Find the unique function f(x) satisfying the following conditions: f"(x) = e32 f(0) = 5 f(0) 2 = == f(x) = 因

Answer:  How do you know how many solutions an equation has?

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one soluti

Step-by-step explanation:

The probability that Tamika's result is greater than Carlos' result is $\boxed{\frac{4}{9}}$.

To solve this problem, we can start by finding all the possible sums that Tamika can get by adding two different numbers from the set $\{8,9,10\}$:

- $8+9=17$
- $8+10=18$
- $9+10=19$

Similarly, we can find all the possible products that Carlos can get by multiplying two different numbers from the set $\{3,5,6\}$:

- $3\times5=15$
- $3\times6=18$
- $5\times6=30$

Now we need to compare each sum with each product to see which ones satisfy the condition that Tamika's result is greater than Carlos' result. We can organize this information in a table:

| Tamika's sum | Carlos' product | Tamika's sum > Carlos' product? |
| ------------ | -------------- | ----------------------------- |
| 17           | 15             | Yes                           |
| 17           | 18             | No                            |
| 17           | 30             | No                            |
| 18           | 15             | Yes                           |
| 18           | 18             | No                            |
| 18           | 30             | No                            |
| 19           | 15             | Yes                           |
| 19           | 18             | Yes                           |
| 19           | 30             | No                            |

Out of the 9 possible combinations, there are 4 that satisfy the condition, namely when Tamika gets a sum of 17, 18 (twice), or 19 and Carlos gets a product of 15 or 18. Therefore, the probability that Tamika's result is greater than Carlos' result is $\boxed{\frac{4}{9}}$.

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There are 135,135 different ways to assign grades in the graduate class under the given conditions.

We'll need to use the concept of combinations.

A combination is a selection of items from a larger set, such that the order of the items doesn't matter.

In this case, we want to find the number of ways to assign 8 A's, 5 B's, and 2 C's to a class of 15 students.
To do this, we can use the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)
Where C(n, r) represents the number of combinations of choosing r items from a set of n items, n! is the factorial of n (n*(n-1)*(n-2)...*1), and r! is the factorial of r.
First, assign the A's:

We have 15 students and need to choose 8 to give A's to.

Use the combination formula:
C(15, 8) = 15! / (8! * 7!) = 6435.
Now, 7 students remain, and you need to choose 5 to give B's to:
C(7, 5) = 7! / (5! * 2!) = 21
Finally, the remaining 2 students will receive C's, so there's only one way to assign C's:
C(2, 2) = 2! / (2! * 0!) = 1
Since we want the number of ways to assign all grades simultaneously, multiply the number of combinations for each grade:
Total combinations = 6435 * 21 * 1 = 135,135.

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The probability that a randomly selected dinner bill will be at least $39.10 is approximately 0.0322.

a. The random variable in this case is the amount of money spent on dinner bills in the local restaurant on a daily basis.

b. To find the probability that a randomly selected bill will be at least $39.10 To do this, we can use the formula  z = (x - μ) / σ

Where

Substituting the values, we get:

z = (39.10 - 28) / 6

z = 1.85

We need to find the probability of getting a z-score of 1.85

The probability can be determined by using a conventional normal distribution table and is as follows:

P(z > 1.85) = 1 - P(z < 1.85) = 1 - 0.9678 = 0.0322

Therefore, the probability that a randomly selected dinner bill will be at least $39.10 is approximately 0.0322.

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Answer:

Height of Bigfoot 5 = Height of Bigfoot 2 + 4.9

Substituting the expressions we derived earlier, we get:

(x + 4.9) = x + 4.9

Simplifying the equation, we see that x cancels out on both sides, leaving us with:

4.9 = 4.9

This equation is true for any value of x, which means that we cannot determine the height of Bigfoot 2 from this information alone.

Therefore, we need additional information or data to solve for the value of x and determine the height of Bigfoot 2.

The vertex of the  parabola is (1, -1), x = 1 as the equation of the axis of symmetry and the roots of the parabola are x = 0 and x = -2

The graph represents the given parabola

As a general rule:

The vertex of a parabola is the minimum or the maximum of a quadratic funtion

In this case, we have

Minimum = (1, -1)

This means that the vertex of the given parabola is (1, -1)

The equation of the axis of symmetry is the x-coordinate of the vertex

In this case, we have

x = 1 as the equation of the axis of symmetry

These are the points where the graph crosse the x-axis

In this case, the roots of the parabola are x = 0 and x = -2

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The calculated values of the first four terms of the sequence are -4, -2, 2 and 10

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

a1 = -4

an = 2a(n - 1) + 6

Using the above as a guide, we have the following equations

a(2) = 2a1 + 6

a3 = 2a2 + 6

a4 = 2a3 + 6

Substitute the known values in the above equation, so, we have the following representation

a2 = 2 * -4 + 6 = -2

a3 = 2 * -2 + 6 = 2

a4 = 2 * 2 + 6 = 10

Hence, the first four terms of the sequence are -4, -2, 2 and 10

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Answer:

4c² - 17c + 32

Step-by-step explanation:

To expand (c -2)², use the identity (a - b)² = a² - 2ab + b²

(c - 2)² = c² - 2*c*2 + 2²

            = c² - 4c + 4

Use FOIL method to find (3c + 1)(c -4)

(3c  + 1)(c - 4) = 3c*c  - 3c *4 + 1*c - 1*4

                     = 3c² - 12c + 1c - 4

                      = 3c² - 11c  - 4  {Combine like terms}

7(c - 2)² - (3c + 1)(c -4) = 7*(c²- 4c + 4) - (3c² - 11c - 4)

Multiply each term of c² - 4c + 4 by 7 and each term of 3c² - 11c - 4 by (-1)

                                    = 7c² - 7* 4c + 7*4  - 3c² + 11c + 4

                                     = 7c² - 28c + 28 - 3c² + 11c + 4

                                     = 7c² - 3c² - 28c + 11c + 28 + 4

 Combine like terms,

                                     = 4c² - 17c + 32

Thus, the rate at which the boy's shadow is lengthening when he is 20 feet from the light is 3.75 feet/s.

To solve this problem, we need to use similar triangles.

Let's call the length of the boy's shadow "x" and the distance from the streetlight to the boy "y". At the moment he is 20 feet from the light, we have:

y = 20 feet (given)
x + 6 = length of the boy's shadow

We can set up a proportion to relate the length of the boy's shadow to the height of the streetlight:

(x + 6)/x = 15/6

Cross-multiplying and simplifying, we get:

6x + 90 = 15x
9x = 90
x = 10 feet

So at the moment the boy is 20 feet from the light, his shadow is 10 feet long. To find the rate at which his shadow is lengthening, we need to take the derivative of this equation with respect to time:
x + 6 = (y - 15)/y * (y') + 6

where y' is the rate at which the boy is walking away from the light (5 feet/s). Plugging in y = 20 feet and solving for x', we get:
x' = (15/20) * 5 = 3.75 feet/s

Therefore, the rate at which the boy's shadow is lengthening when he is 20 feet from the light is 3.75 feet/s.

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Once a model of reality is constructed around certain assumptions, it can be tested to determine its value in predicting outcomes.

Once a model of reality is constructed around certain assumptions, it can be tested to determine its value in predicting outcomes. This involves comparing the model's predictions with actual observed data or outcomes to assess its accuracy and reliability. By testing the model against real-world data, we can evaluate its validity and determine if it accurately represents the underlying reality or phenomenon being studied.

Producing data and graphing equations are related activities that can be part of the process of testing a model, but they are not the primary purpose of the model itself. Producing data involves collecting and generating empirical data that can be used to assess the model's predictions or outcomes. Graphing equations can be a way to visualize the relationships between variables in the model, but it is not the main purpose of the model itself. The primary purpose of constructing a model is to make predictions or generate hypotheses about how a system or phenomenon works, and testing these predictions against real-world outcomes is the key step in evaluating the model's value.

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Answer:

A

Step-by-step explanation:

the answer is A. because the direction of arow is left. and at point 8, the point is hollow.

Answer: hi i am not sure what questions you need but look below.

1. D. The temperature dropped 4 degrees each hour for 5 consecutive days.

2. Brenda simplified the expression correctly.

Step-by-step explanation:

1. the equation is -4(5)=-20.

- means that the number is decreasing or below zero. so If the temp. dropped 4 degrees each hour for 5 days then the expression for that would be -4(5)=-20

2. Brenda is correct because -5x+(2+x)= -5+x+2

You must break the expression up. -5x +x and -5x + 2. Sine -5x+x= -4x and you cant simplify -5x+2 because they dont have the same variable, your answer is -4x+2.

You are welcome

Since the output of the sigmoid function is 0.64, the predicted probability of the observation being malignant is 0.64. We need to set a threshold probability to classify the observation as malignant or benign.

If we set the threshold probability at 0.5, the observation would be classified as malignant, since the predicted probability (0.64) is greater than the threshold probability. However, the choice of threshold probability depends on the specific problem and the costs associated with false positives and false negatives. So, the predicted category would be malignant if the threshold probability is set at 0.5.

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Thus, the length of a side of the regular hexagon is 8 centimeters using the Pythagorean theorem.

The key to solving this problem is to realize that the perpendiculars drawn from the interior point to the sides of the hexagon form a right triangle with one leg being the perpendicular and the other leg being a side of the hexagon. We also know that the hexagon is regular, meaning all sides have the same length.

Let's label the length of the side of the hexagon as "x". We can use the Pythagorean theorem to find the length of each perpendicular as follows:

- For the perpendicular that is 4 cm long, we have x^2 = 4^2 + (x/2)^2
- For the perpendicular that is 5 cm long, we have x^2 = 5^2 + (x/2)^2
- For the perpendicular that is 6 cm long, we have x^2 = 6^2 + (x/2)^2
- For the perpendicular that is 8 cm long, we have x^2 = 8^2 + (x/2)^2
- For the perpendicular that is 9 cm long, we have x^2 = 9^2 + (x/2)^2
- For the perpendicular that is 10 cm long, we have x^2 = 10^2 + (x/2)^2

Simplifying each equation and using a bit of algebra, we get:

- 3x^2 = 16^2
- 7x^2 = 25^2
- 12x^2 = 36^2
- 24x^2 = 64^2
- 33x^2 = 81^2
- 40x^2 = 100^2

Solving for x in each equation, we find that x = 8 cm. Therefore, the length of a side of the regular hexagon is 8 centimeters.

In summary, we used the fact that the perpendiculars from an interior point to the sides of a regular hexagon form right triangles to set up equations using the Pythagorean theorem. Solving for the length of a side of the hexagon in each equation, we found that it is 8 cm long.

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Mo's conjecture that a pentagon cannot contain 4 right angles is correct.

A pentagon is a five-sided polygon. In order for a polygon to contain a right angle, it must have at least one interior angle measuring 90 degrees.

The sum of the interior angles of a pentagon is given by the formula (n-2) x 180 degrees, where n is the number of sides. For a pentagon, this formula gives us (5-2) x 180 = 540 degrees.

In order for a pentagon to contain four right angles, the sum of the interior angles that are right angles would have to be 4 x 90 = 360 degrees. However, this is impossible because the remaining interior angles would have to add up to 540 - 360 = 180 degrees.

Since a pentagon only has five interior angles, it is not possible for three of them to add up to 180 degrees, which means it is impossible for a pentagon to contain four right angles.

Therefore, Mo's conjecture that a pentagon cannot contain 4 right angles is correct.

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(a) Without more information, we cannot determine the initial number of insects. (b) The differential equation satisfied by P(t) is: dP/dt = kP, where k is the growth rate of the insect population.

(c) To find the time it takes for the population to double, we can use the formula:

2P(0) = P(0)e^(kt)

where P(0) is the initial population size. Solving for t, we get:

t = ln(2)/k

(d) Without more information, we cannot determine the time at which the population will equal a certain value.
Hi! To answer your question, I need the specific function P(t). However, I can provide you with a general framework to answer each part of your question once you have the function.

(a) To find the initial number of insects, evaluate P(t) at t=0:
P(0) = [Insert the function with t=0]

(b) To find the differential equation satisfied by P(t), differentiate P(t) with respect to t:
dP(t)/dt = [Insert the derivative of the function]

(c) To find the time at which the population doubles, first determine the initial population, P(0), then solve for t when P(t) is twice that value:
2*P(0) = P(t)
Solve for t: [Insert the solution for t]

(d) To find the time at which the population equals a specific value (let's call it N), set P(t) equal to N and solve for t:
N = P(t)
Solve for t: [Insert the solution for t]

Once you have the specific function P(t), you can follow these steps to find the answers to each part of your question.

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Answer:

the second option

Step-by-step explanation:

because that is supposed to be the median of the data

The half-life of the substance is approximately 17.78 days.

The exponential decay model for the mass of the substance can be written as:

[tex]m(t) = m0 \times e^{(-rt)},[/tex]

where m0 is the initial mass, r is the decay rate parameter (as a decimal), and t is time in days.

If we want to find the half-life of the substance, we need to find the value of t when the mass has decreased to half of its original value (m0/2). In other words, we need to solve the equation:

m(t) = m0/2

[tex]m0 \times e^{(-rt)} = m0/2[/tex]

[tex]e^{(-rt) }= 1/2[/tex]

Taking the natural logarithm of both sides, we get:

-ln(2) = -rt

t = (-ln(2)) / r

Substituting the value of r (0.039), we get:

t = (-ln(2)) / 0.039

t ≈ 17.78 days

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In the marketing class of 50 students who evaluated their instructor using the given scale, the descriptive summary of the survey results indicated that the majority of students rated the instructor as either average or poor, with 45% in each category.

This suggests that the instructor's performance might not have been highly effective or satisfactory for most of the students. Meanwhile, a small percentage of students found the instructor to be good (8%) and even fewer rated them as superior (2%). No students rated the instructor as inferior.

Based on these findings, the conclusion can be drawn that the instructor's performance was perceived as predominantly average or poor by the class, indicating potential areas for improvement in their teaching approach or methods to better cater to students' needs and expectations.

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The probability is 28/45, which simplifies to 0.6222 or approximately 62.22%.

To calculate the probability of both light bulbs being good, we'll use the terms:

sample space, favorable outcomes, and probability.
Sample space:

This is the total number of possible outcomes when selecting two light bulbs.

Since there are 10 light bulbs in the drawer, the sample space is the number of ways to choose 2 light bulbs from 10, which can be calculated using combinations.

So, the sample space is C(10,2) = 10! / (2! * (10-2)!) = 45 possible outcomes.
Favorable outcomes:

These are the outcomes where both light bulbs are good.

There are 8 good light bulbs in the drawer,

so the number of favorable outcomes is the number of ways to choose 2 good light bulbs from the 8, which is C(8,2) = 8! / (2! * (8-2)!) = 28 favorable outcomes.
Probability: To find the probability of both light bulbs being good, divide the number of favorable outcomes by the sample space.

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(G) (-9, 12) is the point on the given line.

We can use the point-slope form of the equation of a line to find the equation of the line with slope -1/3 and passing through the point (6, 7):

y - y' = m(x - x'), where m is the slope, and (x', y') is the given point.

Plugging in m = -1/3, x' = 6, and y' = 7, we get:

y - 7 = (-1/3)(x - 6)

Multiplying both sides by -3, we get:

-3y + 21 = x - 6

x + 3y = 27

This is the equation of the line.

To find another point on this line, we can substitute each of the given points into the equation and see which one satisfies it. We can also check the answer choices one by one. Let's start with (F) (-3, 8):

x + 3y = 27

-3 + 3(8) = 21, so this point does not satisfy the equation and is not on the line.

Next, let's try (G) (-9, 12):

x + 3y = 27

-9 + 3(12) = 27, so this point does satisfy the equation and is on the line.

We can stop here and conclude that the answer is (G) (-9, 12). However, just for completeness, let's also check the other answer choices:

(H) (12, 13):

x + 3y = 27

12 + 3(13) = 51, so this point does not satisfy the equation and is not on the line.

(J) (18, -3):

x + 3y = 27

18 + 3(-3) = 9, so this point does not satisfy the equation and is not on the line.

Therefore, the answer is (G) (-9, 12).

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∈Answer:

x ≥ 7/2

Step-by-step explanation:

-2x + 7 ≤ 0

(-2x + 7) + (-7) ≤ -7

-2x + 7 - 7 ≤ -7

-2x ≤ -7

2x/2 ≥ 7/2

x ≥ 7/2

x ∈ [7/2,∞)

To change the subject you need to isolate the variable, for example the first two equations solved for t are:

Let's look at the first equations:

at² = b

We can change the subject to t. To do so, we just need to isolate the variable t in one of the sides.

if we divide both sides by a we will get:

t² = b/a

Now apply the square root in both sides:

t = √b/a

For the second equation:

t² + m = n

Now subtract m in both sides:

t² = n - m

Now again, apply the square root in both sides:

t = √(n - m)

And so on, that is how you can change the subject.

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On flipping a coin, the number of total possibility for obtaining least one head if we flip the coin seven times are equal to 127.

We have an experiment for flip a coin and keep a record of the results.

Number of total possible outcomes on flipping a coin = 2 = { H, T}

Number of trials or a coin is flipped = 7

We have to determine the number of ways that at least one head if we flip the coin seven times. When we flip a two-sided coin n times, there are [tex]2^ n[/tex] possible outcomes. So, when a coin is flipped 7 times then total possible number of outcomes = 2⁷ = 128

Let's consider an Event A : getting at least one head in seven flips

Complement of this event is getting no head and it is denoted by [tex]A^ c =[/tex]{ T T T T T T T }

and this event will be occur in one way only. So, Number of ways of obtain at least one head if you flip the coin five times = 128 - 1 = 127 ways.

Hence, required value is 127 ways.

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Answer:

20fish

Step-by-step explanation:

so 1/2 of 16 is 8

or 1/4 of 32 is 8

so 8+32=40

40 1/2 is 20

so 20 fish caught on Monday

The space would cost at, $833.34 per month.

:: Total area = 1000 square feet

:: Cost per feet per year = $10

Therefore,

Total cost per year would be, equal to the product of total area and cost per unit area per year.

That is,

Total cost per year = 1000 x $10

That is, $10,000.

Now, we know, there are 12 months in an year.

So, cost per month is, ( total cost per year / 12 )

That is, therefore,

Cost per month = ($10,000 / 12)

Which equals to, $833.34 per month. (rounded off)

So,

The space cost at, $833.34 per month.

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The space cost you $833.33. per MONTH

To calculate the monthly cost, we first need to determine the annual cost of the space.

Given that the cost is $10 per square foot per year, we know, there are 12 months in an year and the space is 1,000 square feet, the annual cost of the space would be:

Annual cost = the space  * cost

Annual cost = 1,000 square feet * $10/square foot = $10,000

To convert this to monthly cost, we divide the annual cost by 12 (the number of months in a year):

Monthly cost = $10,000 / 12 = $833.33

Therefore, the monthly cost of the 1,000 square feet of space in the new building would be $833.33.

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The probability that Max will get the job is 3/10 or 0.3.

To see why, we can use the fact that the sum of the probabilities of all possible outcomes is equal to 1. Let A, B, and C represent the events that the first, second, and third companies respectively get the job.

Then the probability that Max gets the job is equal to the probability of event AB~C (i.e., none of the other companies gets the job).

The probability of A is 1/5, the probability of B is 1/2, and the probability of C is 3/10 (since the sum of the probabilities of all three events is 1). Using the formula for the probability of the intersection of independent events, we have:

P(AB~C) = P(~A) * P(~B) * P(~C) = (4/5) * (1/2) * (7/10) = 14/50 = 0.28

So the probability that Max gets the job is 0.3, or 3/10.

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The perimeter of the triangle is 23 ft.

We have,

We can use the triangle inequality theorem to check whether this triangle can exist.

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check whether this condition holds for the sides given:

5 + 7 = 12, which is greater than 11, so the condition holds.

5 + 11 = 16, which is greater than 7, so the condition holds.

7 + 11 = 18, which is greater than 5, so the condition holds.

Therefore, this triangle can exist.

To find the perimeter of the triangle, we simply add up the lengths of the three sides:

Perimeter = 5 + 7 + 11 = 23 ft

Therefore,

The perimeter of the triangle is 23 ft.

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The triangle inequality theorem states that a triangle with sides of 5, 7, and 11 feet is feasible.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Any two triangle sides' lengths added together must be bigger than the third side's length.

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The probability that exactly 20 random numbers will fall in the interval 0.1 to 0.35 is approximately 0.0223, or 2.23%.

To solve this problem, we need to use the binomial probability formula:
[tex]P(X = k) = (n choose k)  p^k  ( (1 - p)^{n-k}[/tex]

where:
- X is the random variable representing the number of successes (random numbers in the interval 0.1 to 0.35)
- k is the number of successes we want (exactly 20)
- n is the total number of trials (100)
- p is the probability of success (the probability that a randomly generated number falls in the interval 0.1 to 0.35)

To find p, we need to determine the fraction of the interval 0 to 1 that is between 0.1 and 0.35:
[tex]p = (0.35 - 0.1) / 1 = 0.25\\p = \frac{0.35-0.1}{1} = 0.25[/tex]

Now we can plug in the values and calculate the probability:

[tex]P(X = 20) = (100 choose 20) (0.25)^{20}   (1-0.25)^{100-20}[/tex]
= 0.0223

Therefore, the probability that exactly 20 random numbers will fall in the interval 0.1 to 0.35 is approximately 0.0223, or 2.23%.

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The horizontal distance along the grid line from the highest grid elevation point to the 97 contour is 52.38 feet.

To solve this problem, we first need to determine the location of the highest grid elevation point on the grid line labeled 96.33 and 97.48.

Let's assume that the highest grid elevation point is located at a distance of x feet from the grid line labeled 96.33. Therefore, the distance from the same point to the grid line labeled 97.48 would be 50 - x feet (as the total length of the grid line is 50 feet).

Now, we need to determine the location of the 97 contour on the same grid line. Let's assume that the 97 contour intersects the grid line at a distance of y feet from the grid line labeled 96.33.

Since the highest grid elevation point is on the same grid line, it must also be on the 97 contour. Therefore, we can set the elevation at the highest point equal to 97 and use this information to solve for x and y.

We can set up two equations based on the information we have:

x² + y² = d² (Equation 1)

x + (50 - x) = y (Equation 2)

where d is the horizontal distance we are trying to find.

We can simplify Equation 2 to:

50 = y

Substituting this into Equation 1, we get:

x² + 50² = d²

Rearranging this equation, we get:

d² = x² + 2500

Now we can substitute 97 for the elevation at the highest point, and solve for x:

(97 - 96.33)/0.01 = x/50

x = 33.5 feet

Substituting this value of x into the equation for d², we get:

d² = (33.5)² + 2500 = 2742.25

Taking the square root of both sides, we get:

d = 52.38 feet (approx.)

Therefore, the horizontal distance along the grid line from the highest grid elevation point to the 97 contour is approximately 52.38 feet.

Learn more about grid line at https://brainly.com/question/28272514

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