From the top of a lighthouse, the angles of depression to the top and bottom of a flagpole are 23° and 42°, respectively. If the flagpole is 75 feet from the lighthouse, how tall is the pole? [Round your answer to the nearest tenth of a foot. Type in the number only.]

Answer:

Below

Step-by-step explanation:

3% loss means 97% (.97 in decimal ) remains

after 2 years :

 27 900 ( .97)^2 = £  26251 .11

The number of acres that can be planted per pound of seed is 0.16.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

32 pounds = 5-acre field

Divide 32 into both sides.

1 pound = 5/32 acre field

1 pound = 0.16 acre field

Thus,

0.16-acre field can be planted per pound of seed.

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Answer:

Step-by-step explanation: infinity or undefined.

Answer:

here is your answer = 56.7m

The size roll which is the better value is $1.17 per ounce.

To determine which size roll is the better value, we need to compare the price per ounce of each roll.

To find the price per ounce of the 7-ounce roll, we divide the total cost by the number of ounces: $8.33 ÷ 7 ounces = $1.19 per ounce.

To find the price per ounce of the 16-ounce roll, we divide the total cost by the number of ounces: $18.72 ÷ 16 ounces = $1.17 per ounce.

Since $1.17 per ounce is less than $1.19 per ounce, the 16-ounce roll is the better value. It is cheaper per ounce than the 7-ounce roll.

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Answer:

  b)  250,000

Step-by-step explanation:

You want to estimate the product of 5,398 and 47 by rounding to the nearest thousand and ten.

Rounding 5,398 to the nearest thousand gives 5000.

Rounding 47 to the nearest ten gives 50.

The product of these is the estimate you want:

  5000·50 = 250,000

There are [tex]7\frac{1}2}[/tex] grams on the scale in all once she added 2 5/6 grams to the scale.

The International System of Units (SI) is the modern form of the metric system and is the most widely used measurement system in the world. It consists of seven basic units of seven basic quantities.

Length is the meter, mass is the kilogram, time is the second, electric current is the ampere, temperature is the kelvin, amount of matter is the mole, and luminosity is the cand. SI also includes derived units such as Newton (force) and Pascal (pressure), which are combinations of base units. SI is the standard measurement system in most countries around the world and is used in scientific, engineering, and commercial applications.

Given,

initial weight = [tex]4\frac{2}{3} = \frac{14}{3}[/tex]

Final weight = [tex]2\frac{5}{6} = \frac{17}{6}[/tex]

Final weight = [tex]\frac{14}{3} + \frac{17}{6} = \frac{45}{6} = \frac{15}{2} = 7\frac{1}{2}[/tex]

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The statement [tex]P\land Q[/tex] in Tautology is represented as P and Q , and the symbol "[tex]\land[/tex]" is called as AND operator .

What is Tautology ?

Tautology can be defined as a compound statement which always results in Truth value. It does not matter what individual part consists of, the result in tautology is always true.

AND Operator : The AND is represented by the symbol "[tex]\land[/tex]". When the 2 simple statements are used in forming the compound statement by using AND operator , then it is called as a conjunction of two statements .

The AND operator returns TRUE value only when both the statements P and Q are TRUE , if any one of the statement is FALSE , then it returns FALSE value .

The given question is incomplete , the complete question is

What is represented by [tex]P\land Q[/tex] in Tautology ?

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The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached

The values of the constants in the sinusoidal function, h = a + b·(c·t) are;

a = 30

b = -20

c = π/1.5

A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.

The diameter of the Ferris wheel = 40 m

The location of the axle above the ground = 30 m

The time it takes to make a complete a rotation = 3 minutes

The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;

h = a + b·cos(c·t)

The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.

Therefore;

At t = 0, h = 30 - 40/2 = 10

h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b

a + b = 10

Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;

a = 30

a + b = 10, therefore;

b = 10 - a

b = 10 - 30 = -20

b = -20

At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50

50 = a + b·cos(1.5·c)

50 = 30 - 20 × cos(1.5·c)

20 × cos(1.5·c) = 30 - 50 = -20

cos(1.5·c) = -1

cos(π) = -1

Therefore; 1.5·c = π

c = π/1.5

The equation is therefore;

h = 30 - 20·cos((π/1.5)·t)

a = 30, b = -20, c = π/1.5

Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel

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I would choose to draw a sample of 20 marbles in order to make a more accurate prediction.

In general, it is generally better to draw a larger sample if you are trying to make a prediction. This is because a larger sample will provide more information and will therefore lead to a more accurate prediction.

For example, imagine that you are trying to predict the proportion of red marbles in a bag based on the samples that you draw. If you draw a sample of 10 marbles, there is a good chance that the proportion of red marbles in your sample will be different from the true proportion of red marbles in the bag.

However, if you draw a sample of 20 marbles, the proportion of red marbles in your sample will be more likely to be closer to the true proportion of red marbles in the bag.

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The height of the tree is closest to 40 feet.

We can use the proportion of similar triangles to determine the height of the tree.

Let h be the height of the tree and s be the length of the shadow cast by the tree.

We know that the height of the building is 60 feet and the length of its shadow is 21.5 feet. So:

(h/s) = (60/21.5)

We also know that the length of the shadow cast by the tree is 18 feet.

So we can substitute that into the proportion and solve for h:

h = (60/21.5) * 18

h = (60*18)/21.5

h ≈ 40

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The measures of the angles of the parallelogram are

The measure of ∠A = 72°

The measure of ∠B = 108°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the measure of ∠A = ( 5y - 3 )°

The measure of ∠C = ( 3y + 27 )°

For a parallelogram , opposite angles are congruent

So , measure of ∠A = measure of ∠C

Substituting the values in the equation , we get

( 5y - 3 )° =  ( 3y + 27 )°

On simplifying the equation , we get

( 5y - 3 ) =  ( 3y + 27 )

Subtracting 3y on both sides of the equation , we get

2y - 3 = 27

Adding 3 on both sides of the equation , we get

2y = 30

Divide by 2 on both sides of the equation , we get

y = 15

So , the measure of ∠A = ( 5y - 3 )°

The measure of ∠A = ( 5 ( 15 ) - 3 ) )°

The measure of ∠A = ( 75 - 3 )°

The measure of ∠A = 72°

Now , for a parallelogram , same-side interior angles (consecutive angles) are supplementary

So , the measure of ∠A + the measure of ∠B = 180°

Substituting the values in the equation , we get

72° + the measure of ∠B = 180°

Subtracting 72° on both sides of the equation , we get

The measure of ∠B = 108°

Hence , the measures of angles of the parallelogram are 72° and 108° respectively

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a = 13.   b^0 = 1,  y=a(1),  13 = a   325 = 13(b)^2    b^2 = 325/13 = 25

b = sqr25 = 5   y=13(5)^x is the exponential equation going through the two given points

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The required point that satisfies each system of equation is (12, -1). Option B is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

To equations are given as,
y = -1/3x + 3 - - - - (1)
y = -3/4x + 8 -- - - - (2)

From equation 1 and 2
-1/3x + 3 = -3/4x + 8
3/4x - 1/3x = 8 - 3
9x - 4x / 12 = 5
5x = 60
x = 12

Now, to evaluate the y ordinate put the above x in equation 1
y = -1/3(12) + 3
y = -4 + 3
y = -1

Thus, the required point that satisfies each system of equation is (12, -1). Option B is correct.

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Answer:

[tex] \sf \: h(-3) = 13[/tex]

Step-by-step explanation:

Given information,

→ h(a) = a² + 4

The value of h(a) when a is -3,

→ h(a) = a² + 4

→ h(-3) = (-3)² + 4

→ h(-3) = 9 + 4

→ [ h(-3) = 13 ]

Hence, required answer is 13.

Answer:

y = -3/2 or -1.5

Step-by-step explanation:

-2/3 + y = -2 1/6

-2 1/6 = -13/6

So, our equation is

-2/3 + y = -13/6

Add 2/3 to both sides

y = -3/2

So, the answer is

y = -3/2 or -1.5

Answer:
Y= -3/2
in decimal form it is -1.5
in mixed number form it is -1 1/2

Step-by-step explanation:

Answer:

y =x+3

y =-x²+[?]

Find the gradient;

What is the formula for the gradient of a graph?

Finding the gradient of a straight-line graph

X2 = 2

Y2 = 7

ΔX = 4

ΔY = 3

θ = 36.869897645844°

Equation of the line:

y = 0.75x + 5.5

When x=0, y = 5.5

When y=0, x = -7.3333333333333

OR

X2 = -6

Y2 = 1

ΔX = -4

ΔY = -3

θ = 216.86989764584°

Equation of the line:

y = 0.75x + 5.5

When x=0, y = 5.5

When y=0, x = -7.3333333333333

Reasonable algorithms expand at polynomial rates or less quickly. Unreasonable algorithms expand exponentially. Even for relatively small problem sizes, the time to solve an unreasonable algorithm increases very quickly.

When the algorithm takes an excessively long time, we say that the number of steps is an exponential function of the size of the input (or some other function that is larger than any polynomial). Simply increasing the input size (n) by 1 doubles the number of steps for an algorithm that runs in 2n time.

Depending on the polynomial, polynomial time can be further decomposed. Algorithms with a runtime of approximately n2 operate in quadratic time. (If the input size is doubled, the number of steps is quadrupled.) In practise, polynomial time algorithms that take longer than cubic (n³) time are uncommon.

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In geometry, a line segment is bordered by two distinct points on a line. Or we can say a line segment is a portion of the line that connects two points.

The length of the line segment does not differ and the distance between them does not change. The units in which a line can be estimated are centimetres, millimetres, meters, inches, or feet.

A closed-line segment has both endpoints, whereas an open-line segment has two endpoints. A line segment that has only one endpoint is known as a half-open line segment.

A line segment with two endpoints P and Q and is denoted by the bar symbol (—).

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4.5 is the length of each part in feet. This can be solved by using the concept of feet.

foot, plural feet, any of a wide range of ancient, medieval, and modern linear measurements (often 25 to 34 cm) based on the length of the human foot and used only in English-speaking nations, where it typically consists of 12 inches or one-third yard.

The foot measured [tex]11^{\frac{1}{42}[/tex] inches in antiquity. The typical man's foot measures 12 inches in length nowadays.

Given that:

The length of the wooden board is given as = 108 inches.

As it is cut in 2 equal parts, it becomes: 108/2 = 54 inches in each

We have to calculate the length of each part in feet, so divide 54 by 12.

As we know,

12 inches = 1 feet

Thus, 54 inches = 54/12 feet = 4.5 feet

So, the length of each part is 4.5 feet.

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My teacher:
- 5'3
- 5.25 ft
- 63 in
- 160 cm

An example of a parent function is [tex]f(x) = x^{2}[/tex], which is the parent function to any quadratic equation.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

Here are a few examples to understand this concept further.

Let us take [tex]f(x) = x^{2}[/tex], which is the parent equation of any quadratic equation. The graph of this parent function is a parabola, which is shown below.

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Answer:

Isosceles triangle

Step-by-step explanation:

Thorough explanation: Through the angles in the triangle ABC.

First, observe that angle ACD = 50 degrees (given)

Since lines AB and DE are parallel to each other,

angle BAC = angle ACD = 50 degrees (by the property of alternate angles)

It is also given that angle ABC = 80 degrees.

Since ABC is a triangle, the sum of the three angles must add up to 180 degrees.

Angle BAC + Angle ABC + Angle ACB = 180 degrees

50 + 80 + Angle ACB = 180

Angle ACB = 180 - 50 - 80

                   = 50 degrees

Since two of the angles, angles ACB and BAC are the same at 50 degrees, triangle ABC is an isosceles triangle. (With sides AB and BC equal)

We label points A=(x1,y1)=(1,1) A = (x1, y1) = (1,1) and A′=(x2,y2)=(3,3) A ′ = (x 2, y 2) = (3,3) to identify the centre of dilation. The centre of dilation's coordinates are then determined using the formula. (xo,yo) ( xo,yo) ( xo,yo )

When the scale factor exceeds 1, the dilation becomes an enlargement. If it falls within the range of 0 and 1, the dilation is a contraction. The point from which the image is dilated is known as the centre of dilation (or point of dilation).

The equation for the circle must be converted into standard form, (x h), in order to be able to determine the centre and radius.[tex](x-h)^2+(y-k)^2=r^2[/tex], where r is the radius and h and k are the coordinates for the centre.

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Yes, a triangle whose sides have lengths 10.2 cm, 5.8 cm and 4.5 cm is possible.

As we know if these sides form a triangle, then

the sum of two sides > the third side

Now, the sum of 10.2 cm and 5.8 cm = 16 cm > 4.5 cm

The sum of 5.8 cm and 4.5 cm = 10.3 cm > 10.2 cm

The sum of 10.2 cm and 4.5 cm = 14.7 cm > 5.8 cm

Here the sum of the two sides is greater than the third side in all three cases.

Therefore a triangle whose sides are 10.2 cm, 5.8 cm and 4.5 cm is possible.

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Answer:

y=[tex]-\frac{1}{4}[/tex] x -6

Step-by-step explanation:

y=mx+b is the slope-intercept formula, m representing the slope and the b representing the y-intercept. Pick two points shown in the graph,

such as (4,-7) and (8,-8) and use what is called rise over run. This means you count the distance between these two points by subtracting the y values (rise) and placing the difference in a fraction over the difference between the x values (run). This is where you get the fraction [tex]\frac{1}{4}[/tex]. Because the slope is going down from left to right, it means that the slope is negative, hence the [tex]-\frac{1}{4}[/tex]. The y-intercept is the point where the line intercepts the y-axis, which in this case is -6, so if you replace the representative letters with the corresponding numbers in the slope-intercept formula, the answer is y=[tex]-\frac{1}{4}[/tex] x -6.

The missing side of a right triangle without using a calculator can be found by using the Pythagoras theorem .

What is Pythagoras Theorem ?

The Pythagoras Theorem states that the square of the hypotnuse (longest side) is equal to the sum of the square of the perpendicular and base .

that means : [tex]Hypotnuse^{2} = Perpendicular^{2} + Base^{2}[/tex]  ;

let the missing side of the right triangle  be the hypotnuse ;

So , missing side can written as :  [tex]Hypotnuse = \sqrt{Perpendicular^{2} + Base^{2}}[/tex] .

For Example : Let the right triangle has sides lengths as perpendicular = 6 and hypotnuse = 10

The length of side "base" is unknown.

So ,  to find length of side b, we put the known values into theorem:

[tex]10^{2} = 6^{2} + Base^{2}[/tex] ;

[tex]base^{2} = 100 - 36[/tex] ;

So , the missing side "base" = 8 ;

Therefore , the missing side without using calculator can be found by the Pythagoras Theorem .

The given question is incomplete , the complete question is

How do you find the missing side of a right triangle without a calculator when the other two sides are given ?

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The equation can be written using the arithmetic operation and the cost is

$32.91.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The cost for each roses, bows and vases are given as $1.99, $0.99 and $7.99 respectively.

Then, the equation for the total cost is as below,

⇒ 3 × 1.99 + 3 × 0.99 + 3 × 7.99 = 32.91

Hence, the equation for the cost is given in the answer part and the cost is $32.91.

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A. 5/10, -6/11, 7/12, -8/13

B. f(n) = n/(n+5)

C. Positive

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.

Here, we have

A. From inspection of the sequence, the pattern is:

Add 1 to the numerator of the previous term.

Add 1 to the denominator of the previous term.

Make every other term negative.

Hence, assuming the pattern continues, the next four terms in the sequence will be:

5/10, -6/11, 7/12, -8/13

B. An explicit formula for an arithmetic sequence allows you to find the [tex]n^{th}[/tex] term of the sequence.

f(1) = 1/6

f(2) = -2/7

We can see that the numerator is the position of the term (n) in the sequence.  So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.

The denominator is 5 more than the position of the term in the sequence.  So when n = 1 the denominator is 1 + 5 = 6, and when n = 2 the denominator is 2 + 5 = 7.

We observe that if the numerator (the value of n) is odd then the term is positive, and if the numerator  (the value of n) is even then the term is negative.

Hence, the rule for the nth term is:

f(n) = n/(n+5)

If n is odd then f(n) is positive.

If n is even then f(n) is negative.

C. 53 is an odd number.

As the function f(n) is positive when n is odd, the sign of f(53) is positive.

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