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2 years ago

Determine whether each of these sets is the power set of a set, where a and b are distinct elements.

1 answer:

4 0

A. $\varnothing$ cannot be the power set of any set. Consult Cantor's theorem, which says that the cardinality of the power set of any set (even the empty set) is strictly greater than the cardinality of the set.

(No part b?)

c. Also not the power set of any set, because any power set must have $2^n$ elements, where $n$ is the cardinality of the original set. The cardinality of this set is 3, but there is no integer $n$ such that $2^n=3$ . This set would be a power set if $\{\varnothing\}$ (that is, the set containing the empty set) were a member of it.

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Which would prove that ΔABC ~ ΔXYZ? Select TWO options.

gulaghasi [49]

Answer:

$\frac{BA}{YX}=\frac{BC}{YZ}$ , ∠C ≅∠Z

$\frac{AC}{XZ}=\frac{BA}{YX}$ , ∠A≅∠X

$\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}$

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding sides are

BA and YX

BC and YZ

AC and XZ

The corresponding angles are

∠A and ∠X

∠B and ∠Y

∠C and ∠Z

$\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}$

and

∠A≅∠X

∠B≅∠Y

∠C ≅∠Z

therefore

$\frac{BA}{YX}=\frac{BC}{YZ}$ , ∠C ≅∠Z

$\frac{AC}{XZ}=\frac{BA}{YX}$ , ∠A≅∠X

$\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}$

3 0

2 years ago

Read 2 more answers

Jenny is taking a vacation to Florida. She travels 70 kilometers per hour for 2 hours, and 63 kilometers per hour for 5 hours. O

Helga [31]

Jenny traveled 70 km/h over 2 hours and 63 km/h over 5 hours. Her travel time was a total of 7 hours.

We need to find out how far she traveled during this 7-hour period.

70 km/h * 2 h = 140 km
63 km/h * 5 h = 315 km

Then, we can add 140 km and 315 km to get a total distance traveled of <em>455 km/h.</em>

We were asked to find the average <em>speed.</em> We can find it now, since we have total distance traveled (455 km) and total time taken (7 hours).

Then,
455km / 7h = 65 km/h.

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2 years ago

Which point on the number line represents the product (5)(-2)(-1)

galben [10]

Point +10.

(-2)*(-1) gives +2 (a negative number multiplied for another negative gives a positive number).

2*5 = +10

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2 years ago

Read 2 more answers

Given the first type of plot indicated in each pair: which of the second plots could not always be generated from it? a. dot plo

Elenna [48]

Answer:

Step-by-step explanation:

Dot plot is usually in the form of stem & leaf. The only difference is that, stem& leaf presents the actual values while dot plot usually represent the value in dots. Hence, we can easily generate dot plot from stem & leaf!

For (a) dot plot and box plot, dot plot presents all the data while box plot presents only the five-num statistics, namely:

1. minimum

2. 1st quartile (Q1)

3. median

4. 3rd quartile (Q3)

5. Maximum

And outliers, if any!

Thus, dot plot cannot directly generate box plot

For (b). Histogram and stem & leaf. Although both usually help us understand the skewness of data distribution, however, histogram deals with frequency distribution (counts of number of occurrence) and plotted on the intervals and stem&leaf list the values.

For (d). Even though dot plot shoots up and down like the histogram, the content is different. In dot plot, it is the actual value represented in dots. But in histogram, it is the frequency distribution of the class intervals.

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2 years ago

How many six-digit odd numbers are possible if the leftmost digit cannot be zero

Romashka [77]

For the leftmost digit there are 9 possibilities!

4 0

2 years ago