can square roots have a decimal value? if yes then how

The slope and y-intercept of the linear function are -5 and 7 respectively.

Linear functions are those whose graph is a straight line. In other words, a linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line.

A linear function has one independent variable and one dependent variable.

A linear function has the following form. y = mx + b.

where

Therefore, let's find the slope of the function.

slope = m = Δy / Δx

using (0, 7) and (4, -13)

slope = m = -13 - 7 / 4 - 0

slope = - 20 / 4

slope = -5

Let's find the y-intercept using (0, 7).

y = -5x + b

7 = -5(0) + b

b = y-intercept = 7

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Considering the expression of a line, the y intercept has a value of 3.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷(x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)=(2,15) and (x₂, y₂)=(6,39), the slope m can be calculated as:

m= (39 - 15)÷(6 - 2)

m= 24÷ 4

m= 6

Considering point 1 and the slope m, you obtain:

15= 6×2 + b

15= 12 +b

15 - 12= b

3=b

Finally, the value of the y intercept is 3.

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Answer:

(-5, -7) and (-2, -1)

Step-by-step explanation:

The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2).  (Blue line on the attached graph).

The graph of the inverse function is a reflection in the line y = x.

Therefore, the endpoints of the inverse function are:

The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.

Answer:

(-5, -7) and (-2, -1)

Step-by-step explanation:The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2).  (Blue line on the attached graph).The graph of the inverse function is a reflection in the line y = x.Therefore, the endpoints of the inverse function are:(-5, -7) and (-2, -1)The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.

Step-by-step explanation:

a. The polynomials are given as follows:

1. 2x^4 + 18x³ - 4.

2. -8x³ + 4x + 2.

3. 2x² - x - 10

4. 3x³ + 10x² + 9x + 2.

b. The resulting degrees are given as follows:

1. 4.

2. 3.

3. 2.

4. 3.

c. The end behavior of each polynomial is given as follows:

1. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> ∞.

2. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> -∞.

3. As x -> -∞, f(x) -> ∞, as x -> ∞, f(x) -> ∞.

4. As x -> -∞, f(x) -> -∞, as x -> ∞, f(x) -> ∞.

The polynomials are obtained doing the operations and then combining the like terms.

Hence:

(6x³ + 3x² - 4) + (2x^4 - 3x² + 12x³)

2x^4 + (6 + 12)x³ + (3 - 3)x² - 4.

2x^4 + 18x³ - 4.

(10 + 4x - 3x³) - (5x³ + 8)

10 + 4x - 3x³ - 5x³ - 8

-8x³ + 4x + 2.

(x + 2)(2x - 5)

2x² - 5x + 4x - 10

2x² - x - 10

(x + 2)(3x² + 4x + 1)

3x³ + 4x² + x + 6x² + 8x + 2

3x³ + 10x² + 9x + 2.

The degree of a polynomial is given by the highest exponent in it's equation.

The end behavior of a polynomial is calculated as the result of elevating negative infinity and then positive infinity to the highest exponent of the polynomial, considering the leading coefficient.

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The value of ∠WXY = 20.

What is Exterior angle theorem?

The exterior angle theorem describes the connection between the two remote angles in a triangle and the external angle created by an extended side outside the triangle.

Given: Measure of angle YWX = (3x + 17) °

Measure of angle WXY = (3x + 2) °

Measure of angle XYZ = (10x − 5) °

Therefore, m∠XYZ = m∠YWX + m∠WXY (exterior angle theorem)

⇒ (10x − 5) ° = (3x + 17) ° + (3x + 2) °

Solve for x,

⇒ 10x - 5 = 3x + 17 + 3x + 2

⇒ 10x - 6x = 17 + 7

⇒ 4x = 24

⇒ x = 6

∴ ∠WXY = (3x + 2) = 18 + 2 = 20

Hence, value of ∠WXY = 20.

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The independent variables, the ones that are intentionally manipulated, are temperature and surface time.

The dependent variable, the one that you measure the response in, is the reaction time.

The physical concept of temperature indicates in the numerical form how hot or cold something is. Temperature is measured with a thermometer.

Thermometers are calibrated in numerous temperature scales that historically have depended on various reference factors and thermometric materials for definition. The most common scales are the Celsius scale with the unit image °C (previously referred to as centigrade), the Fahrenheit scale (°F), and the Kelvin scale (okay), the latter being used predominantly for clinical functions. The kelvin is one of the seven base units within the worldwide machine of gadgets (SI).

Absolute zero, i.e. 0 kelvin or −273.15 °C, is the bottom factor within the thermodynamic temperature scale. Experimentally, it can be approached simplest very intently, however, no longer genuinely reached, as diagnosed in the 0.33 law of thermodynamics. it'd be not possible to extract power as the warmth from a body at that temperature.

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As the tree grows 1& 3/4 feet per year, it will take 9 years to reach a height of 37 feet.

Division is a basic procedure in which an integer is divided. It's best to imagine of it as a number of things being distributed among a particular number of persons, such as in the previous example. In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 implies dividing 15 into three equal groups of five. Dividend Divisor = Quotient + Remainder is the formula for dividing two numbers. The dividend is the number that is being divided in this case. The divisor is the number, which divides the number (dividend) into equal parts.

Here,

37 - 21 and 1/4 = 36 and 4/4 - 21 and 1/4 = 15 and 3/4 = 63/4

63/4 divided by 1 and 3/4 = 63/4  divided by 7/4 = 63/4 * 4/7 = 9 years

It will take 9 years to reach at the height of 37 feet as the tree grow 1& 3/4 feet per year.

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Complete question:

A tree grow 1& 3/4 feet per year. How long will it take the tree to grow from a height of 21 & 1/4 feet to a height of 37 feet?

Answer:

------------------------------------

Calculate it from end to start.

Before guard 3 he had:

Before guard 2 he had:

Before guard 1 he had:

This is the number of plants stolen.

The snow level at 8 a.m., when x = 8, was 30cm.

The simplest equation for expressing and resolving an unknown number is a linear equation in one variable. It is usually a straight line and is easily pictorial portrayed. A simple way to convey a mathematical assertion is with a linear equation. Unknown numbers can be represented by any variable or symbol. There are several easy ways to solve a linear equation.

y = 2x + 14.

Here, y is the amount of snow in inches, and x is the number of hours after midnight

To find the snow level at 8 a.m. we take the value of x = 8.

⇒ y = 2*8 + 14

⇒ y = 16 + 14

⇒ y = 30cm

So, The snow level at 8 a.m., when x = 8, was 30cm.

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this question is incomplete. The complete question is

the snow level is modeled by the function y = 2x + 14. Here, y is the amount of snow in inches, and x is the number of hours after midnight (x = 0). 10. What was the snow level at 8 a.m., when x = 8?

Answer:

B) 4%

Step-by-step explanation:

The total is

.8 + 4 + .2 = 5

[tex]\frac{r}{t}[/tex] = [tex]\frac{.2}{5}[/tex] = 0.04 = 4%  To change a decimal to a percent multiply by 100%

The given equation is a linear equation.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

g(x) = 1/3x - 6

We need to identify whether the given equation is Linear, Quadratic, Exponential, or None and why.

g(x) is the term that shows the rate of change with respect to x.

1/3 is the coefficient of the variable x

and the 6 is the constant term in the equation.

so, comparing the given equation with standard form of linear equation,

y = mx + c.

we can say here,

y = g(x)

m = 1/3,

c = 6

Hence, the given equation is a linear equation.

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Answer:

To find out how many tiles Ellis will need, we first need to find the total area of the extension that she plans to build. To do this, we can find the area of each of the three sides of the extension separately and then add them together.The extension will have a length of 6.25 m and a width of 1.5 m, so its area will be 6.25 m * 1.5 m = 9.375 m^2.There will be three sides of the extension, so the total area of the extension will be 3 * 9.375 m^2 = 28.125 m^2.Each tile has an area of 0.25 m * 0.25 m = 0.0625 m^2.Therefore, Ellis will need a total of 28.125 m^2 / 0.0625 m^2 = 448 tiles. Since each package contains 25 tiles, she will need to buy 448 tiles / 25 tiles/package = 18 packages of tiles.

Step-by-step explanation:

The  probability that between 78% and 86% were non-teacher workers from private schools is 0.7689

Eighty-four percent of non-teacher workers were employed in private schools.

p = 0.84

q = 1 - p = 1 - 0.84 = 0.16

if a random sample of 200 non-teacher workers from private schools was selected

We need to find the  probability that between 78% and 86% were non-teacher workers from private schools.

n = 200

μρ = 0.84

αp = √(p(1 - p)/n) = √(0.84(0.16)/200) = 0.026

P(0.78 < P < 0.86) = P((0.78 - 0.84)/0.026 < (p - μp)/σp < (0.86 - 0.84)/0.026)

= P(-2.31 < z < 0.77)

= P(z < 0.77) - P(z < -2.31)

using z table

0.7794 - 0.0103

= 0.7689

Therefore, the  probability that between 78% and 86% were non-teacher workers from private schools is 0.7689.

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The given statement "the coefficients of dummy variables in multiple regression models must always be positive." is True.

Regression model:

In statistics, regression model means a statistical technique that relates a dependent variable to one or more independent variables.

Given,

Here we have the statement the coefficients of dummy variables in multiple regression models must always be positive.

Now, we have to find whether the given statement is true or not.

In order to find the statement creditability, we must know the definition of the terms coefficient and dummy variables.

Dummy variable refers the variable that takes values of 0 and 1, where the values indicate the presence or absence of something

Where as the coefficient means a number or symbol by which another number or symbol is multiplied.

Based on this definition we have found that the given statement is true.

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Answer:

P'(4,4)

Step-by-step explanation:

⭐ What does it mean to translate a figure?

In the notation you are given ([tex]T__ < x-4,y+7 > P = P'[/tex]), point P is going to be moved 4 units to the left and 7 units up.

⭐How do we translate P?

P' = (8-4, -3 + 7)

∴ P' = (4,4)

The 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

It is given to us that -

Numbers of items produced per hour by machine a and by machine b are normally distributed

There is a standard deviation of 8.4 items for machine a and a standard deviation of 11.3 items for machine b

The mean hourly amount produced by machine a for a random sample of 40 hours was 130 units

The mean hourly amount produced by machine b for a random sample of 36 hours was 120 units

We have to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines.

Let us say that -

x = Number of units of machine a

y = Number of units of machine b

According to the given information, we have

Number of units of machine a = x⁻ = 130

Standard deviation of machine a = σx = 8.4

Number of hours of machine a = [tex]n_{x}[/tex] = 40

Similarly,

Number of units of machine b = y⁻ = 120

Standard deviation of machine b = σy = 11.3

Number of hours of machine a = [tex]n_{y}[/tex] = 36

We know that mean of the differences can be find out as -

d⁻ = x⁻ - y⁻

=> d⁻ = 130 - 120

=> d⁻ = 10

In order to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines, we have to make use of the formula mentioned below -

d⁻ - [tex]z_{a/2}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])] < μd < d⁻ + [tex]z_{a/z}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])]  ---- (1)

From the z-score table, for a 95% confidence interval, we have -

α = 0.05

α/2 = 0.025

=> F(z) = 1 - α/2 = 1 - 0.025 = 0.975

For a z-distribution function of 0.975, we have -

[tex]z_{a/2}[/tex] = 1.96

Substituting all the values in equation (1), we have

d⁻ - [tex]z_{a/2}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])] < μd < d⁻ + [tex]z_{a/z}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])]

=> [tex]10-1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex] < μd < [tex]10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex]

=> [tex]10-1.96\sqrt{1.764+3.54 }[/tex] < μd < [tex]10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex]

=> [tex]10-(1.96 * 2.303)[/tex] < μd < [tex]10+(1.96 * 2.303)[/tex]

=> 10 - 4.516 < μd < 10 + 4.516

=> 5.483 < μd < 14.516

=> μd = 10 ± 4.516

Thus, the 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

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The absolute value of the complex number - 3 + 2i is √13 plotted on the z plane(a + ib).

As the name suggests it is a combination of real numbers and imaginary numbers.

A complex number (a + ib) where a is the real part and b is the imaginary part.

'i' here is called iota and i = √-1, i² = - 1, i³ = - i and i⁴ = 1.

We know the absolute value or magnitude of a complex number

z = a + ib is | z | = [tex]\sqrt{a^2+b^2[/tex].

∴ The absolute value of z = -3 + 2i is,

| z | = [tex]\sqrt{(-3)^2 + (2)^2[/tex].

| z | = [tex]\sqrt{13}[/tex].

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Therefore the maximum value of function f(x,y,z)=[tex]x^{2} y^{2} z^{2}[/tex] =1/27

And the minimum value is 0

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable) (the dependent variable) (the dependent variable). Mathematics uses functions frequently, and functions are essential for specifying physical relationships in the sciences.

Here,

The function is given as:

f(x,y,z)=[tex]x^{2} y^{2} z^{2}[/tex]

[tex]x^{2} +y^{2}+ z^{2}[/tex]=1

=>[tex]x^{2} +y^{2}+ z^{2}[/tex]-1=0

Using Lagrange multiplies, we have:

L(x,y,z,λ)=f(x,y,z) +λ(0)

Substitute f(x,y,z)=[tex]x^{2} y^{2} z^{2}[/tex]  and [tex]x^{2} +y^{2}+ z^{2}[/tex]-1=0

Differentiate

L(x)=[tex]2xy^{2} z^{2}[/tex]+2λx

L(y)=[tex]2yx^{2} z^{2}[/tex]+2λy

L(z)=[tex]2zx^{2} y^{2}[/tex]+2λz

L(λ)=[tex]x^{2} +y^{2}+ z^{2}[/tex]-1

Equating to 0

[tex]2xy^{2} z^{2}[/tex]+2λx =0

[tex]2yx^{2} z^{2}[/tex]+2λy = 0

[tex]2zx^{2} y^{2}[/tex]+2λz = 0

[tex]x^{2} +y^{2}+ z^{2}[/tex]-1 = 0

Factorize the above expressions

[tex]2xy^{2} z^{2}[/tex]+2λx =0

2x([tex]y^{2} z^{2}[/tex]+λ)=0

2x=0 and ([tex]y^{2} z^{2}[/tex]+λ)=0

x=0 and  [tex]y^{2} z^{2}[/tex]= -λ

[tex]2yx^{2} z^{2}[/tex]+2λy = 0

2y([tex]x^{2} z^{2}[/tex]+λ)=0

2y=0 and ([tex]x^{2} z^{2}[/tex]+λ)=0

y=0 and  [tex]x^{2} z^{2}[/tex]= -λ

[tex]2zx^{2} y^{2}[/tex]+2λz = 0

2z([tex]y^{2} x^{2}[/tex]+λ)=0

2z=0 and ([tex]x^{2} y^{2}[/tex]+λ)=0

z=0 and  [tex]x^{2} y^{2}[/tex]= -λ

So we have ,

x=0 and  [tex]y^{2} z^{2}[/tex]= -λ

y=0 and  [tex]x^{2} z^{2}[/tex]= -λ

z=0 and  [tex]x^{2} y^{2}[/tex]= -λ

The above expression becomes

x=y=z=0

This means that,

[tex]x^{2} +y^{2}+ z^{2}[/tex]=1

[tex]x^{2} +x^{2}+ x^{2} =1 \\3x^{2 } =1[/tex]

x= ±1/[tex]\sqrt{3}[/tex]

So,

y= ±1/[tex]\sqrt{3}[/tex]

z= ±1/[tex]\sqrt{3}[/tex]

The critic points are

x=y=z=±1/[tex]\sqrt{3}[/tex]

x=y=z=0

Therefore the maximum value of function f(x,y,z)=[tex]x^{2} y^{2} z^{2}[/tex] =1/27

And the minimum value is 0

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The common ratio of the geometric sequence will be negative 2.

Given that:

Geometric sequence: 17, -34, -68, .....

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The common ratio of the geometric sequence is calculated as,

r = (-34) / (17)

r = - 2

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The value of x is 23.22°. By using the Cosine rule

The Cosine Rule of trigonometry states that the square of any side of a given triangle is equal to the sum of the squares of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle included between them. The Law of cosines and Cosine Formula are other names for the cosine rule.

The expression for representing cosine rule is expressed as:

c² = a² + b² - 2ab cos C

Given,

a = 26

b = 50

c = 29

Substituting the value to the equation:

c² = a² + b² - 2ab cos C

29² = 26² + 50² - 2(26)(50) cos C

841 = 676 + 2500 - 2600cosC

2335 =2600cos C

cos C = [tex]\frac{2335}{2660}[/tex]

C = 23.22°

The value of x is 23.22°

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Answer: 23.2 rounded to nearest tenth

Step-by-step explanation:

Answer:

question 1: T
question 2: F
question 3: C

Step-by-step explanation:

Answer:

1. True

2. False

3. D. {2,4,9,16}

Step-by-step explanation:

⭐What is a function?

Therefore, #1 is a function because for every x-value, there is 1 y-value.

Therefore, #2 is NOT a function because 6 has 2 y-values, and 12 has 2 y-values.

⭐What is the range of a function?

Therefore, {2,4,9,16} is the range of #3 because it lists all of the y-values in ascending order.

The correct option A: graph A, shows the logarithmic function;

f(x) = log₃x + 1

f(x) = log₃x + 1

f(1) = log₃1 + 1

f(1) = 0 + 1

f(1) = 1

(1, 1)

f(3) = log₃3 + 1

f(3) = 1 + 1

f(3) = 2

(3, 2)

Thus, the graph must contain the points   (1, 1), (3, 2).

Therefore, graph A define the given logarithmic function;

f(x) = log₃x + 1.

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The given situation can be represented in inequality as t ≤ 45 °F.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

So, we are instructed to use t to denote the refrigerator's temperature (in°F).

Additionally, we are informed that the lab refrigerator's maximum temperature is 45 °F.

It must be either lower than or equal to 45 °F for the temperature inside the refrigerator to be no higher than that.

As a result, t must be lower than or equal to 45 °F.

Therefore, it can be expressed as inequality as follows:

t ≤ 45 °F

Therefore, the given situation can be represented in inequality as t ≤ 45 °F.

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Complete question:
The temperature inside the lab refrigerator is at most 35 Fahrenheit used to represent the temperature in Fahrenheit of the refrigerator in inequality.

The difference between 5 hundreds 6 tens and 4 ones is the value of zeros after 1.

Each digit in a number has a unique place and value. A number might contain multiple digits. The first digit will be at the ones place, the second digit at the tens place, and the third digit at the hundreds place, starting from the right.

There are 10 tens in hundred.

5 hundreds= 5*100

6 tens =6*10

4 ones= 4*1

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The difference between 5 hundreds 6 tens and 4 ones is the value of zeros after 1.

Explain hundred, tens and ones.

Hundred, tens, and ones are a way of representing numbers in base 10. This means there are ten digits (0-9) used to represent all numbers. When counting in hundreds, tens, and ones, the number 100 is the largest number represented with one digit, followed by the numbers from 101 to 199. Tens are represented with two digits, such as 20, 30, 40, 50, and so on. Ones are single digits, such as 1, 2, 3, 4, and so on. This system of counting is used to represent all numbers, no matter how large or small.

How many tens are in hundred?
There are 10 tens in hundred.
5 hundreds= 5*100
6 tens =6*10
4 ones= 4*1

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If the 34% of the college students major in STEM than the probability that exactly 15 of them major in STEM is 0.1162   .

In the question ,

it is given that ,

percent of students that major in STEM is = 34% ;

that means , p = 0.34 ; so , q = 0.6

number of students randomly selected (n) = 40 ,

By the Binomial Probability Distribution ,

we get ;

p(x = 15) = ⁴⁰C₅*(0.34)¹⁵*(0.66)²⁵

Simplifying the above value further ,

we get ;

p(x = 15) = 0.1162 .

Therefore , the required probability is 0.1162 .

The given question is incomplete , the complete question is

The 34% of all college students major in stem (science, technology, engineering, and math). if 40 college students are randomly selected, find the probability that exactly 15 of them major in stem  .

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Answer: 25 cars

Step-by-step explanation:

Take 10 divided by 8 = 1.25 car per men

Then take 1.25 times 20 = 25 cars

q = 40 is the value of q in quadratic equation.

What is quadratic equation explain?

The equation x ax2+bx+c=0 is a quadratic equation, which is a second-order polynomial equation in a single variable. with a ≠ 0 .

                    The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial equation. The answer could be simple or complicated.

the roots of a quadratic expression

             ax² + bx + c = 0

Since x' and x'' are the roots of this equation, then we can write the Vieta's formula

                 x' + x'' = -b/a

               x' * x'' = c/a

let's replace the 2nd equation of the Vieta's formula by that and make it a Linear System.

                  x' + x'' =  14/1

                 x' * x'' = 6

after solve the equations

               x' = 10

Solving the  equations

       10 + x''=14

           x'' = 4

Since we have a=1

   x^2-14x + q = 0

      Then we can make q as the parameter c.

    q = x' * x'' = 4 * 10 ⇒ 40      

x2−14x+ 40 = 0

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The complete question is -

The difference between the roots of the quadratic equation x2−14x+q=0 is 6. Find q.

Answer:

the range of the function y = -3/4x + 3/2 when the domain is {-6,-2,6} is {15/4, 3, -3/4}. The range is the set of all possible values of y for x in the given domain, which includes the values 15/4, 3, and -3/4.

Step-by-step explanation:

The range of a function is the set of all possible values of the output (y) for a given set of inputs (x). To determine the range of the function y = -3/4x + 3/2 when the domain is {-6,-2,6}, you can plug in each value from the domain into the function and solve for y.

When x = -6, y = (-3/4)(-6) + 3/2 = 9/4 + 3/2 = 15/4.

When x = -2, y = (-3/4)(-2) + 3/2 = 3/2 + 3/2 = 3.

When x = 6, y = (-3/4)(6) + 3/2 = -9/4 + 3/2 = -3/4.

Answer: x=500,000

Step-by-step explanation:

60,000=.12x

60,000/.12=x/.12

500,000=x

When a radionuclide has a half-life of 19 hours, it will take approximately 32.3 hours for the sample of this nuclide to decay to about 85 percentage of its proportion.

The computation of the time of proportional decay can be calculated using the given values and putting them into the generalized formula.

Number of Hours Taken = Total Life x Required Decay Proportion

Number of Hours Taken = 19×2×85%

Number of Hours Taken = 38 × 0.85

Number of Hours Taken = 32.3

Therefore, it will take 32.3 hours for the nuclide to decay to about 85 percentage in its proportion.

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