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Jessica can walk 1.5 kilometers in 30 minutes. How long will it take her to walk 2.5 kilometers?
2 answers:
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From the given dimensions, of MI, IN, NT, TM, and MN, the quadrilateral
MINT can be drawn as shown in the attached image.
<h3>What are the steps for the construction of MINT?</h3>The given dimensions of the quadrilateral MINT are;
MI = 5 cm
IN = 6 cm
NT = 7 cm
TM = 3 cm
MN = 9 cm
The side MN is a diagonal of MINT, therefore;
ΔMIN, and ΔMTN are triangles with a common base = MN
The steps to construct MINT are therefore;
- Step 1; Draw the line MN = 9 cm.
- Step 2; Place the compass at point <em>M</em> and with a radius MI = 5 cm, draw an arc on one side of MN.
- Step 3; Place the compass at <em>N</em> and with radius IN = 6 cm, draw an arc to intersect the arc dawn in step 1 above.
- Step 4; Place an arc at point <em>M</em> and with radius TM = 3 cm draw an arc on the other side of MN.
- Step 5; Place the compass at point <em>N</em> and with radius NT = 7 cm, draw an arc to intersect the arc drawn in step 3.
- Step 6; Join the point of intersection of the arcs to points <em>M</em> and <em>N</em> to complete the quadrilateral MINT.
Please find attached the drawing (showing the construction arcs) of the
quadrilateral MINT created with MS Word.
Learn more about types of geometric construction here:
Answer:
1) 1 element
2) 13 elements
3) 22 elements
4) 40 elements
Step-by-step explanation:
1) Only one element will have no tails: the event that all the coins are heads.
2) 13 elements will have exactly one tile. Basically you have one element in each position that you can put a tail in.
3) There are elements that have exactly 2 tails. From those elements we have to remove the only element that starts and ends with a tail and in the middle it has heads only and the elements that starts and ends with a head and in the 11 remaining coins there are exactly 2 tails. For the last case, there are
possibilities, thus, the total amount of elements with one tile in the border and another one in the middle is 78-55-1 = 22
4) We can have:
- A pair at the start/end and another tail in the middle (this includes a triple at the start/end)
- One tail at the start/end and a pair in the middle (with heads next to the tail at the start/end)
For the first possibility there are 2 * 11 = 22 possibilities (first decide if the pair starts or ends and then select the remaining tail)
For the second possibility, we have 2*9 = 18 possibilities (first, select if there is a tail at the end or at the start, then put a head next to it and on the other extreme, for the remaining 10 coins, there are 9 possibilities to select 2 cosecutive ones to be tails).
This gives us a total of 18+22 = 40 possibilities.