# 4
You measure your distance from a tree and the angle of elevation from the ground to the top of the tree. The triangle shown represents the
situation. Find the height of the tree. Round to the nearest hundredth

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

To know more about Binomial theorem :

brainly.com/question/30095070

#SPJ11

In math, floor plans show a 2D view of a building or room from above in topics like finance and measurements. Used in real estate, design, and construction. A floor plan provides a detailed layout of the space. It visualizes spatial relationships in a space.

Floor plans are drawn to scale to accurately represent the proportions of physical space. Measurements can be taken from the floor plan for finance, measurement, and planning.

Floors plans are crucial in finance to calculate costs like flooring, painting, or carpeting by determining the area of a building or a room. They can assist in estimating square footage for rental/leasing pricing. Floor plans are helpful for measuring walls and areas within a space.

This data is valuable for financial calculations, such as material estimation for building or renovation projects. A floor plan visually represents a physical space for calculations, measurements, and financial estimations related to buildings or rooms.

Learn more about   floor plan from

https://brainly.com/question/32442663

#SPJ1

See full question below

Explain the meaning of term floor plan in this context for maths lit topic Finance,measurement and plans

The dimension of the wood block in centimeter is  40cm by 20cm by 70cm , the volume is  56000 cubic centimeters .

In the question ,

it is given that ,

the dimension of the block of wood is 0.4m by 0.2m by 0.7m ,

that means

the length of the wood block = 0.4 m

we know that 1 m = 100 cm , So 0.4 m = 40 cm

0.2 m = 20 cm

and

0.7 m = 70 cm

So , the length of the wood block = 40 cm

the width of the wood block = 20 cm

the height of the wood block = 70 cm

The Volume of the wooden block = length × width × height

Substituting the values , we get

Volume = 40 × 20 × 70

= 56000 cm³

Therefore , The dimension of the wood block in centimeter is  40cm by 20cm by 70cm , the volume is  56000 cubic centimeters .

Learn more about Volume here

https://brainly.com/question/191151

#SPJ4

Answer:

The answer is 240

Step-by-step explanation:

So since your trying to find the area of 12ft, 4ft, and 5ft you have to multiply them all. So 12x4= 48x5= 240.

Hope this helps :)

Answer: surface area = 240 ft^3

Step-by-step explanation:

Assuming you are talking about the surface area of a rectangular prism, the surface area equation for rectangular prisms is SA = l x w x h (surface area = length x width x height). You multiply 12 by 4 by 5 to get your answer.

The measure of <x in the diagram shown given the complementary angles is 23°.

Complementary angles are angles whose sum add up to 90°

So,

<67° + <x = 90°

subtract 67° from both sides

x = 90° - 67°

x = 23°

In conclusion, <x is a complementary angle with a value of 23°.

Read more on complimentary angles:

https://brainly.com/question/16281260

#SPJ1

Answer:

use trial and error

Step-by-step explanation:

lma0

The area of the given figure is 12 square meters

The given figure is a parallelogram

Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four

The height of the parallelogram = 2 meters

The base length of the parallelogram = 6 meters

The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram

Substitute the values in the equation

The area of the parallelogram = 2 × 6

Multiply the numbers

= 12 square meters

Therefore, the area is 12 square meters

Learn more about parallelogram here

brainly.com/question/29147156

#SPJ4

I have solved the question in general , as the given question is incomplete

The complete question is :

What is the area of the figure ?

The cοοrdinates οf the fοurth vertex are (4,-1).

Tο find the fοurth vertex οf the parallelοgram, we need tο use the fact that οppοsite sides οf a parallelοgram are parallel and have the same length. We can use the given three vertices tο determine the vectοr representing οne οf the sides οf the parallelοgram. Then, we can extend that vectοr tο find the fοurth vertex.

Let's take the vectοrs representing twο adjacent sides οf the parallelοgram:

v1 = (-4,1) - (-2,-5) = (-2,6)

v2 = (6,-7) - (-4,1) = (10,-8)

Since οppοsite sides οf a parallelοgram are parallel, v1 and v2 must be parallel. This means that we can find the fοurth vertex by adding v1 tο the third vertex, (6,-7):

v4 = (6,-7) + v1 = (6,-7) + (-2,6) = (4,-1)

Therefοre, the cοοrdinates οf the fοurth vertex are (4,-1).

Learn more about parallelοgram

https://brainly.com/question/27802021

#SPJ1

Complete question:

Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.

Answer:

his answer is true.

Step-by-step explanation:

The probability that a person treated for an energy drink-related emergency was under 40 given that the person was at least 18 years old is approximately 0.550 or 55.0%.

In general, probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in a sample space. Event probability P(E) = (number of favourable outcomes) (Sample space).

We must use conditional probability to determine the likelihood that a person treated for an energy drink-related emergency was under 40, given that the person was at least 18 years old.

We can use the following formula:

P(A | B) = P(A and B) / P(A and B) (B)

where A is the event "the person is under 40" and B is the event "the person is over 18".

According to the table, 11,146 people under the age of 40 and over the age of 18 were treated for energy drink-related emergencies. The total number of people over the age of 18 who have been treated for energy drink-related emergencies is 20,244.

So,

P(A, B) = 11,146

P(B) = 20,244

Therefore,

P(A and B) / P(B) = 11,146 / 20,244 0.550

So the probability that a person treated for an energy drink-related emergency was under 40 is approximately 0.550 or 55.0% if the person was at least 18 years old.

To know more about probability visit:

https://brainly.com/question/30719832

#SPJ1

The average score of all students, calculated by taking a weighted average based on the number of students in each group, is 38. The overall performance is slightly below the group averages.

The average score of students in the first, second, and third groups are 39, 32, and 43, respectively. There are 24 students in the first group, 26 students in the second group, and 27 students in the third group.

To find the average score of all students, we need to take a weighted average of the scores in each group, with the number of students in each group as the weights.

Here's how to do it: First, we calculate the total number of students:24 + 26 + 27 = 77. Then, we calculate the total score across all students: 39*24 + 32*26 + 43*27 = 936 + 832 + 1161 = 2929

Finally, we divide the total score by the total number of students to get the average score:2929/77 = 38. The average score of all students is 38.

This means that the overall performance of all the students is slightly below the average of the scores in each group.

For more questions on average score

https://brainly.com/question/13832161

#SPJ8

Answer:

0.9

Step-by-step explanation:

\(\frac{-3}{5} * -1.5\\\frac{-3}{5} * \frac{-15}{10} \\ =\frac{-3}{10} *-3\\ =\frac{9}{10} =0.9\)

The percentage increase per year in the winner's check over the given period. If the winner's prize increases at the same rate, it will be $1,454,735,139.69 in 2040.

To calculate the percentage increase per year in the winner's check over the period from 1895 to 2007, we can use the following formula:

Percentage Increase = (Final Value - Initial Value) / Initial Value * 100

a. Calculating the percentage increase:

Initial Value = $140

Final Value = $1,171,000

Percentage Increase = (1,171,000 - 140) / 140 * 100 ≈ 835,714.29%

b. To estimate the winner's prize in 2040, we can assume the same annual percentage increase will continue. We need to calculate the number of years from 2007 to 2040 and apply the percentage increase to the 2007 prize.

Number of years = 2040 - 2007 = 33 years

Estimated prize in 2040 = 1,171,000 * (1 + (Percentage Increase / 100))^33

Estimated prize in 2040 = 1,171,000 * (1 + (835,714.29 / 100))^33 ≈ $1,454,735,139.69

Therefore, if the winner's prize increases at the same rate, it is estimated to be approximately $1,454,735,139.69 in 2040.

Learn more about percentage here: https://brainly.com/question/92258

#SPJ11

Answer:

1.   5 in.

2.   12 in.

3.   3.5 in.

4.   30 ft

5.   4 m

6.   32 mm

7.   53.41 m

8.   18.85 ft

9.   87.96 in

10.  56.56 mm

11.   20.57 in

12.  25.71 yd

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

area of shaded region = area of whole figure - area of non shaded region

area of whole figure: The whole figure is a rectangle

The area of a rectangle can simply be calculated by multiplying the width by the length

The given width is 10ft and the given length is 8ft

Hence area of whole figure = 10 * 8 = 80ft²

Area of non shaded region: the non shaded region also creates a rectangle

Like stated previously the area of a rectangle can simply be calculated by multiplying the width by the length

The given width is 5ft and the given length is 8ft

Hence, area of non shaded region = 5 * 8 = 40ft²

Finally we can find the area of the shaded region.

We can easily do this my subtracting the area of the nonshaded region from the area of the whole figure

If we have identified that the area of the whole figure is 80 and the area of the non shaded region is 40

Then, area of shaded region = 80 - 40 = 40ft²

Answer:

It is C

Step-by-step explanation:

Graph the inequality by finding the boundary line, then shading the appropriate area.

y > 3 5 x − 1.5

3. The amount that should be returned to Meenaski for buying 12 books worth R250.75 each and giving the shopkeeper R4,000, using mathematical operations, is R991.

4. The number of crayon sets that can be bought for R2,750 if one set costs R25, using division operation, is 110.

5. Manu will pay R1,700, exchanging his old bike for a new bike.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

These mathematical operations are performed to solve algebraic problems using the relevant mathematical operands and rules.

The number of books bought = 12

The unit cost of each book = R250.75

The total cost of the 12 books = R3,009 (R250.75 x 12)

The amount advanced to the cashier = R4,000

The balance to be returned = R991 (R4,000 - R3,009)

The cost of a set of crayon = R25

The amount of money for the purchase = R2,750

The number of crayon sets that can be bought with R2,750 = 110 (R2,750/R25).

The price of the new bicycle = R2,500

The value of the old bike for exchange = R800

The amount to be paid = R1,700 (R2,500 - R800)

Learn more about mathematical operations at https://brainly.com/question/20628271.

#SPJ1

The price of the new bicycle is R2,500. The bike on exchange is worth R800.  How much does he pay for his new bike?

Answer:

i think its d :both a and b

Step-by-step explanation:

i think

Answer:

\(\displaystyle alternate\:interiour\:angles\:theorem\)

Step-by-step explanation:

Alternate means they are on OPPOSITE sides diagonal from each other, and interiour is self-explanatory, so you can see what the answer is from here.

I am joyous to assist you at any time.

The current drawn by 9 identical motors will be 124.2 amps current

Current is the flow of electrical charge carriers like electrons. Current flows from negative to positive points. The SI unit for measuring electric current is the ampere (A). One ampere of current is defined as one coulomb of electrical charge moving past a unique point in a second.

since , one motor of 2hp draws = 13.8 amps current

hence , 9 identical motor will pull = 13.8 * 9 (each will pull same amount of current )

                                                         = 124.2 amps current

The current drawn by 9 identical motors will be 124.2 amps current

To learn more about current

https://brainly.com/question/23323183?referrer=searchResults

#SPJ1

24.5 kg

first you have to divide 31.5 by 9, which is 3.5

then you multiply 7 by 3.5 to get 24.5

The proportionality constant between half-life and inverse rate constant affects the slope of a plot of ln(t1/2) vs. 1/t. Half-life is the amount of time it takes for half of the initial quantity of a substance to decay or react to form a product.

The rate constant is the proportionality constant in the rate law equation that relates the rate of the reaction to the concentration of reactants raised to some power. The rate constant is also used in the equation for the half-life of a reaction.The half-life of a reaction is proportional to the inverse of the rate constant. Mathematically, it can be represented a :t1/2 ∝ 1/kTherefore, as the rate constant increases, the half-life of the reaction decreases and vice versa. In other words, there is an inverse relationship between the half-life of a reaction and the rate constant.

This relationship can be observed in a plot of ln(t1/2) vs. 1/t. The slope of this plot is equal to the proportionality constant between half-life and inverse rate constant, which is given by the expression:k = ln(2)/t1/2Therefore, the slope of the plot is directly proportional to ln(2), which is a constant. This means that the proportionality constant between half-life and inverse rate constant does affect the slope of a plot of ln(t1/2) vs. 1/t.

To know more about proportionality visit:

https://brainly.com/question/8598338

#SPJ11

The statement that accurately describes the form of the sampling distribution is:The inspecting dissemination is regularly circulated with a mean of 37 and standard deviation 1.41.

According to the central limit theorem, regardless of how the population distribution is shaped, the sampling distribution of the sample mean will be approximately normally distributed for a sufficiently large sample size.

For this situation, irregular examples of 32 are drawn from Meredith's patient populace, which fulfills the state of a sufficiently huge example size. The central limit theorem can be used to determine the sampling distribution's mean and standard error.

In this instance, the population mean, which is 37, is equal to the mean of the sampling distribution.

The population standard deviation divided by the square root of the sample size is the sampling distribution's standard error. For this situation, the standard mistake is 8 partitioned by the square foundation of 32, which is around 1.41.

Therefore, the statement that accurately describes the form of the sampling distribution is:

The inspecting dissemination is regularly circulated with a mean of 37 and standard deviation 1.41.

To know more about central limit theorem refer to

https://brainly.com/question/898534

#SPJ11

The equivalent of the given expression ⁴√7⁵ × √7³ in exponential form is  7^11/4.

Given the data in the equation;

⁴√7⁵ × √7³

Since fourth and square roots can be written as power 1/4 and 1/2 respectively.

7^(5 × 1/4) × 7^(3 × 1/2 )

7^(5/4) × 7^(3/2 )

From exponent rule, n^a × n^b = b^(a + b )

7^(5/4 + 3/2 )

7^11/4

The equivalent of the given expression ⁴√7⁵ × √7³ in exponential form is  7^11/4.

Hence, option D) 7^11/4 is the correct answer.

Learn more about exponent rule here: brainly.com/question/219134

#SPJ1

1 ) P be Pepperoni, Q be Quail, R be Ricotta cheese, S be Sausage.

To translate Geoff's order using Discrete Math,

2 ) Geoff is a truth-teller. Based on his last statement, where ricotta (R) is implied from pepperoni (P) or quail (Q) , we would have no way of knowing if R is true/false if (P or Q) was false- so, R must be true if (P or Q) is false because of the whole “innocent until proven guilty” thing. therefore, since a lie in P or Q would lead to truth, Geoff must be a truth-teller because he can’t tell all lies.

Using this information, that Geoff always tells the truth.

For the third statement, if Geoff is lying then the truth is "I must have pepperoni or quail and I cannot have ricotta cheese."

~[(P ∨ Q) → R] = [(P v Q) ∧ ~R)]

Or in more general terms, ~(a → b) = (a ∧ ~b)

Which, gives us (a → b) = (~a ∨ b)

Anyhow, even if Geoff tells all lies, there is a valid statement that can be made: Pepperoni and sausage, no quail, no ricotta.

Also, if Geoff tells the truth, there's nothing that says he can't have quail with pepperoni: pepperoni, quail, and ricotta is also valid.

Learn more about Discrete math:

https://brainly.com/question/13425324

#SPJ4

The value of ACD of a trapezium is 26.56°.

Let ABCD be a trapezoid with BCǀǀAD and AB=BC=CD= ½ AD.

ACD can be determined by using the Pythagorean theorem or using the theorem of Pythagoras.

The theorem of Pythagoras states that if you draw a right-angled triangle with the hypotenuse as c and the legs a and b.

The sum of squares of the legs (a and b) equals the square of the hypotenuse (c).

Therefore, by using the Pythagorean theorem ; AC² = AB² + BC²

=> AC² = (1/2 AD)² + (1/2 AD)²

=> AC² = 1/4 AD² + 1/4 AD²

=> AC² = 1/2 AD².

Hence,AC² = 1/2 AD²

ACD is a right-angled triangle where AC is the hypotenuse.

Thus, using the theorem of Pythagoras, we can write: AD² = AC² + CD²

=> AD² = [√(1/2 AD²)]² + (AD/2)²

=> AD² = 1/2 AD² + 1/4 AD²

=> AD² = 3/4 AD²=> AD = √4/3 AD

Thus, ACD=ACD = tan¯¹(√1/2 AD²/AD/2) = tan¯¹(√2/4) = 26.56°

Therefore, ACD is 26.56°.

To know more about "PYTHAGOREAN THEOREM" refer here:

https://brainly.com/question/343682#

#SPJ11

Answer:

if im not mistaken, x = 13!!