Consider the random experiment of tossing 3 fair coins and observing how many of them come to rest with the heads side of the coin facing upwards. (Assume that each of the coins comes to rest with either its heads side or its tails side facing upwards (i.e., none of the coins comes to rest balanced on its edge).) Letting A denote the event that at least 1 of the coins comes to rest with its heads side upwards, B denote the event that none of the coins comes to rest with its heads side upwards, and S denote the sample space, which of the following statements does not include an abuse of notation?

a. S = 16
b. S = AUB
c. S - 4
d. S = 3
e. P(B) = φ

Answers

Answer 1

Answer:

b. S = AUB

Step-by-step explanation:

Since the coins are tossed  3 times and each coin has head, H and tail, T(2 sides), the sample space is S = 2 × 2 × 2 = 2³ = 8

All the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH,THT and TTT

Since S denote the sample space

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

Since A denote the event that at least 1 of the coins comes to rest with its heads side upwards, the possible outcomes are HTT, HHT, HHH, THH, TTH, HTH and THT

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

Also B denote the event that none of the coins comes to rest with its heads side upwards, that is no heads. The possible outcome is TTT

So, B = {TTT}

Since S denote the sample space

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

So, A ∪ B = {HTT, HHT, HHH, THH, TTH, HTH,THT} ∪  {TTT} = {HTT, HHT, HHH, THH, TTH, HTH,THT, TTT} = S

So, S = A ∪ B

So, S = A ∪ B does not denote an abuse of notation.

The answer is b.


Related Questions

PLS PAKI ANSWER KAILANGAN LANG PO KASI EH
NONSENSE(REPORT)​

Answers

Answer:

1)  2/20 x 200 = 1/10 x 200 = 20

2) 3/20 x 200 = 30

3) 4/20 x 200 = 1/5 x 200 = 40

4) 5/20 x 200 = 1/4 x 200 = 50

5) 18/20 = 9/10 x 200 = 180

Rolling a fair Eight-sided die produces a uniformly distributed set of numbers between 1 and 8 with a mean of 4.5 and a standard deviation of 2.291. Assume that n eight-sided dice are rolled many times and the mean of the n outcomes is computed each time.

Required:
a. Find the mean and the standard deviation of the resulting distribution of sample means for n=36.
b. The mean of the resulting distribution of the sample means is:________

Answers

Answer:

a. The mean is 4.5 and the standard deviation is 0.3818.

b. 4.5

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 4.5 and a standard deviation of 2.291.

This means that [tex]\mu = 4.5, \sigma = 2.291[/tex]

a. Find the mean and the standard deviation of the resulting distribution of sample means for n=36.

By the Central Limit Theorem, the mean is 4.5 and the standard deviation is [tex]s = \frac{2.291}{\sqrt{36}} = 0.3818[/tex]

The mean is 4.5 and the standard deviation is 0.3818.

b. The mean of the resulting distribution of the sample means is:________

By the Central Limit Theorem, 4.5.

A rectangular Carrer has a perimeter of 240cm breadth of 50cm.What is it's length

Answers

Step-by-step explanation:

The perimeter of a rectangle is the length of all its 4 sides. Formula to calculate the perimeter of a rectangle is:

Perimeter of Rectangle = 2 × Length + 2 × Breadth

The perimeter can be represented using a model as below.

Perimeter = Length + Breadth + Length + Breadth

= 2 × Length + 2 × Breadth

Length + Breadth = Perimeter ÷ 2

Match the metric measurement on the left with an equivalent unit of measurement on the right

Answers

Answer:

ans:

0.3 hectoliter = 3000 centiliters0.03 liter = 30 milliliter

Match the metric measurement on the left with an equivalent unit of measurement on the right are as follows;

0.3 hectoliter       3 deciliters

0.03 liters             30 milliliters

30 centimeter     3 Deciliters

3000 Milliliters    0.3 Decaliters

What is the unit measurement?

A standard unit of measurement is a quantifiable language that describes the magnitude of the quantity.

Match the metric measurement on the left with an equivalent unit of measurement on the right is determined in the following steps given below.

1. 0.3 hectoliter = 0.3 × 10 = 3 deciliters

2. 0.03 liters = 0.03 × 1000 = 30 mililiters

3. 3 Centiliters = 0.3 Deciliters then 30 centimeter = 3 Deciliters

4. 3000 Milliliters = 0.3 Decaliters

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Equation of lines acellus pls help ofooehhenxkdoke

Answers

Answer:

Firstly you must find the slope of two point

Step-by-step explanation:

m=(y2-y1)/(x2-x1) m=-8/4 = -2 after this step you should choose one point. I want to choose (3,1) y-1=2*(x-3). our equation y=2x-7

In which number is the value of the 9 ten
times the value of the number nine in the number 920

Answers

Answer:

9 hundreds that is the answer

solve the equation
[tex] \frac{1}{6 - d} = \frac{1}{d - 5} [/tex]​

Answers

Answer:

5.5

Step-by-step explanation:

[tex] \frac{1}{6 - d} = \frac{1}{d - 5} \\ \\ \therefore \: 6 - d = d - 5 \\ \\ 6 + 5 = d + d \\ \\ 11 = 2d \\ \\ d = \frac{11}{2} \\ \\ d = 5.5[/tex]

For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains below a critical value y0 (a deficit), preceded by and followed by periods in which the supply exceeds this critical value (a surplus). An article proposes a geometric distribution with p = 0.365 for this random variable. (Round your answers to three decimal places.)

a. What is the probability that a drought lasts at most 3 intervals?
b. What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

Answers

Solution :

a). P(X = x)

     =   [tex]$p(1-p)^x$[/tex]  for x = 0, 1, 2, ....

   P(x ≤ 3) = 0.837

b). Expectation = [tex]$\frac{(1-p)}{p}$[/tex]

                        = 1.7397

  Variance = [tex]$\frac{(1-p)}{p^2}$[/tex]

                 = 4.7663726

  Standard deviation = 2.1832

 Therefore, mean + standard deviation

                  = 1.7397 + 2.1832

                  = 3.9229

[tex]$P(x > 3.9229) = 0.1626$[/tex]

So the required P = 2 x 0.1626

                             = 0.325

solution - 12. The digit in the tens place of a two-digit number is three times that in the units place. If the digits are reversed, the new number will be 36 less than the original number. Find the original number. Check your solution.​

Answers

Answer:

62

Step-by-step explanation:

t=digit in the tens place

u=digit in the units place

t=3*u

original number=t*10+u

number with reversed digits=u*10+t

u*10+t=t*10+u-36

u*10+(3*u)=(3*u)*10+u-36

10u+3u-30u-u=-36

-18u=-36

u=2

t=3*u=6

Original number = 62

Check the solution:

6=3*2 ok

26=62-36 ok

(View attachment)

a) Write ordered pairs.
b) Write the domain and range.
c) Why isn't the relation a function?
d) Which ordered pair should be removed to make the relation a function?

Answers

Answer:

in a relationship that maps elements from one set (the inputs) into elements from another set (the outputs), the usual notation for the ordered pairs is:

(x, y), where x is the input and y is the output.

In this case, the point where the arrow starts is the input, and where the arrow ends is the output.

a)

The ordered pairs are:

(28, 93)

(17, 126)

(52, 187)

(34, 108)

(34, 187)

b) The domain is the set of the inputs, in this case the domain is the set where all the arrows start, then the domain is:

{17, 28, 34, 52}

And the range is the set of the outputs, in this case the range is:

{93, 108, 126, 187}

c) A function is a relationship where the elements from the domain, the inputs, can be mapped into only one element from the range.

In this case, we can see that the input {34} is being mapped into two different outputs, then this is not a function.

d) We can remove one of the two ordered pairs where the input is {34},

So for example, we could remove:

(34, 108)

And then the relation would be a function.


Aball has a density of 0.5 g/ml and a mass of 125 grams. What is the volume of the ball?

Answers

Answer:

250

Step-by-step explanation:

Density = mass / volume

density = 0.5 g / mL

mass = 125 g

0.5 = 125 / V                 Multiply both sides by V

0.5 * V = 125                 Divide by 0.5

0.5V 0.5 = 125/0.5

V = 250

When doing these kinds of ratios make sure that you get the numbers all on one side before you actually do the division or multiplication. That way you won't get confused.

Find the net change in the value of the function between the given inputs.
h(t) = t2 + 9; from −4 to 7

Answers

The answer should be from 1 to 23

Find an equation for the line parallel to 3x-5y=2 with​ y-intercept (0,1/5). Write the answer in ​ slope-intercept form.

Answers

y= 3x/5 - 2/5 .i think

The perimeter of a parallelogram must be no less than 40 feet. The length of the rectangle is 6 feet. What are the possible measurements of the width? Write an inequality to represent this problem. Use w to represent the width of the parallelogram. [Hint: The formula for finding the perimeter of a parallelogram is P = 2 l + 2 w . What is the smallest possible measurement of the width? Justify your answer by showing all your work.

Answers

Answer: [tex]14\ ft[/tex]

Step-by-step explanation:

Given

Length of rectangle is [tex]6\ ft[/tex]

Perimeter must be greater than 40 ft

Suppose l and w be the length and width of the rectangle

[tex]\Rightarrow \text{Perimeter P=}2(l+w)\\\Rightarrow P\geq 40\\\Rightarrow 2(l+w)\geq40\\\Rightarrow l+w\geq20\\\Rightarrow w\geq20-6\\\Rightarrow w\geq14\ ft[/tex]

So, the smallest width can be [tex]14\ ft[/tex]

in order for the parallelogram to be a rhombus x=

Answers

Answer:

17

Step-by-step explanation:

Properties used:-

All sides of rhombus are equal therefore in the triangles

EQUAL SIDE OPPOSITE TO ANGLES, ANGLES BECOME EQUAL

then we use alternate interior angles

Then we get,

3x-11=x+23

2x=34

x=17

4. The electrical resistance of a wire varies inversely as the square of its radius. If the resistance is 0.80 ohm when the radius is 0.4cm. Find the resistance whom the radius is 0.7cm.​

Answers

9514 1404 393

Answer:

  0.261 ohm

Step-by-step explanation:

If the radius increases by a factor of 0.7/0.4= 7/4, the square of this factor is (7/4)^2 = 49/16. The inverse of this square is 16/49, which is the factor by which the resistance changed.

The resistance of the larger wire is ...

  (16/49)(0.80 ohm) ≈ 0.261 ohm

Write the equation for a parabola with a focus at ( 7, 2) and a directrix at y = -2
y = ?

Answers

A parabola with an equation, y2 = 4ax has its vertex at the origin and opens to the right.
It's not just the '4' that is important, it's '4a' that matters.
This type of parabola has a directrix at x = -a, and a focus at (a, 0). By writing the equation as it is, the position of the directrix and focus are readily identifiable.
For example, y2 = 2.4x doesn't say a great deal. Re-writing the equation of the parabola as y2 = 4*(0.6)x tells us immediately that the directrix is at x = -0.6 and the focus is at (0.6, 0)

find the simultaneous equation for:
4x+3y=7
2x+5y=7​

Answers

Answer:

x = 1 and y = 1

Step-by-step explanation:

You can eliminate x first to get the value of y which is 1 and then replace it in one of the equations.

find the area of the shape

Answers

Answer:

The area is 91 cm²

Step-by-step explanation:

The shape is a kite.

area of a kite = ½(p*q)

Where, p and q are the diagonals of the kite.

p = 13 cm

q = 7 + 7 = 14 cm

The area of the kite = ½(13 * 14)

= ½(182)

Area = 91 cm²

Find the length of the third side. If necessary, round to the nearest tenth

Answers

[tex]\huge\bold{Given:}[/tex]

Length of the base = 8

Length of the hypotenuse = 17

[tex]\huge\bold{To\:find:}[/tex]

The length of the third side ''[tex]x[/tex]".

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\longrightarrow{\purple{x\:=\: 15}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Using Pythagoras theorem, we have

(Perpendicular)² + (Base)² = (Hypotenuse)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + (8)² = (17)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] + 64 = 289

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 289 - 64

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 225

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]\sqrt{225}[/tex]

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]15[/tex]

Therefore, the length of the missing side [tex]x[/tex] is [tex]15[/tex].

[tex]\huge\bold{To\:verify :}[/tex]

[tex]\longrightarrow{\green{}}[/tex] (15)² + (8)² = (17)²

[tex]\longrightarrow{\green{}}[/tex] 225 + 64 = 289

[tex]\longrightarrow{\green{}}[/tex] 289 = 289

[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

PLEASE HELP MEEEEEEE EMERGENCY :(​

Answers

Answer:

Ok ☺️✌️✌️✌️Ok ok ok ok

How much would $100 invested at 8% interest compounded continuously be
worth after 15 years? Round your answer to the nearest cent.
A(t)=Poet
O A. $332.01
O B. $220.00
O C. $317.22
D. $285.67

Answers

Answer:

Step-by-step explanation:

A = [tex]pe^{rt}[/tex]

A = 100[tex]e^{.08 *15}[/tex]

A=. $332.01

The value of the investment after 15 years is $332.01.

Option A is the correct  answer.

What is compound interest?

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

The continuous compounding formula is given by:

[tex]A = Pe^{rt}[/tex]

Where:

A = the ending amount

P = the principal (initial investment)

e = the mathematical constant (approximately equal to 2.71828)

r = the interest rate (as a decimal)

t = the time period (in years)

Using this formula, we can find the value of the investment after 15 years:

A = 100 \times e^{0.08 \times 15} ≈ $332.01

Therefore,

The value of the investment after 15 years is $332.01.

Learn more about compound interest here:

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2) O número 6 e divisor de qual número a seguir ? Faça as divisões por 6 e verifique qual é exata

A) 64

B)72

C)128

D)80

POR FAVOR ME AJUDEM EU NÃO ESTOU COSENGUINDO !!!!!!!

Answers

Answer:please write in english

Step-by-step explanation:

12.10.4 Test (CST): Income and Budgeting
Question 12 of 25
What is the y-intercept of the line passing through the point 5.-6) with a
slope of - 1/7?
A.47/7
B.37/7
C.-37/7
D.-47/7

Answers

Answer:

C.-37/7

Step-by-step explanation:

Given the following data;

Points (x, y) = (5, -6)

Slope, m = -1/7

Mathematically, the equation of a straight line is given by the formula;

y = mx + c

Where;

m is the slope.

x and y are the points

c is the intercept.

To find the y-intercept of the line, we would use the following formula;

y - y1 = m(x - x1)

y - (-6) = -⅐(x - 5)

y + 6 = -⅐x + 5/7

y = -⅐x + (5/7 - 6)

y = -⅐x - 37/7 = mx + c

Therefore, y-intercept (c) = -37/7

Solve the exponential equation: 210 = 42x

Answers

Answer:

to get x you need to divide

210/42= 5

x=5

210 = 42x

210/42=5

42*5=210

so remove the x it'd be 210 = 42(5)

x = 5

what is equal to -10> ?

Answers

Answer:

It's answer is - 9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4......

(a+b)2=??? hihihihihihii

Answers

(A+B)^2 is equivalent to (a+b) • (a+b)

A recent study of 28 employees of XYZ company showed that the mean of the distance they traveled to work was 14.3 miles. The standard deviation of the sample mean was 2 miles.a. Find the 95% confidence interval of the true mean.b. If a manager wanted to be sure that most of her/his employees would not be late, how much time would she/he suggest they allow for the commute if the average speed were 30 miles per hour

Answers

Answer:

- At 95% confidence interval, the true mean is ( 13.5245 < μ < 15.0755 )

- the time allowed will be  0.50 hours or 30 minutes

Step-by-step explanation:

Given the data in the question;

sample size; n = 28

mean; x" = 14.3 miles

standard deviation; S = 2 miles.

degree of freedom DF = n - 1 = 28 - 1 = 27

confidence interval = 95%

level of significance = 1 - 95% = 1 - 0.95 = 0.05

so

[tex]t_{\alpha /2, df[/tex] = [tex]t_{0.025, df=27[/tex] = 2.0518

Hence, we have;

x" + [tex]t_{\alpha /2, df[/tex]( S/√n ) = 14.3 + 2.0518( 2/√28 )

= 14.3 + 0.7755

= 15.0755     { Upper Limit }

Also,

x" - [tex]t_{\alpha /2, df[/tex]( S/√n ) = 14.3 - 2.0518( 2/√28 )

= 14.3 - 0.7755

= 13.5245    { Lower Limit }

Therefore, at 95% confidence interval, the true mean is ( 13.5245 < μ < 15.0755 )

b)

If a manager wants to be sure that the employees are not late, then he/she should consider the upper bound of the confidence interval as the permissible distance range.

Now given that the average speed were 30 miles per hour

suggested time will be;

t = Upper limit / speed

t = 15.0755 / 30

t = 0.50 hours or 30 minutes

Therefore, the time allowed will be  0.50 hours or 30 minutes

Which statement is true about the two stars labeled in this diagram? This is an elliptical galaxy and Star A is older than Star B. This is a spiral galaxy and Star A is older than Star B. This is a spiral galaxy and Star B is older than Star A. This is an elliptical galaxy and Star B is older than Star A.

Answers

Answer:

a

Step-by-step explanation:

Help me plz I need to get a good score

Answers

Answer:

x+59 =180( sum of linear pair )

x=180-59

x=121

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