01106115 Ex-1 Find the height of a tree if the angle of elevation Of its top Changes from 25 to 50° as the Observer advanced 15 meters toward
it's base​

Answer:

Step-by-step explanation:

[tex]\frac{30\sqrt{2^{4n-2} +2^{4n+1} } }{(3^{n} +3^{n+1} )^2} \\=\frac{30\sqrt{2^{4n} *2^{-2} +2^{4n} *2^{1} } }{3^{2n} (1+3^{1}) } \\=\frac{30*2^{2n} \sqrt{\frac{1}{2^{2} }+2 } }{4*3^{2n} } \\=\frac{30*2^{2n}*\frac{3}{2} }{4*3^{2n} } \\=\frac{45(2^{2} )^{n} }{4(3^{2} )^{n} } \\=\frac{45}{4} *(\frac{4}{9} )^{n} \\[/tex]

it is a G.P. with common ratio r=4/9 <1

[tex]s=\frac{a}{1-r} ,a=first~term\\s=\frac{\frac{45}{4} *(\frac{16}{81} )}{1-\frac{4}{9} } [by~n=2]\\s=\frac{20}{9} *\frac{9}{5} \\=4[/tex]

The quadratic function that best matches the provided data is as follows: y = -9.38x2 - 74.8x + 186.1 with a 1594.61 squared difference total.

A function in mathematics is a connection between two groups of numbers, known as the domain and the range, where each element in the domain has a unique relationship with each element in the range. The range is the set of possible output values that the function can generate, and the domain is the set of input values for which the function is defined. Algebraic expressions or formulas that explain how the output values are arrived at based on the input values are frequently used to depict functions.

given

The greatest fit will be determined by the function with the smallest sum of squared differences.

The outcome is as follows after computing the sums of squared differences for each function:

Sum of squared differences for y = 9.38x2 + 74.8x + 186.1 is 406.27.

Sum of squared differences for y = -9.38x2 + 74.8x + 186.1 is 406.27.

Sum of squared differences for y = 9.38x2 + 274.8x + 186.1 is 18681.95.

sum of squared disparities is 1594.61 when y = -9.38x2 - 74.8x + 186.1.

The quadratic function that best matches the provided data is as follows: y = -9.38x2 - 74.8x + 186.1 with a 1594.61 squared difference total.

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Answer:

Step-by-step explanation:

Given,

Let length be x and breadth (x - 5).

Perimeter of rectangle is calculated by :

[tex] \: \: \boxed{ \pmb{ \sf{Perimeter_{(rectangle)} = 2(l + b)}}} \\ [/tex]

On substituting the values we get :

[tex]\dashrightarrow \: \: 130 = 2(x + x - 5) \\ [/tex]

[tex]\dashrightarrow \: \: 130 = 2(2x - 5) \\ [/tex]

[tex]\dashrightarrow \: \dfrac{130}{2} = (2x - 5) \\ [/tex]

[tex]\dashrightarrow \: \: 65 = 2x - 5 \\ [/tex]

[tex]\dashrightarrow \: \: 65 + 5 = 2x \\ [/tex]

[tex]\dashrightarrow \: \: 70 = 2x \\ [/tex]

[tex]\dashrightarrow \: \: \frac{70}{2} = x \\ [/tex]

[tex]\dashrightarrow \: \: 35 = x \\ [/tex]

Hence,

The given prescription lacks important information about the frequency and route of administration. Knowing how often a medication should be taken and how it should be administered is crucial for ensuring that patients receive the appropriate dose and achieve the desired therapeutic effect.

Without the frequency information of how (e.g., orally, intravenously, etc.) and when  (e.g., daily, twice daily, etc.)  to take medicine on prescription, patients may take the medication incorrectly or miss doses, potentially leading to ineffective treatment or adverse effects.

Healthcare providers should always provide clear and complete instructions for medication use to ensure patient safety and optimal treatment outcomes.

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Let X and Y be independent random variables, uniformly distributed in the interval [0, 1 ]. The CDF of X - Y is FZ(z) = (1/2)(1+z)^2 for -1 ≤ z ≤ 0, 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1, 0 for z < -1 or z > 1. The PDF of X - Y is fZ(z) = z + 1 for -1 < z < 0, 1 - z for 0 < z < 1, 0 otherwise.

To find the CDF of X - Y, we first note that the range of X - Y is [0, 1]. Let Z = X - Y, then:

FZ(z) = P(Z ≤ z) = P(X - Y ≤ z)

We can write this as an integral over the joint distribution of X and Y:

FZ(z) = ∫∫[X - Y ≤ z] fXY(x, y) dx dy

Since X and Y are independent, the joint distribution is simply the product of their marginal distributions:

fXY(x, y) = fX(x) fY(y) = 1 * 1 = 1

for 0 ≤ x, y ≤ 1.

Thus, we have:

FZ(z) = ∫∫[X - Y ≤ z] dx dy

= ∫∫[Y ≤ X - z] dx dy

= ∫0^1 ∫0^(x-z) 1 dy dx + ∫0^1 ∫(x-z)^1 1 dy dx

= ∫0^(1+z) (1-z) dx

= (1/2)(1+z)^2 for -1 ≤ z ≤ 0

= 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1

Therefore, the CDF of X - Y is:

FZ(z) =

(1/2)(1+z)^2 for -1 ≤ z ≤ 0

1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1

0 for z < -1 or z > 1

To find the PDF of X - Y, we differentiate the CDF:

fZ(z) = dFZ(z)/dz =

z + 1 for -1 < z < 0

1 - z for 0 < z < 1

0 otherwise

Therefore, the PDF of X - Y is:

fZ(z) =

z + 1 for -1 < z < 0

1 - z for 0 < z < 1

0 otherwise

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In response to the stated question, we may respond that Given that she is an M, the probability that the chosen female is both a M and a C is 0.6.

Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how probable an event appears to be to occur. Probability is a mathematical term for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.

a) The girl has a 0.65 chance of being a Clothes Pony (C).

b) The girl has a 50% chance of being a Makeup Missie (M).

c) The girl has a 0.30 chance of being both a Clothing Pony and a Makeup Missie.

d) Using the conditional probability formula, we can calculate the likelihood that the chosen female is both a M and a C provided that she is a M:

P(C|M) = P(C and M) divided by P (M)

Part (c) tells us that P(C and M) = 0.30, while Part (b) tells us that P(M) = 0.50. Therefore:

P(C|M) = 0.30 / 0.50 = 0.6

Given that she is an M, the likelihood that the chosen female is both a M and a C is 0.6.

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Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

The local tide measurement data contradict the satellite data because the number of decreasing local sea level trends is greater than the number of increasing local sea level trends. So correct option is C.

Measuring tides involves observing and recording changes in the water level of oceans, seas, and other bodies of water over time. Tides are caused by the gravitational pull of the moon and sun on the Earth's water, which results in a rhythmic rise and fall of water levels.

Tide measurements are important for a variety of reasons, including understanding ocean circulation, predicting flooding and storm surges, and planning shipping routes. Tidal data is also used in climate research, as changes in sea level can indicate long-term climate trends.

The local tide measurement data contradict the satellite data because the number of decreasing local sea level trends is greater than the number of increasing local sea level trends.

The measurement is done because the land surfaces are dynamic with some locations rising or sinking relative to sea level changes are different across world coasts.

Therefore, the Option C is correct.

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The complete question is:

Answer:

15.8823% error

Step-by-step explanation:

Percent Error Formula

abs([tex]\frac{(a-x)}{x}[/tex]) * 100%

abs:  absolute value

a:  actual value

x:  expected value

Percent Error = abs([tex]\frac{14.3 - 17}{17}[/tex]) * 100%

                       = abs(-0.158823) * 100%

                       15.8823% error

Answer: 24kg

Step-by-step explanation:

Ratio given:

Dog = 3 (Weight of cat)

Substitute the (Weight of cat) with the given unit:

Dog = 3(8kg)

Multiply

Dog = 24kg

a) The value of Hy = 1.15

b) The proportion of cartons with less than 1.15 broken eggs is 0.60

c) The answer is B)This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like.

(a) Hy = 0.67, which means that on average, there are 0.67 broken eggs per carton.

Hy = (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1

= 0.67

(b) The proportion of cartons with less than 0.67 broken eggs is 0.60 which is probability of 0 broken eggs.. This may be surprising as the probability of having less than 0.67 broken eggs is only 0.60, but this is due to the fact that the distribution is skewed towards higher values.

(c) Hy is not equal to the simple average of 0, 1, 2, 3, and 4 because the distribution is not symmetrical. The probabilities are weighted towards higher values, which increases the mean. Additionally, the value of zero should be included in the calculation, as it represents a possible outcome. Therefore, the correct formula for Hy is (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1 = 0.67.

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--The question is incomplete, answering to the question below--

"Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs.

y 0 1 2 3 4

p(y) 0.60 0.20 0.15 0.03 0.02

(a) Calculate and interpret Hy  

(b) In the long run, for what proportion of cartons is the number of broken eggs less than Hy? (Round your answer to two decimal places).

Does this surprise you?

Yes

No

(c) Explain why Hy is not equal to (0 + 1 + 2 + 3 + 4)/5 = 2.0.  

A. This computation of the mean is incorrect because the value in the denominator should equal the maximum y value.

B. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like

C. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when

D. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs."

The length of the base of the triangle is 8 yards.

The formula for calculating a triangle's area is

A = 1/2 * base * height,

where A represents the triangle's area, base its base length, and height its height measured perpendicularly from base to top.

Given that, height of triangle is half of 28 yards and an area of 56 sq. yards.

The area of triangle is given as:

A = 1/2 * base * height

Substitute the value of h = 1/2 (28) = 14 yards, and area = 56.

56 = 1/2 * base * 14

base = 56(2) / 14

base = 8 yards

Hence, the length of the base of the triangle is 8 yards.

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Answer:

2

Step-by-step explanation:

since d=7 and the equation is d-5 in the place of d we'll put 7 therefore 7-5=2

Answer:

u8hiuhihihoiho'hjoihuiytrdeee

Step-by-step explanation:

Continuous variables can take on an infinite number of values whereas discrete variables can only take a value from a finite number of values.

Continuous and discrete variables are two types of variables in statistics. Continuous variables are variables that can take on an infinite number of values, including any fractional value within a particular range.

In contrast, discrete variables can only take on a finite number of values. These values can be counted or enumerated, and there are no fractional values between them.

The distinction between continuous and discrete variables is important in statistical analysis because it affects the methods that can be used to analyze and interpret the data.

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Using matrices, we can find that the products of EH and FG are defined, the rest does not satisfy.

A matrix is a rectangular array of values that are defined for mathematical operations including addition, subtraction, and multiplication.

The quantity of rows and columns in a matrix—also referred to as the order of the matrix—determines its size. A 6 4 symbol and 6 by 4 reading are used to symbolise and denote the order of a matrix having 6 rows and 4 columns.

Here in the question,

When the matrices, E and H are multiplied, the resulting matrix is a defined matrix.

Similarly, we can see when F and G are multiplied, the resulting matrix is a defined matrix.

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Where F_pivot is the magnitude of the force exerted on the pivot point.

What are perpendicular lines?

Perpendicular lines are lines that intersect at a right angle (90 degrees). In other words, if you draw a line perpendicular to another line, the two lines will form four right angles at the point where they intersect.

(a) The torque applied by the adult rider (on the left) can be calculated as the product of the force applied by the rider and the perpendicular distance from the pivot to the force. Let F_a be the force applied by the adult rider and let r_a be the perpendicular distance from the pivot to the force. Then, the torque applied by the adult rider is:

τ_a = F_a * r_a

The perpendicular distance r_a can be calculated using the Pythagorean theorem:

r_a = sqrt((L/2 - d)^2 + Xoffset^2)

Therefore, the torque applied by the adult rider is:

τ_a = F_a * sqrt((L/2 - d)^2 + Xoffset^2)

(b) Similarly, the torque applied by the child rider (on the right) can be calculated as:

τ_c = F_c * sqrt((L/2 + d)^2 + Xoffset^2)

where F_c is the force applied by the child rider and r_c is the perpendicular distance from the pivot to the force, which can be calculated using the Pythagorean theorem.

(c) The torque applied by the board can be calculated as the sum of the torques applied by the two riders:

τ_b = τ_a + τ_c

Substituting the expressions for τ_a and τ_c, we get:

τ_b = F_a * sqrt((L/2 - d)^2 + Xoffset^2) + F_c * sqrt((L/2 + d)^2 + Xoffset^2)

(d) To determine the distance d in terms of given quantities and variables, we can use the condition for static equilibrium, which requires that the sum of the torques about the pivot point is zero:

τ_a + τ_c = 0

Substituting the expressions for τ_a and τ_c and simplifying, we get:

F_a * (L/2 - d) = F_c * (L/2 + d)

Solving for d, we get:

d = (F_a/F_c - 1) * L/4

Substituting F_a = Mg and F_c = mg, where M is the mass of the adult rider, m is the mass of the child rider, and g is the acceleration due to gravity, we get:

d = (M/m - 1) * L/4

(e) The magnitude of the force exerted on the pivot point by the see-saw while in use can be calculated using the condition for static equilibrium, which requires that the sum of the forces in the vertical direction is zero:

F_a + F_c = Mg + mg

Substituting F_a = Mg and F_c = mg, we get:

F_pivot = Mg + mg

Therefore, where F_pivot is the magnitude of the force exerted on the pivot point.

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We show that at n = 1 the basis step works, but the inductive step fails.

Let consider the Inequality

[tex]\frac{1}{2}\cdot\frac{3}{4}\dots\dots\frac{2n-1}{2n} < \frac{1}{\sqrt{3n}}[/tex]

We must demonstrate that while the fundamental step of mathematical induction proves the aforementioned inequality, the inductive step does not.

Mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.

It involves proving that a statement holds true for a base case (typically zero or one), and then proving that, if it holds true for any given natural number, it must also hold true for the next natural number.

This process is repeated until the statement has been shown to be true for all natural numbers.

Basic Step: n = 1

1/2 < 1/√3, which is true.

Hence we proved that at n = 1  the basic steps of mathematical induction works.

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The complete question is:

Suppose that we want to prove that

[tex]\frac{1}{2}\cdot\frac{3}{4}\dots\dots\frac{2n-1}{2n} < \frac{1}{\sqrt{3n}}[/tex]

for all positive integers n.

Show that if we try to prove this inequality using mathematical induction, the basis step works, but the inductive step fails.

Answer:

Step-by-step explanation:

[tex]tanx=\frac{15}{18}[/tex]     (tan is opposite/adjacent     SOHCAHTOA)

[tex]x=tan^{-1}(\frac{15}{18}) = 39.8[/tex]

the correct options are A), B), and E).

why it is and what is Gallon?

A) 2 quarts = 8 cups

B) 8 cm = 80mm

E) 96 inches = 8 feet

The number 8 cannot correctly fill in the blank for statements C and D.

C) 1 gallon = 16 cups, so 4 gallons = 64 cups, not 8 cups.

D) 1 hour = 60 minutes, so 96 minutes = 1 hour and 36 minutes, not 8 hours.

Therefore, the correct answers are A), B), and E).

A gallon is a unit of measurement for volume commonly used in the United States and some other countries. There are two different sizes of gallons: the US gallon and the imperial gallon.

The US gallon is defined as exactly 3.785411784 liters, and is used for measuring liquids such as gasoline, milk, and other beverages.

The imperial gallon, which is used in the United Kingdom and some other countries, is defined as exactly 4.54609 liters.

In both cases, a gallon is typically divided into smaller units such as quarts, pints, and fluid ounces for measuring smaller amounts of liquid.

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Answer:

The store with a 40% off sale.

Step-by-step explanation:

Since 1/3 of 100% is approximate, 33.4% and 40% will obviously be better. The 40% off sale is better by approximately 6.6%.

Answer:

(6/x) - (5y)

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Answer:

Step-by-step explanation:

By choosing the LIFO method for inventory, the following items would be decreased (compared to what would have happened if they chose to use FIFO):

Net income

Taxes payable

Total assets

Owner's equity

This is because the LIFO method results in higher cost of goods sold and lower ending inventory, which in turn decreases net income and taxes payable. Lower ending inventory also decreases total assets and owner's equity.

The items that would be decreased by the choice of LIFO (compared to what would have happened if they chose to use FIFO) are Ending inventory and Net profit

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Inventory costs in 2012 were rising

Now,

LIFO stands for last-in, first-out, and FIFO stands for first-in, first-out. These are two ways of assigning costs to the units of inventory that you sell. FIFO assumes that you sell the oldest units first, while LIFO assumes that you sell the newest units first1.

The choice of LIFO or FIFO has implications on a company’s financial statements as this decision impacts the value of inventory, cost of goods sold, and net profit2. If inventory costs are rising during a period, then LIFO will result in a lower value of ending inventory, a higher cost of goods sold, and a lower net profit compared to FIFO1.

Therefore, by unitary method the answer will be Ending inventory and Net profit

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Answer:

a) Simple interest = PRT/100 = (800 x 1.5 x 5)/100 = $60

b) Future value = P(1 + RT) = 800(1 + 0.015 x 5) = $870

Total time of loan = 6 months

Phyllis pays $200 two months into the loan, so she still owes $800 for the remaining 4 months.

Simple interest = PRT/100 = (800 x 2 x 4)/100 = $64

Total interest = $64 + $20 = $84

a) Exact interest = PRT/365 = (500 x 4.5 x 90)/36500 = $5.48

b) Future value = P(1 + RT) = 500(1 + 0.045 x 90/365) = $508.22

a) Ordinary interest = PTR/100 = (3500 x 3.5 x 60)/360 = $183.75

b) Proceeds = P - I = 3500 - 183.75 = $3316.25

c) Amount to be paid at maturity = P = $3500

d) Due date = May 4 + 60 days = July 3

APY = (1 + R/n)^n - 1 = (1 + 0.16/4)^4 - 1 = 0.1664 or 16.64%

Future value = P(1 + R/n)^(nt) = 4500(1 + 0.04/2)^(2 x 2) = $5,011.03

P = FV/(1 + R/n)^(nt) = 8000/(1 + 0.06/4)^(4 x 5) = $5,764.44

Interest = (900 x 0.12) + (500 x 0.1) = $132

APR = (132/900) x (365/20) x 100% = 730%

Future value = PMT x ((1 + R/n)^(nt) - 1)/(R/n) = 1000 x ((1 + 0.08/4)^(4 x 4) - 1)/(0.08/4) = $47,490.08

Future value = PMT x ((1 + R/n)^(nt) - 1)/(R/n) x (1 + R/n) = 50 x ((1 + 0.06/12)^(12 x 2.5) - 1)/(0.06/12) x (1 + 0.06/12) = $1,327.10

Answer:

-2 squared+3+1=0

I hope it helps

Answer:

Y = 4

Step-by-step explanation:

given x varies inversely as y then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the condition x = 10 when y = 6 , then

6 = [tex]\frac{k}{10}[/tex] ( multiply both sides by 10 )

60 = k

y = [tex]\frac{60}{x}[/tex] ← equation of variation

when x = 15 , then

y = [tex]\frac{60}{15}[/tex] = 4

Answer:

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. Solving for the radius, we have:

r = C/(2π) = 50.24/(2π) ≈ 8

So the radius of the circle is approximately 8 units.

The formula for the area of a circle is A = πr^2, so we have:

A = π(8)^2 = 64π ≈ 201.06

Therefore, the area of the circle is approximately 201.06 square units.

The first rational expression is 63m²+20m−32. To rewrite this with a common denominator of (3m−4)(m+8)(m−7), first we need to find the LCD (Lowest Common Denominator) of both terms. So, we need to multiply each numerator and denominator of the first rational expression by (3m−4)(m+8)(m−7).

In the numerator, we need to multiply 63m² by (3m−4)(m+8)(m−7):

63m² × (3m−4)(m+8)(m−7) = 63m³ - 224m² + 784m - 504

In the denominator, we need to multiply 1 by (3m−4)(m+8)(m−7):

1 × (3m−4)(m+8)(m−7) = 3m³ - 12m² + 24m - 16

Therefore, the rewritten rational expression is:

63m³ - 224m² + 784m - 504/3m³ - 12m² + 24m - 16

The second rational expression is 3m³m²−25m+28. To rewrite this with a common denominator of (3m−4)(m+8)(m−7), we first need to find

√9+25 = 28

π-4 = -0.8571

³√-27 = -3

2 / 3 = 0.6667

18÷2 = 9

√-27​ = 5.196

In mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).

We have √9+25 = 28

find the square root of 9 = 3

3 + 25 = 28

π-4 = 3.14 - 4

= -0.8571

³√-27 = ³√3³

= 3

2÷3 = 0.6667

18÷2 = 9

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question:

given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27​

find the value of the terms