Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)

The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.



0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58


What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.

Answer:

area=36.5

Step-by-step explanation:

8×4=32

8-5=3 for the base of the triangle

7-4=3 for the height of the triangle

3×3=9

9÷2=4.5

4.5+32=36.5

area=36.5

We can see here that the figures that have the same area are: A. Figures I and II.

Area is a measure of the size of a two-dimensional surface or shape. It refers to the amount of space inside the boundaries of a flat object, such as a rectangle, triangle, or circle. Area is typically measured in square units, such as square meters, square feet, or square centimeters.

The area of Figure I which is a rectangle is = l × b = 2cm × 5.8cm = 11.6cm².

The area of Figure II which is a parallelogram is = b × h = 4cm × 2.9cm = 11.6cm².

Thus, Figures I and II have the same area.

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No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69

A newsletter publisher believes that under 69% of their readers own a Rolls Royce.

No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.

Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.

Null Hypothesis (H0): p ≤ 0.69

Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.

Alternative Hypothesis (H1): p > 0.69

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The average rate of change of f(x) from x = -3 to x = 6 is 7.

What is meant by average?

The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.

To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.

For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:

[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]

The value of the function at [tex]x = 6[/tex] is:

[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]

The difference in the function values is:

[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]

The difference in the input values is:

6 - (-3) = 9

Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:

average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]

So, the average rate of change of f(x) from x = -3 to x = 6 is 7.

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There are 100,947 ways to assign the tasks to the 7 people.

This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.

Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,

The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is

(17 + 6) choose 6 = 23 choose 6 = 100947

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Answer:

10 + 2x

also,

2x + 10

Step-by-step explanation:

"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)

"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.

"product" means multiplying. So the "product of 2 and a number" is 2x.

So to translate this word phrase into an algebraic expression, you get:

10 + 2x

but also 2x + 10 is the same thing.

The length of the reflected line segment is approximately 11.66 units.

The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.

Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.

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Answer:

(a) To write 9 N as a number in standard form, we need to express it as a number between 1 and 10 multiplied by a power of 10. To do this, we can divide 9 N by 10 until we get a number between 1 and 10:

9 N = 480 × 10^9

9 N ÷ 10 = 48 × 10^9

9 N ÷ 10^2 = 4.8 × 10^9

9 N ÷ 10^3 = 0.48 × 10^9

9 N ÷ 10^4 = 0.048 × 10^9

9 N ÷ 10^5 = 0.0048 × 10^9

Therefore, 9 N = 4.8 × 10^10.

(b) To write N as a product of powers of its prime factors, we can first factorize N:

480 × 10^9 = 2^5 × 3 × 5 × 10^9

Then, we can express 10^9 as 2^9 × 5^9 and substitute it in the factorization:

2^5 × 3 × 5 × 2^9 × 5^9 = 2^14 × 3 × 5^10

Therefore, N = 2^14 × 3 × 5^10.

(c) To find the largest factor of N that is an odd number, we need to remove all factors of 2 from the factorization of N. We can do this by dividing N by 2 as many times as possible:

N = 2^14 × 3 × 5^10

N ÷ 2 = 2^13 × 3 × 5^10

N ÷ 2^2 = 2^12 × 3 × 5^10

N ÷ 2^3 = 2^11 × 3 × 5^10

N ÷ 2^4 = 2^10 × 3 × 5^10

N ÷ 2^5 = 2^9 × 3 × 5^10

N ÷ 2^6 = 2^8 × 3 × 5^10

N ÷ 2^7 = 2^7 × 3 × 5^10

N ÷ 2^8 = 2^6 × 3 × 5^10

N ÷ 2^9 = 2^5 × 3 × 5^10

N ÷ 2^10 = 2^4 × 3 × 5^10

N ÷ 2^11 = 2^3 × 3 × 5^10

N ÷ 2^12 = 2^2 × 3 × 5^10

N ÷ 2^13 = 2 × 3 × 5^10

N ÷ 2^14 = 3 × 5^10

Therefore, the largest factor of N that is an odd number is 3 × 5^10.

The size of angle DAB in the quadrilateral is 49°.

The sum of the interior angles of a quadrilateral is 360°. We can say:

∠A + ∠B + ∠C + ∠D = 360°

∠A + 34° + ∠C + 228° = 360°

∠A  + ∠C + 262° = 360°

∠A  + ∠C = 360 - 262

∠A  + ∠C = 98

Since angles DAB and BCD are the same size. This implies ∠A  = ∠C. Thus:

∠A  + ∠A = 98

2∠A  = 98

∠A = 98/2

∠A  = 49°

Therefore, the size of angle DAB is 49°.

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Complete Question

Check the attached image

b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.

Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.

We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.

Using this information, we can create an equation:

6b + 12p = 60

Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:

b + 2p = 10

Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":

b + 2(2) = 10

b + 4 = 10

b = 6    

So if Evelyn buys two purses, she also buys six bracelets.

In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.

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Answer:

slope of 3/4 = line C

undefined slope = line A

Step-by-step explanation:

remember that slope is [tex]\frac{rise}{run}[/tex]. Pick any two points on the graph and count up and over to find the rise/run.

OR

use the slope formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] to plug the two points into and find the slope.

- vertical lines are always undefined.

- horizontal lines have a slope of 0

Using the given values, the values of the expression and equations are:

25. -0.8

28. S ≈ 137.22

29. V ≈ 50.94

From the question, we are to evaluate each of the expressions for the given values

25.

[-b + √(b² -4ac)]/2a

a = 2, b = 8, c = 5

Substituting the values into the expression

[-b + √(b² -4ac)]/2a

= [-8 + √((8)² - 4(2)(5))]/2(2)

= [-8 + √(64 - 40)]/4

= [-8 + √(24)]/4

= [-8 + 2√6]/4

= -2 + 1/2(√6)

= -0.775

≈ -0.8

28.

S = 2πrh + 2πr²

r = 2.3, h = 7.1 (Take π = 3.14)

Thus,

S = 2(3.14)(2.3)(7.2) + 2(3.14)(2.3)²

S = 103.9968 + 33.2212

S = 137.218

S ≈ 137.22

29.

V = 4/3 πr³

r = 2.3(Take π = 3.14)

V = 4/3 × 3.14 × (2.3)³

V = 50.939

V ≈ 50.94

Hence, the value of V is 50.94

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Answer:

153

Step-by-step explanation:

The relationship in the row is below

4³ +2³ +1³ =64 + 8 +1 = 72

1³ + 2³ +6³= 1 + 8 + 216

3³ + 1³ + 5³ = 27 +1 +125 = 153

All numbers below the first level are raised to power 3 and added together

The expression or equation that correctly represents the situation given is y = 2x.

Based on the table, for each package of cashews 2 cans of peanuts are required. Here are some examples:

Based on this relationship and assuming y represents the cans of peanuts and x represents the packages of cashews a possible equation to represent this situation would be y = 2x.

Note: This question is incomplete; below I attach the missing information:

Write an equation to represent this relationship:

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In conclusion, the power series converges absolutely over an interval given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex]is a natural number.

The interval over which the power series converges absolutely is given by [tex]\left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n\in\mathbb{N}\;\;\;\text{and}\;\;\;n>N, where N\in\mathbb{N}[/tex] is a natural number.

In other words, for any given N, the series will converge absolutely over the interval \left|x-7\right|>\frac{\left|a_n+1\right|}{\left|a_n\right|}\;\;\;\forall\;\;\;n>N.

This means that the series will converge absolutely over a larger interval as N increases, since the terms \frac{\left|a_n+1\right|}{\left|a_n\right|} get closer to 1 for larger values of n.

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The value of the given lengths are as follows:

a.) KL = 11.1ft

LO = 5.7ft

b.) m<OMN = 45°

For Side LO ;

7/11 = 7√2/7√2+LO

7(7√2+LO) = 11×7√3

69.3+7LO = 108.9

7LO = 108.9-69.3

LO = 39.6/7

LO = 5.7 ft

For KL ;

This can be solved using the Pythagorean theorem;

c²= b²+a²

C = 5.7+7√2 = 15.6

b = 11

a²= 15.6²-11²

= 243.36 - 121

= 122.36

a= √122.36

a= 11.1ft

For angle OMN;

This can be solved using SOHCAHTOA.

Sin∅ = opposite/hypotenuse

opposite = 7

hypotenuse = 7√2

sin∅ = 7/7√2

sin∅ = 0.707106781

∅= sin-1 0.707106781

∅ = 45°

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The solution of the system 2 -1 5 with -2 -1 in real form is (x, y) = (7/4, 7/2).

To solve the system with the given coefficients, first, let's rewrite it as a linear system of equations:

2x - y = 5
-2x - y = -2

Now, let's solve this system step-by-step:

Step 1: Solve for y in the first equation:
y = 2x - 5

Step 2: Substitute the expression for y from Step 1 into the second equation:
-2x - (2x - 5) = -2

Step 3: Simplify and solve for x:
-2x - 2x + 5 = -2
-4x = -7
x = 7/4

Step 4: Substitute the value of x back into the expression for y:
y = 2(7/4) - 5
y = 7/2

The solution in real form is (x, y) = (7/4, 7/2).

Regarding the ellipse with counterclockwise orientation, the trajectory can be described as a smooth, closed curve in the shape of an ellipse. The ellipse will have a major and minor axis, with the points on the ellipse moving continuously in a counterclockwise direction along the curve.

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The given equation 3x + 7y = 11 is equal to (1,-2).

The given equation is 3x + 7y = 11.

To find the solution of the equation, we need to consider the given options:

(6,-1)(1,-2)(0,4)

Now substitute each value of x and y in the given equation, we get,

If x = 6 and y = -13(3 × 6) + (7 × -1) = 18 - 7 = 11 ≠ 11

If x = 1 and y = -2(3 × 1) + (7 × -2) = 3 - 14 = -11 ≠ 11

If x = 0 and y = 4(3 × 0) + (7 × 4) = 0 + 28 = 28 ≠ 11

Therefore, the given equation 3x + 7y = 11 is equal to (1,-2).

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The given angles and measures is given below:

In mathematics and geometry, an angle is a measure of the space between two intersecting lines, rays, or line segments, usually expressed in degrees, radians, or grads. It is the measure of the opening between two lines that intersect at a common point, called the vertex of the angle.

5) tan x = 153 / 41

x = tan^-1 ( 153 / 41 )

75 degrees

6) tan y = 25/25

y = tan^-1 ( 25/25 )

45 degrees

7) sin z = 10/28

z= sin^-1 ( 10/28 )

21 degrees

8) cos a = 47/50

a = cos^-1( 47/50)

20 degrees

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The Polynomials that are listed in the question are the options labelled;

B, C, E

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents.

The variables represent unknown values, while the coefficients are constants that multiply the variables or their exponents. The exponents indicate the power to which the variables are raised.

Polynomials can be added, subtracted, multiplied, and divided to create more complex expressions, and they are used in a wide range of mathematical applications, including algebra, calculus, and geometry.

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the amount of sand in the top cone when the height of the sand is only 1 inch is (h-1)/h times the amount of sand in the top cone originally.

the cones are similar, their volumes are proportional to the cube of their heights. Let's denote the height of the top cone as h, and the radius of the top and bottom bases as r. Then, the volume of the top cone can be expressed as:

V₁ = (1/3)π[tex]r^2[/tex]h

If the height of the sand in the top cone is reduced to 1 inch, then the height of the remaining sand in the top cone is (h-1) inches. The volume of the remaining sand in the top cone can be expressed as:

V₂ = (1/3)π[tex]r^2[/tex](h-1)

To compare the amount of sand in the top cone in these two scenarios, we can take the ratio of their volumes:

V₂/V₁ = [(1/3)π[tex]r^2[/tex](h-1)] / [(1/3)π[tex]r^2[/tex]h] = (h-1)/h

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The final result for the money is [tex]172.40[/tex] after you multiply it by a percent.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Rather than being stated as a fraction, a percent is a piece of an entire thing expressed as just a number between zero and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the total by its entirety and multiply the result by 100 to get the percentage.

[tex]w-[0.15]=146.54[/tex]

so [tex]w-85p=146.54[/tex]

[tex]146.54[/tex] divided by [tex]80=1.724[/tex] so when you make it a percent it turns it into [tex]172.40[/tex] which is the final answer for the money.

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The zeroes of the factored polynomial as required to be determined in the task content are: x = -6 and x = 8.

It follows from the task content that the zeroes of the completely factorised polynomial are to be determined.

Since the given polynomial is; x² - 2x - 48 which has been factorised completely to; (x + 6) (x - 8).

Ultimately, the zeroes of the Polynomial are as follows;

x + 6 = 0; x = -6.

and

x - 8 = 0; x = 8.

Conclusively, the zeroes of the polynomial are; x = -6 and x = 8.

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The value of angle x in the right triangle KJI is approximately 63.4 degrees.

What is trigonometric ratios ?

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

These ratios are defined as follows:

Sine (sin) of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the angle to the length of the hypotenuse.

Tangent (tan) of an angle is the ratio of the length of the side opposite to the angle to the length of the adjacent side.

Finding the value of x :

We can use the trigonometric ratios to find the value of angle x in the right triangle KJI.

First, we can use the Pythagorean theorem to find the length of the hypotenuse KI:

[tex]KI^2 = KJ^2 + JI^2[/tex]

[tex]KI^2 = 27^2 + 48^2[/tex]

[tex]KI^2 = 729 + 2304[/tex]

[tex]KI^2 = 3033[/tex]

[tex]KI =\sqrt{3033}[/tex]

Next, we can use the sine function to find the value of angle I:

[tex]sin(I) = JI / KI[/tex]

[tex]sin(I) = 48 / \sqrt{3033}[/tex]

[tex]I = sin^-1(48 / \sqrt{3033})[/tex]

[tex]I = 63.4[/tex] degrees

Therefore, the value of angle x in the right triangle KJI is approximately 63.4 degrees.

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A dependent variable that maintains constant measurements throughout an experiment will be depicted by a straight, horizontal line in a graph.

In an experiment, the dependent variable is the variable being measured, and it is expected to change in response to changes in the independent variable. However, if the dependent variable remains constant throughout the experiment, it indicates that it is not affected by the independent variable.

When such a situation arises, the data points for the dependent variable will be located at the same level or value, resulting in a horizontal line in the graph.

This straight, horizontal line represents the constant measurements of the dependent variable, and it can provide valuable insights into the nature of the relationship between the independent variable and the dependent variable.

A dependent variable that maintains constant measurements throughout an experiment may indicate a flaw in the experimental design, such as an incorrect assumption about the nature of the relationship between the independent variable and the dependent variable, or an uncontrolled confounding variable.

Therefore, it is important to carefully analyze the data and the experimental design to identify and address any potential issues.


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Using the stars and bars technique, Candice can distribute her 24 pieces of candy among her four siblings in 2,925 different ways. If she must give each sibling at least one of each type of candy, there are 67,200 ways to distribute the candy among the four siblings.

(A) To solve this problem, we can use the technique of stars and bars. We have a total of 24 pieces of candy to share among four children. We can represent this using 24 stars, with 3 bars to separate the stars into four groups, one for each child. For example, the following arrangement represents giving 6 pieces of candy to the first child, 10 pieces to the second child, 3 pieces to the third child, and 5 pieces to the fourth child:

*****|**********|***|****

The number of ways to arrange the stars and bars is equal to the number of ways to choose 3 positions out of the 27 possible positions for the stars and bars. Therefore, the number of different ways that Candice can share her candy with her three younger brothers is:

C(27, 3) = 27! / (3! * 24!) = 2925

(B) Now, we need to ensure that each child receives at least one Tootsie roll and one Twizzler. We can give each child one of each candy to start, and then distribute the remaining 13 Tootsie rolls and 7 Twizzlers using the stars and bars technique. We have 13 Tootsie rolls and 7 Twizzlers to distribute among four children, which can be represented using 13 stars and 3 bars for the Tootsie rolls, and 7 stars and 3 bars for the Twizzlers. The number of ways to arrange the stars and bars for each type of candy is:

C(16, 3) = 560 for the Tootsie rolls

C(10, 3) = 120 for the Twizzlers

To find the total number of ways to distribute the candy, we can multiply the number of ways for each type of candy:

560 * 120 = 67200

Therefore, there are 67,200 different ways for Candice to share her candy with her three younger brothers after her mother asks her to give at least one of each type of candies to each of her brothers.

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Complete question:

After a (not very successful) trick or treating round, Candice has 15 Tootsie rolls and 9 Twizzlers in her pillow case. Her mother asks her to share some of the loot with her three younger brothers.

(A) How many different ways can she do this?

(B) How many different ways can she do this after her Mother asks her to give at least one of each type of candies to each of her brothers?

Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:

18x = projected income

We can solve for x by dividing both sides of the equation by 18:

x = projected income / 18

Substituting the given projected income of $216, we get:

x = 216 / 18 = 12

Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.

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Answer: 40

Step-by-step explanation:

25/100 x ? = 10

multiply both sides by 100/25

x= 10 x 100/25

x=10

The steps to find the depth through which the storm submerges the lowest parts of the Pensacola Beach is given below.

As it has been given in the question, Pensacola beach is located 5-10 feet above sea level.

The ocean water rises upto 5.5 feet during a storm

Hence you need to add up the height of the highest tide on 16 September to 5.5 feet.

If the combined height of the highest tide and the storm tide is greater than 10 feet, then the whole Pensacola beach submerges.

You just subtract the combined height of the storm and the highest tide from the height of the beach.

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Portions of Pensacola Beach, a coastal community built on a barrier island, are located at 3 - 10 feet above sea level.

Hurricane Sally, which struck Pensacola on September 16, 2020 and brought a 5.5 foot storm.

Combined with a high tide on September 16,202, by how many feet did that storm surge submerge the lowest parts of Pensacola Beach? (Hint: use the information in question and change the date on the tidal chart to September 16, 2020) Now, compare your answers above, and think about how the type (pattern) and size of the tides differ for these two locations