I need help please, Consider triangle ABC. Determine whether each statement is true of false.

ololo11 [35]

Answer:

y ≥ x² -2x -3
y ≤ x +3

Step-by-step explanation:

When matching graph to inequality, the first things to look for are the nature of the boundary line (solid or dashed), and the direction of shading relative to the boundary line (above or below, left or right).

<h3>Boundary line</h3>

The boundary line of the solution set of an inequality will be solid if the line is <em>included</em> in the solution. That is, the inequality will include the "or equal to" case. The corresponding inequality symbols are ≤ or ≥.

The boundary line of the solution set will be dashed if the line is <em>not included </em>in the solution. The corresponding inequality symbols are < or >.

<h3>Shading</h3>

The shading will be above the boundary line if the solution set includes larger y-values than those on the boundary. This will be the case when the inequality is of the form y > ( ) or y ≥ ( ).

For inequalities of the form y < ( ) or y ≤ ( ), the shading will be below the boundary line.

Similarly, the shading for an inequality of the form x > ( ) will be right of the boundary line, where x-values are greater. For inequalities of the form x < ( ), the shading will be to the left of the boundary line.

<h3>Application</h3>

In the given graph, both boundary lines are solid, so both inequalities will include the "or equal to" case. This eliminates choices A, B, D.

The shading is above the quadratic boundary line, and below the linear boundary line, so the inequalities can be expected to be of the forms ...

y ≥ x² +...
y ≤ x +...

These forms match choice C:

y ≥ x² -2x -3
y ≤ x +3

7 0

2 years ago

Let X equal the number of typos on a printed page with a mean of 4 typos per page.

timama [110]

Answer:

a) There is a 98.17% probability that a randomly selected page has at least one typo on it.

b) There is a 9.16% probability that a randomly selected page has at most one typo on it.

Step-by-step explanation:

Since we only have the mean, we can solve this problem by a Poisson distribution.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

In this problem, we have that $\mu = 4$

(a) What is the probability that a randomly selected page has at least one typo on it?

Thats is $P(X \geq 1)$ . Either a number is greater or equal than 1, or it is lesser. The sum of the probabilities must be decimal 1. So:

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

$P(X \geq 1) = 1 - P(X < 1)$

In which

$P(X < 1) = P(X = 0)$ .

So

$P(X = 0) = \frac{e^{-4}*4^{0}}{(0)!} = 0.0183$

$P(X \geq 1) = 1 - P(X < 1) = 1 - 0.0183 = 0.9817$

There is a 98.17% probability that a randomly selected page has at least one typo on it.

(b) What is the probability that a randomly selected page has at most one typo on it?

This is $P = P(X = 0) + P(X = 1)$ . So:

$P(X = 0) = \frac{e^{-4}*4^{0}}{(0)!} = 0.0183$

$P(X = 1) = \frac{e^{-4}*4^{1}}{(1)!} = 0.0733$

$P = P(X = 0) + P(X = 1) = 0.0183 + 0.0733 = 0.0916$

There is a 9.16% probability that a randomly selected page has at most one typo on it.

3 0

3 years ago

Order the numbers from least to greatest. <br> 0.5, <br> -2, <br> 1/4, <br> -6.3

adoni [48]

Answer:

Given

Step-by-step explanation:

We have:

0.5

-2.0

-6.3

1/4 = 0.25

So ordering from least to greatest the greater negative integer comes since it is to the far left on the number line to the greater positive integer. Therefore the answer is:-

-6.3, -2, 0.25, 0.5

= -6.3, -2, 1/4, 0.4

5 0

3 years ago

Read 2 more answers

Suppose that 100,000 men were screened for prostate cancer for the first time. Of these, 4,000 men had a positive result on the

Virty [35]

An actual two-by-two table is a tabular representation containing two rows and two columns.

The columns consist of the tested True positive for prostate cancer and tested True Negative for prostate cancer
The rows consist of the predicted positive screening and predicted negative values

Mathematically, the set-up of the two-by-two table for this data can be computed as:

Tested True Positive for cancer True Negative Total

Predicted Positive 800 3200 4000

Predicted Negative 100 95900 96000

Total 900 99100 100000

The prevalence rate of prostate cancer in this population is:

$\mathbf{ =\dfrac{900}{100000}}$

$\mathbf{ =\dfrac{9}{1000}}$

= 9 per thousand.

The calculation of the sensitivity of this screening is as follows:

$\mathbf{=\dfrac{TP}{TP+PN_1}}$

where;

TP = True positive for cancer
PN₁ = Predicted Negative for true positive cancer

∴

$\mathbf{=\dfrac{800}{800+100}}$

= 0.889

= 88.9%

The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.

The calculation of the specificity of this screening is as follows:

$\mathbf{=\dfrac{PN_2}{PN_2+TN}}$

where;

TN = True positive for cancer
PN₂ = Predicted Negative for true negative cancer

∴

$\mathbf{=\dfrac{95900}{95900+3200}}$

= 0.9677

= 96.77%

The interpretation shows that 96.7% of an actual negative is correctly identified as such.

The positive predicted value of the screening test is computed as:

$\mathbf{= \dfrac{TP}{TP + TN}}$

$\mathbf{= \dfrac{800}{800 + 3200}}$

= 0.2

= 20%

The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.

Learn more about tabular representation here:

brainly.com/question/8307968

6 0

2 years ago

What would the second point be with point (-2,-5) to get a line with the slope of -1

choli [55]

Answer:

A second point would be (-1, -6)

Step-by-step explanation:

Because the slope is -1, we know that for every number that x increases, we change y the amount of the slope. So, if we increase x by 1, we change y by -1.

x value

-2 + 1 = -1

y value

-5 - 1 = -6

3 0

3 years ago