1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aliya0001 [1]
3 years ago
7

30 POINTS!!!!

Mathematics
1 answer:
Marina86 [1]3 years ago
4 0

Given

Tom and Martin both worked 9 hours this week and sold $360 worth of meals

Tom's percent of tips was 15% while Martin's was 20%

Find out the most money this week between Tom and Martin

To proof

In this question take two cases

FIRST CASE

Martin worked 9 hours

sold worth of meals = $360

Martin's percent of tip = 20%

First convert 20% in decimal form

= \frac{20}{100}

= 0.20

than the equation becomes

Martin makes money = 9 × 2.50 + 0.20 × 360

                                   = 22.5 + 72

                                   = $ 94.5

SECOND CASE

Tom worked 9 hours

Tom's percent of tips = 15%

sold worth of meals = $360

First 15 % is written in decimal form

= \frac{15}{100}

= 0.15

than the equation becomes

Tom  makes money = 9 × 2.15 + 0 .15× 360

                                =  19.35 + 54

                                = $ 73.35

Thus martin makes money is $94.5

Thus tom makes money is $73.35

Hence Martin makes more money than tom

Hence proved


You might be interested in
Which expression is equivalent? 7 − 4(2x − 3)
Gekata [30.6K]
7-8x+12 = -8x+19
Your answer is D. 
7 0
3 years ago
Read 2 more answers
62% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal places. If 48 owned dogs are r
dedylja [7]

Answer:

a) 0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b) 0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c) 0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d) 0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

Step-by-step explanation:

To solve this question, we use the binomial probability distribution, and also it's approximation to the normal distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

62% of owned dogs in the United States are spayed or neutered.

This means that p = 0.62

48 owned dogs are randomly selected

This means that n = 48

Mean and standard deviation, for the approximation:

\mu = E(x) = np = 48*0.62 = 29.76

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{48*0.62*0.38} = 3.36

a. Exactly 30 of them are spayed or neutered.

This is P(X = 30), which is not necessary the use of the approximation.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 30) = C_{48,30}.(0.62)^{30}.(0.38)^{18} = 0.1180

0.1180 = 11.80% probability that exactly 30 of them are spayed or neutered.

b. At most 33 of them are spayed or neutered.

Now we use the approximation. This is, using continuity correction, P(X \leq 33 + 0.5) = P(X \leq 33.5), which is the pvalue of Z when X = 33.5. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{33.5 - 29.76}{3.36}

Z = 1.11

Z = 1.11 has a pvalue of 0.8665

0.8665 = 86.65% probability that at most 33 of them are spayed or neutered.

c. At least 31 of them are spayed or neutered.

Using continuity correction, this is P(X \geq 31 - 0.5) = P(X \geq 30.5), which is 1 subtracted by the pvalue of Z when X = 30.5. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{30.5 - 29.76}{3.36}

Z = 0.22

Z = 0.22 has a pvalue of 0.5871

1 - 0.5871 = 0.4129

0.4129 = 41.29% probability that at least 31 of them are spayed or neutered.

d. Between 24 and 30 (including 24 and 30) of them are spayed or neutered.

This is, using continuity correction, P(24 - 0.5 \leq X \leq 30 + 0.5) = P(23.5 \leq X \leq 30.5), which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 23.5.

X = 30.5

Z = \frac{X - \mu}{\sigma}

Z = \frac{30.5 - 29.76}{3.36}

Z = 0.22

Z = 0.22 has a pvalue of 0.5871

X = 23.5

Z = \frac{X - \mu}{\sigma}

Z = \frac{23.5 - 29.76}{3.36}

Z = -1.86

Z = -1.86 has a pvalue of 0.0314

0.5871 - 0.0314 = 0.5557

0.5557 = 55.57% probability that between 24 and 30 of them are spayed or neutered.

8 0
3 years ago
A farmer sells 6.5 kilograms of pears and apples at the farmer's market. 4 5 of this weight is pears, and the rest is apples. Ho
jeka94

Answer:

Step-by-step explanation:

3 0
3 years ago
A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also ca
valkas [14]

Answer:

30

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
How will the graph of line y = -5x + 7 be affected if the 7 is changed to –7?
dybincka [34]

Answer:a

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • What is the length of one leg of the triangle?
    13·2 answers
  • Quotient of 8 decreased by 2 times t and 3
    5·1 answer
  • How many ways can a person select 3 videotapes from a collection of 10 tapes?
    9·1 answer
  • Which is the slope of the line with equation 7 x − 3 y = 21 ?
    7·1 answer
  • Find the average height of the building shown in the table 1.667 1.483 1.483 1.451 1.381
    8·2 answers
  • If the probability of david passing his exam is 1/4 what is the probabilty of him failing​
    14·2 answers
  • The table below shows claude's assets and liabilities. what is the total value of his assets
    9·2 answers
  • MARKING BRAINLEIST IF CORRECT AND QUICK
    9·2 answers
  • Jamal buys 33 bolts that cost $0.38 each.
    15·1 answer
  • SUMMATIVE TEST
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!