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professor190 [17]
3 years ago
11

Otis tutors math students on sunday afternoons. he charges $35 for each of the first 10 students. he changed $40 for each additi

onal student the maximum number of students he will accept is 20.
answer each question below:

a. what did otis make if 8 students came on the first sunday?

b. what did otis made if 17 students came of the second sunday

c. if a is the amount that otis makes from S students that he tutors, write A as a piece wise function of S
Mathematics
1 answer:
lions [1.4K]3 years ago
7 0
For A it’ll be $280
B-$630
C- I don’t know
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1. Total selling price: $420,<br> Maine sales tax rate:<br> 5 percent.<br> Find the sales tax.
denpristay [2]

Answer: 21

Step-by-step explanation:

5%x420= 21

7 0
3 years ago
An account earns simple interest. (a) Find the interest earned. (b) Find the
Debora [2.8K]

Answer:

#a. $80

#b. $1680

Step-by-step explanation:

We are given;

  • Amount invested (principal) is $1600
  • Rate of interest is 5%
  • Time = 1 year

We are required to determine the amount of simple interest earned and the amount or balance in the account after 1 year.

#a. Interest earned

To calculate simple interest we use the formula;

I = (PRT) ÷ 100

Where, P is the principal, R is the rate, T is the time and I is the simple interest.

Therefore;

I = (1600 × 5 × 1) ÷ 100

 = $80

Therefore, simple interest earned is $80

#b. Balance of the account (Amount accrued)

We are going to use the formula;

A = P + I , where A is the amount accrued, P is the principal and I is the simple interest earned.

Therefore;

Account balance = $1600 + $80

                            = $1680

Thus, the account balance after 1 year will be $1680

8 0
3 years ago
10/21 + ( 2/3 - 1/7 ) =
Marizza181 [45]
Simplify 2/3 - 1/7 to 11/21
10/21 + 11/21
Simplify 
 The answer is 1.
7 0
3 years ago
Read 2 more answers
Helppppppppppppppppppppppppppppppppppppppppppppp
jek_recluse [69]
You’re trying to find the better buy so you want to find out how much you’re paying per unit (in this case kg)

So you divide the price by the unit (kg)

And find the better buy by looking at which price is cheapest.

Your answer is the 7.48 kg bag


Hope this helps and good luck!!

8 0
2 years ago
A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates w
sveta [45]

Answer:

(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412  

(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318  

And the 95% confidence interval would be given (-0.1412;-0.0318).  

We are confident at 95% that the difference between the two proportions is between -0.1412 \leq p_A -p_B \leq -0.0318

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p_A represent the real population proportion for business  

\hat p_A =\frac{75}{400}=0.1875 represent the estimated proportion for Business

n_A=400 is the sample size required for Business

p_B represent the real population proportion for non Business

\hat p_B =\frac{137}{500}=0.274 represent the estimated proportion for non Business

n_B=500 is the sample size required for non Business

z represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

Solution to the problem

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.96  

And replacing into the confidence interval formula we got:  

(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412  

(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318  

And the 95% confidence interval would be given (-0.1412;-0.0318).  

We are confident at 95% that the difference between the two proportions is between -0.1412 \leq p_A -p_B \leq -0.0318

7 0
3 years ago
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