A radioactive substance has a half-life of 8 years. How much of the original 3.2 grams of the substance would be left after 36 years? Which equation best models this situation?

The True statement is:

All the four function cut the y axis at (0, 3)

The point at which the line or curve crosses the graph's axis is referred to as the intercept. When a point crosses the x-axis, it is referred to as the x-intercept. When a point crosses the y-axis, it is referred to as the y-intercept.

We have Four function

f(x) = 4[tex](2)^x[/tex] -1

g(x) = 3[tex](1/4)^x[/tex]

h(x) = [tex](1/2)^x[/tex] + 2

k(x) = -[tex]3^x[/tex] + 4

We have represented all the graph given below.

First, there is no function whose have negative y intercept.

Only f(x) have negative x intercept.

But all the four function cut the y axis at (0, 3)

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Step-by-step explanation:

a) BD/AD=AB/AC=AD/CD; BD/AB=AB/BC=AD/AC; AD/AB=AC/BC=CD/AC;

b) if BC=2 and DC=10, then it is possbile to write:

BD/AD=AB/AC=AD/10; BD/AB=AB/2=AD/AC; AD/AB=AC/2=10/AC, then

AC/2=10/AC and AC²=20. According to the Pyphagorean's theorem AD²=AC²+CD² and AD=√120≈10.96

The least distance by Pythagorean theorem is equal to √5. (Correct choice: B)

In this problem we find the representation of a point and a line on Cartesian plane. There is a least distance between the point and the line when the line segment between them is perpendicular to the line. The line segment AC fulfill these features. Given the location of points A and C, we can determine the distance by means of Pythagorean theorem:

d = √[(Δx)² + (Δy)²]

Where:

If we know that A(x, y) = (1, 3) and C(x, y) = (3, 2), then the least distance between the point and the line:

d = √[(3 - 1)² + (2 - 3)²]

d = √[2² + (- 1)²]

d = √5

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We will make ₹1,048,575 for the month. The solution has been obtained by using the arithmetic operations.

The four basic operations, often referred to as "arithmetic operations", are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.

We are given that for the first day of each month, a penny is earned. Thereafter, each workday wages will double what they were the day before.

Now, since there are 20 workdays in a month so, the total amount earned is as follows:

⇒ 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1,024 + 2,048 + 4,096 + 8,192 + 16,384 + 32,768 + 65,536 + 131,072 + 262,144 + 524,288

⇒ ₹ 1,048,575

Hence, we will make ₹ 1,048,575 for the month.

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Option A is the correct answer as EF/QR = CE/SQ is not correct, as the triangles contain no vertex C.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Although having the same form, each might have different sizes.

There are no matching angles that are not equal.

Similar equivalent side ratios exist.

Given that, EFG and QRS are similar.

We know that for similar triangles the ratio of length of the segments of the corresponding triangle are equal.

Thus, EF/QR = CE/SQ is not correct, as the triangles contain no vertex C.

Hence, option A is the correct answer.

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Using the equation, we found the following:

1) Expected Population in the year 2014 = 41100

2) Predicted year when the population will reach 54000 = 2020

3) The rate of population changes = 2150

4) The number of years for the population doubled since 2008 =9.12

What is a linear equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

Given,

the population in 2008 = 28,200

the population in 2012 = 36,800

The population is growing linearly.

Assume a linear equation,

p(x) = 36800 + kx

where,

   p(x) = population

  x = years since 2012.

k = increase in population

p(0) = 36800

p(-4) = 36800 - 4k

28200= 36800 -4k

4k = 36800 - 28200

k = 2150

Then the linear equation becomes,

p(x) = 36800 + 2150x

1) Population in 2014

x = 2014 - 2012 = 2

From the equation,

p(2) = 36800 + 2150 * 2 = 41100

2) x when p(x) = 54000

From the equation,

54000  = 36800 + 2150x

2150x = 17200

x = 8

Year = 2012 + 8 = 2020

3) Rate of population change = (population in 2012 - population in 2008) / number of years = 36800-28200 / 4 = 2150

4) Population doubled since 2008

p(x) = 2 * 28200 = 56400

We have to find x , when p(x) = 56400

Using the linear equation,

56400 = 36800 + 2150x

x = 9.12

Therefore using the equation, we found the following:

1) Expected Population in the year 2014 = 41100

2) Predicted year when the population will reach 54000 = 2020

3) The rate of population changes = 2150

4) The number of years for the population doubled since 2008 =9.12

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Mr Smith looks their children 1 times 1

Surface Area of cuboid = 2 (lb + bh + hl)

According to the question :

length = x, width = x-5, height = 0.5x

250 = 2 ( x × (x-5) + (x-5) × 0.5x + 0.5x × x )

250 = 2 ( x² - 5x + 0.5x² - 2.5x + 0.5x²)

250 = 2 ( x² - 5x + x² - 2.5x )

250 = 2 ( 2x² - 7.5x )

250 = 4x² - 15 x

4x² - 15x -250 = 0

In square prism , A cracker box in the shape of a square prism with a base side length of   [tex]SA - \frac{2S^{2} }{4S} = h[/tex].

What is square prism?

The bases of a square prism are square, and the other four faces are rectangles. A square prism is a cuboid object in three dimensions.

                                    Angles and sides that are in opposition to one another are congruent. A magnet bar is an illustration of the shape of a square prism.

we know that'

The formula to calculate the surface area of a square prism is

          [tex]Q = 2s^{2} + 4sh[/tex]

  subtract 2s² both sides

    SA - 2s² = 4sh

  Divide by 4s both sides

     [tex]SA - \frac{2S^{2} }{4S} = h[/tex]

   Rewrite

   [tex]SA - \frac{2S^{2} }{4S} = h[/tex]

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The linear equation in this situation is y=20x which will have its solution as per the values of 'x'.

For instance, the cost of a good for a certain amount can be determined using a linear equation.

The linear equation in this situation is y=20x.

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The distance between points A and B is 6 units.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

We are given that;

The points= (-1.4) and B (5.-2)

Now,

To find the distance between points A (-1.4) and B (5.-2), we can use the distance formula:

d = [tex]\sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.

Substituting the values we have:

[tex]\sqrt{(5 - (-1))^2 + (-2 - (-4))^2}[/tex]

d = [tex]\sqrt{(5 + 1)^2 + (-2 + 2)^2}[/tex])

d = [tex]\sqrt{(6^2 + 0^2)}[/tex]

d = [tex]\sqrt{36}[/tex]

d = 6

Therefore, by the distance formula answer will be 6 units.

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The centroid of the region is at the point (0, 2/5).

To find the centroid of the region bounded by the curves y=2-x² and y=x, we first need to find the limits of integration and the expressions for the x-coordinate and y-coordinate of the centroid.

The curves intersect at (1,1) and (-1,1), so we will integrate over the interval [-1,1].

To find the x-coordinate of the centroid, we need to evaluate the following integral:

x' = (1/A) ∫[a,b] xf(x) dx

where;

A = ∫[a,b] (f(x) - g(x)) dx

In this case, f(x) = 2 - x² and g(x) = x, so

A = ∫[-1,1] (2 - x² - x) dx

= [2x - (1/3)x³ - (1/2)x²] | from -1 to 1

= (4/3)

Now we can evaluate the x-coordinate of the centroid:

x' = (1/A)∫[-1,1] x*(2-x²-x) dx

= (1/(4/3))∫[-1,1] (2x - x³ - x²) dx

= (3/4) [(x²/2) - (1/4)x⁴ - (1/3)x³] | from -1 to 1

= 0

So the x-coordinate of the centroid is 0.

To find the y-coordinate of the centroid, we need to evaluate the following integral:

y' = (1/A) ∫[a,b] (1/2) [f(x)² - g(x)²] dx

y' = (1/(4/3)) ∫[-1,1] (1/2)[(2-x²)² - x²] dx

= (3/4)[(8/15)x⁵ - (2/3)x³ + (1/2)x] | from -1 to 1

= (2/5)

So the y-coordinate of the centroid is 2/5.

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The factor that both trinomials have in common is; C: (x + 2)

In mathematics, a polynomial is defined an expression that consists of variables that are also referred to as indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² - 7x - 18

The trinomial of james is;

x² - 7x - 18

Factorizing this gives;

x² + 2x - 9x - 18

= x(x + 2) - 9(x + 2)

= (x + 2)(x - 9)

The trinomial of Kaitlin is;

x² + 14x + 24

Factorizing this gives;

x² + 12x + 2x + 24

= x(x + 12) + 2(x + 12)

= (x + 2)(x + 12)

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The total amount the mechanic will need in retirement savings to meet their retirement income goa is (B) $950,000, the correct option is B

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

Annual gross wage=  $47,500

Percentage saved= 80%

Draw in 1 year=4%

Now,

To calculate the total amount the mechanic will need in retirement savings to meet their retirement income goal, we can follow these steps:

Determine the retirement income goal: The mechanic wants to live off 80% of their current annual gross wage, which is:

0.8 x $47,500 = $38,000 per year

Calculate the amount of savings needed to generate the retirement income: The mechanic wants to draw 4% of their savings in the first year, so the amount of savings needed to generate $38,000 per year is:

$38,000 / 0.04 = $950,000

Therefore, by the given interest rate answer will be $950,000.

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Answer:

k=77

steps:

k/11=7

k=7*11

k=77

Answer:

Step-by-step explanation:

[tex]\tt \cfrac{k}{11} =7[/tex]

The opposite of division is multiplication, so we need multiply both sides by 11:-

[tex]\tt \cfrac{k}{11}\times 11 =7\times 11[/tex]

[tex]\tt k=7\times 11[/tex]

[tex]\tt k=77[/tex]

______________________

Hope this helps! :)

Answer: C is less than or equal to 7

Step-by-step explanation: because the numbers of cars are not less nor greater than 7

The image triangle has vertices after the dilation by a scale factor of 3 are M'(0,12), N'(12,6), and P'(6,-6).

To find the image coordinates of a triangle after dilation, we need to multiply the coordinates of each point by the scale factor.

In this case, the scale factor is 3.

So the image coordinates of the triangle with vertices M(0,4), N(4,2), and P(2,-2) after dilation by a scale factor of 3 are:

M' = (3 * 0, 3 * 4) = (0, 12)

N' = (3 * 4, 3 * 2) = (12, 6)

P' = (3 * 2, 3 * (-2)) = (6, -6)

Hence, the image triangle has vertices M'(0,12), N'(12,6), and P'(6,-6).

In summary, the image coordinates of the triangle after dilation by a scale factor of 3 are M'(0,12), N'(12,6), and P'(6,-6).

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Answer:

Quadratic since it times by 4 every time

Step-by-step explanation:

Answer: Restaurant B

Step-by-step explanation:

First, Divide 14.52 by 11 as shown below to get the cost per burger for Restaurant A:

14.52/11 = 1.32

Next, divide 2.58 by 2 for the cost of the burger at Restaurant B:

2.58/2 = 1.28

Now we can see that Restaurant B's burgers are 4 cents cheaper than Restaurant A.

Good Luck!

Answer:

Step-by-step explanation:

We need to divide 8625/1725

I used calculator and got 5.

Kayla has 5 pizzas.

Each pizza has 12 slices so we multiply 5x12.

That is 60.

FAQ:

Why do we multiply 5 by 12?

Answer: Each pizza has 12 slices. If we want to know how many slices 2 pizzas have, we would multiply 12 by 2. The ratio of pizza to slice is 12:1.

Pizza is 12x bigger than individual slice

(I want pizza now)

Answer:

Step-by-step explanation:

To solve the differential equation x^2y'' − 3xy' + 3y = x^4e^x using variation of parameters, we can follow these steps:

Step 1: Find the complementary solution y_c by solving the homogeneous equation:

x^2y'' − 3xy' + 3y = 0

The characteristic equation is r(r-1) - 3r + 3 = 0, which simplifies to r^2 - 4r + 3 = 0. Factoring, we get (r-1)(r-3) = 0, so the roots are r=1 and r=3. Therefore, the complementary solution is:

y_c = c1x + c2x^3

where c1 and c2 are arbitrary constants.

Step 2: Find the particular solution y_p using variation of parameters. We assume that the particular solution has the form:

y_p = u1(x)*y1(x) + u2(x)*y2(x)

where y1 and y2 are solutions to the homogeneous equation (in this case, y1=x and y2=x^3) and u1 and u2 are functions to be determined.

We need to find the derivatives of y1 and y2:

y1' = 1, y1'' = 0

y2' = 3x^2, y2'' = 6x

Substituting into the differential equation and simplifying, we get:

x^2(u1''y1 + u2''y2) + x(u1'y1 + u2'y2) = x^4e^x

Plugging in y1 and y2 and simplifying, we get:

x^2(u1''*x + u2''*x^3) + x(u1'*1 + u2'*3x^2) = x^4e^x

We can write this equation in matrix form as:

[x^2x, x^2x^3] * [u1'', u2''] + [x1, x3x^2] * [u1', u2'] = [0, x^4e^x]

Taking the determinant of the coefficient matrix [x^2x, x^2x^3; x1, x3x^2], we get:

(x^2x)(x3x^2) - (x^2x^3)*x = 2x^4

Therefore, the inverse of the coefficient matrix is:

[3x, -x^3] / (2x^4)

Multiplying by the column vector [0, x^4e^x] gives:

[u1', u2'] = [3x, -x^3] * (1/(2x^4)) * [0, x^4e^x]

Simplifying, we get:

u1' = (3/2)*e^(-x), u2' = -(1/2)xe^(-x)

Integrating u1' and u2' with respect to x, we get:

u1 = -(3/2)*e^(-x), u2 = -(1/2)*xe^(-x) + C

where C is an arbitrary constant.

Therefore, the particular solution is:

y_p = -(3/2)xe^(-x) + Cx^3e^(-x)

where C is an arbitrary constant.

Step 3: The general solution of the differential equation is the sum of the complementary solution and the particular solution:

y = y_c + y_p

Answer:

(-5, 2)

Step-by-step explanation:

We can see that the g(x) is a translated form of f(x) using the formula:

y = (x - h)³ + k,

where (h, k) is the origin of the graph's translation.

We can assign the following h and k values based on the given g(x):

g(x) = (x + 5)³ + 2

h = -5

k = 2

Finally, we can form an ordered pair (h, k):

(-5, 2)

Xander's ending balance is -$68

Let's start by calculating Xander's balance after each transaction:

Now let's consider the fees and charges:

So the total fees and charges are $20.00 + $15.00 + $1.00 = $36.00.

Therefore, Xander's ending balance is -$32.00 - $36.00 = -$68.00.

So the answer is -$68.00.

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First, we need to find the number of people who went to the pool in the second, third, and fourth weeks.

Number of people in second week = 1,120 - 125 = 995

Number of people in third week = 995 + 145 = 1,140

Number of people in fourth week = 1,140 - 132 = 1,008

To find the percent decrease, we need to find the difference between the number of people in the first week and the fourth week, and then divide by the number of people in the first week.

Difference between first and fourth weeks = 1,120 - 1,008 = 112

Percent decrease = (112/1,120) x 100% = 10%

Therefore, the percent decrease in the number of people who went to the pool over these four weeks is 10%.

The geometric probability of the cube is 0.64

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Next, we calculate the volumes of the cube and the cylinder using the following formulas

V(Cube) = l³

V(Cylinder) = πr²h

So, we have

V(Cube) = 3.2³ = 32.768

V(Cylinder) = 3.14 * (4.5/2)² * 3.2 = 50.868

The geometric probability of the cube is then calculated as

P = V(Cube)/V(Cylinder)

So, we have

P = 32.768/50.868

Evaluate

P = 0.64

Hence, the probability is 0.64

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Jaden's questions about the missing students influence the development of the plot in many ways.

Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used in all areas of mathematics, including algebra, geometry, calculus, and statistics. Numbers are used to represent quantities and can be represented in a variety of ways, such as numerals, symbols, words, and graphs. Numbers can be used to measure and compare objects, define relationships between objects, and help solve problems.

Firstly, they cause the Puppetmaster to challenge her curiosity. The mysterious disappearances of the students compel the Puppetmaster to find out why they have gone missing, and to take measures to ensure that no one else goes missing. This encourages the Puppetmaster to become more involved in the game, and creates tension between her and the other players.

Secondly, Jaden's questions emphasize the close connection between the players and the Puppetmaster. The players rely on the Puppetmaster for guidance and safety, and her actions in response to Jaden's questions demonstrate her commitment to the players' wellbeing. This serves to strengthen the bond between the players and the Puppetmaster.

Thirdly, Jaden's questions persuade the teachers to begin a search for the missing students. By raising awareness of the situation, Jaden encourages the teachers to take action to investigate the disappearances and to protect the remaining students.

Finally, Jaden's questions highlight the entertainment value that the game provides each player. Her questions demonstrate her enthusiasm for the game, which encourages the other players to play with greater enthusiasm. This serves to increase the intensity of the game, and to make the game more exciting for all involved.

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The value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Measure of arc ML=76 Degrees and

Measure of Angle JLK = 54 Degrees

We have to find the value of x

O is the centre of the circle.

As we see the figure angle L is corresponding to 54 degrees.

x=54

Hence, the value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.

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803.84 square inches is the surface area of a cylinder with an 8-inch radius and 8-inch height.

Any solid shape has a surface area equal to the total of the areas of its faces. For instance, to calculate the surface area of a cuboid, we add the areas of all the rectangles that make it up.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr² + 2πrh

where r is the radius and h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given values, we get:

Surface Area = 2 × 3.14 × 8² + 2 × 3.14 × 8 × 8

= 401.92 + 401.92

= 803.84 square inches

the surface area of the cylinder with radius 8 inches and height 8 inches is 803.84 square inches.

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16 + 5

Because Dan has 16 pencils and he gets 5 more

√49 is a rational number. √50 is an irrational number. √127 is an irrational number. 125 is a rational number because it is equal to a perfect cube of the whole number 5.

A real number is considered to be irrational if it cannot be written as a simple fraction. It cannot be described using a ratio. When p and q are numbers and q is not identical to 0, N is not equivalent to p/q if N is irrational. An illustration of this is the illogic of the integers

A actual number that's unable to be written as the ratio between two integers—that is, as p/q, where both p and q both are integers—is an irrational number.

√49 is a rational number because it is equal to 7, which is a whole number.

√50 is an irrational number because it cannot be expressed as a fraction of two integers and it is not a perfect square.

√127 is also an irrational number because it cannot be expressed as a fraction of two integers and it is not a perfect square.

125 is a rational number because it can be expressed as 5^3, which is a perfect cube of the whole number 5.

Therefore, the correct statements are:

√49 is a rational number.

√50 is an irrational number.

√127 is an irrational number.

125 is a rational number because it is equal to a perfect cube of the whole number 5.

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