How many half-lives would be necessary for a sample of parent isotopes to decay to the point that only one-fourth of the sample is composed of parent isotopes?

Answer:

Yes, it can be simplified into this: (wouldn't allow me to put the ± sign in the equations :P)

[tex]\frac{-3+2\sqrt{5} }{2} \\\frac{-3-2\sqrt{5} }{2}[/tex]

Step-by-step explanation:

Answer:

(-3 + √20)/2 = (-3 + √4√5)/2

= (-3 + 2√5)/2

= (-3/2) + √5

Using the graph we can see that the value is:

f(-3) = 6

(or f(3)= 7, depengin on which you need).

so here we have the graph of f(x), to find the value of f(-3), you first need to find x = -3 on the horizontal axis.

Then move vertically until you meet the graph of the function, once you do that, you can move horizontally until you meet the vertical axis, and at that point you can identifty the value of the function.

We can see that:

f(-3) = 6

(if instead you wanted f(3), it is equal to 7, but it wasn't in the options)

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In the given equation, 2x-9÷x-4 = 3, the solution to the equation is x = 3.

A quadratic equation is a second-degree polynomial equation in one variable of the form [tex]ax^2[/tex] + bx + c = 0, where x is the variable, and a, b, and c are constants, with a ≠ 0.

To solve for x in the equation 2x - 9 / (x - 4) = 3, we can begin by multiplying both sides by (x - 4) to eliminate the fraction in the equation:

2x - 9 = 3(x - 4)

Expanding the right side, we get:

2x - 9 = 3x - 12

Now we can simplify by subtracting 2x from both sides:

-9 = x - 12

And adding 12 to both sides:

3 = x

Therefore, the solution to the equation is x = 3.

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Your question seems incomplete, the probable complete question is

Solve for x:

2x-9÷x-4 = 3

Answer:

153.86 units²

Step-by-step explanation:

 You need to find the area of a circle, given that its radius is 7.

I am going to apply the formula:

A = πr²

whereas -

here's a diagram for reference -

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 7\ cm}\end{picture}[/tex]

--

Plug all the data into the formula:

A = 3.14 * 7^2

A = 3.14 * 49

A = 153.86

[tex]\bigstar[/tex] Therefore, the area is 153.86 units²

It depends on the specific nature of the expense and the accounting method being used. Generally, miscellaneous expenses would be debited to an expense account, which would decrease the net income, and would be credited to a cash or accounts payable account, representing the payment for the expense. However, there may be certain miscellaneous expenses that are credited to a revenue account or a liability account, depending on their nature and purpose within the business.

The map shown the western lands that Georgia ceded to the federal government. The Option A is correct.

Georgia ceded its western land to federal government because of financial struggles faced after the American Revolutionary War.

The state had accumulated debts and lacked the financial resources to manage and develop the western lands within its borders which were inhabited by Native American tribes.  Also, there were concerns about potential conflicts with Native American tribes and the need for federal protection.

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The solution has a pH of 2.13, which is a measurement of a solution's acidity or alkalinity.

An aqueous solution's pH is a measure of how basic or acidic it is. The negative logarithm of the concentration of hydronium ions (H₃O⁺) is what this term, which means "power of hydrogen," is defined as. The pH scale goes from 0 to 14, where 0 is the most acidic and 14 is the most basic (or alkaline).

Since the concentration of hydronium and hydroxide ions in a solution with a pH of 7 is equal, this value is regarded as neutral. In contrast to bases, which have a pH above 7, acids have a pH below 7. The difference in the concentration of hydronium ions is represented by each full number on the pH scale.

The pH of a solution can be determined using the formula:

pH = -log[H⁺]

where [H⁺] is the concentration of hydronium ions in moles per liter.

In this case, [H⁺] = 7.4×10⁻³ moles/liter.

Substituting into the formula:

pH = -log(7.4×10⁻³) = 2.13

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The number of homeruns Luis Gonzales will have after 100 games can be expected using probability as 55.

Given that,

Luis Gonzales plays baseball for the Arizona Diamondbacks.

Number of games played in a season = 20

Number of games he had homeruns = 11

So there is a chance to get 11 homeruns from 20 games.

Probability of having homeruns = 11/20 = 0.55

If he played 100 games,

Expected number of homeruns he would get = 100 × 0.55 = 55

Hence the expected number of homeruns he has in 100 games is 55.

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If a company starts with 3 employees and plans to triple the number of employees each year, then the number of employees can be represented by the function: f(n) = 3^n

To find the function to represent this situation we have to consider the information. In this formula we have to incluide the following information:

The number of employees at the end of the n year is equal to 3 raised to the power of n.

where,

n = number of years since the start of the company.

So, for example, if we want to know how many employees the company will have at the end of the second year, we can plug in n = 2 into the function:

According to the above, the company will have 9 employees at the end of the second year, and if we want to know how many employees the company will have at the end of the third year, we can plug in n = 3 into the function:

So, the company will have 27 employees at the end of the third year.

In general, the formula tells us that the number of employees at the end of the nth year is equal to 3 raised to the power of n.

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The two chords of the circle are same and x = 3

Given data ,

Let the circle be represented as C

Now , the length of the two chords of the circle are

The length of chord JK = 52 units

The length of chord LM = 18x - 2

Now , the two arcs subtended by the chords are the same , so

The lengths of the chords are same

Now , JK = LM

On simplifying , we get

52 = 18x - 2

Adding 2 on both sides , we get

18x = 54

Divide by 18 on both sides , we get

x = 54/18

x = 3

Hence , the chords are solved and x = 3

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Answer: 51.34

Step-by-step explanation:

you need to use SOH CAH TOA

here they give opp and adj

Use tan

tan∅=opp/adj=10/8   now use that tan^(-1) (10/8)  in calculator

x=51.34

Answer:

1) Solving for x in Radians

x=1.21991691+ πn, for any integer n

2) Solving for x in Degrees

x=69.89609063+180n, for any integer n

Step-by-step explanation:

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

Answer:  Starting with 2(tan x - sqrt(3)) = 2:

First, divide both sides of the equation by 2 to simplify:

tan x - sqrt(3) = 1

Next, add sqrt(3) to both sides:

tan x = 1 + sqrt(3)

To solve for x, we need to take the arctan of both sides:

x = arctan(1 + sqrt(3))

In degrees, this is:

x = 75 degrees

In radians, this is:

x = 5π/12 radians

Step-by-step explanation: can i get brainliest pretty pls

The correct option for the approximation of the area under the curve would be B.  The rectangles are circumscribed because the function is decreasing.

Inscribed rectangles come into contact with the curve at their top-right corners when it is an increasing function, and if it is a decreasing function they touch the curve's top-left corners.

Consequently, inscribed rectangles always give low approximations of the area beneath the curve where functions are increasing, alternatively while overestimating the area for decreasing functions. If the function is ascending, then the rectangles become circumscribed since their top-left edges adhere to the curve, while in declining functions, these remain inscribed instead since their top-left points coincide with the graph.

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The system of equations when solved by substitution is x = 1 and y = 0

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

4x+4y=4

y=0

Substitute 0 for y in the first equation

So, we have

4x + 4(0) =4

This gives

4x = 4

Divide by 4

x = 1

Hence, the solution is x = 1 and y = 0

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Answer:

12

Step-by-step explanation:

a general linear function can be written as

y= mx +b

where "m" is the pendient and "b" it's the point where the funcion has x=0

so u have to solve your ec. for y

[tex]6x + by = k[/tex]

[tex]by = - 6x + k[/tex]

[tex]y = - \frac{6}{b}x + \frac{k}{b} [/tex]

if u see your graph, when x=0 the function's value is 1, so k/b= 1, then k=b

then if we know b , we know k

as I said, m is the pendient, in this case -(6/b) is the pendient

As u may know, the pendient equals tan(alpha)

in this case alpha its the angle between the positive x axis and the function (the big one), we dont have that angle in a triangle to know its tangent, but we have (180-alpha) the littleone, and its tangent is 1/2 (see your graph)

so, for redunction to the first quadrant we have that

[tex] \tan( \alpha ) = - \tan(180 - \alpha ) = - \frac{1}{2} [/tex]

then,

[tex] - \frac{6}{b} = - \frac{1}{2} [/tex]

b=12

k=12

The value of k if the equation of the line drawn is 6x + by = k will be 12.

A general linear function can be written as; y= mx +b, where "m" is the pendient and "b" it's the point where the funcion has x=0

Given that;

6x + by = k

by = k - 6x

y = k/b - 6x/b

When x=0 the function's value is 1, thus, k/b= 1, then k=b

In this case -(6/b) is the pendient

The angle between the positive x axis and the function (the big one), we dont have that angle in a triangle to know its tangent, but we have (180-alpha) the littleone, and its tangent is 1/2.

then,

-6/b = -1/2

b=12

k=12

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The answers are:

B. The graph of f(x) is shifted up 50 units

E. The graph of f(x) is shifted right 10 units

F. The graph of f(x) is reflected over the x-axis

The given function is f(x) = x²

This is an upward-facing vertical parabola.

The vertex is the smallest.

The vertex's origin is at (0, 0).

g(x) = –5x² + 100x – 450

This is an open downhill vertical parabola.

The vertex is the greatest

The first thing to notice is that fx) opens up whereas g(x) opens down, indicating that a reflection across the x-axis was used.

Find the g(x) vertex.

change the form to vertex

g(x) = –5x² + 100x – 450

Complete the square

g(x) = -5(x² - 20x) - 450

g(x) = -5(x² - 20x + 100) - 450 + 500

g(x) = -5(x² - 20x + 100) + 50

g(x) = -5( x - 10)² + 50

The vertex is located at (10, 50).

To the vertex from (0,0) to (10,50)

The translational principle is

(x,y) ------> (x+10,y+50)

This implies ----> The translation is 50 units up and 10 units to the right.

The adjustments are

The f(x) graph is moved forward by 50 units.

The f(x) graph is 10 units to the right.

Over the x-axis is a reflection of the f(x) graph.

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The complete question is,

Which transformations have been applied to the graph of f(x) = x² to produce the graph of g(x) = –5x² + 100x – 450? Check all that apply.

A.The graph of f(x) = x² is shifted up 25 units.

B.The graph of f(x) = x² is shifted up 50 units.

C.The graph of f(x) = x² is shifted down 950 units.

D.The graph of f(x) = x² is shifted left 10 units.

E.The graph of f(x) = x² is shifted right 10 units.

F.The graph of f(x) = x² is reflected over the x-axis.

Cameron will drink 98 liters of water in seven weeks.

Unit conversion is the process of converting a measurement expressed in one unit to an equivalent measurement expressed in another unit.

To find the answer in Liters we need to convert the daily amount of water from milliliters to liters.

This involves using a conversion factor (1 liter = 1000 milliliters) to convert the units from milliliters to liters.

Here we have

Cameron drinks 2,000 milliliters of water every day  

Let's convert the daily amount of water Cameron drinks from milliliters to liters by dividing by 1000:

2000 milliliters / 1000 = 2 liters

So, Cameron drinks 2 liters of water every day.

To find out how many liters he will drink in seven weeks, we need to multiply his daily intake by the number of days in seven weeks.

There are 7 days in a week, so:

7 weeks x 7 days =  49 days

The amount of water taken by Cameron can be

2 liters/day x 49 days = 98 liters

Therefore,

Cameron will drink 98 liters of water in seven weeks.

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Answer: X> -1 (third one down)

Step-by-step explanation: open circle means x cannot be that value and the line moving forward to the right means that x can be anything greater than -1

The expected value is calculated by multiplying the probability of each outcome by its corresponding value and then summing up all the values. In this case, the possible outcomes are either the man dies and the insurance company pays out the death benefit of $100,000, or he does not die and the insurance company keeps the premium of $260.

Expected value = (probability of death x death benefit) + (probability of no death x premium)

Expected value = (0.00248 x $100,000) + (0.99752 x $260)

Expected value = $248 + $259.38

Expected value = $507.38

Therefore, the expected value for the person buying the insurance is $507.38, rounded to the nearest dollar.

The rule that best describes this transformation is  option A) (x, y) (x, y-7)

The term  Coordinate geometry entails is the study of of geometric shapes by plotting them in the coordinate axes.

Note that from the image attached:

Coordinates of A  = (2,6)     Coordinates of A' = (2,-1)

Coordinates of B= (1,2)      Coordinates of B'=(1,-5)

Coordinates of C=(4,2)      Coordinates of C'=(4,-5)

From the above,  the x-coordinate is not altered but there is a difference of 7 units in y-coordinates. Hence, The rule that best describes this transformation is (x, y-7)

Hence, The rule that best describes this transformation is ( (x, y) (x, y-7)

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See full question below

Triangle ABC was transformed to create triangle A’B’C’. Which rule best describes this transformation?

A) (x, y) (x, y-7)

B) (x, y) (x, -y)

C) (x, y) (x-7, y)

D) (x, y) (-x, y)

Answer: leaves

Step-by-step explanation:

Joey should carefully observe the leaves of the plants during his experiment. Photosynthesis primarily occurs in the leaves, where chlorophyll, the pigment responsible for capturing sunlight, is located. The process of photosynthesis converts sunlight, carbon dioxide, and water into glucose and oxygen. Polluted air can negatively impact photosynthesis by reducing the availability of carbon dioxide or by damaging the chlorophyll and other components involved in the process.

The length of string of the kite is 13 m.

Question :-

A boy is flying a kite which is 12 m high from the ground the horizontal distance of the boy from the kite is 5 m, find the length of string of the kite?

Solution :-

The scenario is setting up a picture of a right triangle, where the horizontal distance of the boy from the kite is the base and the height of the kite from the ground is the height of triangle, and the length of the string is acting as a hypotenuse,

So, using the Pythagoras theorem,

12² + 5² = x²

x = √144+25

x = √169

x = 13 m

Hence, the length of string of the kite is 13 m.

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So, the standard deviation of the probability distribution is approximately 2.780.

To find the standard deviation for the probability distribution, we first need to find the mean (or expected value) of the distribution.

The mean is given by:

μ = ∑(x * P(x))

where x is the number of adults with a college degree and P(x) is the corresponding probability from the table.

μ = (00.0081) + (10.0756) + (20.2646) + (30.4116) + (4*0.2401)

μ = 2.8

So, the mean number of adults with a college degree in a sample of 4 is 2.8.

Next, we can use the formula for the standard deviation of a probability distribution:

σ = √∑[(x - μ)² * P(x)]

where x is the number of adults with a college degree, μ is the mean we just calculated, and P(x) is the corresponding probability from the table.

σ = √ [(0-2.8) ²0.0081 + (1-2.8) ²0.0756 + (2-2.8) ²0.2646 + (3-2.8) ²0.4116 + (4-2.8) ²*0.2401]

σ = √ [7.72404]

σ = 2.780

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The stock price according to the constant growth dividend model is $71.57.

What is percent?

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%

We can use the constant growth dividend model to calculate the stock price:

Next Dividend / (Required Rate of Return - Growth Rate) Stock Price

Since the problem only provides the last dividend, we need to calculate the next dividend first. We can use the growth rate to find the next dividend:

Next Dividend = Last Dividend × (1 + Growth Rate) = $5.95 × (1+0.0314) = $6.14

Stock Price $6.14 / (0.1188 -0.0314) $71.57

Therefore, the stock price according to the

constant growth dividend model is $71.57.

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The expression that gives the surface area of a sphere with radius as r would be =4πr². That is option A.

A sphere is defined as the shape whose surface is made up of all the points that are an equal distance from the point that is the shape's center.

The formula that can be used to calculate the surface area of a sphere is given as;

S.A = 4πr²

Since the radius given is in terms of r, therefore, the expression that shows the surface area of a sphere would be = 4πr².

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The critical value is at x = -3/4, and the solution set is  ( -3/4, ∞)

We can define the critical values as the problematic values. For example, we can't divide by zero, so the value of x that makes the denominator equal to zero is a critical value.

4x + 3 = 0

4x = -3

x = -3/4

That is the critical value.

Now let's solve the inequality.

-5/(4x + 3) < 0

That is true as long as the denominator is positive, so:

4x + 3 > 0

x > -3/4

The solutions et is ( -3/4, ∞)

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