A customer decides to build a fence around the backyard shown. The fence will not have any gates. The yard is rectangular, with the house being an equal distance from both property lines. As a result, the fence will have five sections. The short sections, connecting to the house, are each 10 feet in length. The yard has a length of 80 feet and a width of 65 feet. How many feet of fencing is needed?

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

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 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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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 probability that a male student is taller than 74 inches is 0.3085.

We are given that

σ = 4 inches.

We are also told that 95% of the heights are between 62 inches and 78 inches, which means that 2.5% of the heights are below 62 inches and 2.5% of the heights are above 78 inches.

Using a standard normal distribution table, we can find the z-scores corresponding to these percentages:

The z-score corresponding to the 2.5% below 62 inches is -1.96.

The z-score corresponding to the 2.5% above 78 inches is 1.96.

For the lower limit:

-1.96 = (62 - μ) / 4

For the upper limit:

1.96 = (78 - μ) / 4

Solving for μ in both equations, we get:

μ = 70.08 for the lower limit

μ = 73.92 for the upper limit

Now, the average of these two estimates:

μ ≈ (70.08 + 73.92) / 2 ≈ 72 inches.

To approximate the probability that a male student is taller than 74 inches, we can standardize the height value using the z-score formula:

z = (x - μ) / σ

z = (74 - 72) / 4 = 0.5

As, the probability that a standard normal random variable is greater than 0.5, which is 0.3085.

Therefore, the probability that a male student is taller than 74 inches is 0.3085.

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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 side length x=6.63.

By using Pythagoras' theorem on right angle triangle,

"The square of the hypotenuse side is equal to the sum of squares of the other two sides". (Pythagoras' theorem)

(12)^2=(10)^2+(x)^2

(x)^2=144-100

(x)^2=44

The side length is x=6.333.

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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.

Answer:

Step-by-step explanation:

A) $50.40

B) $50.68

Answer:

Step-by-step explanation:

Volume = s³    (where s is the side)

Volume = 3.5³

Volume = 42.875

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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To solve the inequality 2/3k - 6 < 24, we can start by adding 6 to both sides of the inequality:

2/3k - 6 + 6 < 24 + 6

Simplifying the left side gives:

2/3k < 30

To isolate k, we can multiply both sides by 3/2:

2/3k * 3/2 < 30 * 3/2

Simplifying the left side gives:

k < 45

Therefore, the inequality 2/3k - 6 < 24 expressed in its simplest form is k < 45.

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 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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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 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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The approximate area to the left of z= 2​ is 0.978

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

The left of z= 2​

The area to the left of z is calculated by calculating the probability that the z-score is less than 2

In other words, this is represented as

Area = (z < 2)

This can then be calculated using a statistical calculator or a table of z-scores,

Using a statistical calculator, we have the area to be

Area =  0.97725

When this value is approximated, we have the approximated area to ve

Area =  0.978

Hence, the area is 0.978

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Hello

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

10/35 > 6/35

=> 2/7 > 6/35

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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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 completed two-column table that we can  use to prove the congruence of ∠BAD and ∠DCB indicates that the missing proof in step 6 of the table is substitution.

Therefore correct option is option B

Congruent angles are described as angles that have the same measurement.

The two-column table is shown below;

 Statements                                                           Reasons

1. ABCD is a parallelogram with diagonal                Given

2. ║ and ║                                                       Definition of a parallelogram

3. ∠2≅∠3, ∠1≅∠4                                              Alt. int. ∠s are ≅

4. m∠2 = m∠3 and m∠1 = m∠4                         Measures of ≅ ∠s are =

5. m∠1 + m∠2 = m∠4 + m∠2                              Addition prop. of equality

6. m∠1 + m∠2 = m∠4 + m∠3                              Substitution

7. m∠1 + m∠2 = m∠BAD                                     Angle addition property

m∠3 + m∠4 = m∠DCB

8. m∠BAD = m∠DCB                                          Substitution

9. ∠BAD ≅ ∠DCB                                              Angles are congruent if   their measures are the same    

Therefore, the missing reason in the partial proof is therefore substitution.

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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.

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 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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Answer:

D={x|x≥2}, R={y|y≥0}.

Step-by-step explanation:

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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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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