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3 years ago

Parts of a Parabola????

Mathematics

1 answer:

eduard3 years ago

7 0

Answer:

the directrix and focus the axis of symmetry (goes through the focus, at right angles to the directrix) the vertex (where the parabola makes its sharpest turn) is halfway between the focus and directrix.

Step-by-step explanation:

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An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.

SCORPION-xisa [38]

Answer:

(a)See below

(b)I) 0.125 (ii)0.828125 (iii)0.234375 (iv) 0.625 (v)0.65625

Step-by-step explanation:

When an 8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

$[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)]$

PART A

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:

$1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64$

PART B

I) A prime number

The number of products that gives prime numbers = 8

The probability that the product is a prime number

$=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125$

ii) Not a perfect square

Number of products that results in perfect squares =11

The probability that the product is not a perfect square

$=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125$

iii) A multiple of 5

Number of products that are multiples of 5=15

The probability that the product is a multiple of 5

$=\dfrac{15}{64}\\=0.234375$

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

The probability that the product less than or equal to 21

$=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625$

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

The probability that the product is divisible by 4 or 6

$=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625$

8 0

3 years ago

15 points. What is the value of k?

Lubov Fominskaja [6]

Answer:

k = 10

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ZYM is an exterior angle of the triangle, thus

4k + 5 + 6k + 10 = 115, that is

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

7 0

3 years ago

Read 2 more answers

At a certain construction site, there is a pile containing 55 tons of sand. Four trucks, each of which holds 11.4 tons of sand,

antoniya [11.8K]

11.4 multiplied by 4 trucks = 45.6 tons in the trucks.
55 - 45.6 = what remains in the pile which would be 9.4 tons.

5 0

4 years ago

Read 2 more answers

15. Simplify sin(90° - O) cos 0 - sin(180° +0) sin e.

dalvyx [7]

Answer: cos²(θ) + sin(θ)sin(e)

Step-by-step explanation:

sin (90° - θ)cos(Ф) - sin(180° + θ) sin(e)

Note the following identities:

sin (90° - θ) = cos(x)

sin (180° + θ) = -sin(x)

Substitute those identities into the expression:

cos(x)cos(x) - -sin(x)sin(e)

= cos²(x) + sin(x)sin(e)

4 0

3 years ago

6x-3=3x+12 x= What is the value of x in this equation

goldenfox [79]

Answer:

x = 5

Step-by-step explanation:

6x - 3 = 3x + 12

-3x -3x

_____________

3x - 3 = 12

+3 +3

_____________

3x = 15

15 divided by 3 = 5

x = 5

You can double check this by replacing x with (5)

If it is right both sides should equal the same

6(5) - 3 = 3(5) + 12

30 - 3 = 15 + 12

27 = 27

This would prove that x = 5

7 0

3 years ago

Read 2 more answers