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Assoli18 [71]
3 years ago
10

Which point on the graph shows the price of 6 ounces of cheese? Use the formula y=x÷2 to find y when x is 6.

Mathematics
1 answer:
RSB [31]3 years ago
7 0

The value of y is 3 when x is 6.

Solution:

The given table is the amount of cheese in ounces and the cost price.

Let x represents the amount of cheese and y represents the cost price.

The formula which derived from the table is y = x ÷ 2.

That is $y=\frac{x}{2}.

<u>To find the value of y when x is 6:</u>

$y=\frac{x}{2}

Substitute x = 6 in the formula, we get

$y=\frac{6}{2}

y = 3

Hence the value of y is 3 when x is 6.

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Answer:

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we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.

Step-by-step explanation:

As a result of step 2, we can assume normal distribution for the null hypothesis

<em>step 3:</em>

z statistic is computed as follows:

z=\frac{X-M}{\frac{\sqrt{p*(1-p)} }{\sqrt{N} } } where

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  • M is the expected proportion of correct answers according to the null hypothesis (0.5)
  • p is the probability of correct answer (0.5)
  • N is the total number of questions in the test (40)

z=\frac{0.75-0.50}{\frac{\sqrt{0.5*(0.5)} }{\sqrt{40} } } ≈ 3.16

And corresponding p value for the z-statistic is p≈0.001.

Since p<0.05, we reject the null hypothesis and conclude that the student knows more than half of the answers and is not just guessing in 0.05 significance level.

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Step-by-step explanation:

Given

(x₁, y₁) = (2, 4)

(x₂, y₂) = (6, a)

(x₃, y₃) = (-1, 1)

A = 9 sq.units

Area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:

A=\frac{\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|}{2}

substituting the values (x₁, y₁) = (2, 4), (x₂, y₂) = (6, a), (x₃, y₃) = (-1, 1), A = 9 in th formula

A=\frac{\left|x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)\right|}{2}

9=\frac{\left|2\left(a-1\right)+6\left(1-4\right)+-1\left(4-a\right)\right|}{2}

Multiply both sides by 2

\frac{2\left|2\left(a-1\right)+6\left(1-4\right)-1\left(4-a\right)\right|}{2}=9\cdot \:2

simplify

\left|2\left(a-1\right)+6\left(1-4\right)-1\left(4-a\right)\right|=18

As the area is always positive.

so

2\left(a-1\right)+6\left(1-4\right)-1\cdot \left(4-a\right)=18

2\left(a-1\right)-18-\left(4-a\right)=18

Add 18 to both sides

2\left(a-1\right)-18-\left(4-a\right)+18=18+18

simplify

2\left(a-1\right)-\left(4-a\right)=36

3a-6=36

3a=42

Divide both sides by 3

\frac{3a}{3}=\frac{42}{3}

a=14

Thus, the value of a  = 14

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