$\left\{\begin{array}{ccc}4x-3y=2&|\text{add 3y to both sides}\\3x+5y=16\end{array}\right\\\left\{\begin{array}{ccc}4x=3y+2&|\text{divide both sides by 4}\\3x+5y=16\end{array}\right\\\left\{\begin{array}{ccc}x=0.75y+0.5&(*)\\3x+5y=16\end{array}\right\\\\\text{substitute}\ (*)\ \text{to the second equation}\\\\3(0.75y+0.5)+5y=16\qquad\text{use distributive property}\\\\(3)(0.75x)+(3)(0.5)+5y=16\\\\2.25y+1.5+5y=16\qquad\text{subtract 1.5 from both sides}\\\\7.25y=14.5\qquad\text{divide both sides by 7.25}$

$\boxed{y=2}\\\\\text{substitute the value of y to}\ (*):\\\\x=0.75(2)+0.5\\\\x=1.5+0.5\\\\\boxed{x=2}\\\\Answer:\ x=2\ and\ y=2\to(2,\ 2)$

7 0

3 years ago

Assume the readings on thermometers are normally distributed with a mean of 0degreesc and a standard deviation of 1.00degreesc.

Tanzania [10]

Let Z be the reading on thermometer. Z follows Standard Normal distribution with mean μ =0 and standard deviation σ=1

The probability that randomly selected thermometer reads greater than 2.07 is

P(z > 2.07) = 1 -P(z < 2.07)

Using z score table to find probability below z=2.07

P(Z < 2.07) = 0.9808

P(z > 2.07) = 1- 0.9808

P(z > 2.07) = 0.0192

The probability that a randomly selected thermometer reads greater than 2.07 is 0.0192

3 0

4 years ago

Special precision bolts are made by another machine. These are for jobs that require more exact measurements. The bolts must be

klio [65]

The solutions of the inequality is 7.99<x<8.01. I think this solutions means the radius of hole in the bolt or something along that, but I'm not sure.

3 0

3 years ago