Question 4 options: parallelogram abcd is a rectangle. ax = 3y − 5bd = 5y what is the value of y? enter your answer in the box. y =

⇒If parallelogram A B CD is a rectangle, then Diagonals of parallelogram that is of rectangle will be of equal Length.

That is , Diagonal AC = Diagonal B D

⇒Given, AX= 3 y- 5

So, AC= 2 × (3 y- 5)→→[Diagonals of Parallelogram Bisect each other]

And, B D = 5 y

So,A C = B D ⇒→→Diagonals of a rectangle are equal.]

→2 ×(3 y - 5) = 5 y

→ 6 y - 10 = 5 y →→[Using Distributive Property of subtraction with respect to multiplication]

Combining Like terms that is Variables with Variables and Constant with Constant.

→ 6 y - 5 y = 10

→  y = 10

Step-by-step explanation:

The mean of the set of data given is

Mean = (275.4 + 276.8 + 273.9 + 275.0 + 275.8 + 275.9 + 276.1)/7 = 275.56

Standard deviation = √(summation(x - mean)^2/n

n = 7

Summation(x - mean)^2 = (275.4 - 275.56)^2 + (276.8 - 275.56)^2 + (273.9 - 275.56)^2 + (275.0 - 275.56)^2 + (275.8 - 275.56)^2 + (275.9 - 275.56)^2 + (276.1 - 275.56)^2 = 5.0972

Standard deviation = √(5.0972/7) = 0.85

We would set up the hypothesis test.

For the null hypothesis,

µ = 275

For the alternative hypothesis,

µ ≠ 275

This is a 2 tailed test.

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 7

Degrees of freedom, df = n - 1 = 7 - 1 = 6

t = (x - µ)/(s/√n)

Where

x = sample mean = 275.56

µ = population mean = 275

s = samples standard deviation = 0.85

t = (275.56 - 275)/(0.85/√7) = 1.74

We would determine the p value using the t test calculator. It becomes

p = 0.132

Because the p-value of 0.132 is greater than the significance level of 0.05, we would fail to reject the null hypothesis. We conclude the data does not provide convincing evidence that the mean amount of juice in all the bottles filled that day differs from the target value of 275 milliliters.