A sample of 6 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 2.88,2.91,2.97,2.97,2.92,2.87

Standard deviation = 0.039 mm

Step-by-step explanation:

The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.

Mathematically,

Standard deviation = σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean

N = number of variables = 6

We first calculate the mean

xbar = (Σx)/N

xbar = (2.88+2.91+2.97+2.97+2.92+2.87)/6

xbar = (17.52/6) = 2.92 mm

Σ(x - xbar)² = [(2.88 - 2.92) + (2.91 - 2.92)² + (2.97 - 2.92)² + (2.97 - 2.92)² + (2.92 - 2.92)² + (2.87 - 2.92)²] = 0.0092

σ = √[Σ(x - xbar)²/N] = √(0.0092/6) = √0.0015333

σ = 0.039 mm

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

$35.59 in pounds

step-by-step explanation: