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Tems11 [23]
3 years ago
6

Which of the following statements is always true of similar polygons?

Mathematics
2 answers:
UkoKoshka [18]3 years ago
7 0

1. D

2. A

3. B

4. A

5. C

k0ka [10]3 years ago
6 0
The correct answer among all the other choices is D. both (a) and (b). The statements that are always true of similar polygons are corresponding angles of similar figures have the same measure and the lengths of corresponding sides form equivalent ratios. Thank you for posting your question. I hope this answer helped you. Let me know if you need more help. 
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Each day, X arrives at point A between 8:00 and 9:00 a.m., his times of arrival being uniformly distributed. Y arrives independe
astraxan [27]

Answer:

Y will arrive earlier than X one fourth of times.

Step-by-step explanation:

To solve this, we might notice that given that both events are independent of each other, the joint probability density function is the product of X and Y's probability density functions. For an uniformly distributed density function, we have that:

f_X(x) = \frac{1}{L}

Where L stands for the length of the interval over which the variable is distributed.

Now, as  X is distributed over a 1 hour interval, and Y is distributed over a 0.5 hour interval, we have:

f_X(x) = 1\\\\f_Y(y)=2.

Now, the probability of an event is equal to the integral of the density probability function:

\iint_A f_{X,Y} (x,y) dx\, dy

Where A is the in which the event happens, in this case, the region in which Y<X (Y arrives before X)

It's useful to draw a diagram here, I have attached one in which you can see the integration region.

You can see there a box, that represents all possible outcomes for Y and X. There's a diagonal coming from the box's upper right corner, that diagonal represents the cases in which both X and Y arrive at the same time, under that line we have that Y arrives before X, that is our integration region.

Let's set up the integration:

\iint_A f_{X,Y} (x,y) dx\, dy\\\\\iint_A f_{X} (x) \, f_{Y} (y) dx\, dy\\\\2 \iint_A  dx\, dy

We have used here both the independence of the events and the uniformity of distributions, we take the 2 out because it's just a constant and now we just need to integrate. But the function we are integrating is just a 1! So we can take the integral as just the area of the integration region. From the diagram we can see that the region is a triangle of height 0.5 and base 0.5. thus the integral becomes:

2 \iint_A  dx\, dy= 2 \times \frac{0.5 \times 0.5 }{2} \\\\2 \iint_A  dx\, dy= \frac{1}{4}

That means that one in four times Y will arrive earlier than X. This result can also be seen clearly on the diagram, where we can see that the triangle is a fourth of the rectangle.

6 0
3 years ago
Solve for x: 3|x-3| 2=14<br> a. No solution<br> b. x=-1,x=8.3<br> c. x=0,x=7<br> d. x=-1,x=7
VMariaS [17]
I am looking  on the answers, and there is only one case, when a or b or c or d pass:   3|x-3| + 2 = 14.  So I assume, that before two is plus. Then:

3|x-3|+2=14    |minus 2
3|x-3|=12        |divide 3
|x-3|=4 

From absolute value definition you've got two ways:

x-3=4     or     x-3=-4
x=7        or     x=-1

And  answer d) passes

3 0
3 years ago
Because of the commutative property of multiplication 3/4X4=4X3/4 However these expressions can be calculated in different ways
elena55 [62]

Answer:

We obtain same product by both the methods.  

Step-by-step explanation:

We are given the following in the question:

Commutative property of multiplication:

\dfrac{3}{4}\times 4  =4\times \dfrac{3}{4}

Different ways to find the product:

1. First way

\dfrac{3}{4}\times 4\\\\=3\times \dfrac{4}{4}\\\\=3

2. Second way

\dfrac{3}{4}\times 4\\\\=\dfrac{12}{4}\\\\=3

We get the same product for both the calculations.

5 0
3 years ago
A salesperson earns ​$105 commission selling ​$2625 worth of television sets.
Bad White [126]
The commission percent is 4%
Take (commission / sales) *100
8 0
3 years ago
Find the product of (x + 5)(x − 5).
AfilCa [17]

Answer:

x² - 30 + 5x

Step-by-step explanation:

(x + 5)(x − 5)

=x(x − 5)+5(x − 5)

=x² - 5 + 5x - 25

=x² - 30 + 5x

6 0
3 years ago
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