Nicole is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 18 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 41^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 44^{\circ} ∘ . If her eyes are 1.68 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest meter if necessary.

The probability that the sample mean will be within 5 points of the population mean is 0.95 or 95%

The Central Limit Theorem (CLT), a foundational idea in statistics, holds that, regardless of the underlying population distribution, the distribution of the sample means will be about normal given a big enough sample size. The CLT is crucial because it enables us to draw conclusions about a population based on a sample, even when the population is not normal.

According to the CLT, as the sample size grows, sample means will approach population means and their standard deviations will fall. The standard error, also known as the standard deviation of the sample means, is calculated by dividing the standard deviation of the population by the square root of the sample size.

According to the Question

The sample mean for a random sample of 100 individuals is most likely to be within 5 points of the population mean. The distribution and standard deviation of the population, however, would determine the precise likelihood. The standard error may be used to determine a confidence interval for the population mean if the population standard deviation is known. A 95% confidence interval is frequently used, which is equivalent to 1.96 standard deviations from the mean. In this instance, especially with a large sample size, there is a good likelihood that the sample mean will be within 5 points of the population mean.

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Answer:

No

Step-by-step explanation:

I got the postulates mixed up. These triangles have the same angle measurements but the lengths of the sides are different so the answer is no. These triangles do not follow the AAS, SSS, SAS, or ASA postulates.

Answer:

Step-by-step explanation:

Yes, it is congruent because SSA.

The dimensions of the new practice court is 45.5 feet by 29.5 feet.

The equations should be completed as 160 = 2W + 2L; W = L - 16

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

Since the width of the rectangular lot is 16 feet less than the length, we have:

W = L - 16

Substituting the given parameters into the perimeter formula, we have;

160 = 2L + 2W

160 = 2(L - 16) + 2L

160 = 2L - 32 + 2L

160 = 4L - 32

4L = 182

L = 45.5 feet.

For the width, we have:

W = L - 16

W = 45.5 - 16

W = 29.5 feet.

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The bottom of the ladder is 9 feet from the wall.

Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.

The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.

We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.

Therefore, the bottom of the ladder is 9 feet from the wall.

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Answer:

5 bags

Step-by-step explanation:

if there are 5 pounds of trail mix and each bag needs to contain 1 pound, that can be equally divided into 5 bags where each bag contains 1 pound each

Answer:

H (Height) = 3

Step-by-step explanation:

We have the formula A = 1/2(a+b)h

Let's identify all variables

A = 24

a = 9

b = 7

h = ?

Lets plug all that in:

24 = 1/2(9+7)h

9+7 = 16

24 = 1/2(16)h

Half of 16 is 8 so to simplify the rest...

24 = 8h

To get h alone we will divide both sides of the equation by 8

24/8 = h

24/8 = 3

Making H = 3

a.) The number of pounds of empty cans needed by the class is 200 pounds.

b.) The number of empty cans needed by the class to collect are 5486 cans.

The books will cost a total amount of $ 50.

If $ 0.25 per pound is the current price for aluminium at the recycling centre, the number of pounds the class will have to collect is found by dividing the total amount needed by cost per pound is,

⇒ 50/0.25 = 200

b.) Six empty cans weigh 3.5 ounces.

1 pound = 16 ounces

200 pounds = 200 × 16 = 3200 number of ounces

3200/3.5 = 914.29

914.29 × 6 = 5485.7 cans ≈ 5486 cans

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The proportionality is 0.45, then the equation is C = 0.45 n. The number of peppers you buy for $20 will be 44.44. Then the table is completed below.

What are proportion and ratio?

A collection of consecutively ordered numbers a and b expressed as a/b, where b is never equal to zero, is referred to as a ratio. A statement is considered proportionate when there is equality between two items.

Let n be the number of peppers and C be the price. The proportionality is then provided as,

C ∝ kn

With n = 5 and a cost of C = 2.25, we obtain

2.25 = k (5) (5)

k = 2.25 / 5

k = 0.45

The equation is then presented as,

C = 0.45 n

You will be told how many peppers you get for your $20 purchase as,

20 = 0.45 n

n = 44.44

Then the table is completed below.

Number of peppers             Cost

             1                              $0.45

            2                              $0.90

            3                              $1.35

            4                              $1.80

            5                              $2.25

           10                              $4.50

           15                              $6.75

          20                              $9

         100                              $45

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Answer:

A) ΔDFG

and

C) ΔFEG

Answer: FEG

Step-by-step explanation:

It can't be the others, so process of elimination.

Answer: 640

Step-by-step explanation:

6.4 * 100 = 640

The resultant speed is 52.48 and the direction of the airplane is west to north.

The resultant velocity of an object is defined as the sum of its individual vector velocities, and the sum of the vector forces on an object is equal to the scalar product of the object's mass and its acceleration vector.

Given

The plane is initially flying with a velocity of magnitude v=500mph.

at an angle of  30° North toward the west

The velocity of the plane airplane can be written as:

[tex]v_a=-500(sin 30i+cos30j)[/tex]

Now the wind is encountered with the speed of v=70mph at an angle of N 45°E

[tex]v_w=70(cos45i+sin45j)\\[/tex]

resultant velocity:

[tex]v_R=v_a=v_w\\\\[/tex]

[tex]v_R=-500(sin 30i+cos30j)+70(cos45i+sin45j)\\\\v_R=i(-250+49.49)+j(433.01+49.49)\\\\v_R=i(-200.51)+j(482.5)\\\\tan\alpha =\frac{482.5}{-200.51} \\\\tan\alpha =2.406\\\\\alpha =tan^-^1(2.406)[/tex]

α=52.48° west of North.

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Answer:

yeah you can

Step-by-step explanation:

what do you need help with lol

The value of the sides, NM and OL are 16 and 8 respectively

To determine the value of x, we have the note the properties of a parallelogram.

The properties of a parallelogram includes;

Then, we have;

NM = OL

substitute the values

x + 12 = 2x + 8

Now, collect like terms

x = 4

NM = 4 + 12 = 16

OL = 16

Hence, the value are 4 and 16

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The value of your declining channel in 2016, given the depreciation rate, would be $ 40. 99

The value of the channel can be found by the formula :

= Original value of the channel x ( 1 - rate of depreciation ) ^ number of years

Rate of depreciation = 13 %

Number of years :

= 2016 - 2002

= 14 years

The value of the channel is therefore:

= 288 x ( 1 - 13 %) ¹⁴

= $ 40. 99

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If the individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms , then the sample mean resistance associated with the ten resistors is 99.16 ohms .

The resistors of randomly selected 100 ohms resistors are recorded as :

⇒ 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98, and 102.6  ;

we have to fins the sample mean resistance associated  with the 10 resistors .

the number of resistors(n) = 10 ;

the sum of 10 resistors is ⇒ 79.9 + 85.9 + 87.0 + 96.7 + 107.4 + 100.8 + 115.4 + 117.9 + 98 + 102.6

⇒ 991.6/10 = 99.16 .

Therefore , the sample mean resistance is 99.16 ohms .

The given question is incomplete , the complete question is

The resistances of then randomly selected 100-ohm resistors have been recorded: 79.9, 85.9, 87.0, 96.7, 107.4, 100.8, 115.4, 117.9, 98, and 102.6 ohms. The individual resistances are known to follow a normal distribution with a mean of 100 ohms and a standard deviation of 10 ohms.

Calculate the sample mean resistance associated with the ten resistors .

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Answer:

y=4x+2

Step-by-step explanation:

slope (12-0)/(5-2)=4

y=4x+b

plug in (2,0)

b=2

y=4x+2

ALGOL 68 is a language that prioritized orthogonality as a key design requirement. ALGOL 68's primary objectives and design tenets are as follows:

1. a thorough and clear design;

2. an orthogonal design

3. Safety

4. Efficiency: Mode-independent parsing, independent compilation, loop optimization, representations in small and big character sets, static mode verification, etc.

As a programming language, Algol 68 offers certain unique and practical concepts that were ground-breaking at the time and have appeared, in varying degrees, in various languages afterwards.

Orthogonal design, which means that core concepts stated in the language can be used anyplace that usage can be said to "make sense." Completeness and clarity of explanation (as facilitated by the adoption of two-level grammar, which sparked many critical reactions).

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Answer:

The dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:

Length = 10 kilometers

Width = 12 kilometers

Explanation: To find the dimensions of a rectangular tract of land when its perimeter and area are known, you can use the formulas:

Perimeter = 2(length + width)

Area = length * width

We know that:

Perimeter = 44 kilometers

Area = 120 square kilometers

So, we can use these values to set up the following equation:

44 = 2(length + width)

And we can solve for length and width.

44 = 2(length + width)

22 = length + width

And now we know that the sum of the length and width of the rectangular tract is 22 kilometers.

Now we have to use the area formula:

Area = length * width

120 = length * width

We can use the value we have for the sum of the length and width to find either the length or the width of the rectangular tract.

For example, we can use the equation:

length = 22 - width

And substitute it into the area equation:

120 = (22 - width) * width

And then we can solve for width:

120 = 22 * width - width^2

width^2 - 22 * width + 120 = 0

We can use the quadratic formula to solve for width.

width = (22 +/- sqrt(22^2 - 4 * 1 * 120))/ 2

So,

width = (22 +/- sqrt(484 - 480))/ 2

width = (22 +/- sqrt(4))/ 2

width = (22 +/- 2)/ 2

width = (24)/ 2

width = 12

So, the width of the rectangular tract is 12 kilometers.

And we can use the equation:

length = 22 - width

to find the length

length = 22 - 12 = 10

So, the dimensions of the rectangular tract of land with a perimeter of 44 kilometers and an area of 120 square kilometers are:

Length = 10 kilometers

Width = 12 kilometers

The perimeter of the given composite figure is given as follows:

105 ft.

The perimeter of a polygon is obtained as the sum of all the outer side lengths of the polygon.

The side lengths for the polygon in this problem are given as follows:

Hence the perimeter for the polygon is calculated as follows:

45 + 40 + 15 + 5 = 105 ft.

(sum of all the outer side lengths).

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The balance of Jamie's checking account in the month of May is given as follows:

$20.

The balance in the month of May is obtained applying the proportions in the context of this problem.

He swiped his card for $69 in the restaurant which caused this account to be overdrawn by nine, hence the June balance is of:

-9 + 69 = $60.

The balance in Jamie's checking account in the month of June was thrice the amount of what it was in the month of May, hence the May's balance is given as follows:

3x = 60

x = $20.

The problem asks for the balance of the checking account in the month of May.

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Elle can buy maximum 0.6 liters of goat milk and 1.2 liters of cow's milk.

What System of linear inequalities?

A system of linear inequalities is similar to a system of linear equations, except that it is made up of inequalities rather than equations. To represent scenarios with various restrictions, systems of linear inequalities are utilized.

Let x be the number of liters of goat milk and y be the number of liters of cow's milk that Elle wants to buy. We know that:

x + y ≤ 80 (because Elle wants to spend at most Php80)

130x + 65y ≤ 80 (because each liter of goat milk costs Php130 and each liter of cow's milk costs Php65)

This is a system of linear inequalities, and the solution set is the set of all possible combinations of x and y that satisfy both inequalities.

The inequality 130x + 65y ≤ 80 represents a line in the plane, and the inequality x + y ≤ 80 represents a region that is "bounded" by this line.

The solution set for the inequalities are x <= 0.6 and y <= 1.2.

So, Elle can buy maximum 0.6 liters of goat milk and 1.2 liters of cow's milk.

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[tex]27\cdot 9^{3x}\implies 3^3\cdot (3^2)^{3x}\implies 3^3\cdot 3^{6x}\implies {\Large \begin{array}{llll} 3^{3+6x} \end{array}}[/tex]

The figure drawn by Mike is rectangle according to the angles and dimensions.

As the statement mentioned, the sides are at 90° degree or perpendicular to each other. It is seen in only two figures, which are square and rectangle. The square has all the sides equal whole rectangle has opposite sides equal.

As the length and width is different in the figure, the opposite sides signifying length and width will be equal. Therefore, opposite sides will be equal in the figure and hence it will be rectangle.

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The outside temperature t when Arianna ate breakfast was 55°F.

An equation is a mathematical statement showing that two expressions are equal. It is written with an equal sign (=) between two expressions, with one expression on the left side of the equal sign, and the other expression on the right side.

According to the given statements-  

Let the outside temperature at the time of breakfast be t°F.

The temperature dropped by 20°F by the time of dinner.

So the temperature at the time of breakfast = t - 20

Also, when she ate dinner the temperature was 35°F

So the equation for outside temperature t when Arianna ate breakfast will be -

t - 20 = 35

Simplifying we get,

t = 35 + 20

t = 55°F

Hence, the outside temperature t when Arianna ate breakfast was 55°F.

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(a) The speed in feet per second is 110 feet per second.

(b) The speed in kilometers per hour is 120.75 kilometers per hour

The speed limit on certain interstate highways, s = 75 miles per hour

a) We have to find the speed in feet per second.

1 mile = 5280 feet

75 miles = 75 x 5280

75 miles = 396,000 feet

s = 396,000 feet/hour

s = 39600/3600 feet/second

s = 110 feet per second

b) We have to find the speed in kilometers per hour.

1 mile = 1.61 km

75 miles = 75 x 1.61

75 miles = 120.75 km

s = 120.75 kilometers per hour

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Answer:

In Explanation

Step-by-step explanation:

The constant of proportionality is a value that relates two variables that have a proportionate relationship. It is often represented by the letter "k".

For example, if two variables x and y are directly proportional, their relationship can be represented by an equation of the form y = kx, where k is the constant of proportionality. In this equation, the value of k represents the ratio of y to x and it is constant, meaning that it does not change as the values of x or y change.

In physics, the constant of proportionality also appears in many mathematical models of natural phenomena, such as Hooke's law (F = km) which relates the force applied on an object (F) to its displacement (x) with a spring constant (k), and Ohm's law (V = IR) which relates the voltage (V) across a resistor to the current (I) flowing through it with a resistance constant (R).

The constant of proportionality can have different units of measure depending on the context and is used to make quantitative predictions about the relationship between the variables. In some cases, it can be used to determine the behaviour of a system or physical process.

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22084.78 gallons is the volume of your pool.

Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. The base's surface area, B, is equal to its length x width.

Dimensions of the pool = 4.93 m x 9.69 m x 1.75 m

Volume = 4.93 x 9.69 x 1.75

             = 83.6 cubic meter

1 cubic meter = 264.172 gallons

83.6 cubic meter = 83.6 x 264.172

                            = 22084.78 gallons

Hence, 22084.78 gallons is the volume of your pool.

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