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3 years ago

True or false and why: Angles that are congruent are also equal

Mathematics

1 answer:

taurus [48]3 years ago

7 0

Answer: True

Angles are congruent if they have the same angle measure in degrees. They can be at any orientation on the plane. In the figure above, there are two congruent angles. Note they are pointing in different directions.

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In a circle, a 90° sector has area 64π ft2. Solve for the radius of the circle. A. 16 ft. B. 12 ft. C. 18 ft. D. 8 ft.

SSSSS [86.1K]

The answer is A. Working the formula backwards you get that r^2=256, so r=16

3 0

3 years ago

Read 2 more answers

The effect of a monetary incentive on performance on a cognitive task was investigated. The researcher predicted that greater mo

riadik2000 [5.3K]

Answer:

1) $H_0:\mu_5=\mu_{25}=\mu_{50}$

2) $H_a:\mu_{50}>\mu_{25}>\mu_{5}$

3) A Type I error happens when we reject a null hypothesis that is true. In this case, that would mean that the conclusion is that there is evidence to support the claim that the greater the incentive, the more puzzles are solved, but that in reality there is no significant difference.

4) A Type II error happens when a false null hypothesis is failed to be rejected. In this case, that would mean that there is no enough evidence to support the claim that the greater the incentive, the more puzzles are solved, but in fact this is true.

5) The probability of a Type I error is equal to the significance level, as this is the chance of having a sample result that will make the null hypothesis be rejected.

Step-by-step explanation:

As the claim is that the greater the incentive, the more puzzles were solved, the null hypothesis will state that this claim is not true. That is that there is no significant relation between the incentive and the amount of puzzles that are solved. In other words, the mean amount of puzzles solved for the different incentives is equal (or not significantly different):

$H_0:\mu_5=\mu_{25}=\mu_{50}$

The research (or alternative hypothesis) is that the greater the incentive, the more puzzles were solved. That means that the mean puzzles solved for an incentive of 50 cents is significantly higher than the mean mean puzzles solved for an incentive of 25 cents and this is significantly higher than the mean puzzles solved for an incentive of 5 cents.

$H_a:\mu_{50}>\mu_{25}>\mu_{5}$

A Type I error happens when we reject a null hypothesis that is true. In this case, that would mean that the conclusion is that there is evidence to support the claim that the greater the incentive, the more puzzles are solved, but that in reality there is no significant difference.

A Type II error happens when a false null hypothesis is failed to be rejected. In this case, that would mean that there is no enough evidence to support the claim that the greater the incentive, the more puzzles are solved, but in fact this is true.

The probability of a Type I error is equal to the significance level, as this is the chance of having a sample result that will make the null hypothesis be rejected.

4 0

3 years ago

You pick a card at random from an ordinary deck of 52 cards. If the card is an ace, you get 9 points; if not, you lose 1 point.

Andreyy89

Answer:

$a = 9\\b = 48\\c = -1$

Step-by-step explanation:

We know that:

In a deck of 52 cards there are 4 aces.

Therefore the probability of obtaining an ace is:

P (x) = 4/52

The probability of not getting an ace is:

P ('x) = 1-4 / 52

P ('x) = 48/52

In this problem the number of aces obtained when extracting cards from the deck is a discrete random variable.

For a discrete random variable V, the expected value is defined as:

$E(V) = VP(V)$

Where V is the value that the random variable can take and P (V) is the probability that it takes that value.

We have the following equation for the expected value:

$E(V) = \frac{4}{52}(a) + \frac{b}{52}(c)$

In this problem the variable V can take the value V = 9 if an ace of the deck is obtained, with probability of 4/52, and can take the value V = -1 if an ace of the deck is not obtained, with a probability of 48 / 52

Therefore, expected value for V, the number of points obtained in the game is:

$E(V) = \frac{4}{52}(9) + \frac{48}{52}(-1)$