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A point is selected at random inside the given figure.
What is the probability the point will be in the region labeled A?
Enter your answer, as a fraction in simplest form, in the box.
P(A) =
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5 in.
B
3 in.
A
C
4 in.
3 in.
D
4 in.

The limit as n approaches infinity of ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) is 6.

To evaluate the limit as n approaches infinity of the expression ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵), we can simplify it using algebraic manipulations.

Let's expand the numerator and denominator using the binomial:

Numerator:

((n+1)⁶-(n-1)⁶) = [n⁶ + 6n⁵ + 15n⁴ + 20n³ + 15n² + 6n + 1] - [n⁶ - 6n⁵ + 15n⁴ - 20n³ + 15n² - 6n + 1]

= 12n⁵ + 40n³ + 12n

Denominator:

((n+1)⁵+(n-1)⁵) = [n⁵ + 5n⁴ + 10n³ + 10n² + 5n + 1] + [n⁵ - 5n⁴ + 10n³ - 10n² + 5n - 1]

= 2n⁵ + 20n³ + 2n

Now, let's simplify the expression by canceling out common terms:

((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) = (12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)

As n approaches infinity, we can see that the highest power of n in the numerator and denominator is n⁵.

We can divide all terms by n⁵ to determine the limit:

lim(n→∞) [(12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)]

= lim(n→∞) [(12 + 40/n² + 12/n⁴) / (2 + 20/n² + 2/n⁴)]

= 12/2

= 6

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Answer:

[tex]w=\frac{82}{17}[/tex]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Decimal form: 4.82352941

having a great day and thx for your inquiry :)

Here is the descriptive statistics table for the four variables, including skew and kurtosis for each variable:

Variable Mean Median Standard Deviation Skewness Kurtosis

Height 68.2 68.0 3.0 0.2 -0.6

Weight 170.0 168.0 30.0 0.4 -0.6

Age 25.0 25.0 2.0 0.0 -1.0

IQ 100.0 100.0 15.0 0.0 -1.0

The skewness and kurtosis values for all four variables are close to 0, which suggests that the data is approximately normally distributed.

In addition to the descriptive statistics table, we can also assess normality by creating a histogram of the data.

The histograms for height, weight, and age are all approximately bell-shaped, which suggests that the data for these variables is approximately normally distributed. However, the histogram for IQ is slightly skewed to the right, which suggests that the data for IQ may not be truly normally distributed.

Overall, the descriptive statistics and histograms suggest that the data for height, weight, and age is approximately normally distributed.

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The mean of M1 + M2 is 1.4

The standard deviation is  1.104536.

The mean of the number of mistakes = 0.7

The standard deviation of the number of mistakes = 0.781

(a) Mean of M1 + M2:

Mean of (M1 + M2)

= Mean(M1) + Mean(M2)

= μ + μ

= 2μ

=  2 * 0.7

mean of M1 + M2= 1.4

(b) Standard deviation of M1 + M2:

Standard deviation of (M1 + M2)

= √(Variance(M1) + Variance(M2))

Variance for (M1) = (σ²) = (0.781)² = 0.610561

Variance for (M2) = (σ²) = (0.781)² = 0.610561

Standard deviation for (M1 + M2)

= √(0.610561 + 0.610561)

= √1.221122

Standard deviation = 1.104536

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The cost of the burger is $10.50, the cost of the souvenir is $28.00, and the cost of the pass is $42.00.

Let's assume the cost of the pass is x dollars.

According to the given information:

The burger costs 1/4 of the souvenir, so the burger's cost is[tex](1/4) \times x[/tex]dollars.

The souvenir costs 2/3 of the pass, so the souvenir's cost is [tex](2/3) \times x[/tex]dollars.

Mark had $4.50 left over after buying these items, so we can set up the following equation:

[tex]43.00 - [(1/4) \times x + (2/3) \times x] = $4.50[/tex]

Simplifying the equation, we have:

[tex]43.00 - [(1/4) \times x + (2/3) \times x] = $4.50[/tex]

[tex]43.00 - (1/4 + 2/3) \times x = $4.50[/tex]

[tex]43.00 - (3/12 + 8/12) \times x = $4.50[/tex]

[tex]43.00 - (11/12) \times x = $4.50[/tex]

To solve for x, we'll isolate the variable on one side of the equation:

$43.00 - $4.50 = (11/12) * x

$38.50 = (11/12) * x

Now, we can solve for x by multiplying both sides of the equation by (12/11):

[tex](12/11) \times $38.50 = x[/tex]

$42.00 = x

Therefore, the cost of the pass is $42.00.

Now we can find the costs of the burger and the souvenir:

The burger costs 1/4 of the souvenir, so its cost is (1/4) * $42.00 = $10.50.

The souvenir costs 2/3 of the pass, so its cost is (2/3) * $42.00 = $28.00.

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The scale factor from triangle D to triangle D' is 4

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

The triangles

From the triangles, we have the following parameters

Using the above as a guide, we have the following:

Scale factor of the dilation = Corresponding side length of D' / Side length of D

So, we have

Scale factor of the dilation = 32/8

Evaluate

Scale factor of the dilation = 4

Hence, the scale factor of the dilation is 4

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The Eric's time can be represented by the equation t = (d/60) - 2.

To create a second equation showing how long it would take Eric to travel the same distance as Noah, we can use the formula distance = speed x time. Let's call the distance that both Noah and Eric travel "d" (since we don't know the actual distance).

We know that Noah's speed is 135 mph and Eric's speed is 60 mph. We also know that Eric takes two hours longer to travel the same distance as Noah.

So, if we let "t" be the time it takes Noah to travel "d" distance, then Eric's time can be represented as "t + 2" hours. Putting all of this together, we can create the following equation: d = 135t (for Noah) and d = 60(t + 2) (for Eric).

From this second equation, we can solve for Eric's time by dividing both sides by 60, which gives us t + 2 = d/60.

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The amount of money Gillians owes for student loans is $12,250

How to determine this

When Gillians net worth = $90,500

House(Current value) = $87,900

Checking account = $950

Credit- card = -$2,650

Automobile(current value) = $10,300

Student loans = ?

Investment = $5,000

Personal loans = 1,200

Savings account = $2,450

To calculate the money Gillians Owen owes student loans

Let x represent the student loans

$90,500 = $87,900 + $950 - $2,650 + $10,300 + x + $5,000 - $1,200 + $2,450

$90,500 = $102,750 + x

Collect like terms

x = $90,500 - $102,750

x = 12,250

Therefore, the money Gillians owes student loans is $12,250

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The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

In mathematics, a graph is a visual representation of a set of data, which consists of points, called vertices or nodes, and lines connecting them, called edges or arcs.

Graphs are often used to represent mathematical functions, data sets, or relationships between objects, and they can be used to model real-world phenomena.

Graphs can be drawn on a coordinate plane or in a more abstract form, and they can be used to analyze and understand complex systems and relationships.

The correct statements are:

If "positive" end behaviour:

The arrows point in the same direction.

The right arrow is up.

The graph hits the y-axis.

If "negative" end behaviour:

The arrows point in opposite directions.

The right arrow is down.

The graph hits the X-axis.

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Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

The term (x - 1) is a factor of both of the given polynomials as;

x² + x - 2

2x² - 5x + 3

Given that (x - a) is a factor of a polynomial p(x), then x = a is a zero of the polynomial, which means that:

p(a) =0.

When x - 1 is a factor of any of the given polynomials, then we need to evaluate them in x = 1 and check if we get zero.

a) x² + x - 2

Evaluate it in x = 1;

1² + 1 - 2 = 0

so (x - 1) is a factor.

b) 2x² - 5x + 3

Evaluating this in x = 1;

2*1² - 5*1 + 3

2 - 5 + 3 = 0

(x - 1) is a factor.

Therefore, the correct option is the last one, it is a factor of both polynomials.

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Answer:

5376

Step-by-step explanation:

volume of prism = 8 X 6 X 14 = 672.

volume of cube = 1/2 X 1/2 X 1/2 = 1/8.

672 / (1/8)

= 672 X (8/1)

= 5376.

5376 cubes will fit into it

volume: 2,160cm

please let me know if this was what you needed or if it was something else.

Answer:

First, let's calculate the total cost of buying the shares:

1000 shares * $15.23/share = $15,230

Next, we need to calculate the commission paid to the broker for buying the shares:

$15,230 * 0.0075 = $114.23

So, the total cost of buying the shares including the commission is:

$15,230 + $114.23 = $15,344.23

Now, let's calculate the total revenue from selling the shares:

1000 shares * $18.78/share = $18,780

We also need to calculate the commission paid to the broker for selling the shares:

$18,780 * 0.0075 = $140.85

So, the total revenue from selling the shares after the commission is:

$18,780 - $140.85 = $18,639.15

The total profit from buying and selling the shares is:

$18,639.15 - $15,344.23 = $3,294.92

The rate of return is the profit divided by the total cost, expressed as a percentage:

($3,294.92 / $15,344.23) * 100% = 21.5%

Therefore, Omar's rate of return is 21.5%.

Answer:

Step-by-step explanation:

[tex]8x^5 + 3x^4 - 23x\\= 8x^5+3x^4+0x^3+0x^2-23x+0[/tex]

The value of the missing angle x is: 38°

We know that the sum of angles in a triangle is 180 degrees and as such:

∠DAE = 180 - (82 + 68)

∠DAE = 30°

Now, we know that alternate angles are congruent. Thus:

∠DAE ≅ ∠ADC = 30°

Opposite angles of a parallelogram are equal (or congruent) Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees).

Thus:

∠BAE = ∠BDE = 82 + 30

= 112°

Thus:

∠ABC = ∠ACB = 68°

Thus:

∠BAC = 180 - 2(68)

∠BAC = 44°

Thus:

x = 112 - (44 + 30)

x = 112 - 74

x = 38°

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Answer:

-0.5. is 5

Step-by-step explanation:

i need the poits

The relation shown in the graph is not a function because it violates the vertical line test.

We have,

The relation shown in the graph is not a function because it violates the vertical line test.

The vertical line test states that for a relationship to be a function, every vertical line drawn on the graph should intersect the graph at most once.

However, in this case, the U-shaped graph intersects the vertical line at multiple points, such as (-2, -2) and (2, 2).

Therefore, the relation does not meet the criteria of a function.

Thus,

The relation shown in the graph is not a function because it violates the vertical line test.

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The inequality 2|x - 3| + 6 > 10 has the solution set:

x < 1 or x > 5

To solve the inequality 2|x - 3| + 6 > 10, we need to isolate the absolute value expression |x - 3|.

We can do this by subtracting 6 from both sides of the inequality:

2|x - 3| > 4

Then we can divide both sides by 2:

|x - 3| > 2

Now we need to consider two cases, one where x - 3 is positive, and another where it is negative:

When x - 3 is positive, the inequality |x - 3| > 2 becomes:

x - 3 > 2

Solving for x gives:

x > 5

When x - 3 is negative, the inequality |x - 3| > 2 becomes:

-(x - 3) > 2

Solving for x gives:

x < 1

Therefore, the solution set for the inequality 2|x - 3| + 6 > 10 is:

x < 1 or x > 5

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The complete question:

Match each absolute value inequality on the left side with its solution set on the right

2|x - 3| + 6 > 10 - 2

The probability of the point being in region A is 0.5294.

The area of the entire figure can be found by adding the areas of the four triangles:

Area of entire figure

= Area of triangle ABC + Area of triangle ACD + Area of triangle ABD + Area of triangle BCD

= (1/2)(5)(3) + (1/2)(3)(4) + (1/2)(4)(3) + (1/2)(3)(4)

= 7.5 + 6 + 6 + 6

= 25.5 square inches

Similarly, the area of region A can be found by adding the areas of triangles ABC and ABD:

Area of region A

= Area of triangle ABC + Area of triangle ABD

= (1/2)(5)(3) + (1/2)(4)(3)

= 7.5 + 6

= 13.5 square inches

Therefore, the probability of the point being in region A is:

P(A) = Area of region A / Area of entire figure

P(A) = 13.5 / 25.5

P(A) = 0.5294

So the probability of the point being in region A is 0.5294.

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To answer these questions, I would need more information about the population being referred to. Specifically, I would need to know the number of residents who have only completed high school and are under age 50, as well as the total number of residents who have only completed high school. I would also need to know the number of residents aged 20-29 who have completed only high school or just some college, as well as the total number of residents aged 20-29.

Do you have this information available?

The correct statement is the center of the circle does not lie on the x-axis or the y-axis.

Given the equation of a circle, x² + y² – 2x – 8 = 0. Transform this equation in standard form of equation of circle

The standard form of the equation is (x – 1)² + y² = 8, and the radius of this circle is not the same as the radius of the circle whose equation is x² + y² = 9. Also, the center of the circle does not lie on the x-axis or the y-axis.

Therefore, the correct statement is the center of the circle does not lie on the x-axis or the y-axis.

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The inequality representing the amount Jeremiah spends on dinner daily is x ≥ $14.50. Two examples of amounts Jeremiah might spend are $16.75 and $22.00.

1. To represent the amount Jeremiah spends on dinner daily, we can use the inequality symbol "≥" (greater than or equal to) since it says "at least." Let's use the variable x to represent the amount.

2. The inequality representing the amount Jeremiah spends is x ≥ $14.50.

3. Example 1: Jeremiah might spend $16.75 on dinner, which satisfies the inequality since $16.75 is greater than $14.50.

4. Example 2: Jeremiah might spend $22.00 on dinner, which also satisfies the inequality as $22.00 is greater than $14.50.

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

Yes, (s + t)^2 is equivalent to s^2 + 2st + t^2. This can be shown through the process of expanding the expression (s + t)^2 using the FOIL method (multiplying first, outer, inner, and last terms).

First, we can rewrite (s + t)^2 as (s + t)(s + t).

Now, we do the multiplication and combine like terms:

s*s + s*t + t*s + t*t

s^2 + st + st + t^2

s^2 + 2st + t^2

Your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.

Since the final exam counts for 15% of the course grade, the weighted average can be calculated as follows:

Weighted average = (0.85 × 80%) + (0.15 × final exam score)

If we assume that your friend wants to get the highest possible grade, then they would need to get a perfect score on the final exam, which would be 100%.

Plugging this into the equation above, we get:

Weighted average = (0.85 × 80%) + (0.15 × 100%) = 83%

Therefore, the best course grade your friend can earn is 83%.

We can set up an equation where x is the minimum score needed on the final exam:

Weighted average = (0.85 × 80%) + (0.15 × x) = 75%

Simplifying this equation, we get:

0.85 × 80% + 0.15x = 75%

68% + 0.15x = 75%

0.15x = 7%

x = 46.67%

Therefore, your friend would need to score at least 46.67% on the final exam to earn a 75% for the course.

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Answer:20%

Step-by-step explanation:

Answer:

[tex]\large {\mbox{R = 3.6}}[/tex]

Step-by-step explanation:

The formula for finding a magnitude of an earthquake on the Richter Scale is given as
[tex]R = \log\left(\dfrac{A}{A_0}\right)\\[/tex]

[tex]\rm{where}\\\textrm{A - measure of amplitude of quake wave}\\\textrm{$A_0$ = amplitude of smallest detectable wave}\\[/tex]

Given A = 0.3954 and A₀ = 0.0001, we can plug in these values into the R equation to get

[tex]R = \log\left(\dfrac{0.3954}{0.0001}\right)\\\\= \log(3954)\\\\= 3.597\\\\= 3.6\text { rounded to the nearest tenth}[/tex]

1) The translation made is 2 units up, 1 units left.

2) The translation made is 2 units right, 1 unit up.

Since, A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Chess player moves a knight from the location (3,2) to (5,1) on a chessboard.

And, the player moves the knight from (5,1) to (6,3),

Since, Translation for (3,2) to (5,1|) is,

⇒ 2 units up, 1 units left.

And, Translation for (5,1) to (6,3) is,

⇒ 2 units right, 1 units up.

Hence, When a player moves a knight from the location (3, 2) to (5, 1) on a chessboard the translation made is 2 units up, 1 units left.

And, When the player moves the knight from (5, 1) to (6, 3), the translation made is 2 units right, 1 units up.

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