A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his

Mazyrski [523]

Answer:

$23\sqrt{3}\ un^2$

Step-by-step explanation:

Connect points I and K, K and M, M and I.

1. Find the area of triangles IJK, KLM and MNI:

$A_{\triangle IJK}=\dfrac{1}{2}\cdot IJ\cdot JK\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 2\cdot 3\cdot \dfrac{\sqrt{3}}{2}=\dfrac{3\sqrt{3}}{2}\ un^2\\ \\ \\A_{\triangle KLM}=\dfrac{1}{2}\cdot KL\cdot LM\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 8\cdot 2\cdot \dfrac{\sqrt{3}}{2}=4\sqrt{3}\ un^2\\ \\ \\A_{\triangle MNI}=\dfrac{1}{2}\cdot MN\cdot NI\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 3\cdot 8\cdot \dfrac{\sqrt{3}}{2}=6\sqrt{3}\ un^2\\ \\ \\$

2. Note that

$A_{\triangle IJK}=A_{\triangle IAK}=\dfrac{3\sqrt{3}}{2}\ un^2 \\ \\ \\A_{\triangle KLM}=A_{\triangle KAM}=4\sqrt{3}\ un^2 \\ \\ \\A_{\triangle MNI}=A_{\triangle MAI}=6\sqrt{3}\ un^2$

3. The area of hexagon IJKLMN is the sum of the area of all triangles:

$A_{IJKLMN}=2\cdot \left(\dfrac{3\sqrt{3}}{2}+4\sqrt{3}+6\sqrt{3}\right)=23\sqrt{3}\ un^2$

Another way to solve is to find the area of triangle KIM be Heorn's fomula, where all sides KI, KM and IM can be calculated using cosine theorem.

7 0

3 years ago

Your height and weight are examples of which level of measurement? A. Ordinal B. Nominal C. Ratio D. Interval

Ivahew [28]

Answer:

C. Ratio

True for this case we have a clear definition of the 0 since the 0 for the heigth and the weigth represent absence of mass. And the differences between numerical values for the two variables are meaingful.

Step-by-step explanation:

We want to know which type of variable represent the weigth and the height. Let's analyze one by one the options given:

A. Ordinal

False since by definition an ordinal variable is "is a categorical variable for which the possible values are ordered". And for this case the height and the weigth are not categorical since represent quantitative data.

B. Nominal

False by definition and ordinal variable is which one that can't be represented by numeric values, and for this case the weight and the height are not example of this definition.

C. Ratio

True for this case we have a clear definition of the 0 since the 0 for the heigth and the weigth represent absence of mass. And the differences between numerical values for the two variables are meaingful.

D. Interval

False on this scale we don't have a clear definition of the 0. And for this case the heigth and the weight have a known definition of the 0 corresponding to the absence of mass. And since the ratios are meaingful for the heigth and the weigth then can't be an interval variable.

8 0

3 years ago

Which inequality describes the possible values of x?

11111nata11111 [884]

Answer:

Step-by-step explanation:

ive done this before and the answer to the equation is c and also truss me on this if you want. I wouldnt

6 0

3 years ago

6,780,000 in scientific notation

klio [65]

Answer:

105 = 100,000 x 6.78 = 678,000

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

What is the answer 3 3/4 - 2 5/6=

Rom4ik [11]

Answer:

11/12

Step-by-step explanation:

3 3/4 - 2 5/6

Convert to improper fractions

15/4 - 17/6

Find a common denominator (12)

45/12 - 34/12

Subtract

11/12

Hope this helps :)

7 0

3 years ago

Read 2 more answers