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anzhelika [568]
3 years ago
11

You pick 7 digits (0-9) at random without replacement, and write them in the order picked. What is the probability that you have

written the first 7 digits of your phone number
Mathematics
1 answer:
Pie3 years ago
7 0

Answer:

= .0000001

Step-by-step explanation:

The odds of getting 1 number of out the 10 possible number (0-9) equal 10 is 1/10

There are 7 numbers to pick

P(xxx-xxxx) = 1/10 * 1/10 *1/10 * 1/10 * 1/10 * 1/10 *1/10

                 = .0000001

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F(x)=x3−x2 and g(x)=2x+10, then (g ∘ f)(3)=
RUDIKE [14]

Answer:

Step-by-step explanation:

f(3)= 3^3 - 3^2 = 27 - 9 = 18

g(18)= 2(18) + 10 = 36 + 10 = 46

5 0
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A $50 cost is put on sale for $35
nasty-shy [4]
You got 30% off yaaa
7 0
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guys it's really important I'm begging you to answer as many as possible!!!!! it's a practice paper due tomorrow please answer a
alexira [117]

Step-by-step explanation:

5b.

P (6, -1), Q (1, 3), R (x, 8)

the distance between points is found via Pythagoras for right-angled triangles, as the distance is the Hypotenuse c, and the coordinate differences of x and y are the "legs".

for PQ

c² = (6-1)² + (-1 - 3)² = 5² + (-4)² = 25 + 16 = 41

now we need find the x, so that we get 41 as the square of the distance for QR

41 = (1-x)² + (3-8)² = (1-x)² + (-5)² = (1-x)² + 25

aha ! the 41 and 25 terms are the same as above.

that means (1-x)² must be equal to 16.

=>

1-x = 4 => x = -3

or

1-x = -4 => x = 5

so, R could be either (-3, 8) or (5, 8).

5c.

(4 + sqrt(7))/(2×sqrt(7) + 5) = a + b×sqrt(7)

let's use the old trick of

(a+b)(a-b) = a² - b²

to get rid of the sqrt(7) in the denominator.

we multiply with

(2×sqrt(7) - 5)/(2×sqrt(7) - 5)

=>

(4 + sqrt(7))×(2×sqrt(7) - 5) / (2×sqrt(7) + 5)×(2×sqrt(7) - 5) =

= (8×sqrt(7) - 20 +2×7 - 5×sqrt(7)) / (4×7 - 25) =

= (3×sqrt(7) - 6) / 3 = sqrt(7) - 2

now, we see

sqrt(7) - 2 = a + b×sqrt(7)

a = the sum of every term without sqrt(7) = -2

b = the sum of all factors of sqrt(7) = 1

6a.

similar triangles.

EBA and DFA are similar triangles due to the parallel baselines and the sharing of the same "legs" and therefore using the same angles.

and that means that all the lengths of lines in one triangle are the result of the lengths of the corresponding lines in the other triangle multiplied by the same factor.

since E is the midpoint of AD, that means this factor is 2 :

AE×2 = AD.

therefore, FA = AB×2 and AB = FA/2

that proves that B is the midpoint of FA.

that also means that L is the midpoint of DF.

and DF = EB×2 or EB = DF/2

as L is the midpoint of DF, it means that LF = DF/2 = EB.

6b.

x - 2/x = 5

i.

let's square everything.

(x - 2/x)² = 25

x² - 2×2x/x + 4/x² = 25

x² - 4 + 4/x² = 25

x² + 4/x² = 29

ii.

let's multiply with (x - 2/x) again.

(x² + 4/x²)×(x - 2/x) = 29×5

x³ - 2x²/x + 4x/x² - 8/x³ = 145

x³ - 2x + 4/x - 8/x³ = 145

x³ - 8/x³ - 2×(x - 2/x) = 145

x³ - 8/x³ - 2×5 = 145

x³ - 8/x³ = 155

6c.

I can't draw here, but let's transform the equations into regular line equations :

2y - x = 8

2y = x + 8

y = (1/2)x + 4

when assuming x = 0 for one point. and y = 0 for a second point we get (0, 4) and (-8, 0)

y - 2x = 1

y = 2x + 1

same trick as above with x = 0 and y = 0 :

(0, 1) and (-1/2, 0). but we could also use x=1 to get an integer as x coordinate for the second point: (1, 3)

7a.

i.

the radius is half the diameter = (18+8)/2 = 13 cm

ii.

the shortest chord through M creates a right-angled triangle with the radius from 0 to the point on the circle, where the chord ends as the Hypotenuse. one leg is M0, which is

13 - 8 = 5 cm

the other leg is half of the length of the chord, as the chord goes up and down of AB.

so,

13² = 5² + x²

169 = 25 + x²

144 = x²

x = 12 cm

so, the whole chord is 2×12 = 24cm long.

7b.

3/(sqrt(6) + sqrt(3)) rationalized is

3×(sqrt(6) - sqrt(3)) / (sqrt(6) + sqrt(3))×(sqrt(6) - sqrt(3))

3×(sqrt(6) - sqrt(3)) / (6 - 3) =

3×(sqrt(6) - sqrt(3)) / 3 = sqrt(6) - sqrt(3)

1/(sqrt(3) + sqrt(2)) rationalized is

(sqrt(3) - sqrt(2)) / (sqrt(3) + sqrt(2))×(sqrt(3) - sqrt(2))

(sqrt(3) - sqrt(2)) / (3 - 2) = sqrt(3) - sqrt(2)

4/(sqrt(6) + sqrt(2)) rationalized is

4×(sqrt(6) - sqrt(2)) / (sqrt(6) + sqrt(2))×(sqrt(6) - sqrt(2))

4×(sqrt(6) - sqrt(2)) / (6 - 2) =

4×(sqrt(6) - sqrt(2)) / 4 = sqrt(6) - sqrt(2)

so, we have in total

sqrt(6) - sqrt(3) + sqrt(3) - sqrt(2) - sqrt(6) + sqrt(2) = 0

the whole expression is eliminating every term and is simply 0.

3 0
2 years ago
What is the length of the sude of a cube whose volume is 35937 cm³​
sweet-ann [11.9K]

The answer is 33. The side lengths of a cube are all the same and the volume is length x width x height. So, you just cube 35,937 cm to get 33 cm.

7 0
3 years ago
if we represent the length of a line by a, how may we represent the length of a line that is 3 inches shorter. If the combined l
ddd [48]

Answer:

The lines' lengths are: 8 inches and 5 inches.

Step-by-step explanation:

Calling "a" the length of the line, a line that is 3 inches shorter can be written in math terms as:

a - 3

If the combined (added) length of these two lines is 15 inches, then we can write:

a + (a - 3) = 15

a + a - 3 = 15

2 a - 3 = 15

2 a = 15 + 3

2 a = 18

then

a = 18/2 = 9

Therefore, the length of one line is 8 inches, and the length of the shorter line is:

8 - 3 = 5 inches

7 0
3 years ago
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