MATHEMATICS HIGH SCHOOL

A coin is to be tossed until a head appears twice in a row. What is the sample space for this experiment? If the coin is fair, what is the probability that it will be tossed exactly four times?

Answers

Answer 1

Answer:

Answer: $(2)/(16)$

Step-by-step explanation:

if the coin is tossed four times then the possible sample space is formed

$S=\left \{ HH, THH, HTHH, TTHH, HTTHH, THTHH, TTTHH, ...\right \}$

For the probability that the coin is tossed only four times is when

For tossing four times sample space is

S=( HHHH HHHT HHTH HHTT

HTHH HTHT HTTH HTTT

THHH THHT THTH THTT

TTHH TTHT TTTH TTTT )

out of the above required ones are HTHH,TTHH

so the probability is $(2)/(16)$

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What multiples of 2 are not factors of 24?

Answers

a factor of 24 is a number that can be multilied by another number (normally whole (not fraction or decimal) numbers)

so a factor must be less than the number

any multiple of 2 greater than 24 will work so
just any even number greater than 24 exg 26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60, and so on

The area of a rectangular city park is 25/54 square miles. The length of the park is 5/9 mile. what is the width in miles of the park?

Answers

$(25)/(54)$ divided by $(5)/(9)$
= $(25)/(54)$ multiplied by $(9)/(5)$
= $(5)/(6)$ miles

the minute hand of a clock is 6 inches long and moves from 3 o'clock to 5 o'clock. how far does the tip of the minute hand move? express your answer round to two decimal places

Answers

$from\ 3\ o'clock\ to\ 5\ o'clock\ is\ 2\ hours\n\n12\ hours\ \ \ \rightarrow\ \ \ 360^0\n2\ hours\ \ \ \ \rightarrow\ \ \ \ \alpha \n\n \alpha = (2\cdot360^0)/(12) =60^0\n\nx= (60^0)/(360^0) \cdot 2 \pi\cdot 6\ [in]= (1)/(6) \cdot12 \pi \ [in]=2 \pi \ [in]\approx2\cdot3.14\ [in]=6.28\ [in]$

Suppose you want to make a certain kind of tropical punch using bananas,oranges, and papayas. This is what you know.
You know the recipe takes seven pieces of fruit.
You don't know how many of each to put in the punch, but you know that
there are twice as many oranges as bananas.
You know that the seven pieces of fruit cost $5.25, where bananas cost $.50
each, oranges cost $.75 each, and papayas cost $1.25 each.
How many pieces of each type of fruit do you need to make the tropical punch?

Answers

Answer: 4 oranges, 2 bananas, and 1 papaya

Step-by-step explanation:

because there are twice as many oranges as bananas and 7 total fruit so 4 is the max amount of oranges you can have which leaves 2 bananas and 1 left over which is the papaya. Then to check work plug in the amount of fruit times their price which totals $5.25.

Final answer:

To make the tropical punch with a total of $5.25, you will need 1 banana, 2 oranges and 4 papayas based on their individual costs and the given relationship between bananas and oranges.

Explanation:

This is a linear algebra problem where we need to solve a system of linear equations. Let's denote the number of bananas as 'b', oranges as 'o', and papayas as 'p'. We have several pieces of information to form our equations:

1. The total pieces of fruit we have is 7. So, b + o + p = 7.

2. Oranges are twice as numerous as bananas, so o = 2b.

3. The total cost of the fruits is $5.25. So, 0.5b + 0.75o + 1.25p = 5.25.

By substituting o = 2b and re-arranging the equations, we obtain that b=1, o=2, and p=4. Hence, to make the tropical punch, we need 1 banana, 2 oranges, and 4 papayas.