What is the place value of 5 in 5,475,807,139

By the law of total probability,

[tex]P(A\cap B)=P[(A\cap B)\cap C]+P[(A\cap B)\cap C'][/tex]

but the events A, B, and C are mutually independent, so

[tex]P(A\cap B)=P(A)P(B)[/tex]

and the above reduces to

[tex]P(A)P(B)=P(A)P(B)P(C)+P(A\cap B\cap C')\implies P(A\cap B\cap C')=P(A)P(B)(1-P(C))=P(A)P(B)P(C')[/tex]

which is to say A, B, and C's complement are also mutually independent, and so

[tex]P(A\cap B\cap C')=0.5\cdot0.8\cdot(1-0.3)=0.12[/tex]

By a similar analysis,

[tex]P(A\cap B'\cap C)=P(A)P(B')P(C)=0.03[/tex]

[tex]P(A'\cap B\cap C)=P(A')P(B)P(C)=0.12[/tex]

These events are mutually exclusive (i.e. if A and B occur and C does not, then there is no over lap with the event of A and C, but not B, occurring), so we add the probabilities together to get 0.27.

Final answer:

The probability that exactly two of the independent events A, B, and C occur is 0.43, calculated by adding the probabilities of each possible pair of events occurring while the third does not.

Explanation:

The student is seeking the probability that exactly two out of the three events A, B, and C occur given their individual probabilities P(A) = 0.5, P(B) = 0.8, and P(C) = 0.3, and the fact that they are mutually independent events. To find this, we ned to consider the three scenarios where exactly two events occur: A and B, A and C, and B and C. The probability for each scenario is found by multiplying the probabilities of the two events occurring and then multiplying by the probability of the third event not occurring.

For example, the probability of A and B both occurring but not C is P(A) × P(B) × (1 - P(C)). To find the total probability that exactly two events occur, we sum up the probabilities of all three scenarios:

P(A and B but not C) = P(A) × P(B) × (1 - P(C))

P(A and C but not B) = P(A) × (1 - P(B)) × P(C)

P(B and C but not A) = (1 - P(A)) × P(B) × P(C)

We then calculate and sum these probabilities:

P(A and B but not C) = 0.5 × 0.8 × (1 - 0.3) = 0.5 × 0.8 × 0.7 = 0.28

P(A and C but not B) = 0.5 × (1 - 0.8) × 0.3 = 0.5 × 0.2 × 0.3 = 0.03

P(B and C but not A) = (1 - 0.5) × 0.8 × 0.3 = 0.5 × 0.8 × 0.3 = 0.12

Adding these probabilities together provides the final answer:

Σ P(exactly two events) = 0.28 + 0.03 + 0.12 = 0.43

Therefore, the probability that exactly two of the events A, B, and C occur is 0.43.

Answer:

y = - 3x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, - 2) ← 2 points on the line

m = [tex]\frac{-2-4}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

Note the line crosses the y- axis at (0, 4) ⇒ c = 4

y = - 3x + 4 ← equation of line

Answer:

  (x, y, z) = (1-z, z, z) . . . . . . . an infinite number of solutions

Step-by-step explanation:

Use the first equation to substitute for x in the remaining two equations.

  (-5y +4z +1) -2y +3z = 1 . . . . substitute for x in the second equation

  -7y +7z = 0 . . . . . . . . . . . . . . simplify, subtract 1

  y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z

__

  2(-5y +4z +1) +3y -z = 2 . . . . substitute for x in the third equation

  -7y +7z = 0 . . . . . . . . . . . . . . subtract 2; collect terms

  y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z

This is a dependent set of equations, so has an infinite number of solutions. Effectively, they are ...

  x = 1 -z

  y = z

  z is a "free variable"

Answer:

  373/500 = 0.746

Step-by-step explanation:

373 out of 500 is represented by the fraction 373/500.

This value is easily converted to a decimal number by multiplying numerator and denominator by 2:

  (373×2)/(500×2) = 746/1000 = 0.746

_____

You can also divide 373 by 500 using a calculator to get the decimal result.

Five friends went to see a movie. Each person paid $5.

This is a total of $40.

$62.50 - $40 = $22.50.

We now have $22.50 to divide by 5 people.

So, $22.50/5 = $4.50.

Each person paid $4.50 for popcorn.

Answer:

The horizontal speed of the truck is 102.39 km/hr.

Step-by-step explanation:

Given that,

Speed of airplane = 125 km/h

Angle = 35°

We need to calculate the horizontal speed

Using formula of horizontal speed

[tex]u_{x}=u\cos\theta[/tex]

Where, u = speed

Put the value into the formula

[tex]u_{x}=125\times\cos35^{\circ}[/tex]

[tex]u_{x}=102.39\ km/hr[/tex]

Hence, The horizontal speed of the truck is 102.39 km/hr.

Answer:

v = 102.4 km/h

Step-by-step explanation:

Given:-

- The speed of the airplane, u = 125 km/h

- the angle the airplane makes with the ground, θ = 35°

Find:-

How fast must a truck travel to stay beneath an airplane?

Solution:-

- For the truck to be beneath the airplane at all times it must travel with s projection of airplane speed onto the ground.

- We can determine the projected speed of the airplane by making a velocity (right angle triangle).

- The Hypotenuse will denote the speed of the airplane which is at angle of θ from the truck travelling on the ground with speed v.

- Using trigonometric ratios we can determine the speed v of the truck.

                                  v = u*cos ( θ )

                                  v = (125 km/h) * cos ( 35° )

                                  v = 102.4 km/h

- The truck must travel at the speed of 102.4 km/h relative to ground to be directly beneath the airplane.

Answer:

y = 2x - 1

Step-by-step explanation:

Note the difference between consecutive terms of y are constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 9 - 7 = 2

Thus the equation is of the form y = 2x ± c ← c is a constant

Substitute values of x to determine the required value of c

x = 0 : 2 × 0 = 0 ← require to subtract 1 for y = - 1

x = 1 : 2 × 1 = 2 ← require to subtract 1 for y = 1

x = 2 : 2 × 2 = 4 ← require to subtract 1 for y = 3, and so on

Thus the required equation is

y = 2x - 1

The first one f(x) = -1/3x + 5

Answer:

f(x)=-1/3+5

Step-by-step explanation:

hope this helps

Answer:

Part a) 30+m

Part b) $36

Step-by-step explanation:

Part a) Identify an expression that represents the amount Susan spent on the fruits

The complete question in the attached figure

Let

m ------> the number of apples

n -----> the number of oranges

q ----> the amount Susan spent on the fruits

we know that

m+n=15 ----> (in total she needs 15 fruits)

n=15-m -----> equation A

q=3m+2n ----> equation B

Substitute equation A in equation B

q=3m+2(15-m)

q=3m+30-2m

q=30+m -----> expression that represents the amount Susan spent on the fruits

Part b) Identify the amount she spent if she bought 6 apples

we know that

If m=6 apples

substitute the value of m in the expression of Part a)

q=30+m -----> q=30+6=$36

Time for light A's Flash = 4 seconds

Time for light B's Flash = 6 seconds

Duration between the lights = 6-4=2

Duration to flash again = LCM of 6, 4

2/6,4

2/3,2

3/3,1

/1,1

2x2 x 3

4 x 3

= 12 seconds

Final answer:

The two street lights will flash together again after 12 seconds. This is determined by finding the least common multiple of the intervals at which each street light flashes (4 seconds and 6 seconds), which is 12 seconds.

Explanation:

The question you've posed is about finding the least common multiple (LCM) of two numbers, which in this case are the intervals at which two street lights flash: 4 seconds and 6 seconds. To determine when the street lights will flash together again, we must find the smallest time interval that is a multiple of both 4 and 6. The multiples of 4 are 4, 8, 12, 16, and so on. The multiples of 6 are 6, 12, 18, 24, and so on. The smallest multiple they have in common is 12 seconds.

To arrive at this answer, you can either list out the multiples as above or use a shortcut by calculating the LCM. Here's a step-by-step breakdown:

Write down the prime factors of each number: 4 = 2 x 2 and 6 = 2 x 3.

For each distinct prime factor, take the highest power present in the factorization of either number. Here, this gives us 22 (from 4) and 3 (from 6).

Multiply these together to get the LCM: 22 x 3 = 4 x 3 = 12.

Therefore, the two street lights will flash together again after 12 seconds.

Answer: exponential because it's a ratio :)

Step-by-step explanation:

Answer:

Exponential. Because of its cumulative nature (gain of weight) and its growth rate (5%).

Step-by-step explanation:

It's a growth graph given by an exponential function because every gain of weight is cumulative to the earlier week's. This function can be modeled this way since the rate of growth (5%) was given, which is added by 1 then plugged into the formula. [tex]y=90(1.05)^{t}[/tex] Besides, this model is identical to Interest Composite Rate, which follows the same basic structure, namely Cumulative Growth at a given rate.

Answer:

  B.  (f + g)(x) = 6x² – 5x + 12

       (f- g)(x) = 6x² + 5x – 2

Step-by-step explanation:

1) (f +g)(x) = f(x) + g(x) = (6x² + 5) + (7 -5x) = 6x² -5x +12

__

2) (f-g)(x) = f(x) -g(x) = (6x² + 5) - (7 -5x)

  = 6x² +5 -7 +5x . . . the minus sign outside multiplies all the terms inside

  = 6x² +5x -2

In this Mathematics problem, we are asked to add and subtract given functions f(x) and g(x). The sum results in (f+g)(x) = 6x^2 - 5x + 12 and the difference results in (f-g)(x) = 6x^2 + 5x - 2.

The question is asking about finding the sum (f+g) and the difference (f-g) of two functions, f(x) and g(x). To answer this, we add (or subtract) the two given functions together.

For the function (f+g)(x), you simply add f(x) = 6x2 + 5 and g(x) = 7 - 5x together to get (f+g)(x) = 6x2 - 5x + 12. Thus, the sum of the two functions is 6x2 - 5x + 12.

Similarly, for the function (f-g)(x), we subtract g(x) from f(x) to get (f-g)(x) = 6x2 + 5x - 2. Thus, the difference of the two functions is 6x2 + 5x - 2.

So, the correct answer is B, (f+g)(x) = 6x2 - 5x + 12 and (f-g)(x) = 6x2 + 5x - 2.

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To calculate the compound interest, the formula[tex]A=p(1+r)^t[/tex] is used with the principal amount of $2,000, an annual interest rate of 10%, and a time frame of 10 years. The correct calculation results in a future balance of $5,187, when rounded to the nearest dollar. The correct option is d.

The equation [tex]A=p(1+r)^t[/tex] is used to calculate the compound interest on a savings account. To find out how much money will be in the account after a certain number of years, we can follow these steps:

After performing the calculation, we get:

A =[tex]2000(1 + 0.10)^{10[/tex] = [tex]2000(1.10)^{10[/tex] = 2000 ×2.59374 = $5,187.48

Therefore, rounded to the nearest dollar, you will have $5,187 in your account after 10 years. The correct answer is D. $5,187.

Answer:

Statements                                                      Reasons

AC+CD=AD and AB+BD=AD         Segment Addition Postulate

AC+CD=AB+BD                            Transitive/Substitution Property

AC=BD                                         Given

BD+CD=AB+BD                            Substitution Property

CD=AB                                         Subtraction Property

AB=CD                                         Symmetric Property

Step-by-step explanation:

By segment addition postulate, we can say the following two equations:

AC+CD=AD and AB+BD=AD.

By either substitution/transitive property, you can say AC+CD=AB+BD.

You are given AC=BD, so we use substitution and write AC+CD=AB+AC.

After using subtraction property (subtracting both sides by AC), you obtain CD=AB.

By symmetric property, you may say AB=CD.

So let's write it into the 2 column-proof you have there:

Statements                                                      Reasons

AC+CD=AD and AB+BD=AD        Segment Addition Postulate

AC+CD=AB+BD                            Transitive/Substitution Property

AC=BD                                          Given

BD+CD=AB+BD                             Substitution Property

CD=AB                                          Subtraction Property

AB=CD                                          Symmetric Property

Properties/Postulates used:

Transitive property which says:

If a=b and b=c, then a=c.

Substitution property which says:

If a=b, then b can be substituted(replaced with) for a.

Subtraction property which says:

a=b implies a-c=b-c.

Segment Addition Postulate says:

If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.

Answer:

B:45 degrees.

Step-by-step explanation:

We are given that a square ABCD .

We have to find the measure of angle BAC.

We know that each angle of square is of 90 degrees.

We know that diagonal AC bisect the angle BAD.

Therefore, measure of angle BAC=Measure of angle CAD.

Measure of angle BAD=[tex]\frac{1}{2}\times 90=45^{\circ}[/tex]

Hence, the measure of angle BAC=45 degrees.

Answer:B:45 degrees.

Answer:

45

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the problem statement, we can setup the following equation:

[tex]125,000 = 45,000 + 125E[/tex]

where [tex]E[/tex] is the number of employees being trained.

Solving for [tex]E[/tex] will give us the answer:

[tex]125,000 = 45,000 + 125E[/tex]

[tex]80,000 = 125E[/tex]

[tex]E = 640[/tex]

[tex]\text{Hello there!}\\\\\text{The most that they can spend is \$125,000}\\\\\text{We know that the fixed cost of the program is \$45000}\\\\\text{They also need to pay \$125 for each employee}\\\\\text{We need to solve:}\\\\125000-45000=80000\\\\\text{Now divide 80,000 by 125 to see how many employees they can train}\\\\80000\div125=640\\\\\boxed{\text{They can train 640 employees}}[/tex]

The opportunity cost of Susan attending college for a year is $51,400 ($11,400 of actual college expenses and $40,000 of foregone income from her previous job).

The opportunity cost of attending college is determined not only by the actual expenditure but also by the income you forgo by not working. In Susan's case, her actual expenses include $8,000 for tuition, $900 for books, and $2,500 for food, which total to $11,400. However, since she quit her $40,000 a year job to attend college, that lost income is also part of her opportunity cost. So, we add the lost income to her college expenses to get the total opportunity cost. Therefore, the opportunity cost of Susan attending college for the year would be $51,400 ($40,000 + $11,400).

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Answer:

y=-8(x+6)

Step-by-step explanation:

The equation of a line is [tex]y=mx+b[/tex] where m is the pending and b is the y intercept,

First we are going to calculate m:

If you have two points [tex]A=(x_{1},y_{1})\\B=(x_{2},y_{2})[/tex],

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case we have A=(-5,-8) and B=(-7,8)

[tex]x_1=-5, y_1=-8\\x_2=-7,y_2=8[/tex]

Replacing in the formula:

[tex]m=\frac{8-(-8)}{(-7)-(-5)}\\\\m=\frac{16}{-2} \\\\m=-8[/tex]

Then [tex]y=-8x+b[/tex].

We have to find b, we can find it replacing either of the points in [tex]y=-8x+b[/tex]:

Replacing the point (-5,-8):

[tex]y=-8x+b\\-8=-8.(-5)+b\\-8=40+b\\-8-40=b\\-48=b[/tex]

Or replacing the point (-7,8):

[tex]y=-8x+b\\8=-8.(-7)+b\\8=56+b\\8-56=b\\-48=b[/tex]

The answer is the same with both points.

Then we have:

y=-8x-48

y=-8(x+6)

Answer:

  The line of reflection is at y = x+6.

Step-by-step explanation:

The perpendicular bisector of AA' is a line with slope 1 through the midpoint of AA', which is (-4, 2). In point-slope form, the equation is ...

  y = 1(x +4) +2

  y = x + 6 . . . . . . . line of reflection

Answer:

  (a) |s - x| ≤ 3/16

  (b) 4 15/16 ≤ x ≤ 5 5/16

Step-by-step explanation:

(a) The absolute value of the difference from spec must be no greater than than the allowed tolerance:

  |s - x| ≤ 3/16

__

(b) Put 5 1/8 for s in the above equation and solve.

  |5 1/8 - x| ≤ 3/16

  -3/16 ≤ 5 1/8 -x ≤ 3/16

  3/16 ≥ x -5 1/8 ≥ -3/16 . . . . multiply by -1 to get positive x

  5 5/16 ≥ x ≥ 4 15/16 . . . . . . add 5 1/8

Pieces may be between 4 15/16 and 5 5/16 inches in length.

An absolute value inequality can be used to represent the acceptable range of lengths for a piece of wood in a woodshop class. For a specified length of 5 1/8 inches, the acceptable lengths for the piece would be between 4 15/16 inches and 5 5/16 inches.

Your task in woodshop class is to cut pieces of wood to within 3/16 inch of the teacher's specifications. The difference between the specification s and the measured length x of a cut piece is represented by (s-x).

(a) You can represent this situation with the absolute value inequality |s - x| ≤ 3/16, which shows that the difference between the specification and the measured length must be less than or equal to 3/16 inch.

(b) If the length of one piece is specified to be s = 5 1/8 inches, you can substitute that value into the inequality to find the acceptable range of lengths: |5 1/8 - x| ≤ 3/16. Solving the inequality gives you the range 5 - 3/16 inches ≤ x ≤ 5 + 3/16 inches, or between 4 15/16 inches and 5 5/16 inches.

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Answer:

  (a)  domain

  (b)  "argument," or "independent variable"

Step-by-step explanation:

You may want to refer to your notes for terminology related to functions. Different terms are used, depending on the context.

__

The set of valid inputs for a function is called the domain.

__

The input variable x is called the argument, or independent variable.

The set of valid inputs for a function is referred to as the domain, and the variable x is known as the independent variable in a function or an equation.

The set of valid inputs for a function is called the domain (a), and the input variable x is called the independent variable (b).

In the context of the equation of a line, such as y = mx + b, the independent variable x is usually plotted on the horizontal axis. When you select a value for x, it is considered independent because it can be chosen freely, and then you solve the equation for y, which is the dependent variable because its value depends on the chosen x. An example would be setting x to a specific number to see what y would be, demonstrating how the equation represents a straight line on a graph with m representing the slope and b representing the y-intercept.

In triangle ABC, BD bisects angle ABC into two parts with measures 2y and 5y-12. The measure of angle ABC is the sum of its parts, equating to 7y-12. Without additional information, the exact value of y and thus, the measure of angle ABC, cannot be determined.

The given problem involves a geometrical concept related to triangles, specifically angle bisectors. In triangle ABC, BD is an angle bisector, dividing angle ABC into two angles with measures 2y for angle ABD and 5y-12 for angle DBC. To find the measure of the whole angle ABC, we need to understand that the angle bisector divides the angle into two parts, where their measures are equal to the sum of the parts' measures.

Given:

Since BD is an angle bisector, the sum of the measures of angles ABD and DBC equals the measure of angle ABC. Thus, to find m ABC, we add the measures of angle ABD and angle DBC:

m ABC = m ABD + m DBC = 2y + (5y - 12) = 7y - 12

To solve for y, we note that additional information is required that is not provided in the question. However, the measure of angle ABC in terms of y is 7y - 12, showcasing the relationship between the angle and its bisector.

Answer:

Mutually exclusive, dependent events

Step-by-step explanation:

Two events A and B are mutually exclusive if [tex]P(A\cap B)=0[/tex]

Two events A and B are independent if [tex]P(A\cap B)=P(A)\cdot P(B)[/tex]

Remark: All mutually exclusive events are dependent.

Now,

A = the first symptom occurs

B = the second symptom occurs

[tex]P(A)=0.5\ (\text{or } 50\%)[/tex]

[tex]P(B)=0.45\ (\text{or } 45\%)[/tex]

[tex]P(A\cup B)=0.95 \ (\text{or }95\%)[/tex]

Use the rule

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\ \\0.95=0.5+0.45-P(A\cap B)\\ \\P(A\cap B)=0.5+0.45-0.95=0.95-0.95=0[/tex]

Thus, the events A and B are mutually exclusive (disjoint) and dependent (accordint to the remark)

Answer:

0.65

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]

In this problem we have

[tex]x=4+4+13+13=34[/tex]

because

total of three=4

total of jack=4

total of club=13

total of diamond=13

[tex]y=52\ cards[/tex]

substitute

[tex]P=\frac{34}{52}=0.65[/tex]

Answer:

l = 10.5 cm and A = 21 cm2

Step-by-step explanation:

Area is w*l

Perimeter is 2(w+l)

Replacing the information known in the problem you can get the length with the perimeter

P = 2(w+l)

25 = 2(2+l)

12.5 = 2 + l

10.5 cm = l

with the length now you can find the area

A = w*l

A = 2*10.5

A = 21 cm2

Answer:

The percentage is approximately 99.7%

Step-by-step explanation:

In order to understand this question you must understand the bell curve. (I would suggest googling a picture of the bell curve)

The mean of the bell curve is 67.5, meaning +1 standard deviation would be 70.9 (67.5+3.4). This would mean that 34% of the sample is between 67.5" and 70.9" (The bell curve % goes 34/14/2/.1 in that order)

When looking at the bell curve of this data, you would find that ±3 standard deviations gives you the range of 57.3" to 77.7". This would represent roughly (2+14+34+34+14+2)% of the sample. This excludes the .2% that are above or below 57.3" to 77.7". Therefore, the only answer that is close would be 99.7%

Using the empirical rule for a normal distribution, the calculation shows that approximately 99.7% of adults in town have heights between 57.3 and 77.7 inches.

The heights of the adults in this town follow a bell-shaped distribution known as the normal distribution. This means that the values are symmetrically distributed around the mean, with most values close to the mean and fewer values farther away. The empirical rule states that approximately 68 percent of the data falls within one standard deviation of the mean, about 95 percent falls within two standard deviations, and about 99.7 percent falls within three standard deviations.

In this case, the mean is 67.5 inches and the standard deviation is 3.4 inches. Thus, one standard deviation away from the mean is a range from 67.5 - 3.4 = 64.1 inches to 67.5 + 3.4 = 70.9 inches. Two standard deviations away from the mean is a range from 64.1 - 3.4 = 60.7 inches to 70.9 + 3.4 = 74.3 inches. Three standard deviations away from the mean is a range from 60.7 - 3.4 = 57.3 inches to 74.3 + 3.4 = 77.7 inches.

Therefore, according to the empirical rule, we would predict that about 99.7 percent of adults in the town have heights between 57.3 and 77.7 inches.

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Answer: true

Step-by-step explanation: x-values are not repeated

Answer:

True

Step-by-step explanation:

For a relation to be a function, each value of x in the domain maps to exactly one unique value of y in the range.

This is the case here, thus this is a function.

The probability of a spyware program breaking into a system depends on the complexity of the password rules. By calculating the total number of possible passwords based on given rules and comparing it to the number of guessing attempts (1,000,000), one can determine the probability for each scenario.

The probability of a spyware program guessing a password correctly can be calculated by determining the total number of possible unique passwords and then seeing how many attempts the spyware has in comparison.

In all cases, the probability of the spyware breaking in is the quotient of the number of attempts made (1,000,000) and the total number of possible passwords for each scenario.

Answer:

  15 cups

Step-by-step explanation:

To make 15 lattes, Charles will triple his recipe, so use 3×5 = 15 cups of milk.

Answer:

  20 ft

Step-by-step explanation:

The tree's shadow is 34/8.5 = 4 times the length of the person's shadow, so the tree is 4 times a tall as the person:

  4×5 ft = 20 ft . . . . . the height of the tree

_____

Shadow lengths are proportional to the height of the object casting the shadow.

Using the ratio given from the shadow of the 5-foot person, we set up a proportion and solve for the height of the tree, which is 20 feet.

The question is asking about the height of a tree, which can be figured out through a method called similar triangles in geometry. In this case, Phil, Melissa, Noah, and Olivia observed a 5-foot tall person casting an 8.5-foot shadow and a tall tree casting a 34-foot shadow.

From this, we can set up a proportion to find out the height of the tree. This would look like 5/8.5 = x/34, where x is the height of the tree. Cross multiplying and solving for x gives us x = (5*34)/8.5, which equals to 20 feet. Therefore, the height of the tree is 20 feet.

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