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VMariaS [17]
3 years ago
12

The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap cost $1 and the chicken wrap cost$1.8

0. Today they made $98.80 from the 70 wraps sold. How many of the wraps sold were vegetarian?
Mathematics
1 answer:
vfiekz [6]3 years ago
6 0
Let us assume the number of vegetarian wraps made = x
Let us assume the number of chicken wraps made = y
Then
x + y = 70
x = 70 - y
And
x + 1.80y = 98.80
Putting the value of x from the first equation in the second equation, we get
x + 1.80y = 98.80
70 - y + 1.80y = 98.80
0.80y = 28.80
y = 36
Putting the value of y in the first equation, we get
x + y = 70
x + 36 = 70
x = 34
From the above deduction, we can conclude that the number of vegetarian warps sold was 34. I hope the answer has come to your desired help.
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This is a binomial probability. For i, we will apply the Binomial probability formula

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\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}

Note that I made the probability of being defective as the probability of success = p

and probability of none defective as probability of failure = q

Exactly 2 are defective becomes the binomial probability

\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}

Hence the answer is 0.1157

(ii) None is defective becomes

\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}

hence the answer is 0.4823

(iii) All are defective

\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}

(iv) At least one is defective

This is 1 - probability that none is defective

\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}

Hence the answer is 0.5177

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