question 9 the black-footed ferret was declared extinct in 1979, but a small population of the animals was found in wyoming in 1981. some of the wild ferrets were captured and bred in captivity. the animals bred in captivity were then reintroduced into the wild. suppose 131 ferrets are found in a wild population in the first year. in the next year, there are 196 ferrets in the same population. calculate the growth rate from the first year to the second year: a.65.0% b.66.8% c.33.1% d.85.1% e.49.6%

Answer:

tan 19 = x/25

Step-by-step explanation:

x = tan 19 ✖️ 25

x = 0.3443 ✖️ 25

x = 8.6075

x = 8.61 (2 decimal places)

To minimize the cost of the fence, we need to find the dimensions that result in the least total cost. Let the width (along the driveway) be x feet and the length (perpendicular to the driveway) be y feet. We know that the area of the garden is 800 square feet, so xy = 800.

The cost of the fence along the driveway is $6 per foot, so the cost for the width is 6x. The cost of the fence on the other three sides is $2 per foot, so the cost for the length is 2y on both sides, and 2x for the other width. The total cost (C) can be represented as: C = 6x + 2y + 2x + 2y = 8x + 4y.

To minimize the cost, we need to find the minimum value of this expression, subject to the constraint xy = 800. We can rearrange the constraint equation to get y = 800/x. Substitute this into the cost equation: C = 8x + 4(800/x), Now, to minimize the cost, we'll find the critical points by taking the derivative of C with respect to x and setting it equal to 0 dC/dx = 8 - (3200/x^2) = 0 . Multiplying by x^2 and rearranging, we get: x^3 = 400.

Taking the cube root, we have: x ≈ 7.37 feet, Now, find the corresponding value of y using the constraint equation: y = 800/x ≈ 108.6 feet, So, the dimensions that will minimize the cost are approximately 7.37 feet for the width and 108.6 feet for the length. To find the minimum cost, plug these dimensions back into the cost equation: C = 8(7.37) + 4(108.6) ≈ $458.96, The minimum cost for the fence is approximately $458.96.

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Answer:

x = 5

Step-by-step explanation:

This is a simple equation if you look at it right and don't get scared by the "x."

All we need to do is figure out what times 3 = 27. We can do this easily by diving 27 by 3.

27 ÷ 3 = 9

Since our "equation" is 3(x + 4) = 27 we know whatever is in the parenthesis () has to equal to 9. We already get 4 so:

5 + 4 = 9.

3 times 9 = 27.

5 is your answer.

Hope this helps and have a nice day!

PS if you could mark brainliest that'd be great! I'm very close the "expert" rank. Haha, sorry I usually don't ask.

Answer:

amount of taffy made in 7 days = 4758.32 kg

average amount of taffy made per day = 4758.32 ÷ 7

answer = 679.76 kg

Answer:

679.76 kg of taffy

Step-by-step explanation:

Given: Ted's Taffy shops makes 4,758.32 kg of taffy a week. How much do they make a day?

First, divide the amount of taffy with 7 (a week):

4,758.32 kg / 7

= 679.76 kg of taffy

Therefore, Ted's Taffy Shop makes an average of 679.76 kg of taffy per day.

A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

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Answer:

2.829 mm

Step-by-step explanation:

Correct:  2.83 mm

Measured(mm)    Difference (mm)

2.837             0.007

2.829            -0.001  Smallest deviation from actual.

2.812            -0.018

2.805            -0.025

The measurement of the piece of metal that is the most accurate is 2.837 cm.

A piece of metal with a length of 2.83 cm was measured using four different devices.

Which of the following measurements is the most accurate?

A piece of metal with a length of 2.83 cm was measured using four different devices.

Accuracy is the degree to which the measured value is close to the correct value.

The difference between the accepted value and the measured value of the quantity is called the error of measurement.

The measurement for the first device is,

\(=2.83 - 2.837\\\\=-0.007\)

The measurement of the first device is -0.007.

The measurement for the second device is,

\(=2.83 - 2.829\\\\=-0.001\)

The measurement of the second device is -0.001.

The measurement for the third device is,

\(=2.83 - 2.812\\\\=-0.018\)

The measurement of the third device is -0.018.

The measurement for the fourth device is,

\(=2.83 - 2.805\\\\=-0.025\)

The measurement of the fourth device is -0.02.

Hence, The measurement that is the most accurate is 2.837 cm.

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Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

40%

Step-by-step explanation:

Out Of students in the sample, 90/200 fraction of the students were male.

The Number of male students =90

The Number of female students =110

So, total students = 90+110 =200

There is a fraction, containing numerator(upper value) and denominator(lower value).

When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.

A proper fraction is also called fraction which is less than 1.

A Fraction of students who were male = male students/ total students

A Fraction of students who were male =90/200

Hence, 90/200 fraction of the students were male.

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The modulus is 1, argument is π/4 and the principal value is π/4 mod 2π

From the question, we have the following parameters that can be used in our computation:

\(z = \sqrt{ \frac{1 + i}{1 - i}\)

Rationalize the expression

So, we have

\(z = \sqrt{ \frac{1 + i}{1 - i} = \frac{(1 + i)(1 + i)}{(1 - i)(1 + i)} = \frac{1 + 2i + i^2}{1 - i^2} = \frac{1 + 2i - 1}{1 + 1} = \frac{2i}{2} = i\)

This means that

z = √i

The modulus of a complex number is calculated as

|z| = √(a^2 + b^2)

where z = a + bi. In this case, a = 0 and b = 1

So, we have

|z| = √(0^2 + 1^2)

|z| = 1

The argument of a complex number is calculated as

\(\arg(z) = \tan^{-1} \left( \frac{b}{a} \right)\)

So, we have

\(\arg(z) = \tan^{-1} \left( \frac{1}{0} \right)\)

This gives

arg(z) = π/4

The principal value of the argument of z is

arg(z) mod 2π

So, we have

π/4 mod 2π

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Answer: Yes it is possible

Here's an example

Original set = {1,2,3,5,7,11}

Subset A = {1,2,3}

Subset B = {3,5,7}

The number 3 is in both subsets A and B.

{1,2,3} is a subset of {1,2,3,5,7,11} since 1,2, and 3 are part of the original set. Similar reasoning applies to subset B as well.

Something like {1,2,9} is not a subset because 9 is not found in the original set.

Answer:

A. 24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

16 isnt divisible by 3, 8*3 is 24 and 3*8 is 24. so that is your lcm

Answer:

-9.56

Step-by-step explanation:

Answer:

X=63 y=27

Step-by-step explanation:

X and 117 are on a straight line. All straight lines = 180 degrees.

180 - 117 = 63

90 - 63 = 27

Answer:

can you he lp me

Step-by-step explanation:

Answer:

1. 0.019

2. 4-28

3. 4

4. 6:00

5. 6

6. 16

7. 7

8. >

9. <

10. >

Answer:

\(Area = 18\)

Step-by-step explanation:

Given;

\(a = 2\\ h = 4\\ b=7\)

See attachment for trapezium

Required

The area

From the attachment, the formula is:

\(Area = \frac{1}{2} * (a + b) * h\)

\(Area = \frac{1}{2} * (2 + 7) * 4\)

\(Area = \frac{1}{2} * 9 * 4\)

\(Area = 18\)

Answer:

Step-by-step explanation:

5x7=35 hours(Gary’s total free time per week)

7+8=15 hours(Gary is spending his time on the internet+Playing video games)

35h.....100%

15.........x%

x=42,8%=>43%

Answer:

  HA congruence postulate

Step-by-step explanation:

In order to show W is equidistant from A and Z, we must demonstrate that WA ≅ WZ. The HA congruence postulate can be used for that purpose.

__

WX bisects AXZ, so ∠WXA≅∠WXZ by the definition of an angle bisector. By the reflexive property of congruence, WX≅WX. The angles at A and Z are given as right angles.

So, we have triangles WAX and WZX that are right triangles with congruent hypotenuse and corresponding angle. These are the preconditions for the application of the HA congruence postulate. That postulate says the triangles WAX and WZX are congruent, so ...

WA ≅ WZ by CPCTC. Hence W is equidistant from the outside rays.

__

Additional comment

The definition of distance from a point to a line is the perpendicular distance from the point to the line. In this geometry, the perpendicular distances from W to the outside rays are the lengths of segments WA and WZ. That is why we need to show those lengths are the same.

Answer: 1 tablespoon

Step-by-step explanation:

The function g(x) = \(x^2\) + (2/x) has a relative minimum at (x, y), and it does not have a relative maximum.

To find the relative extrema of the function g(x), we need to find its critical points and apply the Second Derivative Test.

First, let's find the critical points by taking the derivative of g(x). The derivative of g(x) is given by g'(x) = 2x - (2/\(x^2\)). To find the critical points, we set g'(x) equal to zero and solve for x:

2x - (2/\(x^2\)) = 0

\(2x^3 - 2\) = 0

\(x^3 - 1\) = 0

\((x - 1)(x^2 + x + 1)\) = 0

From this equation, we find one critical point x = 1.

Next, we apply the Second Derivative Test to determine whether the critical point x = 1 corresponds to a relative minimum or maximum. Taking the second derivative of g(x), we get:

g''(x) = 2 + (4/\(x^3\))

Substituting x = 1 into g''(x), we find:

g''(1) = 2 + (4/\(1^3\)) = 6

Since g''(1) is positive, the Second Derivative Test tells us that the function g(x) has a relative minimum at x = 1. However, it does not have a relative maximum. Therefore, the relative minimum point is (x, y) = (1, 3).

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Answer:

Ur answer should be 2.

8) a) The new fastest time is 56.7 seconds, b) The overall percentage improvement is 19 %.

9) The height after the first increase is 1.375 meters and after the second increase is 1.54 meters.

In this problem we have two examples from real life, in which percentages are used. The first is the distance traveled by a runner in a given time and the second is the growth of a person in time. Change in variables based on percentages are described by the following formula:

C' = C · (1 + r / 100)     (1)

Where:

Now we proceed to resolve on each case. 8) a) Please notice that the runner must cover the trail in less time and percentage time must be negative. If we know that C = 70 and r = - 10, then his new fastest time is:

C' = 70 · (1 - 10 / 100)

C' = 70 · 0.90

C' = 63

And again: (C' = 63, r = - 10)

C'' = 63 · (1 - 10 / 100)

C'' = 63 · 0.90

C'' = 56.7

The new fastest time is 56.7 seconds.

b) And the overall percentage improvement is:

r = (|C'' - C| / C) × 100 %

r = (|56.7 - 70| / 70) × 100 %

r = 19 %

The overall percentage improvement is 19 %.

9) If we know that C = 1.25 and r = 10, then the height next year is:

C' = 1.25 · (1 + 10 / 100)

C' = 1.375

And again: (C' = 1.375, r = 12)

C'' = 1.375 · (1 + 12 / 100)

C'' = 1.54

The height after the first increase is 1.375 meters and after the second increase is 1.54 meters.

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To find the first derivative of f(x), we need to integrate the second derivative with respect to x once.

f'(x) = ∫ f''(x) dx = ∫ x(x-a)(x-b)^2 dx

f'(x) = ∫ (x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2) dx

f'(x) = 1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C

where C is the constant of integration.

To find the second derivative of f(x), we need to differentiate f'(x) with respect to x.

f''(x) = d/dx [1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C]

f''(x) = 1 x^4 - 1(a+b)x^3 + 1(a^2+3ab+b^2)x^2 - 1ab(a+b)x + 1ab^2

f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2

Therefore, the second derivative of f is given by f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2.

The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.

The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),

where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to

\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).

This can be written as nine-eighths of the length of the box squared.

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Answer:

=9(y-3)

take 9 as a common factor then divide it by everyone 8nside

Answer:

(5, -7).

Step-by-step explanation:

Solution is the point of intersection.

(5, -7).

Answer:

I AM SO SORRY I CAN NOT READ IT!!

Step-by-step explanation:

Answer:

I’m pretty sure its A

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

It passes the horizontal line test

Answer:

Step-by-step explanation:

In order to find the coordinates of P and Q, we have to find the intersection of the circle and the line. Do this by subbing in y=x-4 into the circle equation for y:

\((x-3)^2+((x-4)+2)^2=25\) becomes

\((x-3)^2+(x-2)^2=25\) and then FOIL all that out to get

\(x^2-6x+9+x^2-4x+4=25\).  Combine like terms to get

\(2x^2-10x-12=0\) and factor to get the zeros of

x = 6 and x = -1.

When x = 6, y = 2; when x = -1, y = -5. That answers part a.

The length of PQ is found then using the distance formula:

\(d=\sqrt{(6-(-1))^2+(2-(-5))^2}\) to get

\(d=\sqrt{98}\) which, in decimal form, i 9.89949937. That answers part b.

The perpendicular bisector requires that we find the midpoint of PQ:

\(M=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})\) which, for us, is

\(M=(\frac{6-1}{2},\frac{2-5}{2})=(2.5, -1.5)\)

The perpendicular slope to the given line is the opposite reciprocal of the one given, so the perpendicular slope is -1. The equation for the perpendicular bisector of PQ goes through the midpoint with the slope of -1:

\(y+1.5=-1(x-2.5)\) and

y = -x + 1 is the perpendicular bisector of PQ.

Answer:

9000 panels

Step-by-step explanation:

See attached for detailed explanation.

Remember that percent means division by a 100.

Answer:

(-2, 4)

Step-by-step explanation:

Reflection over the x-axis would mean the point would flip upwards, this would affect the y coordinate.