Work out the recipricol of 0.5

Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, 15, 52, 25, 34, and 43Therefore, the probability of the sum being 7 or at least one die being 1 is:P(sum is 7 or at least one die is 1) = 15/36 = 5/12

Hence, P(sum is odd) = 7/36, P(sum is 5) = 1/9, P(sum is 7) = 1/6, P(sum is 7 and at least one die is 1) = 5/18, and P(sum is 7 or at least one die is 1) = 5/12.

In the given experiment of rolling two dice, the following probabilities are to be determined:

P(sum is odd), P(sum is 5), P(sum is 7), P(sum is 7 and at least one of the die is 1), and P(sum is 7 or at least one of the die is 1).The sum of two dice is odd if one die has an odd number and the other has an even number. The possibilities of odd numbers are 1, 3, and 5, while the possibilities of even numbers are 2, 4, and 6. Therefore, the following outcomes satisfy the condition:

1, 22, 24, 36, 42, 44, and 66Thus, the probability of the sum being odd is: P(sum is odd) = 7/36The sum of two dice is 5 if one die has 1 and the other has 4, or one die has 2 and the other has 3. Thus, the following outcomes satisfy the condition:1, 42, 3Therefore, the probability of the sum being 5 is: P(sum is 5) = 4/36 = 1/9The sum of two dice is 7 if the dice show 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, or 6 and 1.

Thus, the following outcomes satisfy the condition:1, 63, 54, 45, 36, and 2Therefore, the probability of the sum being 7 is: P(sum is 7) = 6/36 = 1/6The sum of two dice is 7 and at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, or 1 and 5. Thus, the following outcomes satisfy the condition:1, 61, 11, 12, 21, 13, 31, 14, 41, and 15

Therefore, the probability of the sum being 7 and at least one die being 1 is:P(sum is 7 and at least one die is 1) = 10/36 = 5/18The sum of two dice is 7 or at least one die is 1 if the dice show 1 and 6, 6 and 1, 1 and 1, 1 and 2, 2 and 1, 1 and 3, 3 and 1, 1 and 4, 4 and 1, 1 and 5, 2 and 5, 5 and 2, 3 and 4, or 4 and 3.

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Answer:

x = - 2

Step-by-step explanation:

the equation of a vertical line parallel to the y- axis is

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through all points with an x- coordinate of - 2 , then

x = - 2 ← equation of line

Answer: x = 18

Step-by-step explanation:

x - 3 = 15

x = 15 + 3

x = 18

[tex]\huge{\color{pink}{\underline{\color{pink}{\underline{\color{cyan}{\textbf{\textsf{\colorbox{purple}{Answer ≈}}}}}}}}}[/tex]

Step-by-step explanation:

Given ,

≈> x – 3 = 15

•add 3 on both the sides

≈> x –3 + 3 = 15 + 3

≈> x = 18

The product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.

WHAT IS BOX METHOD ?

The box method, also known as the grid method, is a visual method used to multiply two numbers or two binomials. It involves creating a grid or box and filling it in with the products of the digits in each row and column. The method works for both single-digit and multi-digit numbers.

To use the box method for multiplying two numbers, we draw a box with two rows and two columns. We write one number along the top row and the other number along the left column. Then, we multiply the digits in each row and column and write the products in the corresponding cell of the box. Finally, we add the numbers in each cell of the box to get the product of the two numbers.

The box method can be used to multiply two binomials, such as (4x + 7) and (3x - 8). To use the box method, we draw a box with four cells, and we write the two binomials along the top and left sides of the box, like this:

     |  4x  |  7

-------------------

 3x  |      |

-------------------

    |      |

Then, we fill in the four cells of the box by multiplying the corresponding terms. For example, the top-left cell is filled by multiplying 4x and 3x, which gives 12x². The other cells are filled in a similar way:

     |  4x  |  7

-------------------

 3x  | 12x² | 28x

-------------------

    | -21x | -56

Next, we combine the terms in each row and column of the box, and write the final answer as the sum of these terms:

12x² + 28x - 21x - 56

Simplifying this expression gives:

12x² + 7x - 56

Therefore, the product of (4x + 7) and (3x - 8) is 12x² + 7x - 56.

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Answer: 105

Step-by-step explanation:

OBTUSE ANGLE (105°) IS FORMED AT 2:30 IN THE CLØCK.

As we know 12 division OF 360° CIRCLE GIVES 30°

AT TWO PM THE ANGLE BETWEEN HOUR AND MINUTE HAND IS 60° AFTER 30 MIN ARM ROTATES 180° AND HOUR ARM 30°/2 = 15°

SO THE ANGLE BETWEEN TWO ARMS IS (180-(60-15)

105

Answer: Felipe has walked 25.1 meters.

Step-by-step explanation:

Felipe walks the length of his living room, which is 9.1 meters. He then turns and walks the width of his living room, which is 3.5 meters. Finally, he walks back to the corner he started from, which is another 9.1 meters.

The total distance that Felipe has walked is the sum of the distances he covered in each of these three parts of his walk. So, we need to add up 9.1 meters, 3.5 meters, and 9.1 meters to get the total distance.

9.1 m + 3.5 m + 9.1 m = 21.7 m

Therefore, Felipe has walked 21.7 meters so far. However, he still needs to walk back to the corner he started from. This distance is equal to the diagonal of the rectangle formed by his living room.

We can use the Pythagorean theorem to find the length of this diagonal. The length and width of the rectangle are 9.1 meters and 3.5 meters, respectively. Let d be the length of the diagonal, then:

d² = 9.1² + 3.5²

d² = 83.06

d ≈ 9.11 meters

Therefore, the total distance that Felipe has walked is approximately:

21.7 m + 9.11 m ≈ 25.1 m

So, Felipe has walked about 25.1 meters.

Answer:

Felipe has walked 25.2 meters in total.

Step-by-step explanation:

To find out how far Felipe has walked, we need to calculate the perimeter of his living room. The perimeter is the distance around the outside of a shape.

The formula for the perimeter of a rectangle is:

perimeter = 2(length + width)

Given that the length of Felipe's living room is 9.1 meters and the width is 3.5 meters, we can substitute these values into the formula and get:

perimeter = 2(9.1 + 3.5)

perimeter = 2(12.6)

perimeter = 25.2 meters

Function P represents the perimeter, in inches, of a square with the side length x inches. So, the perimeter of a square can be represented as P = x + x + x + x, which simplifies to P = 4x. This way is more efficient to write than the former.

Complete the table provided: x 0 1 2 3 4 5 6 P(x) 0 4 8 12 16 20 24. When x = 0, the perimeter of the square is 0.When x = 1, the perimeter of the square is P = 4(1) = 4. When x = 2, the perimeter of the square is P = 4(2) = 8. When x = 3, the perimeter of the square is P = 4(3) = 12. When x = 4, the perimeter of the square is P = 4(4) = 16. When x = 5, the perimeter of the square is P = 4(5) = 20. When x = 6, the perimeter of the square is P = 4(6) = 24.

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Answer:

To find the greatest common factor, we need to find the largest factor that divides both terms evenly. We can factor each term as follows:

8a³b5 = 2³ * a³ * b5

16a²b7 = 2⁴ * a² * b7

The greatest common factor is the product of the lowest exponent of each prime factor that appears in both terms. Therefore, the greatest common factor is:

GCF = 2³ * a² * b5 = 8a²b5

To find the least common multiple, we need to find the smallest multiple that both terms share. We can start by writing out the prime factorization of each term:

8a³b5 = 2³ * a³ * b5

16a²b7 = 2⁴ * a² * b7

The least common multiple is the product of the highest exponent of each prime factor that appears in either term. Therefore, the least common multiple is:

LCM = 2⁴ * a³ * b7 = 16a³b7

So, the greatest common factor is 8a²b5 and the least common multiple is 16a³b7.

The answer of the given question based on finding the m∠LKM from the given circle the answer is the measure of ∠LKM is 140° degrees.

In geometry,  diameter of circle is  line segment that passes through  center of  circle and has both endpoints on circle. The diameter is the longest chord (line segment connecting two points on  circumference) of  circle. The length of  diameter is twice the length of radius, which is distance from the center of  circle to any point on  circumference.

The diameter i important property of a circle and is used to calculate other properties, like the circumference and area of the circle

Since MK is a diameter of the circle, it passes through the center of the circle, which we can label as point O. Therefore, ∠LKM is an inscribed angle that intercepts arc LM.

By the Inscribed Angle Theorem, we know that the measure of an inscribed angle is equal to half the measure of the arc that it intercepts. Therefore, to find the measure of ∠LKM, we need to find the measure of arc LM.

We are given that the measure of arc LK is 100° degrees. Since arc LM is the sum of arcs LK and KM, and MK is a diameter (so arc KM is also a semicircle with a measure of 180 degrees), we can write:

m(arc LM) = m(arc LK) + m(arc KM) = 100 + 180 = 280° degrees

Therefore, the measure of ∠LKM is:

m∠LKM = 1/2 * m(arc LM) = 1/2 * 280 = 140° degrees

So the measure of ∠LKM is 140° degrees.

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The giraffe is 15 feet tall based on the relation between the length of neck of giraffe and it's height.

Firstly convert the mixed fraction to fraction.

Length of neck of giraffe = (4×2)+1/2

Length of neck = 9/2 feet

Now, let us assume the height of giraffe be x. So, equation will be -

30% × x = 9/2

Rewriting the equation

30/100 × x = 9/2

Cancelling zero

3x/10 = 9/2

Again rewriting the equation

x = 90/6

Performing division on Right Hand Side of the equation

x = 15 feet

Thus, height of giraffe is 15 feet.

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A fast food restaurant estimate that 45% of their customers buy drinks with their purchases. Last week, 6200 customers did not buy soft drinks. They have a total of 11272 customers.

when in a percentage we take 100%

if 45% take soft drinks with their purchases

then the other 55% did not take soft drinks with their purchases

therefore, we have 6200 customers who did not buy soft drinks with their purchases.

now we know that 11272 are there total customers

therefore, now we have to subtract 6200 from 11272

we get 5072.

therefore 5072 customers who buy soft drinks with their purchases.

A fast food restaurant estimate that 45% of their customers buy drinks with their purchases. Last week, 6200 customers did not buy soft drinks. They have a total of 11272 customers

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The equation of the circle graphed in this problem is given as follows:

x² + y² = 34.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The center of the circle is at the origin, hence:

x² + y² = r².

The diameter of the circle is given by segment AC, which is the hypotenuse of a right triangle of sides 10 and 6, hence it's length is obtained applying the Pythagorean Theroem as follows:

d² = 10² + 6²

d = sqrt(10² + 6²)

d = 11.66.

The radius is half the diameter, hence:

r = 11.66/2

r = 5.83.

Then the equation of the circle is given as follows:

x² + y² = 5.83²

x² + y² = 34.

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The population will be approximately 84,161 in 2033 according to the exponential growth function.

The given information in the problem is;Population in 2008 = 39,700

Annual growth rate = 3%

We need to find out the population in 2033.

The formula for continuous exponential growth is;P(t) = P₀e^(rt)

where;P₀ is the initial populationr is the annual growth rate (in decimal form)t is the time elapsed (in years)

We are given P₀ = 39,700r = 0.03t = 2033 - 2008 = 25 years

Put these values in the formula of continuous exponential growth;

P(25) = 39,700e^(0.03 x 25)P(25)

= 39,700e^(0.75)P(25)

= 39,700 x 2.1170000493605122P(25)

= 84,161.13

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Step-by-step explanation:

No,

if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular

A=πr2

A=3.142*36

A=113.112 cm3

If 7/9 of the box is green counters, and there are 24 yellow counters in the box, then there are 84 green counters .

Let's assume that the total number of counters in the box is x.

We are given that 7/9 of the box is filled with green counters, which means that the remaining 2/9 of the box must be filled with yellow counters. We are also given that there are 24 yellow counters in the box.

We can set up an equation to represent the relationship between the number of yellow counters and the total number of counters:

2/9 x = 24

To solve for x, we can multiply both sides of the equation by the reciprocal of 2/9, which is 9/2:

(2/9) x * (9/2) = 24 * (9/2)

x = 108

This means that there are a total of 108 counters in the box. To find out how many of these are green counters, we can use the fact that 7/9 of the box is filled with green counters:

(7/9) * 108 = 84

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The expression represents the difference of 7 and twice the product of a and b is 7 - 2ab

Let's break down the given problem step by step. First, we need to find the product of a and b, which is done by multiplying the two variables together using the multiplication symbol (*). Then, we need to multiply this result by 2, which is done by placing the entire product inside parentheses and then multiplying it by 2 using the multiplication symbol again.

Once we have found twice the product of a and b, we need to subtract it from 7. This can be done using the subtraction symbol (-), which we place between 7 and the expression we just found.

Putting it all together, the expression we get is:

7 - 2ab

where a and b are the two variables we were given.

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If a statistic used to estimate a parameter is said to be unbiased, then the mean of the sampling distribution of the statistic is equal to the true value of the parameter it is being used to estimate (B).

In statistics, when a sample statistic is unbiased, it means that the statistic does not deviate from the population parameter that it is trying to estimate. The unbiased estimator is not consistently overestimating or underestimate the true population parameter value.

It is measured by the mean of the sampling distribution. In other words, if we take every possible sample of the same size n from the same population and calculate the statistic, the mean of those statistics would be equal to the true value of the parameter being estimated.

Option (A) is not true, because it is not necessary for the statistic to be exactly equal to the true value of the parameter for every possible sample, only that the average of the statistic over many samples is equal to the true value.

Option (C) is not necessarily true, as the sampling distribution of the statistic may have a different standard deviation than the population distribution.

Option (D) is not true, as unbiasedness applies to any type of statistic, not just proportions.

Option (E) is not true, as the mean of the sampling distribution of an unbiased statistic does not depend on the sample size, only on the true value of the parameter being estimated.

Therefore, the correct option is (B) The mean of the sampling distribution of the statistic is equal to the true value of the parameter it is being used to estimate.

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Number of  prints Jim ordered last month is 271

Let's assume Jim ordered "P" prints last month. The cost of ordering "P" prints would be the sum of the monthly charge and the cost of each print, which is given by the equation:

Cost = Monthly Charge + (Cost per Print x Number of Prints)

Substitute the values in the equation

$17.79 = $6.95 + ($0.04 x P)

Simplifying the equation, we get:

$10.84 = $0.04 x P

Dividing both sides by $0.04, we get:

P = $10.84 / $0.04

Divide the numbers

P = 271

Therefore, Jim ordered 271 prints last month.

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The answer is (001). This is because B (001) has h and k as non-zero integers, which does not match the criteria for the {100} family.

The question is asking which of the planes (A), (B), (C), and (D) is not part of the {100} family for a tetragonal crystal.A tetragonal crystal is a three-dimensional structure made up of four faces that intersect at right angles, forming a unit cell. Each face of the unit cell is defined by a Miller index. A Miller index is a set of three integers written in the form {hkl}, which describes the orientation of the face relative to the crystal lattice. In a tetragonal crystal, the {100} family is the set of faces described by {hkl} such that h = k = 0 and l ≠ 0.

Therefore, A (010), C (110), and E (all of these planes are in the {100} family) are all part of the {100} family for a tetragonal crystal, while B (001) is not.  because B (001) has h and k as non-zero integers, which does not match the criteria for the {100} family. In conclusion, the correct answer to the question is B (001).

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Answer:

  (2x -4)/(x -1)

Step-by-step explanation:

You want to simplify (2x² -2x -4)/(x² -1).

Simplifying a rational expression generally means cancelling common factors from the numerator and denominator. To do that, you must factor both the numerator and the denominator.

The numerator coefficients have a common factor of 2. Removing that can simplify the problem of factoring the numerator:

  2x² -2x -4 = 2(x² -x -2)

To factor the quadratic, you look for factors of -2 that have a sum of -1. Those would be -2 and +1. The middle term is written as a sum using these values.

  = 2(x² -2x +x -2)

This can now be factored by grouping terms in pairs, and factoring each pair.

  = 2((x² -2x) +(x -2)) = 2(x(x -2) +1(x -2))

  = 2(x +1)(x -2)

The denominator is the difference of squares, so is factored according to the pattern for that:

  a² -b² = (a -b)(a +b)

  x² -1 = (x -1)(x +1)

Now you know enough to be able to simplify the expression. The common factors (x+1) cancel.

  [tex]\dfrac{2x^2-2x-4}{x^2-1}=\dfrac{2(x+1)(x-2)}{(x+1)(x-1)}\\\\=\dfrac{2(x-2)}{x-1}=\boxed{\dfrac{2x-4}{x-1}}[/tex]

__

Additional comment

Even though the factor (x+1) has disappeared from the expression, the simplified form still carries the restriction that x ≠ -1. The graph of the original expression will have a "hole" at (-1, 3), where it is undefined. Otherwise, the graph looks like a graph of (2x-4)/(x-1).

Answer:

Step-by-step explanation:

The probability that more than 8 hours are needed to grade all of the exams is about 52%

The probability of a standard normal distribution is the area under the curve of the normal distribution function within a specified interval.

Let X represent the random variable to grade an exam, and let Y represent the total time to grade all exams

The number of students = 50

Therefore;

Y = 50·X

The properties of the normal distribution indicates that we get;

E(Y) = E(50·X) = 50·E(X) = 50 × 9.7 = 485

Var(Y) = Var(50·X) = 50²·Var(X) = 50² × 1.92² = 9025

The standard deviation, SD(Y) = √(Var(Y)) = √(9025) = 95

The probability that more than 8 hours are needed can be found using the z-score of the normal distribution as follows;

8 hours = 480 minutes

Z = (480 - 485)/95 ≈ -0.0526

The probability obtained from a standard normal table, is therefore;

P(Z > -0.0526) = 1 - 0.48006 ≈ 0.52

The probability that more than 8 hours are needed to grade all students is therefore about 0.52 or 52%

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Answer:

y = - [x - 1] + 2

Step-by-step explanation:

I think this is right

Im sorry if not :)

There are 48 toy soldiers, which is 6 x 8 of them.

The anger Eminem expresses in "Like Toy Soldiers" is a result of his personal beefs with rappers Ja Rule and Benzino, who was the editor of The Source at the time. The song, "Toy Soldiers," by Martika, was sampled on the 2004 release Encore.

Let's name Leo's collection of toy soldiers "x" the amount.

As a result of the problem statement, we are aware of:

There are no more when he arranges them in groups of four, proving that x is divisible by four.

Six remain after he divides them into groups of seven, proving that (x - 6) is divisible by seven.

He organizes them into fives. If there are still 3 after multiplying by 5, (x - 3) can be divided by 5.

We may create a system of equations based on these three conditions:

x = 4a (from the first condition)

x - 6 = 7b (from the second condition)

x - 3 = 5c (from the third condition)

where a, b, and c are integers.

4a - 6 = 7b

4a - 3 = 5c

Now we need to solve for a, b, and c.

7b = 4a - 6

7b + 6 = 4a

Since 7 and 4 are relatively prime, we know that (7b + 6) must be divisible by 4. Therefore, we can write:

7b + 6 = 4k

where k is some integer. Solving for b, we get:

b = (4k - 6) / 7

Since b is an integer, k must be 2, which gives us:

b = (4(2) - 6) / 7 = -1

We can try the next possible value of k, which is 3:

b = (4(3) - 6) / 7 = 0

x - 3 = 5c

6 - 3 = 5c

c = 1

6 divided by 4 is 1 with no remainder.

(6 - 6) divided by 7 is 0 with a remainder of 0.

(6 - 3) divided by 5 is 1 with a remainder of 0.

Therefore, the answer is 48, which is 6 times 8.

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 The 32 ways to get a five-card combination containing two jacks and three aces.

(a) A full house consists of three of one kind and two of another kind. Therefore, there are 13 different choices for the rank of the triplet and 4 cards of the same rank. Once the triplet has been chosen, there are 12 choices for the rank of the pair and 4 cards of the same rank. Therefore, the number of ways to get a full house is as follows:$${13}{\times}{4}{\times}{12}{\times}{4}={7488}$$Therefore, there are 7488 ways to get a full house.(b) In this case, the two jacks and three aces must be chosen out of the 4 jacks and 4 aces in the deck. Therefore, the number of ways to get a five-card combination with two jacks and three aces is as follows:$$\frac{{4\choose2}{4\choose3}{44\choose0}}{5!}={32}$$Therefore, there are 32 ways to get a five-card combination containing two jacks and three aces.

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Answer:

Step-by-step explanation:

Let x be the measure of the smaller angle.

Since the two angles are supplementary, we have:

x + (x + 174.8°) = 180°

Simplifying the equation gives:

2x + 174.8° = 180°

Subtracting 174.8° from both sides gives:

2x = 5.2°

Dividing by 2 gives:

x = 2.6°

Therefore, the smaller angle measures 2.6°, and the larger angle (which is supplementary) measures:

x + 174.8° = 2.6° + 174.8° = 177.4°

Answer:

90 miles

Step-by-step explanation:

We know

She has driven 30 miles so far, which is one-third of the way home.

What is the total length of her drive?

We Take

30 x 3 = 90 miles

So, the total length of her drive is 90 miles.​

Given expression is $(1 + ax)^n$If $n$ is a positive integer then by using binomial theorem,

we can expand the given expression as$(1 + ax)^n$ $= 1 + nax + \frac{n(n - 1)}{2!}(ax)^2 + \frac{n(n - 1)(n - 2)}{3!}(ax)^3 + ... $Let the first few terms in the expansion of $(1 + ax)^n$ be$1 + 4ax + 6a^2x^2 + 4a^3x^3 + a^4x^4$Thus,$1 = \binom{n}{0}$ $⇒ nC_0 = 1$$nax = \binom{n}{1}$ $⇒ nC_1a^1x^1 = 4a$x $⇒ n = 4$ $\ \ \ \ $ $⇒ a = \frac{1}{4x}$The given expression becomes $\left(1 + \frac{x}{4}\right)^4$

Expanding this using binomial theorem, we get$\left(1 + \frac{x}{4}\right)^4$ $= \binom{4}{0}1^4\left(\frac{x}{4}\right)^0 + \binom{4}{1}1^3\left(\frac{x}{4}\right)^1 + \binom{4}{2}1^2\left(\frac{x}{4}\right)^2 + \binom{4}{3}1^1\left(\frac{x}{4}\right)^3 + \binom{4}{4}1^0\left(\frac{x}{4}\right)^4$$= 1 + x + 3x^2 + 4x^3 + \frac{1}{4}x^4$

Hence, the first few terms in the expansion of $(1 + ax)^n$ are $1 + 4ax + 6a^2x^2 + 4a^3x^3 + a^4x^4$ where $n = 4$ and $a = \frac{1}{4x}$. The expression can be further simplified to $1 + x + 3x^2 + 4x^3 + \frac{1}{4}x^4$.

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he tree nearest the house is our starting point. Our point person is taking the clinometer reading 15.24 meters from the tree's base and they get a reading of 237`. Our point person is 1.83 meters in height.

How tall is the tree, rounded to the nearest meter?The height of the tree can be determined by using the tangent formula. The tangent formula is tan θ = h/d where θ = angle of elevation, h = height of the object, and d = horizontal distance.

The clinometer reading is the angle of elevation. Hence, we can use the given data to determine the height of the tree.The point person is standing at 15.24 m from the base of the tree. Therefore, the horizontal distance (d) is 15.24 m. The angle of elevation (θ) is 237 degrees (given in the question).

Convert the degrees to radians as tan function uses radians. Convert degrees to radians:[tex]237 × (π/180) = 4.135[/tex]radians.Now we can use the tangent formula to determine the height of the tree:tan θ = h/dtan 4.135 = [tex]h/15.24h = 15.24 × tan 4.135h = 15.24 × 0.07311h ≈ 1.1132[/tex] metersThe height of the tree is 1.1132 meters. But, we have to round the answer to the nearest meter. Therefore, the height of the tree, rounded to the nearest meter, is 1 meter.

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The domain ofA is Answer: "d. [tex]a(x) = -x^2 + 300x[/tex], Domain = {x|0 < x < 6000 "}

A farmer has 600 yards of fencing to enclose a rectangular garden. The area A of the rectangle as a function of the width x of the rectangle can be expressed as follows:

[tex]A = x(300 - x) = 300x - x^{2}[/tex]

The domain of A is given by the interval of values of x that can be chosen for the width of the rectangle. The width of a rectangle must be positive, so we have 0 < x. If the farmer has 600 yards of fencing, we can get the maximum value of x as follows:

600 = 2x + 300x = 600/3 = 200

So we have x < 200.

Therefore, the domain of A is {x | 0 < x < 200}.

Rewriting the equation of A, we get:

A(x) = -x² + 300x, Domain = {x | 0 < x < 200}.

In yards, the answer would be {x | 0 < x < 6000}.

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