An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the exact area of each shaded region in the figure. Then find the approximate area of the entire shaded region, rounded to the nearest whole unit.

A. The distance she must walk to return to the starting point is approximately 1912.325 ft, or 1912 ft 3 in.

B. She is walking towards the north, the heading is N 1° 20' W.

C. Acreage = 7.55 acres (rounded to 3 decimal places).

A. Convert the angles to decimal degrees:

N. 27° 40′ E. = 27.667°

N. 56° 31′ E. = 56.517°

S. 4° 26′ W. = -4.433°

Now, calculate the distances between the points:

AB = √(696.2917² + 3.5² - 2*696.2917*3.5*cos(27.667°)) = 696.2227 ft

BC = √(487.9792² + 11.75² - 2*487.9792*11.75*cos(56.517°)) = 487.9385 ft

CD = √(1691.125² + 1.5² - 2*1691.125*1.5*cos(-4.433°)) = 1691.1415 ft

B. Finding the distance from D back to A, calculate the distance and angle between AD:

AD = √(AB² + BD² - 2*AB*BD*cos(θ)) where θ = 180° - 4°26' - 27°40' = 147.9°

Substituting AB and BD:

AD = √(696.2227² + 1691.1415² - 2*696.2227*1691.1415*cos(147.9°)) = 1912.3246 ft

Therefore, the distance she must walk to return to the starting point is approximately 1912.325 ft, or 1912 ft 3 in.

C. Finding the heading she walks from D back to A, calculate the angle between AD and the north-south axis:

θ' = atan((AB*sin(27.667°) - BD*sin(θ))/AD) = atan((696.2227*sin(27.667°) - 1691.1415*sin(147.9°))/1912.3246)

θ' = -1.344°

Since she is walking towards the north, the heading is N 1° 20' W.

Lastly, to calculate the acreage of this plot of land, we use Heron's formula to determine the area of triangle ABC:

s = (AB + BC + AC)/2 = (696.2227 + 487.9385 + 1392.625)/2 = 788.8931 ft

A = √(s(s-AB)(s-BC)(s-AC)) = 328756.0207 ft²

Convert to acres:

Acreage = 328756.0207/43560 = 7.55 acres (rounded to 3 decimal places).

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Using mathematical operations, Cindy's answer would have been 15 if she had worked the problem correctly by following her teacher's instructions.

The correct value can be determined by reversing Cindy's calculations to find the certain number as follows:

(x - 9) ÷ 3 = 43

x = 43 x 3 + 9

x = 138

With the certain number, x = 138, the correct mathematical operations can be performed as follows:

(138 - 3) ÷ 9

135 ÷ 9

= 15

Thus, Cindy's correct answer would have been 15 if she had performed the correct mathematical operations, according to her teacher's instructions.

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The equation in slope-intercept form for the line that has slope of -2/5 and y-intercept of -4 is written as: y = -2/5x - 4.

The slope-intercept form for any given straight line or linear relationship can be expressed as y = mx + b, where:

m = slope of the line

b = the y-intercept

Given the following:

slope (m) = -2/5.

y-intercept (b) = -4

To write the equation, substitute m = -2/5 and b = -4 into y = mx + b:

y = -2/5x - 4

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Step-by-step explanation:

Look at the table for z = 1.67  

You have the wrong table.......the table you posted is for negative z-scores

for z -score = + 1.67 , the value is .9535    = 95.35 %

Answer:

1. True

2.True

3.True

4.False

5.False

6.True

7.True

8.True

Step-by-step explanation:

1. The area of a rectangle is found by the formula A=bh.

2. There are 4 rectangles making up the lateral area of the prism. 2+3=5. 5*6=30, and multiply by 2 since there are two of the 2x6 and two of the 3x6 rectangles to get 60. The bases of the prism have an area of 6 square inches each.

60+12+12=84

3. 3*5=15

4. The base is not a square, so you cannot multiply by 4 to get the area of all the triangles. You can multiply by two, and also multiply 1/2(3)(4) by 2 to get the area of the other two triangles.

5. The base is a triangle. 1/2(3)(4)=6.

6. 2[1/2(3)(4)]=12. 2(8*5)=80. 3*8=24. 80+24+12=116

7. A cube has 6 identical sides, so you can find the area of one side and multiply by 6 to get the surface area of the cube.

8. 9^2=81. 81*6=486.

Answer:

Based on the residual plot, we can check for the following conditions:

I. The true relationship between x and y is linear:

We can check this condition by looking at the pattern of the residuals in the plot. If the residuals are randomly scattered around zero, without any discernible pattern, then it suggests that the true relationship between x and y is linear. If there is a pattern in the residuals, then it suggests that the true relationship is not linear. Since we are not given a residual plot to examine, we cannot determine whether this condition is met.

II. The standard deviation of y is constant for different levels of x:

We can check this condition by looking at the spread of the residuals in the plot. If the spread of the residuals is roughly the same for all values of x, then it suggests that the standard deviation of y is constant for different levels of x. If the spread of the residuals increases or decreases as x increases, then it suggests that the standard deviation of y is not constant for different levels of x. From the residual plot, we cannot determine whether this condition is met.

III. The value of 0 is contained in the confidence interval:

This condition refers to the confidence interval for the slope of the regression line. If the confidence interval includes 0, then it suggests that the slope is not significantly different from 0 and there is no significant linear relationship between x and y. From the residual plot, we cannot determine whether this condition is met.

Therefore, based on the given information, we cannot determine which conditions appear to be met based on the residual plot.

Where is the given proof

Answer:

GH = 6.2

Step-by-step explanation:

The matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

performing the row operation 4R₁ + R₂ — R₂ on M, we have;

4(1) + (-5) = -1 {row 2 column 1}

4(0) + 2 = 2 {row 2 column 2}

4(3) + (-2) = 10 {row 2 column 3}

Therefore, the matrix formed by performing the row operation 4R₁ + R₂ — R₂ on M will have R₁ = [1 0 3] and R₂ = [ -1 2 10]

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The proportion is solved and ratio of minutes spent talking to teachers to minutes spent talking to students is given by 2 : 1

Given data ,

The principal spends 96 minutes talking to the teachers

And , the principal spends 48 minutes talking to students

Now , the basic ratio of minutes spent talking to teachers to minutes spent talking to students, we need to simplify the ratio by dividing both values by their greatest common factor

So , A : B = 96 : 48

On simplifying the proportion , we get

A : B = 2 : 1

Hence , the proportion is 2 : 1

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b. The range is 32 - 16 = 16. and IQR  4

c. 32

a. Here is a box and whisker plot to represent the given data:

The horizontal axis shows the range of the data, and the vertical axis represents the frequency. The box represents the middle 50% of the data, with the bottom of the box being the 25th percentile and the top of the box being the 75th percentile. The whiskers represent the lowest and highest values within 1.5 times the interquartile range (IQR) of the box, and any points outside the whiskers are considered outliers.

b. The range is the difference between the highest and lowest values in the data set. In this case, the range is 32 - 16 = 16.

c. There is one outlier in the data set, which is the value of 32. It is outside the whiskers of the box and is considered to be an outlier.

The interquartile range (IQR) is the difference between the 75th and 25th percentiles of the data set. In this case, the IQR is:

IQR = Q3 - Q1

   = 22 - 18

   = 4

where Q1 is the first quartile (the value below which 25% of the data falls), and Q3 is the third quartile (the value below which 75% of the data falls).

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Answer: 5.3 repeated portions or about 5 portions

Step-by-step explanation: 25 pounds = 400 ounces

400/75 = 5.3 repeated

Answer:33

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to classify the functions shown in the tables as linear, quadratic, or exponential.

We notice all of the tables have x-values that are evenly spaced. this means we can look at the differences between y-values to determine the kind of function the table represents.

The differences have the following interpretation:

The differences of y-terms are constant at 3 -5 = -2.

The function is linear.

The differences of y-terms are constant at 5 -2 = 3.

The function is linear.

We observe that the y-values have a minimum. We don't need to take differences to know this is not linear or exponential. Of the offered choices, the only one that makes sense is "quadratic."

The differences of y-terms are ...

  1 -5 = -4, 5 -1 = 4, 17 -5 = 12, 37 -17 = 20

The differences of differences are ...

  4 -(-4) = 8, 12 -4 = 8, 20 -12 = 8

The second differences are constant.

The function is quadratic.

The first differences are ...

  3 -1 = 2, 9 -3 = 6, 27 -9 = 18, 81 -27 = 54

The second differences are

  6 -2 = 4, 18 -6 = 12, 54 -18 = 36

We note that the first and second differences are not constant, but the ratio of terms at every level is 3/1 = 6/2 = 12/4 = 3.

The function is exponential.

Answer:

the average amount Mrs. Gordon pays in interest each month, we need to determine the total interest paid over the six-month period and divide it by the number of months.

The total interest paid can be found by subtracting the cost of the stove from the total amount paid over six months:

Total interest paid = Total amount paid - Cost of the stove

The total amount paid over six months is calculated by adding the monthly payments:

Total amount paid = $160/month * 6 months

Let's perform the calculations:

Total amount paid = $160/month * 6 months = $960

Total interest paid = Total amount paid - Cost of the stove

= $960 - $850

= $110

Now, to find the average amount Mrs. Gordon pays in interest each month, we divide the total interest paid by the number of months:

The average amount paid in interest each month = Total interest paid / Number of months

= $110 / 6 months

≈ $18.33

Therefore, Mrs. Gordon pays an average of approximately $18.33 in interest each month.

According to the graph, the function that best describes the graph is

[tex]f(x)=|x| = \left\{ \begin{array}{cl}x - 2 \text{ for x \lt -3 } \\8 \text{ for -3 \lt x \lt 5}\\-x + 10 \text{ for x \gt 6}\end{array} \right.[/tex]
(option d).

As we all know that the term function is defined as a rule or relationship that maps each element in one set, called the domain, to exactly one element in another set, called the range.

While we looking into the graph we have identified that there is a straight line that cross the point (0, 8) within the range of -3 to 5.

And then the next line is moves downwards from the range of x whose value is greater than 6.

Final upward slope is moves the range of -3 or less While we looking into these range value we have identified that the the function that refers the graph is (option d).

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∠WTA and ∠HTC are vertical angles. Thus, they are equal.

As WA || HC, that means ∠AWT and ∠THC are alternate interior angles and are equal. Additionally, ∠WAT and ∠TCH are also alternate interior angles and are equal.

∠WTA = ∠HTC, ∠AWT = ∠THC, and ∠WAT = ∠TCH

Since both triangles have the same angle measurements, they are similar.

Answer:

  61°

Step-by-step explanation:

You want the angle XCA in the figure, given that angle XBA is 70°, and ABCD is a rectangle with AB=5.6m and BC=6.4m. Angles at A are right angles.

The length of diagonal AC is found using the Pythagorean theorem.

  AC² = AB² +BC²

  AC = √(5.6² +6.4²) = 0.8√113 ≈ 8.504 . . . . meters

The length XA is found using the tangent function:

  Tan = Opposite/Adjacent

  tan(B) = XA/AB

  XA = AB·tan(B) = 5.6·tan(70°) . . . . meters

The angle XCA is found from the tangent relation:

  tan(XCA) = XA/AC

  tan(XCA) = 5.6·tan(70°)/(0.8√113) = 7·tan(70°)/√113

  angle XCA = arctan(7·tan(70°)/√113) ≈ 61.07°

The angle XC makes with the horizontal is about 61°.

The statement that is true about the given circle equation is:

Option A: The circle is centered at (−6, 3) and has a radius of 11.

The standard form for finding the equation of a circle is given by the expression:

(x - h)² + (y - k)² = r²

where:

(h, k) represents the coordinates of the center of circle

r represents the radius of the circle

We are given the equation of the circle as:

(x - 6)² + (y - 3)² = 121

Now, 121 can also be written as 11². Thus, the equation of the circle can be rewritten as:

(x - 6)² + (y - 3)² = 11²

Comparing with the standard form of equation of a circle gives:

Coordinates of center = (-6, 3)

Radius = 11

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The missing probability is P(A or B) = 131/200

It should be noted that in order to find the probability of the union of two events A and B, i.e., P(A or B), we can use the following formula:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = P(A) + P(B) - P(A and B) = (9/20) + (1/4) - (9/200)

Simplifying the expression, we get:

P(A or B) = 45/100 + 25/100 - 9/200 = (90+50-9)/200 = 131/200

The probability is 131 / 200.

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The ratio of the surface area of Pyramid A to Pyramid B is: 36/49

We have the information from the question is:

Pyramid A and Pyramid B are similar.

The volume of Pyramid A is 648 [tex]m^3[/tex]

The volume of Pyramid B is 1029 [tex]m^3[/tex]

To find the ratio of the surface areas of Pyramid A to Pyramid B.

Now, As we know that:

If two solids are similar, then the ratio  of their volumes is equal to the cube

of the ratio of their corresponding linear measures.

[tex]\frac{Vol of A}{Vol of B} =(\frac{a}{b} )^3 =\frac{684}{1029}=\frac{216}{343}\\ \\ \frac{a}{b}=\frac{6}{7}[/tex]

If two solids are similar, then the n ratio of their surface areas is equal  to the square of the ratio of their  corresponding linear measures.

Surface area of A/ Surface area of B [tex]=(\frac{a}{b} )^2=\frac{36}{49}[/tex]

So, the ratio of the surface area of Pyramid A to Pyramid B is: 36/49

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The value c = 3 is not a solution to the inequality

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

122 c

Express properly

So, we have

1 ≥ c

When this inequality is rewriiten. we have

c ≤ 1

This means that the values of c do not exceed 1

The number 3 exceeds 1

So, it means that c = 3 is not a solution to the inequality

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The solution to the equation is x = 33/5.

We can start by simplifying both sides of the equation using the distributive property and combining like terms:

4/3 (x + 6) = 2x - 3 + x

4/3 x + 8 = 3x - 3

Next, we can isolate the variable x on one side of the equation by subtracting 4/3 x and adding 3 to both sides:

4/3 x - 3x = -8 - 3

-5/3 x = -11

Finally, we can solve for x by dividing both sides by -5/3:

x = -11 / (-5/3)

x = 33/5

Therefore, the solution to the equation is x = 33/5.

The simplified expression of  2x multiplied by 7 with the exponent of 4 is 4,802x.

The expression is simplified by applying the rules of multiplication and exponent rules.

the expression = 2x(7⁴)

simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401

Multiply the resultant solution of 2,401 as follows;

= 2,401 x (2x)

= 4,802x

Thus, the simplified expression of  2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of multiplication.

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Answer:

1.235 kg

Step-by-step explanation:

Let's assume that each packet of flour and salt weighs the same.

When we remove 7 packets of flour, we are left with 5 packets of flour and 8 packets of salt. The total number of packets is 13 and their total mass is 9.9 kg.

Therefore, the average mass of each packet is 9.9 kg ÷ 13 = 0.76 kg.

Since we know that 12 packets of flour and 8 packets of salt have a total mass of 19 kg, we can subtract the mass of the 12 packets of flour (12 × 0.76 kg = 9.12 kg) from the total mass to find the mass of the 8 packets of salt:

19 kg - 9.12 kg = 9.88 kg

Finally, we can divide the mass of the 8 packets of salt by the number of packets to find the mass of each packet:

9.88 kg ÷ 8 = 1.235 kg

Therefore, each packet of salt weighs approximately 1.235 kg.

It will take Lisa and Felipe approximately 4.95 hours to fill the order by working together.

To solve this problem, we can use the formula:

1/T = 1/T₁ + 1/T₂

where T is the time taken to complete the job when both Lisa and Felipe work together, T₁ is the time taken by Lisa to complete the job, and T₂ is the time taken by Felipe to complete the job.

Substituting the given values into the formula, we get:

1/T = 1/9 + 1/11

Simplifying the right-hand side of the equation, we get:

1/T = (11 + 9)/(9 x 11)

1/T = 20/99

Multiplying both sides by 99, we get:

T = 99/20

Therefore, working together, Lisa and Felipe can complete the job in 4.95 hours, or approximately 4 hours and 57 minutes.

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The whisker plot with the data provided should includes a range that goes from 7 to 49, and a median of 23.

A whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data along with some important statistical information, such as the median, quartiles, and outliers. It is particularly useful for comparing the distribution of different data sets or for identifying potential outliers in a data set.

To create a whisker plot, follow these steps:

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Answer:

angle x is 160

Step-by-step explanation:

180 - 20

The calculated value of x in the right triangle is 8.7

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

The right triangle

The value of x in the right triangle can be calculated using the following sine ratio

sin(75) = x/9

Cross multiply the equation

So, we have

x = 9 * sin(75)

Evaluate the products

x = 8.7

Hence, the value of x in the right triangle is 8.7

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The probability that the average length of a randomly selected bundle of steel rods is greater than 168.58 cm is 0.7486

First, we need to calculate the z-score for the sample mean:

z = (x - μ) / (σ / √n)

z = (168.58 - 169) / (2.2 / √10)

z = -0.67

Next, we need to find the probability that a randomly selected bundle of steel rods will have a mean length greater than 168.58 cm. This is equivalent to finding the area under the standard normal distribution curve to the right of z = -0.67.

Using a standard normal distribution table or calculator, we find that the probability is 0.7486.

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Answer:

a) f(g(1)) = f(0) = 5

b) f(g(2)) = f(-3) = 8

c) g(f(2)) = g(3) = -8

d) g(f(3)) = g(2) = -3

e) g(g(1)) = g(0) = 2

f) f(f(3)) = f(2) = 3