Help please with these:

If a translation maps zl onto ZK, which of the following statements is true? G HS 1 K НІ is twice the measure of 2JK: GH is twic

murzikaleks [220]

9514 1404 393

Answer:

(d) ∠H ≅ ∠J

Step-by-step explanation:

We already know that ∠G is congruent to itself. If we show (by translation or other means) that ∠I ≅ ∠K, then we know that ΔGHI ~ ΔGJK. The third angle in each triangle will be congruent, too.

∠H ≅ ∠J

_____

The problem is concerned with angles, so the first two answer choices are irrelevant. If two angles are shown congruent, the triangles are congruent by AA similarity, so the third answer choice is incorrect.

6 0

3 years ago

Convert radians to degrees Show all the work 6. 3.8 radians 8. 5π/4(this is a fraction)

e-lub [12.9K]

Answer:

Below in bold.

Step-by-step explanation:

Degrees = radians * 180/π.

6. 3.8 radians = 3.8 * 180 / π

= 217.7 degrees to nearest hundredth.

8. 5π/4 radians = 5π/4 * 180/π

= 5*180/4

= 225 degrees.

8 0

3 years ago

Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper c

aalyn [17]

Answer:

a) This means that there is a 33% probability that one car chosen at random will have less than 49.5 tons of coal.

b) There is a 0.04% .probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal

Step-by-step explanation:

Problems of normally distributed samples can be 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:

The actual weights of coal loaded into each car are normally distributed, with mean = 50 tons and standard deviation = 0.9 ton. This means that $\mu = 50, \sigma = 0.9$

(a) What is the probability that one car chosen at random will have less than 49.5 tons of coal? (Round your answer to four decimal places.)

This is the pvalue of Z when $X = 49.5$

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

$Z = \frac{49.5 - 50}{0.9}$

$Z = -0.44$

$Z = -0.44$ has a pvalue of 0.33.

This means that there is a 33% probability that one car chosen at random will have less than 49.5 tons of coal.

(b) What is the probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal? (Round your answer to four decimal places.)

Now we have to use the standard deviation of the sample, since we are working with the sample mean. That is

$s = \frac{\sigma}{\sqrt{n}} = \frac{0.9}{\sqrt{35}} = 0.15$

Now, we find pvalue of Z when $X = 49.5$

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

$Z = \frac{49.5 - 50}{0.15}$

$Z = -3.33$

$Z = -3.33$ has a pvalue of 0.0004.

This means that there is a 0.04% .probability that 35 cars chosen at random will have a mean load weight of less than 49.5 tons of coal

7 0

3 years ago

A probability is the numeric value representing the _________, _________, or _________that a particular event will occur.

Nimfa-mama [501]

Answer:

chance; likelihood; possibility

Step-by-step explanation:

Probability is likelihood or the chance or the probability of the occurring of an event.

Probability is also the number of the ways of achieving the success. It is total number of the possible outcomes.

Thus, probability is:

$P=\frac {Number\ of\ favorable\ outcomes}{Total\ number\ of\ outcomes}$

4 0

4 years ago

What is this one?? -5-(15y-1)=2(7y-16)-y

sesenic [268]

Answer:

y=1

Step-by-step explanation:

Let's solve by opening the bracket first

-5-(15y-1)=2(7y-16)-y

Open the bracket

-5-15y+1=14y-32-y

Collect like terms

-5+1+32=14y-y+15y

-5+33=14y+14y

28=28y

Divide both sides by 28

y=1

Therefore the final answer is 1

3 0

3 years ago