6.6 as a mixed number

for the given license plate configuration, determine how many different plates are possinle if letters and digits (a) can ba rep

Inessa05 [86]

Answer:

a) 1,757,600 different plates possible.

b) 1,404,000 different plates possible.

Step-by-step explanation:

The permutations formula is important to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

(a) can be repeated:

There are 3 letters, each one with 26 possible outcomes.

2 digits, each with 10 possible outcomes

So

T = 26*26*26*10*10 = 1757600

1,757,600 different plates possible.

(b) cannot be repeated:

Here the permutations formula is used.

Three letters, from a set of 26.

Two digits, from a set of 10. So

$T = P_{(26,3)}*P_{(10,2)} = \frac{26!}{(26-3)!}*\frac{10!}{(10-2)!} = 1404000$

1,404,000 different plates possible.

4 0

3 years ago

Transversal cuts parallel lines and at points X and Y respectively. The point nearest to C is X, and the point nearest to D is Y

hammer [34]

Answer: The answer is (B) ∠SYD.

Step-by-step explanation: As mentioned in the question, two parallel lines PQ and RS are drawn in the attached figure. The transversal CD cut the lines PQ and RS at the points X and Y respectively.

We are given four angles, out of which one should be chosen which is congruent to ∠CXP.

The angles lying on opposite sides of the transversal and outside the two parallel lines are called alternate exterior angles.

For example, in the figure attached, ∠CXP, ∠SYD and ∠CXQ, ∠RYD are pairs of alternate exterior angles.

Now, the theorem of alternate exterior angles states that if the two lines are parallel having a transversal, then alternate exterior angles are congruent to each other.

Thus, we have

∠CXP ≅ ∠SYD.

So, option (B) is correct.

5 0

3 years ago

Whoever helps me will be lucky for the rest of your life

Anvisha [2.4K]

Answer:

A) 3.5

16 shovels full

Step-by-step explanation:

9x + 13 = 17x - 15

8x = 28

x = 3.5

20 + 5x = 32 + 4.25x

0.75x = 12

x = 16

7 0

3 years ago

If f(x)=-2x+9, then find the value of the x value that makes F(x)=-22

Lostsunrise [7]

-22 = -2x + 9
-31 = -2x
-31/-2 = x
x = 15.5

5 0

3 years ago

Polygon ABCD is a quadrilateral. <br><br> What would prove that ABCD is a parallelogram

masya89 [10]

Answer:

Step-by-step explanation:

Parallelogram are square, rectangle, rhombus, and rhomboid and all with opposite lines that are parallel. Where each angle add up to 360. There are many quadrilaterals that are not parallelogram lesser known ones like convex quadrilaterals that are not parallelograms as they have no parallel lines and do not add up to 360. Polygons that intersect are not parallelograms. We can therefore show upon the parallelogram that there are 2 parallel lines within 4 lines of ABCD and if needed used in analogy with a 3 vertices triangle. Parallelogram like other quadrilaterals have 4 vertices but the angles of a parallelogram would alternate when drawn corner to corner. Diagonals must intersect at the opposite angle. We call them diagonals (not diagonal line) on a parallelogram, simply as where one crosses the other crosses and they become the plural.

6 0

3 years ago