A surveyor wants to find the height of a tower used to transmit cellular phone calls. he stands 120 ft away from the tower and measure the angle of evolution to be 40° . how tall is the Tower?

Elements of following sets are

A = {1}

B = {-1, 1}

C = Q ∩ [0, 1]

Sets

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set. A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

Given that

A = {n ∈ N : cos(nπ) greater than or equal to 0}

B = {cos(nπ) : n ∈ N}

C = {q + r : q, r ∈ Q ∩ [0, 1]}

Therefore elements of

A = {1}

as cos 2[tex]\pi[/tex], cos 4[tex]\pi[/tex], cos 6[tex]\pi[/tex], cos 8[tex]\pi[/tex] and so on is equal to 1.

B = {-1, 1}

as cos [tex]\pi[/tex] , cos 2[tex]\pi[/tex], cos 3[tex]\pi[/tex], cos 4[tex]\pi[/tex], cos 5[tex]\pi[/tex] and so on is equal to -1 and 1.

C = Q ∩ [0, 1]

as q and r both belongs to Q ∩ [0, 1] and their sum will be also equal to Q ∩ [0, 1].

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There are a specific quantity of $5 bills, and Brad has 6 boxes. In order to ensure that no two boxes contain the same amount of money, he wants to place his bills into some or all of the boxes. The least amount of money he needs to do $30 is within each box.

How do you tell whether an equation has an unlimited number of solutions?

Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 If you use a formula with infinite solutions to simplify the equation A set of two or more linear equations with two or more variables constitutes a system of linear equations.

If all the equations in the system are taken into account simultaneously, or if you use the approach where you obtain both sides equal, the system has an infinite solution.

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First, we need to find the sample space for two dice. Since each dice has 6 faces, the sample space is

which consist in 36 elements.

Part A.

In this case, we need to find the combinations where the sum of the 2 dice is even. The combinations are:

for instance, in the upper left corner, the sum is 1+1=2, which is an even number and similarly for the other cases.

As we can note, there are 18 possible combinations. Then, the probability is

Part B.

In this case, we need to find the possible combinations where the sum of the 2 dices is greater than 7. The possible combinations are:

Since there are 15 possible combinations, the probability is given by

Part C.

This case is the intersection of the two cases from above. The possible combinations are:

Since there are 9 possible combinations, the probability is

Part D.

We need to find the possible combinations where the sum is even or the sum is greater than 7. Then, this case is the union of case A and B. Then the possible combinations are:

Since there are 18+6=24 combinations, the probability is

The correct options for the intersecting line EF are-

For the given question;

Line EF intersects the lines AB and DC,

Where, AB = DC

Thus, from the given figure it is shown that;

Thus, the statement true about the given diagram are found.

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Ok, so

We want to find the equation of an ellipse centered at the origin with a horizontal major axis of 8 units and a minor axis of 6 units.

For this, let's remember the form of the equation of an ellipse:

Where the center of the ellipse is located at the point (h,k).

If the ellipse is centered at the origin, then, h=0 and k=0, so the form of our equation will be:

Now, we're given that our ellipse has a horizontal major axis of 8 units and a minor axis of 6 units. Since the major and minor axis are given by the parameters 2a and 2b, then, a=4 and b=3. the greater number will divide the x² term and a>b.

So, the equation of this ellipse is:

The graph of this ellipse will be something like:

T(x) = 0.06x + 4.5

We are meant to find 'x' when T(x) = $ 11.70

Substitute for T(x) = $ 11.70 in the given function

Thus,

11.70 = 0.06x + 4.5

11.70 -4.5 = 0.06x

7.2=0.06x

Hence, the original price of the hotel room if the tax on the room was $1170 is $120

a. The linear equation that models the price-sales relationship is: y = -500x + 5000

b. daily sales: $1,250.

To write the linear equation for a relationship, find the unit rate/slope (m) and the starting value/y-intercept, then substitute the values into y = mx + b.

a. Using two points from the problem, (6, 2000) and (8, 1000), find the unit rate (m):

Unit rate (m) = change in y / change in x = (2000 - 1000)/(6 - 8)

Unit rate (m) = 1000/-2

Unit rate (m) = -500

Find the y-intercept (b) by substituting m = -500 and (x, y) = (6, 2000) into y = mx + b:

2000 = -500(6) + b

2000 = -3000 + b

2000 + 3000 = -3000 + b + 3000

5000 = b

b = 5000

To write the linear equation, substitute m = -500 and b = 5000 into y = mx + b:

y = -500x + 5000

b. Substitute x = 7.5 into y = -500x + 5000:

y = -500(7.5) + 5000

y = -3750 + 5000

y = 1,250

The daily sales would be $1,250.

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The common ratio, r = (1/4)/(3/16)

= (1/4)(16/3)

= 4/3

OR

(1/3)/(1/4) = (1/3)(4/1)

= 4/3

The common ratio of a geometric sequence is the ratio of any two consecutive terms.

Suppose we are given a geometric sequence: a1, a2, a3, ...

The common ratio is given as:

a2/a1 = a3/a2 = ...

The graph on the right which is a graph of C is Option D. See the explanation below.

A graph is a graphic (such as a sequence of one or more points, lines, line segments, curves, or regions) that depicts the change of one variable in comparison to another.

What is the explanation for the above?

Note that the graph is calibrated at 25 per unit. Hence where x = 0, given the equation C(0) = 0.25x + 75

We have:

0.23 (0) + 75

Hence

C = 75

Tracing this back to the graph, by inference we see that the graph that depicts x as being on the x-axis with y on 75 is option D.

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Search for the numbers that divide all of the given set.

Notice that all three of them can be divided by two:

Therefore, 2 is the first common factor. Now, take the numbers 10, 6 and 12 and repeat the procedure. Notice that all of them are divisible by 2:

Therefore, 2 is the next common factor. Now, take the numbers 5, 3 and 6 and repeat the procedure. Notice that 3 is not divisible by 2 and 5 is not divisible by 3. Since there are no more numbers lower tan 3 that divide all of the numbers, there are no more common factors.

The common factors were 2 and 2. Multiply all the common factors to find the greatest common factor:

Therefore, 4 is the greatest common factor of 20,12 and 24.

ok

P1 = (-20, 0)

P2 = (0, 15)

slope = (15 - 0) / (0 + 20)

slope = 15/20

slope = 3/4

Equation of the line

y - 0 = 3/4(x + 20)

y = 3/4x + 3/4(20)

y = 3/4x + 15

Result y = 3/4x + 15

The problem is false

Step-by-step explanation:

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Answer:

38.26% prefer comedies

If 350 people are asked, 134 people will prefer comedies

Explanation:

First, we need to find the percentage of people that prefer comedy. Taking into account the table, 44 people prefer comedy from the 115 people in total.

So, the percentage of students that prefer comedy is calculated as

44/115 x 100% = 0.3826 x 100% = 38.26%

Then, if 350 are asked about their favorite movie genres, the number of people that will prefer comedies is equal to 350 people times the percentage calculated before, so

350 x 38.26% = 350 x 0.3826 = 133.9 = 134

Therefore, 134 people will prefer comedies.

The y-intercept of the total fee paid by Tyrell on his trip to Chicago when the cab travels 0 miles, the total fee will be $10.00.

The total fee paid by Tyrell is made up of a fixed cost and a variable cost. The fixed fee is the fee that is incurred regardless of the miles travelled. The variable fee is the fee that changes with the distance travelled.

The total fee paid can be modelled as a linear function. A linear function is a single variable that is raised to the power of one.

Total fee = fixed fee + variable fee

Variable fee = (change in total fee ) / (change in total miles)

(17.50 - 13) / (5 - 2)

4.50 / 3 = 1.50

Fixed fee = $13 - (1.50 x 2)

$13 - 3 = $10

The fixed fee, $10 is equivalent to the y-intercept.

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Answer:

its a- For every additional mile the cab travels, the total fee increases by $10.00.

Step-by-step explanation:

hope this helps

Given

-6 is less than x , 3 is greater than x

Find

Write the inequality

Explanation

-6 is less than x

this implies , -63 is greater than x

this implies , 3>x....................2

from 1 and 2 , we obtain

-6Final Answer

the inequality is - 6 < x < 3

The value of p is 8 by the law of exponents.

What is exponents?

The base b and the exponent, or power, n, are used in the mathematical operation known as exponentiation. Its symbol is Bn, and its pronunciation is "b to the n."

An exponent is the number of times a number has been multiplied by itself. For instance, the phrase 2 to the third, which is represented as 23, means 2 to the power 3, 2 x 2 x 2 = 8, not 23, and 2 x 3 = 6, respectively.

Remember that every number multiplied by one is equal to itself. Exponents are a technique of expressing extremely large numbers in terms of powers.

The number of times a number has been multiplied by itself is the exponent, so to speak.

Given that,

9^p/9^5 = 9^3

By laws of exponents and power,

Here, p - 5 = 3

         p = 3 + 5

         p = 8

The value of p is 8 by the law of exponents.

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Recalling the definition of the sine of an angle in a right triangle, we know that:

Isolate x from this equation:

Use a calculator to find the numerical value of x:

Therefore, to the nearest tenth:

The number of bacteria after the increase is 217

Bacteria in a culture when the scientist first observed = 155

Percentage: Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.

Increase in number of bacteria post observation = 40%

Bacteria after increase:

= 155 + 40% of 155

= 155 + 0.40*155

= 155 + 62

= 217

So, bacteria after the increase is 217

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Answer:

m<ABF = 34

m<FDC = 51

m<CFD = 92

Answer:

I am not sure about this.

We know that

• The ball is dropped from 1600 meters high.

• Each time it bounces 3/4 of its original height.

This situation creates a geometric sequence where the reason is 3/4. To find the first three terms of this sequence, we just have to multiply each term with 3/4. We know that the first term is 1600.

The second term is 1200 meters.

The third term is 900.

To find an equation, we have to use the geometric sequence formula-

Replacing the information we have the equation that represents the situation of this problem.

At last, the height after 4 bounces is

The height of the third bounce is 675 meters.

Therefore, the height of the ball after 4 bounces is 506.25 meters.

3) In general, a dilation is an enlargement of the sides of a shape, even if it is a 3D shape.

Furthermore, the volume of a prism is given by the formula

Then,

Therefore,

The answer to part 3) is 7290 m^3

4) Due to similar reasoning, in general, the area of a shape is given by

If we apply a dilation to that area,

Where k is the dilation factor.

Thus, in our case,

Therefore,

The answer to part 4) is 7558272 cm^3

5) From the answer to question 3)

Thus,

The answer to part 5) is 2.5

Formula for Profit Percentage = (Profit/C.P.) 100Where C.P. denotes the article's cost price, i.e. the price at which the article was originally purchased.

Jane bought a car for £24000

 she sold it for £26000

profit = 2000

profit percentage = 2000/26000 x100 = 7.7%

Here,

Jane bought a car for £24000

 she sold it for £26000

profit = 2000

profit percentage = 2000/26000 x100 = 7.69%

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Answer:  1i=1f

Step-by-step explanation:

The average velocity of the particle in the time interval between 3s and 5s is 20 ms⁻¹ and its instantaneous velocity at 4s is 20 ms⁻¹.

How to determine average velocity and instantaneous velocity?
Average velocity is defined as the body's overall displacement divided by its time of motion. While instantaneous velocity is defined as a body's speed at a certain instant in time, or its displacement at that instant. When the velocity is constant, average and instantaneous velocities will equalize at just one condition.
The definition of instantaneous velocity is the rate of change of position over a relatively brief time period (almost zero). Simply said, the speed of an object at that precise moment. The definition of instantaneous velocity is "The velocity of an item in motion at a certain point in time." The instantaneous velocity of an object may be equal to its standard velocity if it has uniform velocity.
Mathematically, average velocity = [s(t₂) - s(t₁)]/[t₂ - t₁]
Instantaneous velocity at time, t is = (ds/dt) at time = t

Given, the displacement for the particle is given by s = 3t² - 4t + 5
Time interval, t₁ = 5s and t₂ = 3s;
Using formula in literature, average velocity of the particle in the time interval between 3s and 5s is:
Average velocity = (s(5) - s(3))/(5 - 3) = (60 - 20)/2 = 20 ms⁻¹
Instantaneous velocity at t = 4 is ds/dt at that time-frame:
Now, v = ds/dt = 6t -4
Now, v(4) = 6(4) - 4 = 20 ms⁻¹
The average velocity of the particle in the time interval between 3s and 5s is 20 ms⁻¹ and its instantaneous velocity at 4s is 20 ms⁻¹.

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Answer:

-2 < 5 - 2x < 2

-7 < - 2x < -3

7/2 > x > 3/2

3.5 > x > 1.5

1.5 < x < 3.5

The percentage of the dealer markup from the original price will be; 1.24 %

Suppose the value of which a thing is expressed in percentage is "a Suppose the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part into 100 parts; then we multiply it by b so that we collect b items per 100 items(that is exactly what b percent means).

Given that the original price of a gold, watch was $500. And the dealer sells this item for $620.

Then the percentage of the dealer markup from the original price will be;

The change = amount/ original  x 100%

= 620/ 500  x 100%

= 1.24  x 100%

Therefore, The markup percentage was; 1.24 %.

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The symmetric point on parabola is x = -3

What is symmetric point in parabola ?

The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.

The vertex form of a parabola's (or a quadratic) equations is given by the following formula:

y = a(x - h)² + k   ,   where (h, k) is the vertex and the axis of symmetry is given by the line  x = h.

Where, vertex is given (h, k) = (-3, 1)

so the axis of symmetry is,

=> x = -3

Therefore, The symmetric point on parabola is x = -3

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The most appropriate choice of circle will be given by

x coordinate of the center decreases by 2

Fourth option is correct

What is circle?

Circle is a round two dimensional figure where all the points on the circle maintains a fixed distance from a point known as the center of the circle. The fixed distance of the point on the circle from the center of the circle is known as radius of the circle.

Equation of circle is (x - a)^2 + (y - b)^2 = r^2, where (a, b) is the center of the circle and r is the radius of the circle.

Here,

(x-2)^2 + (y - 3)^2 = 25

(x-2)^2 + (y - 3)^2 = 5^2

This is the equation of circle with center (2, 3) and radius 5 units

On shifting the circle 2 units to the left, the coordinate of center of circle changes to (0, 2)

That means x coordinate of the center decreases by 2

So fourth option is correct

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Solution