Graph the following function, f(x)=x^3 +3

The value of x from the figure is 13

The sum of angles on a straight line is 180 degrees.

From the given diagram;

Simplify

15x - 15  = 180

Add 15 to both sides

15x - 15 + 15 = 180 + 15

15x = 195

x = 195/15

x = 13

Hence the value of x from the figure is 13

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The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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Answer:

c=200+0.4Yd find determine equlibirum level investment is =400

Answer:im pretty sure its D

Step-by-step explanation:it goes through the origin

Let's divide the shaded region into two areas:

area 1: x = 0 ---> x = 2

ares 2: x = 2 ---> x = 4

In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.

Area 1:

\(A\frac{}{1} = ∫g(x)dx = ∫xdx = \frac{1}{2} {x}^{2} | \frac{2}{0} = 2\)

Area 2:

\(A\frac{}{2} = ∫(g(x) - f(x))dx\)

\(= ∫(x - {(x - 2)}^{2} )dx\)

\( = ∫( - {x}^{2} + 5x - 4)dx\)

\(= ( - \frac{1}{3}{x}^{3} + \frac{5}{2} {x}^{2} - 4x) | \frac{4}{2}\)

\( = 2.67 - ( - 0.67) = 3.34\)

Therefore, the area of the shaded portion of the graph is

A = A1 + A2 = 5.34

Answer:

\(t \: = 3.92 \: sec\)

Step-by-step explanation:

When (t =0)

Height of cliff = 248 feet = 75.5m

Using Newton's equations of motion:

\(s = ut + \frac{1}{2} a {t}^{2} \)

75.5 = 0 * t + 4.9 * t^2

Solving further :

\(t \: = 3.92 \: sec\)

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

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Answer:

5696

Step-by-step explanation:

i assume you are referring to tax of 16%

16/100 x 35600 = 5696

Answer:

Try contacting the Help center located at the bottom part of the home page of this site. It is recoverable as long as no violation committed

The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables

The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

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The graphs of f(x) and g(x) are transformed function from the function y = x^2 and the solution of the set of inequalities is (±1.581, -0.5)

The complete question is in the attached image (the first graph)

From the graph, we have:

f(x) = x^2 - 3 and g(x) = -x^2 + 2

To derive y ≤  x^2 - 3, we simply change the equality sign in the function f(x) to less than or equal to.

To derive y > -x^2 + 2, we simply change the equality sign in the function g(x) to greater than

The inequalities of the graphs become

y ≤ x^2 - 3 and y > -x^2 + 2

From the graph of the above inequalities (see attachment 2), we can see that the curves of the inequalities intersect at (±1.581, -0.5)

Hence, the solution of the set of inequalities is (±1.581, -0.5)

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Answer:

A. (-4, 6 )

Step-by-step explanation:

Signals of x and y in each quadrant:

Suppose we have a point P(x,y).

In the first quadrant, we have that both are positive, that is, x > 0, y > 0.

In the second quadrant, x is negative, while y is positive, that is, x < 0, y > 0.

In the third quadrant, both are negative, that is, x < 0, y < 0.

In the fourth quadrant, x is positive while y is negative, that is, x > 0, y < 0.

In this question:

In the second quadrant, we have x negative and y positive, so the ordered pair that best describes is given by option A.

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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Answer:

Grouped Frequenct Distribution

UnGrouped Frequency Distribution

Step-by-step explanation:

The volume of the cone is approximately 167.27 cubic inches.

The volume of a cone can be calculated using the formula:

V = (1/3)πr²h

where V is the volume of the cone, r is the radius of the circular base of the cone, h is the height of the cone, and π is the mathematical constant pi (approximately 3.14).

The volume of a cone can be calculated using the formula:

V = (1/3)πr²h

where r is the radius of the circular base of the cone, h is the height of the cone, and π is approximately 3.14.

We are given that the diameter of the circular base of the cone is 8 inches. Since the diameter is twice the radius, the radius is 4 inches. We are also given that the height of the cone is 10 inches.

Substituting these values into the formula for the volume of a cone, we get:

V = (1/3)π(4²)(10)

Simplifying this expression, we get:

V = (1/3)π(16)(10)

V = (1/3)(160π)

V ≈ 167.27 cubic inches

Therefore, the volume of the cone is approximately 167.27 cubic inches.

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Answer:

Kendriya z-score keva product

Answer: $26

Step-by-step explanation:

   If $19.50 is 3/4, we need to find 4/4.

3/4 -> 0.75

4/4 -> 1

    We will set up a proportion and solve.

\(\frac{19.5}{0.75} =\frac{x}{1}\)

19.5 = 0.75x

26 = x

         The professional ball is $26.

Answer:

$26

Step-by-step explanation:

19.50 = 3/4

so

to find 1/4, we do 19.50 / 3 = 6.5

6.5 = 1/4

so the price of a professional ball would be 4/4 (1 whole)

6.5 x 4 = 26

Hope this makes sense.

- profparis

Answer:

66 square feet

Step-by-step explanation:

please review the attachment for a detailed explanation

A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459    , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

\($$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$\)

as population variance is unknown so we used sample variance

\($$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$\)

Now

\(\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$\)

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

\($$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$\)

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Answer

The answer is 16.3

Answer:

16.3

Step-by-step explanation:

16.328 rounded to the nearest tenth is 16.3

a) The value of x is 21

b) The value of the expression is 135.

c) The value of the expression is 135.

Here we know that the lines G and M are parallel, meaning that the two shown angles are alternarte exterior angles, and thus, have the same measure, then we can write:

5*(x + 6) = 9*(x - 6)

We can solve that linear equation for x:

5x + 30 = 9x - 54

30 + 54 = 9x - 5x

84 = 4x

84/4 = x

21 = x

Then the measures of the angles are:

a1 = 5*(21 + 6) = 135°

a2 = 9*(21 - 6) = 135°

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The required simplification of the expression is \(\csc^2\theta-1.$$\)

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This implies that these trig functions provide the relationship between the angles and sides of a triangle.

Using the equation cos2(x) + sin2(x) = 1, one can change sin to cos. Rearranging this results in sin(x) = sqrt(1 - cos(x)), which means that sin(x) = cos(1 - cos(x)). Utilizing the equation sin(x) = cos(pi/2 - x) is another method of converting sin to cos.

\($(\frac{-\cos\theta}{\sin\theta})\cdot(\frac{-\cos\theta}{\sin\theta})=\frac{\cos^2\theta}{\sin^2\theta}=\frac{1-\sin^2\theta}{\sin^2\theta}=\frac{1}{\sin^2\theta}-1=\csc^2\theta-1.$$\)

Thus, required simplification of the expression is \(\csc^2\theta-1.$$\)

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Answer:

The percentage of adults in the town whose heights are between 60.1 and 74.1​ inches

P( 60.1≤X≤74.1) = 2.26 %

Step-by-step explanation:

Step(i):-

Given that the heights of the adults in one town have a mean of 67.1 inches

Mean of the Population = 67.1 inches

The standard deviation of the Population = 3.5inches

Let X₁ =60.1

\(Z = \frac{x-mean}{S.D} = \frac{60.1-67.1}{3.5} = -2\)

Let X₂ = 74.1

\(Z = \frac{x-mean}{S.D} = \frac{60.1-74.1}{3.5} = -4\)

Step(ii):-

The probability of adults in the town whose heights are between 60.1 and 74.1​ inches

P( X₁ ≤X≤X₂) = P(Z₁≤Z≤Z₂)

                    = P( -2≤ Z≤-4)

                   = |A(-4) -A(-2)|

                   = A(4) - A(2)|     (∵ A(-Z) =A(Z))

                  = 0.4998 - 0.4772

                 = 0.0226

Final answer:-

The probability of adults in the town whose heights are between 60.1 and 74.1​ inches

P( X₁ ≤X≤X₂) = 0.0226

The percentage of adults in the town whose heights are between 60.1 and 74.1​ inches

P( 60.1≤X≤74.1) = 2.26%

95.44% of adults in the town have heights between 60.1 and 74.1​ inches

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

\(z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation\)

Given that μ = 67.1, σ = 3.5.

For x = 60.1:

\(z=\frac{60.1-67.1}{3.5}=-2\)

For x = 74.1:

\(z=\frac{74.1-67.1}{3.5}=2\)

From the normal distribution table, P(60.1 < x < 74.1) = P(-2 < z < 2) = P(z < 2) - P(z < -2) = 0.9772 - 0.0228 = 95.44%

95.44% of adults in the town have heights between 60.1 and 74.1​ inches

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The given differential equation:

y''' − 2y'' + y' = 2 − 24ex + 40e5x,

y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2

Therefore, the next solution is 13/2

Differential Equation:

In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.

Now,

Given differential equation is

y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ                 ------------ (1)

Auxiliary equation is m³ - 2m² +2m = 0

Now,

   m(m² - 2m +2) = 0

⇒ m(m-1)² = 0

Therefore, m = 0,1,1

Therefore,

\(y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}\)

Now, we have to find the particular solution by method of undetermined coefficient.

   \(y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}\)

⇒ \(y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}\)

⇒ \(y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}\)

⇒ \(y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}\)

Putting these values in differential equation (1), we get:

y'''(0) = 13/2

Complete Question:

Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2

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Answer: z=24/7

Step-by-step explanation:

Answer:

x×25+y×14.5( greater than or equal to symbol)250

Answer:25x+14.5y (greater than but equal to) 250

Step-by-step explanation:

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

To determine the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\), we need to consider the situation and the constraints given.

The function A(t) represents the area of the rectangular garden as a function of the length of one of its sides, which is denoted by t.

We are also told that Marama plans to fence the garden with 28 feet of wired fencing.

Now, let's break down the problem and find the appropriate values for the domain.

We know that the perimeter of a rectangle is the sum of all its sides. In this case, since we have a rectangular garden, the perimeter can be represented as:

\(Perimeter = 2t + 2w\),

where t is the length of one side (the width) and w is the length of the other side (the width).

The problem states that Marama plans to use 28 feet of wired fencing. Therefore, the perimeter of the garden must equal 28 feet:

\(2t + 2w = 28\).

Simplifying this equation, we have:

\(t + w = 14\).

We can express w in terms of t as \(w = 14 - t\).

The area of a rectangle is given by the product of its length and width:

\(Area = t \times w\).

Substituting the expression for w from step 2, we have:

\(A(t) = t \times (14 - t)\).

Simplifying further:

\(A(t) = 14t - t^2\).

To determine the appropriate values of the domain, we need to consider the context of the problem. Since we are dealing with a physical garden, both the length and width must be positive numbers. Additionally, the values of t must be feasible given the constraints of the perimeter.

We know that \(t + w = 14\), so \(t + (14 - t) = 14\), which simplifies to \(14 = 14\).

This shows that the value of t can range from 0 to 14, inclusive.

Therefore, the appropriate values of the domain for the graph of the function \(A(t) = -t^2 + 14t\) are \(t \epsilon [0, 14]\).

To illustrate this graphically, we can plot the function \(A(t) = -t^2 + 14t\) and mark the appropriate values of the domain on the x-axis (representing t):

   ^

   |

A(t)|

   |

   |_______________________________

   0              t             14

The domain for the function is the interval [0, 14], which represents the feasible values for the length of one side of the rectangular garden.

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In a case whereby the function is y = -5x + 4, the range of the function of the domain is  {14, 4, -21}

A function's range  serves as one which encompass conceivable values for y. Y = f(x) is the formula to determine a function's range.

We were told to get the range of the function,  which implies that we will be plugging each value in the domain into the given function  so that we can observe the output (y-value) .

When x = -2:

y = -5(-2) + 4 = 1

When x = 0:

y = -5(0) + 4 = 4

When x = 5:

y = -5(5) + 4 = -21

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Answer:

The slope is equal to 5.

Step-by-step explanation:

Point 1 (0, 5)

Point 2 (3, 20)

m=y2-y1/x2-x1

m=5-20/0-3

m=-15/-3=

m=5

Answer:

Step-by-step explanation:

We need to find the value (f-g)(2), so we need first to substitute 2 into the given functions f(x) and g(x) and then subtract the result of g(2) from f(2).

Here, f(x) = 3x^2 + 1 and g(x) = 1 - x,

So, We will substitute 2 into these functions:

f(2) = 3(2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13

g(2) = 1 - 2 = -1

Now, we can subtract g(2) from f(2):

(f-g)(2) = f(2) - g(2) = 13 - (-1) = 13 + 1 = 14

Hence, the required value of (f-g)(2) is 14.

Answer:

The correct answer is 3. To solve for g(-2), we substitute -2 for x in the equation g(x) = 2x + 5. This gives us g(-2) = 2(-2) + 5, which simplifies to -4 + 5 = 1. Next, we substitute the value of g(-2) into the equation for f(g(x)) = 4 - x^2. Thus, f(g(-2)) = 4 - (1)^2, which equals 4 - 1 = 3.

Answer:

$1,078

Step-by-step explanation:

The tax amount is taken out of his taxable income,

The tax amount is $1583.

A tax is a mandatory contribution that a local, regional, or national government collects from individuals or businesses. Public works and services like roads and schools, as well as programs like Social Security and Medicare, are financed by tax revenue.

In economics, taxes go to whoever has to pay them, whether it's the entity being taxed, like a business, or the people who buy the goods from the business. Payroll taxes, federal and state income taxes, and sales taxes are just a few of the taxes to take into account from an accounting perspective.

Given

adjusted gross income = $26,045

exemption =  $12,400

to find tax by  taxable income

 taxable income =  adjusted gross income - exemption

taxable income =  26,045 - 12400

taxable income = $13,645

The question is incomplete, the table is attached

Therefore, I will employ the 2016 single taxable income tax bracket and rate table.

Using the table, the tax amount on an income of $13,645 is:

Tax = $927.50 + 15% × (Amount - $9275)

So, we get:

Tax = $927.50 + 15% ×($13645 - $9275)

$1583,

Hence, Allie's tax amount is $1583.

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The table for Question is in image attached.