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Measuring a Pond: A surveyor is measuring the width of a pond. The transit is setup at point C and forms an angle of 37° from point A to point B. The distance from point C to point A is 54 feet and the distance from point C to point B is 72 feet. How wide is the pond from point A to point B?

m/ABC=86° (because of the cyclic quadrilaterals). Hence, Option (B) is correct.

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

m/ABC +  m/ADC  = 180°

m/ABC + 94° = 180°

m/ABC = 180° - 94°

m/ABC = 86°

Similarly, one can find m/DCB

m/DAB +  m/DCB  = 180°

99° + m/DCB = 180°

m/DCB = 180° - 99°

m/DCB = 81°

Hence, m/ABC = 86°

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The surface area of Grace's shipping box is 664 square inches.

We have,

The box can be divided into six rectangles, each of which represents the face of the box.

To find the surface area of the box, we need to find the area of each face and then add them all up.

The top and bottom of the box are both 10 inches by 14 inches, so the area of each of these faces is:

= 10 x 14

= 140 square inches

The sides of the box are both 14 inches by 8 inches, so the area of each of these faces is:

= 14 x 8

= 112 square inches

The front and back of the box are both 8 inches by 10 inches, so the area of each of these faces is:

8 x 10

= 80 square inches

To find the surface area of the whole box, we add up the areas of all six faces:

= 2(140) + 2(112) + 2(80)

= 280 + 224 + 160

= 664 square inches

Therefore,

The surface area of Grace's shipping box is 664 square inches.

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Answer:

  10.  x = 4

  11. UT = 44

Step-by-step explanation:

You want the value of x and the length of segment UT that bisects chord PR at point U into halves marked UP = (9x -3) and UR = (7x +5). The radius of circle T is 55 units.

Point U is the midpoint of chord PR, so ...

  UP = UR

  9x -3 = 7x +5

  2x = 8 . . . . . . . . . add 3-7x

  x = 4 . . . . . . . . divide by 2

Segments UP, UT and TP form a right triangle with one leg ...

  UP = 9(4) -3 = 33

and hypotenuse 55.

We observe that the ratio of these measures being 33/55 indicates triangle PUT is a 3-4-5 right triangle, with scale factor 11. That means UT is 4·11 = 44 units.

  UT = 44 units

__

Additional comment

Recognizing triangles made from Pythagorean triples, such as {3, 4,5}, {5, 12, 13}, {7, 24, 25}, or {8, 15, 17} can save a lot of work. If you don't recognize these, you can find the missing side length from ...

  TP² = UP² +UT²

  UT = √(TP² -UP²) = √(55² -33²) = √1936 = 44

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The surface area of the cuboid that has length = 4 yd, width = 2 yd and height = 3 yd is 44 square yards.

To find the surface area of a cuboid, we need to add up the area of all six faces. The formula for the surface area of a cuboid is:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the cuboid, respectively.

Substituting the given values, we get:

Surface Area = 2(4 x 2) + 2(4 x 3) + 2(2 x 3)

Surface Area = 8 + 24 + 12

Surface Area = 44

This means that there are 44 square yards of material needed to cover all six faces of the cuboid.

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Answer:

  (3) 60°

Step-by-step explanation:

You want the measure of the third angle (E) in triangle EFG, given that two of the angles have measures 75° (angle F) and 45° (angle G).

The angle sum theorem tells you the sum of angles in any triangle is 180°. This means ...

  E + F + G = 180

  E + 75 + 45 = 180

  E = 60 . . . . . . . . . . . . . subtract 120 from both sides and simplify

The measure of angle E is 60°.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$850\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 850\left(1+\frac{0.026}{4}\right)^{4\cdot 5}\implies A=850(1.0065)^{20} \implies A \approx 967.60[/tex]

The function y=x+3 has the greatest y intercept.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The given function is y=x, it has y intercept which is zero

The given function is y=-x, it has y intercept which is zero

Function is y=x+3, it has y intercept which is three

Function is y=2x, it has y intercept which is zero

Hence, the function y=x+3 has the greatest y intercept.

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The calculated value of the mode(s) of the data is (a) 1

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

1, 0, 2, 2, 3, 0, 1, 1, 4, and 5

By definition, the mode of a data is the data that has the highest frequency

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

The data element 1 has the highest frequency of 3

Other data elements have lesser frequencies

Hence, the mode(s) of the data is (a) 1

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The five number summary of the data set for the box plot would be :

First, order the numbers in ascending order:

2, 8, 9, 11, 14, 15, 17, 19, 20

The minimum is the smallest number which is 2. The maximum is the largest number which is 20.

The median is the number in the middle which is 19. The Q1 is the number in the middle of the first half of the numbers which is 9. The Q3 is the number in the middle of the second half which is 19.

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Answer:

min=2

1st quartile= 8.5

median=14

3rd quartile=18

max=20

Step-by-step explanation:

This is a linear equation problem with two variables. One way to solve it is by using the substitution method. Let x be the price of the tie and y be the price of the pair of pants. Then we have:

$$

\begin{aligned}

x + y &= 87.18 \\

x &= y - 2.12

\end{aligned}

$$

Substituting x into the first equation, we get:

$$

\begin{aligned}

(y - 2.12) + y &= 87.18 \\

2y - 2.12 &= 87.18 \\

2y &= 89.30 \\

y &= 44.65

\end{aligned}

$$

Therefore, the price of the pair of pants is $44.65. To find the price of the tie, we plug y into the second equation:

$$

\begin{aligned}

x &= y - 2.12 \\

x &= 44.65 - 2.12 \\

x &= 42.53

\end{aligned}

$$

Therefore, the price of the tie is $42.53.

Answer:

42.53

Step-by-step explanation:

write equation

tie + pants = 87.18

since ties cost 2.12 less than pants,

tie = pants -2.12

now substitute back into first equation

pants - 2.12 + pants = 87.18

solve for pants by adding 2.12 to the other side

divide by 2 since there are 2 pants on one side

find pants and then substitute value into the tie equation to find the price of the tie

The value of x, considering the Pythagorean Theorem, is given as follows:

x = 9.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The sides for the problem are given as follows:

15 and 8 (segment of 8 is the radius, which is the distance from the center to a point on the circumference of the circle).

Hence the hypotenuse is obtained as follows:

h² = 15² + 8²

h² = 289

h = 17.

Hence the value of x is obtained as follows:

x = 17 - 8

x = 9.

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Using similar side theorem, the side with equivalent proportion to the given side is RQ/SQ

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

In this problem, we can use this same theory to find the equivalent side of the given proportion.

OQ / PQ = RQ / SQ

The equivalent side is RQ/SQ

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The value of x will be 16.

Given ,

Parallelogram with two sides:

side 1 = 3x + 20

side 2 = 5x - 12

In parallelogram the opposite side are equal and parallel.

Thus,

side 1 and side 2 will be equal and parallel.

Equating both sides to get the value of x,

3x + 20 = 5x - 12

x = 16

Hence the value of x can be found out by property of parallelogram.

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The best estimate of the number of centimeters (cm) in 1 yard is; Yard ⇒ feet ⇒ inches ⇒ centimeters

If we have to determine the number of centimeters in 1 yard, the best way is;

Here we convert  yard to feet = 1 yard = 3 ft

Then, we convert ft to inches = 1 ft = 12 inches

                                                  3 ft = 3 × 12 = 36 inches

Now, we convert inches to centimeters = 1 inch = 2.54 cm

                                            36 inches = 36 × 2.54 = 91.44 cm

Therefore, the best path is Yard to feet to inches to centimeters

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The ratio of technicians to all the helpers at the Harper Middle School fall play is 9 : 24.

The ratio of technicians to all helpers can be calculated by dividing the number of technicians by the total number of helpers.

Number of technicians = 9

Total number of helpers = 15 ushers + 9 technicians = 24

The ratio of technicians to all helpers = 9 / 24

The ratio will then be:

The ratio of technicians to all helpers =  9 : 24

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Complete question:

There are 15 ushers and 9 technicians helping at the Harper Middle School fall play. What is the ratio of technicians to all helpers?

Answer:

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

There are 15 black pens out of total 80.

The probability of a black pen is:

The  value of function f (α + β) is determined as  (3√3  +  1)/3,  (2√2 - 3)/3.

The value of f (α + β) is calculated by applying the following formula as follows;

The given functions;

for α:  x²  +  y² = 4

y is given as -1, the value of x is calculated as;

x²  +  (-1)² = 4

x²  +  1 = 4

x² = 3

x = √3

α = (√3, - 1)

for β:  x²  +  y² = 1

x is given as ¹/₃, the value of y is calculated as;

(¹/₃)² + y² = 1

¹/₉ + y² = 1

y² = 1 - ¹/₉

y² = ⁸/₉

y = √ (8/9)

y = 2√2/3

β = (¹/₃, 2√2/3)

The  value of function f (α + β) is calculated as;

f(α + β) =  (√3, - 1) + (¹/₃, 2√2/3)

f(α + β) = (3√3  +  1)/3,  (2√2 - 3)/3

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The shape of the fence is a rhombus.

Option C is the correct answer.

We have,

To determine the shape of the fence with the given coordinates, we can analyze the properties of different quadrilaterals.

Square: All four sides are equal in length, and all angles are right angles.

Rectangle: Opposite sides are equal in length, and all angles are right angles.

Rhombus: All four sides are equal in length, but the angles are not necessarily right angles.

Trapezoid: At least one pair of opposite sides are parallel.

Let's analyze the given coordinates to determine the shape of the fence:

Side 1: Distance between (-16, 1) and (-6, 5) = √(((-6) - (-16))² + (5 - 1)²) = √(10² + 4²) = √(116)

Side 2: Distance between (-6, 5) and (4, 1) = √((4 - (-6))² + (1 - 5)²) = √(10² + (-4)²) = √(116)

Side 3: Distance between (4, 1) and (-6, -3) = √((-6 - 4)² + (-3 - 1)²) = √((-10)² + (-4)²) = √(116)

Side 4: Distance between (-6, -3) and (-16, 1) = √((-16 - (-6))² + (1 - (-3))²) = √((-10)² + 4²) = √(116)

We can see that all four sides of the fence have equal lengths, which means it is either a square, rectangle, or rhombus.

To further differentiate between these shapes, we need to consider the angles.

The angle between side 1 and side 2:

tan(angle) = (5 - 1)/(-6 - (-16)) = 4/10 = 0.4

angle ≈ 21.8°

The angle between side 2 and side 3:

tan(angle) = (1 - 5)/(4 - (-6)) = (-4)/10 = -0.4

angle ≈ -21.8°

The angle between side 3 and side 4:

tan(angle) = (-3 - 1)/(-6 - (-16)) = (-4)/10 = -0.4

angle ≈ -21.8°

The angle between side 4 and side 1:

tan(angle) = (1 - (-3))/(-16 - (-6)) = 4/10 = 0.4

angle ≈ 21.8°

All four angles are approximately 21.8° or -21.8°. This indicates that the fence is a rhombus since its sides are equal in length but its angles are not right angles.

Therefore,

The shape of the fence is a rhombus.

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Answer:

Step-by-step explanation:

76 RPMs

The value of inequality :  x≤-9

Given,

Inequality 4(x-3) + 4 ≤ 10+ 6x

Firstly,

The distributive property: 4x-12 + 4 ≤ 10+ 6x

Then,

Combine like terms: 4x -8 ≤ 10+ 6x

Then,

The addition property of inequality: 4x ≤ 18 + 6x

Then,

The subtraction property of inequality: -2x ≤ 18

Then,

The division property of inequality:

Divide both sides of inequality by 2,

So,

x≤-9

Hence after last step the value of x is less than or equal to -9 .

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Answer:

To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.

From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:

Number of stories: 5

Number of cards used: 40

To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).

Ratio = Number of stories / Number of cards used

Ratio = 5 / 40

Now, we can use this ratio to calculate the number of cards needed for 100 stories:

Number of cards for 100 stories = Ratio * Number of stories

Number of cards for 100 stories = (5 / 40) * 100

Calculating the result:

Number of cards for 100 stories = (0.125) * 100

Number of cards for 100 stories = 12.5

Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.

Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.

Answer:

Step-by-step explanation:

The interest rate for the first period is $287.22

To obtain the first period interest, we use simple interest formula;

Simple Interest = Principal * Rate * Time

Given:

Principal = $45,687.23

Annual interest rate = 7.555%

Interest period = Monthly

Convert the annual interest rate to a monthly interest rate.

Monthly interest = Annual interest/ 12 = 7.555/12 = 0.6295%

Interest = Principal * Monthly interest rate * Time

Since it's the first period, the time is 1 month:

Interest = $45,687.23 * 0.62958333% * 1

Interest = $45,687.23 * 0.0062958333

Interest ≈ $287.22

Therefore, the first period interest is $287.22.

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Answer: 127

Step-by-step explanation:

360 - 70 - 36 = 254

254/2 = 127

D = 127

The number of ways to draw the socks in each case is given as follows:

a) 90 ways.

b) 48 ways.

c) 42 ways.

The Fundamental Counting Theorem states that if there are m ways for one trial and n ways for another trial, then there are m x n ways in which the two trials can happen simultaneously.

This can be extended to more than two trials, where the number of ways in which all the trials can happen simultaneously is the product of the number of outcomes of each individual trial, according to the equation presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For item a, we have that there are no restrictions, hence there are 10 options for the first sock and 9 for the second, hence:

10 x 9 = 90.

For item b, we need one of each, hence the possible combinations are:

Hence:

6 x 4 + 4 x 6 = 48.

For item c, we can take 6 then five(two blue) or 4 then 3(two white), hence:

6 x 5 + 4 x 3 = 42.

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Answer:

15*8*10-7*8*11=584

Step-by-step explanation: