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3 years ago

It's in the picture plzz help

Mathematics

1 answer:

zaharov [31]3 years ago

7 0

ANSWER:

Total monthly budget in dollar = $3665.

Now,

[i] Percent of taxes,

755/3665 × 100 = 20%

[ii] Percent of housing,

790/3665 × 100 = 22%

[iii] Percent of food,

350/3665 × 100 = 9%

[iv] Percent of savings,

700/3665 × 100 = 20%

[v] Percent of transportation,

245/3665 × 100 = 7%

[vi] Percent of clothing,

110/3665 × 100 = 3%

[vii] Percent of utilities,

185/3665 × 100 = 5%

[viii] Percent of entertainment,

110/3665 × 100 = 3%

[ix] Percent of other spending,

420/3665 × 100 = 11%

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Answer:

(10) Person B

(11) Person B

(12) $P(5\ or\ 6) = 60\%$

(13) Person B

Step-by-step explanation:

Given

Person A $\to$ 5 coins (records the outcome of Heads)

Person $\to$ Rolls 2 dice (recorded the larger number)

Person A

First, we list out the sample space of roll of 5 coins (It is too long, so I added it as an attachment)

Next, we list out all number of heads in each roll (sorted)

$Head = \{5,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,0\}$

$n(Head) = 32$

Person B

First, we list out the sample space of toss of 2 coins (It is too long, so I added it as an attachment)

Next, we list out the highest in each toss (sorted)

$Dice = \{2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6\}$

$n(Dice) = 30$

Question 10: Who is likely to get number 5

From person A list of outcomes, the proportion of 5 is:

$Pr(5) = \frac{n(5)}{n(Head)}$

$Pr(5) = \frac{1}{32}$

$Pr(5) = 0.03125$

From person B list of outcomes, the proportion of 5 is:

$Pr(5) = \frac{n(5)}{n(Dice)}$

$Pr(5) = \frac{8}{30}$

$Pr(5) = 0.267$

From the above calculations:  $0.267 > 0.03125$  Hence, person B is more likely to get 5

Question 11: Person with Higher median

For person A

$Median = \frac{n(Head) + 1}{2}th$

$Median = \frac{32 + 1}{2}th$

$Median = \frac{33}{2}th$

$Median = 16.5th$

This means that the median is the mean of the 16th and the 17th item

So,

$Median = \frac{3+2}{2}$

$Median = \frac{5}{2}$

$Median = 2.5$

For person B

$Median = \frac{n(Dice) + 1}{2}th$

$Median = \frac{30 + 1}{2}th$

$Median = \frac{31}{2}th$

$Median = 15.5th$

This means that the median is the mean of the 15th and the 16th item. So,

$Median = \frac{5+5}{2}$

$Median = \frac{10}{2}$

$Median = 5$

Person B has a greater median of 5

Question 12: Probability that B gets 5 or 6

This is calculated as:

$P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}$

From the sample space of person B, we have:

$n(5\ or\ 6) =n(5) + n(6)$

$n(5\ or\ 6) =8+10$

$n(5\ or\ 6) = 18$

So, we have:

$P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}$

$P(5\ or\ 6) = \frac{18}{30}$

$P(5\ or\ 6) = 0.60$

$P(5\ or\ 6) = 60\%$

Question 13: Person with higher probability of 3 or more

Person A

$n(3\ or\ more) = 16$

So:

$P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Head)}$

$P(3\ or\ more) = \frac{16}{32}$

$P(3\ or\ more) = 0.50$

$P(3\ or\ more) = 50\%$

Person B

$n(3\ or\ more) = 28$

So:

$P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Dice)}$

$P(3\ or\ more) = \frac{28}{30}$

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Answer:

Step-by-step explanation:

Angel ran 1 lap in 2 minutes.

Jayden ran 3 laps in 5 minutes.

How many minutes does it take Angel to run one kilometer? What about Jayden?

How far does Angel run in one minute? What about Jayden?

Who is running faster? Explain your reasoning.

IM Commentary

Parts (a) and (b) of the task ask students to find the unit rates that one can compute in this context. Part (b) does not specify whether the units should be laps or km, so answers can be expressed using either one.

The purpose of part (c) is to give students an opportunity to make use of the unit rates that they found in parts (a) and (b). While it is possible for students to solve part (c) in other ways, the solution shown represents the kind of reasoning with unit rates that 7th graders should be able to do. It is important to note that the answer can be determined using different unit rates as long as the reasoning behind it is correct.

Solution

We can create a table that shows how far each person runs for a certain number of laps:

Number of laps Number of km

1 25

2 45

3 65

We can see from the table that 1 km is exactly half way between 2 and 3 laps. So it will take 2.5 laps to run 1 km.

Since it takes Angel 2 minutes to run 1 lap, she will take

2.5 laps1 km⋅2 minutes1 lap=5 minutes1 km.

So it takes Angel 5 minutes to run 1 km.

Since it takes Jayden 5 minutes to runs 3 laps, she runs 1 lap in 53 minutes. Thus, it takes Jayden

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