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3 years ago

When using the given diagram to determine the area of the pentagon by decomposition, which statements are correct?:

Mathematics

1 answer:

pogonyaev3 years ago

6 0

Answer:

Options (B) and (E)

Step-by-step explanation:

Area of ΔABC = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(14)(6)$

= 42 in²

Area of trapezoid ADEC = $\frac{1}{2}(b_1+b_2)h$

[Here, $b_1$ and $b_2$ are the parallel sides and 'h' is the height of the isosceles trapezoid given]

= $\frac{1}{2}(10+14)(8)$

= 96 in²

Area of the pentagon = Area of triangle ABC + Area of trapezoid ADEC

= 42 + 96

= 138 in²

Therefore, Options (B) and (E) are the correct options.

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What is the measure of the angle at the tail end of the kite?

Alja [10]

Answer:

79 inches if don't believe me dont

Step-by-step explanation:

just putting in words give me points so

6 0

3 years ago

10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.

erastova [34]

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

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 combinations 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 success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

$p = \frac{4}{6} = 0.6667$

10 normal six sided dice are thrown.

This means that $n = 10$

Find the probability of obtaining at least 8 failures.

This is:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

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

$P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951$

$P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867$

$P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174$

Then

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992$

0.2992 = 29.92% probability of obtaining at least 8 failures.

8 0

3 years ago

Is sin(x) even or odd ? prove with examples ?

zloy xaker [14]

Answer:

$\text{sin}(x)$ is an odd function.

Step-by-step explanation:

We are asked to prove whether $\text{sin}(x)$ is even or odd.

We know that a function $f(x)$ is even if $f(x)=f(-x)$ and a function $f(x)$ is odd, when $f(-x)=-f(x)$ .

We also know that an even function is symmetric with respect to y-axis and an odd function is symmetric about the origin.

Upon looking at our attachment, we can see that $\text{sin}(x)$ is symmetric with respect to origin, therefore, $\text{sin}(x)$ is an odd function.