Beatrice has two coins. The first coin is fair and the second coin is biased. The biased coin comes up heads with probability 2/3 and tails with probability 1/3. Beatrice selects one of the two coins at random and flips the selected coin 4 times. The result is HHTH. What is the probability that the fair coin was selected?

Answer:

Step-by-step explanation:

x²+y²-2x-10y+1=0

compare with x²+y²+2gx+2fy+c=0

center is (-g,-f)

radius=√(g²+f²-c)

2g=-2

g=-1

2f=-10

f=-5

radius=(1,5)

c=1

let eq. of circle be x²+y²-2x-10y+c=0

∵ it passes through (2,-3)

2²+(-3)²-2(2)-10(-3)+c=0

4+9-4+30+c=0

c=-39

eq. of circle is is x²+y²-2x-10y-39=0

Answer:

  length ≈ 5.583 ft

  width ≈ 3.583 ft

Step-by-step explanation:

If we let x represent the length of the table in feet, then the width is (x-2). The area is ...

  A = LW

  20 = x(x -2)

Writing this in standard form gives ...

  x^2 -2x -20 = 0

The coefficients used in the quadratic formula are a=1, b=-2, c=-20. The solutions are ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(-20)}}{2(1)}\\\\=\dfrac{2\pm\sqrt{4+80}}{2}=1\pm\sqrt{21}[/tex]

Of these values, the only one that makes sense is ...

  length = 1+√21 ≈ 5.583 ft

  width = length -2 ≈ 3.583 ft

Let width is x

length be x+2

On solving

we get

x is around 3.58 or 3.6ft

Answer:

click on image

Step-by-step explanation:

click on the image

Answer:

i dont understand

Step-by-step explanation:

i took test

Answer:

Hope that help you mark me brinilylist

Step-by-step explanation:

Given that 5 pounds of rice at a store cost $6.50.

Then 1 pound of rice at a store cost = $6.50/5= $1.3

So the equation for the cost can be written as:

C=1.3P just like we write equation y=mx

Now we have to graph the cost C, vs pounds of rice.

Variable for Pounds of rice is not given so let it be "P"

So let's make a table for the number of pounds (P) and cost (C)  we can graph the points from that table to get the final graph.

The Attached graph is the final graph.

Step-by-step explanation:

Speed is the correct answer

Answer:

5 sqrt(6) = x

Step-by-step explanation:

The pythagorean theorem states

a^2 + b^2 = c^2

Where a and b are the legs and c is the hypotenuse

7^2 + (sqrt(101))^2 = x^2

49+101 = x^2

150 = x^2

Take the square root of each side

sqrt(150) = sqrt(x^2)

sqrt(25*6) = x

5 sqrt(6) = x

Answer:

x=19/12

Step-by-step explanation:

(4x-3)/2 = 5/3

4x-3 = 10/3

3 = 9/3

4x = 10/3 + 9/3 = 19/3

x = 19/12

Hey there!

4x - 3/2 = 5/3

ADD 3/2 to BOTH SIDES

4x - 3/2 + 3/2 = 5/3 + 3/2

CANCEL out: -3/2 + 3/2 because it gives you 1

KEEP: 5/3 + 3/2 because it helps solve for the x-value.

NEW EQUATION: 4x = 5/3 + 3/2

SIMPLIFY IT!

4x = 19/6

DIVIDE 4 to BOTH SIDES

4x ÷ 4 = 19/6 ÷ 4

CANCEL out: 4 ÷ 4 because it gives you 1

KEEP: 19/6 ÷ 4 because it helps solve for the x-value

NEW EQUATION: x = 19/6 ÷ 4

SIMPLIFY IT!

x = 19/24

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

its 3 OR C

Step-by-step explanation:

Answer:216691116

Step-by-step explanation:

Answer:

216,691,116

Step-by-step explanation:

Answer:

it would have snowed 1 2/5 feet more the previous day than the current day.

Answer:

D. -1 the amount of water decreases by 1 gallon every minute.

Step-by-step explanation:

15, 0 -> 12, 3  

3 - 0 = 3  

-------

12 - 15 = -3

3/ -3 = -1

Answer:

248 is your answer

Step-by-step explanation:

The two angles are supplementary, therefore together they add to 360. So take 360 and subtract 112, you get 248. Hope this helps you :)

Answer:   (1,-5)

In other words, x = 1 and y = -5

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Work Shown:

6x + y = 1

6(1) + y = 1

6 + y = 1

y = 1-6

y = -5

The solution as an ordered pair is (1,-5)

Notice I started with the second equation and substituted in the first equation. The idea is to somehow reduce the two variables into one variable, so you can solve for that remaining variable.

Answer:

6x+y=1

or,6×1+y=1

or,6+y=1

or,y=6-1

ans,y=5

Answer:

Invalid

Step-by-step explanation:

This is invalid because you don't have to go some were to love something.

Answer:

Invalid

Step-by-step explanation:

All graduates love football;

This means all people who are graduates will love the football, it tells us nothing at all about people who are not graduates;

These people may love football or they may not;

Tom loves the football, thats all we are told;

He could, therefore, fall into either category, being a graduate since all graduates love the football or not being a graduate, since these might also love the football.

Answer:

I think is there answer is 26.606

There needs to be values to answer the question.

Answer: A. (4/8)

Step-by-step explanation: If there is 4 black swans and 8 swans in total you could see it's 4 black swan out of 8 total swans. You could do

8/8 - 4/8 = 4/8 to find out the answer too.

Using the t-distribution, it is found that since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.

At the null hypothesis, it is tested if the average box of cereal does not contain more than 368 grams, that is:

[tex]H_0: \mu \leq 368[/tex]

At the alternative hypothesis, it is tested if it contains, that is:

[tex]H_1: \mu > 368[/tex]

We have the standard deviation for the sample, hence, the t-distribution is used to solve this question.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

In this problem, the values of the parameters are: [tex]\overline{x} = 372.5, \mu = 368, s = 15, n = 25[/tex].

Hence, the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{372.5 - 368}{\frac{15}{\sqrt{25}}}[/tex]

[tex]t = 1.5[/tex]

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05, with 25 -1 = 24 df, is of [tex]t^{\ast} = 1.71[/tex].

Since the test statistic is less than the critical value for the right-tailed test, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.

You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/13873630

Answer: Benchmark numbers can be used to state that the square root of 60 is between 6 and 7.

Answer: 50 and 100

Step-by-step explanation:

( sorry if this is not what you meant ;-; )

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Explanation:

Race 1

Let's convert Malcom's distance to inches so we can compare his distance to his sister's.

1 yard = 3 feet

10 yards = 30 feet (multiply both sides by 10)

1 foot = 12 inches

30 feet = 360 inches (multiply both sides by 30)

In Malcom's first race, he ran 360 inches. He has run the furthest compared to his sister who ran 300 inches.

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Race 2

Convert Malcom's distance from feet to inches.

1 foot = 12 inches

18 feet = 216 inches (multiply both sides by 18)

Malcom runs 216 inches compared to his sister's distance of 180 inches. Malcom is the winner again.

------------------------

Race 3

120 inches = 120/12 = 10 feet

Divide by 12 to convert from inches to feet, or you could have these steps

12 inches = 1 ft

120 inches = 10 feet

after multiplying both sides by 10.

Malcom runs 10 feet compared to 5 feet which his sister runs.

In each race, Malcom has ran the furthest.

ANSWER:

y= -1/5x - 5

Since it is parallel, that means that the slope (-1/5x) is the same.

Since it is passing through the point (-10, 3), substitute the numbers in for x and y which means: -3= -1/5*(-10) + b

b stands for the new y-intercept

do the equation, and you should get the answer above!

Answer:

i think x = -5, y = -7 is a other solution set

Answers:

[tex]L(1,0) \to L \ ' \ (4.5,0)\\\\J(-1,-1) \to J \ ' \ (-4.5, 4.5)\\\\K(-1,1) \to K \ ' \ (-4.5,4.5)\\\\[/tex]

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Explanation:

We multiply each coordinate of each point by the scale factor 4.5

For example, point L(1,0) moves to L ' (4.5, 0)  since 4.5*1 = 4.5

This trick only works because the origin is the center of dilation. If the center is some other point, then you'd have to translate first, dilate, then translate back again.

Answer:

43 messages

Step-by-step explanation:

Given:

146 messages = $21.90

x messages = $6.45

Finding x by cross-multiplication:

x = 146*6.45/21.90 = 43

Hope this helps! :)

Step-by-step explanation:

the answer is shown in the photo

Answer:

60

Step-by-step explanation: