Can a triangle have two 30° angles? two 60° angles? two 90° angles? Explain.

Mathematics

1 answer:

Savatey [412]3 years ago

7 0

Answer:

Step-by-step explanation:

Two 30 - yes, 180 - 30 - 30 = 120. It is possible for 2 angles to be 30, the remaining angle would also be 120

Two 60 - yes, 180 - 60 - 60 = 60. It is possible for 2 angles to be 60, the remaining angle would also be 60

Two 90 - Not possible. The entire angles of a triangle have to equal 180, this would mean only 2 angles.

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A blue spruce grows an average of 6 inches per year. A hemlock grows an average of 4 inches per year. If a blue spruce is 4 feet

meriva

Answer: it will take 12 years for both trees to be of the same height.

Step-by-step explanation:

Let x represent the number of years that it will take for the blue spruce and the hemlock to be the same height.

A blue spruce grows an average of 6 inches per year. If a blue spruce is 4 feet tall,

1 inch = 0.0833 feet

6 inches = 6 × 0.0833 = 0.4998 feet

it means that its height in x years would be

0.4998x + 4

A hemlock grows an average of 4 inches per year. If a hemlock is 6 feet tall.

4 inches = 4 × 0.0833 = 0.3332 feet

it means that its height in x years would be

0.3332x + 6

The number of years that it will take both trees to be of same height is

0.4998x + 4 = 0.3332x + 6

0.4998x - 0.3332x = 6 - 4

0.1666x = 2

x = 2/0.1666

x = 12

6 0

4 years ago

(HMMT Combo 2009) Two jokers are added to a 52 card deck and the entire stack of 54 cards is shuffled randomly. What is the expe

myrzilka [38]

The expected number of cards from the card deck that will be strictly between the two jokers is $\frac{52}{3}$ .

The most popular deck of cards used today is a normal 52-card deck of French-suited playing cards. [a] It is the only standard pack[b] used for playing cards in English-speaking nations; but, in many other nations throughout the world, it is used alongside other traditional, frequently older, standard packs with various suit systems, like those with German-, Italian-, Spanish-, or Swiss suits. The English pattern pack is the only one widely accessible in Britain and America and the most popular pattern of French-suited cards globally. The Belgian-Genoese pattern, which was created in France but is also used widely in Spain, Italy, the Ottoman Empire, the Balkans, and much of North Africa and the Middle East, is the second most popular.

Let all pairs of the positions (m,n) of the jokers are equally likely

$P[0]=P[|m-n|=1]=\frac{53}{\left(\begin{array}{c}54 \\2\end{array}\right)}=\frac{2}{27}$

$P[1]=P[|m-n|=2]=\frac{52}{\left(\begin{array}{c}54 \\2\end{array}\right)}=\frac{104}{1431}$

$P[k]=P|m-n|=k+1=\frac{54-k-1}{\left(\begin{array}{c}54 \\2\end{array}\right)}$

the expected value will be

$\begin{array}{l}\sum_{k=1}^{52} \frac{54-k-1}{\left(\begin{array}{c}54 \\2\end{array}\right)} k \\=\frac{1}{1431}\left(\sum_{k=1}^{52} 53 k-k^{2}\right) \\=\frac{1}{1431}\left(\frac{53}{2}(52)(53)-\frac{1}{6}(52)(53)(105)\right)\\=\frac{52}{3}\end{array}$