From his eye, which stands 1.55 meters above the ground, Tyler measures the angle of elevation to the top of a prominent skyscraper to be 57^{\circ} ∘ . If he is standing at a horizontal distance of 112 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other.

Let [tex]$V_1, V_2$[/tex] be two subspaces of V.

Suppose is a subspace of V.

Then if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then we must have [tex]$x_1 \in V_1 \cup V_2$[/tex] and [tex]$x_2 \in V_1 \cup V_2$[/tex] so that we must have [tex]x_1+x_2 \in V_1 \cup V_2$.[/tex]

But this by definition means [tex]$x_1+x_2 \in V_1$[/tex] or [tex]$x_1+x_2 \in V_2$[/tex].

Only the elements that are already present in the two subspaces are combined.

A subspace is formed by the union of two subspaces of a vector space, and each subspace contains the other.

Either way, by the existence of additive inverses and closure properties for subspaces we have:

[tex]\left(x_1+x_2\right)+\left(-x_1\right) \in V_1[/tex]

Or

[tex]\left(x_1+x_2\right)+\left(-x_2\right) \in V_2[/tex]

By associative/commutative properties we have:

[tex]x_2 \in V_1[/tex] or [tex]x_2 \in V_1[/tex]

Thus we have shown if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then [tex]$x_1 \in V_2$[/tex] or  [tex]$x_2 \in V_1$[/tex].

If [tex]$x_1 \in V_2$[/tex] for all [tex]$x_1 \in V_1$[/tex] then we have [tex]$V_1 \subseteq V_2$[/tex].

If [tex]$x_2 \in V_1$[/tex] for all [tex]x_2 \in V_2[/tex] then [tex]$V_2 \subseteq V_1$[/tex].

In either case, we see one subspace is a subset of the other.

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In decimal form, 549/999 is expressed as.549, which repeats.

Why do we use decimals?

One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

Divide 549 by 999 to get the decimal equivalent of 549/999.

The solution is.549549.

Over the repeated numerals is a bar.

In decimal form, 549/999 is expressed as.549, which repeats.

In decimal form, 549/999 is expressed as.549, which repeats.

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5.12 grams of 35% silver and 8.88 grams of 40% silver should be mixed to obtain 14 grams of 37%  amount of pure silver.

Let x be the number of grams of 35% silver and y be the number of grams of 40% silver.

We know that the total amount of silver is 14 grams, which is the sum of x and y. Therefore,

x + y = 14

We also know that the total amount of pure silver is 37%, which is the sum of 35% pure silver and 40% pure silver. Therefore,

0.35x + 0.40y = 0.37(x+y)

Substituting the first equation in the second equation,

0.35x + 0.40y = 0.37(14)

Solving for x and y,

x = 5.12 and y = 8.88

5.12 grams of 35% silver and 8.88 grams of 40% silver should be mixed to obtain 14 grams of 37% pure silver.

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To make b the subject of the equation, we have: b = 2a + c

Subject of formula is the process expressing a required alphabet in the terms of others in a given expression. It involves the applications of arithmetic operations so as to arrive at the required answer.

Thus, rearranging the equation and make b the subject in the question, we have;

a = 1/2 (b - c)

a = (b - c)/ 2

multiply through by 2

2a = b - c

express b in terms of a and c to have;

b = 2a + c

Therefore, after rearranging the equation, b as a subject is:

b = 2a + c

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To find out how long it will take the hose to fill the larger aquarium, we need to compare the volume of water in each aquarium. The volume of the first aquarium is 8 x 9 x 12 = 864 cubic inches, and the volume of the second aquarium is 22 x 27 x 29 = 14,938 cubic inches. The second aquarium is 14,938 / 864 = 17.2 times larger than the first aquarium.

The time it takes to fill the first aquarium is 5 minutes, so it will take 5 x 17.2 = 86 minutes to fill the second aquarium with the same hose.

It will take 86 minutes to fill the second aquarium.

The length of the x is 12 units .

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c² = a²+ b², where c is the hypotenuse and a,b are the other two sides.

Since the given triangle is a right anlgled triangle so we will use Pythagorean theorem:

using Pythagorean theorem :

H² = P² + B²

where H is hypotenuse , P is perpendicular and B is base of the triangle

H = 13

P = 12

B = x

=> 13² = 12² + x²

=> 169 = 144 + x²

=> x² = 169- 144

=> x² =25

=> x = 5

so the value of x = 5 units

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Complete question:

given the triangle below, find the length of side x.

Answer:

9.44

Step-by-step explanation:

7.19+2.25 =9.44

A dynamic array is an array with a big improvement: automatic resizing.

Explanation :

Initial Values:

n = 2

arr[0] = [ ]

arr[1] = [ ]

Query 0: Append 5 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]

last answer = 0

arr[0] = [5]

arr[1] = [ ]

Query 1: Append 7 to arr[( 1 ⊕ 0 ) % 2 )] = arr[1]

arr[0] = [5]

arr[1] = [7 ]

Query 2: Append 3 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]

last answer = 0

arr[0] = [5, 3]

arr[1] = [7 ]

Query 3: Assign the value at index 0 to arr [( 1 ⊕ 0 ) % 2 )] = arr[1] to

Last Answer, print Last Answer.

last answer = 7

arr[0] = [5, 3]

arr[1] = [7 ]

Query 4: Assign the value at index 1 to arr [( 1 ⊕ 7 ) % 2 )] = arr[0] to

Last Answer, print Last Answer.

last answer = 3

arr[0] = [5, 3]

arr[1] = [7 ]

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The right response is E. n = 100 at whatever degree of confidence.

We are aware that the sample size's square root and the margin of error are inversely proportional. The margin of error therefore decreases as n increases, but we also know that margin of error is proportional to the critical value, which increases as confidence level increases. However, for t and z, and for a relevant confidence level, the critical value lies between 1-3, so the sample size has the greatest impact.Because of this, choice E is the right one.

Therefore, The right response is E. n = 100 at whatever degree of confidence.

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The minimum equation initial height at which the car can be released and still stay in contact with the track at the top of the loop is 8.90 m.

hmin = 8.90 m

We can use the equation for centripetal force to solve for the minimum initial height hmin at which the car can be released and still stay in contact with the track at the top of the loop.

Fc = mv2/r

where Fc is the centripetal force, m is the mass of the car, v is the speed of the car, and r is the radius of the loop.

We know that the mass of the car is 250 kg, the speed of the car is 14 m/s, and the radius of the loop is 20 m.

We can rearrange the equation to solve for hmin:

Fc * r = m * v2

hmin = (m * v2) / Fc

hmin = (250 kg * (14 m/s)2) / (25000 N)

hmin = 8.90 m

The minimum initial height at which the car can be released and still stay in contact with the track at the top of the loop is 8.90 m.

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The probability result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners.

The podcast host is polling the next 100 listeners who send her fan emails in order to find out how they like the show. The results of the poll show that 80 out of 90 listeners polled said they liked it. This result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners. This means that the results of the poll may not be reflective of the opinion of all of the podcast host's listeners. Furthermore, the results may be influenced by the volunteer bias, as the respondents may have volunteered to take part in the poll because they already liked the show and wanted to show their support. Additionally, the results may be affected by non-response bias, as those who chose not to take part in the poll may have different opinions than those who did.

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To evaluate f(-x) when f(x) = x/(x^2 + 1), we need to substitute -x for x in the function.

So f(-x) = (-x)/((-x)^2 + 1)

Simplifying the denominator we get:

f(-x) = (-x)/(x^2 + 1)

The function f(-x) is equivalent to the function f(x) with the x-value negated. The value of the function f(-x) is the same as the value of the function f(x) but with the x-value negated.

It's important to note that we can also express this as f(-x) = -f(x)

So the value of f(-x) is x/(x^2 + 1) with the x-value negated.

The value of 3.8 in mixed number and improper fraction are 3 8 / 10 and 38 / 10.

Fractions are numbers that are written in 2 parts: a numerator and a denominator. The numerator is the top value while the denominator is the bottom value.

A mixed fraction is a combination of fractions and whole number.

Let's write the decimal 3.8 as a mixed fraction and improper fraction.

Hence, as a improper fraction,

3.8 = 38 / 10

In mixed fraction,

3.8 = 38 / 10 = 3 8 / 10

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The lines represent different routes taken by people walking in a city, where each block is 140m by 140m in size. The routes are determined by randomized variables, such as starting point, destination, and available pathways.

For a route that is 140m by 140m:

1. Calculate the diagonal length of the route: √2 x 140 = 196.4 m

2. Calculate the perimeter of the route: 4 x 140 = 560 m

3. Calculate the area of the route: 140 x 140 = 19600 m2

When calculating a route that is 140m by 140m, the first step is to calculate the diagonal length of the route. This is done by using the Pythagorean Theorem, which is written as √2 x 140. The result of this calculation is 196.4m. The second step is to calculate the perimeter of the route. This is done by multiplying the length of each side of the route by 4, which gives a total of 560m. The final step is to calculate the area of the route. This is done by multiplying the length and width of the route (140m x 140m), which gives a total of 19600m2. By using these calculations, one can easily measure the length, width, and area of a route that is 140m by 140m.

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Answer:

her mother is 45 years old

Step-by-step explanation:

daughter = n

mother = n + 22

n + n + 22 = 68

2n = 46

x = 23

n + 22 = 23 + 22 = 45

Answer: mothers age = 45 years old

Step-by-step explanation:

mothers age = 22 + x

daughters age= x

create the equation:

22 + x + x = 68

           2x = 68 - 22

           2x = 46

              x = 23 (daughters age)

in order to get the mother's age you should add 22 to daughter's age (23) as they say the mother is 22 years older than the daughter

therefore: 22 + 23 = 45 years old

$281.88 is the total amount sam paid for television.

percentage, a relative value indicating hundredth parts of any quantity.

Given that television was originally priced at $522, but Sam waited to buy it until the television was on sale for 50% off.

Let us find the 50% of 522

50/100×522

0.5×522

$261

8% sales tax on the sale price

8/100×261

0.08×261

$20.88

The total he paid is $261+$20.88 is $281.88.

Hence, $281.88 is the total amount sam paid for television.

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In the word problem 17 less than a number is at least -1 the number in reference is 16

In place of mathematical symbols, word problems are mathematical problems that are presented in everyday language. The fact that word problems must first be converted into mathematical equations and then those equations must be solved is a problem when dealing with word problems.

Word problems are mathematical problems that are presented in everyday language rather than using mathematical symbols. When dealing with word problems, it is a problem that word problems must first be transformed into mathematical equations, and then those equations must be solved.

Given

17 less than a number is at least -1, i.e.

x - 17 = -1

x = - 1 + 17

x = 16

Thus, in the word problem 17 less than a number is at least -1 the number in reference is 16.

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Answer:

if we multiply 11/4 to 4/11 it gives product as 1

Katie  after 1 hour of driving, he had 6.75 gallons of gas. Also, after 6 hours of driving, she had 1.5 gallons left.

We can write these values as coordinate points, on the form:

As a result, the sentence: "After an hour of driving, Katie had $6.75 worth of gas." can be seen as the following:

(1,6.75)

And: "After 6 hours of driving, there was only 1.5 gallons left" will have the point:

(6,1.5)$

Part B

With this in mind, we can find the slope of a linear function that passes through those two points. Then,

[tex]$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1.5-6.75}{6-1}=\frac{-5.25}{5}=-1.05$[/tex]

Thus, the slope is -1.05.

Part C

Now, we will write a linear equation that relates[tex]$\mathrm{g}$[/tex] and[tex]$\mathrm{h}$[/tex]. As we already have the slope, we can use it to find the y-intercept as:

[tex]$$y=m x+b$$[/tex]

[tex]$g=m h+b$[/tex]Writing it with the variable[tex]s $\mathrm{g}$[/tex]and [tex]$\mathrm{h}$[/tex].

[tex]$$1.5=(-1.05)(6)+b$$[/tex]

[tex]1.5+6.3=b \\[/tex]

7.8=b

This means that an equation for g in terms of h is given by:

[tex]$$g=-1.05 h+7.8$$[/tex]

Part D

For this portion, we will apply the linear equation we discovered for calculating how much gas she will still have after a three-hour drive. Thus, h will have a value of 3, and we replace on the function to get the following result:

[tex]g=-1.05(3)+7.8 \\[/tex]

=-3.15+7.8

=4.65

This means that Katie will have 4.65 gallons left after driving for 3 hours.

The complete question is,

Katie noticed that after 1 hour of driving, she had 6.75 gallons of gas. After 6 hours of driving, there was only 1.5 gallons left. (Hint: Leave your answers as decimals). A.) Represent the information as two coordinate pairs in the form of (h, g), where h is the number of hours driven and g is the gallon of gas left. B.) Calculate the slope between the two coordinates. C.) Assuming the relationship between h and g is linear, create an equation for g in terms of h. D.) How much gas would she have left after dving for 3 hours?

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The perimeter of a rectangle is the sum of all four sides of the rectangle is 32.4g + (-2k).

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The perimeter of a rectangle is the sum of all four sides of the rectangle is 32.4g + (-2k).

In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.The perimeter of a shape is defined as the total distance around the shape.

It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions. For example, imagine a triangle made of a wire of length L. The same wire can be reused to make a square, considering that all the sides are equal in length. Look at the image below showing the perimeter of a rectangular park.

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Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]

Step-by-step explanation:

[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]

The Python program above defines the class Cse20, which is used to generate a subject.

The class Cse20, which is used to generate a subject, is defined in the preceding Python program ( instance of the Cse20 object). The getter methods, such as get length, get title, and get length in days, return a topic's length, title, and length in days, respectively, but the __str__ and __add__ methods override the topic's string object and addition of length, respectively.

class Cse20_topic:

  def __init__(self, title, length):

      self.title = title

      self.length = length

  def get_length(self):

      return self.length

  def get_title(self):

      return self.title

  def get_length_in_days(self):

      return self.length*7

  def __str__(self):

      return f'Title: {self.title}, length: {self.length}'

  def __add__(self, other):

      return self.length+other.length

The complete question is:

Write the implementation of a class Cse20 Topic that represents a topic in the cse20 class. The class should implement the init function, getters, and override the str and add functions.

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The appropriate interval width for a random sample of 110 observations.

a) w=1

b) w=2

c) w=2

and d) w=4

The interval width is a value that is used to divide the usage distribution into usage rate intervals.

we shall determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following.

let's start.

we are aware the formula to calculate class width.

[tex]w=\frac{L.O-S.O}{N.C}[/tex],

where,

w for width, L.O is stand for largest observation and S.O for smallest observation and N.C is number of classes.

We solve it by options.

so first come on option (a)

given interval is 20 to 85.

[tex]w=\frac{85-20}{110} \\w=\frac{65}{110} \\w=0.59[/tex]

since we need to round upward the class width, w=1

for option (b)

[tex]w=\frac{190-30}{110} \\\\w=\frac{160}{110} =1.45[/tex]

since we need to round upward the class width, w=2

for option (c)

[tex]w=\frac{230-40}{110} \\\\w=\frac{190}{110}=1.73[/tex]

since we need to round upward the class width, w=2

for option (d)

[tex]w=\frac{360}{110} =3.27[/tex]

since we need to round upward the class width, w=4,

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the factors for 28 are 1,2,4,7,14 and 28

Answer:23.2

Step-by-step explanation:

10/2=5

10/5=2

116/5=23.2

Answer:

580 ft.

Step-by-step explanation:

The height of the cellphone tower can be found using the following proportion:

(shadow of cellphone tower) / (shadow of 10 foot post) = (height of cellphone tower) / (10 feet)

Solving for the height of the cellphone tower:

(116 feet) / (2 feet) = (height of cellphone tower) / (10 feet)

Which brings us to:

116 ÷ 2 = x ÷ 10

58 = x ÷ 10

580 = x

The cell phone tower is 580 ft.

The answer to the equation X + 5 3 2 a + 20 3 a + 2 3 3x + 2 12 2 3 4x-1 1/4-x is [tex]33 x-\frac{1}{4}$$[/tex] .

Simplify [tex]$34 x-1 \cdot \frac{1}{4}-x: \quad 33 x-\frac{1}{4}$[/tex]

[tex]$$34 x-1 \cdot \frac{1}{4}-x$$[/tex]

like phrases together

[tex]$$=34 x-x-1 \cdot \frac{1}{4}$$[/tex]

Add comparable elements: [tex]34 x-x=33 x$[/tex]

[tex]$$=33 x-1 \cdot \frac{1}{4}$$[/tex]

Multiply: [tex]$1 \cdot \frac{1}{4}=\frac{1}{4}$[/tex]

[tex]=33 x-\frac{1}{4}$$[/tex]

Both the addition rule and the multiplication/division rule are introduced to us in algebra 1 as the two rules for solving equations. According to the equation addition rule, an equation's solution set can be changed by adding the same amount to either side of an equation without doing so.

Identification, prioritisation, and selection of potential solutions are all steps in the process of problem solving, which also involves characterising the issue at hand, figuring out its root cause, and putting a plan of action into action. Algebraic Golden Rule: "Do unto one side of the equal sign as you will unto the other."

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The approximate number of defective parts the factory produced is 7200.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, During a quality control check, a factory found that 5% of the parts it produces are defective.

Let, 'x' be the number of defective parts.

Therefore, 'x' is 5% of 144000 which can be numerically expressed as,

(5/100)×144000.

= 5×1440.

= 7200.

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An identity is an equation that is always true for any value of the variable. To verify that an equation is an identity, we can substitute different values for the variable and see if the equation still holds true.

The given equation is (5sinx+5cosx)^2=25sin2x+25

We can start by expanding the left side of the equation:

(5sinx+5cosx)^2 = (5sinx)^2 + 2(5sinx)(5cosx) + (5cosx)^2

= 25sin^2x + 50sinxcosx + 25cos^2x

= 25(sin^2x + cos^2x) + 50sinxcosx

= 25 + 50sinxcosx

Now we can use the trigonometric identity sin^2x + cos^2x = 1 to simplify the equation further:

25 + 50sinxcosx = 25 + 50(sinxcosx) = 25 + 25sin2x

Now we can see that the left side of the original equation is equal to the right side of the equation, 25sin2x+25.

Therefore, the equation (5sinx+5cosx)^2 = 25sin2x+25 is an identity for all values of x.

The equation in the form y = a(x-r)(x-s) to represent the parabola is d. y = -4(x-2)(x-2).

What is the parabola?

The parabola is a smooth curve without any sharp points. It has a minimum value of a turning point called the vertex. As we can see the minimum value of this parabola is at zero, zero. That is this parabola exists only above the origin. The parabola is symmetrical about a central line called the axis of symmetry.

To represent the parabola shown in the form y = a(x-r)(x-s), we need to first identify the vertex and the axis of symmetry of the parabola.

The vertex of the parabola is (4,-4) and the axis of symmetry is x = 4.

Given that the vertex form of the parabola is y = a(x-h)² + k where (h,k) is the vertex.

Therefore, substituting the values we get:

y = a(x-4)² -4

Now, we need to find the value of a which will give us the same parabola.

If we look at the parabola, we can see that the y-coordinate of the vertex is -4 and the x-coordinate is 4.

So we substitute these values into the equation to get:

-4 = a(4-4)² -4

Solving this equation gives us a = -1

So the equation that represents the parabola is:

y = -1(x-4)² -4

which is the same as y = -1(x-4)(x-4)

thus the correct answer is d. y=-4(x-2)(x-2)

Hence, The equation in the form y = a(x-r)(x-s) to represent the parabola is d. y = -4(x-2)(x-2).

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Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are [tex]7 , -28 , 112,-448[/tex].

Geometric sequence is type of sequence in which ratio of two consecutive term is equal.

Let the geometric sequence be [tex]G_{1} , G_{2} , G_{3} , G_{4}[/tex] and common ratio be [tex]r[/tex]

According to the question,

                                            [tex]G_{1} = G_{2} + 35[/tex]              (eq 1)

                                         ⇒ [tex]G_{1} = rG_{1} +35[/tex]          ∵ [tex]G_{2}= rG_{1}[/tex]

                                         ⇒ [tex]G_{1} (1-r) = 35[/tex]

                                         ⇒ [tex]1-r = \frac{35}{G_{1} }[/tex]

                                         ⇒ [tex]r = 1 -\frac{35}{G_{1} }[/tex]                 (eq 2)

Also according to the question,

                                                [tex]G_{3} = G_{4} + 560[/tex]

                                             ⇒ [tex]G_{3} = rG_{3} + 560[/tex]

                                             ⇒ [tex]G_{3} (1-r) = 560[/tex]

                                             ⇒ [tex]r^{2} G_{1} (\frac{35}{G_{1} } ) = 560[/tex]

                                             ⇒ [tex]35r^{2} = 560[/tex]

                                             ⇒ [tex]r^{2} = 16[/tex]

                                              ⇒ [tex]r=[/tex] ±[tex]4[/tex]  

     ∴  [tex]r = -4[/tex] as we can see that value is decreasing at even term and at even term the power of common ration is odd.

Now putting [tex]r= -4[/tex] in eq 2 we get :

      [tex]G_{1} =7[/tex]

Hence , Geometric sequence will be [tex]7 , -28 , 112,-448[/tex].

Learn more about Geometric Sequence :

https://brainly.com/question/11266123

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