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Finding a final amount in a word problem on exponential growt...
A principal of $4000 is invested at 5.25% interest, compounded annually. How much will the investment be worth after 11 years?
Use the calculator provided and round your answer to the nearest dollar.
$
X
5 ?

The inequality for the given graph is y ≥ - 3x + 4.

The act of illustrating which area of the number line has values that would "satisfy" the specified inequality is known as graphing the inequality. Take a look at the first inequality, "x > -5." The values that may be used to substitute x in our inequality to produce a true statement can be shown on a graph of our inequality.

A graphed system of inequality problems on a coordinate plane. Each axis on the x and y axes scales by two. Between the coordinates zero, two, and three, zero, there is a solid line that represents an inequality. The area for the disparity that is shaded is below the line.

First of all, we saw from the graph that the line is not dotted. So, we will use the signs ≥ or ≤.

Now find the slope

From the graph, consider

(x₁, y₁) = (0, 4)

(x₂, y₂) = (1, 1)

So, slope = (y₂ - y₁) /(x₂ -x₁)

= (1 - 4)/(1 - 0)

= - 3

The y-intercept is given as

y = mx + b

4 = -3 (0) + b

b = 4

So, the equation is

y= - 3x + 4

From the graph, the shaded region is above the line. So, inequality will be

y ≥ - 3x + 4

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The probability of getting 3 is P(A) = 1/216. The probability that sum being 3 is 1 / 216.

When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. A dice can show a minimum of one and a maximum of six dots, for a total of six sides, giving it a total of 6 * 6 * 6 = 216 possible outcomes.

:When three dice are thrown simultaneously, the probability that the sum is 3 is 1/216. The probability can be calculated as follows:

Let A be the event that the sum is 3. The number of ways to get 3 is 1, i.e., (1, 1, 1). The total number of possible outcomes is 6³,

since each die can have 6 possible outcomes.

Therefore, the probability of getting 3 is P(A) = 1/216.

In conclusion, the probability that sum being 3 is 1 / 216.

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The product of (4x² - 2x)( -3x³ - 4x² + 1) is, - 12x⁵ - 10x⁴ + 8x³ + 4x² - 2x.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, Are the product of two quadratic expressions (4x²-2x)(-3x³-4x²+1).

= 4x²(- 3x³ - 4x² + 1) - 2x(- 3x³- 4x² + 1).

= - 12x⁵ - 16x⁴ + 4x² + 6x⁴ + 8x³ - 2x.

= - 12x⁵ - 10x⁴ + 8x³ + 4x² - 2x.

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The answer is ln s² / y⁶.

We are supposed to write the following expression as a single logarithm using the properties of logarithms: ln y+2 ln s − 8 ln y.

Using the properties of logarithms, we know that log a + log b = log (a b).log a - log b = log (a / b). Therefore,ln y + 2 ln s = ln y + ln s² = ln y s². ln y - 8 ln y = ln y⁻⁸.

We can simplify the expression as follows:ln y+2 ln s − 8 ln y= ln y s² / y⁸= ln s² / y⁶.This is the main answer which tells us how to use the properties of logarithms to write the given expression as a single logarithm.

We know that logarithms are the inverse functions of exponents.

They are used to simplify expressions that contain exponential functions. Logarithms are used to solve many different types of problems in mathematics, physics, engineering, and many other fields.

In this problem, we are supposed to use the properties of logarithms to write the given expression as a single logarithm.

The properties of logarithms allow us to simplify expressions that contain logarithmic functions. We can use the properties of logarithms to combine multiple logarithmic functions into a single logarithmic function.

In this case, we are supposed to combine ln y, 2 ln s, and -8 ln y into a single logarithmic function. We can do this by using the rules of logarithms. We know that ln a + ln b = ln (a b) and ln a - ln b = ln (a / b).

Therefore, ln y + 2 ln s = ln y + ln s² = ln y s². ln y - 8 ln y = ln y⁻⁸. We can simplify the expression as follows:ln y+2 ln s − 8 ln y= ln y s² / y⁸= ln s² / y⁶.

This is the final answer which is a single logarithmic function. We have used the properties of logarithms to simplify the expression and write it as a single logarithm.

Therefore, we have successfully used the properties of logarithms to write the given expression as a single logarithmic function. The answer is ln s² / y⁶.

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The point which is √2 distance away from the point (-1, 5) is (-1, 5 - √2).

In order to find a point that is √2 away from (-1, 5), we need to find a point that is at a distance of √2 from (-1, 5). Let the point we need to find be (x, y),

Using the distance formula, we can set up the following equation:

√[(x - (-1))² + (y - 5)²] = √2,

Simplifying this equation,

We get,

(x + 1)² + (y - 5)² = 2,

This equation represents a circle with center (-1, 5) and radius √2.

So, one point that satisfies this equation is (-1, 5 - √2), which is √2 away from (-1, 5).

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Answer:

Step-by-step explanation:

30/10x = 3x

Answer:

\(30\div10x\)

Step-by-step explanation:

Using x for the unknown number, "the quotient of thirty and ten times a number" is written as:

\(30\div10x\)

Answer:

×=

\( \frac{ab}{?c + a} \)

Answer:

x = \(\frac{ab}{c+a}\)

Step-by-step explanation:

a(b-x) = cx

ab - ax = cx

ab = cx + ax

ab = x (c + a)

divide both sides by (c + a) for x to stand alone

x  = ab/ c + a

Step-by-step explanation:

a ) 12 , 17 , 22 , 27 , 32

according to the given sequence, they added 5 in the numbers

b ) 83 , 77 , 71 , 65 , 59

in this given sequence they just subtracted 6 from the number

hope this answer helps you dear...take care and may u have a great day!

Answer:

Describe two ways you think a sound wave could be stopped or could change change direction.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

A vector equation of a surface in three-dimensional space is a function that maps a pair of parameters, say u and v, to a three-dimensional point in space (x, y, z) represented as a vector. The vector equation can be written in the form of r(u, v) = <x(u, v), y(u, v), z(u, v)>.

In general, there are different ways to represent the same surface using vector equations. For example, the surface of a sphere of radius r centered at the origin can be represented by the vector equation r(u, v) = <r sin(u) cos(v), r sin(u) sin(v), r cos(u)>, where u is the polar angle (measured from the positive z-axis) and v is the azimuthal angle (measured from the positive x-axis).

Vector equations can be useful in studying the geometry and properties of surfaces, such as determining their tangent planes, normal vectors, curvature, and surface area. They can also be used to parametrize surfaces for numerical calculations and simulations.

The surfaces described by the given vector equations are:

1.The surface is a hyperbolic paraboloid.

2.The surface is a part of a cylinder with radius 3 and axis parallel to the y-axis.

3.The surface is a plane parallel to the xy-plane and shifted upwards by 1 unit.

4.The surface is a twisted cylinder along the y-axis.

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By iteration, g(10) = 60 for (i) and g(10) = 14 for (ii)

Given information: The recursive formula are(i)  t(n) = t(n - 2) + 2n, t(1) = 1, t(0) = 0(ii) t(n) = t(n - 1) + n/2, t(1) = 1.Solve by iteration:

1. The recursive formula is t(n) = t(n - 2) + 2n, t(1)

                                                   = 1, t(0)

                                                   = 0.

This can be written as, t(n) = t(n - 2) + 2nOr, t(n + 2) = t(n) + 2(n + 2) (Add 2(n + 2) to both sides)

Let, the initial value of t(n) be g(n)

Therefore, t(n + 2) = g(n + 2)g(n) + 2(n + 2)

This iteration will be used until the value converges to the answer.

2. The recursive formula is t(n) = t(n - 1) + n/2, t(1) = 1.

This can be written as, t(n) = t(n - 1) + n/2Or, t(n + 1) = t(n) + (n + 1)/2

Let, the initial value of t(n) be g(n)

Therefore, t(n + 1) = g(n + 1)g(n) + (n + 1)/2

This iteration will be used until the value converges to the answer.

3. t(0) = 0 and t(1) = 1.This is given.

The iterative method is used when no exact formula can be found that will provide the n-th term of the sequence directly.

The iteration for

(i) becomes, g(0) = 0,

g(1) = 1.g(2)

     = g(0) + 2(2)

     = 4g(3)

     = g(1) + 2(3)

     = 7g(4)

     = g(2) + 2(4)

     = 12g(5)

     = g(3) + 2(5)

     = 17g(6)

     = g(4) + 2(6)

     = 24g(7)

     = g(5) + 2(7)

     = 31g(8)

     = g(6) + 2(8)

     = 40g(9)

     = g(7) + 2(9)

     = 49g(10)

     = g(8) + 2(10)

     = 60

The iteration for

(ii) becomes, g(1) = 1.g(2)

                           = g(1) + (2)/2

                           = 2g(3)

                           = g(2) + (3)/2

                           = 3.5g(4)

                           = g(3) + (4)/2

                           = 5g(5)

                           = g(4) + (5)/2

                           = 6.5g(6)

                           = g(5) + (6)/2

                           = 8g(7)

                           = g(6) + (7)/2

                           = 9.5g(8)

                          = g(7) + (8)/2

                          = 11g(9)

                          = g(8) + (9)/2

                          = 12.5g(10)

                          = g(9) + (10)/2

                          = 14.

The values of g(n) converge to the corresponding values of t(n).

Therefore, the required answers are: g(10) = 60 for (i) and g(10) = 14 for (ii).

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This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

Answer:5 million

Step-by-step explanation: Because 300 thousand is below 500 thousand so if its below 500 thousand it cant round up it rounds down.

Answer:

y = 4/3 x - 4

Step-by-step explanation:

The slope-intercept form of the equation of a line

The equation of a line can be expressed in several forms. One of them is the slope-intercept form:

y = mx + b

Where

m = slope

b = y-intercept

We are required to convert the equation of the line:

4x - 3y = 12

It can be done by solving for y.

Subtracting 4x:

- 3y = - 4x + 12

Dividing by -3;

y = 4/3 x - 4

Answer:

Should be $300

let me know if it's correct:)

Answer:

x = -8 + sqrt(10) and x = -8 - sqrt(10)

Step-by-step explanation:

The quadratic equation to be solved is:

2(x + 8)² + 9 = 29

First, we need to simplify the left-hand side of the equation by expanding the squared term:

2(x + 8)(x + 8) + 9 = 29

Simplifying further, we get:

2(x² + 16x + 64) + 9 = 29

Distributing the 2, we get:

2x² + 32x + 128 + 9 = 29

Combining like terms, we get:

2x² + 32x + 137 = 29

Subtracting 29 from both sides, we get:

2x² + 32x + 108 = 0

Dividing both sides by 2, we get:

x² + 16x + 54 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula :

The equation presented is a quadratic equation in standard form, ax² + bx + c = 0, where a = 1, b = 16, and c = 54. To solve this equation, we can use the quadratic formula, x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in the values, we get x = (-16 ± sqrt(16² - 4(1)(54))) / 2(1) = (-16 ± sqrt(16)) / 2 or (-16 ± 2sqrt(10)) / 2. Simplifying, we get x = -8 ± sqrt(10). Therefore, the two solutions to this equation are x = -8 + sqrt(10) and x = -8 - sqrt(10).

Answer:

$281

Step-by-step explanation:

To find the total admission cost, you do (12.5 x 4) + (8.25 x 28), which gives you $281.

Answer: should be cos 52

Step-by-step explanation: :)

Answer:

a hope it helps make brainlliest ty the tasmanian

The correct answer is option d. 928.02. This can be answered by the concept of sum of squares.

The sum of squares due to regression (SSR) is a statistical term that measures the total amount of variation in the dependent variable that can be explained by the regression model. It is also known as the explained sum of squares. SSR is an important component of the analysis of variance (ANOVA) used in regression analysis to assess the goodness of fit of the regression model.

In the given options, option d. 928.02 is the correct answer as it represents the sum of squares due to regression (SSR). Option a. 1434, option b. 505.98, and option c. 50.598 are not correct as they do not represent the sum of squares due to regression (SSR).

Therefore, the correct answer is d. 928.02.

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Water main valves should be located at frequent intervals in a grid system.

The flow and temperature in pipes and plumbing fittings are controlled by water valves. The valves regulate steady flow and volume when they are correctly placed and used. Water valves are made of brass, plastic, stainless steel, bronze, cast iron, and galvanised pipe, among other materials.

The master cutoff valve for the house will typically feature a wheel (a gate valve) or a straight handle (ball valve). The wheel on gate valves (seen on the right) is turned clockwise until the water is shut off. To turn off the water, turn the handle of a ball valve a quarter turn in the opposite direction. Every house has two main water shutoff valves: one inside and one near the intersection of your property and the street.

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The function that represents the mass of the sample after x years is,

⇒ m (x) = 340 (0.9875)ˣ

And, The percentage rate of change per quarter is of -1.25%.

Now, Based on the information given, we know that the mass of Element X decreases by 5% every year.

To find the quarterly rate of change, we can divide 5% by 4 to get 1.25% per quarter.

Hence, Using this quarterly rate of change, we can write the function as:

⇒ m(x) = 340  (1 - 0.0125)ˣ

⇒ m (x) = 340 (0.9875)ˣ

where x represents the number of quarters that have passed since the start of the experiment.

Hence, The function that represents the mass of the sample after x years is,

⇒ m (x) = 340 (0.9875)ˣ

And,

Hourly rate of change:

Since, Decreases by 5% every year, which means that for 4 quarter, the rate of change is of -5%. So

-5%/4 = -1.25%

Hence, The percentage rate of change per quarter is of -1.25%.

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888030 ways are there for teachers to select the students.

What is the combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we have

A teacher selects 7 students from her class of 27 students.

We have to find how many ways are there for her to select the students of the chosen students.

The order of selecting the students does not matter here so the number of ways to select 7 students from the class of 27 to work together on a project is:

C(27,7) = 27!/(7!*(27-2)! = 888030

Hence, 888030 ways are there for teachers to select the students.

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Answer:

C

Step-by-step explanation:

hope this helps I'm sorry if you need work I will do it if so

Answer:

0.03 3.00 4.00 516388383

A. The new coordinates for Square BCDE after reflecting it across the y-axis are B(6,7), C(2,6), D(3,2), and E(7,3).

B. To reflect a figure across the y-axis, we need to change the sign of the x-coordinates while keeping the y-coordinates unchanged.

For Square BCDE with vertices B(-6,7), C(-2,6), D(-3,2), and E(-7,3), we can see that the y-coordinates remain the same, while the x-coordinates change sign.

Reflecting B(-6,7) across the y-axis gives us B(6,7).

Reflecting C(-2,6) across the y-axis gives us C(2,6).

Reflecting D(-3,2) across the y-axis gives us D(3,2).

Reflecting E(-7,3) across the y-axis gives us E(7,3).

Therefore, the new coordinates for Square BCDE after reflecting it across the y-axis are B(6,7), C(2,6), D(3,2), and E(7,3).

For Trapezoid JKLM with vertices J(-4,3), K(-2,7), L(2,7), and M(3,3), we are given that the trapezoid lies on the line y=1. Reflecting the trapezoid across the line y=1 is equivalent to reflecting it across the x-axis.

To reflect a figure across the x-axis, we need to change the sign of the y-coordinates while keeping the x-coordinates unchanged.

Reflecting J(-4,3) across the x-axis gives us J(-4,-3).

Reflecting K(-2,7) across the x-axis gives us K(-2,-7).

Reflecting L(2,7) across the x-axis gives us L(2,-7).

Reflecting M(3,3) across the x-axis gives us M(3,-3).

Therefore, the new coordinates for Trapezoid JKLM after reflecting it across the line y=1 (equivalent to reflecting it across the x-axis) are J(-4,-3), K(-2,-7), L(2,-7), and M(3,-3).

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Step-by-step explanation:

The sum of two opposite interior angles equals an exterior angle

50+?=115

?=115-50=65°

Answer:

60 degrees

Step-by-step explanation:

angles on a straight line add up to 180 degrees.

so do 180-115=60

because its an equilateral triangle, you can check whether it adds up to 180

60+60+50=180

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The equation of the parabola in any form is; (x + 5)² = 4(y - 4)

The general equation of a parabola is given by the expression;

y = a(x – h)² + k or x = a(y – k)² + h.

Where (h, k) denotes the coordinates of the vertex

2p = 5 - 3

2p = 2

p = 1.

Thus, the coordinates of the vertex will be;

Vertex (-5, 5 - 1) = (-5, 4)

Therefore the equation of parabola is expressed as;

(x + 5)² = 4(y - 4)

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Answer:

y = -27

Step-by-step explanation:

y=-15-12

y=-27

Answer:

y = -27

Step-by-step explanation:

12 + y = -15

-12         -12

y = -27

check:

12-27=-15