Please, help me please

Thanks!!

Answer:

False

Step-by-step explanation:

No we can't find the square root of negative number.

Hope it helped you

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Por lo tanto, la altura del edificio es de 313.6 metros.

Por lo tanto, la velocidad con la que la piedra choca en el suelo es de 78.4 m/s.

Para determinar la altura del edificio y la velocidad de la piedra al chocar en el suelo, necesitamos utilizar las ecuaciones de la caída libre.

a) La altura del edificio se puede calcular utilizando la fórmula de la caída libre:

h = (1/2) * g * t^2

Donde h es la altura del edificio, g es la aceleración debido a la gravedad (aproximadamente 9.8 m/s^2) y t es el tiempo de caída (8 segundos).

Sustituyendo los valores conocidos en la fórmula, obtenemos:

h = (1/2) * 9.8 * (8^2)

h = 1/2 * 9.8 * 64

h = 313.6 metros

b) La velocidad con la que la piedra choca en el suelo se puede calcular utilizando la fórmula de la velocidad en caída libre:

v = g * t

Donde v es la velocidad, g es la aceleración debido a la gravedad (9.8 m/s^2) y t es el tiempo de caída (8 segundos).

Sustituyendo los valores conocidos en la fórmula, obtenemos:

v = 9.8 * 8

v = 78.4 m/s

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To approximate sin1 correct to four decimal places using the Maclaurin series, we need to determine the number of initial terms needed such that the absolute value of the error term is less than or equal to 0.0001.

The Maclaurin series for sinx is given by:

sin x = x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...

To find the error term, we can use the alternating series estimation theorem, which states that the error between the actual value and the approximation using an alternating series is less than or equal to the absolute value of the next term in the series.

So for sin1, we want to find the number of initial terms n such that:

|(1^(2n+1))/(2n+1)!| <= 0.0001

Solving for n using a calculator or computer software, we get n = 5. Therefore, we need at least 6 initial terms of the Maclaurin series for sinx to approximate sin1 correct to four decimal places.

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Taring a kitchen scale before weighing an ingredient is essential to obtain accurate measurements by removing the weight of the container, streamlining the process, and ensuring precise and reliable results in culinary preparations.

Taring a kitchen scale before weighing an ingredient is necessary to accurately measure the weight of the ingredient without including the weight of the container or vessel in which it is placed. Taring essentially resets the scale to zero, accounting for the weight of the container so that only the weight of the ingredient being added is measured.

By taring the scale, you eliminate the need to manually subtract the weight of the container from the final measurement. This allows for more precise and efficient measurements in recipes or other culinary applications.

Taring is particularly important when working with small or precise quantities of ingredients, where even a slight variation in weight can significantly impact the final outcome of a dish. It ensures that the weight of the container does not contribute to the measurement, providing accurate and reliable results.

Additionally, taring simplifies the weighing process by eliminating the need to calculate or estimate the weight of the container separately. It saves time and reduces the chances of errors in measurements, promoting consistency and precision in cooking and baking.

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There are 462 different ways to select a planning board of 6 scientists from a group of 11 scientists.

The problem requires selecting 6 scientists from a group of 11 scientists. This is a combination problem, and the formula for combination is nCr, where n is the total number of items, and r is the number of items to be selected. The formula is given by:

nCr = n! / (r! * (n-r)!)

Where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.

Using the given formula, the number of ways of selecting a planning board of 6 scientists can be calculated as:

11C₆ = 11! / (6! * (11-6)!)

= (11109876!) / (6! * 54321)

= (1110987) / (5432*1)

= 462

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The correct statement regarding the domain of the function is given as follows:

The domain of (f/g)(x) = x³/(x² - 4) is all real numbers except x = -2 and x = 2.

The function for this problem is given as follows:

(f/g)(x) = x³/(x² - 4)

The values that are outside the domain are the values of x for which the denominator is of zero, hence:

x² - 4 = 0

x² = 4

[tex]x = \pm \sqrt{4}[/tex]

[tex]x = \pm 2[/tex]

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There are 48 ways for the driver to load the shipment so that one of the heavier vehicles is directly over the rear axle of the trailer.

In order for one of the heavier vehicles to be directly over the rear axle of the trailer, there are only two options: either the station wagon or the minivan can be in that position. Therefore, we can consider the problem as two separate cases:

Case 1: Station wagon over the rear axle
In this case, we have four vehicles remaining to be loaded onto the trailer: three compact cars and the minivan. The order in which they are loaded onto the trailer does not matter, since the station wagon's position is fixed. Therefore, the number of ways to load the remaining vehicles is simply the number of permutations of 4 items, which is 4! = 24.

Case 2: Minivan over the rear axle
This case is identical to the first case, except that the station wagon is replaced by the minivan. Therefore, the number of ways to load the remaining vehicles is again 4! = 24.

Total number of ways:
Since the two cases are mutually exclusive, we can simply add the number of ways from each case to get the total number of ways:
24 + 24 = 48

Therefore, there are 48 ways for the driver to load the shipment so that one of the heavier vehicles is directly over the rear axle of the trailer.

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1. The final amount is $936 and the simple interest is $216.

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

1. Using the formula for simple interest:

Simple Interest = (Principal * Rate * Time)

Where:

Principal = $720

Rate = 6% = 0.06

Time = 5 years

Simple Interest = ($720 * 0.06 * 5) = $216

To find the final amount, we can add the simple interest to the principal:

Final Amount = Principal + Simple Interest = $720 + $216 = $936

Therefore, the final amount is $936 and the simple interest is $216.

Similarly,

2. The simple interest for a principal of $720, an interest rate of 6%, and a time period of 5 months is $18.

3. The simple interest for a principal of $720, an interest rate of 6%, and a time period of 5 days is $0.59.

4. Simple Interest is $506.11 and the Final Amount is $6,398.26.

5. The simple interest is $593.19 and the final amount is $27,561.63.

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The correct answer is (a) there is enough evidence to conclude that age and drink preference is dependent.

Using the formula for the chi-square test of independence, we can calculate the test statistic as:

X² = Σ (O-E)^2 / E

Performing this calculation on the given data, we get:

X² = (50-62.5)²/62.5 + (100-87.5)²/87.5 + (200-250)²/250 + (200-200)²/200 + (50-50)²/50 + (200-150)²/150 + (50-37.5)²/37.5 + (150-162.5)²/162.5 + (200-250)²/250 + (50-50)²/50 = 34

Using a chi-square distribution table with (2-1)*(4-1)=3 degrees of freedom and a significance level of 0.05, the critical value is 7.815.

Since the calculated test statistic of 34 is greater than the critical value of 7.815, we can reject the null hypothesis of independence and conclude that there is enough evidence to support the alternative hypothesis that age and drink preference are dependent.

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Answer: A

Step-by-step explanation: Okay! So the first thing we notice when looking at the diagram is that the units are in centimeters. We want these in feet. They tell us that 1cm = 4ft. Now we know that the actual scale would have the length be 12 ft, and the width would be 8 ft.

Now, we look at the size they want it increased by: 20%. In order to do this, we must multiply the length and width by 0.2. Then we take THOSE values, and add them to the original.

Let's work it out.

Step 1. Multiplying values by 0.2 (20%)

    Length:  (12ft)(0.2)= 2.4

    Width:    (8ft)(0.2)= 1.6

Step 2. Now that we've found 20% of our original length and width, we must add those values to the original length and width.

    Length: 12ft + 2.4ft = 14.4 ft

    Width:   8ft + 1.6ft= 9.6ft

Those are your final answers! Hope that helps :)

Answer:

(12 - 2 √22) ft

Step-by-step explanation:

by Pythagoras' Theorem:

in right-angled triangle, the square of the hypotenuse will equal the sum of the squares of the other two sides.

call the ladder L, call the distance of bottom of ladder from bottom of wall G, call the vertical height of the wall where the top of ladder meets it H.

we have L² = G² + H²

H² = L² - G²

   = 13² - 5²

   = 169 - 25

   = 144

H = √144 = 12.

the ladder is opposite the right-angle, ie it's the hypotenuse.

the ladder is 5ft from the wall.

if bottom of ladder is pulled out 4ft more, this reduces the height H.

the length of ladder L remains the same (can't compress a ladder)

G, the floor distance, is now 5 + 4 = 9ft

H² = L² - G²

    = 169 - 9²

    = 169 - 81

    = 88

H = √88

   = √(4 X 22)

   = √4 X √22

   = 2√22

The vertical height, H, was 12 ft.  it's now 2 √22

so it has moved down the wall (12 - 2 √22) ft.

The differential of the function t = v 8 uvw is "dt = 8vuw dv + 8uvw du + 8uvw dw".

To find the differential of the given function, we differentiate each variable with respect to the others and multiply by the corresponding coefficient. Here, we have three variables, v, u, and w, and the coefficient 8 appears in front of each variable. So, the differential of the function t = v 8 uvw is dt = 8vuw dv + 8uvw du + 8uvw dw. This expression represents the change in t for small changes in v, u, and w.

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The error in using s10 as an approximation to the sum of the series is less than or equal to 2.79892 × 10^-5.

The given series is a p-series with p = 5, which means it converges if and only if p > 1. Therefore, the series converges.

To find the tenth partial sum, we need to add up the first ten terms of the series:

s10 = 1/1^5 + 1/2^5 + 1/3^5 + ... + 1/10^5

Using a calculator or computer, we get:

s10 ≈ 1.036393

To estimate the error in using s10 as an approximation to the sum of the series, we need to find the remainder term R10:

R10 = ∑ from n=11 to infinity of (1/n^5)

Since we cannot find the exact value of this infinite series, we can use an estimation method such as the integral test:

∫ from 11 to infinity of (1/x^5) dx = [-1/4x^4] from 11 to infinity = 1/4(11^4)

Therefore, we have:

R10 ≤ ∫ from 11 to infinity of (1/x^5) dx = 1/4(11^4) ≈ 2.79892 × 10^-5

So the error in using s10 as an approximation to the sum of the series is less than or equal to 2.79892 × 10^-5.

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The rounding up of the numbers indicates that the sum and differences of the numbers are;

Rounding up of numbers is an estimation method used to provide values that have a particular degree of accuracy.

The sums and difference of the integers obtained using the prescribed method are as follows;

1) 28 + 53 ⇒ 30 + 50 = 80

2) 58 + 31 ⇒ 60 + 30 = 90

3) 73 + 45 ⇒ 70 + 50 = 120

4) 37 + 44 ⇒ 40 + 40 = 80

5) 66 - 21 ⇒ 70 - 20 = 50

6) 53 - 50 ⇒ 50 - 50 = 0

7) 51 - 16 ⇒ 50 - 20 = 30

8) 20 - 11 ⇒ 20 - 10 = 10

9) 86 + 6 ⇒ 90 + 10 = 100

10) 94 + 87 ⇒ 90 + 90 = 180

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The lines that have an x-intercept of (3,0) and a y-intercept of (0,-4) are:

y = 4/3x - 4

y + 4 = 4/3(x - 3)

To find a line with a given x-intercept and y-intercept, we can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope of the line, and b is the y-intercept (the y-coordinate where the line intersects the y-axis).

Both of these lines pass through points (3,0) and (0,-4), so they have the desired x- and y-intercepts.

The other lines do not pass through both of these points

y = -4/3x - 4 does not pass through (3,0)

y = 3x - 4 does not pass through (0,-4)

Y=4/3(x-3) does not pass through (0,-4)

y+4=4/3x does not pass through (3,0)

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Answer:

sin I = 3/5

Step-by-step explanation:

sin I = perpendicular/hypotenuse

      = 18/30

      = 9/15

      = 3/5

The volume of the solid after dilation when its surface area is 224 square units is 96 cubic units

Before dilation

Volume of the solid = 6 cubic units

Surface area of the solid = 14 square units

When solid is dilated:

Volume of the solid = x cubic units

Surface area of the solid = 224 square units

Equate ratio of volume to surface area before and after dilation

6 : 14 = x : 224

6/14 = x/224

cross product

6 × 224 = 14 × x

1344 = 14x

divide both sides by 14

x = 1344/14

x = 96 cubic units

Hence, the volume of the solid is 96 cubic units

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From the data of the number of meters swam by students, range is the best measure of variability and equals 600

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data,

Let the data set be represented as A

Now, the value of A is

A = { 200, 450, 600, 650, 700, 800 }

The appropriate measure of variability for the given data is the range. The range is the difference between the largest and smallest values in the data set.

And, range = 800 - 200

R = 600

Hence, the range of the data set is R = 600

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Answer:

Step-by-step explanation:

ƒ(5)= -4(5)²+7(5)

ƒ(5)= -100+35

ƒ(5)= -65

[tex]\frac{f(5)}{5}[/tex]=[tex]\frac{65}{5}[/tex]

ƒ=13

To find the displacement of the particle at time t, we need to integrate its velocity function v(t) over the interval [0, t]:

s(t) = ∫v(t) dt

s(t) = ∫(t^2 - 2t - 24) dt

s(t) = (1/3)t^3 - t^2 - 24t + C

where C is the constant of integration.

To find the value of C, we need to use the initial condition that the particle is at the position s(0) = 0. Substituting t = 0 and s(0) = 0 into the above equation, we get:

0 = 0 + 0 - 0 + C

C = 0

Therefore, the displacement of the particle at time t is given by:

s(t) = (1/3)t^3 - t^2 - 24t

To find the displacement over the entire interval [0, 6], we can substitute t = 6 into the above equation:

s(6) = (1/3)(6^3) - 6^2 - 24(6)

s(6) = 36 - 36 - 144

s(6) = -144

Therefore, the displacement of the particle over the interval [0, 6] is -144 meters.

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True. Selective distribution is a strategy in which a manufacturer limits the number of outlets at which its product is sold.

This strategy is often used for medium- and higher-priced products or stores that consumers don't expect to find on every street corner. By limiting the availability of the product, the manufacturer can maintain a premium image and prevent price erosion.

In contrast, products that are widely available and low-priced are more likely to be distributed through intensive distribution, in which the manufacturer tries to get the product into as many outlets as possible.

This strategy is effective for products with high turnover rates and where consumers prioritize convenience and accessibility over brand image.

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The area of the region bounded by the graphs is 6 square units.

Option A is the correct answer.

We have,

To find the area of the region bounded by the graphs of y = 3 - x² and

y = 2x², we need to find the points of intersection between these two curves and calculate the definite integral of the difference between the two functions over the interval where they intersect.

Setting the two equations equal to each other, we have:

3 - x² = 2x².

Rearranging this equation, we get:

3 = 3x².

Dividing both sides by 3, we have:

1 = x²

Taking the square root of both sides, we find:

x = ±1.

So the two curves intersect at x = -1 and x = 1.

To find the area of the region between the curves, we integrate the difference between the upper curve (y = 3 - x²) and the lower curve

(y = 2x²) over the interval [-1, 1]:

A = ∫[-1, 1] (3 - x² - 2x²) dx.

Simplifying the integrand, we have:

A = ∫[-1, 1] (3 - 3x²) dx.

A = ∫[-1, 1] 3(1 - x²) dx.

A = 3 ∫[-1, 1] (1 - x²) dx.

Integrating term by term, we get:

A = 3 [x - (x³/3)] evaluated from -1 to 1.

Plugging in the limits of integration, we have:

A = 3 [(1 - (1³/3)) - ((-1) - ((-1)³/3))].

Simplifying further, we find:

A = 3 [(1 - 1/3) - (-1 - 1/3)].

A = 3 [(2/3) - (-4/3)].

A = 3 [(2/3) + (4/3)].

A = 3 (6/3).

A = 6 square units.

Therefore,

The area of the region bounded by the graphs is 6 square units.

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The sum ∑ k=1^3 (-1)^k * 1 * sin(pi/k) is an example of a finite series. A series is the sum of the terms in a sequence. In this case, the sequence is defined by the terms (-1)^k * 1 * sin(pi/k) for k=1, 2, 3.

The sum of these terms is calculated by adding up each term one by one, which gives us the total value of the series. In this series, the values of k are limited to the integers 1, 2, and 3. For each value of k, we evaluate the product of (-1)^k, 1, and sin(pi/k) and then add up these values to get the sum.

The sine function sin(pi/k) gives the ratio of the side opposite to the angle pi/k in a right triangle with hypotenuse 1. Since pi is a constant, the value of sin(pi/k) changes as k varies, resulting in different terms for the series. The factor (-1)^k alternates between 1 and -1 as k increases, leading to terms that are positive and negative.

The sum of the series can be computed by adding up all the terms. In this case, we obtain the value 3 - (3/2)sqrt(3). This final value is a real number that represents the total value of the sum of the series.

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Lani uses the fraction 1/3 of a yard of ribbon for each bow.

Fractions represent a part of a whole, and are used to express values that are not whole numbers.

To find the required fraction divide the total amount of ribbon by the number of bows to find the amount of ribbon used per bow.

We also use the concept of fractions to represent the amount of ribbon used per bow as a part of a yard.

Here we have

Lani uses 2 yards of ribbon to make 6 bows. each bow uses the same amount of ribbon.

To find the fraction of a yard of ribbon used for each bow, we need to divide the total length of ribbon used by the number of bows.

Hence, The amount of ribbon used for each bow is:

=> 2 yards/ 6 bows

= 1 yards/3bow

Therefore,

Lani uses the fraction 1/3 of a yard of ribbon for each bow.

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We need to round our answer to the nearest person, the number of people who purchased snowboards on the day before data collection is approximately 223. Therefore, the correct answer is not provided among the options.

To determine the number of people who purchased snowboards the day before the manager started collecting data, we need to work backwards from the information given.

Let's assume the number of people who purchased snowboards on the day before data collection started is represented by "X."

From the given data, we know that on Day 5, there was a 12% increase in the number of people who bought snowboards compared to the previous day. So, if X represents the number of people who bought snowboards on the day before data collection, we can calculate the number of people who bought snowboards on Day 5 as follows:

X + (12% of X) = 250

Converting 12% to a decimal, we have:

X + (0.12X) = 250

Combining like terms:

1.12X = 250

Now, we can solve for X:

X = 250 / 1.12 ≈ 223.21

Since we need to round our answer to the nearest person, the number of people who purchased snowboards on the day before data collection is approximately 223.

Therefore, the correct answer is not provided among the options.

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The time taken by her for haircut is 21 minutes and to color is 50 minutes.

Assume that

Haircut takes   = x minutes

To Color takes = y minutes

According to the question

The expression for time be,

3x + 4y = 263 ...(i)

The expression for time be,

x + y = 71  ...(ii)

Apply elimination method to solve it,

After equation(i) - 3x(ii) we get,

y = 50 minutes

Now plug it into (ii) we get,

x = 21 minutes.

Hence,

Haircut takes   = 21 minutes

To Color takes = 50 minutes

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The first premise states that Newton, Maxwell, and Einstein worked with physics. This means that they were all involved in the study and exploration of physical phenomena and natural laws. Newton's laws of motion, Maxwell's equations of electromagnetism, and Einstein's theory of relativity are all significant contributions to the field of physics. This premise is important in understanding the cartoon's message that even the greatest minds in physics could not have predicted the events of 2020. It is a reminder that science and knowledge are constantly evolving and that we must remain open to new discoveries and possibilities.

The translation of the first premise is a statement about the involvement of Newton, Maxwell, and Einstein in the field of physics. It acknowledges their contributions to the study of physical phenomena and natural laws. It is a recognition of their status as some of the most influential scientists in history, whose work has had a profound impact on our understanding of the world around us.

The first premise of the cartoon highlights the importance of physics and the contributions of some of its most prominent figures. It underscores the idea that science and knowledge are constantly evolving and that we must remain open to new discoveries and possibilities. It is a reminder that even the greatest minds in physics could not have predicted the events of 2020, and that we must continue to push the boundaries of our understanding of the world around us.

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Suppose that v1, v2, v3 is an orthogonal basis for w. Then, we have:

v1 · v2 = 0 (v1 and v2 are orthogonal)

v1 · v3 = 0 (v1 and v3 are orthogonal)

v2 · v3 = 0 (v2 and v3 are orthogonal)

To show that multiplying v3 by a non-zero scalar c gives a new orthogonal basis v1, v2, cv3, we need to show that v1, v2, and cv3 are mutually orthogonal.

First, note that v1 and v2 are still orthogonal to each other, as c does not affect their inner product.

Now, let's check the inner products between v1, v2, and cv3:

v1 · cv3 = c(v1 · v3) = c(0) = 0 (v1 and v3 are orthogonal)

v2 · cv3 = c(v2 · v3) = c(0) = 0 (v2 and v3 are orthogonal)

(cv3) · (cv3) = c^2(v3 · v3) ≠ 0 (v3 is a non-zero vector)

So, v1, v2, and cv3 are mutually orthogonal, except for the fact that cv3 is no longer a unit vector. However, we can normalize cv3 to get a unit vector u3:

u3 = (1/|cv3|)cv3 = (1/|c|)cv3

Then, we have the new orthogonal basis v1, v2, u3. Note that this basis spans the same subspace as the original basis v1, v2, v3, since multiplying v3 by a non-zero scalar does not change the span of the basis.

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In this exercise, a random sample of 30 heights of adult females or adult males living in America was gathered and converted to inches. Confidence intervals were then constructed for the mean height of the sample at 90%, 95%, and 99% confidence levels.

Reflection questions were also answered, including summarizing the characteristics of the sample, finding x (sample mean), s (sample standard deviation), interpreting the confidence intervals, and calculating the percent difference between the sample mean and the average height of the population.

The sample consisted of 30 randomly selected heights of either adult females or adult males living in America. The sample mean (x) was found to be 65.87 inches with a sample standard deviation (s) of 3.18 inches. Confidence intervals were then constructed for the mean height of the sample at 90% (63.95, 67.79), 95% (63.34, 68.4), and 99% (62.39, 69.35) confidence levels. The confidence intervals show that we are 90%, 95%, and 99% confident that the true population mean height lies within these ranges.

According to the National Center for Health Statistics, the average height of adult females in the United States is 63.7 inches, and the average height for adult males is 69.2 inches. Based on this, the percent difference between the sample mean and the population mean for adult females is -2.95%, and for adult males, it is -4.71%. This means that the sample mean height is slightly lower than the population mean height for both groups. It is important to note that the sample was relatively small and may not be entirely representative of the population, and thus the percent difference should be interpreted with caution.

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