The population of the town is 2500 and is decreasing at a rate of 3% per year. determine the population after 11 years

Answer:

To determine the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, we can use the SOLVE process as follows:

S: Write down the given information and identify the problem.

We are given the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, and we need to find the value of the missing coefficient "a".

O: Organize the information and decide on a plan.

To find the value of "a", we can substitute specific values for x into the polynomial and solve for a.

L: Carry out the plan.

For example, let's say we substitute x = 2 into the polynomial. We get:

P(2) = 2^4 - 32^3 + a2^2 - 6*2 + 14

= 16 - 24 + 4a - 12 + 14

= -4 + 4a + 2

= 4a - 2

We are given that P(2) = 4a - 2 = 0, so 4a = 2.

Solving for a, we get:

a = 2 / 4

= 0.5

V: Check the solution.

We can check the solution by substituting 0.5 for a in the original polynomial and verifying that it gives us the correct result for P(x) when x = 2.

P(x) = x^4 - 3x^3 + 0.5x^2 - 6x + 14

Substituting x = 2 and a = 0.5, we get:

P(2) = 2^4 - 32^3 + 0.52^2 - 6*2 + 14

= 16 - 24 + 1 - 12 + 14

= 0

Since P(2) = 0, our solution appears to be correct.

Therefore, the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14 is 0.5.

The best way for the data to be measured is called ordinal.

Option b.

Ordinal data is a type of categorical data in which the categories have a natural order or ranking. In this case, the students are ranking the instructor on a scale of 0 to 5, with 0 being the lowest and 5 being the highest. This type of data is best measured using ordinal measures, as it allows for the ranking of the data in a meaningful way.

Filtered data refers to data that has been filtered or sorted in some way. Nominal data is a type of categorical data in which the categories do not have a natural order or ranking. Numerical data is a type of data that is measured on a numerical scale, such as height or weight.

Therefore, the correct answer is b. ordinal.

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Answer:

 I believe the answer is 4.5E-5 or 4.55

Please correct me If I am wrong

Step-by-step explanation:

100,000 cm =1 km

Answer:

-1

Step-by-step explanation:

1. A water wheel rung’s height as a function of time can be modeled by the equation:

h - 8 = -9 sin6t

(b) Determine the maximum height above the water for a rung.

Given the rung's height modeled by the equation;

h - 8 = -9 sin6t

h(t) = -9sin6t + 8

At maximum height, the velocity of the rung is zero;

dh/dt = 0

dh/dt = -54cos6t

-54cos6t = 0

cos6t = 0/-54

cos6t = 0

6t = cos^-1(0)

6t = 90

t = 90/6

t= 15

Substitute t = 15 into the expression to get the maximum height;

Recall:

h(t) = -9sin6t + 8

h(15) = -9sin6(15) + 8

h(15) = -9sin90 + 8

h(15) = -9(1)+8

h(15) = -9+8

h(15) = -1

hence the maximum height above the water is -1

Answer:

f(1/4) = -5.25

Step-by-step explanation:

Plug 1/4 as x

4x^2 + 2x - 6

= 4*1/4^2 + 2x1/4 - 6

= 4*1/16 + 1/2 - 6

= 1/4 + 1/2 - 6

= 3/4 - 6

= -5 1/4 = -5.25

Answer:

f(1/4)=-5.25

Step-by-step explanation:

Answer:

58.14 inches

Step-by-step explanation:

Pitagoras:

Diagonal² = length² + width²

Diagonal² = 44² + 38²

Diagonal² = 1936 + 1444

Diagonal² = 3380

√Diagonal² = √3380

Diagonal = 58.137 = 58.14inches

Answer:

the desired line is y = 3x - 4

Step-by-step explanation:

The slope formula is not needed here.  If the given line is y = 3x - 2, we can see immediately that the slope is 3, in both cases.

Find the y-intercept as follows:

y = mx + b => 5 = 3(3) + b, or b = -4

Then the desired line is y = 3x - 4

So the surface area of the three boxes is 32 1/3 square feet.

Surface area is the total area that the surface of a three-dimensional object covers. It is measured in square units (such as square inches, square feet, or square meters). Surface area is an important concept in many areas of math and science, including geometry, architecture, physics, and engineering. It is used to calculate the amount of material needed to cover or construct an object, to determine heat transfer rates, and to analyze the strength and stability of structures.

Here,

To find the surface area of a rectangular prism, we need to find the area of each face and add them together. The rectangular prism has three boxes, so we need to find the surface area of each box and multiply by 3 to get the total surface area.

Face 1: The top and bottom faces are both rectangles with dimensions 5 feet by 1 1/2 feet. The area of each face is:

5 ft x 1 1/2 ft = 7.5 sq ft

Face 2: The front and back faces are both rectangles with dimensions 1 1/2 feet by 1 1/3 feet. The area of each face is:

1 1/2 ft x 1 1/3 ft = 2 sq ft

Face 3: The left and right faces are both rectangles with dimensions 5 feet by 1 1/3 feet. The area of each face is:

5 ft x 1 1/3 ft = 6 2/3 sq ft

To find the total surface area, we add up the areas of all three faces:

Total surface area = (7.5 sq ft x 2) + (2 sq ft x 2) + (6 2/3 sq ft x 2)

Total surface area = 15 sq ft + 4 sq ft + 13 1/3 sq ft

Total surface area = 32 1/3 sq ft

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Answer:

the answer is 32 1/3!

Step-by-step explanation:

I took the k12 4.12 unit test: Three-Dimensional Geometry -
Good luck with the rest of the test! ^_^
(This was my least favorite unit test of the whole semester)

The ratio of the radius of the larger tank to the radius of the smaller tank is approximately 1.10.

Let's assume the radius of the smaller tank is 'r'. Since the larger tank's volume is 1.20 times its height, and the volume of a cylinder is calculated as πr²h, we can set up the following equation:

1.20πr²h = 218

Similarly, for the smaller tank:

πr²h = 150

Dividing the first equation by the second equation, we get:

(1.20πr²h) / (πr²h) = 218/150  

1.20 = 218/150

To find the ratio of the radii, we can take the square root of the above ratio, as the ratio of the radii is proportional to the square root of the volume ratio. Taking the square root of both sides, we have:

√1.20 = √(218/150)  

√1.20 ≈ 1.10

Therefore, the ratio of the radius of the larger tank to the radius of the smaller tank is approximately 1.10.

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Answer: y=-0.5x+4.5

Step-by-step explanation: y=mx+b, m is the slope = -1/2 or -0.5, and b is the y-int, which is 4.5

The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

It would be (4, -5)

Hope this helps!

Answer:

1

Step-by-step explanation:

Since we are taking the area of a square, you can take the square root of its area to find the side lengths.

√1 = 1

Answer:

\(9x^{10}\)

Step-by-step explanation:

\((x^a)^b=x^{ab}\)

so

\((3x^5)^2=9x^{10}\)

The magnitude of the vector sum (A + B) is approximately 4.974.

To find the magnitude of the vector sum (A + B), we need to add the corresponding components of vectors A and B and then calculate the magnitude of the resulting vector.

Given:

Vector A: (5.1, 0)

Vector B: (-2.6, -4.3)

To find the vector sum (A + B), we add the corresponding components:

(A + B) = (5.1 + (-2.6), 0 + (-4.3))

= (2.5, -4.3)

Now, let's calculate the magnitude of the vector (2.5, -4.3):

Magnitude = sqrt((2.5)^2 + (-4.3)^2)

= sqrt(6.25 + 18.49)

= sqrt(24.74)

≈ 4.974

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Answer:

11

Step-by-step explanation:

20 for first month. leaves 140. 140 ÷14 = 10

10+1 =11

The amount you could save per month would be 25% of your discretionary money.

Discretionary income is the money you have left over after paying taxes and necessary cost-of-living expenses.

The formula for discretionary money is: Discretionary money = Realized income - Fixed expenses. Inputting data, we have: Discretionary money = $3,543.22 - Fixed expenses

Amount to be saved = 25% of discretionary money

Amount to be saved = 0.25 * (Realized income - Fixed expenses)

Therefore, the amount savable is calculated as 0.25 times the difference between your realized income and fixed expenses.

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Answer:

The value of f(-8) is 54

Step-by-step explanation:

Plug -8 in for x, a negative, and a subtraction sign is an addition.

Hope this helps!

Therefore, The integral would be ∫[0,5] (3/2)x - 6 dx. Integrating this equation would give us the area of the region under the curve.

Explanation: To evaluate the integral by interpreting it in terms of areas, we need to find the area of the region under the curve. For part 1 of 3, we are given a segment of the line y = (3/2)x - 6 that begins at (0, -6) and ends at (5, 3/2).
To find the area of this region, we need to integrate the equation from x = 0 to x = 5. The integral would be:
∫[0,5] (3/2)x - 6 dx
Integrating this equation would give us the area of the region under the curve.
To evaluate the integral by interpreting it in terms of areas, we need to find the area of the region under the curve. For part 1 of 3, we are given a segment of the line y = (3/2)x - 6 that begins at (0, -6) and ends at (5, 3/2). To find the area of this region, we need to integrate the equation from x = 0 to x = 5.

Therefore, The integral would be ∫[0,5] (3/2)x - 6 dx. Integrating this equation would give us the area of the region under the curve.

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Answer:

40

Step-by-step explanation:

The volume of a cylinder is = to \(\pi\)\(r^{2}\)h, so plug in the values and you get that each crayon has a volume of about 0.15 inches. 6/0.15 = 40. :)

Answer:

Step-by-step explanation:

its A in the hint it tell you to look at the outer part which is perimeter

Given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.

In a data set with a, b, c, d, e, and f numeric variables, given there is a strong correlation of these pairs (f, a), (f, c), (d, e), (a, d), we can set up a regression model as

Of-a + c Of-a + b + c + d + e Of-a + C + d + e Of-a + C + e.

Given two predictor variables with a correlation of 0.32879, we should expect there is multicollinearity between them.

The statement that is true regarding the given two predictor variables with a correlation of 0.32879 is:

we should expect there to be multicollinearity between them.

Multicollinearity is a situation in which two or more predictor variables in a multiple regression model are highly correlated with one another. Multicollinearity complicates the understanding of which predictor variables are significant in the regression model's estimation.

Therefore, given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.

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The figure above shows two circles, one inside the other. The equation x^2 + y^2 = 2 represents the smaller circle, while the larger circle is not explicitly defined in the question.

However, we can see from the graph that the center of both circles is at the origin (0,0) and that the larger circle has a radius twice as big as the smaller circle.

Therefore, the radius of the larger circle is 2 times the radius of the smaller circle, which is the square root of 2. So the answer is (a) √2.
The given equation of the circle is x^2 + y^2 = 2. To find the radius of this circle, we can rewrite the equation in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

In this case, the equation is already in the standard form with h = 0, k = 0, and r^2 = 2. Therefore, the radius of the larger circle is r = √2. So, the correct answer is a) √2.

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Answer:

1) Arithmetic since it decreases by 3 so, -3n + 38.

2) Arithmetic since it decreases by 20 each time, so -20n+17

Step-by-step explanation:

Answer:

B x = 3 or -12

Step-by-step explanation:

(btw this / is a fraction sign and this ^ is the power of sign)

Let's solve your equation step-by-step.

x^2+9x−36=0

For this equation: a=1, b=9, c=-36

1x^2+9x+−36=0

Step 1: Use quadratic formula with a=1, b=9, c=-36.

x= −b±√b^2−4ac/2a

x= −(9)±√(9)2−4(1)(−36)/2(1)

x= −9±√225/2

= x= 3 or x= -12

Answer:

\(\frac{1}{2}\)×\(\frac{1}{4}\)=\(\frac{1}{8}\)

Step-by-step explanation:

This sentence isn't always true.

The trick is to use fractional numbers .

let's analyse this example :

1/2=0.5 and 1/4=0.25 but 1/8=0.125

0.125<0.25<0.5

The product of two positive numbers is less than either number i.e. 4 × (1/2) = 2 < 4 which counterexample shows that the conjecture is false.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 12*2 = 24

We have been that conjecture "The product of two positive numbers is always greater than either number."

As per the given condition,

For example: 4 × (1/2) = 2 < 4

Therefore, the product of two positive numbers is less than either number i.e. 2 < 4.

Hence, the above counterexample shows that the conjecture is false.

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Answer:

9^6

Step-by-step explanation:

9^3 x 9^3

They have the same base of 9, so we add the ^3 with ^3 equal to ^6

So, the answer is 9^6

Answer: \(9^6\)

Step-by-step explanation:

       When multiplying exponents, you can add the exponents together if the bases are the same. 3 + 3 = 6. We can see this being done below where we expand and then simplify the expression.

               \(9^3*9^3=(9*9*9)*(9*9*9)=9^6\)

Answer:

b on edge 2020

Step-by-step explanation:

A 10 cm deep beaker mercury will have the same hydrostatic pressure as 133.5 cm deep water.

The hydrostatic pressure exerted by a fluid is given by:

P = ρ.g.h

Where:

ρ = fluid density

g = gravitational acceleration

h = fluid depth

We want to compare 2 types of fluid, water and mercury.

Divide both sides of the equation by h

P/h = ρ.g

Since pressure is held constant, then the fluid density is inversely proportional to the fluid depth.

Therefore,

h_water : h_mercury = ρ_mercury : ρ_water

Given that:

ρ_mercury = 13.55 ρ_water and h_mercury = 10 cm

Then,

h_water : 10 = 13.55 ρ_water : ρ_water

h_water : 10 = 13.55 : 1

h_water = 13.55 × 10 = 135.5 cm

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