A point is chosen at random on AK. what is the probability that the point will be on DF?

Answer:

there are no choices

Step-by-step explanation:

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

Answer:

f(x)=5(1.18)^x

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:

Division to get 28

Step-by-step explanation:

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:

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:

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: 2/7 = 8/28

1/4 = 7/28

Therefore Mr Pham mowed more.

8+7 = 15 so 15/28 of lawn has been mowed, therefore 13/28 of the lawn is left still to be mowed.

Mr. Pham mowed more of the lawn than his son.

it still needs ¹³/₂₈ of the lawn to be mowed.

Step-by-step explanation:

Answer: 1/4 is greater than 2/7 mowed most of the lawn.

Step-by-step explanation:

First, draw a fraction model for [tex]\frac{2}{7}[/tex] and [tex]\frac{1}{4}[/tex] and partition it. Then, how ever many you get write it as a fraction. Then, see whose answer is greater.

Answer:

784

Step-by-step explanation:

you take the 49 and times is by 16

there are 4 sides

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:

144 i think

Step-by-step explanation:

triangular prism calculator

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:

5+-2

Step-by-step explanation:

it

Answer:

Exact Form:

2√3/3

Decimal Form:

1.15470053

Step-by-step explanation:

Multiply

2√3

and

√3√3.2√3√

3

√

3

Raise

√

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1

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2

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2

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Use the power rule

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.

2

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Tap for fewer steps...

Rewrite

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2

.

2

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3

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3

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2

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Answer:

10

Step-by-step explanation:

Since it's a right angle, it's already 90 degrees. So, you add 48 + 32 which gives you 80. 80 minus 90 equals 10.

48 + 32 = 80

90 - 80 = 10

Answer:

7 3/4

Step-by-step explanation:

Answer:

7 3/4 is greater

Step-by-step explanation:

it might help to find a common denominator

7 3/4= 7 9/12

7 1/2= 7 6/12

hope this helps (u can also use decimals)

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:

=£75

Step-by-step explanation:

ratio=5(lottie):1(Ollie)

we do 15/1 which will stay the same as 15

15/1=15

Then we times 15 by 5( lotties share)=75

15*5=75

Therefore lottie got £75

=£75

Answer:

75 : 15

Step-by-step explanation:

Answer:

$3,400,000

Step-by-step explanation:

170,000/ 5% for the increase

170,000/ 5% = $3,400,000

Answer:

$36

Step-by-step explanation:

60% of 90 is 54

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

Answer:I got the answer correct because i have to take the test

Step-by-step explanation:

The relation between the area and the circumference is given by:

"The area is 1/2 times the radius times the circumference".

We know that for a circle of radius R we have:

If you take the quotient between the area and the circumference, you get:

A/P = (pi*R^2)/(2*pi*R) = R/2

So the area is R/2 times the circumference, or, using the terms given in the list:

"This means that the area is 1/2 times the radius times the circumference"

If you want to learn more about circles, you can read:

https://brainly.com/question/25306774

Answer:

A and d is the correct answer

Step-by-step explanation:

A and d is matter fact correct answer

Answer:

yes i believe it is correct

Step-by-step explanation:

Answer:

The answer would be

Sin 60°=x/14

X=7v3