14. A zip wire is shown as the dashed line AC in the diagram.
The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.
CD=2.6 BD=12
The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5⁰.
Work out the least possible height of the post $A B$ Give your answer correct to 3 significant figures.

Answer:

-3/2

Step-by-step explanation:

[tex]-\frac{7}{12}=1 \frac{5}{6}+d \\ \\ -\frac{7}{12}=\frac{11}{12}+d \\ \\ -7=11+12d \\ \\ -18=12d \\ \\ d=-3/2[/tex]

The value of x for the given triangle is x = 86°.

What is triangle?

Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.

From the given triangle we have to find the value of x.

By triangle's property.

(x - 45)° + (x + 3)° = (x + 44)°

              2x - 42 = x + 44

                 2x -x = 44 + 42

                       x = 86°

Hence, the value of x for the given triangle is x = 86°.

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Standard deviation of given data corrected to one decimal place is 6.9(rounding off)

The average degree of variability in your datasets is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.

In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.

Given: Data values = 13,2,16,18,19

Mean of data is given as m,

[tex]=\frac{13+2+16+18+19}{5} \\=\frac{68}{5}\\ =13.6[/tex]

Standard deviation, σ

[tex]=\sqrt{\frac{(m-x)^{2} }{n-1} } \\=\sqrt{\frac{(13.6-13)^{2} +(13.6-2)^{2}+(13.6-16)^{2} +(13.6-18)^{2} +(13.6-19)^{2} }{4} }\\ =\sqrt{\frac{0.36+134.56+5.76+19.36+29.16}{4} }\\ =\sqrt{\frac{189.2}{4} }\\ =6.87[/tex]

Hence, standard deviation of given data is 6.9(rounding off)

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The absolute difference rounded to three decimal places is 2.674.

What is polynomial?

An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given: f(x) = tan(2x)

Then f(5.4) = tan(2 x 5.4) = tan(10.8) = tan(54/5)

The second degree Taylor polynomial centered at x =  5 is given by,

T2(x) = Σ(n = 0, 2) f^n(5)/5!(x - 5)^n

Now,

f°(x) = f(x) = tan(2x)

f(5) = tan(2 x 5) = tan(10)

f'(x) = d/dx(tan(2x))

f'(x) = 2 sec^2x = 2( 1 + tan^2(x))

f'(5) = 2(1 + tan^2(10))

f"(x) = d/dx[2(1 + tan^2(2x)]

f"(x) = 0 + 2(2tan(2x)(2sec^2(2x))

f"(x) = 8 tan(2x)(1 + tan^2(2x))

f"(5) = 8 tan(10)(1 + tan^2(10)

Then

[tex]T_2(x) = \frac{tan(10)}{0!}(x - 5)^0 + \frac{2 + 2tan^210}{1!}(x - 5)^1 + \frac{8(tan(10)(1+tan^2(10)}{2!}(x - 5)^2 \\T_2(5.4) = tan(10) + 2(1 + tan^2(10)) (5.4 - 9) +4tan(10)(1 + tan^2(10)(5.4 - 5)^2\\T_2(5.4) = \frac{16}{25} tan^310 + \frac{4}{5}tan^2(10) + \frac{41}{25} tan(10) + \frac{4}{5}[/tex]

The absolute difference is,

[tex]|f(5.4) - T_2(5.4)| = 2.673745[/tex]

|f(5.4) - T2(5.4)| ≈ 2.674

Hence, the absolute difference rounded to three decimal places is 2.674.

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John's average speed for the whole race would be;  12.8 kilometers per hour

The first part of the race was 14 km long, and he completed it in 1 hour.

Now, formula for speed is;

Speed = distance/time

Thus, John's speed in the first part of the race would be;

14/1 = 14km/hr

The second part was 18 km long, and he completed this part in an hour and a half. This means that his speed in the second part of the race is;

18/1.5 = 12km/hr

Average speed = Total distance/total time

Total distance for both parts of the race is;

14 + 18 = 32km

Total time for the race is;

1 + 1.5 = 2.5 hours

John's average speed for the whole race would be;

32/2.5 = 12.8 kilometers per hour

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Answer:

a) 53.33 miles per hour

b) 1.7 pages per minute

c)2.25 $ per avocado

Step-by-step explanation:

a) 320/6 = 53.33333

b) 68/40 = 1.7

c) 27 /12 = 2.25

you might want to write an essay on, but it's your choice.

Answer: Graphed: f(x)=-9x+14gx     Answer: =-3x2

Use the given functions to set up and simplify .

Exact Form: x=0,-1/3

Decimal Form: x=0,-0.3

Step-by-step explanation:

The equation of the line passing through the points (-3,-15/2) and(1,-3/2) is  3x - 2y - 6 = 0.

What is the equation of a line?

An algebraic way to represent a collection of points that together make a line in a coordinate system is called the equation of a line. An algebraic equation, commonly known as the equation of a line, can be created using the various points that together make up a line in the coordinate axis as a collection of variables (x, y). It is possible to determine whether a specific point lies on a line by utilising the equation of a line.

The equation of a line passing through two points [tex](x_{1} ,y_{1} )[/tex] & [tex](x_{2},y_{2})[/tex] is given by

               [tex]\frac{y-y_{1} }{x-x_{1} } = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Given, two points are  (-3,-15/2) and(1,-3/2).

[tex](x_{1} ,y_{1} )[/tex] = (-3,-15/2) and  [tex](x_{2},y_{2})[/tex] = (1,-3/2).

So, The equation of line passing through (-3,-15/2) and (1,-3/2) is given by

or, [tex]\frac{y+\frac{15}{2} }{x+3 } = \frac{-\frac{3}{2} +\frac{15}{2} }{1 +3 }[/tex]

or, [tex]\frac{y+\frac{15}{2} }{x+3 } = \frac{6}{4 } =\frac{3}{2}[/tex]

or, 2(y+7.5) = 3(x+3)

or, 2y + 15 = 3x + 9

or, 3x - 2y - 6 = 0

Hence, the required equation of the line is 3x - 2y - 6 = 0.

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Answer:

base = 8

Step-by-step explanation:

In an isosceles triangle, the legs are equal.

P = 28 = 2L + 8

2L + 8 = 28

2L = 20

L = 20/2 = 10 (length of each leg)

P = 2L + b  (sum of the lengths of the 2 legs and the base)

28 = 2(10) + b

b = 28 - 20 = 8

Answer:im assuming you need to know the difference and its nine

Step-by-step explanation: 34-25=9

Answer: The value of the account after t years can be found using the formula:

Value = 2900 * (1 + 0.0061/4)^(4t)

The annual growth rate, or APR, is 6.1%. When this rate is compounded quarterly, the effective annual growth rate, or APY, is 6.17%, which is the nearest hundredth of a percent.

Therefore, the function showing the value of the account after t years is:

Value = 2900 * (1 + 0.0061/4)^(4t)

And the annual growth rate, or APY, is 6.17%.

The age of Stacy is 24 years old provided the age of Ann is 59 years old.

Two or more expressions with an equal sign are defined as an equation.

Given that, Ann is 11 more than two times older than Stacy.

Let the age of Stacy and Ann be s and a respectively, then:

a = 11 + 2s

Substitute a = 59 into the above equation:

59 = 11 + 2s

2s = 59 -11

s = 24

Hence, the age of Stacy is 24 years old provided the age of Ann is 59 years old.

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The true statement is that 2 in 142 represents a greater value than 2 in 124 because 142 > 124.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol. The place values on the left ofthe decimal point start as ones, tens, hundreds, and so on.

The place value on the right of the decimal point starts from a point and goes to right as tenths, hundredths, and so on.

We are given that encore or points for an NBA Team are usually as whole numbers.

For example, 1, 2, 3, 4, e.t.c. points of an NBA Team are not in decimals or fractions.

The withiner of points awarded for an NBA match is called Discrete because that can be counted with a given amount of time.

Hence, 2 in 142 represents a greater value than 2 in 124 because 142 > 124.

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The probability that an individual will take far longer than 21 days to complete it is 0.12.

In the descriptive analysis, the standard deviation is the amount of scatter or dispersal of the pieces of data in relation to their mean. It provides information on the distribution of values within the sample data and serves as a gauge for how widely apart the measured values are from the mean.

As per the information available in the question,

Meantime, μ = 14 days

Standard deviation, ρ = 6 days

Assume the time to pass the kidney stone be x.

The probability that it will take someone more time than 21 days to complete it.

Let's find out the Z-score first,

Z-score = (x - μ)/ρ

Substitute values in above equation,

= (21 - 14)/6

Z-score = 1.166.

The probability that it will take someone more time than 21 days to complete it :

P(x > Z) = P(x > 1.16) = 0.12

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k(n) is also the number of partitions of n into distinct, odd parts. We begin with the generating function P(x) = ∑p(n) x_n which counts all partitions of all numbers n, with weight x_n for a partition of n.

How do you explain partitioning numbers?

By breaking huge numbers into smaller parts, partitioning helps to simplify the solution of arithmetic issues involving large numbers. 782, for instance, may be divided into: 700 + 80 + 2. It aids children in understanding the real value of each digit. They will perceive 782 as 700, 80, and 2, rather than as a terrifying number.

The numbers of partitions of 10 with number of parts {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} are respectively {1, 5, 8, 9, 7, 5, 3, 2, 1, 1}. (There are 20 partitions of 10 into an odd number of parts and 22 partitions of 10 into an even number of parts.)

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[tex]A=Pe^{rt} \\ \\ 15000000=10000000e^{12r} \\ \\ 1.5=e^{12r} \\ \\ \ln(1.5)=12r \\ \\ r=\frac{\ln(1.5)}{12} \\ \\ r \approx \boxed{0.0338}[/tex]

The exponential growth rate of the population of the country is given by the relation r = 1.8595 %

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population of the country in 2010 be = 12 million

Let the final population of the country in 2022 = 15 million

Now , let the growth rate be represented as r

And , growth rate r = [ ln( final population - ln (initial population ) / no of years ] x 100

Growth Rate = (ln(15 ) - ln(12 )) / (2022 - 2010)

r = (2.70805 - 2.48491) / 12

r = 0.018595

r = 1.8595 %

Hence , the growth rate r = 1.8595 %

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Answer:

x = 7

Step-by-step explanation:

Given equation,

→ -14 - x = -21

Now the value of x will be,

→ -14 - x = -21

→ -x = -21 + 14

→ -x = -7

→ [ x = 7 ]

Hence, the value of x is 7.

Answer:

x=7

Step-by-step explanation:

Isolate the variable by dividing each side by factors that dont contain the variable

Answer:

You have to multiple to get you answer

Step-by-step explanation:

Answer:

[tex] 4\frac{1}{5} [/tex]

Step-by-step explanation:

[tex] 4\frac{2}{3} \times \frac{9}{10} [/tex]

[tex] \frac{14}{3} \times \frac{9}{10} [/tex]

[tex] \frac{126}{30} [/tex]

[tex] \frac{21}{5} [/tex]

Answer: it describe the steepness of the line

Step-by-step explanation:

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The inequality expression p + 1.4 ≤ 0.5 is false for p = 0.1

From the question, we have the following parameters that can be used in our computation:

p + 1.4 ≤ 0.5;

p = 0.1

Substitute p = 0.1 in p+ 1.4 ≤ 0.5;

So, we have the following representation

0.1 + 1.4 ≤ 0.5;

Evaluate the like terms

This gives

1.5 ≤ 0.5;

The above inequality is false

This is because 1.5 is greater than 0.5

Hence, p + 1.4 ≤ 0.5; p = 0.1 is false

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The correct answer is option is a) x^4 – 6x^2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 ,  e) 6x^4 = -x^2 + 5.

How do you write a quadratic form?

A quadratic equation can be expressed using the formula au^2+bu+c=0. where u is a mathematical expression. In each case, the leading term's exponent is equal to the middle term's exponent multiplied by two.

What is quadratic standard form?

Standard form refers to the quadratic function f(x) = a(x - h)2 + k, where an is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.

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All angles are:

a = 37

b = 143

c = 37

d = 58

e = 37

f = 53

g = 48

h = 94

k = 96

m = 26

p = 69

r = 111

s =  69

What is sum of angles of a triangle?

A triangle's total angles equal the straight angle (180 degrees, radians, two right angles, or a half-turn) in a Euclidean space. Three angles, one at each vertex and bounded by two neighbouring sides, make up a triangle.

For a very long period, it was unknown if there were any alternative geometries for which the total is different. During the 19th century, this issue had a particularly significant impact on mathematics. Ultimately, it was determined that the response was correct: in other geometries, this total can be higher or smaller, but it must then depend on the triangle. Its deviation from 180° represents an instance of an angular defect and is a crucial distinction for geometric systems.

From the fig.

we know,

e=37

b= 143 (vertically opposite angle)

143  +  a = 180 (Linear pair)

a =  180 - 143

a  =  37

e = 37

So,  c = 37 (Vertically opposite angle)

c + d + 85 = 180 (Sum of angles on straight line)

37 + d +  85 = 180

d = 180 - 122

d = 58

e + 90 + f = 180 (Sum of all angles of a triangle)

37 + 90 + f = 180

f = 180 - 127

f = 53

g = 48 (if two sides are equal , then the two angles opposite to the equal    

             sides will also be equal.)

48 + 48 + h = 180 (Sum of angles of a triangle)

h = 180 - 96

h = 94

h+ k = 180 (Linear pair)

94 + k = 180

k = 180 - 94

k = 96

d + k + m = 180 (Sum of angles of a triangle)

58 + 96 + m = 180

m = 180 - 154

m = 26

26 + 85 + p = 180 (Sum of angles of a triangle)

p = 180 - 111

p = 69

p + r = 180 (Linear pair)

r = 180 - 69

r = 111

p = s (corresponding angles)

s = 69

Hence all angles are:

a = 37

b = 143

c = 37

d = 58

e = 37

f = 53

g = 48

h = 94

k = 96

m = 26

p = 69

r = 111

s =  69

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Answer:

The probability of rain on both Monday and Tuesday is .08, or approximately 8%.

Step-by-step explanation:

The probability of an event occurring on two separate days (such as rain on Monday and Tuesday) is calculated by multiplying the probabilities of the two events occurring separately. In this case, the probability of rain on both Monday and Tuesday is given by:

Probability of rain on Monday * Probability of rain on Tuesday = .1 * .8 = .08

Therefore, the probability of rain on both Monday and Tuesday is .08, or approximately 8%.

It's important to note that this probability assumes that the likelihood of rain on each day is independent of the other day. In other words, the probability of rain on Tuesday does not depend on whether or not it rained on Monday. If this is not the case, the probability of rain on both days may be different.

By SAS congruence triangle MLN and triangle OLN are congruent.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that, LM≅LO, ∠MLN≅∠OLN.

LM≅LO (Given)

∠MLN≅∠OLN (Given)

LN≅LN (Reflexive property of congruence)

ΔMLN≅ΔOLN (SAS congruence)

∠M≅∠O (CPTC)

MN≅ON (CPTC)

Therefore, by SAS congruence triangle MLN and triangle OLN are congruent.

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Answer: see below

Step-by-step explanation:

slope intercept form

y=mx+b

m=slope

The first question:-5/2 is the sloop

second question: 5/2 is the sloop

The fraction of the album he recorded in June is 1/2

When all the fractions of the album will be  = 1

Bruno recorded 2/12 was recorded in August

2/12 to the lowest term = 1/6

And 1/3 was recorded in July

So,

The fraction of the rest of the album in June is unknown

Let fraction recorded in June will be = x

x =  1 - 1/6 - 1/3

x = 1/1 - 1/6 - 1/3

x = [tex]\frac{18 - 3 - 6}{18}[/tex]

x = [tex]\frac{9}{18}[/tex]

x = [tex]\frac{1}{2}[/tex] to lowest term

Therefore, he recorded 1/2 of his Album in June

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