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Bogdan [553]
3 years ago
7

One study estimated that bears populate the Kenai Peninsula of Alaska at a rate of 424242 bears per 1,000 \text { km}^21,000 km

2 1, comma, 000, start text, space, k, m, end text, squared of available habitat. According to this study, about how many bears would you expect to find in a habitable region of this peninsula 8,500 \text { km}^28,500 km 2 8, comma, 500, start text, space, k, m, end text, squared in size?
Mathematics
1 answer:
g100num [7]3 years ago
4 0

Answer:

357 bears

Step-by-step explanation:

Given;

Population density of bears in the Kenai Peninsula of Alaska = 42 bears per 1000km^2

Area of habitable region of this peninsula = 8500 km^2

how many bears would you expect to find in a habitable region of this peninsula N;

N = population density × area

N = 42/1000 × 8500

N = 357 bears

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16. A triangle has side lengths of 6, 8, and 10. Is it a right triangle? Explain. (2 points)
timurjin [86]

Answer:

Yes, because when the side lengths of a triangle are in the ratio 3: 4: 5, then it is a right triangle. These sides are 6: 8: 10, then the triangle is a right one.

Step-by-step explanation:

7 0
3 years ago
A storage space in a basement is in the shape of a rectangular prisim. The hieght of the storage space is 5 feet. The length is
Greeley [361]

Answer:

length is 28.86ft

width= 4.12ft

Step-by-step explanation:

<h2>This problem bothers on the mensuration of solid shapes, a rectangular prism.</h2>

The storage space takes the shape of a rectangular prism, and we are required to find the width and length  of the storage space.

let the width of the basement be "w"

Given data

volume v=595ft^{3}

length l = 7w ft

width w= w

height h= 5 ft

We know that the expression for the volume of a rectangular prism is

volume= length * width* height

substituting our data we have to find "w"

595= 7w*w*5\\595=7w^{2}*5\\ 595= 35w^{2} \\

dividing both sides by 35 we have

w^{2}= \frac{595}{35\\}  \\w^{2}= 17\\

find the square root of both sides we have

w=\sqrt{17} \\w= 4.12

since we know that length= 7w and width = w , we can substitute our value for w and find the length and width

length= 7*4.12= 28.86ft\\width = 4.12ft

6 0
3 years ago
Sin(x+y)-sin(x-y)/cos(x+y)+cos(x-y)=tany<br> how do i verify this?
dsp73

Answer:

Step-by-step explanation:

Numerator

sin

x

cos

y

+

cos

x

sin

y

−

[

sin

x

cos

y

−

cos

x

sin

y

)

=

sin

x

cos

y

+

cos

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sin

y

−

sin

x

cos

y

+

cos

x

sin

y

=

2

cos

x

sin

y

Denominator

cos

x

cos

y

−

sin

x

sin

y

+

cos

x

cos

y

+

sin

x

sin

y

=

cos

x

cos

y

−

sin

x

sin

y

+

cos

x

cos

y

+

sin

x

sin

y

=

2

cos

x

cos

y

---------------------------------------------------------------

left side can now be expressed as

2

cos

x

sin

y

2

cos

x

cos

y

=

2

cos

x

sin

y

2

cos

x

cos

y

=

sin

y

cos

y

and  

sin

y

cos

y

=

tan

y

=

right side hence proved

7 0
3 years ago
If a = pi +3j - 7k, b = pi - pj +4k and the angle between a and is acute then the possible values for p are given by​
PIT_PIT [208]

Answer:

The family of possible values for p are:

(-\infty, -4) \,\cup \,(7, +\infty)

Step-by-step explanation:

By Linear Algebra, we can calculate the angle by definition of dot product:

\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|} (1)

Where:

\theta - Angle between vectors, in sexagesimal degrees.

\|\vec a\|, \|\vec b \| - Norms of vectors \vec {a} and \vec{b}

If \theta is acute, then the cosine function is bounded between 0 a 1 and if we know that \vec {a} = (p, 3, -7) and \vec {b} = (p, -p, 4), then the possible values for p are:

Minimum (\cos \theta = 0)

\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0

Maximum (\cos \theta = 1)

\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} < 1

With the help of a graphing tool we get the family of possible values for p are:

(-\infty, -4) \,\cup \,(7, +\infty)

7 0
3 years ago
True or False: Point estimation is a form of statistical inference in which, based on the sample data, we estimate the unknown p
storchak [24]

Answer:

True

Step-by-step explanation:

Point estimation of a population parameter provides an estimate of  a single value calculated from the sample that is likely to be close to its value to the unknown parameter. Itis to be noted that a point estimate will not in general be equal to the population parameter as the random sample used is one of the many possible samples which could be chosen from the population.

For example, in estimation, we may estimate the mean and the variance of a population by computing the mean and the variance of the sample drawn from a population.

6 0
4 years ago
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