A pillar of height 222 ft casts a shadow of 348 ft long.
Find the measure of the angle of elevation of the sun.

Answers

Answer 1

Using tangent of the angle, the angle of elevation is 32.5 degrees

Angle of Elevation

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

In this problem, we have to use the tangent of the angle since we know the opposite and adjacent sides

opposite side = 222adjacent side = 348

Tan θ = opposite / adjacent

tanθ = 222 / 348

tan θ = 0.6379

θ = tan⁻¹(0.6379)

θ = 32.5°

The angle of elevation is 32.5 degrees

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Related Questions

Carla's uncle owns a pizzeria. Her uncle has 4 pounds of mozzarella cheese. He uses pound of the mozzarella to make a large pizza.
How many large pizzas could Carla's uncle make before running out of mozzarella cheese?
O 3 pizzas
4 pizzas
O 5 pizzas
O 6 pizzas

Answers

I could be wrong but is it 6

What is the average number of receipts per quarter at Kingpin Parts?

Answers

Answer: The answer is about 57.5

25. There are 5 teams in a netball competition. Each team must play each other twice. How many games will team play? A. 10 B. 5 C. 8 D. 4






⛑help again please anyone I got a lot of ⚣ homework to do so I'll ask answers for all of them throughout the night >_<​

Answers

Answer:

C-8

Step-by-step explanation:

5 games they each play each other they continue if each team wins then they continue to play to 8 games

Answer:

The answer to your problem would be 10

Step-by-step explanation:

There are 5 teams. So, if each team has to play each other twice, 5x2=10.

Each team plays twice....I think I did that right. I'm really sorry if it's not right.

4.
20% of what number is 38?

Answers

Answer:

190

Step-by-step explanation:

If 38 is 20% then half of 38, 19, is 10%. With that you can divide 19 by 10 and get 1.9. If you take 1.9 and multiply it by 100 you get 190

NO LINKS!! Please help me with this problem.​

Answers

Answers:

Min cost = $464.76

Dimensions = 11.619 feet by 5.164 feet

Each value mentioned above is approximate.

========================================================

Explanation:

x = horizontal dimension

y = vertical dimension

xy = 60

y = 60/x

The amount of outer fencing needed is 2x+2y feet, aka the perimeter of the largest rectangle.

There are 5 vertical inner fences, so we need 5y feet of inner fencing.

Let's set up the cost function.

Cost = 10*(amount of outer fencing) + 5*(amount of inner fencing)

C = 10*(2x+2y) + 5*(5y)

C = 20x+20y+25y

C = 20x+45y

Plug y = 60/x into the cost function.

C = 20x+45y

C = 20x+45(60/x)

C = 20x + (2700/x)

Then use either calculus or a graphing calculator to find the lowest point on the cost curve is roughly located at (11.619, 464.758)

Use the x value x = 11.619 to find its paired y value

y = 60/x

y = 60/11.619

y = 5.16395558998192

y = 5.164

The entire enclosure should be roughly 11.619 feet by 5.164 feet

The total cost is minimized at approximately  $464.76

Answer:

11.619 by 5.164 feet$464.76 minimum cost

Step-by-step explanation:

You want the dimensions and cost of a rectangular enclosure with an area of 60 square feet and 5 internal partitions. The cost of outside fence is $10 per foot, and the cost of partition fence is $5 per foot.

Setup

Let x represent the length of the enclosure, and y the width (and the partition length). Then we have ...

  xy = 60

  10(2x) = cost fencing for length

  10(2y) +5(5y) = cost of fencing for width

We know the cost will be minimized when the cost of fence for the length is equal to the cost of fence for the width.

  20x = 45(60/x)

Solution

  x² = 135 . . . . . . . . . . . multiply by x/20

  x = 3√15 ≈ 11.619 . . . .square root

  y = 60/(3√15) = (4/3)√15 ≈ 5.164 . . . . . find y

Then the cost is ...

  2(10(2x)) = 120√15 ≈ 464.76 . . . . minimum cost

The enclosure is 11.619 by 5.164 feet, for a cost of $464.76.

help meeeeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee

Answers

Answer:

51.85g

Step-by-step explanation:

At t = 25 years,

A(t) = 200e^-0.054t

A(25) = 200(e^-0.054(25))

= 200(e^-1.35)

= 200(0.2592)

= 51.85

What does negative 3 over 8 > −1 indicate about the positions of negative 3 over 8 and −1 on the number line? (4 points) a is located on the right of 0, and −1 is located on the left of 0 b is located on the left of 0, and −1 is located on the right of 0 c is located on the left of −1 d is located to the right of −1

Answers

The expression - 3/8 > - 1 indicates that the value - 3/8 lies between - 1 and 0 on the number line.

It is located to the left of zero on the number line.

What is a number line?

A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

Given, An expression - 3/8 > - 1.

This indicates that the value - 3/8 lies between - 1 and 0 on the number line.

It is located to the left of zero on the number line.

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write an equation for a line parallel to y = − 2 x − 3 and passing through the point (3,-3)

Answers

Equation of line parallel to y = − 2 x − 3 and passing through the point (3,-3) is y = -2x + 3.

When two lines are called parallel?

Two lines are parallel lines if they do not intersect.

The slopes of the lines are the same.

f(x)= mx + b and g(x)= nx + c are parallel if m = n.

According to the given question:

Given equation of line is y = −2x − 3

If the new line is parallel, then it will have the same slope.

y = -2x + b

Now this line passes through the point (x,y) = (3,-3) so put in the x and y values into the equation above, solve for b

-3 = -2(3) + b

b = 3

Therefore the required equation of line is

y = -2x + 3

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Watch help video
Kiran invested $1,500 in an account paying an interest rate of 81% compounded
continuously. Isaac invested $1,500 in an account paying an interest rate of 7%
compounded daily. After 6 years, how much more money would Kiran have in his
account than Isaac, to the nearest dollar?

Answers

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

Kiran has $191254 more amount than Isaac.

What is compound interest?

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

Kiran:

P = $1500

r = 81%

n = continuously

t = 6 years

A = P [tex]e^{rt}[/tex]

[ e = 2.71828 }

A = 1,500.00 x [tex]2.71828^{0.81\times6}[/tex]

A = $193,536.30

Isaac:

P = $1,500

r = 7%

n = 360

t = 6 years

A = 1500 [tex](1 + 0.07/360)^{360\times6}[/tex]

A = $2,282.85

Now,

The difference between Kiran's and Isaac's amount.

= $193,536.30 - $2,282.85

= $191253.45

= $191254

Thus,

Kiran has $191254 more amount than Isaac.

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Find equation of plane pass through points (-2,1,3), (0,4,8) and (-1 ,-1,0)​

Answers

The equation of plane is x + 11y + 7z - 30 = 0

What is equation?

An equation is said to be a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for example, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

Let  ( x₁, y₁, z₁ ) ( x₂, y₂, z₂ ) ( x₃, y₃, z₃ ) be the coordinates,

we know that equation of plane is:

[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right][/tex] = 0

( -2, 1, 3 )  ( 0, 4, 8 )  ( -1, -1, 0 )

[tex]\left[\begin{array}{ccc}x+2&y-1&z-3\\0+2&4-1&8-3\\-1+2&-1-1&0-3\end{array}\right][/tex] = 0

[tex]\left[\begin{array}{ccc}x+2&y-1&z-3\\2&3&5\\1&-2&-3\end{array}\right][/tex] = 0

On solving this determinant,

(x+2) (-9+10) - (y-1) (-6-5) - (z-3) (-4-3) = 0

(x+2) - (y-1) (-11) - (z-3) (-7) = 0

x + 2 + 11y - 11 + 7z - 21 = 0

x + 11y + 7z - 30 = 0

Therefore, this is the required equation.

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Solve the application using polynomials

Answers

volume of rectangular prism: length*width*height

length: x+1width: x-2height: x+1

a) V= (x+1)(x-2)(x+1) = (x²-2x+x-2)(x+1) = (x²-x-2)+(x+1) = (x³+x²-x²-x-2x-2) = x³-3x-2

b) if x= 5, V= 5³-3(5)-2 = 125-15-2 = 108cm³

How long will it take 2000 dollars to double if it is invested at 8% interest compounded semi-annually?

Answers

The time it will take the 2000 dollar invested at 8% is t= 9.006468342 years

Compound Interest

Compound interest can be define as the addition of interest on the loan to the principal sum of the deposit.

2 = (1+8%) ^t

where t is the time of the year

2= (1 +8%)^t

2 = (1+8/100)^t

2 =   ( 1 0.8)^t

Take the log of both sides

log 2 = log 1.08^t

log 2 = t log 1.08

Divide both sides by log 1.08

log 2/ log 1.08 = t

t= 9.006468342 years

Therefore, the time it will take the dollar invested at 8% is t= 9.006468342 years

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Maddy is making banana bread. She has 11 bananas. If she uses 3 bananas for each loaf of bread, how many loaves of banana bread can she make?

Answers

Answer: She can make 3 full loaves

Step-by-step explanation: 3 x 3 = 9   3 x 4 = 12 you dont have 12 you only have 11

technically you can make 3 [tex]\frac{1}{3}[/tex] loaves but if you are looking for full loaves you can only make 3

Use close-but-easier numbers to estimate the answer to this problem
78+43

Answers

Answer: 121

Step-by-step explanation:

78+43=121

78+43=121 An easier way is to forget the the ones just add the tens 40+70=110 now add the ones 110+8+3=121 hope that helps

The following are prices for various cars: $22,000, $28,000, $90,000, 22,000, $26,000. What is the median price?

Answers

The required median of the prices of the various cars is $26,000.

What is the median?

When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top half of data.

here,
Arrange the data set in order,
$22,000, $22,000, $26,000, $28,000, $90,000,

Total number = 5 [ odd numbers ]
Median is given as = n + 1 / 2 th term
                             = 5 + 1 / 2 th term
                             = 3 rd term

Thus, as of the given condition, the median of the prices is $26,000.

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PLEASE HURRRY PLSSSSS I NEED ANSWERSSSS

Answers

The investments arranged from the least to the greatest amount of interest are:

Investment of $1600 at 5% interest rate for 8 years.

Investment of $1600 at 7% interest rate for 8 years.

Investment of $1600 at 7% interest rate for 12 years.

What is simple interest?

Simple interest is the formula that is used to determine the interest that is earned when an amount is investment at an interest rate over a number of years.

Interest earned with simple interest increases linearly over the investment period. This means that the interest earned each year of the investment period is a constant amount.

Simple interest = amount invested x interest rate x year

Simple interest = $1600 x 0.07 x 8 = $896

Simple interest = $1600 x 0.05 x 8 = $640

Simple interest = $1600 x 0.07 x 12 = $1344

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Please help with this question

Answers

Answer:

n=24.90

Step-by-step explanation:

Martina’s chocolate bar. Is 67% cocoa. If the weight of the chocolate bar is 82 grams, how many grams of cocoa does it contain? Round to the nearest tenth

Answers

81*0.66 = 53.46g ≈ 53.5g of cocoa. ANSWERS

If southbrook middle schoolbhas 850 students then how mamy students participate in the various number of sports

Answers

Answer:

Step-by-step explanation:

67876567

3. Find the x-intercept of y = 3.
(3,0)
(0,3)
(3,3)
O no x-intercept

Answers

Answer:

3

Step-by-step explanation:

x-y =3

To find the x intercept, set y=0

x-0 =3

x=3

Step-by-step explanation:

Answer:

x=(3,0)

Step-by-step explanation:

hope this helps

What is the value of x?
Enter your answer in the box.

x =

Answers

The side length RQ of the triangle QRT that is 'x' will be 4 units.

What is trigonometry?

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

In triangle ΔRST, the side RT is given by the sine of angle 60°. Then we have

sin 60° = (2√3) / RT

(√3)/(2) = (2√3) / RT

RT = 2 x 2(√3) / (√3)

RT = 4

In triangle ΔQRT, the side QR is given by the tangent of angle 45°. Then we have

tan 45° = RQ / RT

1 = x / 4

x = 4

The side length RQ of the triangle QRT that is 'x' will be 4 units.

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an ice cream factory makes 180 quarts of ice cream in 2 hours.how many quarts willl be made in 12 hours? please send help

Answers

It would be 1,080 quarts of ice cream made after 12 hours

taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco taco

Answers

The value of R, given the equation, can be found to be $ 786. 99.

How to find the value of R?

To find the value of R, solve the operations in sequences:

First sequence:

= 0.052 / 4

= 0.013

Second sequence:

= ( 1 + 0. 052 / 4) ²⁴ - 1

= 0.363410670624455519270956581199

Solving for R then gives:

= 22,000 x ( 0.013 / 0.363410670624455519270956581199)

= $786.99

In conclusion, the value of R without rounding intermediate values when rounded to the nearest hundredth is $ 786. 99.

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38.
a. Find the bearing from O to A.
b. Find the bearing from O to B.
c. Find the bearing from O to C.
d. Find the bearing from A to O.

Answers

Answer:

a.  335°

Step-by-step explanation:

Bearing: The angle (in degrees) measured clockwise from north.

a.  The bearing from O to A

Measure the angle from the positive y-axis, clockwise to point A.

Angles on a straight line sum to 180°, so the angle between the negative x-axis and point A is (180° - 115°).

Bearing = 270° + (180° - 115°) = 335°

b.  The bearing from O to B

Measure the angle from the positive y-axis, clockwise to point B.

Bearing = 270° - 48° = 222°

c.  The bearing from O to C

Measure the angle from the positive y-axis, clockwise to point C.

Bearing = 180° - 27° = 153°

d.  The bearing from A to O

Measure the angle clockwise from north of point A to point O.

Bearing = 180° - 25° = 155°

PLEASE HELP!!!!!!!!! This assignment is already late and last day to turn in is TOMORROW!!!!!!!!!

Answers

The value of n and m are 110 and 20 respectively if the equations are 2n + 3m = 280 and 2n + 5m = 320.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Two linear equations are:

2n + 3m = 280

2n + 5m = 320

Using the elimination method:

Because the coefficient for n is the same in both equations

-2m = - 40

m = 20

n = 110

Thus, the value of n and m are 110 and 20 respectively if the equations   are 2n + 3m = 280 and 2n + 5m = 320.

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5. At a restaurant, the total bill and the percentage of the bill left as a tip is
represented in the scatter plot. (Lesson 3-4)
Percentage
32
28
24
20
16
12
8
4
4 8 12 16 20 24 28 32
Total

The best fit line is represented by the equation y = -0.632x + 27.1, where x
represents the total bill in dollars, and y represents the percentage of the
bill left as a tip.
a. What does the best fit line estimate for the percentage of the bill left as
a tip when the bill is $15? Is this reasonable?
b. What does the best fit line predict for the percentage of the bill left as a
tip when the bill is $50? Is this reasonable?

Answers

a) The estimate for the percentage of the bill left as a tip with a bill of $15 is of 17.62%, which is reasonable.

b) The estimate for the percentage of the bill left as a tip with a bill of $50 is a non-reasonable -4.5%.

What is the line of best fit?

The line of best fit in this problem is defined as follows:

y = -0.632x + 27.1.

In which the variables are defined as follows:

x is the total bill, in dollars.y is the percentage of the total bill left as a tip.

Hence, for a bill of $15, the estimate is found replacing x by 15, as follows:

y = -0.632(15) + 27.1 = 17.62%.

Which is reasonable, as it is a positive number.

For a bill of $50, the estimate is obtained as follows:

y = -0.632(50) + 27.1 = -4.5%.

Which is not reasonable, as it is a negative number.

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For the two numbers listed, find two factors of the first number such that their product is the first number and their sum is the second number.

−6, −5

Answers

Answer:

-6, 1

Step-by-step explanation:

Possible factors for -6:

1, -6

-1, 6

2, -3

-2, 3

Sums:

1 + -6 = -5  ==> this is it!!

-1 + 6 = 5

2 + -3 = -1

-2 + 3 = 1

Robi has 45 toy cars and 63 motorbike toys. The comparison between the difference and the number of toys that Robi has is​

Answers

Answer:

the answer is 18!

Step-by-step explanation:

63-45 = 18

just subtract the two values to get your answer. the difference is 18.

Hope this helps!

HELPPPPP!!!!!!!! 30 POINTSSSS!!!!!
What is the correlation of the data shown?

A. -1
B. -0.5
C. 1
D. 0

Answers

The correlation of the data shown on the graph is 1

How to determine the correlation?

In this question, the graph represents the given parameter

From the graph, we have the following observations

The x values is on the horizontal axisThe y values is on the vertical axisAs the x values increase, the y values increase (approximately)

When the change (increase) in the x values causes a change (increment) in the y values, then the correlation is positive

From the list of options, we have

-1, -0.5 and 0 are not positive values

This means that the correlation is (c) 1

Hence, the correlation of the data is 1

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A line intersects the points (4, 12) and (-1, -3). What is the slope of the line in simplest form? m = [?]​

Answers

Answer: m = 3

Step-by-step explanation:

-3 - 12 = -15
-1 - 4 = -5
[tex]\frac{-15}{-5}[/tex] = 3

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How did Bandura and Walters resolve the apparent paradox of children punished for aggressive behavior becoming more aggressive?-they pointed out that almost all parents use very light physical punishment-they pointed out that genetic predispositions to aggression override imitation-they pointed out that the measures of parental punishment and child aggression are highly unreliable-they pointed out that parents who use physical punishment with their children are providing their children with aggressive models a client with suspected inhalation anthrax is admitted to the emergency department. which action by the nurse takes the highest priority? a user receives a phone call from a person who claims to represent it services and then asks that user for confirmation of username and password for auditing purposes. which security threat does this phone call represent? What is an equation of the line that passes through the point (8, 0) and is parallel tothe line x + y = 5? Which of the following is a good piece of advice to give to individuals who have multiple bosses in a matrix structured organization?a) Make sure all managers are familiar with your overall workload.b) Keep conflicts you are experiencing to yourself.c) Avoid situations where you have multiple managers as they produce more conflict than benefits.d) Set a schedule so that you work with one manager on certain days and the other manager on the other days. hearth company uses the units-of-production method to estimate depreciation. the company purchased a new machine for $50,000 that will produce an estimated 350,000 units over its useful life. the estimated residual value of the machine is $3,000. what is the depreciation rate per unit? professionals are required to deliver services but the competency of the services is never an issue. true false when 11.8 g of c8h18 underwent a combustion reaction with 8.84 g of o2, it produced 1.15 g of h2o. balance the reaction and answer the following questions. what is the mass (in g) of remaining oxygen gas? the iranians ruled for a thousand years and did not need us arabs even for a day. we have been ruling then for one or two centuries and cannot do without them for an hour A display that needs to be present throughout the entire game should be small enough that it doesnt interfere with the game itself but large enough that the user is able to do what? A. read the display easily out of the corner of their eye B. see it from across the room if need be C. see it and understand what its trying to communicate D. move their avatar over the display box without interfering with the text design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used. when conducting a one-way independent anova with three levels on the independent variable, an f-ratio that is large enough to be statistically significant tells us: