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2 years ago

What is the Median of the numbers 45, 40, 47, 50, 45, 49, 40, 46?

Mathematics

1 answer:

stepan [7]2 years ago

8 0

Answer: 45

Step-by-step explanation:

The Median is the Middle # in the set.

I hope this helps!

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What is the measurement of the longest line segment in a right rectangular prism that is 26 inches long, 2 inches wide, and 2 in

EastWind [94]

Answer:

$6\sqrt{19} \approx 26.153$ inches.

Step-by-step explanation:

The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment $\mathsf{AG}$ .

In this diagram (not to scale,) $\mathsf{AB} = 26$ (length of prism,) $\mathsf{AC} = 2$ (width of prism,) $\mathsf{AE} = 2$ (height of prism.)

Pythagorean Theorem can help find the length of $\mathsf{AG}$ , one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.

Start by finding the length of line segment $\mathsf{AD}$ . That's the black dotted line in the diagram. In right triangle $\triangle\mathsf{ABD}$ (second diagram,)

Segment $\mathsf{AD}$ is the hypotenuse.
One of the legs of $\triangle\mathsf{ABD}$ is $\mathsf{AB}$ . The length of $\mathsf{AB}$ is $26$ , same as the length of this prism.
Segment $\mathsf{BD}$ is the other leg of this triangle. The length of $\mathsf{BD}$ is $2$ , same as the width of this prism.

Apply the Pythagorean Theorem to right triangle $\triangle\mathsf{ABD}$ to find the length of $\mathsf{AB}$ , the hypotenuse of this triangle:

$\mathsf{AD} = \sqrt{\mathsf{AB}^2 + \mathsf{BD}^2} = \sqrt{26^2 + 2^2}$ .

Consider right triangle $\triangle \mathsf{ADG}$ (third diagram.) In this triangle,

Segment $\mathsf{AG}$ is the hypotenuse, while
$\mathsf{AD}$ and $\mathsf{DG}$ are the two legs.

$\mathsf{AD} = \sqrt{26^2 + 2^2}$ . The length of segment $\mathsf{DG}$ is the same as the height of the rectangular prism, $2$ (inches.) Apply the Pythagorean Theorem to right triangle $\triangle \mathsf{ADG}$ to find the length of the hypotenuse $\mathsf{AG}$ :

$\begin{aligned}\mathsf{AG} &= \sqrt{\mathsf{AD}^2 + \mathsf{GD}^2} \\ &= \sqrt{\left(\sqrt{26^2 + 2^2}\right)^2 + 2^2}\\ &= \sqrt{\left(26^2 + 2^2\right) + 2^2} \\&= 6\sqrt{19} \\&\approx 26.153\end{aligned}$ .

Hence, the length of the longest line segment in this prism is $6\sqrt{19} \approx 26.153$ inches.

5 0

3 years ago

Solve for x <br> URGENTTT

brilliants [131]

X=4

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5 0

3 years ago

The chemical Element ,silver , boils at temperatures of 3924°F what is the boiling point for silver in degrees Celsius ? round y

mixer [17]

Answer:

2162.2 degrees Celsius

Step-by-step explanation:

Celsius (°C) = (Fahrenheit - 32) / 1.8

3924-32 = 3892

3982 / 1.8 = 2162.2222222222222222222222

Rounded is 2162.2

8 0

2 years ago

Someone please help me with this asap

Leokris [45]

Answer:

All of these terms are dollar amounts.

Step-by-step explanation:

Here, x + y = 10 (where these numerals represent counts)

(1/2)x + (1/4)y = 4 (where (1/2), (1/4) and 4 are dollar amounts)

Let's eliminate y. To accomplish this, mult. the 2nd eq'n by-4, obtaining

-2x - y = -16, and then combining this with the 1st equation, as follows:

-2x - y = -16

x + y = 10

-------------------

-x = -6, or x = 6. This represents the number of pens purchased by Terrance.

Subbing 6 for x in the first equation, we get y = 4. This represents the number of pencils he bought.

($0.50)x + ($0.25)y = $4.00 (dollar amounts)

5 0

3 years ago

SOMEONE HELP !!!!! PLEASEEEEEEEEEE!!!¡¡¡!¡!¡

vladimir1956 [14]

Answer is a, 57.49.

17.42-12.60-9.62= $-4.80+62.29=57.49

4 0

3 years ago