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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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The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir
Paha777 [63]

Answer:

95​% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                              P.Q. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean time = 5.15 years

            \sigma = sample standard deviation = 1.68 years

            n = sample of college graduates = 4400

            \mu = population mean time

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.</em>

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                               level of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                                              = [ 5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } } , 5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } } ]

                                             = [5.10 , 5.20]

Therefore, 95​% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

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Step-by-step explanation:

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we are given two points as

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x1=1 , y1=2

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now, we can use distance formula

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d=\sqrt{(1-1)^2+(5-2)^2}

d=\sqrt{(0)^2+(3)^2}

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d=3

so, distance between points is 3...........Answer

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