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3 years ago

At a track meet , 10 different runners compete in the 1600m run.

Mathematics

1 answer:

Zanzabum3 years ago

4 0

Answer:

There are 3,628,800 different ways for the runners to finish.

Step-by-step explanation:

Arrangments of x elements:

The number of possible arrangments of x elements is given by the following formula:

$A_{x} = x!$

In this question:

10 different runners, which means that the number of different ways that there are for the runners to finish is an arrangment of 10 elements. So

$A_{10} = 10! = 3628800$

There are 3,628,800 different ways for the runners to finish.

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In circle O, chord AOB is drawn. Point C is located on the exterior of the circle with tangent CB and secant CDA drawn.Itisknown

ser-zykov [4K]

Answer:

(a) 4

(b) 2√3

(d) 120°

Step-by-step explanation:

(a) The relationship between tangents and secants is ...

CB^2 = CD·CA

Filling in the given values, we find ...

CB^2 = 2·(2+6) = 16

CB = √16 = 4

The length of BC is 4 units.

(b) Triangle ABC is a right triangle, so the sides of it satisfy the Pythagorean theorem.

CA^2 = CB^2 +AB^2

8^2 = 16 +AB^2

AB = √48 = 4√3

The radius is half the length of AB, so the radius is 2√3.

(c) The measure of angle C can be determined from the cosine relation:

cos(C) = CB/CA = 4/8 = 1/2

C = arccos(1/2) = 60°

The measure of angle C is 60°.

(d) Arc AD is intercepted by angle ABD, which has the same measure as angle C. Hence the measure of arc AD is twice the measure of angle C.

The measure of arc AD is 120°.

3 0

3 years ago

When rolling a pair of dice at the Bellagio Casino in Las Vegas, there is 1 chance in 36 that the outcome is a 12.

nasty-shy [4]

Yes, that is correct. likewise, the odds of rolling a 1 are $\frac{1}{36}$

3 0

3 years ago

Solve for b: 16b = 12

Zina [86]

Answer:

b = 3/4

Step-by-step explanation:

Hi!!!

You want the value of B. To get that, we have to divide both sides by 16:

$\frac{16}{16}b =\frac{12}{16}$

$\frac{12}{16} = \frac{3}{4}$

Thus the answer to your question is $$\boxed{b = \frac{3}{4} }$ .

<u>Check:</u>

3/4 * 16 = 3 * 4 = 12.

12 = 12

So we are correct!!!

5 0

3 years ago

Katarina [22]

Answer:

Step-by-step explanation:

Comparing the triangles in the given questions, the following can be deduced:

5. The scale factor = $\frac{15}{10}$ = $\frac{12}{8}$ ≠ $\frac{9}{7}$

So that;

QR is similar to UT, PR is similar to US, but PQ is NOT similar to TS.

Thus, the triangles are NOT similar.

6. Scale factor = $\frac{15}{10}$ = $\frac{12}{8}$ = $\frac{9}{6}$

= 1.5

So that;

QR is similar to UT, PR is similar to US, but PQ is similar to TS.

Thus, the triangles are similar by Side-Side-Side (SSS).

7. Here, an exact scale factor can not be determined. Thus, the triangles are NOT similar.

7 0

2 years ago

How do you find this remainder?

makkiz [27]

Answer:

C. 2

Step-by-step explanation:

Look at pic below.

Hope this helps! :)

3 0

3 years ago

Read 2 more answers