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3 years ago

8:12=6:a what is the value of a

Mathematics

2 answers:

Whitepunk [10]3 years ago

7 0

Answer:

Step-by-step explanation:

$\frac{8}{12}=\frac{6}{a}$

$\frac{2}{3}=\frac{6}{a}$

$2a=6\cdot{3}$

$2a=18$

$a=\frac{18}{2}$

$a=9$

statuscvo [17]3 years ago

5 0

Answer:

a = 9

Step-by-step explanation:

So in this case you just cross multiply

8 : 12 = 6 : a

6(12) = 8(a)

72 = 8a

Divide both sides by 8

a = 9

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Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4.

CaHeK987 [17]

Answer:

$y=-\frac{1}{16} x^2$

Step-by-step explanation:

Equation of parabola with focus at (0,-4) and directrix is $y=4$ .

We know that parabola is the locus of all the points such that the distance from fixed point on the parabola to fixed line directrix is the same.

The parabola is opening downwards.

Let any point on parabola is (x,y).

Distance from focus(0,-4) to (x,y) = $\sqrt{(x-0)^2+(y-(-4))^2}=|y-4|$

$\sqrt{(x-0)^2+(y-+4)^2}=|y-4|$

$(x-0)^2+(y+4)^2=(y-4)^2$

$(x)^2+(y+4)^2=(y-4)^2$

$x^2+(y^2+4y+4y+16)=y^2-4y-4y+16$

$x^2+y^2+8y+16=y^2-8y+16$

$x^2+16y^2=0$

$16y=-x^2$

$y=-\frac{1}{16} x^2$

6 0

2 years ago

A fair coin is tossed three times and the events A, B, and C are defined as follows: A: \{ At least one head is observed \} B: \

Yanka [14]

Answer:

a) $P(A)=0.875$

b) $\text{P(A or B)}=0.875$

c) $\text{P((not A) or B or (not C))}=0.625$

Step-by-step explanation:

Given : A fair coin is tossed three times and the events A, B, and C are defined as follows: A: At least one head is observed, B: At least two heads are observed, C: The number of heads observed is odd.

To find : The following probabilities by summing the probabilities of the appropriate sample points ?

Solution :

The sample space is

S={HHH,HHT,HTT,HTH,TTT,TTH,THH,THT}

n(S)=8

A: At least one head is observed

i.e. A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

n(A)=7

B: At least two heads are observed

i.e. B={HHH,HTT,TTH,THT}

n(B)=4

C: The number of heads observed is odd.

i.e. C={HHH,HTT,THT,TTH}

n(c)=4

a) Probability of A, P(A)

$P(A)=\frac{n(A)}{n(S)}$

$P(A)=\frac{7}{8}$

$P(A)=0.875$

b) P(A or B)

Using formula,

$\text{P(A or B)}=P(A)+P(B)-\text{P(A and B)}$

$\text{P(A or B)}=\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{\text{n(A and B)}}{n(S)}$

$\text{P(A or B)}=\frac{7}{8}+\frac{4}{8}-\frac{4}{8}$

$\text{P(A or B)}=\frac{7}{8}$

$\text{P(A or B)}=0.875$

(c) P((not A) or B or (not C))

A={HHH,HHT,HTT,HTH,TTH,TTH,THH,THT}

not A = {TTT} = 1

B={HHH,HTT,TTH,THT}

C={HHH,HTT,THT,TTH}

not C = {HHT,HTH,THH,TTT} = 4

So, not A or B or not C = {HHH,HHT,HTH,THH,TTT}=5

$\text{P((not A) or B or (not C))}=\frac{5}{8}$

$\text{P((not A) or B or (not C))}=0.625$

4 0

3 years ago

PLZ HELP ITS GEOMETRY

Aleks [24]

Answer:

For #5

Step-by-step explanation:

Perpendicular

8 0

3 years ago

Question 1:

boyakko [2]

1. g^2+4 _> -5

2. C_> 5

_> means greater than or equal to, best I could type on a keyboard.

7 0

2 years ago

Read 2 more answers

the rileys are replacing the carpet on their outdoor deck. the deck is a regular hexagon with radius 9ft. the cost for the carpe

love history [14]

Hexagon radius = side = r =9 ft.

Hexagon Area = (3√3)/2 * r²

∴ Area = (3√3)/2 * 9² ≈ 210.444 ft²

The cost for the carpet and installation is $3.75/ft²

∴ The total cost = Area * cost per ft²
= 210.444 * 3.75
= $ 789.166

6 0

3 years ago