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Katyanochek1 [597]
3 years ago
9

At a concession stand, 9 slices of pizza and 5 soft pretzels cost $33.25. If 6 soft pretzels and 4 slices of pizzas cost $19.50,

what is the cost of a soft pretzel and a slice of pizza?

Mathematics
2 answers:
lisabon 2012 [21]3 years ago
8 0
Let x and y represent the costs of a pizza slice and a soft pretzel, respectively. The two purchases can be described by ...
  9x +5y = 33.25
  4x +6y = 19.50

A graph shows the solution of these equations to be
  (x, y) = (3, 1.25)

The cost of a soft pretzel is $1.25.
The cost of a slice of pizza is $3.00.

vichka [17]3 years ago
8 0
9x+5y=33.25
4x+6y=19.50
Multiply the first equation by 6 and the second one by 5 so the ys (soft pretzels) will cancel out and leave you with x (slices of pizza) so you should get:
54x+30y=199.50
20x+30y=97.50
Then subtract the equations leaving you with:
34x=102
X=3
So each piece of pizza is $3
Then plug 3 in for x to get y I’ll just use the first equation
27+5y=33.25
5y=6.25
Y=1.25
Each pretzels costs $1.25
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a) H0: \mu \leq \mu_o

H1: \mu > \mu_o

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t = 1.6 represent the calculated statistic

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b) H0: \mu \geq \mu_o

H1: \mu < \mu_o

n = 13 represent the sample size

t = -1.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 13-1=12

We can calculathe the p value with this formula:

p_v = P(t_{12}

Since p_v >\alpha we fail to reject the null hypothesis on this case at 5% of significance.

c) H0: \mu \geq \mu_o

H1: \mu < \mu_o

n = 25 represent the sample size

t = -2.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 25-1=24

We can calculathe the p value with this formula:

p_v = P(t_{24}

Since p_v we can reject the null hypothesis on this case at 1% of significance.

Step-by-step explanation:

Part a

For this case we assume that we are testing the following system of hypothesis

H0: \mu \leq \mu_o

H1: \mu > \mu_o

n = 13 represent the sample size

t = 1.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 13-1=12

We can calculathe the p value with this formula:

p_v = P(t_{12} >1.6) = 0.068

Since p_v >\alpha we fail to reject the null hypothesis on this case at 5% of significance.

Part b

For this case we assume that we are testing the following system of hypothesis

H0: \mu \geq \mu_o

H1: \mu < \mu_o

n = 13 represent the sample size

t = -1.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 13-1=12

We can calculathe the p value with this formula:

p_v = P(t_{12}

Since p_v >\alpha we fail to reject the null hypothesis on this case at 5% of significance.

Part c

For this case we assume that we are testing the following system of hypothesis

H0: \mu \geq \mu_o

H1: \mu < \mu_o

n = 25 represent the sample size

t = -2.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 25-1=24

We can calculathe the p value with this formula:

p_v = P(t_{24}

Since p_v we can reject the null hypothesis on this case at 1% of significance.

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