PLEASE HELP !!!!! 1) Find the equation of the trend line (line of best fit). SHOW WORK

2) Predict the number of tips that would be collected if 100 costumers were served at the restaurant on a given day. Explain your reasoning.

3)EXPLAIN how to use the regression calculator to make a reasonable prediction given a data table

(I don't know how to attach more than 1 picture by the way )

Answers

Answer 1

Answer:

Answer:

1) y = 1.8741176487x + 3.655964863

2) About $191 using the equation, about $180 or more using the data you are given.

3) I can use the regression calculator by using the largest number of customers you have in the data set and lowest number of customers and compare them to see if the numbers are in ascending or descending order.

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Answers

Answer:

a) $P(X=13)=(24C13)(0.4)^(13) (1-0.4)^(24-13)=0.0608$

$P(X=17)=(24C17)(0.4)^(17) (1-0.4)^(24-17)=0.0017$

$P(X=13 U X=17) = 0.0608+0.0017=0.0624$

b) $P(X \geq 17)=0.000427$

c) $P(X \geq 16)= 1-0.000427=0.9996$

d) $E(X)= np = 22*0.4=8.8$

e) $Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=24, p=0.4)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

3) Part a

$P(X=13)=(22C13)(0.4)^(13) (1-0.4)^(22-13)=0.0336$

$P(X=17)=(22C17)(0.4)^(17) (1-0.4)^(22-17)=0.00035$

$P(X=13 U X=17) = 0.0336+0.00035=0.0340$

4) Part b

$P(X \geq 17)=P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)$

$P(X=17)=(22C17)(0.4)^(17) (1-0.4)^(22-17)=0.00035$

$P(X=18)=(22C18)(0.4)^(18) (1-0.4)^(22-18)=0.0000651$

$P(X=19)=(22C19)(0.4)^(19) (1-0.4)^(22-19)=0.00000914$

$P(X=20)=(22C20)(0.4)^(20) (1-0.4)^(22-20)=0.000000914$

$P(X=21)=(22C21)(0.4)^(21) (1-0.4)^(22-21)=5.81x10^(-8)$

$P(X=22)=(22C22)(0.4)^(22) (1-0.4)^(22-22)=1.76x10^(-9)$

$P(X \geq 17)=0.000427$

5) Part c

$P(X \leq 16)=1-P(X>16)=1-P(X\geq 17) = 1-[P(X=17)+P(X=18)+P(X=19)+P(X=20)+P(X=21)+P(X=22)]$

$P(X \geq 16)= 1-0.000427=0.9996$

6) Part d

The expected value is:

$E(X)= np = 22*0.4=8.8$

7) Part e

The variance is given by:

$Var(X) = np(1-p)= 22*0.4*(1-0,4)=5.28$

Some people take the early retirement option at age 62. According to the Social Security Administration, if you retire at age 62, your retirement benefits will be permanently reduced by 25%. If your monthly benefit, at full retirement age (67), would have been $1300 per month, and you retire at age 62, how much would you lose in total annual income over one year?

Answers

Answer:

$3900.

Step-by-step explanation:

If retirement is taken at the age of 67 years, income = $1300 per month.

% Loss, if retirement taken at the age of 62 years = 25% per month

Loss in dollars per month if retirement taken at the age of 62 years = 25% of Monthly income if retirement is taken at the age of 67 years

$\Rightarrow (25)/(100) * 1300\n\Rightarrow (1300)/(4)\n\Rightarrow 325 \$$

We know that there are 12 months in an year.

So, annual loss in total annual income over one year:

Loss in dollars per month $*$ 12 :

325 $*$ 12 = 3900$

Answer: $3,900

Step-by-step explanation:

What you usually make:

$1300 * 12 months = $15600

What you make with the cut:

$1300 * 0.75 = $975

* 12 months = $11700

15600-11700 = $3900

4/7 in simplest form

Answers

Answer:

4/7

Step-by-step explanation:

it is a propper fraction can not be simplified

Answer:

Step-by-step explanation:

4/7 is in simplest form

Two angles in a triangle are equal and their sum is equal to the third angle in the triangle. What are the measures of each of the three interior angles?