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

Answer: The answer is about 57.5

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

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

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.

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

To learn more about simple interest, please check: https://brainly.com/question/27328409

#SPJ1

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

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.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ1

Answer:

n=24.90

Step-by-step explanation:

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.

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.

Learn more about compound interest here:

https://brainly.com/question/13155407

#SPJ1

Answer: 121

Step-by-step explanation:

78+43=121

Answer: m = 3

Step-by-step explanation:

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

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

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.

Learn more about medians here:
https://brainly.com/question/28060453
#SPJ1

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

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.

Find out more on values at https://brainly.com/question/12307521

#SPJ1

Answer:

Step-by-step explanation:

67876567

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

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

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%.

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:

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.

More can be learned about a line of best-fit at https://brainly.com/question/29613968

#SPJ1

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

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.

The correlation of the data shown on the graph is 1

In this question, the graph represents the given parameter

From the graph, we have the following observations

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

Read more about correlation at

https://brainly.com/question/16355498

#SPJ1

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

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.

To know more about equation of plane visit to:

https://brainly.com/question/17013160

#SPJ9

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

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.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

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

To know more about parallel lines visit

https://brainly.com/question/13228195

#SPJ1

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!

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°).

b.  The bearing from O to B

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

c.  The bearing from O to C

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

d.  The bearing from A to O

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

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

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

Learn more about compounded semi-annually here: https://brainly.com/question/28020457

#SPJ1

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:

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.

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)

  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.

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.

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.

learn more about number line here :

https://brainly.com/question/13425491

#SPJ1