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KATRIN_1 [288]
3 years ago
7

A car race qualifier has 10 participants. How many different ways can the top 6 cars cross the finish line?

Mathematics
1 answer:
sleet_krkn [62]3 years ago
5 0

Answer:

There are 151,200 different ways.

Step-by-step explanation:

For solving this question, we need  the concept of permutation, the permutation gives as the number of ordered arrangement that can be made chosen k elements from a group of n elements. it is calculated as:

\frac{n!}{(n-k)!}

So, in this case, we need to find the number of ways in which 6 top participants from the 10 participants can cross the finish line.

Now, we can replace n by 10 and k by 6 and calculate the number of permutations as:

\frac{10!}{(10-6)!}=151,200

Finally, there are 151,200 different ways in which the top 6 cars can cross the finish line.

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Given that -15 is a root of x² +mx +45 = 0 find the constant m​
o-na [289]

Answer:

m = 18

Step-by-step explanation:

Given :

=> -15 is a root of the polynomial

=>  It is a zero to the solution.

Process :

Substitute -15 in place of x.

=> (-15)² + (-15)m + 45 = 0

=> 225 + 45 - 15m = 0

=> 15m = 270

=> m = 270/15

=> m = 18

5 0
2 years ago
In parallelogram ABCD, what is DC?<br><br> DC = in.
expeople1 [14]
Since ABCD is a parallelogram, line AB and line DC are parallel and has the same value.

To solve this, equate line AB to be equal with line DC.
So,
Line AB = Line DC
(9x-14)in = (3x +4)in
Next group like terms to get the value of x
9x in-3x in = 4in+14in
\frac{6x}{6} = \frac{18in}{6}
x = 3in

Since, we now have the value of x, substitute it to line DC’s equation.
DC=(3x+4)in
DC=(3(3) +4)in
DC=(9 +4) in
DC= 13 in

To check if the value is really correct, substitute X to AB
AB=(9x -14)in
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AB=(27-14)in
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7 0
3 years ago
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The diameter, D, of a sphere is 15 . Calculate the sphere's volume, V . Use the value 3.14 for pi , and round your answer to the
sergeinik [125]

Answer:

V= 1767.2

Step-by-step explanation:

V=4/3πr3

(I'm pretty sure I rounded that right. If not it's 1767.15 before rounding. )

4 0
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What value makes 2 square root 51 equal to 10 square root 51x
scoundrel [369]
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3 years ago
An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of S 46° E to a location i
Alexandra [31]
<h3>Answer: D) 1692 miles</h3>

============================================

Explanation:

A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram

  1. Plot point A and make that the home base. Plot point D directly south of point A. I'm skipping B and C because those will be used to form the triangle later.
  2. Imagine you are standing at point A and looking south at point D. Turn 46 degrees toward the east direction (this is what the notation "bearing of S 46° E" means). Then move 550 miles from A to land on point B. This is the location where the plane makes its first turn.
  3. Plot the points E and F, which are north and south of point B.
  4. Imagine we are at point B and looking directly south at point F. Turn 55 degrees toward the west, which is due to the "S 55° W" and then move 483 miles to arrive at point C. This is the plane's location where it turns around to go back to home base.

The diagram below shows all of this visually summarized. We have the segments

  • AB = 550 miles
  • BC = 483 miles
  • AC = x miles

And we have these angles

  • Angle DAB = 46 degrees and Angle ABE = 46 degrees (blue)
  • Angle ABC = 79 degrees (red)
  • Angle ACB = 55 degrees and Angle FBC = 55 degrees (green)

Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.

------------------------------

Once the diagram is set up, we'll use the law of cosines to find x.

Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.

The interior angles of triangle ABC are

  • A = 46 degrees
  • B = 79 degrees
  • C = 55 degrees

The sides opposite the angles are

  • a = 483 (opposite angle A)
  • b = x (opposite angle B)
  • c = 550 (opposite angle C)

Now we can apply the law of cosines

b^2 = a^2 + c^2 - 2*a*c*cos(B)

x^2 = 483^2 + 550^2 - 2*483*550*cos(79)

x^2 = 434412.180756441

x = sqrt(434412.180756441)

x = 659.099522649229

x = 659

Side AC, or CA, is roughly 659 miles long.

------------

To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)

Distance Traveled = AB + BC + CA

Distance Traveled = 550 + 483 + 659

Distance Traveled = 1692 miles

3 0
2 years ago
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