Ben is going to an amusement park with his scout troop. He has $80 in his wallet. If admission costs $18.95, a book of ride tickets costs $26.50, and lunch costs $9.20, round each amount to the nearest dollar to find out about how much Ben will have left to buy a souvenir. A. $15 B. $25 C. $32 D. $38

Answer:

The answer is below

Step-by-step explanation:

Two triangles are similar if the ratio of their corresponding sides are in the same proportion.

1. ΔWXY is isosceles with legs WX and WY      (given)

2. ΔWVZ is isosceles with legs WV and WZ     (given)

3. WX =  WY, WV = WZ  (definition of an isosceles triangle)

4. \(\frac{WX}{WY}=1\\\\\)

\(\frac{WX}{WY}=\frac{WZ}{WZ} \ \ \\) (definition of ≅)

5. (WZ)(WX) = (WY)(WZ)       (multiplication property)

6. (WZ)(WX) = (WY)(WV)  (substitution property).

7. \(\frac{WY}{WZ}=\frac{WX}{WV}\)      (property of proportion)

8. ∠W = ∠W (reflexive property)

9. ΔWXY ~ ΔWVZ (side - angle - side similarity postulate)

Answer:

♣:  

✔ WX = WY; WV = WZ

♦:  

✔ substitution property

♠:  

✔ SAS similarity theorem

Step-by-step explanation:

just took it :)

Answer:

Slope: 1

Step-by-step explanation:

If you take 2 points on the graph, for example (0,3) and (-3,0), you can find the slope. Use the rise over run method (y2-y1/x2-x1). 0-3=-3 and -3-0=-3. After I did that, I divided it: -3/-3=1.

The rate at which the depth is changing at 1 a.m. is approximately 37.6996 ft/hr.

To find the rate at which the depth is changing at 1 a.m., we need to calculate the derivative of the depth function D(t) with respect to time.

Given D(t) = 2sin(6πt + 65π) + 3, we can find the derivative D'(t) using the chain rule:

D'(t) = 2(6π)cos(6πt + 65π)

Now, let's evaluate D'(t) at 1 a.m., which corresponds to t = 1:

D'(1) = 2(6π)cos(6π(1) + 65π)

Simplifying further:

D'(1) = 12πcos(6π + 65π)

D'(1) = 12πcos(71π)

To calculate the numerical value, we can use an approximation for π:

D'(1) ≈ 12(3.1416)cos(71(3.1416))

D'(1) ≈ 37.6996cos(222.264)

Finally, rounding to 4 decimal places, the rate at which the depth is changing at 1 a.m. is approximately 37.6996 ft/hr.

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Answer:

118.73

Step-by-step explanation:

Answer:

118.74 ft²

Step-by-step explanation:

First, you're going to get the are of the following shapes, one by one.

Area of A Circle = πr²

Area of a Rectangle = bh

Area of a Square = s²

Step 1: Let's find the area for the Circle.

Diameter = 6

Radius = Diameter ÷ 2

6 ÷ 2 = 3

The Radius is 3.

A = (3.14)(3)²

Simplify:

(3.14)(9) = 28.26 ft²

Step 2: Find the Area of the Rectangle.

A = bh

11 × 2 = 22

Area of Rectangle = 22 ft²

Step 3: Find the Area of the Square

A = s²

13² = 13 × 13 = 169 ft²

Step 4: Subtract the Aea of the Circle and Rectangle form the Are of the Square.

169 - 28.26 - 22 = 118.74 ft²

Answer:

D. Addition Property of Equality; Subtraction Property of Equality

Step-by-step explanation:

Answer:

Option C and B

Step-by-step explanation:

In the question step C is 23 + 11 = -11 +(-4x) + 11

which is in the form of a + b = c + a

In step C we have added 11 on both the sides to eliminate 11 from right side of the equation.

property which signifies this step is

Addition property of equality :

In step 'f' expression is

\frac{34}{-4}=\frac{-4x}{-4}

In this step equation has been divided by -4 on both the sides to eliminate 4 from the numerator.

In this step division property of equality has been applied.

Therefore Option C and B are the correct options.

Answer:

9.28

Step-by-step explanation:

x = 9.7 cos 17 degrees = 9.28

Answer: 5/3 or 1.67

Step-by-step explanation:

Answer:

The first option (the uppermost) is correct.

Step-by-step explanation:

When you multiply 1/2 by 3/4, you obtain the result of (1x3) / (2x4).

Simplifying, this gives us the result: 3/8, which is represented by the first choice.

Let me know if this helps!

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Answer:Section 6.1

Solutions and Hints

by Brent M. Dingle

for the book:

Precalculus, Mathematics for Calculus 4

th Edition

by James Stewart, Lothar Redlin and Saleem Watson.

If you remember nothing else from this section remember:

arc length = radius * angle

s = r * q

where the angle, q, is measured in radians.

There are other formulas, but that one is pretty important.

48. A circular arc of length 3 feet subtends a central angle of 25.

Find the radius of the circle.

Start with s = r*q , s = 3 feet, q = 25 = 25*(p/180) = (5/36)p radians

3 = r * (5/36)p Å 3*(36/5) = r*p Å 21.6 = p*r Å r = 21.6/p feet

52. Memphis, Tennessee and New Orleans Louisiana lie approximately on

the same meridian. Memphis has latitude 35 N and New Orleans 30 N.

Find the distance between the cities, given the radius of the earth is

3960 miles.

Again start with s = r*q,

with r = 3960 miles and q = 35 – 30 = 5 = 5*(p/180) = (1/36)p.

and we need to find s = arc length = distance between the cities.

s = 3960*(1/36)p = 110p miles.

60. A sector of a circle of radius 24 miles has an area of 288 square miles.

Find the central angle of the sector.

For this you need a new formula.

The area of a sector of circle = A = ½*r

2

*q ,

where q is the central angle of the sector measured in radians

and r of course is the radius of the circle.

For this problem r = 24 miles, A = 288 sq. miles and we need to find q.

288 = (½)*24

2

*q Å 288 = 288*q Å 1 radian = q (or about 57.3)

62. Three circles with radii 1, 2 and 3 feet are externally tangent to one

another. Find the area of the sector of the circle of radius 1 that is

cut off by the line segments joining the center of that circle to the

centers of the other two circles.

So you start out with:

Notice you know the length of ALL the sides of the triangle, because you know

the radius of each circle. From this you might discern that: 5

2

= 3

2

+ 4

2

. Thus you

have the (length of the hypotenuse)

2

= (length of side A)

2

+ (length of side B)

2

.

And from that you may conclude the triangle is a right triangle, or rather the angle

we are interested in is 90. Thus we use the area formula given in the text:

The area of a sector of circle = A = ½*r

2

*q ,

For this problem r = 1 foot, q = 90 = p/2, and we need to find A

A = ½ * 1

2

* p/2 = p/4 square feet.

Step-by-step explanation:

The linear speed of a point on the equator in miles per hour is 1037 mph. Therefore, option D is the correct answer.

Given that, the radius of the earth is approximately 3960 miles.

Linear speed is the measure of the concrete distance travelled by a moving object. The speed with which an object moves in the linear path is termed linear speed. In easy words, it is the distance covered for a linear path in the given time. Linear Speed Formula is articulated as s=rθ/t.

Any point in the equator would complete a 360° or 2π, revolution in 24 hours. Therefore, the linear speed would be s=rθ/t.

where r is the radius of the Earth and θ is the angular distance (in rad) after time t

Hence, the linear speed would be

s= (3960×2π)/24

= (3960×2×3.14)/24

= 24868.8/24

= 1036.7

≈1037 mph

The linear speed of a point on the equator in miles per hour is 1037 mph. Therefore, option D is the correct answer.

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The simplified expression of -15r + 3(2s - 4r) is 3(-9r + 2s)

The expression can be simplified as follows:

-15r + 3(2s - 4r)

open the brackets

-15r + 6s - 12r

let's combine the like terms

-15r - 12r + 6s

Therefore,

-15r - 12r + 6s

-27r + 6s

-27r + 6s = 3(-9r + 2s)

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The given equation, 9x² + 36y² - 36x + 72y + 36 = 0, represents an ellipse. In standard form, the equation can be written as (x-1)²/4 + (y+1)²/1 = 1. The center of the ellipse is at (1, -1), the vertices are located at (3, -1) and (-1, -1), and the foci are at (2, -1) and (0, -1).

To write the equation 9x² + 36y² - 36x + 72y + 36 = 0 in standard form, we need to complete the square for both the x and y terms. By rearranging the equation, we have 9x² - 36x + 36 + 36y² + 72y + 36 = 0.

Next, we can factor out a 9 from the x terms and a 36 from the y terms: 9(x² - 4x + 4) + 36(y² + 2y + 1) = 0.

Simplifying further, we have 9(x - 2)² + 36(y + 1)² = 36.

Dividing both sides by 36, we get (x - 2)²/4 + (y + 1)²/1 = 1, which is the standard form of an ellipse.

From the standard form, we can determine that the center of the ellipse is located at (1, -1), the vertices are at (3, -1) and (-1, -1), and the foci are at (2, -1) and (0, -1).

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Answer:

1 1/2 times more

Step-by-step explanation:

6.75 ÷ 4.5 = 1.5

When blotting dry a stained slide, rubbing it from side to side may cause the stain to smear or even be removed from the slide completely. This can result in the loss of important information that was being observed under the microscope.

Stains are used to enhance the contrast of the sample being observed and make it easier to distinguish different structures or cells. The stain is absorbed by the sample and binds to specific parts of the cell or tissue, providing a clearer image. However, these stains are often water-soluble and can easily be removed by excessive rubbing or wiping.
To avoid damaging the stained slide, it is important to blot the slide gently and in one direction. The best technique is to use a soft, lint-free cloth or paper towel and gently press down on the slide to remove excess liquid. Blotting the slide in this way will help to prevent the stain from smearing and will preserve the quality of the image.
In conclusion, rubbing a stained slide from side to side while blotting dry can cause the stain to smear or be removed completely, resulting in the loss of important information. To avoid damaging the slide, it is important to blot gently and in one direction using a soft, lint-free cloth or paper towel.

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Answer:

19

Step-by-step explanation:

|-7| +|-5| + 7 = 7+5+7= 19

Answer:

{ -1, 2, -4, 8, -16...}

Step-by-step explanation:

Common ratio : the constant pure number you get when you divide a term to the one before it.

thus, 2 ÷ -1 = -2

to check if the common ratio is -2 , divide each terms in front by the one before it.

... 8 ÷ 4 = -2 we got -2 again so the common ratio of this geometric progression is -2.

(a) The probability that the first ball drawn is a 1 and the last ball drawn is a 6 is 1/30.

(b) The probability that the sum of the numbers on the first and last balls is 7 is 2/15.

(c) The probability that the second ball drawn is a 3 is 1/5.

(d) The probability that the third ball drawn is a 3 is 1/4.

(a) To calculate the probability that the first ball drawn is a 1 and the last ball drawn is a 6, we consider that there are 6 balls in the urn, so the probability of drawing a 1 initially is 1/6. After removing the first ball, there are 5 balls remaining, and the probability of drawing a 6 as the last ball is 1/5. Multiplying these probabilities together gives us (1/6) * (1/5) = 1/30.

(b) To find the probability that the sum of the numbers on the first and last balls is 7, we need to consider all possible combinations that satisfy this condition. The pairs that add up to 7 are (1, 6), (2, 5), and (3, 4). The probability of drawing (1, 6) is (1/6) * (1/5) = 1/30. Similarly, the probability of drawing (2, 5) and (3, 4) are also 1/30 each. Adding these probabilities together gives us 1/30 + 1/30 + 1/30 = 2/15.

(c) The probability that the second ball drawn is a 3 can be calculated by considering that there are initially 6 balls in the urn. The probability of drawing a 3 as the second ball is 1/6, since there is only one ball labeled 3 remaining out of the 6 balls. Therefore, the probability is 1/6.

(d) To calculate the probability that the third ball drawn is a 3, we consider that there are initially 6 balls in the urn. After removing the first and second balls, there are 4 balls left, and only one of them is labeled 3. Therefore, the probability of drawing a 3 as the third ball is 1/4.

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To create a valid matched pair test, the researcher should consider random assignment, similarity, blinding, sample size, and duration.

To create a valid matched pair test, the researcher should consider the following:

Random assignment: The pairs should be randomly assigned to the treatment and control groups to avoid bias.

Similarity: The pairs should be matched based on similar characteristics that could affect the outcome, such as age, gender, prior algebra performance, and socioeconomic status.

Blinding: The researcher should ensure that the students do not know which group they are assigned to, and the person administering the test should also be blinded to the group assignments.

Sample size: The sample size should be large enough to provide sufficient statistical power to detect a meaningful difference between the two groups.

Duration: The length of the study should be sufficient to allow for meaningful differences to occur between the groups, but not so long that other factors could interfere with the outcome.

By considering these factors, the researcher can create two groups that are well-matched and comparable, allowing for a valid matched pair test to be conducted.

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Answer:

Suppose A and B , both has initial volume, say x

120 ML is poured from B to A, then new volumes of A and B will be:

new volume of A (x-120)

new volume of B  (x+120)

Volume of B is now four times volume of A, then

(x+120)= 4(x-120)

(x+120)=4x-180

3x=600

x=200

So, the initial volume of A and B containers is 200

So, at the end, volume of container A = 200-120=80

Hence the answer is 80   :

Step-by-step explanation:

(1)Laurent series expansion for $z$ in the annulus $0 < |z| < 1$:\(\( \frac{1}{{z^2 - z}} \):\[\frac{1}{{z^2 - z}} = \frac{1}{z(z-1)} = \frac{A}{z} + \frac{B}{z-1} = \frac{1}{z} - \frac{1}{z-1}\]\)

(2)Laurent series expansion for $z$ in the annulus $1 < |z| < \infty$:

\(\( \frac{{z+1}}{{z-1}} \):\[\frac{{z+1}}{{z-1}} = 1 + \frac{2}{z-1}\]\)

(3)Laurent series expansion for $z$ in the annulus $1 < |z| < 2$:\(\( \frac{1}{{(z^2 - 1)(z^2 - 4)}} \):\[\frac{1}{{(z^2 - 1)(z^2 - 4)}} = \frac{{A}}{{z+1}} + \frac{{B}}{{z-1}} + \frac{{C}}{{z+2}} + \frac{{D}}{{z-2}}\]\)

What are Laurent series expansions?

Laurent series expansions are a way to represent a complex function as an infinite series in the complex plane. They are a generalization of Taylor series expansions, allowing for both positive and negative powers of the variable.

A Laurent series expansion of a function f(z) around a point z = a is given by:

f(z) = ∑[n = -∞ to ∞] cn (z - a)^n

Here, cn represents the coefficients of the series, and (z - a)^n represents the powers of the variable centered at a.

(1) For the function $\frac{1}{z^2 - z}$:

The function has a simple pole at $z = 0$ and a removable singularity at $z = 1$.

Laurent series expansion for $z$ in the annulus $0 < |z| < 1$:\(\( \frac{1}{{z^2 - z}} \):\[\frac{1}{{z^2 - z}} = \frac{1}{z(z-1)} = \frac{A}{z} + \frac{B}{z-1} = \frac{1}{z} - \frac{1}{z-1}\]\)

(2) For the function $\frac{z + 1}{z - 1}$:

The function has a simple pole at $z = 1$ and a removable singularity at $z = -1$.

Laurent series expansion for $z$ in the annulus $1 < |z| < \infty$:

\(\( \frac{{z+1}}{{z-1}} \):\[\frac{{z+1}}{{z-1}} = 1 + \frac{2}{z-1}\]\)

(3) For the function $\frac{1}{{(z^2 - 1)(z^2 - 4)}}$:

The function has simple poles at $z = \pm 1$ and $z = \pm 2$.

Laurent series expansion for $z$ in the annulus $1 < |z| < 2$:\(\( \frac{1}{{(z^2 - 1)(z^2 - 4)}} \):\[\frac{1}{{(z^2 - 1)(z^2 - 4)}} = \frac{{A}}{{z+1}} + \frac{{B}}{{z-1}} + \frac{{C}}{{z+2}} + \frac{{D}}{{z-2}}\]\)

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Using the .01 level of significance means that, in the long run, a Type I error occurs 1 time in 100. This means that if we perform a statistical test 100 times, and we set the level of significance at .01, then we can expect to observe one false positive result due to chance alone. So, the correct option is 1).

A Type I error occurs when we reject a true null hypothesis, or when we conclude that there is a significant difference or relationship between two variables when in fact there is not.

By setting the level of significance at .01, we are minimizing the risk of making a Type I error while increasing the risk of making a Type II error, which occurs when we fail to reject a false null hypothesis. So, the correct answer is 1).

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The probability that the product of the two chosen numbers will be even and greater than 2 is 9/25.

Probability is a measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event that will not occur, and 1 represents a certain event that will always occur.

According to the given information:

There are 5 balls numbered 1 through 5 in the bowl. The total number of possible outcomes, when Josh chooses a ball, is 5, as there are 5 balls in the bowl.

Now let's consider the probability of choosing a ball with an even number. There are 3 even numbers (2, 4, and 5) out of the 5 possible numbers, so the probability of choosing a ball with an even number is 3/5.

Next, let's consider the probability of choosing a ball with a number greater than 2. There are 3 numbers (3, 4, and 5) greater than 2 out of the 5 possible numbers, so the probability of choosing a ball with a number greater than 2 is also 3/5.

To find the probability that the product of the two chosen numbers will be even and greater than 2, we need to multiply the probabilities of choosing an even number and choosing a number greater than 2.

Probability of choosing an even number: 3/5

Probability of choosing a number greater than 2: 3/5

Multiplying these probabilities, we get:

(3/5) * (3/5) = 9/25

So, the probability that the product of the two chosen numbers will be even and greater than 2 is 9/25.

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A. P(0.1 < X < 0.6) = F(0.6) - F(0.1) = 1 - 0.23 = 0.77.

B. the PDF of X is given by:

f(x) = 0 for x < 0

f(x) = 23 for 0 ≤ x < 1

f(x) = 0 for x ≥ 1

C. X0.6, the 60th percentile of the distribution of X, is equal to 1.

To answer these questions, use the given cumulative distribution function (CDF) and perform the necessary calculations.

(a) To find P(0.1 < X < 0.6), calculate the difference between the CDF values at those points. The CDF is defined as F(x):

P(0.1 < X < 0.6) = F(0.6) - F(0.1)

Since the CDF is given as a piecewise function, evaluate it at the specified points:

F(0.6) = 1

F(0.1) = 0.23

Therefore, P(0.1 < X < 0.6) = F(0.6) - F(0.1) = 1 - 0.23 = 0.77.

(b) To find the probability density function (PDF) f(x), we can differentiate the CDF. The PDF is the derivative of the CDF:

f(x) = d/dx [F(x)]

Differentiating each part of the piecewise CDF function:

For x < 0, f(x) = 0 (since F(x) is constant in this interval).

For 0 ≤ x < 1, f(x) = d/dx [23x] = 23.

For x ≥ 1, f(x) = 0 (since F(x) is constant in this interval).

Therefore, the PDF of X is given by:

f(x) = 0 for x < 0

f(x) = 23 for 0 ≤ x < 1

f(x) = 0 for x ≥ 1

(c) To find X0.6, the 60th percentile of the distribution of X, we need to find the value of x for which F(x) = 0.6. From the given CDF, we know that F(x) = 0.6 for x = 1. So X0.6 = 1.

Therefore, X0.6, the 60th percentile of the distribution of X, is equal to 1.

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The production level that will maximize profit is 300 units

Given,

C(x) = 12000 + 400x − 3.8x^2 + 0.004x^3

P(x) = 4000-8x

First we need to find revenue function

R(x) = x.P(x) = x(4000-8x) = 4000x-8x^2

Now, we need to find marginal revenue

R'(x) = d/dx (4000x-8x^2) = 4000-16x

And now we'll find marginal cost

C'(x) = d/dx (12000+4000x-3.8x^2=0.004x^3) = 400-7.6x+0.012x^2

for maximum profit,

C'(x) = R'(x)

or, 4000-16x = 400-7.6x+0.012x^2

or, 0.012x^2+8.4x-3600 = 0

or, x^2+700x-300000=0

or, (x+1000) (x-300) = 0

so, x=-1000 or, x=300

Production level can not be negative.

So, the production level is 300 units

The production level that will maximize profit is 300 units

The production level that will maximize profit is 300 units

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Answer:

B

Step-by-step explanation:

The ratios of the trigonometry are identical, cos x = 9 / 15 and sin y = 9  / 15.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the angles in the right triangle can be found using trigonometric ratios.

Hence,

sin y = opposite / hypotenuse

sin y = 9 / 15

cos x = adjacent / hypotenuse

cos x = 9 / 15

Therefore, the ratios are both identical(9 / 15 and 9 / 15)

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The probability that the vehicle Bob chooses is used or is a car is 0.6

There are 10 new cars, 4 used cars, 12 new trucks, and some used trucks at Bob's Auto Plaza. We are asked to find the probability that the chosen vehicle is used or is a car.

First, we need to find the total number of vehicles at the dealership:

Total number of vehicles = 10 new cars + 4 used cars + 12 new trucks + used trucks

We don't know how many used trucks there are, but we know that there are at least 4 of them (since there are 4 used cars). So the total number of vehicles is at least:

Total number of vehicles = 10 + 4 + 12 + 4 = 30

Now we need to find the number of vehicles that are used or cars. There are 4 used cars, and 10 new cars, for a total of 14 cars. There are also some used trucks, which we don't know the exact number of, but we know that there are at least 4 of them. So the total number of used or car vehicles is at least:

Total number of used or car vehicles = 4 used cars + 10 new cars + 4 used trucks = 18

To find the probability of choosing a used or car vehicle, we divide the number of used or car vehicles by the total number of vehicles:

Probability of choosing a used or car vehicle = Total number of used or car vehicles / Total number of vehicles

Probability of choosing a used or car vehicle = 18 / 30

Divide the numbers

Probability of choosing a used or car vehicle = 0.6

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The given question is incomplete, the complete question is:

At Bob's Auto Plaza there are currently 10 new cars, 4 used cars, 12 new trucks, and used trucks, Bob is going to choose one of these vehices at random te be the Deal of the Month. What is the probability that the vehicle that Bob chooses is used or is a car? Do not round intermediate computations, and round your answer to the nearest hundredth

The metric system of measurement is based on the number 10.

This system is also known as the International System of Units (SI) and is used in most countries around the world. In the metric system, various units of measurement are defined as multiples or fractions of a base unit, which is defined for each quantity being measured. For example, the base unit for length is the meter, and the base unit for mass is the kilogram. Prefixes such as kilo-, centi-, and milli- are used to indicate multiples or fractions of the base unit, based on factors of 10. For example, a kilometer is 1000 meters, a centimeter is 1/100 of a meter, and a milligram is 1/1000 of a gram. This makes the metric system easy to use and convert between units, as well as consistent and universally recognized.

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Answer:

28 centimeters

Step-by-step explanation:

The level of the pond is dropping each day by 4 cm.  7 days passed, and each day it was dropping at a constant rate.  In order tto find how many centimeters the level of the pond dropped in 7 days, you have to multiply the days passed by the amount dropped each day.

So, 7 days times 4 cm. a day= 28 centimeters dropped.