what conditions does the function f(x) have to meet in order to be able to use the integral test to verify convergence or divergence?

The lowest score a student could have received and still have passed the quiz with a normally distributed class is 55.

This is because the upper 35% of a normally distributed class corresponds to a score of 1.5 standard deviations above the mean. Since the mean was 70 and the standard deviation was 10, that would mean the lowest score a student could have received and still have passed the quiz is 70 + (1.5 * 10) = 70 + 15 = 55.

In summary,
1. Start with the mean of the quiz which is 70.
2. Add 1.5 standard deviations which is 1.5 * 10 = 15.
3. The result is the lowest score a student could have received and still have passed the quiz which is 70 + 15 = 55.

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Plug the corresponding R(s) for each input type and the transfer functions of the given systems into the equations above to find yss and ess for each case. Keep in mind that some systems might not have a finite steady-state response or error for specific input types, depending on the system's type (order and poles).

To determine the steady-state response (yss) and steady-state error (ess) values for the given systems, we need to use their transfer functions and input types (unit step, unit ramp, and unit parabolic). Unfortunately, without information about the specific transfer functions for figures 5.74 a, b, 5.75, and 5.76, it is not possible to provide a definitive answer.

In general, for a system with transfer function G(s), you can calculate the steady-state response and error using the Final Value Theorem:

yss = lim (s -> 0) s * Y(s), where Y(s) = G(s) * R(s) is the system's output.
ess = lim (s -> 0) s * E(s), where E(s) = R(s) - Y(s) is the system's error.

For different input types:
- Unit step input: R(s) = 1/s
- Unit ramp input: R(s) = 1/s^2
- Unit parabolic input: R(s) = 1/s^3

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The total interest earned on a savings bond over 24 quarters with a principal investment of $37,000 and an interest rate of 1.125% per quarter, the savings bond has earned a total interest of $9,990.

The savings bond earns 1.125%/quarter, so its quarterly interest rate is 0.01125. The amount of interest earned in one quarter is the product of the interest rate and the principal amount, which is:

To calculate the interest earned in one quarter, we multiply the principal amount by the interest rate expressed as a decimal.

Interest earned in one quarter = 0.01125 x $37,000 = $416.25

In this case, the interest earned in one quarter is $416.25.

To find the total interest earned over 24 quarters, we multiply the interest earned in one quarter by the number of quarters, which is 24.

After 24 quarters, the total interest earned is:

Total interest earned = 24 x $416.25 = $9,990

Therefore, the savings bond has earned a total interest of $9,990 after 24 quarters.

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Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis. The pre-point image's (-3, 5) is mirrored to the image's point (3, 5).

The x-axis is the horizontal axis and the y-axis is the vertical axis in two-dimensional space. As seen in the image below, they are represented by two number lines that perpendicularly connect at (0, 0).

This is a reflection of the pre-image that was provided over the y-axis:

Segment

10 9 8 7 6 5 -5 -6 -7 -8 -9 -10

Because the point (-5, 3) in the pre-image and its corresponding position (5, 3) in the picture are both at the same distance from the y-axis, they are reflected to one another.

Similar to this, the pre-point image's (-3, 5) is reflected to the image's point (3, 5).

The x-coordinates of all other locations in the pre-image are negated in the image because they have corresponding points there that are equally spaced from the y-axis.

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The value of x is 5

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. All diameters are chord and but all chords are not diameter.

Since the value of the chords are thesame, the arc length RS and PQ are thesame.

Therefore ;

x+17 = 4x+2

collect like terms

4x -x = 17-2

3x = 15

divide both sides by 3

x = 15/3

x = 5

therefore the value of x is 5

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If the length of the garden is 4 meters and 52 meters of fencing is required to completely enclose it, the width of the garden is 22 meters.

To find the width of the garden, we need to use the formula for the perimeter of a rectangle, which is:

P = 2l + 2w

Where:

P = perimeter of the rectangle

l = length of the rectangle

w = width of the rectangle

We know that the length of the garden is 4 meters and the perimeter is 52 meters, so we can plug in the values and solve for the width:

52 = 2(4) + 2w

52 = 8 + 2w

44 = 2w

w = 22

To verify our answer, we can check if the perimeter using this width is indeed 52 meters:

P = 2l + 2w = 2(4) + 2(22) = 8 + 44 = 52

As expected, the perimeter is 52 meters. This means that if we fence in the garden with a width of 22 meters and a length of 4 meters, we will require 52 meters of fencing to completely enclose it.

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The equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

Given,

x+2y=2

y = 1 - [tex]\frac{x}{2}[/tex]

Slope = -1/2 = [tex]m_{1}[/tex]

Let Slope of line perpendicular to line x+2y=2 is [tex]m_{2}[/tex]

⇒  [tex]m_{1}[/tex] *    [tex]m_{2}[/tex] = -1

Then [tex]m_{2}[/tex] = 1/2

Equation of line perpendicular is given by

[tex]y = \frac{1}{2}x + c[/tex]

Since it contains point (5,6)

6 = [tex]\frac{1}{2} (5) + c[/tex]

c= [tex]\frac{7}{2}[/tex]

Then the equation of line is:

[tex]y = \frac{1}{2}x+ \frac{7}{2}[/tex].

Therefore, the equation of the line perpendicular to the line QR in slope intercept is y= [tex]\frac{1}{2}x+\frac{7}{2}[/tex].

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Answer:

Step-by-step explanation:

There are four numbers in the sample space that are less than 4: -3, -2, -1, and 0. Of these, three are less than 2: -3, -2, and -1. Therefore, the probability P(the number is less than 2 | the number is less than 4) is 3/4.

To evaluate 4!, we perform the multiplication 4 x 3 x 2 x 1, which equals 24.

To evaluate 6!, we perform the multiplication 6 x 5 x 4 x 3 x 2 x 1, which equals 720.

To evaluate 5!/3!, we first calculate 5! (which is equal to 5 x 4 x 3 x 2 x 1, or 120) and then divide by 3! (which is equal to 3 x 2 x 1, or 6). Therefore, 5!/3! = 120/6 = 20.

The correct inference procedure for the ecologists to use is A. A one-sample t-interval for a sample mean.

This is because they are trying to estimate the average number of eggs per nest for all robins in the region, so they will need to use a one-sample t-interval for a sample mean to draw inferences about the population.

Ecologists will choose a random sample of nesting robins in a certain region to estimate the average number of eggs per nest for all robins in the region. The correct inference procedure for the ecologists to use is A. A one-sample t-interval for a sample mean.

What is a t-interval for a sample mean?A t-interval for a sample mean is a type of confidence interval that estimates the unknown population parameter, μ, based on the data in a random sample. The t-distribution is used to estimate the population parameter because the population standard deviation is not known.

The following is an illustration of the method of calculating a confidence interval for the mean using a t-distribution:If a sample of n observations is drawn from a normal population, the mean x of the sample is normally distributed with the following properties:Mean: μx = μ.Standard deviation: σx = σ/√n.

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The distance from the tower to the ground anchor is approximately 2091.36 meters.

We can use trigonometry to solve this problem. Let's call the distance from the tower to the ground anchor "x". We can draw a right triangle with the tower as the vertical side, the guy wire as the hypotenuse, and the distance we're trying to find as the horizontal side.

The angle between the tower and the guy wire is 15 degrees, so the angle between the guy wire and the horizontal is 90 - 15 = 75 degrees.

Using the trigonometric function tangent, we can set up the following equation

tan(75) = x / 500

We can solve for x by multiplying both sides by 500 and taking the tangent of 75 degrees

x = 500 × tan(75)

x ≈ 2091.36 meters

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Answer:

$510,000

Step-by-step explanation:

Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.

Remember, 4 or less, round down. 5 or more, round up.

Since the hundreds digit is 4, we do not need to round.

We only need to change the rest of the digits to 0.

So, our answer would be $510,000.

Kathy's speed is 2 mph and Dennis's speed is 2+8 = 10 mph.

Let's assume that Kathy's speed is "x" mph. Since Dennis rides 8 mph faster than Kathy, his speed is "x+8" mph.

We know that Kathy can run 2 miles to the beach in the same amount of time Dennis can ride his bike 10 miles to work. Therefore, we can use the formula:

time = distance/speed

For Kathy: time = 2 miles / x mph

For Dennis: time = 10 miles / (x+8) mph

Since they both take the same amount of time, we can set these two equations equal to each other:

2 / x = 10 / (x+8)

We can then solve for "x" as follows:

2(x+8) = 10x

2x + 16 = 10x

16 = 8x

x = 2 mph

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The total cost for the trip reserved under Santos albert's name is $1,500 (option c).

In Excel, we can use the SUM function to add up a range of numbers. To do this, we first need to select the range of cells containing the costs associated with Santos Albert's reservation. In this case, the costs are located in columns C through G for the row corresponding to Santos Albert.

Once we have selected the range of cells containing the costs, we can use the SUM function to add them up. The formula for this would be "=SUM(C5:G5)", where C5 is the first cell in the range and G5 is the last cell in the range. This formula will add up all of the costs in the range and give us the total cost for Santos Albert's reservation.

So, to answer the question, the total cost for the trip reserved under Santos Albert's name is $1500.

Hence the correct option is (c).

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Step-by-step explanation:

A is not proportional

Use the graph to record the value of y axis when x is 1, 2, 3, 4, 5, 6

And record the values of x when y is 1, 2, 3, 4, 5, 6 till the end

Using the graph Value of y

(1, 0.9) (2,1.5) (3,2.2) (4,2.5) (5, 3) (6,4) (7, 5) (10,6)

Using the graph, find the value of x when y is 1 - 10)

1.2, 2.5, 5,.....

The slope of the graph also shows that it is not proportional

B is proportional

X is 0 and y is 0

When x is 5, y is 10

Ratio x: y = 5:10 = 1:2

When x is 10, y is 20

Ratio x:y is 10: 20 = 1:2 same as above

C is not proportional

When Moyra is 32, daughter is 8

When her daughter is 22, Moyra will also be 4years older, which is 36

32: 8 = 4:1

36: 12 =3:1

Step-by-step explanation:

For Part A, use the function f(x) to find the average of tests taken.

X is number of test taken

f(x) is the average score given said num of tests taken,x,

We want after test number 3 so using the function,

[tex]f(x) = 0.2x + 79[/tex]

Plug in. 3 for x, and we will get our answer.

[tex]f(3) = 0.2(3) + 79 = 79.6[/tex]

Part B: Use the table for the answer.

When 2 test are taken, the average test score is

84

So part B is 84.

Part C:

[tex]f(2) = 0.2(2) + 79 = 79.4[/tex]

[tex]g(2) = 84[/tex]

Since

[tex]g(2) > f(2)[/tex]

The science class had a higher average after 2 tests

Answer:

you shoulda payed attention in class

Step-by-step explanation:

also u know it's bad when the test is so hard you can't even cheat on it

There are a total of 48 soccer games in the season.

Since there are 3 soccer games in a month, there will be 12 games in a season (3 games/month x 4 months). Since 8 games are played at night and assuming that all games are played either during the day or at night, we can calculate the number of games played during the day as:

Number of day games = Total number of games - Number of night games

= 12 games/month x 4 months - 8 night games/month x 4 months

= 48 games - 32 games

= 16 games

Therefore, the total number of games in the season is:

Total number of games = Number of day games + Number of night games

= 16 games + 32 games

= 48 games

So, there are 48 soccer games in the season.


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The intersection of two evens a and b is the event that both a and b occur that is option A is correct.

The intersection of two events A and B is defined as the event that occurs when both A and B occur simultaneously. It is denoted by A ∩ B, where the symbol ∩ represents intersection.

For example, if event A is "getting a head when flipping a coin" and event B is "rolling a 6 on a fair die", then the intersection of A and B would be the event "getting a head when flipping a coin and rolling a 6 on a fair die".

For example, suppose A represents the event "rolling an even number on a dice" and B represents the event "rolling a number greater than 3 on a dice". The intersection of A and B is the event that "rolling a number that is both even and greater than 3 on a dice", which consists of the outcomes {4, 6}.

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Complete Question:

the intersection of two events a and b is the event that:

a) both a and b occur.

b) the union of ac and bc occurs.

c) the union of a and b does not occur.

d) either a or b or both occur.

e) either a or b, but not both.

f) none of the above.

The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).

For option 1: intersection point (1,1)

substitute the values of x & y in the given equation.

1 = 3 (1) - 2

1 = 1

LHS = RHS

For option 2: point (1,1)

substitute the values of x & y in the given equation.

1 = 2 (1) + 3

1 = 5

LHS ≠ RHS

For option 3: point (1,1)

substitute the values of x & y in the given equation.

1 = -2 (1) + 3

1 = 1

LHS = RHS

For option 4: point (1,1)

substitute the values of x & y in the given equation.

1 = - [tex]\frac{1}{2}[/tex] (1) + 3

1 = [tex]\frac{5}{2}[/tex]

LHS ≠ RHS

For option 5: point (1,1)

substitute the values of x & y in the given equation.

1 = - [tex]\frac{1}{3}[/tex] (1) + 3

1 = [tex]\frac{8}{9}[/tex]

LHS ≠ RHS

Therefore, correct option for the given graph is option 1 and option 3.

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Answer:

a) a is 13

b is 14

c is 5

b) a is 5

b is 13

c is-10

c) a is 1

b is 0

c is -4

d) a is -9

b is 0

c is 0

Step-by-step explanation:

hope this will be helpful:)

Boys are taller than girls on average, with a larger center of data and larger range in height;

the dot plots are not shown.

Answer:

8, 8.001, 8.01, 8.1, 9, 11, 13, 16

Step-by-step explanation:

From the instructions given, we know that variable u [tex]\geq[/tex] 8. the  [tex]\geq[/tex]  sign means that the number is greater than or is equal to the number, which is in this case, 8. In the numbers given, (0, 7, 7.999, 8.01, 11, 3, 7.9, 8, 8.1, 13, 5, 7.99, 8.001, 9, 16) we name the numbers greater than or equal to 8 that are stated in the list.

The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37%.

The probability that a haphazardly chosen vagrant pet in a creature covered in Austin is a canine is 11.71%.

The probability that a haphazardly chosen stranded canine in a similar creature cover in Austin is a Chihuahua is 29.37% .

2.76% + 2.86% + 3.44% + 2.65% = 11.71%

11.71/3.44 = .2937

.2937 = 29.37%

Probability is just the way that logical something is to occur.

Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions represented by probability is called statistics.

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From the given information provided, the first 5 nonzero terms of the power series are 1.5 + 13.5x + 60.75x² + 183.375x³ + 1018.1595x⁴.

To find the power series for the given indefinite integral, we can first find the antiderivative of the integrand using substitution. Let u = 9x, du = 9dx, then:

∫(e⁹ˣ - 1) / 6x dx = (1/6) ∫([tex]e^u[/tex] - 1) / u du

We can then expand the integrand into a power series using the Maclaurin series for [tex]e^u[/tex] and ln(1+u):

(1/6) ∫([tex]e^u[/tex] - 1) / u du = (1/6) ∫[Σ(uⁿ/n!) - Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1))] du

= (1/6) [Σ(uⁿ/n! × du) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × du)]

= (1/6) [Σ(uⁿ/n! × 9dx) + Σ(-1)ⁿ(u⁽ⁿ⁺¹⁾/(n+1) × 9dx)]

= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺⁾ xⁿ / (n+1))

We can now simplify and group terms to obtain the power series centered at x=0:

(3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) - (1/6) Σ(-1)ⁿ (9⁽ⁿ⁺¹⁾ xⁿ / (n+1))

= (3/2) Σ(9ⁿ x⁽ⁿ⁻¹⁾ / n!) + (1/6) Σ((-1)ⁿ × (-9)⁽ⁿ⁺¹⁾ × xⁿ / (n+1))

To find the first 5 nonzero terms, we can plug in n=0 through n=4 and evaluate each term:

n=0: (3/2) × 1 = 1.5

n=1: (3/2) × 9x = 13.5x

n=2: (3/2) × 81x² / 2 - (1/6) × 81x² / 3 = 60.75x²

n=3: (3/2) × 729x³ / 6 + (1/6) × 729x³ / 4 = 183.375x³

n=4: (3/2) * 6561x⁴ / 24 - (1/6) * 6561x⁴ / 5 = 1018.1595x⁴

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Answer:

To summarize the typical daily revenue of the food truck now, we would use the new mean of the daily revenue, which takes into account the new sale of $7,100. We can add this new value to the previous sum of daily revenues and divide the total by the number of days to find the new mean:

New mean = (total sum of daily revenues + $7,100) / (number of days + 1)

This would give us the updated measure of center that reflects the new data point.

The mean daily revenue of the food truck now is $6,550.

The average is calculated as the product of all values divided by all possible values. It can also be described as mean. The mean in statistics is the average value for the particular sample or collection of data. It is determined by dividing the sum of the total number of observations by the total number of observations.

To summarize the typical daily revenue of the food truck now, we would use the mean as the measure of the center.

We can calculate the mean daily revenue by adding the daily revenues from the two days ($6,000 + $7,100 = $13,100) and dividing by the number of days (2).

Mean daily revenue = (Total revenue) / (Number of days) = $13,100 / 2 = $6,550

Therefore, the mean daily revenue of the food truck now is $6,550.

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As per integration, the height of the water in the barrel at time = 2 hours is 1.672 feet (option C).

The formula is r(t) = 47-15, where t is the time in hours since the rain began. This formula tells us how fast the water level is changing at any given time t.

In this case, we're asked to find the height of the water in the barrel at t = 2 hours, given that the height at t = 1 hour is 0.75 feet. To solve this problem, we'll integrate the rate formula from t = 1 to t = 2, and add the starting height of 0.75 feet.

∫(47-15)dt from t=1 to t=2 = [47t-15t] from t=1 to t=2 = 0.922

So the total increase in height from t=1 to t=2 is 0.922 feet. Adding this to the starting height of 0.75 feet, we get the height of the water at t=2:

0.75 + 0.922 = 1.672 feet

Therefore, the correct option is (C).

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The probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.

The 10-sided die has 10 faces, each marked with a unique number from 1 to 10. When we talk about the probability of rolling a particular number, we're asking what the chances are of that number coming up when the die is rolled.

In this case, the question asks for the probability of rolling a number 10 or less, which means we're interested in the probability of rolling any number from 1 to 10. Since all the possible outcomes are numbers from 1 to 10, the probability of rolling a number 10 or less is certain, or 1.

This is because the sum of probabilities of all possible outcomes of an experiment is always 1.

Similarly, the probability of rolling a number greater than 10 is impossible, or 0. This is because there are no possible outcomes greater than 10 on the 10-sided die. In general, the probability of an event that cannot occur is always 0.

So, the probability of rolling a number 10 or less is 1, and the probability of rolling a number greater than 10 is 0.

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The larger number if the difference of the numbers is 52 is 65.

A number is five times a smaller number. Let's find the larger number when their difference is 52.

Therefore,

let

x = smaller number

larger number = 5x

There difference is 52. Hence,

5x - x = 52

4x = 52

divide both sides of the equation by 4

x = 52 / 4

x = 13

Therefore,

larger number = 5(13) = 65

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The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2

A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:

ax^2 + bx + c = 0

If a quadratic function has only one root at 3, then it must be of the form:

f(x) = a(x - 3)^2

where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.

To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:

4 = a(0 - 3)^2

4 = 9a

a = 4/9

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The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]

A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.

A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:

[tex]ax^2+bx+c=0[/tex]

If the quadratic function has only one root at 3, it must have the following form:

[tex]f(x)=a(x-3)^2[/tex]

This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.

We know that f(0) = 4, so we can plug these numbers into the equation to get:

[tex]4=a(0-3)^2[/tex]

simplify the above equation

4 = 9a

The value is,

a = 4/9

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Vanessa's vertical climb rate is 0.2 feet per foot of horizontal distance. When she walks 65 feet horizontally up the hill and climbs an additional 25 feet, her total vertical climb will be 21 feet.

For every 40 feet of horizontal distance Vanessa walks, she climbs 8 feet vertically. So her vertical climb rate is 8/40 = 0.2 feet per foot of horizontal distance.

If she walks an additional 25 feet up the hill, her total horizontal distance traveled will be 40 + 25 = 65 feet.

Therefore, her total vertical climb will be 0.2 times her total horizontal distance:

8 + (0.2 * 65) = 8 + 13 = 21 feet

So, Vanessa will have climbed a total of 21 feet vertically after walking 65 feet horizontally up the hill.

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