The rabbit population in Central Park was 150 in the year 2000. The population is increasing by 11% each year. Let x = the number of years since 2000. What will the rabbit population be in 2025?

[tex]72 - 2y^{2} = 2(36-y^{2} )= 2(6-y)(6+y)[/tex]

Find the GCF of the terms: 72 and -2y^2.

Divide each term by the GCF:

Now we have: 2(36 - y^2).

Identify if there is a difference of squares.

Putting it all together, the fully factorized expression is:

2(6 - y)(6 + y).

The x² value having area 0.975 to its right for a curve with 18 degrees of freedom is approximately 29.141.

Using a chi-squared distribution table or a calculator, we can find the critical value of chi-squared for 18 degrees of freedom and an area of 0.975 to the right.

From a chi-squared distribution table, we can find the critical value to be 29.141. Alternatively, using a calculator, we can use the inverse chi-squared distribution function with 18 degrees of freedom and a probability of 0.975 to find the critical value:

import scipy.stats as stats

crit_value = stats.chi2.ppf(q=0.975, df=18)

print(crit_value)

This gives us a critical value of approximately 29.141.

Therefore, the x² value having area 0.975 to its right for a curve with 18 degrees of freedom is approximately 29.141.

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False.

Multiple relational expressions can be placed into the test condition of a for loop. In many programming languages, you can use logical operators (such as &&, ||) to combine multiple relational expressions into a single test condition. This allows you to check for more than one condition simultaneously during each iteration of the loop. Here's a step-by-step explanation:
1. Define your loop variables.
2. Begin your for loop with an initial expression.
3. Combine multiple relational expressions using logical operators in the test condition.
4. Provide an update expression.
5. Write the loop body with the actions to be performed in each iteration.
For example, consider a loop that iterates while 'i' is less than 10 and 'j' is not equal to 5:
```cpp
for (int i = 0, int j = 0; i < 10 && j != 5; i++, j++) {
 // Loop body
}
```
In this case, the loop continues to execute as long as both conditions are met.

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Sarah's percentage error is 35%.

The predicted value is 80 words per minute, and the actual value is 52 words per minute.

To find the percentage error, we need to find the difference between the predicted and actual values, divide it by the predicted value, and then multiply by 100 to get the percentage.

Sarah's percentage error can be calculated as follows:

percentage error = |(predicted value - actual value) / actual value| x 100%

Substituting the given values, we get:

percentage error = |(80 - 52) / 80| x 100%

percentage error = |28 / 80| x 100%

percentage error = 0.35 x 100%

percentage error = 35%

Therefore, Sarah's percentage error is 35%.

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We have the exact value of the trigonometric function at the given real number

(a) cos(19π/6) ≈ 0.9848

(b) cos(-7π/6) ≈ -0.8660

(c) cos(-11π/6) ≈ 0.5

We can use the unit circle to evaluate the trigonometric functions at the given angles. Recall that cosine is the x-coordinate of the point on the unit circle corresponding to the angle in standard position.

(a) cos(19π/6)

First, we convert 19π/6 to degrees:

19π/6 = (19/6) * π ≈ 3.14 * 3.1667 ≈ 9.95 radians

To find the cosine of 19π/6, we need to find the x-coordinate of the point on the unit circle that corresponds to an angle of 9.95 degrees. Since 9.95 is greater than 360 degrees, we can subtract 360 to get an equivalent angle in standard position:

9.95 - 360 = -350.05 degrees

This angle is in the fourth quadrant of the unit circle, where the x-coordinate is positive and the y-coordinate is negative. Therefore, we have:

cos(19π/6) = cos(-350.05) = cos(9.95) ≈ 0.9848

(b) cos(− 7π/6)

To evaluate cos(-7π/6), we first convert -7π/6 to degrees:

-7π/6 = (-7/6) * π ≈ -1.16 * 180 ≈ -209.44 degrees

This angle is in the third quadrant of the unit circle, where the x-coordinate is negative and the y-coordinate is negative. Therefore, we have:

cos(-7π/6) = cos(-209.44) ≈ -0.8660

(c) cos(− 11π/6)

To evaluate cos(-11π/6), we first convert -11π/6 to degrees:

-11π/6 = (-11/6) * π ≈ -1.82 * 180 ≈ -327.27 degrees

This angle is in the fourth quadrant of the unit circle, where the x-coordinate is positive and the y-coordinate is negative. Therefore, we have:

cos(-11π/6) = cos(-327.27) ≈ 0.5

In summary, we have:

(a) cos(19π/6) ≈ 0.9848

(b) cos(-7π/6) ≈ -0.8660

(c) cos(-11π/6) ≈ 0.5

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The standard error (SE) is used to construct the standardized test statistic (Z) in hypothesis testing when comparing a sample proportion (p) to a hypothesized population proportion (p0) using the null hypothesis (H0: p = p0) and alternative hypothesis (HA: p ≠ p0).

In this context, the standard error represents the estimated standard deviation of the sampling distribution of the sample proportion. It quantifies the variability in the sample proportion and reflects how much we would expect the sample proportion to vary from sample to sample if the null hypothesis is true.

To calculate the standard error for the proportion, the formula is:

SE = √[ (p0 * (1 - p0)) / n ]

where p0 is the hypothesized population proportion, and n is the sample size.

The standard error takes into account the hypothesized population proportion (p0) and the sample size (n). It provides an estimate of how much the sample proportion (p) is likely to deviate from the hypothesized proportion due to sampling variability alone.

Once the standard error is calculated, the standardized test statistic (Z) can be obtained by subtracting the hypothesized proportion from the sample proportion and dividing it by the standard error:

Z = (p - p0) / SE

The Z-score indicates the number of standard errors the observed sample proportion is away from the hypothesized proportion. It is used to determine the probability of observing a sample proportion as extreme or more extreme than the one obtained, assuming the null hypothesis is true.

By comparing the Z-score to critical values from the standard normal distribution, we can determine the statistical significance of the observed sample proportion and make conclusions about the null hypothesis.

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Every subgroup of the integers has finite index. It is True.

True. Proof: Let H be a subgroup of the integers. By the division algorithm, for any integer n and any positive integer d, there exist unique integers q and r such that n = dq + r and 0 ≤ r < d. In particular, if we take d = |H|, then for any integer n, we have n = dq + r for some integer q and some 0 ≤ r < |H|. This means that any integer n can be written in the form n = h + r for some integer h in H and some 0 ≤ r < |H|. Therefore, the residue classes {h + r : r = 0, 1, ..., |H| - 1} form a complete set of coset representatives for H in Z. Since there are |H| such cosets, it follows that [Z : H] = |H|. Therefore, every subgroup of the integers has finite index.

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The derivative of the vector function r(t) is:

r'(t) = (3sec^2(3t), 4sec(4t)tan(4t), 3t^2)

To find the derivative of the vector function r(t) = (tan(3t), sec(4t), t^3), we need to take the derivative of each component function separately with respect to t.

Using the chain rule, we have:

r'(t) = (d/dt) (tan(3t), sec(4t), t^3)

= (d/dt) tan(3t), (d/dt) sec(4t), (d/dt) t^3

= 3sec^2(3t), 4sec(4t)tan(4t), 3t^2

Therefore, the derivative of the vector function r(t) is:

r'(t) = (3sec^2(3t), 4sec(4t)tan(4t), 3t^2)

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In this case, the selling price is $1,895, and the purchase price is $1,755. The percentage markup on cost is approximately 8.0%.

The percentage markup on cost is a measure of how much the selling price exceeds the purchase price as a percentage of the purchase price. To calculate it, we use the formula:

Percentage Markup on Cost = ((Selling Price - Purchase Price) / Purchase Price) * 100

Given that the selling price is $1,895 and the purchase price is $1,755, we substitute these values into the formula:

Percentage Markup on Cost = (($1,895 - $1,755) / $1,755) * 100

Simplifying the calculation:

Percentage Markup on Cost = ($140 / $1,755) * 100

Percentage Markup on Cost ≈ 0.0798 * 100 ≈ 7.98%

Rounding to the nearest tenth, the percentage markup on cost is approximately 8.0%.

Therefore, the seller is charging a markup of approximately 8.0% on the original purchase price of the used car.

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If the radius of a circle is 18 meters, the diameter is 36 meters.

Answer:

[tex]\huge\boxed{\sf Diameter = 36\ m}[/tex]

Step-by-step explanation:

Given that,

Radius = 18 m

We know that,

Diameter = 2 × 18

[tex]\rule[225]{225}{2}[/tex]

The probability of the spinner landing on a number that is not odd, P(not odd), is 0.50. Option C

From the given information, the numbers that are not odd are 2, 4, 6, and 8. There are four favorable outcomes.

The total number of possible outcomes is 8, as there are eight equally divided sections on the spinner.

Therefore, the probability of the spinner landing on a number that is not odd, P(not odd), is:

P(not odd) = favorable outcomes / total outcomes = 4 / 8 = 0.5

Rounded to the nearest hundredth, the theoretical probability is 0.50.

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Answer:

-18 = -3(6) + b

-18 = -18 + b

b = 0

y = -3x

Answer:

-3x

Step-by-step explanation:

Let's plug the values into point-slope first. We have all the necessary info to perform such an operation - we have the point and the slope.

Point-slope is:

[tex]\bf{y-y_1=m(x-x_1)}[/tex]

Where y₁ and x₁ are the co-ordinates of the point and m is the slope.

So we plug the data in, like this:

[tex]\bf{y-(-18)=-3(x-6)}[/tex]

Now we can simplify

[tex]\bf{y+18=-3(x-6)}[/tex]

Use the distributive property

[tex]\bf{y+18=-3x+18[/tex]

Subtract 18 from each side

[tex]\bf{y=-3x}[/tex]

Therefore, the equation is -3x.

Events E and F are mutually exclusive with P(EUF) = 0.64 and P(F) = 0.20, therefore the odds against E are 14 to 11.

Given that events E and F are mutually exclusive with P(EUF) = 0.64 and P(F) = 0.20, we can find P(E) using the formula P(EUF) = P(E) + P(F). Solving for P(E), we get P(E) = 0.44.

The odds against E can be found by taking the ratio of the probability of its complement (not E) to the probability of E, which gives us odds against E = P(not E) / P(E) = 0.56 / 0.44 = 14/11.

The odds against E are 14 to 11.

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The value of the quantity after 120 seconds, to the nearest hundredth, is  3255.81.

To calculate the value of the quantity after a given time using continuous decay, we can use the formula:

Final Value = Initial Value × e^(rate × time),

where e is the base of the natural logarithm (approximately 2.71828), rate is the decay rate as a decimal, and time is the duration in the given units.

In this case, the initial value is 980, the decay rate is 60% or 0.60, and the time is 120 seconds.

Using the formula, we can calculate the final value:

Final Value = 980 × e^(0.60 × 120/60)

Let's calculate it step by step:

Final Value = 980 × e^(0.60 × 2)

Final Value = 980 × e^1.2

Now, we can use a calculator to find the approximate value of e^1.2, and then multiply it by 980:

Final Value ≈ 980 × 3.3201169227365472

Final Value ≈ 3255.81

Therefore, the value of the quantity after 120 seconds, to the nearest hundredth, is approximately 3255.81.

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Answer:

-3/5

Step-by-step explanation:

Sec = h/a = 5/4

3-4-5- Right Triangle

Sin = o/h = 3/5

Quadrant 3 = Only +Tan

Thererfore = -3/5

As long as the prevalence of diabetes is the same in both communities, the PPV of Test 1 would not change. The answer is B. Not change.

If Test 1 was administered to community Y, whose diabetes prevalence is equal to the diabetes prevalence in community X, then the PPV would not change. This is because the PPV is dependent on the prevalence of the disease in the population being tested, not on the population itself. Therefore, as long as the prevalence of diabetes is the same in both communities, the PPV of Test 1 would not change. The answer is B. Not change.

If Test 1 was administered to community Y, whose diabetes prevalence is equal to the diabetes prevalence in community X, then the Positive Predictive Value (PPV) would B. Not change. This is because the PPV is influenced by the prevalence of the condition in the population being tested, and since the prevalence is equal in both communities, the PPV would remain the same.

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Using the binomial probability formula or a binomial calculator, we can find that the probability of getting 3, 4, or 5 successes in 7 trials with a probability of success of 0.4 is approximately 0.43122.

To find the probability of getting 3 ≤ x ≤ 5, we need to calculate the probability of getting exactly 3 successes, exactly 4 successes, and exactly 5 successes and then add them together. We can use the binomial probability formula or a binomial calculator to find each probability:

P(x = 3) = (7 choose 3) * (0.4)^3 * (0.6)^4 = 0.2668

P(x = 4) = (7 choose 4) * (0.4)^4 * (0.6)^3 = 0.2903

P(x = 5) = (7 choose 5) * (0.4)^5 * (0.6)^2 = 0.1261

Then, we can add these probabilities to get the final answer:

P(3 ≤ x ≤ 5) = P(x = 3) + P(x = 4) + P(x = 5) = 0.2668 + 0.2903 + 0.1261 = 0.43122

Using a binomial calculator or software such as Excel, we can verify that the answer is approximately 0.43122.

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There are 5 ways to tile a 2 x 6 checkerboard using L-shaped tiles of size 2 x 1.

We can approach this problem using recursion. Let T(n) be the number of ways to tile a rectangular checkerboard of size 2 x n using L-shaped tiles of size 2 x 1. We can analyze the possible tiles that can be placed in the last column of the checkerboard, and then use recursion to count the total number of ways to tile the remaining (2 x (n-1)) board.

Consider the last column of the checkerboard. We can place either a vertical tile, or two horizontal tiles in the column.

Case 1: Last column has a vertical tile

In this case, we can place a horizontal tile in the second-to-last column, and then we are left with a (2 x (n-2)) checkerboard to tile. So the number of ways to tile the (2 x n) checkerboard in this case is T(n-2).

Case 2: Last column has two horizontal tiles

In this case, we must also have two horizontal tiles in the second-to-last column, and then we are left with a (2 x (n-4)) checkerboard to tile. So the number of ways to tile the (2 x n) checkerboard in this case is T(n-4).

Therefore, the recursive formula for T(n) is:

T(n) = T(n-2) + T(n-4)

with the base cases:

T(0) = 1 (there is only one way to tile an empty checkerboard)

T(1) = 1 (there is only one way to tile a 2 x 1 checkerboard)

T(2) = 2 (there are two ways to tile a 2 x 2 checkerboard)

Using this formula, we can calculate T(6):

T(3) = T(1) + T(-1) = 1 (since T(-1) = 0)

T(4) = T(2) + T(0) = 3

T(5) = T(3) + T(1) = 2

T(6) = T(4) + T(2) = 5

So there are 5 ways to tile a 2 x 6 checkerboard using L-shaped tiles of size 2 x 1.

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Answer:

The answer is b

Step-by-step explanation:

The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:

55x + 65x = 960

Simplifying the left-hand side of the equation, we get:

120x = 960

Dividing both sides by 120, we get:

x = 8

Therefore, the correct equation is:

B - 65x - 55x = 960

To construct a frequency distribution for the given data, we need to count the number of books falling into each class interval.
0-99 Number of books:
(40, 45, 45, 55, 55, 60, 60, 70, 70, 70, 70, 70, 70, 75, 75, 80, 80, 83, 85, 85) - 20 books
100-199 Number of books:
(100, 100, 100, 100, 107, 110, 140, 140) - 8 books
200-299 Number of books: None - 0 books
300-399 Number of books:
(300) - 1 book
400-499 Number of books: None - 0 books
500-599 Number of books:
(500) - 1 book
So, the frequency distribution is as follows:
0-99: 20 books
100-199: 8 books
200-299: 0 books
300-399: 1 book
400-499: 0 books
500-599: 1 book

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The probability of rolling a 5 on the (x+1)-th roll is P{X=x, Y=5} = (5/6)^(x-1) * (1/6) * (1/6)^4 * (5/6).

To find P{X=x, Y=1}, we need to calculate the probability of rolling a 6 for the first time on the x-th roll and rolling a 5 on the first roll. Since the rolls are independent, we can use the multiplication rule of probability:

P{X=x, Y=1} = P(X=x and Y=1) = P(X=x) * P(Y=1)

We know that X and Y have geometric distributions with parameters p=1/6 and q=5/6, respectively. Therefore,

P(X=x) = (1-p)^(x-1) * p = (5/6)^(x-1) * (1/6)

P(Y=1) = q = 5/6

Substituting these values into the equation above, we get:

P{X=x, Y=1} = (5/6)^(x-1) * (1/6) * (5/6)

To find P{X=x, Y=5}, we need to calculate the probability of rolling a 6 for the first time on the x-th roll and rolling a 5 for the first time on the fifth roll. Again, we can use the multiplication rule of probability:

P{X=x, Y=5} = P(X=x and Y=5) = P(X=x) * P(Y=5|X=x)

We know that Y has a geometric distribution with parameter q=5/6, given that X=x, the probability of rolling a 5 on the (x+1)-th roll is:

P(Y=5|X=x) = (1-q)^4 * q = (1/6)^4 * (5/6)

Substituting these values into the equation above, we get:

P{X=x, Y=5} = (5/6)^(x-1) * (1/6) * (1/6)^4 * (5/6)

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w⊥ (read "w perp") is the set of all vectors that are orthogonal (perpendicular) to every vector in w. In other words, if v is in w⊥, then v is perpendicular to both u1 and u2.

Now, onto the specific question. We have w=span{u1,u2}, which means that w is the set of all linear combinations of u1 and u2. In other words, any vector in w can be written as c1u1 + c2u2 for some constants c1 and c2.

To determine whether a vector is in w⊥, we need to check if it is perpendicular to both u1 and u2. We can do this using the dot product.

Recall that the dot product of two vectors u and v is defined as u·v = ||u|| ||v|| cos(θ), where ||u|| and ||v|| are the magnitudes of u and v, and θ is the angle between them. If u and v are perpendicular, then cos(θ) = 0 and their dot product is 0 as well.

So, for each vector we are given, we can compute its dot product with u1 and u2 and check if they are both 0.

If they are, then the vector is in w⊥. If not, then the vector is not in w⊥.

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Answer:C) specialization.

Step-by-step explanation:

The objective function formula that is nonlinear is - 2xy/2xy + z

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

- 2xy/2xy + z

- x + y + z

- 3x - 2y + z

A linear function is a function that has a degree of 1

Other functions with other degrees are nonlinear

Using the above as a guide, we have the following functions with a degree of 1

- x + y + z

- 3x - 2y + z

Hence, the objective function formulas that is nonlinear is - 2xy/2xy + z

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Answer:

32°

Step-by-step explanation:

We can model the given scenario as a right triangle, where the height of the triangle is the vertical distance between the kite and the ground (40 feet), and the hypotenuse is the length of the kite's string (75 feet).

The angle made between the ground and string of the kite is the angle that is opposite the triangle's height.

As we have both the side of the triangle that is opposite the angle, and the hypotenuse of the triangle, we can use the sine trigonometric ratio to calculate the measure of the angle.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given values:

Substitute the values into the sine ratio and solve for θ:

[tex]\sin(\theta)=\dfrac{40}{75}[/tex]

[tex]\theta=\sin^{-1}\left(\dfrac{40}{75}\right)[/tex]

[tex]\theta=32.2309526...^{\circ}[/tex]

[tex]\theta=32^{\circ}\; \sf (nearest\;degree)[/tex]

Therefore, the measure of the angle between the ground and the string of the kite is 32° (to the nearest degree).

To test the theory proposed by the researcher using the given information, we need to set up a hypothesis test. Let's define the null and alternative hypotheses:

Next, we need to determine the test statistic and the critical value based on the significance level (α) of 0.05.

The test statistic in this case is the z-score.

To perform the hypothesis test, we need the following information:

- Number of students: n = 124

- Number of students selecting a three-grill display: x = 85

Now, let's calculate the test statistic (z-score) using the formula:

x = (x - np) / sqrt(np(1 - p))

Where:

- p is the hypothesized proportion (under the null hypothesis), which is consistent with the theory proposed by the researcher. We do not have the specific value of p in the question, so we assume p to be 0.5 for testing purposes since we have no prior information.

- np is the expected number of students selecting a three-grill display under the null hypothesis, which is np = n * p.

- sqrt(np(1 - p)) is the standard deviation of the proportion.

Let's calculate the z-score:

p = 0.5

np = 124 * 0.5 = 62

sqrt(np(1 - p)) = sqrt(62 * 0.5 * 0.5) = sqrt(15.5) ≈ 3.937

x = 85

z = (x - np) / sqrt(np(1 - p))

z = (85 - 62) / 3.937

z ≈ 5.84

Now, we compare the calculated z-score to the critical value at the significance level of α = 0.05. Since it is a two-tailed test, we need to find the critical z-values that cut off 2.5% from the upper and lower tails of the standard normal distribution.

The critical z-value for α/2 = 0.05/2 = 0.025 is approximately 1.96.

Since the calculated z-score of 5.84 is larger than the critical z-value of 1.96, we can reject the null hypothesis.

Therefore, based on the given information and using a significance level of α = 0.05, we can conclude that the theory proposed by the researcher is not supported.

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The function evaluated at the given values of the independent variable is:
f(0) = 3
f(-pi/4) = 0
f(pi/3) = -3/2
f(pi) = 3

To evaluate the function f(x) = 3 cos 2x at the given values of the independent variable, we simply substitute those values into the function and simplify the results.

(a) f(0) = 3 cos 2(0) = 3 cos 0 = 3(1) = 3

(b) f(-pi/4) = 3 cos 2(-pi/4) = 3 cos(-pi/2) = 3(0) = 0

(c) f(pi/3) = 3 cos 2(pi/3) = 3 cos(4pi/6) = 3(-1/2) = -3/2

(d) f(pi) = 3 cos 2(pi) = 3 cos(0) = 3(1) = 3

Therefore, the function evaluated at the given values of the independent variable is:

f(0) = 3
f(-pi/4) = 0
f(pi/3) = -3/2
f(pi) = 3

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Based on the provided information to conduct the hypothesis test the condition met are random sampling, sample size, independence. From this sample, the taxpayer calculates a sample mean of $934 and a sample standard deviation of $619.

To conduct a hypothesis test, we need to ensure certain conditions are met. These conditions are:
1. Random sampling :The taxpayer used a random sample of 32 families, which helps to ensure the sample is representative of the population.
2. Sample size: The sample size is 32, which is considered a large enough sample size for a hypothesis test (generally, a sample size of 30 or more is considered large enough).
3. Independence: Since the sample is random and the sample size is less than 10% of the population (assuming there are more than 320 families), the independence assumption can be considered as met.
4. Approximately normal distribution: With a sample size of 32 (which is considered large), the Central Limit Theorem suggests that the sampling distribution of the sample mean will be approximately normal.
With these conditions met, the taxpayer can proceed with a hypothesis test to compare their sample mean with the IRS representative's claimed average and determine whether the real figure for medical care deductions is likely to be lower than $1,250.

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Option A is not a polynomial because it contains a term with a negative exponent, while option B is a polynomial because all the terms have non-negative integer exponents.

A polynomial is a mathematical expression consisting of variables and coefficients, where the variables are raised to non-negative integer powers and are multiplied together. Polynomials are used to represent many different kinds of relationships in mathematics and are essential in areas such as algebra, calculus, and number theory.

In option A, the expression [tex]2/3x^{-2}+x+1[/tex]is not a polynomial because it contains a term with a negative exponent. Any term in which a variable appears with a negative exponent is not a polynomial.

Negative exponents represent the inverse of a term raised to a positive exponent, and as such, they involve division, which is not allowed in polynomials. Therefore, the term [tex]2/3x^{-2[/tex] makes the expression A not a polynomial.

In option B, the expression[tex]x^3+0x^2^x[/tex] is a polynomial because all the terms have non-negative integer exponents. The expression can be simplified to[tex]x^3 + 0x^3[/tex], which is equivalent to [tex]x^3.[/tex]

The constant term [tex]0x^2[/tex], which has a zero coefficient, does not affect the polynomial nature of the expression. The degree of the polynomial is 3, which is the highest power of the variable in the expression.

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To find the height of the tree, we'll use the tangent function in trigonometry, which relates the angle, the height of the tree, and the distance between the hiker and the tree. Here's a step-by-step explanation:

1. We're given the distance between the hiker and the tree as 750 ft, and the angle formed with the ground as 12°.
2. Let's denote the height of the tree as "h".
3. Using the tangent function, we have tan(angle) = height / distance.
4. Plugging in the given values, we get tan(12°) = h / 750 ft.
5. Solve for the height (h) by multiplying both sides by 750 ft: h = 750 ft * tan(12°).
6. Calculate the height using a calculator or any trigonometric tool: h ≈ 750 ft * 0.2126 ≈ 159.45 ft.

So, the height of the tree is approximately 159.45 ft.

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