b) 25% value = 231

75% value = 299

c) 183 minutes

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 265, \sigma = 50$

a) What is the probability that a battery lasts more than four hours?

4 hours = 4*60 = 240 minutes

This is 1 subtracted by the pvalue of Z when X = 240. So

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

$Z = \frac{240 - 265}{50}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.309

1 - 0.309 = 0.691

0.691 = 69.1% probability that a battery lasts more than four hours

b) What are the quartiles (the 25% and 75% values) of battery life?

25th percentile:

X when Z has a pvalue of 0.25. So X when Z = -0.675

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

$-0.675 = \frac{X - 265}{50}$

$X - 265 = -0.675*50$

$X = 231$

75th percentile:

X when Z has a pvalue of 0.75. So X when Z = 0.675

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

$0.675 = \frac{X - 265}{50}$

$X - 265 = 0.675*50$

$X = 299$

25% value = 231

75% value = 299

c) What value of life in minutes is exceeded with 95% probability?

The 100-95 = 5th percentile, which is the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.

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

$-1.645 = \frac{X - 265}{50}$

$X - 265 = -1.645*50$

$X = 183$

8 0

2 years ago

A salesman must commute 1 hour and 48 minutes from his house to the airport, fly to another city and take a bus to his destinati

irina [24]

5 hours and 54 minutes.

4 0

2 years ago

Read 2 more answers

Legalization of marijuana, Part I. The 2010 General Social Survey asked 1,578 US res- idents: \Do you think the use of marijuana

mixer [17]

Answer:

Step-by-step explanation:

a) Sample statistics are used to estimate population value. Since 48% is a sample proportion, therefore, it is a sample statistic.

b) For 95% confidence level, z* = 1.96.

\hat{p}\pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}= 0.61\pm 0.61\sqrt{\frac{0.61(1-0.61)}{1578}}=0.61\pm 0.024 \ or (0.586, 0.634).

We are 95% confident that the true proportion of US residents who think marijuana should be made legal lies between 58.6% and 63.4%.

c)

\\np=1578(0.61)=962.58

\\n(1-p)=1578(1-0.61)=615.42

Since both np and n(1-p), are at least 10, the normal model is a good approximation for these data.

d) As the lower limit of confidence interval is less than 0.5, less than 50% population is also a plausible value of true proportion. This means the statement "Majority of Americans think marijuana should be legalized" is not justified.

4 0

2 years ago

A rectangular field is enclosed by 360 feet of fencing. What is the length, in feet, of the field if it’s length is 6 feet more

Orlov [11]

Answer:

The Field's length is 93ft

Step-by-step explanation:

P=2L+2w

360=2(w+6)+2w

360=2w+12+2w

360=4w+12

348=4w

348/4=w

87=w

L=w+6

L=87+6

L=93

7 0

2 years ago