Mattie planted a small tree in her backyard. The tree was planted when it was only 2 ft tall, and grows at a rate of 1.5 ft per year. How long until the tree is 8 ft tall?​

Since we have both equations set equal to y, we know that:

\(4x+6=3x^{2}+2x-10\\ \\ 3x^{2}-2x-16=0 \\ \\ (3x-8)(x+2)=0\\\\x=\frac{8}{3}, -2\)

If x=8/3, then y=4(8/3)+6=50/3.

If x=-2, then y=4(-2)+6=-2.

So, the solutions, to the nearest tenth, are:

\(x=2, y=-2\\\\x=2.7, y=16.7\)

The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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Given: X-3(x+2)=4X-3(x+2)=4

Find: the solution of the given equation

Explanation:

on solving equation (1) and (2) , we get

Answer:

x = -5

Step-by-step explanation:

    x - 3(x + 2)= 4

    x - 3x - 3*2 = 4     {Distributive property}

   x - 3x  - 6    = 4

Combine like terms in LHS,

         -2x - 6  = 4

Add 6 to both sides,

               -2x = 4 + 6

               -2x = 10

Divide both sides by (-2)

                   x = 10 ÷ (-2)

                   \(\sf \boxed{x= -5}\)

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Answer:

It has two roots

that is †2.4i and -2.4i

Step-by-step explanation:

\(f(x) = ( {x}^{2} + 6) {}^{2} \)

for a root, f(x) is zero

\( {( {x}^{2} + 6)}^{2} = 0 \\ ( {x}^{2} + 6) = 0\)

subtract 6 from both sides:

\(( {x}^{2} + 6) - 6 = 0 - 6 \\ {x}^{2} = - 6\)

remember: from complex numbers, i² is -1

\( {x}^{2} = 6 {i}^{2} \)

take square root on both sides:

\( \sqrt{ {x}^{2} } = \sqrt{ {6i}^{2} } \\ x = i \sqrt{6} \\ x = + 2.4i \: \: and \: \: - 2.4i\)

The edge length of the smallest possible square with an area of 5778 cm² is approximately 76.03 cm.

To calculate the edge length of the smallest possible square with an area of 5778 cm², we can use the formula for the area of a square, which is length multiplied by width. Since a square has all sides equal, we can use the formula A = s², where A represents the area and s represents the side length of the square.
In this case, we have the area of the square given as 5778 cm². To find the side length, we need to take the square root of the area.
√5778 ≈ 76.03 cm
Therefore, the edge length of the smallest possible square with an area of 5778 cm² is approximately 76.03 cm.

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Answer:

Step-by-step explanation:

0.13 repeating

The area of the region bounded on the right by the line g(x) = -x, on the left by the parabola f(x) =\(-(x+5)^2+25\), and below by the x-axis, when integrating with respect to y, is 83.33 square units.

To find the area of the region, we need to integrate the difference between the upper and lower functions with respect to y. In this case, the upper function is g(x) = -x and the lower function is f(x) = \(-(x+5)^2+25\).

First, we need to find the points of intersection between the line g(x) and the parabola f(x). Setting the two functions equal to each other, we have:

\(-x = -(x+5)^2+25.\)

Simplifying the equation, we get:

\(x^2 + 6x - 16 = 0.\)

Solving this quadratic equation, we find two solutions: x = 2 and x = -8.

The integration limits for y will be from 0 to the maximum y-value of the parabola, which is 25.

Now, we can set up the integral to find the area:

Area = \(\(\int_{25}^{0} [g(x) - f(x)] \,dx\)\)

Integrating this expression with respect to y, we find the area to be approximately 83.33 square units.

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The standard deviation of x when the variable is normally distributed is 19.53125 .

Let X be the random variable.

Here, random variable X is normally distributed with mean 1000.

As 40% area is left of the mean and remaining 40% area is right side of the mean, we can say that the probability that the value of the random variable is lied between 925 and 1000 is 0.4 .

The area under normal curve is evenly distributed with respect to the mean (0).

So, 80% of area around the mean is evenly distributed with mean that mean 40% area is left of the mean and 40% area is right of the mean.

By using one of the above, the value of the standard deviation can be obtained.

As the probability that the value of the random variable X is lies between (1000 , 1025 ) is 0.8 .

From the z-table of P(0<Z<z), it can be fount that in the row 1.2 and column 0.08, value is 0.4.

So, by looking in z-table, it is found that the value of P(0<Z<1.28) is 0.4.

By comparing equation (i) and (ii), we have,

Hence, the value of the standard deviation is 19.53125 .

Given that the 80 % confidence interval around X is given by (975 , 1025). That means there are 80% chances that value of the random variable X lies between (975 , 1025).

So, the probability that the value of the random variable X is lies between (975 , 1025) is 0.8.

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Answer:

2 and 14/15

Step-by-step explanation:

To calculate the mean in assembly language, you need to load the data, calculate the sum, calculate the mean, and store the result. This involves adding the data values together using a loop and dividing the sum by the number of data values.

Calculating the mean in assembly language involves the following steps:

Load the data: Load the data values from memory into registers or an array in the data section of the program.

Calculate the sum: Add all the values together using a loop and store the result in a register.

Calculate the mean: Divide the sum by the number of data values to calculate the mean.

Store the result: Store the mean value in memory or display it on the screen.

Here is an example code in x86 assembly language that calculates the mean of 5 data values stored in an array:

section .data

values dd 10, 20, 30, 40, 50  ; array of 5 data values

section .text

global _start

_start:

 mov ecx, 5     ; initialize loop counter to number of data values

 mov esi, values ; point to first value in array

 xor eax, eax    ; clear eax register for sum

sum_loop:

 add eax, [esi] ; add value to sum

 add esi, 4     ; point to next value in array

 loop sum_loop  ; decrement loop counter and loop until ecx = 0

 mov ebx, 5     ; divide by number of data values

 cdq            ; sign extend eax into edx

 div ebx        ; divide edx:eax by ebx, quotient in eax, remainder in edx

 ; eax now contains the mean value, you can store it in memory or display it on the screen

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Answer:

=3.5(-2.3) - 9.75

= -8.05 - 9.75

= negative 17.8

Step-by-step explanation:

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The equilibrium solutions are n = 0 and N = 4600.

(a) To determine when the population is increasing, we need to find the values of N for which dn/dt > 0. Let's analyze the inequality 1.3n (1- N /4600) > 0.

First, note that 1.3n is always positive since the coefficient 1.3 is positive and n represents the number of individuals, which cannot be negative.

Next, consider the factor (1 - N/4600). To determine its sign, we set it equal to zero and solve for N:

1 - N/4600 = 0

N = 4600

Since (1 - N/4600) is negative for N > 4600 and positive for N < 4600, we can conclude that the population is increasing when N < 4600.

Therefore, the values of N for which the population is increasing can be expressed as (-∞, 4600) in interval notation.

(b) Similarly, to determine when the population is decreasing, we need to find the values of N for which dn/dt < 0. Considering the inequality 1.3n (1- N /4600) < 0, we analyze the sign of the factors.

The factor 1.3n is always positive.

For the factor (1 - N/4600), it is negative for N > 4600 and positive for N < 4600.

Thus, the population is decreasing when N > 4600.

The values of N for which the population is decreasing can be expressed as (4600, +∞) in interval notation.

(c) Equilibrium solutions occur when the population remains constant, meaning dn/dt = 0. By setting 1.3n (1- N /4600) = 0, we find the equilibrium solutions:

1.3n = 0 (implies n = 0)

1 - N/4600 = 0 (implies N = 4600)

Therefore, the equilibrium solutions are n = 0 and N = 4600.

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Probability that 50 cars will have no defect is and the 51st is 12  . Probability that 20th car will have defect is 4.56. Probability that exactly one car has a defect is 0.2592.

It is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given Data

(a) Probability that a car has a defect = 40% = 0.4.

Probability that a car with no defect = 1 - 0.4 = 0.6

Probability that 50 cars does not have defect = (0.6)50

Probability that 50 cars will have no defect and the 51st will = (0.6)50(0.4)

Probability that 50 cars will have no defect and the 51st will= 12

(b) This question can be understood in two ways. If the question is simply asking for the probability that the 20th car has a defect it is 40% or 0.4. If the question means 19 cars do not have a defect and the 20th has one, the answer is below -

Probability that 19 cars do not have defect = (0.6)19

Probability that 20th car will have defect = (0.6)19( 0.4)

Probability that 20th car will have defect   = 4.56                                                            

(c) The one car with defect can be chosen in 5 ways.

Probability that the car has a defect = 0.4

Probability that the remaining 4 cars do not have defect = (0.6)4

Probability that exactly one car has a defect = 5( 0.4) (0.6)4 = 0.2592.

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Answer:

Specifically, if we want to think of multiplication as repeated addition, exponentiation as repeated multiplication, and ↑↑ as repeated exponentiation, three groups of five is the way to go. 53 means 5×5×5, not 3×3×3×3×3.

Step-by-step explanation:

The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.

Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.

Therefore, we can write the following inequalities:

P24 - P25 <= 80

This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.

P25-P24 <= 80

This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.

Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.

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Dyscalculia is a learning disorder that affects a person’s ability to do the math.

A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.

The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.

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Answer:

6.

Step-by-step explanation:

Source: Desmos.

When the points are plotted, the shape is a polygon. The polygon has 6 sides.

Picture represents the polygon shape, and its sides

The given differential equation (cos x cos y + 4y)dx + (sin x sin y + 10y)dy = 0 is not exact.

To determine whether the given differential equation (cos x cos y + 4y)dx + (sin x sin y + 10y)dy = 0 is exact, we need to check if it satisfies the condition for exactness, which states that the partial derivative of the coefficient of dx with respect to y should be equal to the partial derivative of the coefficient of dy with respect to x.

Let's calculate the partial derivatives of the given coefficients:

∂/∂y (cos x cos y + 4y) = -sin x sin y + 4

∂/∂x (sin x sin y + 10y) = cos x sin y

Now, we compare the two partial derivatives:

-sin x sin y + 4 ≠ cos x sin y

Since the two partial derivatives are not equal, the differential equation is not exact.

However, we can check if it becomes exact after multiplying it by an integrating factor. To do this, we need to find the integrating factor, which is given by the exponential of the integral of the difference of the partial derivatives:

μ(x) = e^∫(∂/∂x (sin x sin y + 10y) - ∂/∂y (cos x cos y + 4y)) dx

= e^∫(cos x sin y + sin x sin y - (-sin x sin y + 4)) dx

= e^∫(2sin x sin y + 4) dx

Integrating the expression ∫(2sin x sin y + 4) dx is challenging, and there is no simple closed-form solution. Hence, finding the exact solution using an integrating factor may not be feasible or practical in this case.

Therefore, based on the calculation and analysis, we can conclude that the given differential equation (cos x cos y + 4y)dx + (sin x sin y + 10y)dy = 0 is not exact.

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There for the diameter is 2(4.8 )= 9.6 ft

Given: Volume of the cone is 83.7 m³

We know that:

\(\bigstar \ \ \boxed{\sf{\textsf{Volume of cone is given by} : \dfrac{\pi r^2h}{3}}}\)

where r is the radius of the cone and h is the height of the cone

Given: Height of the cone = 5m

Substituting the values in the formula, we get:

\(\sf{\implies \dfrac{\pi r^2(5)}{3} = 83.7}\)

\(\sf{\implies \pi r^2 = 83.7 \times \dfrac{3}{5}}\)

\(\sf{\implies \pi r^2 = 83.7 \times 0.6}\)

\(\sf{\implies \pi r^2 = 50.22}\)

\(\sf{\implies r^2 = \dfrac{50.22}{\pi}}\)

\(\sf{\implies r^2 = 16}\)

\(\sf{\implies r = 4}\)

We know that : Diameter is two times the radius

⇒  Diameter of the Cone is 8 meters

In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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Answer:

Step-by-step explanation:

Sure! I'll perform the mathematical operations using the given numbers and apply the rules of precision. Please find the results below:

(9.11) + (6.232)

The sum of 9.11 and 6.232 is 15.342.

(7.4023) x (19)

The product of 7.4023 and 19 is 140.844.

(9.162) - (2.39)

The difference between 9.162 and 2.39 is 6.772.

(0.00482) x (213)

The product of 0.00482 and 213 is 1.02786.

(8.73) / (5.198)

The division of 8.73 by 5.198 is 1.67920734.

(7644) / (0.13)

The division of 7644 by 0.13 is 58,800.

Please note that the results are rounded to the appropriate number of decimal places based on the precision rules.

Answer:

The data represents data right-skewed because it's numerical data are in the right place and showing the percentage of an event/object.

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Answer:

(n - 10)(n-1)

Step-by-step explanation:

You have to choose two values that multiply to 10 and add to -11. Those to values are -10 and -1.

n² - 10n - 1n + 10

Rearrange them so that they can have a common factor.

n² - 1n - 10n + 10

1n (n - 1) + -10 (n + 1)

1n (n - 1) - 10 (n - 1)/ n-1

(n - 10)(n-1)

We usually measure it in cubic meters or cubic feet. ‪90 ft³‬ is equal to ‪2,544.48 cm³‬.

Length is a term used to describe the magnitude of a line, distance, or size. It usually refers to the measurement of something from end to end, such as the length of a river, the height of a building, or the size of a piece of fabric. Length is typically measured in units such as feet, meters, or even inches. It is an important concept in science, engineering, and mathematics. Length helps us to understand and quantify the size of objects and the space they occupy.

We can find the volume of any three dimensional object by using the formula V = l x w x h, where V is the volume, l is the length of the object, w is the width, and h is the height. This formula is applicable to all three dimensional shapes, including cubes, rectangles, prisms, cylinders, and so on.

To find the volume of a cylinder, we use the formula V = π x r² x h. Here, V is the volume, π is the constant pi, r is the radius of the cylinder, and h is the height. To find the volume of a sphere, we use the formula V = 4/3 x π x r³. Here, V is the volume, π is the constant pi, and r is the radius of the sphere.

We can also use volume to measure liquids or gases. We measure liquids in liters or milliliters, and gases in cubic meters or cubic feet. For example, 1 liter of water is the same as 1,000 milliliters of water.

Volume is an important concept in mathematics and is used to measure many different things. It is used to measure the size of objects, the volume of liquids and gases, and the amount of three dimensional space something occupies. Understanding volume and how to calculate it is an essential skill for anyone studying mathematics.

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The tubes of paint that would be needed to paint the ramp with an area of 3672 square inches is 3 tubes of paint

Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario

We are given the parameters that:

One tube of paint covers 1400 square inches of ramp

The surface area of the ramp from above was given as 3,672 square inches .

Thus:

Number of tubes of paint required = 3672/1400 = 2.62

Approximating to a whole number gives 3 tubes of paint.

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Answer:

21,526 people

Step-by-step explanation:

The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

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