14. In a pattern that starts with 5, the next

DBE is obtained by enlarging ABC. If the area of ABC is 3 square units, what is the area of DBE?

Dennis_Churaev [7]

In two similar triangles, like the one we see above, the ratio of their areas is the square of the ratio of their sides.

Based on the graph, we see that BD is 3 times larger than BA. This means that the area of DBE will be 3² times larger, or 9 times larger, than the area of ABC.

Area of ABC = 3 square units
Area of DBE = 3 * 9 = 27 square units
Answer is A.

5 0

3 years ago

110% OF WHAT NUMBER IS 880? SHOW EVERY STEP PLZ:)

Nookie1986 [14]

So 110% of x is 880 means 1.1x=880

so 1.1x=880
multiply both sides by 10
11x=8800
divide both sides by 11
8800=88 times 100 88=8 times 11
8800/11=800
x=800

5 0

4 years ago

Read 2 more answers

What is the correct order of the numbers from least to greatest. 1/2, 0.6, 6%, 6/5

Anton [14]

Answer:

6%, 1/2, 0.6, 6/5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Test scores of the student in a school are normally distributed mean 85 standard deviation 3 points. What's the probability that

Mrrafil [7]

Answer:

The probability that a random selected student score is greater than 76 is $\\ P(x>76) = 0.99865$ .

Step-by-step explanation:

The Normally distributed data are described by the normal distribution. This distribution is determined by two parameters, the population mean $\\ \mu$ and the population standard deviation $\\ \sigma$ .

To determine probabilities for the normal distribution, we can use the standard normal distribution, whose parameters' values are $\\ \mu = 0$ and $\\ \sigma = 1$ . However, we need to "transform" the raw score, in this case x = 76, to a z-score. To achieve this we use the next formula:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

And for the latter, we have all the required information to obtain z. With this, we obtain a value that represent the distance from the population mean in standard deviations units.

<h3>The probability that a randomly selected student score is greater than 76</h3>

To obtain this probability, we can proceed as follows:

First: obtain the z-score for the raw score x = 76.

We know that:

$\\ \mu = 85$

$\\ \sigma = 3$

$\\ x = 76$

From equation [1], we have:

$\\ z = \frac{76 - 85}{3}$

Then

$\\ z = \frac{-9}{3}$

$\\ z = -3$

Second: Interpretation of the previous result.

In this case, the value is three (3) standard deviations below the population mean. In other words, the standard value for x = 76 is z = -3. So, we need to find P(x>76) or P(x>-3).

With this value of $\\ z = -3$ , we can obtain this probability consulting the cumulative standard normal distribution, available in any Statistics book or on the internet.

Third: Determination of the probability P(x>76) or P(x>-3).

Most of the time, the values for the cumulative standard normal distribution are for positive values of z. Fortunately, since the normal distributions are symmetrical, we can find the probability of a negative z having into account that (for this case):

$\\ P(z>-3) = 1 - P(z>3) = P(z$

Then

Consulting a cumulative standard normal table, we have that the cumulative probability for a value below than three (3) standard deviations is:

$\\ P(z$

Thus, "the probability that a random selected student score is greater than 76" for this case (that is, $\\ \mu = 85$ and $\\ \sigma = 3$ ) is $\\ P(x>76) = P(z>-3) = P(z$ .