The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimated
that the population in the year 2000 was 13500.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Hint: Use an exponential function with base e.
Your answer is P(t) =
(b) Use the function from part (a) to estimate the fox population in the year 2008
Your answer is (the answer must be an integer)

The answer is 46 dollars

The volume of the funnel to the nearest tenth of a unit is approximately 341.4 cubic inches.

What is volume?

Volume is a measure of the amount of space that a three-dimensional object occupies. It is the quantity of space that is enclosed within a closed surface, and is typically measured in cubic units, such as cubic meters ([tex]m^3[/tex]), cubic centimeters ([tex]cm^3[/tex]), cubic feet ([tex]ft^3[/tex]), or gallons (gal).

We can use the formula for the volume of a cone to find the volume of the funnel, since a funnel is essentially a cone with a hole at the top. The formula for the volume of a cone is:

[tex]V = (1/3)\pi r^2h[/tex]

where V is the volume, r is the radius of the circular base, and h is the height of the cone.

Since the funnel has a diameter of 9 inches, its radius is half of that, or 4.5 inches. The height of the funnel is given as 16 inches.

Plugging these values into the formula, we get:

[tex]V = (1/3)\pi(4.5 in)^2(16 in)\\\\= (1/3)\pi(20.25 in^2)(16 in)[/tex]

≈ [tex]341.4 in^3[/tex]

Rounding this answer to the nearest tenth of a unit, we get:

V ≈ [tex]341.4 in^3[/tex]

Therefore, the volume of the funnel to the nearest tenth of a unit is approximately 341.4 cubic inches.

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Using both hoses will take 10 minutes to fill up the kiddie pool. Mary can fill up 1/3 of the pool using the front yard hose in 10 minutes and 1/6 of the pool using the backyard hose in 10 minutes.

To solve this problem, we need to use the concept of rates. Let's assume the rate of the hose in the backyard is x, so the rate of the hose in the front yard is 2x (because it is twice as fast as the other hose).

The combined rate of the two hoses is x + 2x = 3x, which means they can fill the pool in 30/3x = 10/x minutes.

We know that the area of the pool is 600 square feet and each small rock covers 20 square feet, so we need a total of 600/20 = 30 small rocks to cover the pool.

Since the mass of each rock is 20 grams, the total mass of all 30 rocks is 30 x 20 = 600 grams.

To find the density, we divide the total mass (600 grams) by the total volume of the rocks (30 x 20 cubic feet = 600 cubic feet)

Density = 600g / 600 cubic feet = 1g/cubic foot

Therefore, the answer is B. 10 minutes for the pool to fill up, and the density of the rocks is 1 gram per cubic foot.

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For the given problem, a.)The unicycle covers 1.885 meters, in one revolution of wheel. b.) The wheel must rotate 53 times to cover distance of 100 metres.

a.) The circumference of a unicycle's wheel is determined by

                               [tex]\qquad \qquad C = \pi d\\ \text {where, d is the diameter of the wheel. }[/tex]

As a result, the unicycle moves C metres when the wheel revolves once.

Now, on substituting d = 60 cm and π= 3.14.

We obtain,

[tex]C\approx 188.5 cm = 1.885 m[/tex]  (∵ 1m = 100cm)

As a result, when the wheel revolves once, the unicycle goes 1.885 metres.

b.) Now, Distance covered in one rotation by wheel =  [tex]C = 1.885 m[/tex]

To travel 100 metres, wheel need to rotate = 100/C times.

As a result, the number of full rotations necessary is:

[tex]100/C = 100/1.885 = 53.0504 \;rotations[/tex]

Thus, To traverse 100 metres, the wheel must rotate 53.04 times or 53 times( in nearest whole number )

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The volume of the cone is 4.2 units cube.

The volume of a cone can be calculated as follows:

Therefore,

volume of a cone = 1 / 3 πr²h

where

Therefore,

r = 1.5 units

h = 1.8 units

volume of a cone = 1 / 3 × 22 / 7 × (1.5)² × 1.8

volume of a cone = 1 / 3 × 89.1 / 7

volume of a cone = 89.1 / 21

volume of a cone = 4.24285714286

volume of the cone = 4.2 units cube

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Answer:

A. Quadratic

Step-by-step explanation:

The equation y=x^2+7x-15 is a quadratic equation. It might be the result of a quadratic regression.

_____

The descriptors "linear," "quadratic," "exponential," and "power" describe the sort of equation that is used to try to match the data. Quadratic regression returns a quadratic equation.

Answer: Your answer is 504 or if you want it differently it's 84x+252

Hope it helped :D

Answer:

  about 80.03 feet

Step-by-step explanation:

You want the change in height of a bridge with a span of 1068.5 feet and a grade of 7.49%.

The grade of a roadway is the ratio of rise to run:

  grade = rise/run

  7.49% = rise/(1068.5 ft)

Solving for the rise, we have ...

  rise = (1068.5 ft)(0.0749) ≈ 80.03 ft

The height change is about 80.03 feet.

__

Additional comment

Your problem statement tells you to round this value. We cannot see what precision it is asking for, so you'll have to figure the rounded value yourself. The attachment shows the value you'll be rounding.

The percentage with a 95% confidence interval that has an error bound of at most 3%.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the symbol "%". For example, if there are 20 red marbles out of 100 marbles in a jar, we can say that the percentage of red marbles is 20%. Similarly, if a store offers a 10% discount on a $50 item, the discounted price would be $45.

Percentages are commonly used to represent proportions or rates in various contexts, such as finance, and science. They allow us to easily compare and communicate numbers on a standardized scale, making it easier to interpret and analyze data.

To estimate the required sample size, we need to use the following formula:

n = (z*σ / E)^2

where:

n is the sample size we need to estimate the percentage with the desired error bound

z is the z-score for the desired level of confidence (95% in this case), which is 1.96

σ is the standard deviation of the population (unknown)

E is the desired margin of error, which is 3% of the percentage we are trying to estimate

Since we do not know the standard deviation of the population, we can use a conservative estimate of 0.5 (which gives the largest possible sample size).

Substituting the values we have:

n = (1.96 * 0.5 / 0.03)^2

n = 1067.11

So we would need to poll at least 1068 students to estimate the percentage with a 95% confidence interval that has an error bound of at most 3%.

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Answer:

Step-by-step explanation:

Responses 1 and 3 are correct.

When you multiply an exponent by an exponent, like x-squared times x-squared, you'll add the two exponents. That means x-squared times x-squared is x to the fourth power.

If you look at responses 1 and 3, the exponents were added correctly and the coefficients were multiplied correctly.

However, if you look at responses 2 and 4, the exponents were multiplied instead of added, making those two expressions incorrect.

Answer:  (11) Julius asks Rachel if she would like to sell her boat. Rachel privately has no interest in selling her boat and believes that Julius can't afford her boat anyway. Rachel says, "I'd sell my boat to you for $20,000." To Rachel's surprise, Julius responds "Ok, it's a deal." Rachel does not want to sell the boat to Julius for any price. Julius and Rachel have:

Answer:

[tex] \sf \: c \: = \: 28.3[/tex]

Step-by-step explanation:

To find the circumference of a circle .

We have to use the formula,

Where, C = [tex] 2 \pi r [/tex]

[tex] \pi [/tex] = 3.142

[tex] r [/tex] = 4.5m

So,

C = 2 × 3.142 × 4.5

C = 28.278 ≈ 28.3

Answer: 28.3

Step-by-step explanation:

C=2[tex]\pi r[/tex]

=2[tex]\pi[/tex](4.5)

=28.3 m

The inverse of the matrix A by getting its determinant value is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

The matrix is equal to,

A = [tex]\left[\begin{array}{ccc}4&2\\3&2\end{array}\right][/tex]

To find the inverse of a matrix,

we first need to calculate its determinant of the matrix A  we have,

|A| = [tex]\left|\begin{array}{ccc}4&2\\3&2\end{array}\right|[/tex]

⇒ |A| = 4(2) - 2(3)

        = 8 - 6

        = 2

Now we can proceed to find the inverse of A.

Set up the matrix of cofactors.

The matrix of cofactors C is obtained by replacing each element of A with its corresponding cofactor,

which is the determinant of the submatrix obtained by deleting the row and column that contain that element.

For our matrix A, we have,

C = [tex]\left[\begin{array}{ccc}2&-3\\-2&4\end{array}\right][/tex]

Transpose the matrix of cofactors.

The transpose of a matrix is obtained by flipping its rows and columns. For our matrix C, we have.

[tex]C^{T} = \left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]

Divide by the determinant.

The inverse of A is obtained by dividing the transpose of the matrix of cofactors by the determinant of A.

For our matrix A, we have,

A⁻¹ = [tex]C^{T}[/tex] / |A|

   [tex]C^{T} = (1/2)\left[\begin{array}{ccc}2&-2\\-3&4\end{array}\right][/tex]

   [tex]C^{T} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

Therefore, the inverse of the matrix A is equal to [tex]A^{-1} = \left[\begin{array}{ccc}1&-1\\\frac{-3}{2} &2\end{array}\right][/tex]

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The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.

The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.

The point of intersection is (-6, 10).

We have,

To sketch the graph of the system of equations:

x + y = 4

2x + 3y = 18

We can start by solving each equation for y:

y = -x + 4

y = (-2/3)x + 6

Then, we can plot a few points on each graph by choosing values of x and solving for y.

Here are three points for each graph:

x + y = 4:

x = -4, y = 8: (-4, 8)

x = 0, y = 4: (0, 4)

x = 4, y = 0: (4, 0)

2x + 3y = 18:

x = 0, y = 6: (0, 6)

x = 3, y = 4: (3, 4)

x = 9, y = 0: (9, 0)

To plot the graphs, we can use these points and draw a straight line through each set of three points.

The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.

The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.

To find the point of intersection, we can solve the system of equations:

x + y = 4

2x + 3y = 18

One way to solve this system is to use substitution.

We can solve the first equation for x:

x = 4 - y

Then we can substitute this expression for x into the second equation and solve for y:

2(4 - y) + 3y = 18

8 - 2y + 3y = 18

y = 10

Now that we know that y = 10, we can substitute this value into either equation to solve for x:

x + y = 4

x + 10 = 4

x = -6

So the point of intersection is (-6, 10).

Thus,

The graph of x + y = 4 is a line with a y-intercept of 4 and a slope of -1.

The graph of 2x + 3y = 18 is a line with a y-intercept of 6 and a slope of -2/3.

The point of intersection is (-6, 10).

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Answer: 92 ft²

Step-by-step explanation:

To find the surface area of a right prism, we will find the area of each side and add them together. We have three sets of two congruent sides. We will write an equation representing the area of these sides, set it equal to the surface area, and solve by simplifying.

2(8 ft * 3 ft) + 2(3 ft * 2 ft) + 2(8 ft * 2 ft) = Surface Area

2(24 ft²) + 2(6 ft²) + 2(16 ft²) = Surface Area

48 ft² + 12 ft² + 32 ft² = Surface Area

92 ft² = Surface Area

Answer:

Step-by-step explanation:Answer 1 person found it helpful Davis Holmes These outcomes are only estimates of the real odds because they relied on Samara's 100 trials. The measured rates should approach the actual odds as she keeps rolling the dice.Which four kinds of probability are there?Mathematics' study of chance events is known as probability, and there are four major kinds of probability: axiomatic, classical, observational, and subjective.After three tries, Samira is expected to receive a 6.There is approximately a 9% chance that Samira will roll the dice more than 4 times to get a 6.Frequency:1: 162: 143: 134: 9more than 4: 48Note: These results are based on Samira's 100 trials, so they are only an estimate of the actual probabilities. As she continues to roll the dice more times, the observed frequencies should approach the true probabilities.To know more about Probability

Answer:

Step-by-step explanation:

Using the Pythagorean Theorem, we can find the length of the hypotenuse.

a² + b² = c²

6² + 8² = c²

36 + 64 = c²

100 = c²

√100 = c

10 = c

Answer: 10 units

Step-by-step explanation:

To find the hypotenuse of a triangle, use the Pythagorean Theorem (A² + B² = C²).

In this equation, A is 6, B is 8, and C is x, or the hypotenuse.

1. 6² + 8² = x²

2. 36 + 64 = x²

3. 100 = x²

4. √100 = √x²

(Taking the square root of both sides, cancelling out x²)

5. 10 = x

Answer:

We can use a Venn diagram to visualize the information given in the problem.

Let M, B, and C represent the sets of students who pass mathematics, biology, and chemistry, respectively. We are given the following information:

|M| = 10 (the number of students who pass mathematics)

|B| = 30 (the number of students who pass biology)

|C| = 25 (the number of students who pass chemistry)

|M ∩ B| = 11 (the number of students who pass both mathematics and biology)

|B ∩ C| = 10 (the number of students who pass both biology and chemistry)

|M ∩ C| = 7 (the number of students who pass both mathematics and chemistry)

|M ∩ B ∩ C| = ? (the number of students who pass all three subjects)

We know that:

| M ∪ B ∪ C | = |M| + |B| + |C| - |M ∩ B| - |B ∩ C| - |M ∩ C| + |M ∩ B ∩ C|

Substituting the given values:

| M ∪ B ∪ C | = 10 + 30 + 25 - 11 - 10 - 7 + |M ∩ B ∩ C|

Simplifying:

| M ∪ B ∪ C | = 37 + |M ∩ B ∩ C|

We also know that:

| M ∪ B ∪ C | = 70 (the total number of students)

Substituting the value:

70 = 37 + |M ∩ B ∩ C|

Simplifying:

|M ∩ B ∩ C| = 33

Therefore, 33 students pass all three subjects.

Step-by-step explanation:

pls mark branliest i beggggg u

The missing angle C of the given triangle using law of cosine is: 62.1°

The Law of Cosines is defined as a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be communicated as:

c² = a² + b² - 2abcos(C),

where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Thus:

90² = 55² + 50² - 2(55 * 50)cos(C),

2575 = 5500 cos C

2575/5500 = cos C

cos C = 0.4682

C = cos⁻¹0.4682

C = 62.1°

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The triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.

Given that:

The diagram is shown.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio of the corresponding sides of the triangle ΔFGH and ΔLJK is given as,

FG / JL = HF / LK = GH / JK

32/8 = 36/9 = 48/12

4 = 4 = 4

The ratio of the corresponding side will be equal. Then the triangles ΔFGH and ΔLJK are similar triangles. Then the correct option is B.

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A reasonable prediction for the number of times the event of landing on an even number will occur in 550 rolls is 275.

When rolling a fair 6-sided die, there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5). Therefore, the probability of rolling an even number is 3/6 or 1/2.

To predict the number of times the event of landing on an even number will occur in 550 rolls, we can multiply the probability of rolling an even number by the total number of rolls:

Expected number of even rolls = Probability of rolling an even number x Total number of rolls

Expected number of even rolls = (1/2) x 550

Expected number of even rolls = 275

Therefore, a reasonable prediction for the number of times the event of landing on an even number will occur in 550 rolls is 275.

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Answer:

3/2

Step-by-step explanation:

Answer:

  (c)  2/3

Step-by-step explanation:

You want the slope of the line through points (-3, -1) and (3, 3).

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (3 -(-1))/(3 -(-3)) = 4/6 = 2/3

The slope of the line is two thirds, choice C.

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Based on the pattern, the missing section in the middle row is:

9282

The sequence seems to move in a clockwise or counter-clockwise fashion, filling in the digits. Some observations:

• The first and last rows are mirror images of each other, just reversed. So the middle section should continue that pattern.

• Going clockwise, 2 comes before 8. So 9282 fits.

• The digits in each section increase (or decrease) by 1 each time, except for the overlaps at the corners. So 9282 maintains that incremental pattern.

• The total sum of each row is the same: 391283, 9282? 1??391, 219382, 839128, 382193. Filling in 9282 for the middle section keeps the same overall sum.

• No other combination of 2 digits in that range (92-99 or 20-29) fits the pattern on both sides of the missing section. 9282 is the only logical choice.

So with all these clues pointing to 9282, that is the number that belongs in the missing section of the middle row. Let me know if any additional explanation is needed! I can also re-layout the pattern with the missing section filled in if that would be helpful.

give me the brilliant mark

Answer:

radians = degrees x π/180

Therefore, to convert 300 degrees to radians, we have:

radians = 300 x π/180

radians = 5π/3

So, 300 degrees is equal to 5π/3 radians.

The the freshness half-line of milk is 10h, (b) The milk keep fresh at 22°C  for 31.1h (c) The milk keep fresh at 4°C for 55.7h

Recal that Storage temperature refers to the temperature at which food product is stored immediately after preparation and maintained at a safe holding temperature until it is dispensed to the customer

The given relation is T = 190 (1/2)^t/10

a. From the relation, T = 190 (1/2)^t/10

So the freshness half life of milk is 10 hours

b.  22 =  190 (1/2)^t/10

t = 10log₁/₂(190/22) = 31.1 hours

c. = 190 (1/2)^t/10

t= 10log₁/₂(190/22 = 55.7 hours

Milk can keep fresh for 55.7 hours at 4°C

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The shaded area of the diagram is 23 square inches when side of large square is 6 inches.

What is square ?

A square is a geometrical shape that has four sides of equal length and four angles of 90 degrees each. It is a two-dimensional polygon with four vertices or corners. The area of a square can be calculated by multiplying the length of one of its sides by itself (i.e., squaring it) using the formula

[tex]A = s^2[/tex] , where A is the area and s is the length of one side of the square.

To calculate the shaded area, we need to subtract the area of the two small squares from the area of the large square and then subtract the area of the unshaded region (which is the area of the two overlapping squares).

The area of the large square is:

[tex]$(6\text{ in})^2 = 36\text{ in}^2$[/tex]

The area of the two small squares is:

[tex]$(2\text{ in})^2 + (3\text{ in})^2 = 4\text{ in}^2 + 9\text{ in}^2 = 13\text{ in}^2$[/tex]

Therefore, the expression for the shaded area is:

[tex]$36\text{ in}^2 - 13\text{ in}^2[/tex]

Simplifying this expression, we get:

[tex]$23\text{ in}^2$[/tex]

Therefore, the shaded area of the diagram is 23 square inches.

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