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2 years ago

Evaluate the expression. P(9, 3) · P(5, 4)

Mathematics

1 answer:

boyakko [2]2 years ago

6 0

Answer:

$P(9,3) *P(5,4)$

And if we use the permutation formula given by:

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

And replacing we got:

$\frac{9!}{6!} \frac{5!}{4!}= 504*5 = 2520$

Step-by-step explanation:

For this problem we want to find the following expressionÑ

$P(9,3) *P(5,4)$

And if we use the permutation formula given by:

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

And replacing we got:

$\frac{9!}{6!} \frac{5!}{4!}= 504*5 = 2520$

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If you set aside $9000 at the end of each year for the next 22 years in a Roth IRA, how much will you have at your retirement 22

madam [21]

Answer:

$501,049.37

Step-by-step explanation:

For computing the amount after 22 years we need to applied the future value which is shown in the attachment below:

Given that

PMT = $9,000

NPER = 22 years

Annual rate = 0.078

Quarterly= 0.078 ÷ 4 = 0.0195

Effective annual rate = (1.0195^4) - 1 = 0.0803113041

Now applied the formula which is given below

= -FV(RATE;NPER;PMT;PV)

After applying the above formula, the future value is $501,049.37

7 0

2 years ago

Two movie tickets and 3 snacks are $24. Three movies tickets and 4 snacks are $35. How much is a movie ticket and how much is a

Vsevolod [243]

Answer: A movie ticket is $9 while a snack is $2

Step-by-step explanation: We shall let a movie ticket be m while a snack is s. So, from the clues given, if two movie tickets and three snacks cost $24, we can write it as the following expression;

2m + 3s = 24

Also if three movie tickets and four snacks cost $35, we can as well write another expression as follows;

3m + 4s = 35.

Now we have a pair of simultaneous equations which are

2m + 3s = 24 ----------(1)

3m + 4s = 35 ----------(2)

We shall solve this by using the elimination method, since none of the variables has a coefficient of 1. We'll start by multiplying equation (1) by 3 and multiplying equation (2) by 2 (so as to eliminate the m variable)

2m + 3s = 24 -------- x3

3m + 4s = 35 ---------x2

We now arrive at the following

6m + 9s = 72--------(3)

6m + 8s = 70--------(4)

Subtract equation (4) from equation (3) and we arrive at

s = 2

Having determined that s equals 2 we can now substitute for the value of a into equation (1)

2m + 3s = 24

2m + 3(2) = 24

2m + 6 = 24

Subtract 6 from both sides of the equation

2m + 6 - 6 = 24 - 6

2m = 18

Divide both sides of the equation by 2

m= 9

Therefore one movie ticket costs $9 while one snack costs $2

6 0

2 years ago

Sue scored a total of 35 points in two games.she scored 6 times as many points in the second game than in the first.how many mor

kirill115 [55]

Okay,
Both games are: 35
First game: ?
Second game: 6 more than the first.
So,
first we subtract 6 from 35.
35 - 6 = 29
Divide by 2.
49 divided by 2 = 14.5
Add the 6 point= 14.5 + 6 = 20.5
To make sure add.
First game: 14.5
Second game:20.5
14.5 + 20.5 = 35

3 0

2 years ago

The stem-and-leaf plot shows the temperatures of patients who registered at a clinic one day. How many patients registered at th

saveliy_v [14]

As the key suggests, the left part is the integer part of the number, while the digit on the right is the decimal part of the number.

So, for example, the first row describes the two values 97.2 and 97.8, while the second row describes the values 98.1, 98.3 (repeated twice), 98.5, 98.6 and 98.7 (repeater three times).

So, the number of values is given by the number of leaves: you simply have to count how many digits are there on the right part of the screen.

The answer is thus 24

5 0

2 years ago

In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, AE=x2−16 , and CE=6x .

MAXImum [283]

Answer:

<h3>AC=96 units.</h3>

Step-by-step explanation:

We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.

$AE=x^2-16.$ , and CE=6x .

<em>Note: The diagonals of a parallelogram intersects at mid-point.</em>

Therefore, AE = EC.

Plugging expressions for AE and EC, we get

$x^2-16=6x.$

Subtracting 6x from both sides, we get

$x^2-16-6x=6x-6x$

$x^2-6x-16=0$

Factoriong quadratic by product sum rule.

We need to find the factors of -16 that add upto -6.

-16 has factors -8 and +2 that add upto -6.

Therefore, factor of $x^2-6x-16=0$ quadratic is (x-8)(x+2)=0

Setting each factor equal to 0 and solve for x.

x-8=0 => x=8

x+2=0 => x=-2.

We can't take x=-2 as it's a negative number.

Therefore, plugging x=8 in EC =6x, we get

EC = 6(8) = 48.

<h3>AC = AE + EC = 48+48 =96 units.</h3>

5 0

2 years ago