Fine the 91st term of the arithmetic sequence 4,6,8

Answer: i think the awnser to your question is A  real number

Step-by-step explanation:

Taking the absolute value of a number, whether it's negative or positive, always returns either a positive value or zero.

Let's say we have a number line with the point A on it. Think of the absolute value of A as the distance between point A and zero. Since the distance cannot be negative, the absolute value will always return a positive value.

A positive number is always greater than zero, and zero is equal to zero. Therefore, the answer is True.

There are 4,080 different arrangements of first, second, and third place possible for the 17 students running in the race.

To determine the number of different arrangements of first, second, and third place, we need to use the permutation formula.

The number of permutations of n objects taken r at a time is given by:

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

In this problem, we have 17 students running, and we want to determine the number of different arrangements of first, second, and third place, which means we need to find the number of permutations of 17 objects taken 3 at a time.

Using the permutation formula, we get:

P(17,3) = 17!/(17-3)!

= 17!/14!

= 171615

= 4,080

Therefore, there are 4,080 different arrangements of first, second, and third place possible for the 17 students running in the race.

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3) The height is 5.1 inches after 15 hours.

4) The weight is 166 lbs. after 24 weeks.

Depending on the details, there are various ways to express a line's equation. The slope-intercept form and point-slope form are the two most typical forms.

3) It is obvious;

The graph's slope is;

m = 6 - 10/12 - 0

= -4/12 = -0.33

The line's equation is then;

y = -0.33x + 10

If we have 15 hours today, then;

y = -0.33(15) + 10

= 5.1 inch

4) Once more, the slope is;

m = 235 - 238/2 -1

m = -3

y = -3x + 238

24 weeks later, we have that;

y = -3(24) + 238

= 166 ibs

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The comparison distribution in a t test for dependent means is a distribution of the differences between the pairs of scores on the dependent variable.

This distribution is used to determine whether the observed differences between the means of two related groups are statistically significant or could have occurred by chance. The t statistic is calculated by dividing the mean difference between the pairs of scores by the standard error of the mean difference, which is based on the variance of the differences in the sample. The t statistic is then compared to a t distribution with degrees of freedom equal to the number of pairs of scores minus one to determine the probability of obtaining the observed difference by chance.

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Rounding off the solution obtained by solving an integer programming problem as a linear programming problem can provide a feasible solution, but it does not guarantee optimality and may require additional analysis

When solving an integer programming problem, we must consider that the decision variables can only take on integer values. However, solving an integer programming problem directly can be computationally challenging. One approach is to first solve the problem as a linear programming problem, which allows for non-integer values of the decision variables. Then, the solution can be rounded off to obtain integer values.

However, rounding off the solution obtained by solving the problem as a linear programming problem does not guarantee optimality. In fact, the values of decision variables obtained by rounding off may be sub-optimal or might violate some constraints. Therefore, it is important to carefully check the feasibility of the rounded off solution before using it in practice.

In summary, rounding off the solution obtained by solving an integer programming problem as a linear programming problem can provide a feasible solution, but it does not guarantee optimality and may require additional analysis.

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The third-degree Taylor polynomial for f(x) = arcsin(5x) centered at a = 0 is t3(x) = 5x - (125/2)x³.

To find the Taylor polynomial t3(x) for the function f(x) = arcsin(5x) centered at a = 0, we will need to compute the function's derivatives at a = 0 up to the third order.

First, let's compute the first few derivatives of f(x):
f(x) = arcsin(5x)
f'(x) = 5 / sqrt(1 - 25x^2)
f''(x) = 125x / (1 - 25x^2)^(3/2)
f'''(x) = (9375x^2 - 375) / (1 - 25x^2)^(5/2)

Now, let's evaluate these derivatives at a = 0:
f(0) = 0
f'(0) = 5 / sqrt(1) = 5
f''(0) = 0
f'''(0) = -375 / (1)^(5/2) = -375

Using these values, we can write the third-degree Taylor polynomial t3(x) as follows:

t3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3
t3(x) = 0 + 5x + 0 + (-375/6)x^3
t3(x) = 5x - (125/2)x^3

Therefore, the third-degree Taylor polynomial for f(x) = arcsin(5x) centered at a = 0 is t3(x) = 5x - (125/2)x^3.

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When two sides of a triangle measure 18 meters and 13 meters, the measures that could represent the perimeter of the triangle is B. 37 meters

The perimeter of a triangle is the sum of the lengths of its three sides. So, if two sides of a triangle measure 18 meters and 13 meters, the third side must be less than 18 meters + 13 meters = 31 meters.

Therefore, the perimeter of the triangle must be less than 31 meters + 31 meters = 62 meters. Only 37 meters is less than 62 meters, so the answer is (b).

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The area of each tile is 1 sq ft, No of tiles required is 176 sq ft /1 sq ft = 176

What is the area of the rectangle?

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Here, we have

Given: The pool is designed to be a 60 ft by 26 ft rectangle, and the deck around the pool is going to be lined with slate tiles that are 1 ft squares.

We have to find out how many tiles are needed.

The internal Length of the rectangle is 60ft

Internal Breadth of the rectangle is 26 ft

External Length of the rectangle is 60+ 2*1 = 62ft

External Breadth of the rectangle is 26+ 2*1 = 28ft

Area of the deck to be tiled = Outer Area - Inner area

  = (62×28 ) - (60×26)

  = 1736 - 1560

 =  176 Sq ft

Hence, the area of each tile is 1 sq ft, No of tiles required is 176 sq ft /1 sq ft = 176

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Therefore, the force the glove exerts on the ball during the collision can be calculated by measuring the change in momentum of the ball and dividing it by the time of the collision.

The equation used to calculate the force the glove exerts on the ball during the collision is the impulse-momentum equation. This equation states that the force applied to an object is equal to the change in momentum of the object over time. Therefore, the force the glove exerts on the ball during the collision can be calculated by measuring the change in momentum of the ball and dividing it by the time of the collision.

To calculate the force the glove exerts on the ball during the collision, you can use Newton's second law of motion, which states:

Force (F) = Mass (m) × Acceleration (a)

In this scenario, the mass (m) refers to the mass of the baseball, and the acceleration (a) is the change in the baseball's velocity divided by the time it takes for the collision to occur. Keep in mind that the acceleration will have a negative value, as the ball is decelerating during the collision.

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The required farmer should choose a length of 56 feet for the garden to maximize its area.

we need to maximize A with respect to x, subject to the constraint that the perimeter of the garden (the amount of fencing needed) is 200 feet. The perimeter is given by:

P = x + 2y + π*x/2

Substituting y = x/2, we get:

P = x + 2(x/2) + π*x/2
200 = (2 + π/2)*x
x = 56

Therefore, the farmer should choose a length of 56 feet for the garden to maximize its area.

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The equation representing the situation is 20(3 cups) - p(2 cups) = 36 cups, where p represents the number of pots knocked over.

The initial amount of soil in the pots is given by 20 pots multiplied by 3 cups per pot, which gives 20(3 cups). The number of pots knocked over is represented by p, and each knocked-over pot loses 2 cups of soil.

Therefore, the total soil lost due to knocked-over pots is p(2 cups). Subtracting this from the initial amount of soil, we get 20(3 cups) - p(2 cups). The result should be equal to the remaining soil, which is 36 cups. Hence, the equation representing this situation is 20(3 cups) - p(2 cups) = 36 cups. This equation relates the number of pots knocked over (p) to the remaining soil (36 cups).

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y-7=-5(x+2) is the equation of line in point slope form passing through point (-2,7)

The given equation of the line p is 5x-25y=19

We have to find the equation of a line perpendicular to line p that passes through (-2, 7)

Convert equation to slope intercept form 5x-25y=19

-25y=19-5x

25y=5x-19

Divide both sides by 25

y=1/5x - 19/25

So slope is 1/5

Now the slope of perpendicular line is -5

equation of line in point slope form passing through point (-2, 7)

y-7 = -5(x-(-2))

y-7=-5(x+2)

Hence, y-7=-5(x+2) is the equation of line in point slope form passing through point (-2,7)

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Answer:

it would be -7 because 6 and up round up once now 5 and down go down

Step-by-step explanation:

The number of students that leave by bus or car is given as follows:

5801 students.

The union and intersection sets of multiple sets are defined as follows:

The or operation is equivalent to the union operation, meaning that we add the number of students that leave by bus to the number of students that leave by car.

Hence the number of students that leave by bus or car is given as follows:

3232 + 2549 = 5801 students.

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Answer:

0.75, or 3/4, or 75%

They’re all the same, in different formats

Step-by-step explanation:

You can’t actually see the line plot in your answer.

9 1/2 minus 8 3/4 is 3/4.

Given that triangle XYZ and triangle JKL are similar, the length of LJ is 13.12

From the question, we are to determine the length of side LJ given that triangle XYZ and triangle JKL are similar.

From the triangle similarity theorem, we know that

If triangle ABC and triangle DEF are similar,

Then,

AB/DE = BC/EF

Thus,

Since triangle XYZ and triangle JKL are similar, we can write that

XY/JK = ZX/LJ

From the given information,

XY = 8.7

JK = 13.92

ZX = 8.2

Thus,

8.7 / 13.92 = 8.2 / LJ

LJ = (8.2 × 13.92) / 8.7

LJ = 114.144 / 8.7

LJ = 13.12

Hence,

The length of LJ is 13.12

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The p-value for a test concerning a mean is 0.064.

What is p-value?

A p-value, also known as a probability value, is a numerical representation of the likelihood that your data would have occurred under the null hypothesis of your statistical test.

As per question given,

This is two tail list then z = 1.85.

p (z > 1.85) = 1 - p (z < 1.85)

                  = 1 - 0.9678

                  = 0.0322

Thus, the p-value is

p-value = 2 × 0.0322

            = 0.064

Hence, the p-value for a test concerning a mean is 0.064.

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After 6 hours, the population of bacteria in the Petri dish would be 4800.

If the population of bacteria in a Petri dish doubles every 2 hours, we can calculate the population at any given time using the formula

P = P₀[tex]\times 2^{(t/d),[/tex]

where P is the final population, P₀ is the initial population, t is the time elapsed, and d is the doubling time.

In this case, the initial population (P₀) is 600 bacteria, and the doubling time (d) is 2 hours. Let's calculate the population after a certain time, say 6 hours:

[tex]P = 600 \times 2^{(6/2)}\\P = 600 \times 2^3\\P = 600 \times 8\\P = 4800[/tex]

Therefore, after 6 hours, the population of bacteria in the Petri dish would be 4800.

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If the total degrees of freedom (dftotal) in an analysis of variance comparing three treatment conditions is 32, the group size for each condition needs to be determined.



To determine the number of individuals in each group, we need to divide the total number of individuals (dftotal) by the number of treatment conditions (groups).

Given that dftotal = 32 and there are three treatment conditions (groups), we can divide dftotal by the number of treatment conditions to find the number of individuals in each group.

Number of individuals in each group = dftotal / number of treatment conditions

Number of individuals in each group = 32 / 3

Number of individuals in each group ≈ 10.67

Since the groups must have the same size, we need to round the result to the nearest whole number. Therefore, there are approximately 11 individuals in each group.

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The value of Tan D is corect. Sin C is incorrect. From Cot C find cosec C which is equal to 17/15. Therefore sin C = 15/17

Wrong Solution First, we know that cot C is equal to the ratio of the adjacent side to the opposite side in a right triangle. So, cot C = 8/15 implies that the adjacent side is 8 and the opposite side is 15.

Next, we are given that cos D is equal to the ratio of the adjacent side to the hypotenuse in a right triangle. So, cos D = 15/17 implies that the adjacent side is 15 and the hypotenuse is 17.

Now, to find tan D, we can use the relationship between the tangent and sine functions: tan D = sin D / cos D. Since we know cos D = 15/17, we need to find sin D. Using the Pythagorean theorem, we can find the opposite side:

sin D = √(1 - cos^2 D)

= √(1 - (15/17)^2)

= √(1 - 225/289)

= √(289/289 - 225/289)

= √(64/289) = 8/17.

Therefore, tan D = sin D / cos D = (8/17) / (15/17) = 8/15.

Finally, to find sin C, we can use the Pythagorean theorem:

sin^2 C = 1 - cos^2 C = 1 - (15/17)^2 = 1 - 225/289 = 64/289.

Taking the square root of both sides, we get

sin C = √(64/289) = 8/17.

In summary, tan D = 8/15 and sin C = 8/17.

The values of tan D and sin C are  tan D = 8/15 and sin C = 8/17

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About 11.90% of students scored 59.99 or lower on the exam and failed the course (since this is a proportion, we can multiply it by 100 to get the percentage).

To determine the percentage of students who failed the course, we need to find the proportion of students who scored 59.99 or lower on the exam, and then convert this proportion to a percentage.
First, we need to standardize the cutoff score of 59.99 using the formula:
z = (x - μ) / σ
where x is the cutoff score, μ is the mean, and σ is the standard deviation.
Plugging in the values given in the question, we get:
z = (59.99 - 73) / 11 = -1.18
Next, we look up the proportion of scores below a z-score of -1.18 in a standard normal distribution table (or use a calculator or software). This proportion is approximately 0.1190.
Therefore, about 11.90% of students scored 59.99 or lower on the exam and failed the course (since this is a proportion, we can multiply it by 100 to get the percentage).
In other words, roughly 12% of the students failed the course based on the given criteria.

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Based on the given information , the appropriate hypothesis test for this scenario would be an independent samples t-test.

The independent samples t-test is used to compare the means of two independent groups.

To determine if there is a significant difference between them.

In this case, the two groups are women who smoked during pregnancy and women who did not smoke during pregnancy.

The variable of interest is the bone mineral content of healthy newborns.

The null hypothesis (H₀) would state that ,

There is no significant difference in the mean bone mineral content between,

newborns of women who smoked during pregnancy and newborns of women who did not smoke during pregnancy.

The alternative hypothesis (Hₐ) would state that there is a significant difference in the mean bone mineral content between the two groups.

To conduct the independent samples t-test,

We would calculate the t-statistic using the sample means, sample sizes, and standard deviations of the two groups.

The t-statistic is then compared to a critical value from the t-distribution with appropriate degrees of freedom.

To determine if the difference in means is statistically significant.

Assumption of normality and equal variances between the groups, should be checked before conducting the t-test.

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To perform the indicated operations for the expression (2a+6)/(a^2+6a+9) + 1/(a+3), we first need to find a common denominator. The denominators of the two fractions are (a^2+6a+9) and (a+3). To get a common denominator, we can multiply the first fraction by (a+3)/(a+3), which gives:

(2a+6)/(a^2+6a+9) * (a+3)/(a+3) + 1/(a+3)

= (2a+6)(a+3)/(a+3)(a^2+6a+9) + (a^2+6a+9)/(a+3)(a^2+6a+9)

= (2a^2+12a+18+a^2+6a+9)/(a^2+6a+9)(a+3)

= (3a^2+18a+27)/(a+3)(a^2+6a+9)

= 3(a+3)(a+3)/(a+3)(a+3)(a+1)

= 3/(a+1)

Therefore, the simplified form of the expression is 3/(a+1).

The relationship between b (the number of years since the start of the study) and y (the mass of the sample in milligrams) using the exponential function:

y = 750(0.955)ᵇ

The rate of decay is given as 4.5% per year, which means that after one year, the sample will have decayed to 95.5% of its original mass.

After two years, it will have decayed to 95.5% of that amount, and so on. We can express this relationship between b (the number of years since the start of the study) and y (the mass of the sample in milligrams) using the exponential function:

y = 750(0.955)ᵇ

Here, the initial mass of the sample is 750 milligrams, and the factor of 0.955 represents the proportion of the original mass that remains after one year.

Taking this factor to the power of b gives us the proportion of the original mass that remains after t years, which we can multiply by the initial mass to get the current mass of the sample in milligrams.

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Jack's total profit from selling all of his pens is 430p.

To calculate Jack's total profit, we need to consider the profit made from selling 80% of the pens at a 20% profit and the loss incurred from selling the remaining 20% at a reduced price.

Let's break down the calculations :

Cost of purchasing 50 pens

The cost of each pen is 65p, so the total cost of purchasing 50 pens is [tex]50 \times 65p = 3250p.[/tex]

Profit from selling 80% of the pens

Jack sells 80% of the pens, which is[tex]0.8 \times 50 = 40[/tex] pens.

He makes a 20% profit on each pen, which is 20% of 65p = 13p profit per pen.

So, the total profit from selling these 40 pens is [tex]40 \times 13p = 520p.[/tex]

Loss from selling the remaining 20% of the pens

The remaining 20% of the pens is[tex]0.2 \times 50 = 10[/tex] pens.

Jack incurs a loss of 9p on each of these pens.

So, the total loss from selling these 10 pens is [tex]10 \times 9p = 90p.[/tex]

Total profit

To calculate the total profit, we subtract the loss from the profit:

Total profit = Profit - Loss = 520p - 90p = 430p.

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To find the extremum of the function f(x,y) = 2y^2-9x^2 subject to the constraint 3xy = 27x, we can use the method of Lagrange multipliers.

Let g(x,y) = 3xy - 27x be the constraint function. We want to find the critical points of the function f(x,y) subject to the constraint g(x,y) = 0, so we set up the following system of equations:

∇f(x,y) = λ∇g(x,y)

g(x,y) = 0

where λ is the Lagrange multiplier.

Taking the partial derivatives of f(x,y) with respect to x and y, we get:

∂f/∂x = -18x

∂f/∂y = 4y

Taking the partial derivatives of g(x,y) with respect to x and y, we get:

∂g/∂x = 3y - 27

∂g/∂y = 3x

Setting ∇f(x,y) = λ∇g(x,y), we get the following system of equations:

-18x = λ(3y - 27)

4y = λ(3x)

Multiplying the first equation by 4 and the second equation by -6, we get:

-72x = λ(12y - 108)

-24y = λ(-18x)

Simplifying these equations, we get:

4x = λ(y - 9)

y = 3λx/2

Substituting y = 3λx/2 into the first equation, we get:

4x = λ(3λx/2 - 9)

8x = λ^2x - 18λ

x(λ^2 - 8) = 18λ

If x = 0, then y = 0, which is not a critical point since f(0,0) = 0. Therefore, we can divide both sides by x to get:

λ^2 - 8 = 18/ x

If λ^2 - 8 < 0, then there are no critical points since the equation above has no real solutions. Therefore, we assume λ^2 - 8 ≥ 0, which gives:

λ = ±√(8 + 18/x)

Substituting λ into y = 3λx/2, we get:

y = ±√(2x(8 + 18/x))/2

We want to find the extremum of f(x,y) = 2y^2-9x^2, so we evaluate this function at the critical points:

f(x,y) = 2y^2-9x^2 = 2(2x(8 + 18/x))/4 - 9x^2 = (4x^2 + 36) / x - 9x^2

Taking the derivative of f(x,y) with respect to x, we get:

f'(x,y) = (8x - 36)/x^2 - 18

Setting f'(x,y) = 0, we get:

8x - 36 = 18x^2

18x^2 - 8x + 36 = 0

Solving for x, we get:

x = (2 ± √13)/9

Substituting x into y = ±√(2x(8 + 18/x))/2, we get:

y = ±(4 ± √13)√2/3

Therefore, the critical points are (x,y) = x = (2 ± √13)/9, y = ±(4 ± √13)√2/3

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i. π is an irrational number while 22/7 is a rational number.

ii) 22/7 is a rational number since it can be written in the form p/q and π is an irrational number because its values are continuous after the decimal point.

In Mathematics and Geometry, there are six (6) common types of numbers and these include the following:

Part i.

In Mathematics and Geometry, a rational number is a type of number which comprises fractions, integers, terminating or repeating decimals such as the 22/7, 0.12345678901234567890.

Additionally, an irrational number is a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11 or √11.

Part ii.

22/7 should be classified as a rational number because it can be written in the form p/q and π is an irrational number because its values are non-terminating or non-repeating, after the decimal point.

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Step-by-step explanation:

An equation with a variable is a mathematical statement that asserts that two expressions are equal. The variable in the equation represents an unknown quantity that needs to be determined. For example, the equation "2x + 3 = 7" asserts that the expression "2x + 3" is equal to the expression "7", and the variable "x" represents the value that makes this equation true.

An inequality with a variable is a mathematical statement that asserts that one expression is greater than, less than, or equal to another expression. The variable in the inequality represents an unknown quantity that needs to be determined. For example, the inequality "2x + 3 < 7" asserts that the expression "2x + 3" is less than the expression "7", and the variable "x" represents the values that satisfy this inequality.

In summary, the main difference between an equation and an inequality is that an equation asserts that two expressions are equal, while an inequality asserts that one expression is greater than, less than, or equal to another expression.