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2 years ago

The hypotenuse of a right triangle measures 58 cm and one of its legs measures 42 cm. What is the length of the missing leg?

Mathematics

2 answers:

Vesna [10]2 years ago

6 0

24 mm

Step-by-step explanation:

25^2 - 7^2

625 - 49

= 576

missing side = √576 = 24

tresset_1 [31]2 years ago

4 0

Pythagorean theorem
c2 = a2 + b2
58^2 = 42^2 + b2
3364 = 1764 + b2
1600 = b2
b = 40

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Ruben bought 6 comic books for $21 dollars sign, 21.<br> What was the cost for 1 comic book?

Lena [83]

Answer:

$3.5

Step-by-step explanation:

21/6=3.5

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2 years ago

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For each of the following binomial random variables, specify n and p. (a) A fair die is rolled 50 times. X = number of times a 5

Keith_Richards [23]

Answer:

a) $n = 50, p = \frac{1}{6}$

b) $n = 16, p = \frac{1}{100}$

c) $n = 26, p = 0.25, \mu = 6.5$

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $p$ is the probability of X happening.

(a) A fair die is rolled 50 times. X = number of times a 5 is rolled

The die is rolled 50 times, so $n = 50$ .

Each roll can have 6 outcomes. So the probability that 5 is rolled is $p = \frac{1}{6}$

(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.

You buy 16 boxes of cereal, so $n = 16$ .

1 of 100 are winners. So $p = \frac{1}{100}$ .

(c) Jack likes to play computer solitaire and wins about 25% of the time. X = number of games he wins out of his next 26 games.

He plays 26 games, so $n = 26$ .

He wins 25% of the time, so $p = 0.25$

We have that $\mu = np$ . So $\mu = 26*0.25 = 6.5$

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3 years ago

Describe the end behavior of the given function f(x)=2/3x-2

Ipatiy [6.2K]

Answer:

The end behavior of f(x)=2/3x-2 is: as x->+ infinity, f(x)->+ infinity

as x->- infinity, f(x)->- infinity

Step-by-step explanation:

When you are asked about the end behavior of a function, look to see where the function is traveling on the graph. For instance, this graph is linear, so you should look to see if the slope is positive or negative. This linear function is positive, so as x is reaching positive infinity the f(x) would also be reaching positive infinity. As x is reaching negative infinity, f(x) would also be reaching negative infinity. The end behavior of a function describes the trend of the graph on the left and right side of the x- axis. (As x approaches negative infinity and as x approaches positive infinity).

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3 years ago

Express the function f(x) =3x^2-6x-18 in the form a(x + h)^2=k, where a, h and k are constants.Hence state the :

ololo11 [35]

Answer:

The minimum value of f(x) is -21 and it occurs at x = 1

Step-by-step explanation:

f(x) =3x^2-6x-18

Factor out the greatest common factor out of the first two terms

f(x) =3(x^2-2x)-18

Complete the square

-2x/2 =-1 (-1)^2 = 1

Add 1 (But remember the 3 out front so we are really adding 3 so we need to subtract 3 to remain balanced)

f(x) = 3(x^2 -2x+1) -3 -18

f(x) = 3(x-1)^2 -21

This is vertex form

f(x) = a(x-h)^2 +k where (h,k) is the vertex and a is a constant

The vertex is (1,-21)

Since a > 0 this opens upward and the vertex is a minimum

The minimum value of f(x) is -21 and it occurs at x = 1

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2 years ago

A rectangular swimming pool is 50 feet long and 25 feet wide.

Scrat [10]

Answer:

Area = 1250 square feet

Step-by-step explanation:

The formula for area of the bottom of the pool is given by:

Area = length× breadth

= 50 × 25

= 1250 square feet

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2 years ago