The angle of elevation of the top of a radio mast from a point due east of it and 96 m away from its base is 30°. From another point, due west of the mast, the angle of elevation of the top is 60°. Calculate the distance of the second point from the base of the mast.​

The complete question is

"A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7°, 17.5°, 72.5°,73.3°"

The value of angle x would be 16.7 degrees.

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse.

The angle of a right angle is always 90 degrees.

In order to find the value of x, a tan would be used.

This is because we have given the opposite and adjacent sides as 10 ft and 3 ft.

Tan Ф = opposite / adjacent

Tan Ф =  (3/10)

= 16.7 degrees

The value of angle x would be 16.7 degrees.

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Answer: the answer is 16.7°.

Step-by-step explanation: it show below.

Answer:

total money=rupees 50

3/5 of 50= rupees 30

money he spent = rupees 30

money he's left with =50-30=20

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Answer:

Step-by-step explanation:

like u told me social studis

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Answer:

0.8

Step-by-step explanation:

4/5 is 0.8 as a divison expression.

Answer: it's the / that shows the division it's kind of like the order of operations that means it you are doing division than it will be / or as a fraction.

Step-by-step explanation:

hop you like my answer!! :)

The lowest point on the graph occurs at point (3π/2,  -1)

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.

The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

The sine function graph is sinusoidal in nature. This is a sim=ne wave that have smooth periodic oscillation

The attached graph shows sine function graph plotted with the interval [0, 2pi]

The lowest point is observed to occur at  (3π/2,  -1)

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Answer:

hmmm.

Step-by-step explanation:

times it by 12,000

like 12,000 being half a day

hahaha I dont know

The matrix A that represents the set W, consisting of vectors of the form [r, s, t] with real numbers, is constructed by organizing the coefficients of r, s, and t as the columns of A. The resulting matrix A is given by A = [0 0 2 48; s 2 1 0; 0 -5 1 0; 0 0 0 1]

Let's break down the construction of matrix A step by step.

Given that W is the set of all vectors of the form [r, s, t] where r, s, and t are real numbers, we want to find a matrix A such that the column space of A (Col(A)) represents W.

The matrix A will have as its columns the coefficients of r, s, and t in the given expression.

Column 1 of A: Coefficients of r

In the expression, we have 5sr + 3t, so the coefficient of r is s. Therefore, the first column of A will be [0, s, 0, 0] since there is no r term in the expression.

Column 2 of A: Coefficients of s and t

In the expression, we have 2sr - 5t. The coefficient of s is 2, and the coefficient of t is -5. Therefore, the second column of A will be [0, 2, -5, 0] with the corresponding coefficients.

Column 3 of A: Coefficients of r, s, and t

In the expression, we have 2r + s + t. The coefficients of r, s, and t are 2, 1, and 1, respectively. Therefore, the third column of A will be [2, 1, 1, 0] with the corresponding coefficients.

Column 4 of A: Coefficients of r and t

In the expression, we have 48r + t. The coefficient of r is 48, and the coefficient of t is 1. Therefore, the fourth column of A will be [48, 0, 0, 1] with the corresponding coefficients.

Putting it all together, the matrix A that represents W = Col(A) is:

A = [ 0 0 2 48 ]

[ s 2 1 0 ]

[ 0 -5 1 0 ]

[ 0 0 0 1 ]

Each column of A corresponds to the coefficients of r, s, and t in the given expression, forming the column space that represents the set W.

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Answer: $3.83 per package

Step-by-step explanation:

Simply you need to use division

Divide 11.49 by 3

11.49/3

To which you will get

$3.83

Answer:

n + (n+5)

Step-by-step explanation:

A number (N) increased (+) by the total of the number = (N+) and five (5)

A 2.5-foot-radius sand mandala's surface area is 19.63 square feet.

A Tibetan Buddhist practise known as "sand mandala" involves building and tearing down mandalas composed of different coloured sand. The ritualistic breakdown of the sand mandala is followed by ceremonies and viewing when it is finished to represent Buddhism's doctrine on the fleeting nature of material life.

Here is how to calculate a circle's area:

Circle area is equal to  πr² (where r is the radius of the circle)

We can use the radius value that has been provided to solve for the area using the following formula:

The sand mandala's size is πr²= π(2.5)²= π(6.25)= 19.63 square feet.

Hence, the sand mandala has a 19.63 square foot surface area.

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To find the volume of the basketball in terms of π, we need to use the formula for the volume of a sphere. With the given diameter of 28 cm, we can calculate the radius and substitute it into the volume formula to obtain the result.

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius. In this case, we are given the diameter of the basketball, which is 28 cm.

To find the radius, we divide the diameter by 2: 28 cm / 2 = 14 cm. Now we can substitute the radius into the volume formula.

V = (4/3)π(14 cm)^3

= (4/3)π(14 cm)(14 cm)(14 cm)

= (4/3)π(2744 cm^3)

= (10976/3)π cm^3

Therefore, the volume of the basketball in terms of π is (10976/3)π cm^3.

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Answer:

15

Step-by-step explanation:

Use PEMDAS for this:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

-4(3-5)+10-3(7+4)+30 ​= -4(-2)+10-3(11)+30

-4(-2)+10-3(11)+30 = 8+10-33+30

8+10-33+30 = 18-33+30

18-33+30 = -15+30

-15+30 = 15

Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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Answer:

Yes, that is a reasonable conclusion

Step-by-step explanation:

Answer:

This is not a reasonable conclusion.

Step-by-step explanation:

Even though there is a strong negative correlation, not eating vegetables doesn't necessarily cause high blood pressure.

Good luck, hope this helps you out! (◕‿◕✿)

Answer:

375 Adult Tickets.

Step-by-step explanation:

Here, we can simply set up an equation using variable x in place of the unknown student/adult tickets.

x = # of adult tickets sold

x + 65 = # of student tickets sold.

1) x + x + 65 = 815 (set both ticket amounts equal to the total)

2) 2x + 65 = 815 (added common variables together)

3) 2x = 750 (negated the +65, subtracted it from both sides)

4) x = 375 (divided both sides by 2)

5) 815 - 375 = 440 (subtracted the x from the total number of adult tickets, to recieve the amount of childrens' tickets.

Therefore,

Since there were fewer adult tickets sold (-65), 375 is the number of adult tickets, and 440 is the number of student tickets.

1. The central angle is 3π/4

2. The length of the intercepted arc is 55π/6 ft

1.

The central angle is 3π/4

The length of an arc, L = rФ where

Making Ф subject of the formula, we have

Ф = L/r

Since L = 6π and r = 8, substituting the values of the variables into the equation, we have

Ф = L/r

Ф = 6π/8

Ф = 3π/4

The central angle is 3π/4

2.

The length of the intercepted arc is 55π/6 ft

Also, the length of an arc, L with central angle, Ф in degrees is

L = Ф/360 × 2πr where r = radius of circle

Since Ф = 110° and r = 15 ft, substituting the values of the variables into the equation, we have

L = Ф/360 × 2πr

L = 110°/360° × 2π × 15 ft

L = 11/36 × 30π ft

L = 11/6 × 5π ft

L = 55π/6 ft

The length of the intercepted arc is 55π/6 ft

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Answer: C. \(p = 2^{d}\)

Step-by-step explanation:

The population rises exponentially, so the graph will have to go up. It also means the population is doubled directly in relation to days

A unit rate's component is always 1. To find the unit rate, divide the fraction by the fraction such that the denominator is equal to one.

The meaning of math units:

Of mathematics, a unit can be thought of as the right side point in a number or the number one. In this instance, the unit number in the number 6713 is 3. A unit is also a term that may be used to describe the common measurement units.

The dimensions of a unit:

The area of a unit as depicted on the subdivision or annexation map that created the unit is referred to as its size. The lot, tract, or parcel size divided by the number of dwellings is the unit size for two-family and multiple-family homes on a single unit.

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Answer:

6 is your answer i jsut did this its right

Step-by-step explanation:

Answer:

$11.16 - $0.68 = $10.48 - price of four cards without tax

$10.48 : 4 = $2.62 - price of one card without tax

Cheers!

Answer:

the cost of each card including sales tax is 2.79

the cost of each card without sales tax is

11.16-0.68=10.48

10.48÷4=2.62

Step-by-step explanation:

Answer:

n = 12, p = 4

Step-by-step explanation:

Hi there!

n = notebook

p = pen

If we know that one notebook costs 8 dollars more than a pen,

we can set the equation for the cost of the pen as n - 8 = p. Now, we have to create an equation for the total cost. This could be represented as 4n + 2p = 56.

Let’s plug in that equation for the pen into our total cost equation.

This would become \(4n + 2(n-8) = 56\)

Using distributive property, the equation becomes \(4n + 2n - 16 = 56\)

After we combine like terms and add 16 to both sides, we find out that \(6n = 72\) or n = 12

Now that we know the cost of the notebook, we can solve for the pen. Plug in 12 for the n values in the original equation \(4n + 2p = 56\)

This leaves us with 48 + 2p = 56. Subtract 48 from both sides and then divide that by two to find p.

p = 4

I hope this helped!

Answer:

Cost of one notebook = $12

Cost of one pen = $4

Step-by-step explanation:

Let,

Cost of one notebook = x

Cost of one pen = y

According to given statement;

x = y+8    Eqn 1

4x+2y=56    Eqn 2

Putting value of x from Eqn 1 in Eqn 2

4(y+8)+2y=56

4y+32+2y=56

6y=56-32

6y=24

Dividing both sides by 6

\(\frac{6y}{6}=\frac{24}{6}\)

y=4

Putting y=4 in Eqn 1

x = 4+8

x=12

Hence,

Cost of one notebook = $12

Cost of one pen = $4

The orbit type of the Molniya 1-91 satellite is Molniya orbit, characterized by a highly eccentric orbit inclined at an angle of 63.17 degrees to the Earth's equator. The orbital parameters, namely the semi-major axis (a) and the argument of perigee (ω), are required to determine the satellite's position and velocity vectors.

a) The Molniya 1-91 satellite follows a Molniya orbit, which is a type of highly eccentric orbit designed to provide extended dwell time over high latitudes. This orbit is characterized by a high inclination angle of 63.17 degrees with respect to the Earth's equator. Molniya orbits are commonly used for communication satellites that serve polar regions, as they spend a significant portion of their orbit over these areas.

b) To determine the orbital parameters of the Molniya 1-91 satellite, we need to extract the relevant information from the two-line element set. The semi-major axis (a) is not directly provided in the given data. However, we can calculate it using Kepler's third law and the mean motion (n) derived from the second line of the TLE. The argument of perigee (ω) is given as 281.6462 degrees in the TLE. These parameters, along with other orbital elements, are crucial for describing the satellite's orbit.

c) To calculate the position and velocity vectors of the Molniya 1-91 satellite in the geocentric equatorial coordinate frame, we need additional information. The TLE only provides elements related to the orbit's shape and orientation, not the satellite's current position and velocity. Position and velocity vectors can be determined by solving the equations of motion using the orbital parameters and mathematical models of celestial mechanics. However, without up-to-date information on the satellite's time and date, it is not possible to calculate these vectors accurately.

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Answer:

height of person ≈ 6 ft

Step-by-step explanation:

using the tangent ratio in the right triangle.

let the height of the person be h , then

tan16° = \(\frac{h}{21}\) ( multiply both sides by 21 )

21 × tan16° = h , then

h ≈ 6 ft ( to the nearest whole number )

The  values of x is (4,-8) he two vectors will be orthogonal.

Let u=(x+4) i-4 j

x=x i+8 j

Now, U and v are orthogonal.

A number of vectors that are mutually perpendicular to each other, meaning they form an angle of 90° with a magnitude of one unit with each other, are called orthogonal unit vectors.

Therefore, u.v=0

⇒\(((x+4) i-4 j) \cdot(x i+8 j)=0 \\\)

⇒\(x(x+4)-32=0 \\\)

⇒\(x^2+4 x-32=0 \\\)

⇒\(x^2+8 x-4 x-32=0 \\\)

⇒\(x(x+8)-4(x+8)=0 \\\)

⇒x=4, x=-8

Therefore, the value of x=4 and x=-8 the two vectors will be orthogonal.

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There are 1,120 different ways to order an egg, a pancake with a choice of syrup, and a beverage.

Given data: 4 different ways to have an egg cooked, 7 different choices of pancakes, 5 different types of syrups and 8 different beverages.The total number of different ways are there to order an egg, a pancake with a choice of syrup, and a beverage can be calculated as follows: Multiplying the number of choices for each item together.

That is 4 ways to have an egg cooked x 7 choices of pancakes x 5 choices of syrup x 8 beverages= 4 x 7 x 5 x 8= 1120 Thus, there are 1,120 different ways to order an egg, a pancake with a choice of syrup, and a beverage.

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Answer:

x=2599200

Step-by-step explanation:

38000/x=100/6840

(38000/x)*x=(100/6840)*x       - we multiply both sides of the equation by x

38000=0.014619883040936*x       - we divide both sides of the equation by (0.014619883040936) to get x

38000/0.014619883040936=x

The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

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Answer:

37.80

Step-by-step explanation:

a^2 + b^2 = c^2

=> 23^2 + 30^2 = x^2

=> 1429 = x^2

=> 37.80

Hope this heps :)