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3 years ago

You are building a birdhouse that will have a volume of 128 in^3. the birdhouse will have the dimensions shown

Mathematics

1 answer:

Lady bird [3.3K]3 years ago

5 0

$a.\\V-the\ volume\\\\V(w)=4\cdot w\cdot (w+4)=4w^2+16w\ [in^3]\\\\b.\\V=128\ in^3\ \ \ \Rightarrow\ \ \ 4w^2+16w=128\ \ \ \Rightarrow\ \ \ 4w^2+16w-128=0\ /:4\\\\w^2+4w-32=0\\\\w^2+4w+4-36=0\ \ \ \Leftrightarrow\ \ \ (w+2)^2=36\\\\w+2=6\ \ \ \ \ or\ \ \ \ \ w+2=-6\\\\w=4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ w=-8\ \ \ \ (and\ \ \ w>0)\\\\w=4\ \ \ \Rightarrow\ \ \ w+4=8\\\\Ans.\ the\ dimensions\ of\ the\ birdhouse:\ \ 4\ in,\ 4\ in,\ 8 \ in$

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Answer:

the answer is d

Step-by-step explanation:

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3 years ago

A veterinarian’s assistant made a table that shows the animals seen in the office in one week. What is the probability that the

horsena [70]

Answer:

The probability that the pet seen was sick is 53.57%.

Step-by-step explanation:

The probability of an event E is the ration of the number of favorable outcomes to the total number of outcomes.

$P(E)=\frac{n(E)}{N}$

Here,

n (E) = number of favorable outcomes

N = total number of outcomes

Denote the events as follows:

C = the pet is a cat

D = the pet is a dog

O = the pet is some other animal

S = the pet is sick.

The data provided is summarized as follows:

n (C) = 28

n (C ∩ S) = 3

n (D) = 42

n (B ∩ S) = 4

n (O) = 24

n (O ∩ S) = 8

Compute the probability that a cat was sick as follows:

$P(C\cap S)=\frac{n(C\cap S)}{n(C)}=\frac{3}{28}$

Compute the probability that a dog was sick as follows:

$P(D\cap S)=\frac{n(D\cap S)}{n(D)}=\frac{4}{42}=\frac{2}{21}$

Compute the probability that another animal was sick as follows:

$P(O\cap S)=\frac{n(O\cap S)}{n(O)}=\frac{8}{24}=\frac{1}{3}$

Compute the probability that the pet seen was sick as follows:

P (S) = P (C ∩ S) + P (D ∩ S) + P (O ∩ S)

$=\frac{3}{28}+\frac{2}{21}+\frac{1}{3}\\=\frac{9+8+28}{84}\\=\frac{45}{84}\\=0.5357$

Thus, the probability that the pet seen was sick is 53.57%.

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3 years ago

Read 2 more answers

If the square pyramid is sliced by a plane that is parallel to the base, which of the following is the most specific description

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3 years ago

Find the area of the convex polygon with vertices (0,5), (-1,2), (4,4), (-3,-4) and (2,0).

Afina-wow [57]

The area of the convex polygon is 43/2 square units

<h3>How to determine the area of the convex polygon?</h3>

The vertices are given as:

(0,5), (-1,2), (4,4), (-3,-4) and (2,0)

The area is then calculated as:

$A = \frac 12(\left[\begin{array}{cc}x_1&x_2\\y_1&y_2\end{array}\right] + \left[\begin{array}{cc}x_2&x_3\\y_2&y_3\end{array}\right] + ....+\left[\begin{array}{cc}x_n&x\\y_n&y\end{array}\right] )$

So, we have:

$A = \frac12 * (|-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 + 2 * -4 - 0 * -3 -3 * 2 + 4 * 1|)$

Evaluate

$A = \frac12 * (|-43|)$

Remove the absolute bracket

$A = \frac12 * 43$

This gives

$A = \frac{43}2$

Hence, the area of the convex polygon is 43/2 square units