You have 7 balls that are each a different color of the rainbow. In how many distinct ways can these balls be ordered?

Answers

Answer 1

Answer: To solve this question, use a factorial. This is a basic concept in permutations. The first ball can be placed into any of the 7 positions. The second can be placed in 6. The third can be placed in 5, and so on until there are no balls left. One easy way to solve this is to use 7!, or seven factorial. 7! = 7*6*5*4*3*2*1. The answer is 5,040 distinct ways.
Hope that answered your question.

Answer 2

Answer:

Answer:

You have 7 balls that are each a different color of the rainbow. Then, the number of distinct ways in which these balls can be ordered will be given by 7!. 7! = 7*6*5*4*3*2 = 5040 ways. Thus, in 5040 ways, the number of balls can be put in distinct arrangements.

Step-by-step explanation:

In Short Term 5,040

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A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function .How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary. h=-16t^2+112t+30
A. 7 s; 30 ft
B. 3.5 s; 366 ft
C. 3.5 s; 618 ft
D. 3.5 s; 226 ft

Answers

To determine the time it takes for boulder to reach its maximum height, derive the equation and equate to zero.
h = -16t² + 112t + 30
dh / dt = 0 = -32t + 112
The value of t from the equation above is 3.5 s. Substitute this value of t to the original question,
h = -16(3.5 s)² + 112(3.5 s) + 30 = 226 ft
Thus, the answer is letter D.

A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2.Which value can be used as the common ratio in an explicit formula that represents the sequence?

2
6
12

Answers

The common ratio is the current number divided by the previous. So the ratio is 1/2

The sequence is 12, 6, 3, 3/2, 3/4 ...

You can obtain any number multiplying the previous number times 1/2.

6 = 12 *(1/2)

3 = 6*(1/2)

3/2 = 3*(1/2)

Answer:

Common ratio = $(1)/(2)$

Step-by-step explanation:

A sequence that progresses geometrically has the first term as 12.

Each number is the previous number divided by 2.

so the sequence will be 12, 6, 3, 1.5...........

Explicit formula of a geometric sequence is given by

$T_(n)=a(r)^(n-1)$

Where $T_(n)$ = nth term of the sequence

a = first term

r = common ratio

and n = number of term

In this sequence common ratio = $\frac{\text{Successive term}}{\text{previous term}}$

= $(6)/(12)$

= $(1)/(2)$

Therefore, common ratio will be $(1)/(2)$

116 is 145% of what number

Answers

$116\ \rightarrow\ 145\%\nx\ \rightarrow\ 100\%\n\nx= (116\cdot100\%)/(145\%) \n\nx= (4\cdot29\cdot5\cdot20)/(5\cdot29) \ \ \ \Rightarrow\ \ \ x=4\cdot20=80$

116 = 145% x ?
116 = 1.45 x ?
116 ÷ 1.45 = 80
? = 80

20 POINTS ! PLUS BRAINLIEST ANSWERGive the sum of 2x -3 and 7x + 21
Find the measure of angle KMP
Find the measure of the complement of angle KMX

Photo is attached please give correct answers otherwise I will have to report the answer for false info and get my points back

Answers

Give the sum of 2x -3 and 7x + 21
2x-3+7x+21
Add like terms:
9x+18

Find the measure of angle KMP
<KMX + <XMY = 180 (because they are on a line)
2x-3+7x+21=180
9x+18=180
9x=162
x= 18
<XMY and <KMP are vertical angles so they have the same angle measure. So find <XMY with x.
<XMY= 7x+21
<XMY= 7(18)+21
<XMY= 126+21 = 147 degrees
<XMY = <KMP = 147 degrees

First find <KMX to find the complement of it.
<KMX=2x-3
<KMX=2(18)-3
<KMX=36-3
<KMX=33
The complement of an angle is 90 degrees subtracted by the angle itself because complementary angles add up to 90 degrees.
90-33=57
The complement would have 57 degrees.

Answers :
9x+18
147 degrees
57 degrees

Hope this helps :)

sum of 2x-3 and 7x+21
2x-3+7x+21
2x+7x-3+21
9x+18

since KY is a straight line, 2x-3+7x+21=180
9x+18=180
subtract 18
9x=162
divide 9
x=18
subsitute
2x-3
2(18)-3
36-3
33=KMX
other angle is
33+otherangle=180
otherangle=XMY=147
KMP=XMY=147

KMX=33
complement is what adds to 90
33+what=90
subtract 33
what=57
complement is 57 degrees

2x-3+7x+21=9x+18
KMP=147
complement of KMX=57

Here is a list of numbers: 12, 13, 19, 16 ,32, 15, 13.a)work out the range of the numbers in the list.
b)work out the mean of the numbers in the list

Answers

The range of the numbers in the list is 20 and the mean of the numbers in the list is 17.14

Work out the range of the numbers in the list.

To calculate the range of the numbers in the list, subtract the smallest number from the largest number:

Range = Largest number - Smallest number

Range = 32 - 12 = 20

Work out the mean of the numbers in the list

To calculate the mean of the numbers in the list, add all the numbers and divide by the total number of numbers:

Mean = (12 + 13 + 19 + 16 + 32 + 15 + 13) / 7 = 120 / 7

Mean ≈ 17.14

Answers

Answer:

Given the expression $3 (2y-5)$ ......[1]

Distributive property of multiplication states that when a number is multiplied by the sum of two numbers, then the first number can be distributed to both of those numbers and multiplied by each of them separately. i.e,

$a \cdot (b+c) =a\cdot b +a \cdot c$

then, by using distributive property in equation [1]

$3(2y-5) = 3 \cdot 2y - 3\cdot 5$

= $6y-15$

Therefore, the expanded form of 3(2y-5) is; 6y-15

$3\cdot(2y-5)=3\cdot2y-3\cdot5=6y-15$

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