Lisa Callaghan data on the grams of fat and the grams of carbohydrates in 10 sandwiches at a popular restaurant the table below represents the data she recorded which linear equation best fits Lisa's data

Therefore , the solution of the given problem of probability comes out to be (B) Verifying that an event's chance is 0.05 or less is the right response.

The primary goal of a procedure's criteria-based methods is to calculate the probability that a statement is true or that a specific occurrence will occur. Any number range from 0 to 1, where 0 usually represents the likelihood of something happening and 1 typically represents an amount of confidence, can be used to represent chance. A probability illustration displays the possibility that a specific event will take place.

Here,

Several techniques can be used to determine whether it is reasonable to infer that sample data come from a population with a normally distributed population, including:

A. Recognizing anomalies

B. Verifying that an event's probability is 0.05 or lower C.

Examining a histogram visually to see if it approximately resembles a bell shape

D. Creating a normal quantile plot, a type of graph.

Option B is invalid because it doesn't reveal anything about how the sample data are distributed.

The threshold for statistical significance is the chance of an event being 0.05 or less, but it has no bearing on the distribution's shape.

As a result, (B) Verifying that an event's chance is 0.05 or less is the right response.

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9514 1404 393

Answer:

  C. Division: (x^2-5x+3)÷(x-2)=x-3+-3/x-2

Step-by-step explanation:

The set of polynomials is closed under all basic arithmetic operations except division. The reciprocal of a (non-constant) polynomial is not a polynomial.

The division example shown in choice C illustrates the set is not closed under division.

When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.

From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.

It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.

Therefore, the number of flags is 40.

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We're given:

Let x equal the calorie count per serving of the original popcorn.

The light popcorn has a calorie count of 120, which is 25% fewer calories than regular popcorn. This means that 75% of the calorie count of regular popcorn is equal to that of the light popcorn:

\(x*0.75=120\)

\(x*0.75=120\)

⇒ Divide both sides by 0.75:

\(\dfrac{x*0.75}{0.75}=\dfrac{120}{0.75}\\\\x=160\)

Therefore, each serving of regular popcorn has 160 calories.

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

The measure of Angle C is approximately 26°.

A, B, C are vertices of a triangle, where AB = 8 cm, BC = 6 cm. To determine the measure of angle C, we need to use the cosine rule.

The cosine rule states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the angle between them.

Mathematically, we can represent it as follows:a² = b² + c² - 2bc cos(A)where a is the side opposite to angle A, b is the side opposite to angle B, c is the side opposite to angle C.

In this case, we have AB = c = 8 cm, BC = a = 6 cm, and AC = b. We need to find the measure of angle C, which is represented as cos(C).

Using the cosine rule, we can write the equation as follows:$$\begin{aligned} b^2 &= c^2 + a^2 - 2ca\cos(C) \\ \Right arrow b^2 &= 8^2 + 6^2 - 2 \times 8 \times 6 \cos(C) \\ \Right arrow b^2 &= 64 + 36 - 96 \cos(C) \\ \Right arrow b^2 &= 100 - 96 \cos(C) \end{aligned}$$We know that b is a positive length. Hence, b² > 0 or 100 - 96 cos(C) > 0. Solving for cos(C),  

we get: cos(C) < 100/96cos(C) < 1.0417Using a calculator, we can determine the inverse cosine of 1.0417 as:cos⁻¹(1.0417) = 0.4569 radians = 26.201° (rounded to the nearest degree)

Therefore, the measure of angle C is approximately 26°.

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Answer:

7

Step-by-step explanation:

do you really need help

..............

so why I have to wait for 12 min

\( \huge \boxed{\mathbb{QUESTION} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \tt \: 6 y = 42\)

Divide both sides by 6.

\( \tt \: y=\frac{42}{6} \\ \)

Divide 42 by 6 to get 7.

\( \boxed{ \boxed{ \bf \: y = 7}}\)

Answer:

\(5 {x}^{2} + 3 {x}^{2} + 6x = 3x - 6x + 9x \\ 8 {x}^{2} + 6x = - 3x + 9x \\ 8 {x}^{2} + 6x = 6x \\ 8 {x}^{2} = 6x - 6x \\ 8 {x}^{2} = 0 \\ x = 0 \\ thank \: you\)

The statement that all numbers that have 5 as a factor also have 2 as a factor is false, as numbers ending in 5 have five as a factor but are odd numbers, meaning that they do not have two is a factor.

The factors of a number are the numbers by which the number is divisible.

Hence the numbers that have 2 and 5 as factors as the multiples, given as follows:

Numbers that finish in 5 are odd, meaning that they do not have 2 is a factor, hence the statement is false.

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Answer:

60 percent, or 6/10

Step-by-step explanation:

The probability of either A or B is 0.48 and the probability neither A nor B would be 0.52

Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event

probability A will occur pr(A) = 0.39, probability A will not occur pr(A') = 1 - 0.39 = 0.61,

Probability B will occur pr(B) = 0.42, probability B will not occur, pr(B') = 1 - 0.42 = 0.58

For mutually exclusive events if A will occur it means that B will not occur

So, probability either A or B is

= pr(A) x pr(B') + pr(B) x Pr(A')

= 0.39 x 0.58 + 0.42 x 0.61

= 0.4824 and to 2 decimal places the answer becomes 0.48

The probability neither A nor B is equal to 1 - 0.48 = 0.52

In conclusion the probability Either A or B will occur is 0.48 and the probability neither A nor B is 0.52

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\(m = \frac{f(5) - f(0)}{5 - 0} \)

\(m = \frac{ - 10 - 10}{5} = \frac{ - 20}{5} = - 4\)

Step-by-step explanation:

the average rate of change is

(f(high interval end) - f(low interval end))/(high interval end - low interval end)

in our case here

(f(5) - f(0)) / (5 - 0)

(-10 - 10) / 5 = -20/5 = -4

Step-by-step explanation:

let the number of wholewheat bread batches be x

let the number of muffin batches be y

prep condition: 4x + (1/2)y ≤ 16 or 8x + y ≤ 32

baking condition : 1x + (1/2)y ≤ 10 or 2x + y ≤ 20

graph each of those in the first quadrant shading in the region below each one.

Final shading is the region satisfying both conditions.

profit = 35x + 10y

allow this line to "slide" away from the origin as far as you can.

It should be clear that the farthest we can go is the intersection of

8x+y = 32 and

2x + y = 20 or the x and y intercepts of our two boundary lines.

subtract them as they are:

6x = 12

x = 2

then in our head , y = 16

max profit = 2(35) + 10(16) = 230

Just to make sure, I will test the intercepts of our intersecting region, namely (4,0) and (0,20)

for (4,0) profit = 4(35)+1 = 140

for (0,32) profit = 0 + 10(20) = 200

so max profit is 230 when x=2 and y=16

(notice all the prep time and baking time is utelized)

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

25% of the students in the seminar are shorter than 65 inches.

To find the percentage of students who are shorter than 65 inches, we first need to find the number of students whose height is less than 65 inches:

There are three students who are shorter than 65 inches: 62, 60, and 58.

Therefore, the percentage of students who are shorter than 65 inches is:

(3 students / 12 students) × 100% = 25%

Note that the value given for 1% × 5 does not appear to be relevant to this question, and is not necessary for the calculation of the percentage of students who are shorter than 65 inches.

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The answers for the following questions are given below.

Scientific notation, also known as standard form or exponential notation, is a way of writing numbers that are either very large or very small in a compact and convenient way.

It is commonly used in mathematics, science, engineering, and other fields that deal with very large or very small quantities.

In scientific notation, a number is expressed as a product of a decimal number between 1 and 10 (the significand or mantissa) and power of 10.

b) To plot the populations of the three countries on a number line, we can use a logarithmic scale, which will allow us to represent the large differences in population size on a smaller scale. We can start by marking each power of 10 on the number line and then placing the populations of each country accordingly:

|-----------------|------------------|------------------|------------------|------------------|

10⁰              10¹                 10²                 10³                 10⁴

Panama: 4x10⁶      Peru: 3.2x10⁷    Thailand: 7x10⁷

c) To label the furthest right box on the number line so that all three countries' population fit, we need to find the largest population value among the three countries and then round it up to the nearest power of 10. The largest population value among the three countries is 7x10⁷, so we can round it up to 10⁸. Therefore, we can label the furthest right box on the number line as 10⁸.

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Populations on the number line,

B. Panama: 4x10⁶      

Peru: 3.2x10⁷    

Thailand: 7x10⁷

C. We can label the furthest right box on the number line as 10⁸.

Scientific notation, also known as standard form or exponential notation, is a method of writing very large or very small numbers in a compact and convenient manner.

It is widely used in mathematics, science, technology, and other disciplines that deal with very large or extremely small quantities.

A number is expressed in scientific notation as the product of a decimal number between 1 and 10 (the significand or mantissa) and a power of ten.

B). To  compass the populations of the three countries on a number line, we can use a logarithmic scale, which will allow us to represent the large differences in population size on a  lower scale. We can start by marking each power of 10 on the number line and  also placing the populations of each country consequently .

|-----------------|------------------|------------------|------------------|------------------|

10⁰              10¹                 10²                 10³                 10⁴

Panama: 4x10⁶      Peru: 3.2x10⁷    Thailand: 7x10⁷

C). To label the rightmost box on the number line for the populations of all three countries, we need to find the largest population value among the three countries and round it up to the nearest power of ten. The maximum population of the three countries is 7x10⁷, so we can round up to 10⁸. So we can represent the rightmost box on the number line as 10⁸.

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The answer is as:

a) ∠M is congruent to ∠O.

b) the two triangles XYW and ZWY are congruent by angle-angle-side (AAS) congruence.

What is the congruent angle?

When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.

Since ∠NLM ≅ ∠LNO and ∠OLN ≅  ∠MNL, we have:

∠NLM + ∠LNO = ∠OLN + ∠MNL (by the transitive property of angle congruence)

Therefore, ∠NLO = ∠MLN + ∠MIN

Since ∠NLO is a straight angle (180 degrees), we have:

∠NLO = ∠M + ∠O

Substituting ∠M + ∠O for ∠NLO in the previous equation, we get:

∠M + ∠O = ∠MLN + ∠MIN

Rearranging the terms, we get:

∠M - ∠MLN = ∠MIN - ∠O

Using the fact that angle M is supplementary to angle MLN (since they form a straight angle), we have:

∠M - (180 - ∠LNO) = ∠MIN - ∠O

Simplifying, we get:

∠M - ∠LNO = ∠MIN - ∠O

Since ∠OLN ≅  ∠MNI, we have:

∠LNO = ∠MIN

Substituting ∠LNO for ∠MIN in the previous equation, we get:

∠M - ∠LNO = ∠LNO - ∠O

Adding ∠O to both sides, we get:

∠M = 2∠LNO - ∠O

Therefore, ∠M is congruent to ∠O.

#6

Proof:

Since ∠1 ≅  ∠2 and ∠3 ≅  ∠4, we have:

∠1 + ∠3 = ∠2 + ∠4 (by the transitive property of angle congruence)

Therefore, ∠1 - ∠2 = ∠4 - ∠3

Using the fact that opposite angles in a parallelogram are congruent, we have:

∠YXW = ∠1 - ∠2

∠ZWY = ∠4 - ∠3

Substituting these values in the previous equation, we get:

∠YXW = ∠ZWY

Therefore, the two triangles XYW and ZWY are congruent by angle-angle-side (AAS) congruence.

Since corresponding sides of congruent triangles are congruent, we have:

XY cong ZW.

Hence, the answer is as:

a) ∠M is congruent to ∠O.

b) the two triangles XYW and ZWY are congruent by angle-angle-side (AAS) congruence.

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The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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Answer:

a(n)=6*2^(n-1)

Step-by-step explanation:

a(n)=a(1)r^(n-1)

a(1) = 6

a(2)=6r^1=12

r=2

a(n)=6*2^(n-1)

Answer:

the iqr is 42

Step-by-step explanation:

Answer:

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*x-(4*y-7)=0

STEP

1

:

Equation of a Straight Line

1.1     Solve   3x-4y+7  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3x-4y+7  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/4 so this line "cuts" the y axis at y= 1.75000

 y-intercept = 7/4  =  1.75000

Calculate the X-Intercept :

When y = 0 the value of x is -7/3 Our line therefore "cuts" the x axis at x=-2.33333

 x-intercept = -7/3  = -2.33333

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 1.750 and for x=2.000, the value of y is 3.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 3.250 - 1.750 = 1.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  1.500/2.000 =  0.750

Geometric figure: Straight Line

 Slope = 1.500/2.000 = 0.750

 x-intercept = -7/3 = -2.33333

 y-intercept = 7/4 = 1.75000

Answer:

2x + 3 ≥ 6

2x + 3 - 3 ≥ 6 - 3

2x ≥ 3

2x ÷ 2 ≥ 3 ÷ 2

x ≥ 1.5

Answer:

B

Step-by-step explanation:

The points are too scattered to determine any correlation.

Answer:

Diagram B

Step-by-step explanation:

Visually inspecting the three scatterplots, the line of best fit does not accurately fit the points on the second graph. Hence, line of best fit should not have been drawn for the second graph as the relationship isn't linear.

The line of best fit minimizes the sum of the square of the mean distance between each point. Hence, the distance between the line and the best fit line should be as small as possible.

However, the second graph isn't linear, hence , a linear line cannot model the relationship.

Answer:

The answer is D: 130

Step-by-step explanation:

(3x-28) +90+(66-x) = 180

2x + 128 = 180

2x = 52

x = 26

Therefore Angle AOE = 90 + (66-26)

= 130

The percent of the front page taken up by the prom story is 20%

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

The front page

From the front page, we have

Area front page = 5 * 4

Area front page = 20

Also, we have

Prom = 2 * 2

Prom = 4

So, we have

Percentage = 4/20 * 100%

Evaluate

Percentage = 20%

Hence, the percent of the front page taken up by the prom story is 20%

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Answer:

p = 23

Step-by-step explanation:

2p + 2 = 48

    -2        -2

2p = 46

/2     /2

p = 23

Hope this helps and I hope u have an Amazing day!!

Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.

To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:

Assumptions:

Tax depreciation is straight-line over five years.

Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.

Tax on salvage value is 30% of the difference between salvage value and book value of the investment.

The cost of capital is 12%.

Given:

Initial investment cost = $50,000

Useful life of the equipment = 5 years

To calculate the depreciation expense each year, we divide the initial investment by the useful life:

Depreciation expense per year = Initial investment / Useful life

Depreciation expense per year = $50,000 / 5 = $10,000

Now, let's calculate the book value at the end of each year:

Year 1:

Book value = Initial investment - Depreciation expense per year

Book value \(= $50,000 - $10,000 = $40,000\)

Year 2:

Book value = Initial investment - (2 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (2 \times$10,000) = $30,000\)

Year 3:

Book value = Initial investment - (3 \(\times\) Depreciation expense per year)

Book value = $50,000 - (3 \(\times\) $10,000) = $20,000

Year 4:

Book value = Initial investment - (4 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (4 \times $10,000) = $10,000\)

Year 5:

Book value = Initial investment - (5 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (5 \times $10,000) = $0\)

Based on the assumptions, the salvage value is $10,000 in Year 5.

If the asset is scrapped in Year 4, the salvage value is $15,000.

To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:

Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)

For Year 5:

Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)

For Year 4 (if scrapped):

Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)

Now, let's calculate the after-tax cash flows for each year:

Year 1:

After-tax cash flow = Depreciation expense per year - Tax on salvage value

After-tax cash flow = $10,000 - $0 = $10,000

Year 2:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 3:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 4 (if scrapped):

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $15,000 - $1,500 = $13,500

Year 5:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $10,000 - $3,000 = $7,000

Now, let's calculate the net present value (NPV) using the cost of capital of 12%.

We will discount each year's after-tax cash flow to its present value using the formula:

\(PV = CF / (1 + r)^t\)

Where:

PV = Present value

CF = Cash flow

r = Discount rate (cost of capital)

t = Time period (year)

NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment

Let's calculate the NPV:

PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)

PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)

PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)

PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)

PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)

NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000

NPV = $22,954.24 - $50,000

NPV = -$27,045.76

The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.

Therefore, the investment may not be favorable.

Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.

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The complete question may be like :

Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.

You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.

Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.

The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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Answer:

Art

Step-by-step explanation:

...................

Answer:

Music

Step-by-step explanation:

Have a good rest of your day!

Answer:

The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. We can use the fact that 8% of the original amount remains after 100 days to determine the half-life of the isotope.

Let's assume that the initial amount of the substance is 1 unit (it could be any amount, but we're assuming 1 unit for simplicity). After one half-life, half of the original amount remains, or 0.5 units. After two half-lives, half of the remaining amount remains, or 0.25 units. After three half-lives, half of the remaining amount remains, or 0.125 units. We can see that the amount of substance remaining after each half-life is half of the previous amount.

We can use this information to set up the following equation:

0.08 = (1/2)^n

where n is the number of half-lives that have elapsed. We want to solve for n.

Taking the logarithm of both sides, we get:

log(0.08) = n*log(1/2)

Solving for n, we get:

n = log(0.08) / log(1/2) = 3.42

So the number of half-lives that have elapsed is approximately 3.42. Since we know that 100 days is the time for three half-lives (from the previous calculation), we can find the half-life by dividing 100 days by 3.42:

Half-life = 100 days / 3.42 = 29.2 days (rounded to one decimal place)

Therefore, the half-life of the radioactive isotope that leaked into the stream is approximately 29.2 days.