All categories

3 years ago

Help! Geometry question!! Photo attached!

Mathematics

1 answer:

jonny [76]3 years ago

3 0

The triangles are not the same size so a dilation made the original one smaller and a translation moved it to map ABC to A'B'C'.

You might be interested in

David earns 20% commission as a salesperson. He sold a hammock that cost $100. How much commission did David earn?

omeli [17]

He earned $20 because 20% of $100 is $20

6 0

2 years ago

In a recent year, the ACT scores for the math portion of the test were normally distributed, with a mean of 21.1 and a standard

Natali5045456 [20]

Answer:

a) $P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

b) $P(19$

And we can find this probability with this difference:

$P(-0.396$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-0.396$

c) $P(X>26)=P(\frac{X-\mu}{\sigma}>\frac{26-\mu}{\sigma})=P(Z>\frac{26-21.1}{5.3})=P(z>0.925)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.925)=1- P(Z$

d) We can consider unusual events values above or below 2 deviations from the mean

$Lower = \mu -2*\sigma = 21.1 -2*5.3 =10.5$

A value below 10.5 can be consider as unusual

$Upper = \mu +2*\sigma = 21.1 +2*5.3 =31.7$

A value abovr 31.7 can be consider as unusual

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(21.1,5.3)$

Where $\mu=21.1$ and $\sigma=5.3$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel:

$P(z$

Part b

$P(19$

And we can find this probability with this difference:

$P(-0.396$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-0.396$

Part c

$P(X>26)=P(\frac{X-\mu}{\sigma}>\frac{26-\mu}{\sigma})=P(Z>\frac{26-21.1}{5.3})=P(z>0.925)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.925)=1- P(Z$

Part d

We can consider unusual events values above or below 2 deviations from the mean

$Lower = \mu -2*\sigma = 21.1 -2*5.3 =10.5$

A value below 10.5 can be consider as unusual

$Upper = \mu +2*\sigma = 21.1 +2*5.3 =31.7$

A value abovr 31.7 can be consider as unusual

6 0

2 years ago

Help asap plsplspls!! :)

Dmitry_Shevchenko [17]

Converted to a decimal it’s -0.8

8 0

2 years ago

According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated e

slamgirl [31]

Answer:

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that $p = 0.09$

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

$P(X < 4) + P(X \geq 4) = 1$