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-(7-4x)=9

-7 + 4x = 9 add 7 to both sides

4x =9 + 7

4x =16 divide both sides by 4

x = 16/4

x = 4

you have to add seven to both sides than you have to divide by four which would come out to x=4

=(2 log(x)) / (log(2))

0.23. Because 10 to the power of 0 = 1

This is Present Value of a Loan or annuity:

(3076.41/1.0051667)*[1/1.0051667)^(25*12)-1]/[(1/1.0051667)-1]

=$468,547.42

P. S. Because you truncated 6.2% to 5 significant digits, the accurate answer would be slightly different if carried to 10-15 digits=$468,549.18.

Inverse log is just raising 10(or the 'base') to  the the number

LOG(23) = 1.3617      'inverse' log(1.3617)  =  10^(1.3617) = 23

For natural ln use the 'e' function.....      ln(23) = 3.1354      'inverse' ln  = e^(3.1355) = 23

log₂ 8 = 3   'inverse' log₂ (3)  =  2^3  = 8

Asinus, the variance is 12, the standard deviation is the square root of the variance.

Brilliant responses, many thanks everybody.

The numbers wouldn't be allowed to be used more than once in the code to clarify, so the code would be something like 8-5-3-4-11-18-19 out of a list of 20 numbers from 1-20.

So, from that it sounds as though the correct answer would be 1: 390,700,800?

So, pretty improbably then I would guess!

What is the probability of correctly guessing a 7 number random code out of 20 numbers (i.e. 1-20)? The probability needs to be expressed as in 1:1000. Thanks

This question is worded badly because the title asks for a 7 digit code but some of the numbers in the code are 2 digits - this does not make sense.

Anyway....

If the numbers have to be in the right order and there is repeat allowed then it will be  

1/20^7 = 0.00000000078125

0.00000000078125*1000 = 0.00000078125

so that is   a chance of   0.00000078125 in 1000      

I do not like your chances of guessing correctly 

There is no question here. 

Find the (sample) variance of the list:
(67, 70, 74, 75, 77, 68, 72, 76, 69, 72)

The (sample) variance of a list of numbers X = {X_1, X_2, ..., X_n} with mean μ = (X_1 + X_2 + ... + X_n)/n is given by:
(abs(X_1 - μ)^2 + abs(X_2 - μ)^2 + ... + abs(X_n - μ)^2)/(n - 1)

There are n = 10 elements in the list X = {67, 70, 74, 75, 77, 68, 72, 76, 69, 72}:
(abs(X_1 - μ)^2 + abs(X_2 - μ)^2 + abs(X_3 - μ)^2 + abs(X_4 - μ)^2 + abs(X_5 - μ)^2 + abs(X_6 - μ)^2 + abs(X_7 - μ)^2 + abs(X_8 - μ)^2 + abs(X_9 - μ)^2 + abs(X_10 - μ)^2)/(10 - 1)

The elements X_i of the list X = {67, 70, 74, 75, 77, 68, 72, 76, 69, 72} are:
X_1 = 67
X_2 = 70
X_3 = 74
X_4 = 75
X_5 = 77
X_6 = 68
X_7 = 72
X_8 = 76
X_9 = 69
X_10 = 72
(abs(67 - μ)^2 + abs(70 - μ)^2 + abs(74 - μ)^2 + abs(75 - μ)^2 + abs(77 - μ)^2 + abs(68 - μ)^2 + abs(72 - μ)^2 + abs(76 - μ)^2 + abs(69 - μ)^2 + abs(72 - μ)^2)/(10 - 1)

The mean (μ) is given by

μ = (X_1 + X_2 + X_3 + X_4 + X_5 + X_6 + X_7 + X_8 + X_9 + X_10)/10 = (67 + 70 + 74 + 75 + 77 + 68 + 72 + 76 + 69 + 72)/10 = 72:
(abs(67 - 72)^2 + abs(70 - 72)^2 + abs(74 - 72)^2 + abs(75 - 72)^2 + abs(77 - 72)^2 + abs(68 - 72)^2 + abs(72 - 72)^2 + abs(76 - 72)^2 + abs(69 - 72)^2 + abs(72 - 72)^2)/(10 - 1)

The values of the differences are:
67 - 72 = -5
70 - 72 = -2
74 - 72 = 2
75 - 72 = 3
77 - 72 = 5
68 - 72 = -4
72 - 72 = 0
76 - 72 = 4
69 - 72 = -3
72 - 72 = 0
10 - 1 = 9
(abs(-5)^2 + abs(-2)^2 + abs(2)^2 + abs(3)^2 + abs(5)^2 + abs(-4)^2 + abs(0)^2 + abs(4)^2 + abs(-3)^2 + abs(0)^2)/9

The values of the terms in the numerator are:
abs(-5)^2 = 25
abs(-2)^2 = 4
abs(2)^2 = 4
abs(3)^2 = 9
abs(5)^2 = 25
abs(-4)^2 = 16
abs(0)^2 = 0
abs(4)^2 = 16
abs(-3)^2 = 9
abs(0)^2 = 0
(25 + 4 + 4 + 9 + 25 + 16 + 0 + 16 + 9 + 0)/9

25 + 4 + 4 + 9 + 25 + 16 + 0 + 16 + 9 + 0 = 108:
Answer: |12

Hello Pearl,

The slope is = -4/3
The constant is -1

so

\(\LARGE y=-\frac{4}{3}x-1\)

Greeting asinus :- )    !

This is just:    y = -4x/3 - 1

.

There is no equation here, so we can't say if the x,y pairs are solutions!

What is the variance of 67, 70, 74, 75, 77, 68, 72, 76, 69, 72?

\(\large\sigma^2=\frac{\sum\limits_{i=1}^{n} (x_i-\overline x\ )^2 }{n-1} \)  

\(n=10\)

\({\color{blue}\overline x}=\frac{\sum(67, 70, 74, 75, 77, 68, 72, 76, 69, 72)}{10}\color{blue}=72\)

\(\sum\limits_{i=1}^{10} (x_i-\overline x\ )^2 \) = (67-72)²+(70-72)²+(74-72)²+(75-72)²+(77-72)²+(68-72)²+(72-72)²+(76-72)²+(69-72)²+(72-72)²

=25+4+4+9+25+16+0+16+9+0

=108

\(\sigma^2=\frac{108}{10-1}=12\)

\(\sigma=\sqrt{12}=3.4641\)

\(The \ variance \ is \ \sigma =3.4641.\)

   !

There are 7 odd numbers and 6 even numbers in the range.  To get an odd product both of the chosen random numbers must be odd.  

probability that the first number is odd: p1 = 7/13

probability that the second number is odd: p2 = 6/12 → 1/2  (I assume the word "distinct" means the first number is removed from the set before choosing the second number).

Overall probability:   p1*p2 = 7/13*1/2 → 7/26 ≈ 0.269

.

log base 5 x=-4/3 find value of x

\(log_5(x)=\frac{4}{3}\) 

\(x=5^\frac{4}{3}=\sqrt[3]{5^4} =\sqrt[3]{5\times5^3}\)

\(x=5\times\sqrt[3]{5} \) = 8.5499     !

2X = -9+13

2X=4

X=2

the numbers are -4 and 8.

11 is 15 more than the smaller of the two.

n = -18

-18-(-5)=-13

x = 2

2x2-13=-9

That last line has a typo...it  should say  5  5/6     NOT   5  6/6

Most likely you would hear something in the units of    inches per week

Plant grew  (13.5 - 9) inches   in  TWO weeks

4.5 inches/2weeks   =  2.25 inches/week    For the last two weeks

13.5 inches/6weeks = 2.25 inches per week (also) for the entire 6 weeks    2.25 in/wk

Example      sqrt(9)  x   sqrt(16) =  sqrt(9 x 16) = sqrt(144)  = 12