Ask question

Ask question

All categories

2 years ago

8

To raise money to attend Boy Scout camp Alec is selling popcorn.?small bags of popcorn sell for $4 each and large bag sale for $

6 each. he needs to earn at least $300 to attend camp you also earn a badge if he sells 60 bags total of any combination. write a system of linear inequalities to represent this situation

2 answers:

kati45 [8]2 years ago

7 0

Let small bags of popcorn be represented by = x

Let large bags be represented by = y

Price of small bag = $4

Price of large bag = $6

A minimum of $300 is required to attend the camp so

$4x+6y\leq300$ .............(1)

Also given is that a badge is earned if Alec sells 60 bags

So, equation is

$x+y=60$ ............(2)

melamori03 [73]2 years ago

4 0

Answer:

The system of linear inequalities to represent the situation :

x+y = 60

4x+6y≥300

Step-by-step explanation:

We are given that :

Cost of one small popcorn bag is $4

Cost of one large popcorn bag $6

Let no. of small popcorn bags Alec sold be x

Let no. of large popcorn bags Alec sold be y

Cost of x small popcorn bag is $4x

Cost of y large popcorn bag $6y

Since she sold total 60 bags .

So, equation becomes:

x+y = 60 --(a)

Since she had to earn at least $300.

So, equation becomes:

4x+6y≥300 --(b)

Thus the system of linear inequalities to represent the situation :

x+y = 60

4x+6y≥300

You might be interested in

Robert makes $951 gross income per week and keeps $762 of it after tax withholding. How many allowances has Robert claimed? For

MAXImum [283]

Answer:

Option D,four is correct

Step-by-step explanation:

The tax withholding from the gross income of $951 is the gross income itself minus the income after tax withholding i.e $189 ($951-$762)

The percentage of the withholding =189/951=20% approximately

Going by the multiple choices provided,option with 4,189 dollars seems to the correct option as that is the exact of the tax withholding on Robert's gross income and his earnings fall in between $950 and $960

4 0

2 years ago

Craig Campanella and Edie Hall both have night jobs. Craig has every thirteenth night and Edie has every Fifth night off. How of

Andrews [41]

Craig has every 13th night and Edie has every 5th night off.

You have to find LCM - the Least Common Multiple that is the smallest ("least") number that both 13 and 5 will divide into.

Since numbers 13 and 5 are both prime, then LCM(13,5)=13·5=65.

This means, they will have the same every 65th night off.

6 0

2 years ago

The manager at Gabriela's Furniture Store is trying to figure out how much to charge for a book shelf that just arrived. The boo

maria [59]

The shelf should sell for $235.20.

Marking the price up by 60% means taking 160% of the cost:
160% = 160/100 = 1.6; 1.6(147) = 235.20

5 0

2 years ago

Read 2 more answers

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 25% of the incoming calls invol

bagirrra123 [75]

Answer:

a) 0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b) 0.118 = 11.8% probability that exactly 4 of the calls involve a fax message

c) 0.904 = 90.4% probability that at least 4 of the calls involve a fax message

d) 0.786 = 78.6% probability that more than 4 of the calls involve a fax message

Step-by-step explanation:

For each call, there are only two possible outcomes. Either it involves a fax message, or it does not. The probability of a call involving a fax message is independent of other calls. So we use the binomial probability distribution to solve this question.

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.

25% of the incoming calls involve fax messages

This means that $p = 0.25$

25 incoming calls.

This means that $n = 25$

a. What is the probability that at most 4 of the calls involve a fax message?

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$ .

In which

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

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.001 + 0.006 + 0.025 + 0.064 + 0.118 = 0.214$

0.214 = 21.4% probability that at most 4 of the calls involve a fax message

b. What is the probability that exactly 4 of the calls involve a fax message?

$P(X = 4) = C_{25,4}.(0.25)^{4}.(0.75)^{21} = 0.118$

0.118 = 11.8% probability that exactly 4 of the calls involve a fax message.

c. What is the probability that at least 4 of the calls involve a fax message?

Either less than 4 calls involve fax messages, or at least 4 do. The sum of the probabilities of these events is 1. So

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$ . Then

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{25,0}.(0.25)^{0}.(0.75)^{25} = 0.001$

$P(X = 1) = C_{25,1}.(0.25)^{1}.(0.75)^{24} = 0.006$

$P(X = 2) = C_{25,2}.(0.25)^{2}.(0.75)^{23} = 0.025$

$P(X = 3) = C_{25,3}.(0.25)^{3}.(0.75)^{22} = 0.064$

$P(X$

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.096 = 0.904$

0.904 = 90.4% probability that at least 4 of the calls involve a fax message.

d. What is the probability that more than 4 of the calls involve a fax message?

Very similar to c.

$P(X \leq 4) + P(X > 4) = 1$

From a), $P(X \leq 4) = 0.214)$

Then

$P(X > 4) = 1 - 0.214 = 0.786$

0.786 = 78.6% probability that more than 4 of the calls involve a fax message

8 0

2 years ago

You deposit $2,900 into a bank account with a simple interest rate of 10% how do you find your account balance after 5 years

MAVERICK [17]

Formula: A = P(1 + rt)<span>
P= 2,900
R= 10%
T= 5 years

Answer: $4,350.00</span>

6 0

2 years ago