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3 years ago

Using the order of operations , solve the value of the expression.

Mathematics

1 answer:

velikii [3]3 years ago

8 0

Hello.

$\frac{1}{6} (\sqrt{36} \div 3^{-2}) + 4^{3} \div |-8| = \\ \\ \frac{1}{6} (6 \div \frac{1}{9}) + 64 \div 8 \\ \\ \frac{1}{6} \times 54 + 8 \\ \\ \frac{54}{6} + 8 \\ \\ 9 + 8 = \\ \\ 17$

Hope I helped!

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Find the Area of the figure below, composed of a rectangle and one semicircle, with another semicircle removed. Round to the nea

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Answer:

72 square units

Step-by-step explanation:

The figure shown has a uniform horizontal cross section, so is equivalent to a rectangle with length 12 and height 6. Its area is given by the rectangle formula:

A = LW

A = (12)(6) = 72 . . . . square units

Additional comment

Essentially, the semicircle removed from the left side is tacked onto the right side. The rectangle area is unchanged by that.

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3 years ago

What two numbers can add to 4 but multiple to -12

olasank [31]

Answer:

Numbers: 6 and -2

Step-by-step explanation:

Equations

This question can be solved by inspection. It's just a matter of factoring 12 into two factors that sum 4. Both numbers must be of different signs and they are 6 and -2. Their sum is indeed 6-2=4 and their product is 6*(-2)=-12.

However, we'll solve it by the use of equations. Let's call x and y to the numbers. They must comply:

$x+y=4\qquad\qquad [1]$

$x.y=-12\qquad\qquad [2]$

Solving [1] for y:

$y=4-x$

Substituting in [2]

$x(4-x)=-12$

Operating:

$4x-x^2=-12$

Rearranging:

$x^2-4x-12=0$

Solving with the quadratic formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

With a=1, b=-4, c=-12:

$\displaystyle x=\frac{-(-4)\pm \sqrt{(-4)^2-4(1)(-12)}}{2(1)}$

$\displaystyle x=\frac{4\pm \sqrt{16+48}}{2}$

$\displaystyle x=\frac{4\pm 8}{2}$

The solutions are:

$\displaystyle x=\frac{4+ 8}{2}=6$

$\displaystyle x=\frac{4- 8}{2}=-2$

This confirms the preliminary results.

Numbers: 6 and -2

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3 years ago

Your new TV screen has a width that is 4 inches longer than its height. If the screen's diagonal measurement is 20 inches, find

scoundrel [369]

Answer:

So the height is 12

Step-by-step explanation:

Let W be the width

Let W- 4 be the height

W2 +(W-4)2 = 400

So: W2 -4W-192 =0

One uses the quadratic solution:

W = (4 + (16 + 4*192).5)/2 = 16

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3 years ago

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Zinaida [17]

Answer:

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3 years ago

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Put the following in order for the most area in the tails of the distribution. (a) Standard Normal Distribution (b) Student's

tensa zangetsu [6.8K]

Answer:

(b) (c) (a)

Step-by-step explanation:

Standard Normal distribution has a higher peak in the center, with more area in this región, hence it has less area in its tails.

Student's t-Distribution has a shape similar to the Standard Normal Distribution, with the difference that the shape depends on the degree of freedom. When the degree of freedom is smaller the distribution becomes flatter, so it has more area in its tails.

Student's t-Distributionwith 1515 degrees of freedom has mores area in the tails than the Student's t-Distribution with 2020 degrees of freedom and the latter has more area than Standard Normal Distribution

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3 years ago