Using L’Hôpital’s Rule, evaluate
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The perimeter of the irregular shape is 40 cm.

We know that a polygon is defined as a closed figure made up of three or more line segments connected end to end.

Given that the parameters as :

10 cm

15 cm

7 cm

6 cm

2 cm

Perimeter  ; the sum of length of the sides used to made the given figure..

Let Perimeter  = p

Perimeter P = 10 + 15 + 7 + 6 + 2

= 40 cm

The answer will be 40 cm.

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The value of x in the circle is 4√5

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

The circle

The value of x in the circle can be calculated using the following pythagoras theorem

x² = (24/2)² - (16/2)²

When the quotients are evaluated, we have

x² = 12² - 8²

When the exponents are evaluated, we have

x² = 144 - 64

When the difference are evaluated, we have

x² = 80

When the exponents are evaluated, we have

x = √80

Simplify

x = 4√5

Hence, the value of x is 4√5

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The value of angle a is 80 degrees.

The two chords intersect angle theorem, also known as the intersecting chords theorem, states that when two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.

From two chords intersect angle theorem

∠a=(∠b+∠c)/2

in a given case,

∠b=36°

∠c =124°

So, ∠a=(36+124)/2

∠a= 80°

Therefore, the value of angle a will be 80 degrees.

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Complete question:

The measure of angle A and angle C from the given cyclic quadrilateral are 81° and 99° respectively.

From the given figure, m∠D=86°.

Here, m∠D+m∠B=180°  (Opposite angles of cyclic quadrilateral adds to 180° )

86°+m∠B=180°

m∠B=180°-86°

m∠B=94°

Let O be the center of circle.

Since, the legs of the radii are equal, the triangles AOD, DOC and COB are isosceles. Hence, their base angles are congruent. Thus,

77°+2∠ADO=180°

2∠ADO=180°-77°

2∠ADO=103°

∠ADO=103/2

∠ADO=51.5°

∠ADO=∠DAO=51.5°

2∠BAO=180°-121°

2∠BAO=59°

∠BAO=59°/2

∠BAO=29.5°

∠BAD=∠DAO+∠BAO

∠BAD=51.5°+29.5°

∠BAD=81°

So, m∠A=81°

m∠A+m∠C=180°

m∠C=180°-81°

m∠C=99°

Therefore, the measure of angle A and angle C from the given cyclic quadrilateral are 81° and 99° respectively.

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The number used in the blanks to satisfy the inequality is 1/2.

i.e

1/2 x 12 < 12

6 < 12

We have,

___ x 12 < 12

Now,

To fill in the blank we substitute the following.

- 2/2

- 3/2

- 1/2

Substitute each option in the blanks and see which satisfies the inequality.

Now,

2/2 x 12 < 12

1 x 12 < 12

This is not true.

3/2 x 12 < 12

3 x 6 < 12

18 < 12

This is not true.

1/2 x 12 < 12

6 < 12

This is true.

Thus,

The number used in the blanks to satisfy the inequality is 1/2.

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The Experimental probability and the theoretical probabilities are 0.2 and 0.3 respectively.

If the spinner is fair, then each color must have the same probability,

this means that the probability for each color is the number of times that the color (in this case blue) is in the spinner divided by the total amount of colors in the spinner, then the theoretical probability for each color is:

Pt = 1/5 = 0.20

The experimental probability can be found by dividing the number of times that the spinner landed on a given color (in this case for blue we have 15 times) divided by the total number of spins ( 50)

Pe = 15/50 = 0.30

Therefore, the Experimental probability and the theoretical probabilities are 0.2 and 0.3 respectively

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Complete question:

A spinner has 5 equal-sized sections with different colors. You spin the spinner 50 times. The results are shown in the table. Find the theoretical and experimental probabilities of spinning blue.

Red Green Blue Yellow Orange

8           11      15       9          7

The theoretical probability is

The experimental probability is

Hello

2/7 = 2x5/7x5 = 10/35

10/35 > 6/35

=> 2/7 > 6/35

A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = [tex]\bar{x}[/tex] ± ME

where:

[tex]\bar{x}[/tex] is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

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The exponential function that represents this situation is f(x) = 0.0625(2)ˣ

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

(x, y) = (1, 0.125) and (2, 0.25)

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

The function of the situation is

f(x) = a * rˣ

Where

r = 0.25/0.125

So, we have

r = 2

Substitute the known values in the above equation, so, we have the following representation

f(x) = a * (2)ˣ

Using the points, we have

a * (2)² = 0.25

So, we have

a = 0.0625

Hence, the function is f(x) = 0.0625(2)ˣ

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Answer:

(x,y) → (x+ 6,y - 3)

Step-by-step explanation:

I think you posted this question earlier as well? Basically, x moves left and right, while y moves down and up. Therefore, if you wanted to move 3 units down, you would use y-3.

The correct statements are given as follows:

The time it will take for them to complete the puzzle is obtained using the together rate, which is the sum of each separate rates.

The rates are given as follows:

The together rate is:

1/x.

In which x is the time needed to complete the puzzle.

Hence the equation is:

1/7 + 1/5 = 1/x.

The time is then obtained as follows:

1/x = (5 + 7)/35

x = 35/12

x = 2.9 hours.

The party part is incomplete, hence:

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Answer: 54.70

Step-by-step explanation:

We are given an angle and the adjacent side and need to find the hypotenuse meaning we have to use cosine

cos(x) = ADJ/HYP

cos (46) = 38/x

0.69465837045 = 38/x

x = 38/0.69465837045

x = 54.70

Answer:

quadratic formula, completing the square, factorisation

Step-by-step explanation:

Quadratic formula:

x = (-b ± √(b² - 4ac) ÷ 2a)

where a is the value of the first coefficient, b is value of the second and c is value of the constant.

x = ((-b ± √(b² - 4ac)) ÷ 2a)

 = (( -16± √((-16)² - 4(8)(3)) ÷ 2(8))

 = ((-16 ± √(256 - 96)) ÷  16)

= (-16 ± √(160)) ÷  16

= -1 ±  (√10)/4

Completing the square:

divide through by 8

x² + 2x + 3/8 = 0

1) put the x, not ^2, in parenthesis.

(x +  )      = 0

2) half the coefficient (2) of x. that is 1. Put that into same parenthesis.

(x + 1)       = 0

3) we have (x + 1)

4) square this and multiply out. (x + 1)² = x² + x + x +4 = x² +2x + 1

5) this looks just like the original equation (x² + 2x + 3/8) except for +1. What do we have to do to get back to original? 1 – (3/8) = 5/8. We have to subtract 5/8

6) now we have (x + 1)² – 5/8 =0

7) (x + 1)² = 5/8

8) (x + 1) = ± √(5/8)

9) x = ± √(5/8)  - 1

     =  -1 ± (√10)/4

Factorisation:

(8x (- (2√10)) + 8) = 0,

8x = -8 +  (2√10)),

x = -1 + (√10)/4

(x ( + (√10)/4 + 1) = 0

x = -1 -  (√10)/4

If the table does not represent a function, the value of "a" may be: A. -4; D. 2; and F. 5. [Note, no calculation is needed, just apply the criteria that makes a table a function].

A table that represents a function will have each x-value assigned to only one y-values, in order words, on the x-values column, there will be no repeating x-value.

Looking at the table given with the options, we see that:

if a = -4, we will have a repeating x-value, the same with 2 and 5.

However, if we have a represented as 0, 1, and 3, there would be no repeating x-value. Therefore, for the table not to be a function, a may be equal to:

A. -4; D. 2; and F. 5

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The expression for b in terms of a is given as follows:

[tex]b = \ln{(2e^a - 1)}[/tex]

We have the area under a curve, hence integrals are used to obtain the formulas.

For area a, we have that:

[tex]A = \int_0^a e^x dx[/tex]

Applying the Fundamental Theorem of Calculus, we have that:

[tex]A = e^a - 1[/tex]

For area b, we have that:

[tex]B = \int_0^b e^x dx[/tex]

[tex]B = e^b - 1[/tex]

The area B is twice the area A, hence:

[tex]e^b - 1 = 2(e^a - 1)[/tex]

[tex]e^b = 2e^a - 1[/tex]

The natural logarithm is the inverse of the exponential, hence:

[tex]b = \ln{(2e^a - 1)}[/tex]

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Answer:

Step-by-step explanation:

You want to know the nature of the given sequences:

Looking at differences between terms can tell you a lot about the nature of a sequence.

When first differences are constant, the sequence is arithmetic.

When first differences are not constant, but have a common ratio, the sequence is geometric. (The sequence terms will have the same common ratio.)

When second differences are constant, the sequence is quadratic. (Not applicable here.)

First differences are -3, 0, 3. These are not constant. However, second differences are 0 -(-3) = 3 and 3 -0 = 3. These are constant, so this sequence is quadratic, neither arithmetic nor geometric.

First differences are 6, 6, 6. They are constant, so this sequence is arithmetic.

First differences are -200, -40, -8. These are not constant, but have a common ratio of 1/5 — just as the terms of the sequence do.

This sequence is geometric.

__

Additional comment

The first differences are computed by subtracting the term before from each term. 1 -4 = -3; 1 -1 = 0, 4 -1 = 3 for the first sequence. The ratio is found by dividing a term by the term before: 50/250 = 1/5, for example.

For common difference d and first term a1, the general term of an arithmetic sequence is ...

  an = a1 +d(n -1)

For common ratio r, the general term of a geometric sequence is ...

  an = a1·r^(n-1)

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The drama club must sell at least 74 adult tickets to meet the cost requirement, in addition to the 45 student tickets that have already been sold.

Let's use "a" to represent the number of adult tickets sold, and "s" to represent the number of student tickets sold.

Since s = 45, and we want to find the minimum number of adult tickets required to satisfy the $890 cost requirement.

The total revenue from ticket sales can be expressed as:

Revenue = 5s + 9a

We want to find the values of s and a that satisfy the following conditions:

- s + a <= 122 (the maximum capacity of the auditorium)

- Revenue >= 890

Substituting s = 45, we get:

5(45) + 9a >= 890

225 + 9a >= 890

9a >= 665

a >= 73.89

Since we cannot sell a fraction of a ticket, the minimum number of adult tickets we need to sell to meet the cost requirement is 74.

Therefore, the drama club must sell at least 74 adult tickets to meet the cost requirement, in addition to the 45 student tickets that have already been sold.

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Answer:

Step-by-step explanation:

Volume = s³    (where s is the side)

Volume = 3.5³

Volume = 42.875

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

Step-by-step explanation:

To find the volume of a cylinder, you can use the formula:

Volume = π * r^2 * h

Where:

- π is a mathematical constant approximately equal to 3.14159

- r is the radius of the cylinder's base

- h is the height of the cylinder

Let's calculate the volume of the cylinder with the given information:

1. Volume of the first cylinder:

- Radius (r): Let's assume a value of 1 (you can replace this with the actual radius value)

- Height (h): Let's assume a value of 1 (you can replace this with the actual height value)

Volume = π * r^2 * h

= π * 1^2 * 1

= π cubic units

2. Volume of the second cylinder (double the height):

- Radius (r): Same as the first cylinder (1)

- Height (h): Double the height of the first cylinder (2 times the height)

Volume = π * r^2 * h

= π * 1^2 * (2 * 1)

= π * 1^2 * 2

= 2π cubic units

So, the volume of the first cylinder is π cubic units, and the volume of the second cylinder (with double the height) is 2π cubic units.

The value of the angle ∠BAD of the given image is: 60°

The sum of angles in a triangle is 180 degrees. We know that the interior angles of an equilateral angle are equal and as such each of the angles of the equilateral triangle are 60 degrees.

Thus:

∠ADE = ∠AED = ∠DAE = 60 degrees

We know that alternate angles are angles that lie on opposite sides of the transversal line and on opposite relative sides of the other lines.

Thus:

∠BAD = ∠ADE = 60°

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The inverse matrix used to decrypt the message is given as follows:

[tex]\left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

To obtain the inverse matrix, we must have the original matrix side by side with the identity matrix, as follows:

[tex]\left[\begin{array}{cc}2&9\\1&5&\end{array}\right] \left[\begin{array}{cc}1&0\\0&1&\end{array}\right][/tex]

Then we must do row operations on the right matrix so we end with the identity matrix on the right and the inverse matrix on the right.

First we divide the first line by 2, hence:

[tex]\left[\begin{array}{cc}1&4.5\\1&5&\end{array}\right] \left[\begin{array}{cc}0.5&0\\0&1&\end{array}\right][/tex]

Then we want the element a row 2 column 1 to be of zero, hence:

R2 -> R2 - R1

[tex]\left[\begin{array}{cc}1&4.5\\0&0.5&\end{array}\right] \left[\begin{array}{cc}0.5&0\\-0.5&1&\end{array}\right][/tex]

Then we want the diagonal element of the second row to be of 1, hence we multiply by 2, thus:

[tex]\left[\begin{array}{cc}1&4.5\\0&1&\end{array}\right] \left[\begin{array}{cc}0.5&0\\-1&2&\end{array}\right][/tex]

Finally, we want the element of 4.5 to be of zero, hence:

R1 -> R1 - 4.5R2

Then:

[tex]\left[\begin{array}{cc}1&0\\0&1&\end{array}\right] \left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

The inverse matrix is of:

[tex]\left[\begin{array}{cc}-5&-9\\-1&2&\end{array}\right][/tex]

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Answer:

Step-by-step explanation:

A) $50.40

B) $50.68

The probability of randomly picking a school or library-related issue from the ballot is 9/19 or approximately 0.474 (rounded to three decimal places).

To determine the probability of a randomly picked issue being school or library related, you'll need to consider the total number of issues and the number of school and library issues combined.

There are 7 school-related issues, 10 ordinance-related issues, and 2 library-related issues, making a total of 19 issues on the ballot. To find the probability of picking a school or library issue, combine the number of school and library issues: 7 + 2 = 9.

Now, divide the number of school and library issues (9) by the total number of issues (19): 9/19.

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The approximate percentage of daily phone calls numbering between 33 and 39 is about 68%.

The empirical rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.

In this case, the mean is 36 and the standard deviation is 3.

To find the percentage of daily phone calls numbering between 33 and 39, we need to first calculate the number of standard deviations that separate these values from the mean:

For 33: (33 - 36) / 3 = -1

For 39: (39 - 36) / 3 = 1.

So, we are looking for the percentage of data that falls between -1 and 1 standard deviations from the mean.

According to the empirical rule, this interval contains approximately 68% of the data.

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Answer: d.8

the answer is d 8ndndinwidnwidnwidnwidnwiud

The algebraic expression is:

4x + 12

We have,

Algebraic expressions are mathematical statements that involve variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division.

In this case,

We have been given the phrase "Four times a number(x) more than twelve" and we need to translate it into an algebraic expression.

The first step is to identify the key information in the phrase.

Here, the phrase tells us to take a number (which we represent by x) and multiply it by four.

It then says we should add 12 to this.

Now,

Four times a number more than twelve can be translated to four times a number increased by twelve.

And,

Since the number is represented by x, we can write it as 4x + 12.

Thus,

The algebraic expression is:

4x + 12

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The algebraic expression that represents the phrase "Four times a number (x) more than twelve" is 4(x + 12).

We have the statement

"Four times a number(x) more than twelve"​

let the number be x.

So, four times of a number = 4x

Then, the algebraic expression that represents the phrase "Four times a number (x) more than twelve" is 4(x + 12).

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Answer:

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

Standard form for the equation of a circle is:

Using the given endpoints of the diameter find the center, which is the midpoint:

The radius is half the distance between endpoints:

Substitute values into equation:

The inverse of matrix of A, that is A⁻¹ is [tex]\begin{bmatrix}-3 & 2 \\ 2& -1\end{bmatrix}[/tex].

To find the inverse of the matrix A, we can use the formula.  

A⁻¹ = (1 / det(A)) x adj (A)

Where det(A) represents the determinant of matrix A and adj(A) represents the adjugate of matrix A.

First, let's calculate the  determinant of matrix  A

det (A) = (1 x 3)  - (2 x2)

= 3 - 4

= -1

Next, let's calculate the adjugate of matrix A

adj(A) =

[tex]\begin{bmatrix}3 & -2 \\ -2& 1\end{bmatrix}[/tex]

Now, we can calculate the inverse of matrix A using the formula:

A⁻¹  = (1 / det(A)) x  adj(A)

= (1 / -1) *

[tex]\begin{bmatrix}3 & -2 \\ -2& 1\end{bmatrix}[/tex]

Multiplying each element of the adjugate matrix by -1  

A⁻¹ =

[tex]\begin{bmatrix}-3 & 2 \\ 2& -1\end{bmatrix}[/tex]

So , the inverse of the matrix A is:

A⁻¹  =

[tex]\begin{bmatrix}-3 & 2 \\ 2& -1\end{bmatrix}[/tex]

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