A telephone pole is 54 feet tall. A guy wire runs 83 feet, from point A at the top of the telephone pole, to the ground at point B. The base of the telephone pole is at point C. Triangle ABC is a right triangle.

How far from the base of the telephone pole, to the nearest tenth of a foot, is the guy wire secured to the ground at point B?

Step-by-step explanation:

The 'solution ' is the point where the two lines intersect :    ( 0,-1)

The total amount in the account when turning 60 years is A = $ 11,13,706.08

Given data ,

A savings account with an interest rate of 6% per year and you aren't adding any additional funds in the future

Now , you make $80,000 within the year you turn 60

So , the number of years = 60 - 16 = 44 years

And , from the compound interest , we get

A = P ( 1 + r/n )ⁿᵇ

On simplifying , we get

Where A is the final amount, P is the initial amount (which is 0 in this case), r is the annual interest rate (6% or 0.06), n is the number of times the interest is compounded per year (let's assume it is compounded monthly, so n=12), t is the time in years (44 years from age 16 to age 60).

A = 80,000 ( 1 + 0.06/12 )¹²ˣ⁴⁴

A = $ 11,13,706.08

Hence , the amount in account is A = $ 11,13,706.08

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The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

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The ratios for the rectangles and the ovals is 4 : 3

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

Rectangle = 4

Oval = 3

The ratio can be represented as

Ratio = Rectangle : Oval

When the given values are substituted in the above equation, we have the following equation

Rectangle : Oval = 4 : 3

The above ratio cannot be further simplified

This means that the ratio expression would remain as 4 : 3

Hence, the solution is 4 : 3

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For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.

We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).

First, we need to find the value of cosA and sinB:

Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:

cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61

Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:

hypotenuse = √(4² + 3²) = 5

sinB = opposite/hypotenuse = 4/5

Now we can substitute these values into the formula:

cos(A-B) = cosA cosB + sinA sinB

= (60/61)(3/5) + (11/61)(4/5)

= 180/305 + 44/305

= 224/305

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The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.

We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.

To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:

First year: (1, 30)

Fourth year: (4, 120)

The slope, m, of the line can be calculated using the formula:

m = change in y / change in x = (120 - 30) / (4 - 1)

m = 90 / 3

m = 30

The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:

30 = 30(1) + b

b = 0

Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:

y = 30x

or

f(t) = 30t [where t represents the number of years.]

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Answer:

  y = -10·sin(πt/5) +12

Step-by-step explanation:

You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.

The general form of the equation will be ...

  y = A·sin(2πt/T) + B

where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.

We assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:

  B = 2 + 10 = 12

The scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...

  A = 10

The period (T) is given as 10 seconds.

Putting these parameters together gives ...

  y = -10·sin(2πt/10) +12

  y = -10·sin(πt/5) +12

__

Additional comment

We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.

Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.

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The volume of cylinder which is having radius as 5 units and height as 11 units, is 863.5 cubic units.

A "Cylinder" is a 3-dimensional geometric shape that consists of a circular base and a curved surface which extends up from base to fixed height.

The volume(V) of a cylinder is the amount of space enclosed by the cylinder, and it is given by the formula : V = πr²h;, where π is = 3.14, "r" denotes radius of base; "h" denotes the height;

Given that the radius is 5 units and the height is 11 units,

Substituting the values,

We get,

V = π × (5)² × (11);

V = 275π cubic units;

V = 275×3.14 = 863.5 cubic units;

Therefore, the required volume is = 863.5 cubic units.

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The given question is incomplete, the complete question is

If radius is 5 units, and height is 11 units, Find the Volume of the Cylinder.

Answer:

6 1/243

Step-by-step explanation:

6 goes into 1459, 243 times

243*6=1458

1459-1458=1

So there is a remainder of 1

So the answer would be 6 1/243

Answer:

1 1/6 metre

Step-by-step explanation:

1/3 pink + 5/6 purple

To add, we need to get a common denominator

1/3 *2/2 = 2/6

2/6 + 5/6

7/6

Change from an improper fraction to a mixed number

1 1/6 metre

The equation of the Damari's investment is B(x) = 30000 * 1.03ˣ

Damari's investment

Given that

Initial value, a = 30000

B(3) = 32306.72

The function is calculated as

B(x) = a * bˣ

Using B(3), we have

30000 * b³ = 32306.72

So, we have

b³ = 1.077

Take the cube root of both sides

b = 1.03

So, we have

B(x) = 30000 * 1.03ˣ

So, the function is B(x) = 30000 * 1.03ˣ

The boat of Sky's family

Here, we have

Initial value = 6000

Rate of depreciation = 6%

So, the function is

f(x) = 6000 * (1 - 6%)ˣ

So, we have

f(x) = 6000 * (0.94)ˣ

In 2024, we have

x = 2024 - 2021

x = 3

So, we have

f(3) = 6000 * (0.94)³

Evaluate

f(3) = 4983.50

This value is less than the offered value of $5000

This means that Sky's family should take the offer

The rule of the function

Here, we have the graph

From the graph, we have

Initial value, a = 8

Rate, b = 4.8/8

So, we have

Rate, b = 0.6

So, the function is

f(x) = 8 * 0.6ˣ

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8 people didn't use any of the gym pool or track facilities.

The number of people use any facilities need to subtract the total number of people who used at least one facility from the total number of people in the sport centre.

The total number of people who used at least one facility by adding the number of people who used each facility and subtracting the number of people who used two facilities and three facilities:

Total = Gym + Pool + Track - (Gym and Pool) - (Pool and Track) - (Gym and Track) + (Gym and Pool and Track)

Total = 77 + 62 + 65 - 27 - 23 - 31 + 4

Total = 127

The number of people who didn't use any facilities is:

135 - 127 = 8

8 people didn't use any of the gym, pool or track facilities.

The number of individuals who did not utilise any facilities must be subtracted from the total number of individuals who utilised at least one facility.

The total number of individuals who utilised at least one facility is calculated by adding the individuals who utilised each facility and deducting the individuals who utilised two and three facilities:

Total = Fitness Centre + Pool + Track - Fitness Centre and Pool - Fitness Centre and Track - Fitness Centre and Pool and Track

Total = 77 + 62 + 65 - 27 - 23 - 31 + 4

Total = 134-127

= 8

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Answer:

xs7

Step-by-step explanation:

Answer:

he should have subtracted 17 from both sides of the equation

Step-by-step explanation:

x+ 17 = 22

subtract 17 from both sides

X + 17 = 22

-17 -17

x = 5

Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

The circle equation x² + 8x + y² -10y - 32 = 0​ can be graphed using (x + 4)² + (y - 5)² = 73

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

x² + 8x + y² -10y - 32 = 0​

Add 32 to both sides of the equation

This gives

x² + 8x + y² -10y = 32

Group the terms in two's

So, we have

(x² + 8x) + (y² -10y) = 32

When we complete the square on each group, we have

(x + 4)² + (y - 5)² = 16 + 25 + 32

Evaluate the like terms

(x + 4)² + (y - 5)² = 73

Hence, the circle equation can be graphed using (x + 4)² + (y - 5)² = 73

See attachment for the graph

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The x-intercepts, in order from least to greatest, are (2.46, 0) and (5.54, 0).

Use the vertex form of a quadratic function, which is [tex]y = a(x-h)^2 + k,[/tex] where (h, k) is the vertex and "a" is the coefficient of the[tex]x^2[/tex]term. Since the vertex is at (4, 8 1/3), the quadratic function's equation is y = a(x-[tex]4)^2 + 8 1/3.[/tex]

Use the y-intercept to find the value of "a".

The y-intercept is (0,3), so when x=0, y=3.

Plugging these values into the equation above, we get: [tex]3 = a(0-4)^2 + 8 1/3[/tex].

Simplifying, we get 3 = 16a + 25/3, or 9/3 = 16a. Therefore, a = 9/48 or a = 3/16.

To obtain the complete equation, enter the value of "a" into the vertex form equation: [tex]y = (3/16)(x-4)^2 + 8 1/3.[/tex]

To find the x-intercepts, set y = 0 and solve for x.

The equation becomes: [tex]0 = (3/16)(x-4)^2 + 8 1/3[/tex].

Subtracting 8 1/3 from both sides, we get: [tex]-8 1/3 = (3/16)(x-4)^2[/tex]. Multiplying both sides by -1, we get: [tex]8 1/3 = (3/16)(x-4)^2.[/tex]

Take the square root of both sides to isolate[tex]x-4: \sqrt{(8 1/3) } = \sqrt{((3/16)(x-4)^2)}[/tex] Simplifying,

we get: [tex]\sqrt{(25/3)} = (3/4)(x-4).[/tex]

Solving for x, we get two solutions: [tex]x = 4 + 4\sqrt{(3)/3 } or x = 4 - 4\sqrt{(3)/3 }[/tex]

Sort the answers in order of best to worst. The x-intercepts are (2.46, 0) and (5.54, 0) because the first answer is around 5.54 and the second solution is roughly 2.46.

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The calculated number of plants the flower bed can contain is 120

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

Dimensions = 16 m by 9 m

So, the area of the flower bed is

Area = 16 * 9

Evaluate

Area =  144

Also, we have

Each plant requires a space of 1.2m x 1m?

This means that

Plant area = 1.2 * 1

Plant area = 1.2

So, we have

Plants = 144/1.2

Evaluate

Plants = 120

Hence, the number of plants is 120

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Answer:

Step-by-step explanation:

To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.

The area of the flower bed is calculated by multiplying its length and breadth.

So, the area of the flower bed is 16m x 9m = 144 sq.m.

Each plant requires a space of 1.2m x 1m = 1.2 sq.m.

Therefore, the number of plants that can be planted in the flower bed is:

144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.

So, you can plant 120 plants in the rectangular flower bed.

About 88.49% of cellphone plans have charges that are less than $83.60.

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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The difference in temperature between Rome and Munich is given as follows:

6ºC.

The difference in temperature between Rome and Munich is given by the subtraction of Rome's temperature by Munich's temperature.

The bar graph in the context of this problem gives the temperature for each town.

From the bar graph given by the image presented at the end of the answer, the temperatures for Rome and Munich are given as follows:

Hence the difference in temperature between Rome and Munich is given as follows:

11 - 5 = 6ºC.

The graph is given by the image presented at the end of the answer.

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The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]

Cross-multiplying, we get:

[tex]$AB^2 = BC \cdot AD$[/tex]

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]

Cross-multiplying, we have:

[tex]$AC^2 = BC \cdot AD$[/tex]

Now, we can substitute the derived expressions into the original equation:

[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]

It was made possible by cross-product property.

Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

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Answer:

To convert square millimeters to square centimeters, we need to divide the area in square millimeters by 100 (since there are 100 square millimeters in a square centimeter).

So, the area of the top of Katrina's laptop in square centimeters would be:

57,000 mm² ÷ 100 = 570 cm²

Therefore, the area of the top of Katrina's laptop in square centimeters is 570 cm².

According to the information, there are thousands of different lunch options in this restaurant.

To calculate the number of different lunches in the restaurant we must carry out the following mathematical procedure. We must multiply the different options as shown below:

4 green options x 5 protein options x 8 vegetable options x 4 extra options x 6 topping options = 4 x 5 x 8 x 4 x 6 = 4,800 different lunch options.

Based on the above, we can infer that 4,800 different lunch options can be created with the available ingredients.

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The condition that will prove the two triangles similar is

side JL = 8 * side ZX

angle L = angle Z

Similar triangles are  triangles which have the  similar shape however not necessarily the equal size. More officially, two triangles are comparable if their corresponding angles are congruent and their corresponding aspects are in proportion.

This means that if we had been to scale one triangle up or down uniformly, the ensuing triangle could be much like the original triangle.

In the figure, the scale is 8

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The percentage of refrigerators that have lives between 11 years and 18 years is approximately 83.01%.

The values of 11 years and 18 years using the given mean and standard deviation, and then find the area under the standard normal curve between those two standardized values.

First, we standardize the value of 11 years:

z1 = (11 - 14) / 2.5 = -1.2

Next, we standardize the value of 18 years:

z2 = (18 - 14) / 2.5 = 1.6

Now we need to find the area under the standard normal curve between these two standardized values.

We can use a standard normal table or calculator to find this area.

Using a standard normal table, we can find the area between z = -1.2 and z = 1.6 by finding the area to the left of z = 1.6 and subtracting the area to the left of z = -1.2:

Area = P(-1.2 < z < 1.6) = P(z < 1.6) - P(z < -1.2)

Looking up these values in the standard normal table, we find:

P(z < 1.6) = 0.9452

P(z < -1.2) = 0.1151

Substituting these values, we get:

Area = 0.9452 - 0.1151 = 0.8301

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Step-by-step explanation:

40 :100        yellow to purple,  divide both sides by 20

2:5

Answer:

the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.

Step-by-step explanation:

Hope it helps.

The graph will look like a circle centered at (2, 1) with radius 3.

To graph the equation [tex]x^2 - 4x + y^2 - 2y - 4 = 0[/tex]  by completing the square, we need to rearrange the terms as follows:

[tex](x^2 - 4x + 4) + (y^2 - 2y + 1) = 9[/tex]

This can be simplified to:

[tex](x - 2)^2 + (y - 1)^2 = 3^2[/tex]

So the equation represents a circle with a center at (2, 1) and a radius 3. To graph the circle, we can plot the center point (2, 1) and then draw a circle with radius 3 around that point.

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a. The first term of the arithmetic sequence is 12.

b. The value of n for which the nth term is -33 is 16.

c. The common difference of the arithmetic sequence is -3.

a. The first term, u1, can be found by substituting n=1 into the given formula for the nth term:

u1 = 15 - 3(1) = 12

b. To find the value of n for which the nth term is -33, we set the formula for the nth term equal to -33 and solve for n:

un = 15 - 3n = -33

Adding 3n to both sides, we get:

15 = -33 + 3n

Adding 33 to both sides, we get:

48 = 3n

Dividing both sides by 3, we get:

n = 16

c. The common difference, d, is the difference between any two consecutive terms of the sequence. To find d, we can subtract any two consecutive terms, such as u2 and u1:

u2 = 15 - 3(2) = 9

u1 = 15 - 3(1) = 12

d = u2 - u1 = 9 - 12 = -3

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Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =[tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  [tex]$36.34 + $26.03[/tex]

= [tex]$62.37[/tex]

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Answer:

im an expert

Step-by-step explanation: