The equation P=28+2.54w models the relation between the amount of Randy’s monthly water bill payment, P, in dollars, and the number of units of water, w, used. Interpret the P-intercept of the equation.
Provide your answer below:
The P-intercept, 2.54, means that Randy's monthly water bill payment would be 2 point 5 42.54 dollars if he used 2828 units of water.

Answer:

win=16, lose=12

Step-by-step explanation:

total is 28, and win to lose is 4:3

so 4+3=7 , which means we put them into 7 part

and 28/7=4, each part equal to 4

so the win= 4 time 4=16

            lose = 3 time 4= 12

Answer:

d=1/5

Step-by-step explanation:

Answer: d=2/5

Step-by-step explanation:

The solution of the integral  ∫sin ( x ) cos³( x )dx is equal to ( cos⁴(x) / 4 ) + c , where 'c' is the constant.

Solution of the integral is solved by substitution method :

∫∫sin ( x ) cos³( x )dx ___( 1 )

Let us consider cos ( x ) = t  ____( 2 )

Now differentiate both the side we get,

-sin (x ) dx = dt  

⇒ sin (x ) dx = -dt  ____( 3 )

Substitute the value of ( 2 ) and ( 3 )  in ( 1 ) we get,

∫ t³ ( -dt )

= - ∫ t³ dt

= - t⁴ / 4  + c

Where 'c' is the integral constant .

Relace t = cos (x)

= - cos⁴ ( x ) / 4 + c

Therefore, the integral of the ∫sin ( x ) cos³( x )dx is equal to

( cos⁴(x) / 4 ) + c .

The above question is incomplete, the complete question is:

solve each integral using the information : ∫sinx cos³x dx

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The "Markdown%" is defined by RICS and the majority of the retail business as "Markdown dollars divided by Sales."

Establish the markdown. Subtract the actual selling price from the difference in pricing. After that, multiply this outcome by 100. The outcome is a percentage markdown.

Here,

The "Markdown%" is defined by RICS and the majority of the retail business as "Markdown dollars divided by Sales." The dollar discount is divided by the NET retail sales price to determine the markdown percentage (times 100). As an illustration, a

=>  $30 item is reduced to $24 and sold.

=> The markdown percentage is 25% ($6/$24).

=> Original Sales Price X (100% minus Markdown Percentage)

=>  New Sales Price Paid Percentage=  Discount Percent is 10%

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As segments MN and QR are parallel, the correct statement regarding the triangles is given as follows:

PM/PQ = PN/PR.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

The parallel segments are given as follows:

MN and QR.

Hence the segments that have proportional length are given as follows:

PQ and PQ.

As these segments are divided by segment MN, the proportional relationship is given as follows:

PM/PQ = PN/PR.

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Answer:

He should buy 4 pounds of chocolate candies and 4 pounds of bubble gum.

Step-by-step explanation:

1.50x4 (4 pounds) equals = $6

2.90x4 (4 pounds) equals = $11.6

$11.6 + $6 = $17.6

Hope this helps! <3 (so sorry if this is wrong :C)

Answer:

4:9

Step-by-step explanation:

To find the ratio of males to the total number of people present, we need to divide the number of males by the total number of people.

The total number of people present is the sum of the number of females and the number of males:

Total = 125 females + 100 males = 225 people

So the ratio of males to the total number of people present is:

100 males / 225 people

To simplify this ratio, we can divide both the numerator and denominator by the greatest common factor, which is 25.

So the simplified ratio is:

100/225 = 4/9

So the ratio of males to the total number of people present is 4:9

Dataset 1:

Range = 21

Variance: = 150.33

Standard deviation: = 12.37

Dataset 2:

Range: = 5.6

Variance: = 1.44

Standard deviation: = 1.2

Variance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed.

Dataset 1:

Range: 22-1 = 21

Variance: (sum of squares of deviations from mean) / (number of items - 1) = (902/6) = 150.33

Standard deviation: square root of variance = sqrt(150.33) = 12.37

Dataset 2:

Range: 125.8-120.2 = 5.6

Variance: (sum of squares of deviations from mean) / (number of items - 1) = (7.2) = 1.44

Standard deviation: square root of variance = sqrt(1.44) = 1.2

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The zeros of a polynomial are the values of x for which the polynomial is equal to 0.

What is polynomial?

A polynomial is a mathematical expression consisting of a sum of terms, each term including a variable or variables raised to a non-negative integer power. It is an algebraic expression that can involve constants, variables, and exponents.

To find the rational zeros of a polynomial, use the Rational Zero Theorem. This theorem states that if the polynomial is written in standard form, ax^n + bx^n-1 + cx^n-2 + ... + k = 0, then the possible rational zeros are any rational number that can be expressed as p/q, where p is a factor of k (the constant) and q is a factor of a (the leading coefficient).

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Complete question is:

How to Find All Possible Rational Zeros Using the Rational Zeros Theorem With Repeated Possible Zeros?

Answer:

15,19,26

Step-by-step explanation:

second side of a triangular deck is 4 feet longer than the shortest​ side,

shortest​ side = x

second side = x+4

third side = 2x-4

perimeter = 60 = x+x+4+2x-4 =4x

x=15

second side = x+4 =19

third side = 2x-4 =30-4 =26

Answer:

9x²-16y^4

Step-by-step explanation:

(3x - 4y²) (3x + 4y²)

→ expand the expression

(3x²) - (4y²)

→ simplify the expression

3² × x² - 4² × (y²)²

→ calculate

9x² - 16(y²)²

→ simplify (use (a^m)^n = a^mn

9x² - 16x^4

Answer: 9x² - 16x^4

hope this helps!

As per the probability the equation of E[X] = 2 * P(X=2) + 3 * P(X=3) + ... + 10 * P(X=10)

A die is a cube-shaped object with six faces numbered from 1 to 6. Each face has an equal chance of landing face up when the die is rolled. When you roll a die, you are randomly selecting one of the six numbers.

Let's first calculate the probability that X is equal to 2. To do this, we need to consider two cases:

The first case is when N = 2. In this case, there is only one way to select 2 tags, both with the number 2.

The second case is when N is greater than 2. In this case, there are 9 ways to select the first two tags, both with the number 2. The rest of the tags can be selected in any order.

The probability that X is equal to 2 can be calculated as follows:

P(X=2) = (1/45) + (9/45 * (9/44) * (8/43) * ... * ((10-N+1)/(10-N+2)))

Next, we calculate the expected value of X. The expected value of X is calculated as follows:

E[X] = sum of (each value of X multiplied by its probability)

E[X] = 2 * P(X=2) + 3 * P(X=3) + ... + 10 * P(X=10)

The expected value of X gives us an idea of the average value of X over many trials of rolling the die and selecting the tags.

In conclusion, the probability that X is equal to 2 is calculated by considering two cases, and the expected value of X is calculated by summing up each value of X multiplied by its probability.

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30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level, which is a reference point fomeasuring elevation and depth, and which can vary depending on the location.

Sea level is the average level of the surface of the ocean, which is used as a reference point for measuring elevation and depth. The term "sea level" can also refer to the specific measurement of the height of the ocean's surface at a specific location.

30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level. This means that the location is 30 degrees lower in elevation than the reference point of the average surface of the ocean. This can be measured in either meters or feet, depending on the unit of measurement being used.

One way to think about 30 degrees below sea level is to imagine a point 30 degrees below the level of the water in a swimming pool. This would be considered a very deep point in the pool, and would be much lower than the surface of the water. Similarly, a location that is 30 degrees below sea level is much lower in elevation than the average sea level.

It's important to note that the concept of sea level can vary depending on the location, as sea level can vary due to factors such as ocean currents, tides, and the shape of the ocean floor. Therefore, the reference point for sea level can be different in different locations.

In summary, 30 degrees below sea level refers to a location that is 30 degrees lower in elevation than the average sea level, which is a reference point for measuring elevation and depth, and which can vary depending on the location.

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x = 2y and x*$10 + y*8 = $84 are the required system of equations and when we solve it, we can observe that he spent 6 hours cleaning vehicles and 3 hours gardening.

A group of equations comprising one or more variables is known as a system of equations.

The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.

We must first define the variables:

x is the amount of time spent cleaning autos.

x = the number of landscaping hours.

Since we know Alexander spent twice as much time cleaning vehicles as he did landscaping, we can say:

x = 2y

Additionally, we know that he made $84 in total, so:

x*$10 + y*8 = $84

The set of equations is thus:

x = 2y

x*$10 + y*8 = $84

We simply swap the first equation with the second one to answer it:

(2y)*$10 + y*8 = $84

y*$28 = $84

y = $84/$28 = 3

He thus spent three hours landscaping, and:
x = 2*y = 2*3 = 6

6 hours washing cars.

Therefore, x = 2y and x*$10 + y*8 = $84 are the required system of equations and when we solve it, we can observe that he spent 6 hours cleaning vehicles and 3 hours gardening.

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The result of 626362737287387287373 times 77474747743874837847348734463763786837 represented in scientific notation is 4.80498727057566113882339366151788673587 × 10⁹⁵.

The number you provided in your question can be represented in scientific notation. Scientific notation is a way of expressing numbers in a compact form that is especially useful for very large or very small numbers. The number you provided in your question can be represented in scientific notation as:

7.7474747743874837847348734463763786837 × 10⁷⁷

And 626362737287387287373 can be represented as:

6.26362737287387287373 × 10¹⁸

The product of these two numbers can be calculated as follows:

(7.7474747743874837847348734463763786837 × 10⁷⁷) × (6.26362737287387287373 × 10¹⁸) =

= (7.7474747743874837847348734463763786837 × 6.26362737287387287373) × (10⁷⁷ × 10¹⁸) =

= 48.0498727057566113882339366151788673587 x 10⁹⁵

So, the result of 626362737287387287373 times 77474747743874837847348734463763786837 in scientific notation is:

4.80498727057566113882339366151788673587 × 10⁹⁵

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Men are more likely to have diabetes, heart disease, and stroke, whereas women are more likely to have arthritis and depression, with significant regional variation.

In contrast to a woman, who has a smaller body and bone structure, weaker muscles, and thinner skin and a thinner skull, a man has a larger body, greater bone structure, stronger muscles, and thicker skin and skull. 3. Men and women experienced chronic disease at different rates (2.09 vs 1.90 per 100 person-years, respectively).

The most frequent disease was diabetes (40.9%), which was then followed by COPD (32.8%), stroke (9.6%), CHF (8.2%), MI (5.9%), and lung cancer (2.6%).

Males have one X and one Y chromosome, while females typically have two X chromosomes in their pair. The series of developmental events that give bodies and brains male features are brought on by a gene on the Y chromosome.

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The complete question is"The Most Recent Round Of Data Collection Occurred Over The Course Of September 2013–November, 2013 In HINTS 4 Cycle 3.In This Lab, You Will Be Using A Subset Of The HINTS 4 Cycle 3 Data To Practice Creating Effective And Informative Graphical Representations Of Data, Which May Include Histograms And Circle Graphs. About The Data For This Lab, You Need To

The most recent round of data collection occurred over the course of September 2013–November, 2013 in HINTS 4 Cycle 3.In this lab, you will be using a subset of the HINTS 4 Cycle 3 data to practice creating effective and informative graphical representations of data, which may include histograms and circle graphs. "

Correct option is D, using area of playground the length and width of the playground is length = 10 yd, breadth = 2 yd.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy. A plane figure's area is the space that its perimeter encompasses. The area of a closed figure is the total number of unit squares covering its surface. Area is measured in square units like cm2 and m2.

The area of a shape is the area enclosed by its perimeter or boundary.

A = b × h is the formula for calculating the area, A, of a square or rectangle.

The playground's length is 5 times more than its breadth,

thus l=5w.

However, 10=2 x 5 allows us to write

l=5w, and

area = 20

=l x w

= (5x2) x 2

=20.

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Complete question -

The area of a playground is 20 square yards. The length of the playground is 5 times longer than its width. Find the length and width of the playground.

length = 1 yd, width = 20 yd

length = 2 yd, width = 10 yd

length = 10 yd, width = 2 yd

length = 20 yd, width = 1 y

An event has one outcome or collection of outcomes.

An event in probability is a set of one or more outcomes from a sample space, which is a set of all possible outcomes of a random experiment.

An event represents a situation or condition of interest in a random experiment.

The event can have one outcome or multiple outcomes, and it can be either simple (consisting of a single outcome) or compound (consisting of multiple outcomes).

For example, the event of rolling a six on a single die is a simple event with one outcome

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The length of the hypotenuse for all the right-angled triangles are found using trigonometric functions.

What is the hypotenuse?

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

11) when angle = 30°

 perpendicular = 3

sin 30 = perpendicular/ hypotenuse

0.5 = 3/hypotenuse

hypotenuse = 6

12) sin 30 =perpendicular/ hypotenuse

  0.5 = 8/ hypotenuse

hypotenuse = 16

13) sin 60 = 11√3 / x

   Hypotenuse = x = 11√3/ sin 60 = 11√3 / (√3/2) = 22

14) sin 30 = perpendicular/ hypotenuse

   0.5 = 9/x

x = 18

15) cos 60 = base/ hypotenuse

     0.5 = 1 /x

     x = 2

16) sin 60 = 12√3/x

   √3/2 = 12√3/x

  Hypotenuse = x = 24

Therefore the length of the hypotenuse for all the right-angled triangles are found.

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Answer:

The graph that shows the solution to the system of linear inequalities is the one that has a line with a slope of -2 and y-intercept of 1/2, and another line with a slope of 1 and y-intercept of 1/2. The region of the plane that lies between the two lines and satisfies both inequalities is the solution set.

a. f(x) = 0.75x.

b. g(x) = x - 5.

c. f(50) = 0.75×50 - 5 ⇒ f(50) = 32.5.

d. Yes, The order in which the adjustments are taken does make a difference.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A department store has marked down its merchandise by 25%. It later decreases by $5 the price of items that have not sold.

Let, 'x' be the price of the merchandise.

Therefore, After 25% mark down it would be (75/100)×x = 0.75x and a $5 decrease would be (- $5).

a. A function f(x) to represent the price after the 25% markdown is,

f(x) = 0.75x.

b. A function g(x) to represent the price after the $5 markdown is,

f(x) = x - 5.

c. A composition function to find the price of a $50 item after both price adjustments is f(50) = 0.75x - 5.

f(50) = 0.75×50 - 5.

f(50) = 37.5 - 5.

f(50) = 32.5.

d. It would make a difference, Let's assume the price is $100,

Then a 25% markdown would be $75 and with a decrease of $5 the final price would be $70.

Again, Assuming the price to be $100, 5$ decrease is $95 and 75% of $95 is 0.75×95 = $71.25.

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The probability that an individual with a positive screening test will indeed have the disease is 0.9798.

The probability is equal to the variety of possible outcomes. the total number of outcomes that might occur. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

A medical study team wanted to assess a suggested diabetic screening.

When administered to a random sample of 150 diabetic individuals, the test produced 34 positive findings.

While it produced 9830 negative findings when administered to a random sample of 9850 healthy people.

Assume that 30% of the population has diabetes.

The probability that an individual with a positive screening test will indeed have the disease is 0.9798.

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The board in shape of rectangle must be at least 6.4 feet.

What is a rectangle?

A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.

For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.

A rectangle has two diagonals, that bisects each other. Both the diagonals are equal in length.

Perimeter, P = 2 (Length + Width)

Area of Rectangle=Length*Breadth

Now,

Given length of board they want to cut=1 3/5 feet=8/5 feet.

No. of board they want to cut=4

so, length of rectangular board must be at least=4*8/5 feet

=32/5=6.4 feet

Hence,

            The board in shape of rectangle must be at least 6.4 feet.

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The slope of the linear qeuation is -1/4 = -0.25

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Remember that if a line passes through (x₁, y₁) and (x₂, y₂) the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

We can see the points (0, 1) and (4,0). Then the slope is:

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

The slope is -1/4.

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Step-by-step explanation:

n (TUB)=100-20

=80

from formula,

80 = x (x-5)+x+2x

80= x^2-5x+3x

80=x^2-2x

x^2-2x-80=0

x^2-10x+8x-80=0

x(x-10)+8 (x-10)=0

(x+8)(x-10)=0

either,

x+8=0

×=-8 (neglected)

Or,

x-10=0

×=10

Answer: it is  Konnachair,  dm me there

Step-by-step explanation:

Answer:

Second option

Step-by-step explanation:

Given inequality
[tex]-8t\:+\:2\:\dfrac{1}{4}\ge 42\dfrac{1}{4}[/tex]

Convert mixed fractions to improper fractions:
[tex]2\dfrac{1}{4}=\dfrac{9}{4}[/tex]

[tex]2\dfrac{1}{4}=\dfrac{169}{4}[/tex]

The inequality becomes

[tex]-8t+\dfrac{9}{4}\ge \dfrac{169}{4}[/tex]

Multiply throughout by 4

[tex]-32t + 9 \ge 169[/tex]

[tex]\rightarrow -32t \ge 169-9\\\\-32t \ge 160\\\\-t \ge \dfrac{160}{32}\\\\-t \ge 5\\\\[/tex]

Multiply throughout by -1 (the inequality is reversed):

[tex]t \le -5[/tex]

The second option correctly represents this inequality

Option #1: Solve the inequality and graph the solution set.

Option #2: Test out the options to see which has solutions.

Let's do Option #2:

The first possible answer shows t < -5, so if we pick t = -10, we'd be in that interval.  Let's test if t = -10 is a solution:

      [tex]\begin{aligned}-8(-10) + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]80 + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]82\frac{1}{4} &\stackrel{\checkmark}{\geq} 42\frac{1}{4}\end{aligned}[/tex]

That checked!

So this alone tells us that the bottom two answers are not possible answers, since they do not include -10 in their sets.

But now we need to decide between the top answer or the one right below it.  The only difference between the two number lines is that the top one does NOT include x = -5, while the second one does.  So we need to test out if x = -5 is a solution, just like we did for x = -10.

     [tex]\begin{aligned}-8(-5) + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]40 + 2\frac{1}{4} &\stackrel{?}{\geq} 42\frac{1}{4}\\[0.75em]42\frac{1}{4} &\stackrel{\checkmark}{\geq} 42\frac{1}{4}\end{aligned}[/tex]

Because of the "or equal to" in the inequality, this does check.

Our answer is the second number line, with a closed circle at x = -5 and the shading to the left.

If you wanted to do this by solving the inequality, that work would look like this:

     [tex]\begin{aligned}-8t + 2\frac{1}{4} &\geq 42\frac{1}{4}\\[0.75em]-8t + 2\frac{1}{4}-2\frac{1}{4} &\geq 42\frac{1}{4}-2\frac{1}{4}\\[0.75em]-8t &\geq 40\\[0.75em]\dfrac{-8t}{-8}~ &{\boldsymbol{\leq}}~ \dfrac{40}{-8}\\[0.75em]t &\leq -5\end{aligned}[/tex]

Note that the inequality flipped because we divided both sides of the inequality by a negative number.

The probability that at least one tag is lost is 0.75.

The probability that exactly one tag is lost is equal to the probability of the left tag being lost and the right tag being kept, plus the probability of the right tag being lost and the left tag being kept.

Using the formula for the probability of the union of two events, the probability that at least one tag is lost is:

P(A1 or A2) = P(A1) + P(A2) - P(A1 and A2) = 0.4 + 0.4 - 0.16 = 0.64

The probability of the left tag being lost and the right tag being kept is:

P(A1 and not A2) = P(A1) × (1 - P(A2)) = 0.4 × (1 - 0.4) = 0.24

The probability of the right tag being lost and the left tag being kept is:

P(A2 and not A1) = P(A2) × (1 - P(A1)) = 0.4 × (1 - 0.4) = 0.24

So, the probability of exactly one tag is lost, given that at least one tag is lost, is:

P(exactly one tag is lost | at least one tag is lost) = P(A1 and not A2 or A2 and not A1) / P(A1 or A2) = (0.24 + 0.24) / 0.64 = 0.75

Rounding to two decimal places, the answer is 0.75.

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Answer:

i hope this helpes

Step-by-step explanation:

(a) To find the time necessary to type 50 words per minute, we need to solve the equation:

157/1 + 5.4e^-0.12t = 50

Rearranging the equation to isolate e^-0.12t and using the natural logarithm, we can find t:

ln(N - 157) = ln(5.4) - 0.12t

-ln(N - 157) = 0.12t - ln(5.4)

0.12t = ln(5.4) + ln(N - 157)

t = (ln(5.4) + ln(N - 157)) / 0.12

Plugging in N = 50, we get:

t ≈ 11.52 weeks

(b) To find the time necessary to type 75 words per minute, we follow the same steps as above:

157/1 + 5.4e^-0.12t = 75

ln(N - 157) = ln(5.4) - 0.12t

-ln(N - 157) = 0.12t - ln(5.4)

0.12t = ln(5.4) + ln(N - 157)

t = (ln(5.4) + ln(N - 157)) / 0.12

Plugging in N = 75, we get:

t ≈ 9.32 weeks

Answer:

For 50 wpm : 7.7 weeks approximately

For 75 wpm : 13.3 weeks approximately

Step-by-step explanation:

Given the relationship between N, the typing speed and t, the number of weeks of lessons as:

[tex]\mbox{\large N= \dfrac{157}{1+5.4e^{-0.12t}}}[/tex]

To solve for t for a particular N

cross-multiply the left side with the right side denominator to get

[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{N}}[/tex]

For N= 50 this works out to

[tex]\mbox{\large 1+5.4e^{-0.12t } = \dfrac{157}{50}}[/tex]

[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157}{50} - 1}\\[/tex]
[tex]\mbox{\large 5.4e^{-0.12t } = \dfrac{157-50}{50} } = \dfrac{107}{5} = 2.14[/tex]

Divide by 5.4 both sides:

[tex]\mbox{\large e^{-0.12t } = \dfrac{2.14}{5.4}} = 0.3963\\[/tex]

Take natural logs on both sides

[tex]\mbox{\large \ln(e^{-0.12t}) = \ln(0.3963)\\}[/tex]

[tex]\mbox{\large \ln(e^{-0.12t}) = -0.12 \;\textrm{since $ln(e^x)$ = x}}[/tex]  since ln(eˣ) = x

ln(0.3963) = -0.9256

Therefore

[tex]t = \dfrac{-0.9256}{-0.12} = \dfrac{0.9256}{0.12} = {7.7133 \;weeks\approx \mbox{\large \boxed{7.7 \;weeks}}[/tex]

For N = 75, follow the same strategy and you will end up with

[tex]1+5.4e^{-0.12t}=\dfrac{157}{75} \\\\\\1+5.4e^{-0.12t}= 2.0933\\\\5.4e^{-0.12t} = 2.0933 - 1 = 1.0933\\\\e^{-0.12t} = \dfrac{1.0933}{5.4} = 0.2025\\\\[/tex]

Taking logs on both sides
[tex]-0.12t =-1.5971[/tex]

[tex]t = \dfrac{-1.5971}{-0.12} = 13.3097 \;weeks \approx \boxed{\mbox{\large 13.3 \;weeks}}[/tex]

Step-by-step explanation:

We know that the water level in the tank is 15 cm initially, and after 2 days it has dropped to 14 cm. Therefore, the water level is dropping by 1 cm per day. To find out when the water will run out, we need to know how many days it will take for the water level to drop to 0 cm.

To find this out, we can use the following formula:

Days = (Initial water level - Final water level) / Rate of evaporation per day

Plugging in the values, we get:

Days = (15 - 0) / 1 = 15 days

So, the water will run out in 15 days.