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2 years ago

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An insurance company collected data from a class of high school sophomores on whether or not they have a cell phone and whether

or not they have a car. The two-way table below shows the data collected.
Calculate the relative frequency of the data to determine which association the two-way table suggests.
A. Those who do not have a car tend to have a cell phone.

B. Those who have a car tend not to have a cell phone.

C. Those who have a car tend to have a cell phone.

D. None of the associations listed are correct.

1 answer:

NeX [460]2 years ago

6 0

Answer:

C. Those who have a car tend to have a cell phone.

Step-by-step explanation:

The relative frequency for a data set n is calculated by dividing each frequency $x_i$ by n.

We have a table that relates the use of cars and cell phones.

First, we take from the table the population that has a car.

$n = 18$

Then, of the students who have a car, 12 have a cell phone and 6 do not have a cell phone.

Then we calculate the relative frequencies $f_{x_i}$ for those who have a cell phone and those who do not.

______________________________________________

Relative frequency Students with car n = 18.

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

C<em>ell phone No cell phone Total n</em>

12/18 6/18 18

_______________________________________________

_______________________________________________

Relative frequency Students with car n = 18.

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

C<em>ell phone No cell phone Total n</em>

0.666 0.333 18

________________________________________________

Most students who have a car also have a cell phone.

Now we calculate the relative frequency for students who do not have a car.

_______________________________________________

Relative frequency Students without a car n = 7

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

<em>Cell phone No cell phone Total n</em>

2/7 5/7 7

_______________________________________________

_______________________________________________

Relative frequency Students without a car n = 7

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

<em>Cell phone</em> <em> No</em> <em>cell phone Total n</em>

0.286 0.714 7

_______________________________________________

Most students who do not have a car do not have a cell phone either.

<em>Then these data suggest that. Those who have a car tend to have a cell phone.</em>

Option C

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If you take out a $15,000 loan for a period of 36 months at a 5.4% annual interest rate, how much of your first monthly payment

Tems11 [23]

Answer:

The amount that will go towards the balance is 385.71.

Step-by-step explanation:

The information provided is:

P = Principal of loan = $15,000

r = interest rate = 5.4% p.a. = $\frac{0.054}{12}= 0.0045$

n = number of periods = 36

The amount of the monthly payment that will go towards the balance is:

Amount towards the balance = EMI - Interest

First compute the Equated monthly installments (EMI) as follows:

$EMI=\frac{P\times r\times (1+r)^{n}}{(1+r)^{n}-1} \\=\frac{15000\times0.0045\times(1+0.0045)^{36}}{(1+0.0045)^{36}-1} \\=\frac{79.3125}{0.175}\\=453.21$

Now compute the interest as follows:

$Interest=P\times r\\=15000\times0.0045\\=67.5$

The amount that will go towards the balance is,

Amount towards the balance = EMI - Interest

= 453.21 - 67.5

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Thus, the amount that will go towards the balance is 385.71.

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2 years ago

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Of all the weld failures in a certain assembly, 85% of them occur in the weld metal itself, and the remaining 15% occur in the b

Aloiza [94]

Answer:

a.) 0.1028

b.) 0.6477

c.) 0.0388

d.) 3

e.) 2.55

Step-by-step explanation:

Forming a binomial Probability distribution

n = 20

Probability of success for Weld metal failure = 85%

Probability of success for base metal failure = 15%

We use the probabilit distribution formula of combination to solve the problem.

P(x=r) = nCr * p^r * q^n-r

a.) if exactly 5 are base metal failures, then p = 15 and our solution becomes:

P(x=5) = 20C5 * 0.15^5 * 0.85^15

P(x=5) = 0.1028

b.) probability that fewer than 4 are base metal failure= P(x=0) + P(x=1) + P(x=2) + P(x=3)

P(x=0) = 20C0 * 0.15^0 * 0.85^20 = 0.0388

P(x=1) = 20C1 * 0.15¹ * 0.85^19 = 0.1368

P(x=2) = 20C2 * 0.15² * 0.85^18 = 0.2293

P(x=3) = 20C3 * 0.15³ * 0.85^17 = 0.2428

Probability that fewer than 4 are base metal failures becomes: 0.038 + 0.1368 + 0.2293 + 0.2428 = 0.6477

c.) probability that none of them are results of base metal failure = P(x=0). As earlier calculated,

P(x=0) = 0.0388

d.) mean of base metal failures = np = 20*0.15 = 3

e.) standard deviation of base metal failures = √np(1-p)

=3 * (1 - 0.15) = 3 * 0.85

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2 years ago

At 11:00 a.M., there are 400 members and 150 non-members visiting a museum. After 11:00 a.M., 10 members leave every five minute

alexdok [17]

Answer:

$16:27$

Step-by-step explanation:

GIVEN: At $11:00\text{ A.M.}$ , there are $400$ members and $150$ non-members visiting a museum. After $11:00\text{ A.M.}$ , $10$ members leave every five minutes and $5$ non-members arrive every five minutes.

TO FIND: ratio of members to non-members at $1:00\text{ P.M.}$

SOLUTION:

Total number of members in museum at $11:00\text{ A.M.}$ $=400$

as after every $5$ minutes $10$ members leave

total number of $5$ minutes interval in $2$ hour $=\frac{60}{5}=12$

total members at $1:00\text{ P.M.}$ $=400-10\times24$

$=160$

Total number of non-members in museum at $11:00\text{ A.M.}$ $=150$

as after every $5$ minutes $5$ non-members arrive

total number of $5$ minutes interval in $2$ hour $=\frac{60}{5}=12$

total non-members at $1:00\text{ P.M.}$ $=150+5\times24$

$=270$

ratio of members to non-members at $1:00\text{ P.M.}$ $=\frac{\text{number of members}}{\text{number of non-members}}$

$=\frac{160}{270}$

$=\frac{16}{27}$

Hence the ratio of members to non-members at $1:00\text{ P.M.}$ is $\frac{16}{27}$

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Is it possible for an odd function to have the interval 0 infinity) as its domain?

mojhsa [17]

NO!

Prove by contradiction. First, define the the following terms:

odd function: f(-x) = -f(x)] and domain: all values of x

Proof: Suppose there f(-x) = -f(x) such that x is a negative integer, then f(-x) is a positive number <em>(-(-x) = +x)</em> and -f(x) is a negative number <em>(negative of a positive number is a negative number). </em>Since a positive number cannot equal a negative number, then this is not possible.

Answer: No

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