An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Using the notation 4HH, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HTHT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin, construct a tree diagram to show the 18 elements of the sample space SS.
For the sample space SS
(a) list the elements corresponding to the event AA that a number less than 3 occurs on the die;
(b) list the elements corresponding to the event BB that two tails occur;
(c) list the elements corresponding to the event A′A ′;
(d) list the elements corresponding to the event A′∩BA ′ ∩B;
(e) list the elements corresponding to the event A∪BA∪B.

9514 1404 393

Answer:

  c = 3

Step-by-step explanation:

In order for the function to be continuous at b=3, the left and right limits must be the same. In short, we must have ...

  c(3) +9 = c(3²) -9

  18 = 6c . . . . . . . . add 9-3c to both sides

  3 = c . . . . . . . . . . divide by 6

Function f is continuous when c=3.

Answer:

27

Step-by-step explanation:

The Counting Principle states that the number of possible outcomes is equal to the product of the number of outcomes for each event. In this case, (M)(N)(O).

There are 27 possible outcome if the spinner is spun three times.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A spinner has three sections colored green, purple, and pink.

From the general formula of probability:

Probability = (desired outcomes)/(Total outcomes)

In our case,

the three possible outcomes of this event occurring are Green, Purple, and Purple, Green.

The desired outcomes = 3

The total outcomes = 3 x 3 x 3 = 27

Learn more about probability here:

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Answer:

11.5x 4.5-8 wayy easier all you do is add and multiply

Answer:

it is 1/2

Step-by-step explanation:

The product of a lines slope M and the slope K of a perpendicular is -1:

M*K=-1

This implies

K=-1/M

since

M * -1/M=-1

In our example we are given a line of slope M=-2 therefore the slope K of a line to perpendicular to this line is:

M*K=-1

-2*K=-1

K=-1/-2=1/2

Answer:

A.6.21

Step-by-step explanation:

A=2, b=-10, c=-5

Answer:

[tex] x = \frac{2*\sqrt{3}}{3} [/tex]

Step-by-step explanation:

Reference angle = 30°

Opposite side = x

Adjacent side = 2

Apply the tan trigonometric function, thus:

[tex] tan (30) = \frac{opp}{adj} [/tex]

[tex] tan (30) = \frac{x}{2} [/tex]

[tex] 2 * tan (30) = x [/tex]

[tex] 2 * \frac{1}{sqrt{3}} = x [/tex] (tan 30 = 1/√3)

[tex] \frac{2}{sqrt{3}} = x [/tex]

Rationalize

[tex] \frac{2* \sqrt{3}}{sqrt{3} * \sqrt{3}} = x [/tex]

[tex] \frac{2*\sqrt{3}}{3} = x [/tex]

Answer:

Step-by-step explanation:

x+3 1/2=9

x=9-7/2

x=(18-7)/2=11/2

x=5 1/2

Answer:

3 1/2 + 5 1/2= 9.

Step-by-step explanation:

Hope this helps? im sorry if it doesn't :)

Answer:

Step-by-step explanation:

tax = 7% of $45.09 = 0.07×$45.09 ≅ $3.16

Total cost = $45.09 + $3.16 = $48.25

Answer:

d. 6cm, 6cm, 6cm

Step-by-step explanation:

each one of the rulers is lined correctly and shows that it is 6 cm

[tex]\frac{4}{5}(4+y)[/tex]

Answer:

[tex]\frac{32}{3}[/tex]

Step-by-step explanation:

you simply multiply the bottom number times the whole number:

10*3 =30

then add the top number:

30+2=32

and finally, you put the 32/3

Answer:

yes

Step-by-step explanation:

only like terms can be combined

Answer:

yes. If it's variables, then only like variables can be combined. If it's fractions, then they must be converted to a common denominator before combining.

Step-by-step explanation:

Answer:

1.-179

2.68

3. 11

4. 25

5. -734

Answer:

12 one fourths

Step-by-step explanation:

Answer:

12 one fourths

Step-by-step explanation:

There 3 × 1 1/4 = 3 × 4 = 12 one fourths in 3

Answer:

56

Step-by-step explanation:

Range is difference between greatest and least. This is 97 - 41 = 56

Answer:

8/55

Step-by-step explanation:

4/5 DIVIDED 5 1/2 = 8/55

Answer:

35x48=1680

Step-by-step explanation:

1680

Answer:

The movie ended at 4:15 PM

Step-by-step explanation:

=> It started at 2:30, when you add an hour to that it will become 3:30

=> Then you must add the 45 minutes to it

=> so it will be 3:75, however that is not a right answer and it is not logical

=> so you need to add the first 30 minutes which will give you 4:00

=> then add the rest which is 15 minutes

therefore, your answer is 4:15 PM

hope this helps and i hope it is not too confusing :)

Answer:

4:15

Step-by-step explanation:

Answer:

sorry

Step-by-step explanation:

I don't know ........

Answer:

x = 115

z= 40

y = 140

Step-by-step explanation:

x = 180 - (40 +25) = 115

z = 180 - (115+25) = 40

y = 180 - (40) = 140

Answer:

This is your answer!!!

Step-by-step explanation:

I attached a pic.

Hope it helps!!!

Answer:

The percentage change was of 11.73%.

Step-by-step explanation:

The percentage change of the increase is given by the change multiplied by 100 and divided by the initial value.

Price of £8.95 is increased to £10.

Change: 10 - 8.95 = 1.05

Initial price: 8.95

1.05*100/8.95 = 11.73%

The percentage change was of 11.73%.

Answer:

x = 42/17

y = -12/17

Step-by-step explanation:

4x - 3y = 12

3x + 2y = 6

use the elimination method (definition at the bottom of the page)

multiply both sides of the equation 4x - 3y = 12 by 2

8x - 6y = 24

multiply both sides of the equation 3x + 2y = 6 by 3

9x + 6y = 18

now, add the two equations:

17x = 42

x = 42/17

now, plug this into the equation 3x + 2y = 6

126/17 + 2y = 6

2y = -24/17

y = -12/17

Answer:

[tex]x = 30.7[/tex]

Step-by-step explanation:

Given

See attachment

Required

Find x

To find x, we make use of:

[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

In this case, it is:

[tex]cos(36) = \frac{x}{38}[/tex]

Multiply both sides by 38

[tex]38 * cos(36) = \frac{x}{38}*38[/tex]

[tex]38 * cos(36) = x[/tex]

[tex]38 * 0.8090= x[/tex]

[tex]30.742= x[/tex]

[tex]x = 30.742[/tex]

[tex]x = 30.7[/tex] -- approximated

Answer:

27.50

Step-by-step explanation:

Since it is 16.50 each and they bought 5 packets total an easy way to solve this problem would be that you multiply 16.50 × 5 which will give you how much the total cost of the candy would be:

16.50 × 5 = 82.50

Since that is the total amount you would then divide 82.50 by 3 since Mary and her friends all split the cost three ways (since there are three of them):

82.50 ÷ 3 = 27.50

Which will give you your answer.

Answer:

1100

55100=1100 x 55100

=1100x

Step-by-step explanation:

Hope it is helpful...

The required value of unknown number a would be 2000.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

WE need to determine 55% of what number is 1100.

Let the unknown number is a. then we get;

55% of a = 1100

55/100 of a = 1100

55/100 x a = 1100

Cross mulitiplication, we get;

55a = 1100 x 100

55a = 110000

Divide by 55, we have;

a = 110000/ 55

a = 10000/ 5

a = 2000

Therefore, the required value of unknown number a would be 2000.

More can be learned about proportions at;

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Answer:

The answer is y = 4x - 1.

Step-by-step explanation:

The answer is y = 4x - 1.

Step-by-step explanation:

☆The equation we'll be using: y = mx + b

☆Since we already have the slope. we have to find the y-intercept.

☆\begin{gathered}y = mx + b \\ \\ 7 = 4(2) + b \\ 7 = 8 + b \\ \frac{ - 8 = - 8 \: \: \: \: \: \: \: \: \: \: \: }{ - 1 = b \: \: \: \: \: \: \: \: \: \: } \end{gathered}

y=mx+b

7=4(2)+b

7=8+b

−1=b

−8=−8