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If the length of AB is 10 cm from the center and has a length of 12, find the approximate length from the center to CD.

Lynna [10]

Given–

AB = 12 Cm

CD = 14 Cm

PO = 10 Cm

AP = 1/2 × 12 = 6 Cm

Construction–

Draw NO such that it is the perpendicular bisector of CB.

Hence,

ND = 1/2 × 14 = 7 Cm

To Find,

Measure of NO

Solution,

Here, PO Perpendicular to AB

Hence, APO is a right-angled triangle–

AO² = PO² + AP²

Or, AO² = 10 ² + 6 ²

Or, AO² = 36 + 100

Or, AO = √136 Cm

Or, AO = 11.66 Cm

Also, AO = OD = 11.66 Cm

( Radius of the same circle )

Now, in triangle OND,

OD² = ON² + ND ²

Or, 11.66 ² = ON² + 7²

Or, 136 = ON² + 49

Or, ON ² = 136 – 49

Or, ON ² = 87

Or, ON ² = √87

Or, ON = 9.3 Cm

Therefore, the appropriate length from center to CD is 9.3 Cm.

4 0

3 years ago

Which set of side lengths forms a right triangle?

Digiron [165]

2, 3, 13

Explanation: You take a^2+b^2=c^2 and substitute the side lengths and solve until you find one where a^2+b^2 actually equals c^2 and that’s your answer

7 0

3 years ago

Read 2 more answers

A dime is tossed repeatedly until a head appears. Let N be the trial number on which this first head occurs. Then a nickel is to

Tcecarenko [31]

Answer:

P(X=0) = 1 , E(X)=0

Step-by-step explanation:

If the dime is balanced , then defining the variable Y= number tails until the first head occurs , then Y follows a negative binomial distribution , with parameter k=N-1 and r=1 (N-1 successes until the r-th failure).

Then

P(Y)= C(k+r-1,k)*(1-p)^r*p^k

P(Y)=C(N-1,N-1) * (1-p)^1 * p^(N-1)

P(Y)= (1-p)*p^(N-1)

where

C ( ) = combinations

p= probability of obtaining heads for every toss = 0.5

P(Y)= probability that there are N-1 tails and 1 head at last → we set P(Y)= 0.999

then

0.99= 0.5*0.5^(N-1)

0.999= 0.5^N

thus

N= ln(0.999)/ln(0.5) = 1.443*10⁻³

while X= number of times that the nickel comes up tails with N trials , follows a binomial distribution

P(X=x)= C(N,x)*(1-p)^(N-x)*p^x

for x=0

P(X=0)= C(N,0)*(1-p)^(N-0)*p^0 = 1*(1-p)^N *1 = (1-p)^N

since p=1-p=0.5

P(X=0)=0.5^N = 0.999

and the expected value of X can be calculated through

E(X)=N*p= 1.443*10⁻³*0.5 = 7.217*10⁻⁴

if we take a better approximation , taking P(Y) closer to 1 then P(X=0)→ 1 and E(X)→0

8 0

3 years ago

State whether each of the following represents a function

quester [9]

Need information to answer

8 0

3 years ago

-12x + 12 = 4 - 15x + 9

emmainna [20.7K]

Answer:

x = 1/3

Step-by-step explanation:

-12x + 12 = 4 - 15x + 9

Combine like terms

-12x +12 = -15x+13

Add 15x to each side

-12x+12 +15x = -15x+15x+13

3x+12 = 13

Subtract 12 from each side

3x+12-12 = 13-12

3x = 1

Divide by 3

3x/3 = 1/3

x = 1/3

8 0

3 years ago