MATHEMATICS HIGH SCHOOL

Find the number of permutations

10p8 5p0 6p1 6p6

Answers

Answer 1
Answer: 6p1 i hope this is the answer

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Suppose Ken has 25 coins and nickels and dimes only and has a total of a $1.65 how many of each coin does he have?

Answers

x-\ number\ of\ nickels\ny-\ number\ of\ dimes\n\nx+y=25 \ \ \ | x=25-y\n0.05x+0.1y=1.65\n\n0.05(25-y)+0.1y=1.65\n\n1.25-0.05y+0.1y=1.65\n\n1.25+0.05y=1.65\ \ \ | subtract\ 1.25\n\n0.05y=0.4\ \ \ \ \ | divide\ by\ 0.05\n\ny=8\n\nx=25-8=17\n\nThere\ are\ 17 \ nickels\ and\ 8\ dimes.

The volume of a cube can be written as a function of its edge length, V(x) = x^3. Which is a correct interpretation of V(2x)?(A) The volume of a cube doubles when its edge length doubles.
B) The volume of a cube increases by a factor of 4 when its edge length doubles.
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The volume of a cube increases by a factor of 6 when its edge length doubles.
D The volume of a cube increases by a factor of 8 when its edge length doubles.

Answers

Answer:

D The volume of a cube increases by a factor of 8 when its edge length doubles

Step-by-step explanation:

Volume of a cube is represented by the function

V(x)=x^3

where x represents the edge length of the cube

Now when x=2x i.e., when the edge length is doubled we have

V(2x)=(2x)^3\n\Rightarrow V(2x)=8x^3\n\Rightarrow V(2x)=8(V(x))

It can be seen that the volume of the cube increased by 8 times when edge length doubles.

Answer:

the answer is d

Step-by-step explanation:

Which polynomial is prime?x2 – 36

x2 + 16

x2 – 7x + 12

x2 – x – 20

Answers

x2+16 is the prime polynomial.
x2+16 is the only polynomial that couldn't be factored out anymore

x2-36 --> (x-6)(x+6)
x2-7x+12 --> (x-3)(x-4)
x2-x-20 --> (x+5)(x-4)

Answer:

x^2+16

Step-by-step explanation:

the perimeter of a pool table is 30 ft.The table is twice as long as it is wide.what is the length of the pool table.

Answers

perimeter is legnth +legnth + width + width or
P=2L+2W

L=2W
subsitute L=2W for L in P=2L+2W

P=2(2W)+2W
P=4W+2W
P=6W

we know that Perimiter=30 so
30=6W
divide both sides by 6
5=Width

subsitute W=5 for W in L=2W
L=2(5)
L=10

to check
10=2(10)+2(5)
30=20+10
30=30
checks


Legnght=10
Width=5

the sum of two numbers is 44. the smaller number is 20 less than the larger number. what are the numbers?

Answers

sum means add
x and y are the numbers
sum i 44
x+y=44

smaller s 20 les than larger
x=20+y
or
y=20+x
doesn't matter, just pick one
x=20+y

substue 20+y for x since they are equal
x+y=44
(20+y)+y=44
20+y+y=44
20+2y=44
subtract 20 from both sides
2y=24
divide by 2
y=12
subsitue
x=20+y
x=20+12
x=32

the numbers are 12 and 32
x+(x-20)=44
2x= 64
x=32

Therefore the bigger number is 32 and the smaller number is 12
32+12=44

Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive :)

Answers

Constructive. To prove that there is a positive integer that equals the sum of the positive integers not exceeding it. A plain and simple example is
1.1 + 2 = 3
2.10 + 50 + 100 =160
3.6x + 8x + 2x = 16 x

Notice that the sum of the numbers is always greater than the addends. This only proves that any positive sum of any two positive addends will not compare and thus the addends not exceeding a greater value than the sum.     



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