State the complement of each of the following sets: (a) Engineers with less than 36 months of full-time employment. (b) Samples

A total of 340,000 cattle were placed on feed

What portion of the 340,000 cattle placed on feed fell within the weight range of 700 to 799 pounds?

The fraction representing the total cattle weighing 700 - 799 pounds is 2/5

Let x denote the count of cattle within the 700 - 799 pound range

We can set up a proportion using this fraction

We cross-multiply to solve for x

340000 * 2 = 5x

680000 = 5x

Dividing both sides by 5 gives us

Thus, x= 136,000

So, there are 136,000 cattle in the weight bracket of 700 and 799 pounds

To find the solution for the equations, I will note the equation as I restate the original form. A number, n, (n) is summed with 15 subtracted from 3 times itself (+3n -15). The outcome is (=) 101. (101) Now, we will focus solely on what is contained within the parentheses. n + 3n -15 = 101. The properly formatted expression in your answers is: 3n - 15 + n = 101, as your initial response.

Alright, let's begin.

A right triangle (Triangle 1) has a hypotenuse measuring 115 mm, and angle α = 31.2°. What are the dimensions for a, b, and angle β?

Please see the diagram I have provided.

Utilizing SOH CAH TOA,

Substituting the value of sin 31.2

mm

Likewise,

Substituting the value of cos 31.2

mm

For angle β

tan β =

tan β = 1.65

Using the tangent inverse

β = 58.78°

Thus, we have a = 98.36 mm, b = 59.57 mm, and β = 58.78°:   Final Answer

I hope this is helpful:)

A right triangle (Triangle 1) has lengths of a = 505 mm and b = 286 mm. What are the dimensions for c, α, and β?

Refer to the diagram I’ve attached.

With sides a and b provided, we can find side c using the Pythagorean theorem.

Taking the square root of both sides

c = 580.36 mm

Applying SOH CAH TOA,

tan α =

Taking the tangent inverse

α = 60.48°

Similarly,

tan β =

Taking the tangent inverse

β = 29.52°

Thus, the answer is c = 580.36 mm, α = 60.48° and β = 29.52°:    Final Answer

I hope this is helpful:)