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3 years ago

Determine the function which corresponds to the given graph. (3 points)

Mathematics

1 answer:

damaskus [11]3 years ago

6 0

Answer:

The center of the circle is c=50 and radius of the circle is $r=\sqrt{3}$

Step-by-step explanation:

Given circle equation is

$x^2-4x+y^2+14y=-50\hfill(1)$

Equation (1) can be written as $x^2-4x+y^2+14y+50=0\hfill(2)$

we know that the equation of the circle is of the form

$x^2+y^2+2gx+2fy+c=0\hfill(3)$

with centre (-g,-f) and radius= $\sqrt{g^2+f^2-c}$

when, g,f and c are constants

Now comparing the (2) and (3) equations we get 2g=-4

$g=\frac{-4}{2}$

$g=-2$

$2fy=14$

$f=\frac{14}{2}$

$f=7$

and $c=50$

Now to find the centre and radius of the given circle equation, substituting the values of g,f,c in the formulae of centre and radius

centre=(-g,-f)

=(-(-2),-7)

centre=(2,7)

Radius= $\sqrt{g^2+f^2-c}$

= $\sqrt{(-2)^2+(7)^2-50}$

= $\sqrt{4+49-50}$

= $53-50$

Radius= $\srqt{3}$

The center of the circle is c=50 and the radius of the circle equation $r=\sqrt{3}$

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Your friend Alex is planning a fundraising game night to raise money for a local children's hospital. She invites a few of your

katrin [286]

Step-by-step explanation:

(a) You win $5 if you roll a six, $1 if you roll an odd number, and $0 if you roll a 2 or a 4, and you pay $1.50 for every roll. The expected value is the sum of each outcome multiplied by its probability.

E = (5.00)(1/6) + (1.00)(3/6) + (0)(2/6) + (-1.50)(1)

E = -0.167

You are expected to lose on average about $0.17 per roll, which means Alex has the advantage.

(b) The probability of rolling a 2 or 4 on a fair die is 2/6 or 1/3. The probability of this happening five times is:

P = (1/3)⁵

P = 1/243

P ≈ 0.41%

There is approximately a 0.4% probability that a fair die will roll a 2 or 4 five times.

CI = p ± ME

ME = CV × SE

The margin of error is the critical value times the standard error.

The critical value for 95% confidence is z = 1.960.

The standard error for a proportion is:

SE = √(pq/n)

Given p = 1/6, q = 5/6, and n = 100:

SE = √((1/6) (5/6) / 100)

SE = 0.037

So the confidence interval is:

CI = 1/6 ± (1.960) (0.037)

CI = 0.167 ± 0.073

0.094 < p < 0.240

Since the observed proportion of 0.08 is outside of this interval, we can conclude with 95% confidence that the die is not fair.

(d) Under the current game rules and die probabilities, the expected value is:

E = (5.00)(0.08) + (1.00)(0.33) + (0)(0.59) + (-1.50)(1)

E = -0.77

To make the game fairer, but to still give Alex the advantage so she can make money for her fundraiser, we need to change the rules of the game so that the expected value is less negative.

One simple way to do this is to pay players $2.00 if they roll a 2.

Now the expected value is:

E = (5.00)(0.08) + (1.00)(0.33) + (2.00)(0.29) + (0)(0.30) + (-1.50)(1)

E = -0.19

Now instead of expecting to lose on average $0.77 per roll, players can expect to lose on average $0.19 per roll. This means they have a better chance of winning money, but Alex still has the advantage.

8 0

3 years ago

Swati is substituting t=5 and t=9 to determine if the two expressions are equivalent.

horrorfan [7]

Answer:

No the two expressions are not equivalent.

Step-by-step explanation:

the given two expressions t=5 and t=9 are not equivalent because t being a variable cant take two numbers at a same time.however if they are placed in given two expressions of 't' such that that they give equal value when the first expression gives a value 'a' at t=5 while the other expression gives a value 'a' at t=9 then those two expressions will be equal.

4 0

3 years ago

Read 2 more answers

F(x) = 3x + 2<br> What is f(5)?

kvasek [131]

$f(x)=3x+2\\\\f(5)=3(5)+2 =15+2=17$