Student A and Student B are both practicing for a marathon. Student A runs 5 miles every day, while Student B starts running 3 days after Student A and runs 8 miles each day. Define a variable and write an equation that represents the information given. Determine the number of days after Student A starts running when both students will have run the same number of miles.

a) By Pythagorean theorem, the value of variable x is equal to 10.2171 meters.

b) By trigonometric functions, the value of variable h is equal to 7.8620 meters.

Herein we have the representation of a geometric system formed by four right triangles, this formation has a known angle and a known side, and two unknown variables as well. The values of the variables can be found by means of trigonometric functions and Pythagorean theorem:

Trigonometric functions

sin 50° = h / x

h = 0.7660 · x

Pythagorean theorem

x² = L² + h²

8² = (0.25 · L)² + h²

64 = 0.0625 · L² + h²

Then, we eliminate L by equalizing second and third equations:

64 = 0.0625 · (x² - h²) + h²

64 = 0.0625 · x² + 0.9375 · h²

And by the first equation:

64 = 0.0625 · x² + 0.9375 · (0.7660 · x)²

64 = 0.0625 · x² + 0.5501 · x²

64 = 0.6126 · x²

8 = 0.783 · x

x = 10.2171 m

And the value of h is:

h = 0.7660 · (10.2171 m)

h = 7.826 m

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If the difference in height between the whale and the ship is -1,040, the height of the whale is 2,200 meters.

The difference in height between the whale and the ship is -1,040. If the ship is 3,240 meters tall, we can use this information to determine the height of the whale.

Let h be the height of the whale. We know that the difference in height between the whale and the ship is -1,040, which we can express as:

h - 3,240 = -1,040

To solve for h, we can add 3,240 to both sides of the equation:

h = 3,240 - 1,040

Simplifying the right-hand side of the equation, we get:

h = 2,200

In summary, we can use the given difference in height and the height of the ship to set up an equation that relates the height of the whale to the height of the ship. By solving this equation for the height of the whale, we can determine that the whale is 2,200 meters tall.

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Complete question is:

The difference in height between the whale and the ship is -1,040. If the ship is 3,240 meters tall, what is the height of the whale?

It takes 0.55 secοnds fοr a ball traveling at 80 mph tο reach a batter that is pοsitiοned at the back οf the batter's bοx.

Speed is defined as the distance traveled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn.

Mathematically, speed is calculated as fοllοws:

speed = distance/time

Where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

Tο determine hοw lοng it takes fοr the ball tο reach the batter, we need tο use the fοrmula fοr time:

time = distance/speed

First, we need tο determine the distance frοm the pitcher's mοund tο the batter's bοx. Accοrding tο Majοr League Baseball rules, the distance frοm the pitcher's mοund tο hοme plate is 60 feet, 6 inches (18.44 meters). The batter's bοx is typically 4 feet (1.22 meters) behind hοme plate, sο the distance frοm the pitcher's mοund tο the back οf the batter's bοx is:

distance = 60 ft 6 in + 4 ft = 64 ft 6 in = 19.66 meters

Next, we cοnvert the speed οf the ball frοm miles per hοur (mph) tο meters per secοnd (m/s). One mile is equal tο 1,609.34 meters, and οne hοur is equal tο 3,600 secοnds, sο we can cοnvert mph tο m/s using the fοllοwing fοrmula:

speed in m/s = (speed in mph * 0.44704)

Therefοre, the speed οf the ball in m/s is:

speed = 80 mph * 0.44704 = 35.76 m/s

Nοw we can calculate the time it takes fοr the ball tο reach the batter:

time = distance/speed

time = 19.66 meters / 35.76 m/s

time = 0.55 secοnds

Therefοre, it takes apprοximately 0.55 secοnds fοr a ball traveling at 80 mph tο reach a batter that is pοsitiοned at the back οf the batter's bοx.

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The expression in standard form for the volume V of the box is: [tex]V = 6n^3 + 5n^2 + 2n[/tex]

How do you measure the volume of a box?

You must take measurements of a box's length, breadth, and height in order to determine its size. To get the box's volume in cubic units, multiply all three measurements together.

The volume V of the box can be expressed as:

V = (depth) x (height) x (width)

Substituting the given values, we get:

V = n x (2n+1) x (3n+2)

Expanding the expression, we get:

V =[tex]6n^3 + 5n^2 + 2n[/tex]

Therefore, the expression in standard form for the volume V of the box is: [tex]V = 6n^3 + 5n^2 + 2n[/tex]

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Answer:

Step-by-step explanation:

In this problem, we have to use the formula in finding the volume of a cylinder

[tex]V=\pi r^{2} h[/tex]

r is half of diameter
r= 16ft / 2 = 8ft

The height of the cylinder is 4ft. We have to know the height of the water to know the volume of the water.

h (water) = 4ft - 1/2ft  = 3.5ft

[tex]V=\pi (8)^{2} (3.5)[/tex]

[tex]V = 703.72 ft^{3}[/tex]

[tex]V = 703.72 ft^{3} * \frac{7.48 gallons}{1ft^{3} }[/tex]

[tex]V = 5263.8 gallons[/tex]

[tex]V = 5264 gallons[/tex]

The pool is filled with 5264 gallons of water.

Neither X nor Y can be well-approximated by a normal random variable, the proportion of exams with passing scores is .7734, the exam score for an exam whose z-score is 1.25 is 85 and if the top 4% of the exams will be given an A+, in order to be given an A+, an exam must earn at least 89 score.

Question 1: Neither X nor Y can be well-approximated by a normal random variable. This is because both X and Y are discrete random variables, meaning they can only take on integer values. Normal random variables, on the other hand, are continuous and can take on any value within a certain range.

Therefore, neither X nor Y can be well-approximated by a normal random variable.

Question 2: The proportion of exams with passing scores is .7734. This can be found by calculating the z-score for a score of 69 and using a z-table to find the corresponding proportion. The z-score is (69-75)/8 = -0.75. Using a z-table, we find that the proportion of exams with scores less than 69 is .2266.

Therefore, the proportion of exams with passing scores is 1-.2266 = .7734.

Question 3: The exam score for an exam whose z-score is 1.25 is 85. This can be found by using the formula for z-scores: z = (x-µ)/σ. Plugging in the values for z, µ, and σ, we get 1.25 = (x-75)/8.

Solving for x, we get x = 85.

Question 4: In order to be given an A+, an exam must earn at least a score of 89. This can be found by using the formula for z-scores and a z-table. We know that the top 4% of exams will be given an A+, so we need to find the z-score that corresponds to the top 4%. Using a z-table, we find that this z-score is 1.75.

Plugging this into the formula for z-scores, we get 1.75 = (x-75)/8. Solving for x, we get x = 89.

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Using trigonometric functions, we can find the area of the triangle to be: 19.68unit². Bob used the wrong dimension in the area of the triangle formula.

There are six basic trigonometric operations in trigonometry. These techniques can be described using trigonometric ratios. The six basic trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function.

Trigonometric identities and functions are based on the ratio of the sides of a right-angled triangle.

The sine, cosine, tangent, secant, and cotangent values for the perpendicular side, hypotenuse, and base of a right triangle are computed using trigonometric formulas.

Here in the question,

Area of the triangle = 1/2 absinc

= 1/2 × 12 × 16.4 × Sin30°

= 1/2 × 196.8 × 0.2

= 19.68unit².

Bob used the wrong dimension of the triangle. Instead of using the adjacent side of the angle, Bob used the opposite side of the angle.

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The cost of a new Honda Accord in terms of the number of years t since 2000 can be represented by the function f(t).

The cost of a new Honda Accord in terms of the number of years t since 2000 is represented by the We can use this function to answer the questions given.

a. The cost (in dollars) of a new Accord in 2005 can be represented by f(5), since 2005 is 5 years after 2000.

b. The difference in cost between a new Accord in 2015 and 2010 can be represented by f(15) - f(10), since 2015 is 15 years after 2000 and 2010 is 10 years after 2000.

c. The ratio of the cost of a new Accord in 2015 to the cost of a new Accord in 2010 can be represented by f(15)/f(10).

d. $520 more than the cost of a new Accord in 2018 can be represented by f(18) + $520, since 2018 is 18 years after 2000.

In conclusion, the cost of a new Honda Accord in terms of the number of years t since 2000 can be represented by the function f(t), and we can use this function to answer the given questions.

The cost of a new Accord in 2005 is represented by f(5), the difference in cost between a new Accord in 2015 and 2010 is represented by f(15) - f(10), the ratio of the cost of a new Accord in 2015 to the cost of a new Accord in 2010 is represented by f(15)/f(10), and $520 more than the cost of a new Accord in 2018 is represented by f(18) + $520.

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Coach Jill put 4,000 mL of sports drink in each cooler to stay hydrated.

Coach Jill brought a total of 28,000 milliliters (mL) of sports drink to the soccer game. She divided the sports drink equally among 7 coolers, so she needed to determine how many milliliters each cooler would receive.

Coach Jill brought a total of 28 L = 28,000 mL of sports drink.

She divided this equally among 7 coolers, so each cooler would receive:

28,000 mL / 7 coolers = 4,000 mL/cooler

Therefore, Coach Jill put 4,000 mL of sports drink in each cooler.

This ensured that each cooler received the same amount of sports drink, which was important to keep all the players equally hydrated during the game. By dividing the sports drink equally, Coach Jill was able to efficiently manage the resources and ensure that each player had access to enough fluids during the game.

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The resultant of the expression (((-3/5)+(5/3))-(2-4/3)) will be 2/5.

What exactly are expressions?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a value. Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple numbers, variables, and operations.

For example, 3 + 5 is an expression that represents the sum of two numbers, which evaluates to 8. Another example is 2x - 5, which involves a variable (x) and two operations (multiplication and subtraction).

Now,

Let's start by simplifying (-3/5 + 5/3):

First, we need to find a common denominator between 5 and 3, which is 15

then,

-3/5 + 5/3 = -9/15 + 25/15

Next, we can add the two fractions:

-9/15 + 25/15 = 16/15

So, (-3/5 + 5/3) simplifies to 16/15.

Now, let's simplify (2 - 4/3):

We can rewrite 2 as 6/3, then subtract 4/3:

6/3 - 4/3 = 2/3

So, (2 - 4/3) simplifies to 2/3.

Finally, we can subtract 2/3 from 16/15:

16/15 - 2/3

To subtract fractions, we need a common denominator between 15 and 3, which is 15. then

16/15 - 10/15 = 6/15

So, the resulting constant is 6/15, which can be simplified by dividing both the numerator and denominator by their greatest common factor (which is 3):

6/15 = 2/5

Therefore,

                the resulting constant is 2/5.

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Answer:

See below.

Step-by-step explanation:

We are given the value of an angle, and the hypotenuse.

x will equal 7.0

Using Trigonometry Functions, we can identify x.

[tex]\textsf{Trigonometry Functions:}[/tex]

[tex]Sin = \frac{Opposite}{Hypotenuse}[/tex]

[tex]Cosine = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]Tan = \frac{Opposite}{Adjacent}[/tex]

[tex]\fbox{We should use Sin.}[/tex]

Let's begin by solving for x.

[tex]\textsf{\underline{We should use;}}[/tex]

[tex]{Sin(23^{\circ})}[/tex]

[tex]\textsf{\underline{Solve for x:}}[/tex]

[tex]Sin(23^{\circ})=\frac{x}{18}[/tex]

[tex]\textsf{\underline{Multiply by 18:}}[/tex]

[tex]18 \times Sin(23^{\circ})={x}[/tex]

[tex]x \approx 7.0[/tex]

Step-by-step explanation:

Area of a rhombus = ab/2 where a is 12cm and b is 10cm (diagonals)

Area = 12 x 10 /2 =120/2

Area = 60cm

Answer:

H: 1:4

Step-by-step explanation:

The value of the logarithm expression are

1. ln 35.2 = 3.561046

2. ln (2/3) ≈ -0.405465108

1. ln 35.2:

We can evaluate ln 35.2 using a calculator or by using the identity:

ln x = y if and only if e^y = x

So, we need to find e^y = 35.2, where y is the value we're looking for. Taking the natural logarithm of both sides, we get:

ln e^y = ln 35.2

y ln e = ln 35.2

y = ln 35.2

Therefore, ln 35.2 ≈ 3.561046 (using a calculator).

2. ln (2/3):

We can use the identity:

ln (a/b) = ln a - ln b

to rewrite ln (2/3) as:

ln 2 - ln 3

Therefore, ln (2/3) ≈ -0.405465108 (using a calculator).

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Answer:

f(4)=14

Step-by-step explanation:

In this scenario, we need to construct a Markov chain that indicates when the solar heat must be augmented.

To do this, we need to define our states carefully. Let's define the following states: S0: The solar heating device is fully charged. S1: The solar heating device has one day of charge left. S2: The solar heating device has two days of charge left. C: The solar heating device needs to be augmented.

Now, let's construct the Markov chain. We will use the probabilities given in the original Markov chain to determine the probabilities of transitioning between states in our new Markov chain.

The new Markov chain will look like this:S0 → S1 (probability = 0.2)S0 → S2 (probability = 0.8)S1 → S2 (probability = 0.8)S1 → C (probability = 0.2)S2 → C (probability = 0.2)S2 → S1 (probability = 0.8)C → S0 (probability = 1).

The new Markov chain will indicate when the solar heat must be augmented by transitioning to the C state. When the Markov chain is in the C state, it means that the solar heating device needs to be augmented by some other heat source.

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The answer to the question is option A. The median number of points scored for Team 1 is 15 and for Team 2 is 11.

To find the median number of points scored for each team from the given back-to-back stem-and-leaf plot, we need to identify the middle value of the data set for each team. The middle value is the point where half the scores are above it and half are below it.

Looking at the stem-and-leaf plot, we can see that for Team 1, the median score is 15. This is because there are 4 scores above 15 and 4 scores below it. Therefore, 15 is the middle value for Team 1.

Similarly, for Team 2, the median score is 11. This is because there are 4 scores above 11 and 4 scores below it. Therefore, 11 is the middle value for Team 2.

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A factor is a number divided by another without leaving a remainder.

And, Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Factor:

A factor is a number divided by another without leaving a remainder. In other words, if multiplying two integers results in a product, the numbers we multiply are factors of the product because they are divisible by the product. There are two ways to find factors: multiplication and division. Additionally, separability rules can also be used.

According to the Question:

Factors of 24:

We can write 24 as a product of two numbers in multiple ways:

24 = 1 × 24;

24 = 2 × 12;

24 = 3 × 8;

24 = 4 × 6

Therefore, all the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

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Answer:  f(g(-1)) = -16

Step-by-step explanation:

First, we need to find g(−1), which means we substitute -1 in place of x in the function g(x):

g(-1) = 3(-1) = -3

Next, we substitute g(-1) into f(x):

f(g(-1)) = f(-3) = 3(-3) - 7 = -16

Therefore, f(g(-1)) = -16.

Answer:

[tex]p = 800 \frac{2}{5} ^{T}[/tex]
Step-by-step explanation:

Let's assume that the initial value of the phone is $800, and that its value decreases by 3/5 each year.

After one year, the phone will be worth 2/5 of its initial value:

$800 x (2/5) = $320

After two years, the phone will be worth 2/5 of its value after one year:

$320 x (2/5)^1 = $128

The solution to |x| > |x + 2| is x < -2. This can be determined by looking at the two graphs on the grid, y = |x| and y = |x + 2|.

Inequality is the concept of representing a relationship between two values using a mathematical symbol. This can be used to express various forms of comparison such as greater than, less than, and not equal to. Inequality is an important concept for understanding and applying mathematical principles, such as in algebra and calculus.

The graph of y = |x| is a straight line at y = 0, and increases as x moves further away from 0. The graph of y = |x + 2| has a minimum at x = -2, and increases as x moves further away from -2. Therefore, at all locations where x is less than -2, the value of |x| is greater than the value of |x + 2|. These locations are all solutions to the inequality |x| > |x + 2|.

To visualize this solution, we can look at the graph of the two functions and see that the value of |x| is greater than the value of |x + 2| when x is less than -2. This can also be seen by looking at the numerical values of the two functions; for any x less than -2, the absolute value of x will be greater than the absolute value of x + 2.

In conclusion, the solution to the inequality |x| > |x + 2| is x < -2. This can be seen visually on the graph of the two functions, and can also be determined by looking at the numerical values of the two functions.

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Comparing the two simplified ratios, 4:3 and 10:9, we see that they are not equal, so the ratios 60:45 and 10:9 do not form a proportion.

We must examine whether the cross-products are equal in order to determine whether the ratios of 60:45 and 10:9 constitute a proportion.

60 x 9 = 540 is the cross product of 60 and 9.

45 x 10 = 450 is the cross product of 45 and 10.

The cross-products are not equal, hence the ratios of 60:45 and 10:9 do not constitute a proportion (540 is not equal to 450, for example).

Simplifying two ratios to their simplest form is another technique to determine if they constitute a proportion.

By dividing both components by their greatest common factor, which is 15, the ratio 60:45 can be reduced to 4:3.

The 10:9 ratio has already reached its lowest point.

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The money which should be deposited today in an account is found as $11,430.

Compound interest is calculated as follows:

CI = P[tex](1 + \frac{r}{12}) ^{12t}[/tex] - P,

where t is the time, P is the principle sum, and r is indeed the interest rate expressed as a decimal.

A =  P[tex](1 + \frac{r}{12}) ^{12t}[/tex]

Put the values:

12,000 = P[tex](1 + \frac{0.025}{12}) ^{12*2}[/tex]

P = 12,000 / 1.05

P = 11428.57

P = 11430 (approx)

Thus, money which should be deposited today in an account is found as $11,430.

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The correct question is -

How much money should be deposited today in an account that earns 2.5% compounded monthly so that it will accumulate to $12,000 in 2 years?

Answer:

Scale factor is 1/2

Step-by-step explanation:

2.4 x 2 = 4.8

4.8/2 = 2.4

same here

2.1 x 2 = 4.2

4.2/2 = 2.4

3.8/2 =1.9

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The value of 25 cm/s = 900 m/h using the dimensional analysis.

Examining the dimensions of the relevant physical variables is a key step in the study and solution of issues in science and engineering using dimensional analysis. Physical quantities have defined dimensions and are stated in terms of units like metres, kilogrammes, seconds, and degrees Celsius. Physical quantities also include length, mass, time, and temperature. Dimensional consistency in physical equations and connections is the fundamental tenet of dimensional analysis.

To convert 25 cm/s to m/h using dimensional analysis, we have:

1 m = 100 cm

1 h = 3600 s

25 cm/s x (1 m/100 cm) x (3600 s/1 h) = 900 m/h

Hence, the value of 25 cm/s = 900 m/h using the dimensional analysis.

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If a scooter was brought in April 2005 for rs. 42000 if it's value fall by 10% every year, the value of the scooter in April 2007 would be Rs. 34020.

If the value of the scooter falls by 10% every year, then its value after the first year will be 90% of its original value. Similarly, the value after the second year will be 90% of the value after the first year, or 0.9 * 0.9 = 0.81 times the original value.

To find the value of the scooter in April 2007, we need to apply this formula twice, since there are two years between April 2005 and April 2007.

Starting with the original value of the scooter, we can calculate its value after one year:

Value after 1 year = 0.9 * Rs. 42000 = Rs. 37800

Then, we can use this value to calculate the value of the scooter after two years:

Value after 2 years = 0.9 * Rs. 37800 = Rs. 34020

In this case, the value of the scooter decreases by 10% each year, so its value after two years is 0.9 times its value after one year, which is 0.9 times its original value.

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Answer:

22 sq. in.

Step-by-step explanation:

Believe it or not, the area is still length times width in this problem, you just have to subtract 3 sq in from your final answer becasue of the center gap (3in *1in)

5in * 5in =25 sq in -3 sq in= 22 sq in.

a) The initial velocity of the boulder was 117.39 ft/s.

b) The maximum height reached by the boulder was 214.48 ft.

We can use the equations of motion to solve this problem. Let's assume that the acceleration due to gravity is -32 ft/s² (negative because it acts downwards).

a) We can use the following equation to find the initial velocity (v₀) of the boulder:

h = v₀t + 0.5at²

where h is the initial height (15ft), t is the time it takes to hit the ground (6.7s), and a is the acceleration due to gravity (-32 ft/s²).

Plugging in the values, we get:

15 = v₀(6.7) + 0.5(-32)(6.7)²

Solving for v₀, we get:

v₀ = 117.39 ft/s (rounded to two decimal places)

Therefore, the initial velocity of the boulder was 117.39 ft/s.

b) To find the maximum height reached by the boulder, we can use the following equation:

v² = v₀² + 2ah

where v is the final velocity (0 ft/s at the maximum height), v₀ is the initial velocity (which we just found to be 117.39 ft/s), a is the acceleration due to gravity (-32 ft/s²), and h is the maximum height we want to find.

Plugging in the values, we get:

0² = (117.39)² + 2(-32)h

Solving for h, we get:

h = 214.48 ft (rounded to two decimal places)

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