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pogonyaev
3 years ago
12

Help with math problem- finding first four terms of a sequence with a factorial. An=2(n+1)!

Mathematics
1 answer:
earnstyle [38]3 years ago
7 0

a_1=2\cdot(1+1)!=2\cdot2!=2\cdot1\cdot2=\boxed{4}\\\\ a_2=2\cdot(2+1)!=2\cdot3!=2\cdot1\cdot2\cdot3=\boxed{12}\\\\ a_3=2\cdot(3+1)!=2\cdot4!=2\cdot1\cdot2\cdot3\cdot4=\boxed{48}\\\\ a_4=2\cdot(4+1)!=2\cdot5!=2\cdot1\cdot2\cdot3\cdot4\cdot5=\boxed{240}

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The length of a rectangle is 8 feet longer than the width. If the perimeter is 80 feet, find the length and width of the rectang
Klio2033 [76]

perimeter = 2L + 2W

 L=8+w

perimeter = 2(8+w) +2w

80 =16+2w+2w

80 = 16 +4w

64 =4w

w=64/4 = 16

 l=16+8 =24

 length = 24 feet

width = 16 feet


 check 2(24) +2(16) = 48 + 32 = 80

7 0
3 years ago
4) How much pizza sauce is needed to cover a 16" pizza? (Note: 16" is the diameter of the pizza.) A) 50.24 in2 B) 200.96 in2 C)
never [62]
In order to get how much is being covered, we need to know the formula of the area of a circle.
Area = pi * r^2
Area = pi * (16/2)^2
Area = pi * 8^2
Area = pi * 64
Area = 200.96 in^2

So the correct answer is letter B. 200.96 in^2
4 0
3 years ago
Which figure always has exactly four lines of reflection that map the figure onto itself?
Salsk061 [2.6K]

Answer:

number 3

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Kim is 5 years older than her brother Jack. If the sum of their ages is 21, find each of their ages.
yarga [219]

9514 1404 393

Answer:

  • Kim is 13
  • Jack is 8

Step-by-step explanation:

Let k represent Kim's age. Then Jack's age is k-5 and the total of their ages is ...

  k + (k -5) = 21

  2k = 26 . . . . . . . add 5, collect terms

  k = 13 . . . . . . . . . divide by 2; Kim's age

  k -5 = 8 . . . . . . . Jack's age

Kim is 13; Jack is 8.

7 0
3 years ago
The authors of a paper presented a correlation analysis to investigate the relationship between maximal lactate level x and musc
ArbitrLikvidat [17]

Answer:

a) Sample correlation coefficient, r = 0.7411

bi) test statistic, t = 4.102

bii) P-value = 0.000736

Step-by-step explanation:

a) The formula for the sample correlation coefficient is given by the formula:

r = \frac{S_{xy} }{\sqrt{S_{xx} S_{yy} }} }

S_{xx} = 2,648,130.357\\S_{yy} = 36.7376,\\S_{xy} = 7408.225

r = \frac{7408.225}{\sqrt{2648130.357*36.7376} }

r = 0.7511

b)

i) formula for the test statistic is given by the formula:

t = \frac{r\sqrt{n-1} }{\sqrt{1 - r^{2} } }

sample size, n = 4

t = \frac{0.7511\sqrt{14-1} }{\sqrt{1 - 0.7511^{2} } }

t = 4.102

ii) Degree of freedom, df = n -2

df = 14 -2

df = 12

The P-value is calculate from the degree of freedom and the test statistic using excel

P-value =(=TDIST(t,df,tail))

P-value = (=TDIST(4.1,12,1)

P-value = 0.000736

4 0
3 years ago
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