If your running a race and you passed the person in second place what place would you be in now?

Answer:

The least possible height of the flagpole is 227.33 inches and the greatest possible height is 248 inches

Step-by-step explanation:

Given

See attachment for the system

Required

Determine the least and greatest heights of the flagpole

From the question, we have:

[tex]AB = 7\ to\ 7\frac{1}{2} ft[/tex]

[tex]BE =62in[/tex]

[tex]BC = 20\ to\ 21ft[/tex]

Convert AB and BC to feet (multiply by 12)

[tex]AB = 84in\ to\ 90in[/tex]

[tex]BC = 240in\ to\ 252in[/tex]

The height of the flagpole is represented as: CD

To calculate CD, we make use of the following equivalent ratios:

[tex]CD : AC = BE : AB[/tex]

Express as fraction

[tex]\frac{CD }{ AC } = \frac{BE }{ AB}[/tex]

Make CD the subject

[tex]CD = \frac{BE }{ AB} * AC[/tex]

From the attachment:

[tex]AC = AB + BC[/tex]

Where:

[tex]AB = 84in\ to\ 90in[/tex]

[tex]BC = 240in\ to\ 252in[/tex]

The possible values of AC are:

[tex]AC = 84 + 240 =324in[/tex]

[tex]AC = 84 + 252 =336in[/tex]

[tex]BC = 90 + 240 = 330in[/tex]

[tex]AC = 90 + 252 =342in[/tex]

So:

[tex]CD = \frac{BE }{ AB} * AC[/tex]

[tex]BE =62in[/tex]

When AC = 324 ; AB = 84

[tex]CD = \frac{62}{84} * 324[/tex]

[tex]CD = \frac{62* 324}{84}[/tex]

[tex]CD = \frac{20088}{84}[/tex]

[tex]CD = 239.14in[/tex]

When AC = 336 ; AB = 84

[tex]CD = \frac{62}{84} * 336[/tex]

[tex]CD = \frac{62* 336}{84}[/tex]

[tex]CD = \frac{20832}{84}[/tex]

[tex]CD = 248in[/tex]

When AC = 330 ; AB = 90

[tex]CD = \frac{62}{90} * 330[/tex]

[tex]CD = \frac{62 * 330}{90}[/tex]

[tex]CD = \frac{20460}{90}[/tex]

[tex]CD = 227.33in[/tex]

When AC = 342 ; AB = 90

[tex]CD = \frac{62}{90} * 342[/tex]

[tex]CD = \frac{62* 342}{90}[/tex]

[tex]CD = \frac{21204}{90}[/tex]

[tex]CD = 235.6in[/tex]

So, we have:

[tex]CD = 239.14in[/tex]

[tex]CD = 248in[/tex]

[tex]CD = 227.33in[/tex]

[tex]CD = 235.6in[/tex]

The least possible height of the flagpole is 227.33 inches and the greatest possible height is 248 inches

The given range of the length of the shadow and distance of the student

from the tree of between 7 and [tex]7\frac{1}{2}[/tex] feet and 21 and 22 feet gives;

The greatest possible height of the flagpole in feet ≈ 21.8 feet

The least possible height of the flagpole in feet = 19.3 feet

Height of the student = 62 inches = [tex]5\frac{1}{6}[/tex] feet

Distance of the flagpole to the student = 21 to 22 feet = 252 to 264 inches

Length of the student's shadow = Between 7 and [tex]\mathbf{7\frac{1}{2}}[/tex] feet = Between 84 and 90 inches

Required:

The least and greatest height of the flagpole.

Solution;

By using similar triangles formed by the student and the flagpole, we

have;

[tex]\dfrac{Height \ of \ the \ student}{Length\ of \ the \ student's \ shadow} = \mathbf{\dfrac{Height \ of \ the \ flagpole}{Length\ of \ the \ flagpole's \ shadow}}[/tex]

Which gives;

[tex]\dfrac{62}{84 \ or \ 90} =\mathbf{ \dfrac{h}{252+(84 \ or \ 90) \ or \ 264 + (84 \ or \ 90)}}[/tex]

Based on the method of cross multiplication, h will be the greatest

possible value, when we have, the largest possible value for the

denominator on the right hand side and the least possible value for the

denominator on the left hand side of the equation, and vice versa.

Which gives;

[tex]\dfrac{62}{90} = \mathbf{\dfrac{h_{min}}{252 + 84}}[/tex]

[tex]h_{min} \ in \ feet = \mathbf{\dfrac{\dfrac{62}{90} \times (252 + 84)}{12}} \approx 19.3[/tex]

The least possible height of the flagpole in feet, [tex]h_{min}[/tex] ≈ 19.3 feet

Similarly. we have;

[tex]\dfrac{62}{84} = \mathbf{\dfrac{h_{max}}{264 + 90}}[/tex]

Which gives;

[tex]h_{max} = \dfrac{62}{84} \times (264 + 90) \approx 261.3[/tex]

[tex]h_{max} \ in \ feet \approx \dfrac{261.3}{12} \approx\mathbf{ 21.8}[/tex]

The greatest possible height of the flagpole in feet, [tex]h_{max}[/tex] ≈ 21.8 feet

Learn more about the characteristics of similar triangles here:

https://brainly.com/question/10703692

Add the ratios together:

5 + 2 + 1 = 8

Divide the length of NQ by that:

24/8 = 3

Multiply the ratio of NO by that/l

The ratio of NO is 5, 5 x 3 = 15

NO = 15

Answer:

1.one solution

2.no solution

3.ifinitly many

Step-by-step explanation:

Answer:

1, one solution

2, no solution

3, infinitely many solution

Answer:

$10

Step-by-step explanation:

1000 divided by 100 = 10

so $10  is the answer

then 100 tickets = $1000

PLEASE MARK BRAINLIEST AND GIVE 5 STARS.

Answer:

j = $1.05

Step-by-step explanation:

($12.48 - $1.98) / 10 = j

(Total cost - popcorn cost) / number of juice boxes = cost of one juice box

Answer:

10j+1.98=12.48

j= 1.05

Step-by-step explanation:

Answer:

Step-by-step explanation:

Required equation:

Correct choice is C

Answer:

57.5 students

Step-by-step explanation:

Given that

The 30% students would be arrived by private car

So 15% would be travelled by taxi

And, the remaining i.e. 55% would be walk to school

Since the population of the school is 230

So by car, the students would be

= 230 × 0.30

= 69

By walk, the students would be

= 230 × 0.55  

= 126.50

Now the more students would be

= 126.50 - 69

= 57.5 students

Answer:

[tex]g = 15 - \frac{1}{30}m[/tex]

Step-by-step explanation:

Given

[tex]Initial = 15[/tex]

[tex]mpg = 30[/tex] --- miles per gallon

Required

Determine an equation for this trip

First we have to get the number of gallons per mile from [tex]mpg = 30[/tex]

[tex]\frac{miles}{gallon}=30[/tex]

Inverse the equation

[tex]\frac{gallon}{miles}=\frac{1}{30}[/tex]

This represents the rate in gallons/mile

So, the equation is:

[tex]g= Initial - Rate * m[/tex]

[tex]g= 15 - \frac{1}{30} * m[/tex]

[tex]g= 15 - \frac{1}{30}m[/tex]

Answer:

45+28

Step-by-step explanation:

the

Answer:

9a²-12ab³+4b⁶

Step-by-step explanation:

use FOIL to solve

f-first

o-outer

i-inner

l-last

Answer: 4b^6 - 12ab^3 + 9a^2

yw

Answer:

10 in by 48 in

Step-by-step explanation:

The volume (V) of a rectangular solid is calculated as

V = Ah ( A is the area of the base and h the height )

Here h = 3 and V = 1440 , then

3A = 1440 ( divide both sides by 3 )

A = 480 in²

The area of a rectangle = length × breadth

From the give options

10 × 48 = 480 ← is the only option

Answer:

speed of bus = 33 mi/hr

speed of motorcycle = 31 mi/hr

Step-by-step explanation:

Let the speed of the motorcycle be x mi/h.

Now, we are told that the bus averages 2 mi/hr faster than the motorcycle. Thus, speed of bus = (x + 2) mi/hr

Formula for time is; t = distance/speed

Since distance covered by bus is 165 miles, then t_bus = 165/(x + 2)

Since distance covered by motorcycle is 155 miles, then t_motorcycle = 155/x

We are told that the bus and the motorcycle used the same time to cover their respective distances. Thus;. t_bus = t_motorcycle

Thus;

165/(x + 2) = 155/x

Cross multiply to get;

165x = 155(x + 2)

165x = 155x + 310

165x - 155x = 310

10x = 310

x = 310/10

x = 31 mi/hr

Then speed of bus = 31 + 2 = 33 mi/hr

Answer:

A=542

Step-by-step explanation:

none, sorry

Answer: 542 ft.^2

Steps:

2(l*w) + 2(l*h) + 2(w*h)

2(13*7) + 2(13*9) + 2(7*9)

2(91) + 2(117) + 2(63)

182 + 234 + 126

=542

Answer:

1/5

*I'm sorry if I got it wrong, but if not I hope this helps!*

Step-by-step explanation:

since 3/5 of the students are girls, and 1/3 of the girls have blonde hair, to find what fraction of all the girls have blond hair, we would multiply 3/5(1/3)

3/5(1/3)=3/15=1/5

therefore, 1/5 of all the students are girls with blond hair

Answer: t=40

Step-by-step explanation:

To work out t on its own you have to do the inverse of takeaway which is add so it is 15+25=40.

Answer:

784

Step-by-step explanation:

you take the 49 and times is by 16

there are 4 sides

Answer:

$17.65

Step-by-step explanation:

hope this helped!!

Answer:

What is your question?

______________________________

Please rate my answer and say thanks!

Answer:

Step-by-step explanation:

You can find the cube root of 2 and multiply it by the 6th root of 5.

cube root(2) = 2^(1/3) = 1.2599

6th root of (5) = 0.7418

Product = 1.2599 * 0.7418 = .9346

You need a key that will do fractional powers. Look around on your calculator for ^ that key y^x  or x^y.

Using one of those keys, you would put in 2 ^ 0.33333333 =

If your calculator does not have this key (I recommend you buy one that does. They are less than 10 dollars), then you can use the calculator on windows.

Answer: v=Lwh (volume = length x width x height)

Step-by-step explanation: it would be the first answer, to find volume, it’s finding the amount of space in a 3D object, kind of like area, but multiply the height to the area (bxh)

Answer:

m<ADC = 107

Step-by-step explanation:

You need to know three things to solve this problem.

1) Opposite angles of an inscribed quadrilateral are supplementary.

2) The measure of an inscribed angle is half the measure of its subtended arc.

3) The sum of the measures of all the arcs of a circle is 360 deg.

From 1) we get:

m<A + m<C = 180

72 + m<C = 180

m<C = 108

From 2) we get:

m<C = (1/2)m(arc)BAD

108 = (1/2)[m(arc)AB + m(arc)AD]

216 = m(arc)AB + 122

m(arc)AB = 94

From 3) we get:

m(arc)AB + m(arc)BC + m(arc)CD + m(arc)DA = 360

94 + 120 + m(arc)CD + 122 = 360

m(arc)CD = 24

From 2) we get:

m<ADC = (1/2)m(arc)ABC

m<ADC = (1/2)[m(arc)AB + m(arc)BC]

m<ADC = (1/2)[94 + 120]

m<ADC = 107

Answer:

$36

Step-by-step explanation:

60% of 90 is 54

With $54 off, you'd only pay $36

Answer:

Step-by-step explanation:

Length of the cuboid = ((2x + 5) cm

Width of the cuboid = (3 - x) cm

Height of the cuboid = (2x + 5) cm

Since, volume of the cuboid = Length × Width × Height

                                               = (2x + 5)(3 - x)(x + 1)

                                               = [2x(3 - x) + 5(3 - x)](x + 1)

                                               = (6x - 2x² + 15 - 5x)(x + 1)

                                               = (-2x² + x + 15)(x + 1)

                                               = x(-2x² + x + 15) + 1(-2x² + x + 15)

                                               = -2x³ + x² + 15x - 2x² + x + 15

                                               = -2x³ - x² + 16x + 15

                                               ≈ 15 + 16x - x² - 2x³

Answer:

good luck, i hope this helps :)

Answer:

F

Step-by-step explanation:

Answer:

16,920,000 people speak Spanish at home in the United States, which represents 6.48% of the country's population.

Step-by-step explanation:

Given that approximately 261,000,000 people live in the United States, and of these people 37,600,000 speak a language other than English at home, of which over 45 percent speak Spanish, to determine the number of people who speak Spanish in the United States, the following calculation has to be done:

37,600,000 x 0.45 = X

16,920,000 = X

261,000,000 = 100

16,920,000 = X

16,920,000 x 100 / 261,000,000 = X

6.48 = X

Thus, some 16,920,000 people speak Spanish at home in the United States, which represents 6.48% of the country's population.

Answer:

= 6+8+6+6+8+6+3+8++3+8

10

= 62

10

= 6.2

Step-by-step explanation:

thanks pls mark as brainliest

yes u can get help what is it?

Answer:

Yeah i can  help you ,but the picture u have uploaded is blank.

pls upload again.

Step-by-step explanation:

Pls mark BRAINLIEST