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3 years ago

there are ten chairs in a row. in how many ways can two people be seated so that they are not seated next to each other?

Mathematics

1 answer:

Aliun [14]3 years ago

4 0

Answer: There are 368,947,264 ways to do so.

Step-by-step explanation:

Since we have given that

Number of chairs in a row = 10

Since two people can be seated so that they are not seated next to each other.

For number 8: One sit at either end of the row

For number 7: One sit between last and first chair.

so, the number of ways would be

$8\times 8\times 7\times 7\times 7\times 7\times 7\times 7\times 7\times 7\\\\=8^2\times 7^8\\\\=64\times 5764801\\\\=368,947,264$

Hence, there are 368,947,264 ways to do so.

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There are 42 sixth-grade students and 60 fifth grade students. The students will be put in to the largest possible equal groups

scoundrel [369]

Answer:51 Groups

Step-by-step explanation:

60 students + 42 students = 102

102 divided by 2 = 51 Total groups.

5 0

3 years ago

Find the exact value of sin (arccos(-3/4))

Arturiano [62]

The exact value is
sin(arccos(3/4))The equation for cosine is cos(A)=AdjacentHypotenuse. The inside trig function is arccos(3/4), which means cos(A)=3/4. Comparing cos(A)=AdjacentHypotenuse with cos(A)=3/4, find Adjacent=3 and Hypotenuse=4. Then, using the pythagorean theorem, find Opposite=√7.Adjacent=3Opposite=√7Hypotenuse=4Substitute in the known variables for the equation sin(A)=OppositeHypotenuse.sin(A)=√7 over 4Simplify.√7 over 4

6 0

3 years ago

The sum of two numbers is 47 and the difference is 25 . what are the numbers?

taurus [48]

The numbers are: 36 and 11 .
______________________________________________
Explanation:
______________________________________________
Let us represent the TWO (2) numbers with the variables;
 "x" and "y" .
__________________________________________
 x + y = 47 .

 y − x = 25.
__________________________________________
Since: " y − x = 25 " ;

Solve for "y" in terms of "x" ;

y − x = 25 ;

Add "x" to each side of the equation:
_____________________________________________
 y − x + x = 25 + x ;

to get:

 y = 25 + x .

Now, since:

x + y = 47 ;

Plug in "(25 + x)" as a substitution for "y"; to solve for "x" :

x + (25 + x) = 47 ;

x + 25 + x + 47 ;

2x + 25 = 47 ;

Subtract "25" from each side of the equation:

2x + 25 − 25 = 47 − 25 ;

2x = 22 ;

Divide EACH SIDE of the equation by "2" ;
to isolate "x" on one side of the equation; and to solve for "x" ;

2x / 2 = 22 / 2 ;

 x = 11 ;
______________________________________________
x + y = 47 ;

Plug in "11" for "x" into the equation ; to solve for "y" ;

11 + y = 47 ;

Subtract "11" from EACH SIDE of the equation;
to isolate "y" on one side of the equation; and to solve for "y" ;

11 + y − 11 = 47 − 11 ;

 y = 36 .
___________________________________________
So: x = 11 , y = 36 ;
___________________________________________
Let us check our work:

y − x = 25 ;

36 − 11 =? 25 ? Yes!

x + y = 47 ;

36 + 11 =? 47 ? Yes!
______________________________________________
The numbers are: 36 and 11 .
______________________________________________

5 0

3 years ago

Social security tax that is 6.2% of her gross pay medicare tax that is 1.45% of her gross pay state tax that is 21% of her feder

user100 [1]

Marilyn's net pay will increase by $18.15 as her Federal Withholding Allowance increases from 3 to 4.

<h3>What is Federal Withholding Allowance?</h3>

A Federal Withholding Allowance is an exemption that lowers the amount of income tax you must deduct from an employee's paycheck.

Given: The following are the deductible computation:

For federal withholding allowance = 3:

Social Security Tax: 6.2% of $810 = $\frac{6.2\times810}{100}$ = $50.22
Medicare tax : 1.45% of $810 = $\frac{1.45\times810}{100}$ = $11.745
State tax: (21% of 3)% of $810= $\frac{21\times3 }{100} \times\frac{810}{100}$ = 0.63% of $810 = $\frac{0.63\times810}{100}$ = $5.103

Total = $67.068; deducted amount of his gross pay = $810 - $67.068 $742.932 (3 federal withholding).

For Federal Withholding Allowance = 4:

State tax: (21% of 4)% of $810 = $(\frac{21\times4}{100}) \times\frac{810}{100}$ = 0.84% of $810 = $\frac{0.84\times810}{100}$ = $6.8704

Thus, as we can see from the calculations, the State taxes increased from $5.103 to $6.8704. Hence, the net pay increases by $18.15 as the federal allowance increases from 3 to 4.

To learn more about Federal Withholding Allowance, refer to the link: brainly.com/question/1212566

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4 0

2 years ago

In preparing for holiday festivities, confetti is stuffed into decorative spherical containers. Each container has a diameter of

professor190 [17]

Answer:

C. 905 in³

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, sphere

We know that the volume of a sphere is expresses as

V= 4/3πr³

Given that the diameter of the sphere is 12inches

Radius r= 12/2= 6 inches

Substituting our radius we can solve for the volume

V=4/3(3.142*6³)

V= (4*3.142*216)/3

V= 2714.68/3

V= 904.9in³

Approximately V= 905in³

5 0

3 years ago