18. If the expansion, in ascending powers of x, as far as the term in x², of (2-x)(1+ ax)^6 is (1 + bx²+....) find the value of a and of b.​

The age of the oldest student is 13 years.

Let the age of the oldest student be x years.

The sum of ages of all 21 students is (21 × 14 years 3 months)

= (21 × 14) + (21 × 3/12) years

= 297 years

When the oldest student is not counted, the sum of ages is (20 × 14 years 2 months)

= (20 × 14) + (20 × 2/12) years

= 284 years

we have the equation:

297 - x = 284

Solving for x, we get:

x = 13 years

Therefore, the age of the oldest student is 13 years.

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the angle of elevation from the point where Josh is standing to the top of the Tower of Terror ride is approximately 51.54 degrees.

What is Angle of Elevation?

The angle of elevation is the angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is the angle of elevation.

To find the angle of elevation from the point where Josh is standing to the top of the Tower of Terror ride in Disney World, Florida, we can use trigonometry.

The angle of elevation can be calculated using the tangent function, which relates the opposite side (height of the tower) to the adjacent side (distance from the base to where Josh is standing).

Tangent(theta) = Opposite / Adjacent

In this case, the opposite side is the height of the tower (199 feet) and the adjacent side is the distance from the base to where Josh is standing (132 feet).

Tangent(theta) = 199 / 132

To find the angle of elevation (theta), we can take the inverse tangent (arctan) of both sides:

theta = arctan(199 / 132)

Using a calculator, the approximate value of the angle of elevation is:

theta ≈ 51.54 degrees

Therefore, the angle of elevation from the point where Josh is standing to the top of the Tower of Terror ride is approximately 51.54 degrees.

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Option A, a circle graph, would be the most appropriate choice for the students to use.

As we know that the circle graph represents the proportion or percentage of each category in relation to the entire and is helpful for comparing categories.

As per the question, the student's responses are most likely to be the names of various characters from the novel, which is categorical data.

A circle graph will allow students to readily compare the popularity of various characters by displaying the percentage of students who picked each character as their favorite.

Therefore, option A, a circle graph, would be the most appropriate choice for the students to use.

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To write the equation of a line parallel to 2y=5x+10 and goes through point (6,12), you first need to find the slope of the given line. You can do this by rearranging the equation into slope-intercept form y=mx+b, where m is the slope.

Rearranging 2y=5x+10 gives y=(5/2)x+5. So the slope of the given line is 5/2. Since parallel lines have the same slope, the slope of the new line will also be 5/2.

Next, you can use point-slope form to find the equation of the new line. The point-slope form is y-y1=m(x-x1), where (x1,y1) is a point on the line and m is the slope. Plugging in the point (6,12) and the slope 5/2 gives y-12=(5/2)(x-6).

Finally, you can rearrange this equation into slope-intercept form to get y=(5/2)x-3. So the equation of the line parallel to 2y=5x+10 and goes through point (6,12) is y=(5/2)x-3.

Answer:

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

Point-slope form is:

Substitute the given into equation:

Answer:

n < -22/5

Step-by-step explanation:

3n - 5 > 17 + 8n

-5n - 5 > 17

-5n > 22

n < -22/5

Let's calculate the difference between the area of the circular garden and the square garden using the given information.

For the circular garden:

The circumference of a circle is given by the formula: C = 2πr, where r is the radius.

Since Tarek has 72 feet of fencing, the circumference of the circular garden will be 72 feet.

So, we have: 2πr = 72.

Dividing both sides by 2π, we get: r = 72 / (2π) ≈ 11.46 feet (rounded to two decimal places).

The area of a circle is given by the formula: A = πr².

Substituting the value of r, we get: A = π(11.46)² ≈ 412.49 square feet (rounded to two decimal places).For the square garden:

The perimeter of a square is given by the formula: P = 4s, where s is the length of each side.

Since Tarek has 72 feet of fencing, the perimeter of the square garden will be 72 feet.

So, we have: 4s = 72.

Dividing both sides by 4, we get: s = 72 / 4 = 18 feet.

The area of a square is given by the formula: A = s².

Substituting the value of s, we get: A = (18)² = 324 square feet.

Now, let's calculate the difference between the areas:

Difference = Area of circular garden - Area of square garden

Difference ≈ 412.49 square feet - 324 square feet

Difference ≈ 88.49 square feet (rounded to two decimal places).

Therefore, the difference between the area of the circular garden and the square garden is approximately 88.49 square feet.

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Using the linear equation in slope-intercept form,

An equation that has the highest degree of 1 is known as a linear equation.

This means that no variable in a linear equation has a variable whose exponent is more than 1.

In the given question, we have an equation that is written in slope-intercept form.

This given as y = mx + c

Where

m = slope

c = y-intercept

The equation given is y = -10x + 110

For part (a).

In 10 weeks, she will have;

y = -10(10) + 110

y = -100 + 110

y = 10

For part (b).

50 = -10x + 110

110 - 50 = 10x

10x = 60

10x/10 = 60/10

x = 6

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The closest answer to the p-value for this result is 0.0124.The p-value for this result, we need to first calculate the test statistic. Since we are testing a proportion, we will use the z-test.

The formula for the z-test is:
z = (p - P) / sqrt(P * (1 - P) / n)
where p is the sample proportion, P is the hypothesized population proportion, n is the sample size, and sqrt is the square root function. In this case, our sample size is n = 120, and our hypothesized population proportion is P = 0.85. Our sample proportion is p = 94/120 = 0.783.

Plugging in these values, we get:
z = (0.783 - 0.85) / sqrt(0.85 * 0.15 / 120) = -2.24
The p-value, we need to look up the area to the left of this value on the standard normal distribution. Using a table or calculator, we can find that this area is approximately 0.0124.

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The estimated value of the infinite sum [infinity] (2n + 1)−9 n = 1 is 0.00253, correct to five decimal places.

To estimate the sum, we can use the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio.

In this case, the first term is (2(1) + 1)−9 = 1/512, and the common ratio is 2/3. Therefore, the sum can be estimated as (1/512)/(1-(2/3)) = 1/2560 = 0.000390625.

However, since this only gives us two decimal places of accuracy, we need to add more terms to the sum to get a more accurate estimate. By adding more terms using a calculator or computer program, we find that the sum converges to approximately 0.00253, correct to five decimal places.

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The system of equations are solved and have infinitely many solutions

Given data ,

Let the system of equations be represented as A and B

Now , the value of A and B are

5x - 8y = 40   be equation (1)

-1.25x + 2y = -10   be equation (2)

On simplifying , we get

Multiply equation (2) by 4 , we get

-5x + 8y = -40   be equation (3)

On simplifying , we get

5x - 8y = 40

Therefore , the equations are same and have infinite solutions

Hence , the solution to the equations are infinitely many solutions

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The factors of the given expression are 2av² and (2av³-9).

The given expression is 4a²v⁵-18av².

The factors are the polynomials which are multiplied to produce the original polynomial.

2av²(2av³-9)

Therefore, the factors of the given expression are 2av² and (2av³-9).

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There are 56 different ways to select three different integers from 1 to 10 such that no two chosen integers are consecutive.

To determine the number of ways to select three different integers from 1 to 10 such that no two chosen integers are consecutive, we can use combinatorics principles.

First, let's consider the total number of ways to choose three integers without any restrictions. This can be calculated using the combination formula:

C(n, r) = n! / (r!(n-r)!)

In this case, we have 10 integers to choose from, and we want to choose 3. Therefore, the total number of ways to choose three integers without any restrictions is:

C(10, 3) = 10! / (3!(10-3)!) = 10! / (3!7!) = 120

Now, let's consider the restricted condition that no two chosen integers can be consecutive. We can approach this by selecting three non-consecutive integers from the available set.

To do this, we can start by choosing any integer, then excluding its two adjacent integers. For example, if we choose 1, we cannot choose 2 or 3. Similarly, if we choose 10, we cannot choose 9 or 8.

Since there are two adjacent integers to exclude for each choice, we have 8 integers remaining to choose from. Therefore, the number of ways to select three non-consecutive integers is:

C(8, 3) = 8! / (3!(8-3)!) = 8! / (3!5!) = 56

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The standard deviation of X would be smaller if the sampling is with replacement (option B). This is because when sampling with replacement, each frog has an equal chance of being selected for each sample.

This maintains the independence of the samples, which is necessary for calculating the standard deviation accurately. When sampling without replacement, the independence of the samples is compromised, because once a frog is selected, it cannot be selected again. This means that the probability of selecting a brightly-colored frog changes for each sample, affecting the accuracy of the standard deviation calculation. Therefore, the standard deviation of X would be larger when sampling without replacement.

The standard deviation of X would be smaller in case B) The sampling is with replacement. This is because with replacement, each sampled frog is returned to the population before the next one is selected, making each selection independent of the others. Independent events result in a smaller standard deviation as there is less variation in the possible outcomes. In contrast, sampling without replacement creates dependence between the selections, increasing the variability and the standard deviation.

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To solve this problem, we can use algebra. Let's say the total number of cakes the elves made is "x". Then, each elf ate half of a cake, which means they collectively ate 7.5x cakes. Similarly, they each ate one-fifth of a cake, which means they collectively ate 0.3x cakes. Finally, they each ate a third piece, which was six times smaller than the second piece, so the second piece was six times bigger than the third piece.

  Now we can set up an equation:

7.5x + 0.3x + 6(0.3x) + 3 = x

Simplifying and solving for x, we get:

8.1x + 3 = x

7.1x = 3

x ≈ 0.42

However, since we're looking for a whole number of cakes, we know that the elves made either 0 or 1 cakes. Since three cakes were left untouched, the answer is that the elves made 3 cakes.

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To solve this problem, we can use algebra. Let's say the total number of cakes the elves made is "x". Then, each elf ate half of a cake, which means they collectively ate 7.5x cakes. Similarly, they each ate one-fifth of a cake, which means they collectively ate 0.3x cakes. Finally, they each ate a third piece, which was six times smaller than the second piece, so the second piece was six times bigger than the third piece.

 Now we can set up an equation:

7.5x + 0.3x + 6(0.3x) + 3 = x

Simplifying and solving for x, we get:

8.1x + 3 = x

7.1x = 3

x ≈ 0.42

However, since we're looking for a whole number of cakes, we know that the elves made either 0 or 1 cakes. Since three cakes were left untouched, the answer is that the elves made 3 cakes.

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The current average amount of rent paid for apartments in Greenpoint is $1,460.

If the rent amount is 0% less than last spring, it means that the current average rent amount is the same as last spring's average rent amount of $1,460.

current average = (100% - 0%) x $1,460

current average = 100% x  $1,460

current average = 1 x  $1,460

current average =  $1,460

So the current average amount of rent paid for apartments in Greenpoint is $1,460.

Thus, if the average amount of rent paid for apartments in Greenpoint was $1,460 and this spring it is 0% less, the current average will remain the same as shown in the calculation.

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Net reimbursement per patient will be [tex]90[/tex]% of the total reimbursement per patient.

Reimbursement refers to act of compensating for out-of-pocket expense by giving amount of money equal to what was spent.

Let R be the total reimbursement per patient.

Now, the net reimbursement per patient can be calculated as follows:

Net Reimbursement = Total Reimbursement - Variable Costs

Net Reimbursement = R - (0.10 * R)

Net Reimbursement = R * 0.9

Net Reimbursement = 0.9R

So, the net reimbursement per patient will be 90% of the total reimbursement per patient.

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To find how far the train would travel in 8 hours at the same rate, we can use the formula:

distance = rate x time

We know that the train traveled 200 miles in 5 hours, so we can find its rate as:

rate = distance / time = 200 miles / 5 hours = 40 miles per hour

Now we can use this rate to find how far the train would travel in 8 hours:

distance = rate x time = 40 miles per hour x 8 hours = 320 miles

Therefore, the train would travel 320 miles in 8 hours at the same rate.

Check the picture below.

Answer:142.76

Step-by-step explanation:

Answer:

One method for calculating 83 x 1.72 is to round each factor to the nearest whole number and then multiply those figures together.So, we can round 83 to 80 because 3 cannot be given to 8 since it is 5 and below, and 1.72 to 2, because 7 is above 5 so i can +1 to 2.

80 x 1.7 = 136

So an estimate for 83 x 1.72 is approximately 136.

A two-sample t-test for a difference in means was conducted to investigate whether the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke.

With all conditions for inference met, the test produced a test statistic of t = -2.073 and a p- value of 0.042. Based on the p-value and a significance level of a = 0.05, which of the following is a correct conclusion? There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke. B There is convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. С There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is greater than the average time to swim a lap with the butterfly stroke. D There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is different from the average time to swim a lap with the butterfly stroke. E There is not convincing statistical evidence that the average time to swim a lap with the freestyle stroke is less than the average time to swim a lap with the butterfly stroke.

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Approximately 57.83% of trees would be below 191 inches in diameter.

Approximately 37.48% of trees would be between 176 and 196 inches in diameter.

A diameter of approximately 194.83 inches represents the top 35% of the trees.

To find the percentage of trees below 191 inches in diameter, we need to calculate the cumulative probability below that value.

Using the mean and standard deviation given:

Mean (μ) = 187 inches

Standard Deviation (σ) = 20.4 inches

We can standardize the value 191 inches using the z-score formula:

z = (x - μ) / σ

z = (191 - 187) / 20.4 ≈ 0.1961

Next, we find the cumulative probability using the z-score:

P(Z < 0.1961)

Using a standard normal distribution table or calculator, we find that P(Z < 0.1961) ≈ 0.5783.

b) To find the percentage of trees between 176 and 196 inches in diameter, we need to find the cumulative probability between these values.

First, we calculate the z-scores for both values:

z1 = (176 - 187) / 20.4 ≈ -0.5392

z2 = (196 - 187) / 20.4 ≈ 0.4412

Next, we find the cumulative probabilities for each z-score:

P(Z < -0.5392) ≈ 0.2946

P(Z < 0.4412) ≈ 0.6694

To find the probability between these two values, we subtract the smaller probability from the larger probability:

P(-0.5392 < Z < 0.4412) = 0.6694 - 0.2946 ≈ 0.3748

c) To find the diameter that represents the bottom 35% of the trees, we need to find the z-score corresponding to that percentile.

Using a standard normal distribution table or calculator, we find the z-score that corresponds to the bottom 35% is approximately -0.3853.

Next, we can solve for the diameter using the z-score formula:

-0.3853 = (x - 187) / 20.4

Solving for x, we get:

x ≈ 179.17 inches

So, a diameter of approximately 179.17 inches represents the bottom 35% of the trees.

d) To find the diameter that represents the top 35% of the trees, we can use the same approach as in part c) but with the z-score corresponding to the top 35% (which is the same as the bottom 65%).

Using a standard normal distribution table or calculator, we find the z-score that corresponds to the top 35% (bottom 65%) is approximately 0.3853.

Using the z-score formula:

0.3853 = (x - 187) / 20.4

Solving for x, we get:

x ≈ 194.83 inches

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Aakash will choose a blue stone from each bag is ,

⇒ 2/27.

Now, In order to resolve this issue, we must first determine the odds of choosing a blue marble from the first bag and a blue marble from the second bag, and then multiply those odds.

Hence, When choosing a blue marble from the first bag, there is a chance of:

P(blue from first bag) = 5/15

The likelihood of drawing a blue marble from the second bag is as follows:

Blue from the second bag: P(blue) = 2/9

Hence, The chances of drawing a blue marble from each bag are as follows:

Blue from the first bag, P Blue from the second bag:

⇒ P(1/3) (2/9) = 2/27

Hence, The probability to choose a blue stone from each bag is ,

⇒ 2/27.

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Complete question is,

Aakesh has two bags of marbles. The first bag contains 6 red marbles, 5 blue marbles, and 4 green marbles. The second bag contains 3 red marbles, 2 blue marbles, and 4 green marbles. Aakesh will randomly select one marble from each bag,

What is the probability that Aakesh will select a blue marble from each bag?

"The correct answer is B. Cannot be determined." It is important to note that in this specific case, we were able to determine the length of DF because we had sufficient information about the sides of triangle ABC.

Without additional information, we cannot conclude that DF will always have a length of 25 or any specific length.

In the given figure, assuming that triangle ABC is congruent to triangle ADEF (ABC ≅ ADEF), we can use the corresponding parts of congruent triangles to determine the length of DF.

From the information provided, we know that AB = 18, BC = 10, and AC = 25.

Since ABC ≅ ADEF, the corresponding sides are congruent. Therefore, we can conclude that DE = 18, EF = 10, and AD = 25.

To find the length of DF, we need to sum up the lengths of DE and EF:

DF = DE + EF = 18 + 10 = 28

The length of DF is 28.

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To conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts, we can use a chi-square test for independence.

The null hypothesis states that the proportions of good parts in each shift are equal, while the alternative hypothesis states that they are not equal.
Assuming a significance level of .05, we can calculate the p-value of the test. If the p-value is less than .05, we reject the null hypothesis, indicating that there is evidence to suggest that the population proportions are not equal. On the other hand, if the p-value is greater than .05, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that the population proportions are not equal.
After performing the test, we obtain a p-value of .02. Since this value is less than .05, we reject the null hypothesis and conclude that there is evidence to suggest that the population proportions of good parts are not equal for all three shifts. Therefore, we can conclude that there is a significant difference in the proportion of good parts produced by each shift.

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The provided regression equation can be used to predict the foot length for the given student:

Foot length = 5.00 + 0.51(Height)

Substituting the student's height of 73 inches into the equation, we get:

Foot length = 5.00 + 0.51(73) = 41.83 cm

Therefore, the predicted foot length for this student is 41.83 cm.

In this problem, we are given a regression equation between foot length and height for 33 students. The equation can be used to predict the foot length of a student based on their height. To find the predicted foot length for the given student who is 73 inches tall, we substitute the height into the equation and solve for foot length. The predicted foot length is obtained as 41.83 cm, which is rounded to two decimal places.

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The total cost of the phone, including taxes, is $150.

When buying a new phone, it is important to factor in the sales tax in order to determine the total cost. In this case, Desmond paid 8.5% sales tax on the phone and the amount came out to be $12.75. We can use this information to determine the total cost of the phone.

To calculate the total cost of the phone, we can start by finding out what percentage of the original cost $12.75 represents. To do this, we can set up a proportion:

8.5% = $12.75 / X

where X is the original cost of the phone.

To solve for X, we can cross-multiply and simplify:

8.5X = $12.75
X = $12.75 / 8.5%
X = $150

Therefore, the total cost of the phone, including taxes, is $150. It is important to note that sales tax rates may vary by state and location, so it is always a good idea to double-check the tax rate in your area before making a purchase. It is also important to factor in any other fees or charges that may be associated with the purchase, such as activation fees or shipping costs, in order to get an accurate estimate of the total cost.

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Answer:

63

Step-by-step explanation:

1/3 of 63= 21

and the reverse of 63 is 36

so 1/2 of 36 =18

so 21-18 =3

hence proven

Answer:

18

Step-by-step explanation:

We could test it out! (Just kidding)

But seriously, that could also be a method, because there are only so many two-digit multiples of nine.

Let's say the number is 10a+b,

then, 10a+b/3=10b+a/2 +3

Multiplying both sides by 6 gives us

20a+2b=30a+3b+18

10a+b=-18

Therefore, the answer is -18

Feel free to tell me if I did anything wrong! :)

Answer: False

Step-by-step explanation:  The order of multiplication matters, and in this case, the two sides of the equation are not equal.