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3 years ago

What is the area of the polygon?

Mathematics

1 answer:

Anna11 [10]3 years ago

6 0

If you draw line VR, it divides the figure into a 5×6 rectangle VRDE and a 6×3 triangle VRM.

The area is the sum of the areas of the rectangle and triangle:
rectangle area = 5×6 = 30
triangle area = (1/2)6×3 = 9
total area = 30 + 9 = 39 units²

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A coin, having probability p of landing heads, is continually flipped until at least one head and one tail have been flipped. (a

Natali [406]

Answer:

(a)

The probability that you stop at the fifth flip would be

$p^4 (1-p) + (1-p)^4 p$

(b)

The expected numbers of flips needed would be

$\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1} = 1/p$

Therefore, suppose that $p = 0.5$ , then the expected number of flips needed would be 1/0.5 = 2.

Step-by-step explanation:

(a)

Case 1

Imagine that you throw your coin and you get only heads, then you would stop when you get the first tail. So the probability that you stop at the fifth flip would be

$p^4 (1-p)$

Case 2

Imagine that you throw your coin and you get only tails, then you would stop when you get the first head. So the probability that you stop at the fifth flip would be

$(1-p)^4p$

Therefore the probability that you stop at the fifth flip would be

$p^4 (1-p) + (1-p)^4 p$

(b)

The expected numbers of flips needed would be

$\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1} = 1/p$

Therefore, suppose that $p = 0.5$ , then the expected number of flips needed would be 1/0.5 = 2.

7 0

2 years ago

Kaylin is tracking the progress of a plant’s growth. Today the plant is 4 cm high. The plant grows 0.5 cm per day.

antoniya [11.8K]

Answer: I dont know the answer becuase this makes no sinse what are you trying to ask because all you are saying is how much it grows a day

Step-by-step explanation:

8 0

2 years ago

Combine and simplify the following radical expression <br><br> ASAP ASAP ASAP ASAP

Montano1993 [528]

Answer:

$\sqrt[3]{3}$

Step-by-step explanation:

Our expression is: $\frac{1}{3} \sqrt[3]{81}$ .

Let's focus on the cube root of 81 first. What's the prime factorisation of 81? It's simply: 3 * 3 * 3 * 3, or $3^3*3$ . Put this in for 81:

$\sqrt[3]{81} =\sqrt[3]{3^3*3}=\sqrt[3]{3^3} *\sqrt[3]{3}$

We know that the cube root of 3 cubed will cancel out to become 3, but the cube root of 3 cannot be further simplified, so we keep that. Our outcome is then:

$\sqrt[3]{3^3} *\sqrt[3]{3}=3\sqrt[3]{3}$

Now, let's multiply this by 1/3, as shown in the original problem:

$\frac{1}{3}* 3\sqrt[3]{3}=\sqrt[3]{3}$

Thus, the answer is $\sqrt[3]{3}$ .

<em>~ an aesthetics lover</em>

6 0

3 years ago

Quadrilateral WXYZ is the result of a translation of quadrilateral ABCD . AB¯¯¯¯¯ is parallel to DC¯¯¯¯¯ in the pre-image. Drag

tigry1 [53]

The corresponding segments WX and ZY in the image are parallel.

When a shape is translated from location to another, the size and shape of the figure do not change. Therefore, lines that are corresponding are still parallel.

5 0

3 years ago

Identify the restrictions on the domain of f(x) = quantity x plus 5 over quantity x minus 2. x ≠ 5 x ≠ −5 x ≠ 2 x ≠ −2

horsena [70]

Answer: Third option.

Step-by-step explanation:

By definition, Rational Functions have the following form:

$f(x)=\frac{P(x)}{Q(x)}$

Where $P(x)$ and $Q(x)$ are polynomials.

The Restrictions of the Domain of Rational Functions are those Real numbers that make the denominator equal to zero, because the division by zero is not defined.

In this case, you have the following Rational Function:

$f(x)=\frac{x+5}{x-2}$