An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1050 feet apart..
airplane passes over the line joining them, each observer takes a sighting of the angle
elevation to the plane, as indicated in the figure. If A = 40 degrees and B = 30°, how high is th
airplane?

The value of x in the given trigonometric function is 7.37

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios. The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.

5cos(5x) = 4

divide both sides by 5, it becomes,

cos(5x) = 4/5

cos(5x) = 0.8

taking Arc cos on both sides

5x = Arc cos 0.8

5x = 36.87

x = 36.87/5

x = 7.37 to 2 decimal places

In conclusion the value of x is 7.37

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The volume of the cube with the given side length is 1/125b⁹

From the question, we are to determine the volume of the given cube.

The volume of a cube is given by

V = s³

Where V is the volume of the cube

and s is the side length of a side of the cube

From the given information,

s = 1/5b³

Thus,

The volume of the cube will be

V = 1/5b³ × 1/5b³ × 1/5b³

V = 1/5 × 1/5 × 1/5 × b³ × b³ × b³

V = 1/125 × b⁹

V = 1/125b⁹

Hence,

The volume is 1/125b⁹

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Answer:

x<5

Step-by-step explanation:

1.  add 14 to both sides  

4x - 14  + 14 < 6 + 14

    4x<20

2.  divide both sides by 4

[tex]\frac{4x}{4} < \frac{20}{4}[/tex]

     x<5

                                               Answer = x<5

Answer: 23 years old

Step-by-step explanation:  31-8=23

$841,500 is the maturity value.

Given in question,

MV = P(1+RT)

P = $750,000

R = 13.35%

  = 13.35/100

  = 0.1335

T= 11 months

 = 11/12 years

 = 0.917 years

Putting the value in equation,

MV = 750000(1+0.1335*0.917)

      = 750000(1+0.122)

      = 750000*1.122

      = 814500

Hence, Maturity Value is $814,500.

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Check the picture below, so the ellipse looks more or less like so

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=-4\\ k=10\\ a=8 \end{cases}\implies \cfrac{(x- (-4))^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1\implies \cfrac{(x+4)^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1 \\\\\\ \stackrel{\textit{we know that c = 6}}{6=\sqrt{8^2 - b^2}}\implies 6^2=8^2-b^2\implies b^2=8^2-6^2\implies \underline{b^2=28} \\\\\\ \cfrac{(x+4)^2}{ 8^2}+\cfrac{(y- 10)^2}{ b^2}=1\implies {\Large \begin{array}{llll} \cfrac{(x+4)^2}{ 64}+\cfrac{(y- 10)^2}{ 28}=1 \end{array}}[/tex]

The numbers that opposite 1/15 and 1/16 are -1/15 and -1/16

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

Numbers = 1/15 and 1/16

The opposite of numbers is the negative equivalent of the number

Take for instance, we have a number x

The opposite of x is -x

Using the above as a guide, we have the following representation

Numbers = 1/15 and 1/16

This means that, the opposite numbers can be represented as

Opposite numbers = -1/15 and -1/16

Hence, the opposite numbers are -1/15 and -1/16

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The value of v is -12.5 when u = 15, t = 8, and s = 40.

According to the question,

We have the following expression:

s = (u+v)[tex]t^{2}[/tex]

We have the following values:

u = 15, t = 8, s = 40

Now, we can easily find the value of v by putting all these values in the given expression.

So, we have the following expression:

40 = (15+v)8*8

40 = (15+v)16

Multiplying 16 into the bracket:

40 = 15*16+16v

40 = 240+16v

Subtracting 240 from both sides:

40-240 = 16v

-200 = 16v

Dividing by 16 on both sides:

-200/16 = v

v = -12.5

Hence, the value of v is -12.5 when u = 15, t = 8, and s = 40.

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The perpendicular of the right triangle is 2.62441 inches and the base of the triangle is 3.0164 inches.

According to the question,

We have the following information:

A right triangle has a hypotenuse of length 4 inches. And one angle is 41°.

Now, we will use trigonometric functions of Sin and Cos to find the length of each leg of this triangle.

Sin 41 = Perpendicular/hypotenuse

Perpendicular = 0.6561*4

Perpendicular = 2.62441 inches

Cos 41 = base/hypotenuse

Base = 0.7541*4

Base = 3.0164 inches

Hence, the perpendicular of the right triangle is 2.62441 inches and the base of the triangle is 3.0164 inches.

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The domain of the polynomic function f(x)=−2 · x · (x − 3) · (x − 6) is (- ∞, + ∞).

In this problem we find a polynomic function in factor form, whose definition is presented below:

f(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., n - 1, n}

Where:

The grade of the polynomial is equal to the number of roots. The statement shows a polynomial of grade 3 and, according to function theory, the domain of polynomic functions is the set of all real numbers, whose interval notation is (- ∞, + ∞).

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Answer:

Step-by-step explanation:

a)  x2 to x4   and  x6 to x7

b)  x1 to x2  ,  x3 to x5   ,  x6 to x7

c)  x2, x3, x5, x6, x7

d)  x2.5  , x4 , x5.5 ,  x6.5

The probability that an individual man’s step length is less than 2.2 feet is 0.10 or 10%

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = (X - mean)/S.D

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 2.8 feet and a standard deviation of 0.5 feet.

Find the probability that an individual man’s step length is less than 2.2 feet.

This is the p-value of Z when X = 2.2. So

Z = (2.2 - 2.8)/0.5

Z = 0.6/0.5 = 1.2

Z = 1.2

has a p-value of 0.10

Therefore, the probability that an individual man’s step length is less than 2.2 feet is 0.10 or 10%

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The expression has 3 terms, that are

1st term n²

2nd term 2k³

3rd term 3m²

Given that,

The expression is n²+2k³+3m².

We have to find how many terms are in the expression.

A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these. A single term or a collection of phrases can be used to create an algebraic expression. For instance, 4x and y are the two terms in the formula 4x + y.

Take the expression,

n²+2k³+3m²

There are 3 terms

1st term n²

2nd term 2k³

3rd term 3m²

Therefore, The expression has 3 terms, that are

1st term n²

2nd term 2k³

3rd term 3m²

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The probability of any day being rainy last year is 21/73 .

In the question ,

it is given that ,

In past year ,

the number of days it rained in last past year = 105 days

total number of days in past year = 365 days .

So , the probability of any day being rainy last year is = (number of days it rained )/(total number of days ) .

Substituting the values , we get

probability of any day being rainy last year = 105/365

Simplifying further , we get

= 21/73

Therefore , The probability of any day being rainy last year is 21/73 .

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The box plot that could represent a data set that has an interquartile range of 5 is the box plot first option shown in the image.

What is Interquartile Range?

The interquartile range of a data set is the distance between the lower quartile and the upper quartile on a box plot.

Thus, a box plot that has a lower quartile of 3 and an interquartile range of 5 will have a distance of 5 from the lower quartile to the upper quartile.

Therefore, the box plot that could represent a data set that has an interquartile range of 5 is the box plot shown in the image attached below (see attachment).

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The surface area of prism is 224 square centimeter

The surface area of the prim = 2 × Area of the hexagonal face + 6 × Area of the rectangular face  

The area of the hexagonal face = 42 square centimeter

The area of the two hexagonal face = 2×42

= 84 square centimeter

The area of the one rectangular face = length × width

= 4 × 8

= 32 square centimeter

The area of the 6 rectangular face = 6 × 32

= 192 square centimeter

The surface area of the prim = 32 + 192

= 224 square centimeter

Hence, the surface area of prism is 224 square centimeter

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Answer:

11.25 litres

Step-by-step explanation:

75 ×15/100

=11.25 so the answer should be 11.25 litres

Assume that Chris is not a housekeeper for anyone else. Assume that Angel paid $2,250 in wages for the fourth quarter of 2021. The social security tax is $1,116, Medicare tax is $261 and FUTA tax is $42.

Social security  =12.4%

Medicare = 2.9%

FUTA = 0.6%

a. Social security tax

Yearly salary = $750 × 12 months

Yearly salary  = $9,000

Social security tax  = $9,000 ×12.4%

Social security tax = $1,116

b.  Medicare tax

Yearly salary =$750 × 12 months

Yearly salary = $9,000.00

Medicare tax = $9,000×2.9%

Medicare tax = $261

c. FUTA tax

Yearly salary = $750 × 12 months

Yearly salary = $9,000

The first $7,000 will be  subject to FUTA tax.

FUTA tax = $7,000 ×0.6%

FUTA tax = $42

Therefore the social security tax is $1,116.

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Objective function is a maximum at (3,2),     Z = 3x+y = 3(3) + 1(2) = 9 + 2 = 11

Given,

Maximize: z = 3x +y

Subject to:

x-y≤9

3x + 5y ≤45

x≥0, y≥0​

For the purpose of representing and resolving the linear programming optimization issues, objective functions are frequently used. The choice variables x and y are used in the objective function, which has the form Z = axe + by. The best answer can be obtained by maximizing or minimizing the function Z = ax + by

Plot the constraints and the objective function Z, or z = 3x +y

Push the objective function to the limit permitted by the feasible region to find the maximum.

Objective function is a maximum at (3,2),

Z = 3x+y = 3(3) + 1(2) = 9 + 2 = 11

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The point-slope forms of the equation from the information given is 1. y + 2 = ï½(x-1), 2.y - 3 = 2(x+1) , 3.y - 5 = 1(x-8), 4. y + 7 = -5/7(x+1) and 5.y - 3/2 = -1(x-1/2).

1.

slope m = ï½ and  (h, k) = (1, -2)

The point slope is y + 2 = ï½(x-1)

2.

slope = 2 , point (-1, 3)

y - 3 = 2(x+1)

3.

The line goes through the points (8,5) and (9, 6).

slope m = 6-5 / 9-8

= 1/1

= 1

y - 5 = 1(x-8)

4.

The line goes through the points (-1, -7) and (-8, -2)

slope m = -2+7 / -8+1

= 5/-7

= -5/7

y + 7 = -5/7(x+1)

5.

The line goes through the points (1/2, 3/2) and (-1/4, 5/4)

slope m = 5/4 - 3/2 / -1/4 - 1/2

= 5 - 6 / 4 / -1 + 2 / 4

= -1/1

= -1

y - 3/2 = -1(x-1/2).

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The results of the combinations are given as follows:

A. Number of possible outcomes with red exactly 3 times and Purple exactly 2: 10.

B. Number of possible outcomes with red at least ounce in 4 spins: 175.

C. Number of possible outcomes with red at least ounce in 5 spins: 781.

The outcomes are obtained in two ways, as follows:

The combination formula calculates the number of different combinations of x objects from a set of n elements, according to the equation presented as follows:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

From item a, there are 5 outcomes with 3 and 2 repetitions, hence the number of results is obtained as follows:

[tex]C_{5,3} = \frac{5!}{3!2!} = 10[/tex]

It states that the number of outcomes of n independent trials is given by the multiplication of the number of outcomes for each trial.

For item b, we have that:

Hence the total number of outcomes, without considering the restriction is:

Total = 4^4 = 256.

With no red results, the number of outcomes is:

Total no red = 3^4 = 81.

Hence the number of outcomes with at least one red result, considering complementary events, is:

256 - 81 = 175.

Item c follows the same logic, only with 5 trials instead of four, hence:

4^5 - 3^5 = 781.

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The equation of the function is: y = 11.5x.

The slope = 11.5 garbage bag per hour.

Y-intercept = 0 bag at 0 hour.

The domain: number of hours

Range of the function: number of garbage bags filled.

138 bags will be filled in 12 hours.

The equation of a function can be written as y = mx + b in slope-intercept form. Here, we have:

Given the graph with the points that represents the number of garbage bags filled as a function of time as:

(6, 69); (5, 57.5); (4, 46); (2, 23); (1, 11.5); (3, 34.5)

Use two points, (6, 69) and (4, 46) to find the slope of the function:

Slope (m) = change in y / change in x = (69 - 46)/(6 - 4)

Slope (m) = 23/2

Slope (m) = 11.5

To find the y-intercept (b), substitute m = 11.5 and (x, y) = (6, 69) into y = mx + b:

69 = 11.5(6) + b

69 = 69 + b

69 - 69 = b

b = 0

To write the equation of the function, substitute m = 11.5 and b = 0 into y = mx + b:

y = 11.5x + 0

y = 11.5x

The slope, 11.5, means 11.5 garbage bags were filled per hour.

Y-intercept is zero, which means no bag was filled at 0 hour.

The domain is the set of the number of hours, while the range of the function is the set of number of garbage bags filled.

To find the number of garbage bags that volunteers fill in 12 hours, substitute x = 12 into y = 11.5x:

y = 11.5(12)

y = 138 bags.

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The number of fashion magazines subscription that were sold is approximately 58.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

In other words, percentage is a fraction or a ratio in which the value of whole is always 100.

Therefore, Carolyn’s homeroom sold 207 magazine subscriptions. Of the magazine subscriptions sold, 28 percent were fashion magazines.

The number of fashion magazine subscriptions that were sold can be calculated as follows:

number of fashion magazine sold = 28% of 207

number of fashion magazine sold = 28 / 100 × 207

number of fashion magazine sold = 5796 / 100

number of fashion magazine sold = 57.96

Therefore, about 58 fashion magazines were sold.

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a) She has three quadratic equations as one is the standard form, the other gives the roots, and the other gives the vertex.

b) If the distributive property is applied and the like terms combined, all the equations will have the same result.

c) The most helpful equations will be given for each point.

d) Maximum height of 64 feet after 1 second from h(t)=-16(t-1)^2+64.

e) The shell splashes into the river after a time of three seconds, from h(t)=-16(t+1)(t-3).

f) The shell was at a height of 48 feet when tossed into the river, from h(t)=-16t^2+32t+48.

In standard format, the quadratic function is given as follows:

h(t) = -16t² + 32t + 48.

From this, the relevant information is the initial height from which the shell was tossed off the cliff, which is the c-coefficient of 48 feet.

The roots of the equation are given from the rule presented as follows:

h(t)=-16(t+1)(t-3).

Hence the shell splashes into the river at the positive root of h(t), that is:

t - 3 = 0 -> t = 3.

Expanding the equation, we have that it is equivalent to the first one, as:

-16(t + 1)(t - 3) = -16(t² - 2t - 3) = -16t² + 32t + 48.

The vertex-form quadratic equation is given as follows:

h(t) = -16(t - 1)² + 64.

Meaning that a maximum height of 64 feet was reached after one second.

Expanding the equation, we have that:

h(t) = -16(t - 1)² + 64 = -16(t² - 2t + 1) + 64 = -16t² + 32t - 16 + 64 = -16t² + 32t + 48.

Which is also equivalent to the first one.

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Answer:  Refer to the drawing below

Explanation:

Complementary angles always add to 90 degrees.

Draw a right angle, aka 90 degree angle. Plot points A, B and D on it as shown below. Then add point C somewhere inside the rectangular region formed by this right angle. Lastly, connect a segment from B to C. This helps form angles ABC and CBD. Note how these smaller angles combine to a 90 degree angle.

(angleABC) + (angleCBD) = angle ABD = 90 degrees

The angles are adjacent because they share a common wall, which in this case is segment BC.

Answer:

Think its B.

Step-by-step explanation:

Answer:

[tex]4cd(6-9c)[/tex]

Step-by-step explanation:

Factor out what all terms have in common

The new annual output from the turbine is 1122kw to give a percentage of 87

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Data;

This can be represented mathematically as

87 / 100 = y - 600/ 600

We can solve for y

0.87 = y - 600 / 600

x = 1122kw

The new annual output from the turbine is 1122kw

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