Simplify the expression

Since ln(1/6) is a finite value, the sequence does not diverge. It converges to ln(1/6) as n approaches infinity.

To determine if the sequence diverges, we need to take the limit of the expression as n approaches infinity.

Using the logarithmic identity ln(a/b) = ln(a) - ln(b), we can simplify the expression as follows:

[tex]ln(n^3 8) - ln(6n^3 13n) = ln(n^3) + ln(8) - ln(6n^3) - ln(13n)[/tex]

= [tex]ln(n^3) - ln(6n^3) + ln(8) - ln(13n)[/tex]

= [tex]ln(n^3/6n^3) + ln(8/13n)[/tex]

=[tex]ln(1/6) + ln(8/13n)[/tex]

As n approaches infinity, ln(8/13n) approaches 0, so the limit of the expression is:

lim n→∞ [ln(1/6) + ln(8/13n)]

= ln(1/6)

Since ln(1/6) is a finite value, the sequence does not diverge. It converges to ln(1/6) as n approaches infinity.

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Two balloons A and B apart 150km with given angle of elevation represents observer A is at a distance of  122.5 km approximately from balloon.

Number of observers = 2

Distance between two observers A and B = 150km

Angles of elevation are 42° and 76°.

Let us consider 'h' be the height of the balloon

Let the distance from observer A to the balloon x.

Use trigonometry to find the value of x.

From observer A, the angle of elevation to the balloon is 42°.

This means that the height of the balloon above observer A is ,

h = x ×  tan(42°)

From observer B,

The angle of elevation to the balloon is 76°.

This means that the height of the balloon above observer B is ,

h = (150 - x) × tan(76°)

Since both expressions give the same value for h, set them equal to each other,

⇒ x × tan(42°) = (150 - x) × tan(76°)

Simplifying this equation, we get,

⇒ x × (0.9004 ) = (150 - x) × 4.0107

⇒ 0.9004x = 601.605 - 4.0107x

⇒ 4.9111x = 601.605

⇒ x ≈ 122.5 km

Therefore, the distance from observer A to the balloon as per given angle of elevation is approximately 98.3 km.

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At least 95% of the observed values are expected to lie between mu minus 2 sigma and mu plus 2 sigma.

This is because of the empirical rule, also known as the 68-95-99.7 rule, which states that in a normal distribution, approximately 68% of the observations will fall within one standard deviation of the mean, about 95% of the observations will fall within two standard deviations of the mean, and around 99.7% of the observations will fall within three standard deviations of the mean.

In this case, we are given that x has mean mu and standard deviation sigma. Therefore, about 95% of the values of x are expected to lie between mu minus 2 sigma and mu plus 2 sigma, as this interval covers two standard deviations on either side of the mean.

Mathematically, we can express this as:

P(mu - 2sigma < x < mu + 2sigma) ≈ 0.95

where P is the probability that x falls within the interval mu - 2sigma to mu + 2sigma.

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Answer:

The numerical values of the circumference and area are equal

Step-by-step explanation:

Circumference: 12.57

Area: 12.57

12.57=12.57

Hope this helps! :)

If all the dimensions of a cube increase by a factor of 3/2, the surface area will increase by a factor of 9/2.

If all the dimensions of a cube increase by a factor of 3/2, then the new dimensions of the cube will be 3/2 times the original dimensions.

Let's say the original side length of the cube was "s". Then the new side length would be (3/2)*s.

The surface area of a cube is given by the formula 6s^2, where s is the side length.

So the original surface area of the cube would be:

6s^2

And the new surface area of the cube would be:

6(3/2s)^2
= 6(9/4)s^2
= 27/2 s^2

To find how many times greater the new surface area is compared to the original surface area, we can divide the new surface area by the original surface area:

(27/2 s^2) / (6s^2)
= (9/2)

So the new surface area is 9/2 times greater than the original surface area.

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1. Myla bought an item for P2,500 and decided to sell it with a 2% markup. The selling price will be P2,500 + (2% of P2,500) = P2,500 + P50 = P2,550.

2. Joan sold her old iPhone for P5,000 at an 8% markdown rate. To find the markdown and the original cost, we first calculate the markdown: P5,000 = 92% of original price. So, the original price was P5,000 ÷ 0.92 ≈ P5,434.78. The markdown is P5,434.78 - P5,000 = P434.78.

3. The student assistant bought an item for P520 and sold it for P550. The markup is P550 - P520 = P30.

4. Mother earned P120 on an item at a 60% markdown. Let X be the original price, then X * 60% = P120. X = P120 ÷ 0.60 = P200. So, the mother bought the item for P200.

5. The cost of a t-shirt from the manufacturer is P400. If Loan wants a 30% markup based on the selling price, we'll let X be the selling price, then X - 30% of X = P400. So, 0.7X = P400. X = P400 ÷ 0.7 ≈ P571.43. Loan's selling price will be P571.43.

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At both the 5% and 1% significance levels, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.

Null Hypothesis: The proportion of US adults who have great confidence in banks is 15% or higher.

Alternative Hypothesis: The proportion of US adults who have great confidence in banks is less than 15%.

We can use a one-tailed z-test to test the economist's claim.

The test statistic is

z = (P - p) / √(p * (1-p) / n)

where P is the sample proportion, p is the hypothesized proportion, and n is the sample size.

Using the sample data, we have

P = 149/1325 = 0.1121

p = 0.15

n = 1325

The test statistic is

z = (0.1121 - 0.15) / √(0.15 × (1-0.15) / 1325) = -3.196

Using a significance level of α = 0.05, the critical value for a one-tailed test is -1.645. Since our test statistic is less than the critical value, we reject the null hypothesis.

The p-value for this test is P(Z < -3.196) = 0.0007. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis.

At the 5% significance level, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.

Using a significance level of α = 0.01, the critical value for a one-tailed test is -2.33. Since our test statistic is less than the critical value, we reject the null hypothesis.

The p-value for this test is P(Z < -3.196) = 0.0007. Since the p-value is less than the significance level of 0.01, we reject the null hypothesis.

At the 1% significance level, we have enough evidence to reject the null hypothesis that the proportion of US adults who have great confidence in banks is 15% or higher. Therefore, we can conclude that the economist's claim that less than 15% of US adults have great confidence in banks is supported by the data.

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The height of a 16-year-old boy in the 96th percentile is approximately 73 inches. Rounded to the nearest inch, the answer is 73 inches.

To find the z-score associated with the 96th percentile, we need to find the z-score such that the area to the right of it under the standard normal distribution is 0.96. Using a standard normal distribution table or calculator, we find that the z-score is approximately 1.75.

Next, we can use the z-score formula to find the height of a 16-year-old boy in the 96th percentile:

z = (x - μ) / σ

where z is the z-score, x is the height we want to find, μ is the mean height, and σ is the standard deviation.

Plugging in the values we have:

1.75 = (x - 68.3) / 2.9

Multiplying both sides by 2.9, we get:

x - 68.3 = 5.075

Adding 68.3 to both sides, we get:

x = 73.375

So the height of a 16-year-old boy in the 96th percentile is approximately 73 inches. Rounded to the nearest inch, the answer is 73 inches.

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Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

To answer your question about how many cups of water Abby should add to make 1 gallon of punch, let's first convert all the given measurements to cups. One gallon is equivalent to 16 cups.

1. Orange juice: Abby uses 2 quarts of orange juice. Since there are 4 cups in a quart, she uses 2 x 4 = 8 cups of orange juice.

2. Lemon juice: Abby uses 1 cup of lemon juice.

3. Pineapple juice: Abby uses 2 1/2 pints of pineapple juice. There are 2 cups in a pint, so she uses (2 1/2) x 2 = 5 cups of pineapple juice.

Now, let's add up the cups of orange juice, lemon juice, and pineapple juice: 8 + 1 + 5 = 14 cups. Since Abby wants to make 1 gallon (16 cups) of punch, she will need to add 16 - 14 = 2 cups of water to reach the desired amount.

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If Joe already scored 347 points in math-test, then to get a grade"A" he must score at least 56 marks, which is represented in inequality as n ≥ 56.

Jose has already scored 347 points on his math-tests so far, and he needs to score at least 403 points to get an A for the semester.

Let "minimum-points" he must score on the "remaining-tests" be denoted by "n". We can write an inequality to represent minimum-points as:

⇒ 347 + n ≥ 403,

⇒ n ≥ 403 - 347,

⇒ n ≥ 56.

Therefore, Jose must score at least 56 points on the remaining tests in order to get an A for the semester.

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The given question is incomplete, the complete question is

Jose has scored 347 points on his math tests so far this semester. To get an A for the semester, he must score at least 403 points. Write an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. Let "n" represent the number of points Jose needs to score on the remaining tests.

the area of the circle is 615. 4 m²

The formula that is used to calculate the area of a circle is expressed with the equation.

We have the equation as;

A = πr²

Such that the parameters are given as;

From the diagram shown, we have that;

A = unknown

r = 14m

Now, substitute the values, we get;

Area = 3.14 ×14²

Find the square value

Area = 3.14(196)

Multiply the values

Area = 615. 4 m²

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The value of the reflex angle in this figure is 273 degrees

A reflex angle is an angle that is more than 180 degrees and less than 360 degrees. For example, 270 degrees is a reflex angle. In geometry, there are different types of angles such as acute, obtuse and right angles, which are under 180 degrees.

In this given figure, there's acute angle and an obtuse angle, therefore a reflex angle must be present.

To find the reflex angle in the figure, we have to trace the green part of the figure which will give us;

180° + 93°

i.e the sum of angle on a straight line with an obtuse angle

Reflex angle = 180 + 93 = 273°

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Where the function f(x) = x² + 2x - 3 is given, note that the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4. See the attached graph.

To find the minimum and maximum points of the function f(x), we can complete the square:

f(x) = x^2 + 2x - 3

= (x + 1)^2 - 4

We can see that the function is in the vertex form f(x) = a(x - h)^2 + k, where the vertex is (-1, -4).

Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the vertex is the minimum point. Therefore, the minimum value of the function f(x) is -4.

To find the x-intercepts, we can set f(x) = 0:

(x + 1)^2 - 4 = 0

(x + 1)^2 = 4

Taking the square root of both sides, we get:

x + 1 = ±2

x = -1 ± 2

Therefore, the x-intercepts of the function f(x) are x = -3 and x = 1.

In summary, the x-intercepts of the function f(x) are -3 and 1, and the minimum value of the function is -4, which occurs at the vertex (-1, -4).

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Answer: x = 10

Step-by-step explanation: To solve this equation, you can use the logarithmic property that states loga(b) + loga(c) = loga(bc). So, you can rewrite the left side of the equation as log2((x-6)(x+6)). Then, you can use the property that states loga(b) = c is equivalent to a^c = b to solve for x.

So, you have log2((x-6)(x+6)) = 6, which is equivalent to 2^6 = (x-6)(x+6). Simplifying the left side gives you 64, and expanding the right side gives you x^2 - 36 = 64. Solving for x gives you x = ±√100, which is x = ±10. However, since the original equation includes logarithms.

All the angles of the Rhombus if B-A=20 is angle A = angle C = 80°, and angle B = angle D = 100°.

In a rhombus ABCD, if angle B minus angle A equals 20 degrees (B-A=20°), we can find the degree measures of all the angles.

Step 1: Recognize that in a rhombus, opposite angles are equal. Therefore, angle A = angle C and angle B = angle D.

Step 2: Remember that the sum of the angles in any quadrilateral is 360 degrees. In a rhombus, since the opposite angles are equal, we can represent this as: 2A + 2B = 360°

Step 3: Use the given information, B - A = 20°, to solve for one of the angles. For this, rearrange the equation to isolate B: B = A + 20°

Step 4: Substitute the expression for B from step 3 into the equation from step 2: 2A + 2(A + 20°) = 360°

Step 5: Solve the equation for angle A. 2A + 2A + 40° = 360° → 4A + 40° = 360° → 4A = 320° → A = 80°

Step 6: Now that we have angle A, use the expression from step 3 to find angle B: B = 80° + 20° = 100°

Step 7: Since A = C and B = D, we can now state all the angles of the rhombus ABCD: angle A = angle C = 80°, and angle B = angle D = 100°.

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The perimeter of the equilateral triangle whose area is 16root3/4 is 15.9[tex]\sqrt{3/4} cm[/tex]

You should understand that a triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted

An equilateral triangle is a special case of an isosceles triangle in which all three sides have the same length

Let the sides of the triangle be a

a + a + a = 16root3/4

3a = 16[tex]\sqrt{3/4}[/tex]

a = 5.3[tex]\sqrt{3/4}[/tex]

Therefore the perimeter of the equilateral triangle is

5.3[tex]\sqrt{3/4} + 5.3\sqrt{3/4} +5.3\sqrt{3/4}[/tex]

Therefore, the  perimeter is 15.9[tex]\sqrt{3/4} cm[/tex]

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The angle measure of L in the triangle is approximately 75°.

Based on the given table, we can see that the ratio of the opposite leg length to the adjacent leg length for an angle measure of 75° is approximately 3.73. Looking at the triangle in the question, we can see that the side opposite to angle L is the hypotenuse and the adjacent leg is LK.

Therefore, the ratio of the opposite leg length to the adjacent leg length for angle L is equal to the ratio of the hypotenuse length to the length of segment LK.

From the figure, we can see that the length of segment LK is approximately 3.2 units. Therefore, the length of the hypotenuse is approximately 3.73 times the length of segment LK, or:

hypotenuse length ≈ 3.73 × 3.2 ≈ 11.9

Therefore, the angle measure of L is approximately 75°.

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This new function W(x) = 22 - (11/8) * (x - 16)² will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall.

To modify the function W to model the new arch with dimensions of 32 inches wide and 44 inches tall, we need to adjust the formula to reflect the new proportions.

Currently, the function W is defined as:

W(x) = h/2 - h/(2a) * (x - a)²

Where h is the height of the arch and a is half of the width of the arch.

To modify the function for the new arch, we need to adjust the value of a to reflect the new width of 32 inches. Since a is half the width, we have:

a = 32/2 = 16

We also need to adjust the value of h to reflect the new height of 44 inches. Therefore, the new function for the arch would be:

W(x) = 44/2 - 44/(2*16) * (x - 16)²

Simplifying this expression, we get:

W(x) = 22 - (11/8) * (x - 16)²

This new function will model the shape of the arch with dimensions of 32 inches wide and 44 inches tall. The parabolic shape of the function will remain the same, but the specific coefficients in the function have been adjusted to reflect the new proportions of the arch.

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The coordinates of point P on the directed line segment AB, which divides AB in the ratio 1:3, are (5, 6.5).

To find the coordinates of the point P on the directed line segment AB that partitions AB in the ratio 1:3, we can use the concept of section formula.

Let's assume the coordinates of point P are (x, y). According to the section formula, the coordinates of P can be calculated as follows:

x = (3x2 + 1x1) / (3+1) = (37 + 1(-1)) / 4 = (21 - 1) / 4 = 20/4 = 5

y = (3y2 + 1y1) / (3+1) = (38 + 12) / 4 = (24 + 2) / 4 = 26/4 = 13/2 = 6.5

Therefore, the coordinates of point P on the directed line segment AB, which divides AB in the ratio 1:3, are (5, 6.5).

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The mean number of miles the hiker walked for the 6 days was 6.5 miles.

To calculate the mean or average of a set of numbers, we add up all the numbers and then divide the sum by the number of items in the set. In this case, we have the number of miles the hiker walked on each of the six days. To find the total number of miles the hiker walked, we simply add up all the numbers

8 + 5 + 7 + 2 + 9 + 8 = 39

Next, we divide the total number of miles by the number of days (which is 6) to get the average or mean number of miles the hiker walked per day:

Mean number of miles = Total number of miles / Number of days

= 39 / 6

= 6.5

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Answer: 6

Step-by-step explanation:42/7=6

Using the triple integral to find the volume of the solid bounded by the parabolic cylinder is 32/15 cubic units.

The given solid is bounded by the parabolic cylinder y = 2x², the plane z = 0, the plane z = 2, and the plane y = 4.

To find the volume of the solid using a triple integral, we can set up the integral as follows:

∫∫∫E dV

where E is the region of integration in three dimensions.

Region E can be described as:

0 ≤ z ≤ 2

0 ≤ y ≤ 4

0 ≤ x ≤ √(y/2)

Therefore, the triple integral can be written as:

∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz

Evaluating the integral gives us the volume of the solid:

V = ∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz = 32/15

Hence, the volume of the solid is 32/15 cubic units.

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To solve this problem, we will use the formula for exponential decay as follows: V = P * e^(-rt) where V is the value after t years, P is the initial value, r is the annual interest rate as a decimal, and t is the time in years.

What is Depreciation: Depreciation is dependent on a number of estimates.The method in which companies determine the depreciation value of their assets is different from one another. Some companies may use a straight line method of depreciation and another may count the depreciation according to asset's production value. What is exponential decay: An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time .Given that a brand new Audi R8 is purchased for $148,700 before taxes, and the car depreciates at a rate of 8%, we can find how much it will be worth in 5 years. Using the formula for exponential decay, we have V = P * e^(-rt) where     P = $148,700r = 0.08t = 5. Therefore,V = $148,700 * e^(-0.08 * 5), V = $148,700 * e^(-0.4)V ≈ $82,429.61. Therefore, the car will be worth approximately $82,429.61 in 5 years.

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The expression (x + 1)(x - 3) represents the Area of base of the prism.

a crystal is a polyhedron containing a n-sided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every cross-section that runs parallel to the bases.

According to question:

The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x - 3).

We can find the height of the prism by dividing the volume by the area of the base:

B = V/h = (x + 1)^2(x - 3)/(x + 1) = (x + 1)(x - 3)

Therefore, the expression (x + 1)(x - 3) represents the Area of base of the prism.

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Answer:

It the distance from mid line to top of wave.

Step-by-step explanation:

Answer:

Height of a wave (from mid line to max.

Step-by-step explanation:

The probability to select a male or someone in their 40's for a ceo position is company is equals to the 1/18. So, the option(c) is right answer for the problem.

We have a data of employees' information. It contains gender and age of employees in acme painting company. Randomly one employee is selected. We have to determine chance or probability that a ceo select a male or someone in their 40's. Sample size, n= 18

Probability is defined as chances of occurrence of an event. It is calculated by dividing the favourable response to the possible total outcomes.

Total possible outcomes= 18

number of male in her 40's age = 1

So, probability that select a male or someone in their 40's = 1/18

Hence, required probability is 1/18.

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Complete question:

the above figure completes the question.

the gender and age of acme painting company's employees are shown below. age gender 23 female 23 male 24 female 26 female 27 male 28 male 30 male 31 female 33 male 33 female 33 female 34 male 36 male 37 male 38 female 40 female 42 male 44 female if the ceo is selecting one employee at random, what is the chance he will select a male or someone in their 40s?

a)1/3

b)1/2

c) 1/18

d) 11/18

The radius of the pond is 32 feet, under the condition  that 43 feet from the bank and 75 feet from the point of tangency.

Let us consider that  the center of the circle O, the point of tangency T, and Federico's position P.
We can utilize these two points to form a line. The point of tangency is the place where Federico is closest to the pond. The radius of the pond is considered perpendicular to this line and passes through the point of tangency.

Firstly, we have to  the distance between Federico's position P and covers passes through points T and B (the bank). This distance is equivalent to the given  radius of the circle. We have to apply the formula for the distance between a point and a line to find this distance.

Let us assume this distance as  d.
d = (|BT x BP|) / |BT|

Here
|BT| = line segment length of  BT,
|BP| = line segment length of  BP,
BT x BP = vectors cross product of  BT and BP.

Here we evaluate  |BT| applying the Pythagorean theorem
|BT|² = 75²+ r²

Here,
r = radius concerning the circle.
Then,

|BP|² = 43² + r²
Staging these values into our formula for d:
d = (|BT x BP|) / |BT|
 = (|BT| × |BP|) / |BT|
 = |BP|
 = √(43² + r²)

We want to solve for r, so we can square both sides:

d² = 43² + r²

r² = d² - 43²

r = √(d² - 43²)

Placing in d = 75,

r = √(75² - 43²)
≈ 32 feet
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The negation of each of these statements in terms of quantifiers without using the negation symbo

a) There exists at least one x such that x is not greater than 1.
b) There exists at least one x such that x is not less than or equal to 2.
c) For all x, x is less than 4.
d) For all x, x is greater than or equal to 0.
e) There exists at least one x such that either x is not less than or equal to -1 or x is not greater than 2.
f) For all x, x is not less than 4 and x is not greater than 7.

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Answer:

6

Step-by-step explanation: