Find the equation of the line that passes through ( 4 , 1 ) and is parallel to the line passing through ( 7 , 11 ) and ( 10 , 20 ) .

Check the picture below.

notice, all three sides in the triangle are of different lengths, thus is an scalene triangle.

Answer:

C. Band is the most popular elective among juniors.

Step-by-step explanation:

Let's just arrange your table:

                   Art      Band      Choir      Drama      Total

Juniors:     0.02      0.27        0.24       0.05        0.58

Seniors:     0.12      0.04       0.05       0.21         0.42

Total:         0.14       0.31         0.29        0.26          1

What you see here are portions or percentages of the people who chose under each category.

Here's another way to look at it.

                   Art      Band      Choir      Drama      Total

Juniors:        2%      27%        24%        5%           58%

Seniors:       12%      4%           5%         21%         42%

Total:            14%      31%        29%        26%   100%

If you read it horizontally, you are looking at it based on Juniors and Seniors.

If you read it vertically, you're looking at it based on the elective class.

The totals show how the group looks as a whole. And it gives you an idea of how much of the population chose each elective class.

Let's go back to your choices.

A is wrong, because as you can see, only 12% of the population that are Seniors chose Art. The most popular was actually Drama with 21%.

B. Is wrong as well because  only 5% of the population that are seniors chose Choir.

C. Is true because the as you can see, 27% of the population that are juniors chose Band.

D is wrong because of the above statement.

Now you do not have to make them into percentages to do this. You can also interpret the same thing by looking for the highest relative frequency to determine which one is most popular.

Answer:

C. Band is the most popular elective.

Step-by-step explanation:

Answer: 210

Step-by-step explanation:

55×12=660-500=160+50(down payment)=210

The total amount(interset+down payment) is $210 if the Rahm used a payment plan to purchase wood for a home project. The wood he bought cost $500.

Paying down any outstanding debt, or occasionally more than one obligation, by consolidation into a structured payment schedule is referred to as a payment plan.

We have the wood he bought cost $500.

Here some data are missing, so we are assuming the monthly payment is $55 and duration is 1 year

= 55×12   (1 year = 12 months)

= $660

= 600 – 500

= $160

Down payment = $50

Total amount = 160+50 = $210

Thus, the total amount(interset+down payment) is $210 if the Rahm used a payment plan to purchase wood for a home project. The wood he bought cost $500.

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Answer:

Period=6

Step-by-step explanation:

Given:

t=1cos(1.05h)+37

Using acos(bx-c)+d to find the period of the given function

amplitude= a

period= 2π/Bb

phase shift=c (positive is to the left)

vertical shift=d

comparing with t=1cos(1.05h)+37, we get

a=1

b=1.05

c=0

d=37

period= 2π/b

          =2π/1.05

          =5.983

          =6

Period of function is 6, after every 6 hours the refrigerator sensor will reach its maximum temperature and the cycle will move towards reducing temperature i.e it'll reach the minimum temperature then again the cycle will move upwards raising the temperature to maximum and so one period will be completed!

Answer:

6

Step-by-step explanation:

Felicity set the thermostat of her refrigerator to 37°F. The refrigerator temperature t in degrees Fahrenheit h hours after the temperature sensor in the refrigerator is activated satisfies t=1cos(1.05h)+37. Therefore, the period of the function is 6.

Answer:

2.5 mg

Step-by-step explanation:

Substitute the givens into the equation. A is the initial amount, 16 mg. H is the halflife, 8 days. T is the time in days that has passed, 16 days. So we get P(t)= 10(1/2)^(16/2). This ends up being 10(1/2)^2. 1/2^2 is 1/4. 10(1/4)=2.5 mg

To understand how to use the equation P(t) = A(1/2)^(t/h), let's break down each part of the formula and see how it applies to a real-world situation.
P(t): This represents the remaining amount of the substance at time t, where t is measured in days.
A: This is the initial amount of the substance before any decay has started.
(1/2): This factor represents the principle of half-life, which, in this context, means that the substance is reduced to half its previous amount after each half-life period passes.
t: This is the time that has passed, measured in days.
h: This is the half-life of the substance, which is the amount of time it takes for half of the substance to decay.
The half-life formula can be used to calculate the amount of substance that will remain after a certain amount of time has passed. Here is how you use it:
1. Start by determining the initial amount A of the substance. This is how much of the substance you begin with.
2. Determine the half-life h of the substance, which is usually provided by scientific data or an experiment.
3. Choose the time period t that you are interested in. This is how many days from the start time you want to know the remaining amount of the substance for.
4. Plug the values of A, h, and t into the formula P(t) = A(1/2)^(t/h).
5. Calculate (1/2)^(t/h). This requires you to raise (1/2) to the power of the fraction t/h. This fraction is the number of half-lives that have passed in the time period t.
6. Multiply the initial amount A by the result from step 5 to get P(t), the amount of the substance that remains after t days.
Let's go through an example to make it clear:
Example:
If the initial amount A is 100 grams and the half-life h is 10 days, how much of the substance will remain after 20 days?
Using the formula:
1. A = 100 grams (initial amount)
2. h = 10 days (half-life)
3. t = 20 days (time passed)
Plug the values into the formula:
P(t) = A(1/2)^(t/h)
P(20) = 100(1/2)^(20/10)
Calculate the exponent:
(1/2)^(20/10) = (1/2)^2 = 1/4
Multiply the initial amount by the result of the exponent:
P(20) = 100 * 1/4
P(20) = 25 grams
So after 20 days, 25 grams of the substance would remain.

Answer:

x=6/cos(72) is the exact answer.

[tex]x \approx 19.416[/tex].

Step-by-step explanation:

Sine

opposite

hypotenuse

Cosine

adjacent

hypotenuse

Tangent

opposite

adjacent

Soh Cah Toa is an abbreviation used to help remember the trigonometric ratios.

We see we have the angle measurement 72 degrees given at the bottom. I'm going to label my sides with respect to that angle.

The hypotenuse is x.

The adjacent is 6.

We don't have anything about the opposite side but we don't need it to find x.

So anyways we have this:

The hypotenuse is x and

the adjacent is 6.

If you look at the ratios we want to use cosine.

[tex]\cos(72)=\frac{6}{x}[/tex]

or

[tex]\frac{\cos(72)}{1}=\frac{6}{x}[/tex]

We are going to cross multiply.

x cos(72)=1 (6)

cos(72) * x=6

Now we are going to divide both sides by cos(72) giving us:

x=6/cos(72)

x=6/cos(72) is the exact answer.

Let's put it into our calculator now:

[tex]x \approx 19.416[/tex].

Surveying people coming out of a concert because it will be all people who like the concert they were just attending.

Answer: leaving a concert

Step-by-step explanation:

most of the people leaving the concert probably really like that kind of music so it would be biased to survey them

Answer:

44°

Step-by-step explanation:

The arc of DC in degrees is the same as the angle of DOC. So it is 44°

Yes, y is a function of x in the given equation x = y³ - 10.

In the equation x = y³ - 10, y is indeed a function of x. To determine whether y is a function of x, we need to check if each x-value corresponds to a unique y-value. In this case, for every x, there exists only one corresponding y. Let's consider the equation step by step.

The given equation x = y³ - 10 implies that y³ = x + 10. To solve for y, we take the cube root of both sides, yielding y = [tex](x + 10)^(^1^/^3^)[/tex]. This expression defines y explicitly in terms of x, confirming that for every x, there is a unique y. Thus, the equation satisfies the criteria for a function.

Examining the nature of the equation further, we observe that the term[tex](x + 10)^(^1^/^3^)[/tex] represents a real-valued function. The cube root of any real number is a single-valued function, ensuring that y is indeed uniquely determined by x. Therefore, we can confidently conclude that y is a function of x in the given equation x = y³ - 10.

Answer:

The domain of the function is 0 ≤ h ≤ 50

Independent and dependent variables are h and g respectively.

Step-by-step explanation:

Given function that shows the volume of the water,

[tex]V=121\pi h[/tex]

Where, h represents the height of water ( in meters ) filled on the water tank,

Since, the height can not be negative,

⇒ 0 ≤ h,

Also, the height of the tower is 50 m,

That is, h can not exceed 50,

⇒ h ≤ 50

By combining the inequalities,

0 ≤ h ≤ 50,

Domain of the given function is the set of all possible value of h,

Hence, Domain for the given function is 0 ≤ h ≤ 50

Now, the variable which is taken for measuring the another variable is called independent variable while the variable which is obtained by independent variable is called dependent  variable,

Here, we take different values of h for finding the different values of g,

Therefore, independent and dependent variables are h and g respectively.

Answer:

255 milliliters.

Step-by-step explanation:

The fraction of Compound A in the mixture = 3 / (3+ 5) = 3/8.

So the amount of A to make 680 mls of the drug

= (3/8) * 680

=  255 milliliters.

Joan makes $275/week.

In addition to $275, she also makes 4 percent on sales over $1000.

So, 1250 - 1000 = 250.

Then 250(0.04) = 10.

Let t = amount of her paycheck for the week.

t = $275 + $10

t = $285

Answer:

D

Step-by-step explanation:

Using the product to sum formula

• 2cosAcosB = cos(A+B) + cos(A - B)

note that cos(- 3m) = cos 3m, hence

cos5m cos(- 3m)

= cos 5m cos3m ← A = 5m and B = 3m

= [tex]\frac{1}{2}[/tex] ( 5m + 3m) + cos(5m - 3m) ]

= [tex]\frac{1}{2}[/tex] cos 8m + [tex]\frac{1}{2}[/tex] cos 2m

The expression of cos5mcos(-3m) as a sum or difference results in  1/2cos2m + 1/2cos8m.

To express cos5mcos(-3m) as a sum or difference, we can use the trigonometric identity cos(A)cos(B) = 1/2[cos(A+B) + cos(A-B)].

Applying this identity to the given expression, we get 1/2[cos(5m - 3m) + cos(5m + 3m)] = 1/2[cos(2m) + cos(8m)].

Therefore, the given expression cos5mcos(-3m) can be simplified to 1/2cos2m + 1/2cos8m.

Problem: Same y intercept as x+4y=16, through (4,5)

Y intercept is when x=0 so 4y=16, y=4, y intercept (0,4)

Slope of line through (0,4) and (4,5) is change in y over change in x,

m = (5 - 4)/(4 - 0) = 1/4

Answer: slope 1/4

Check:

The new line is y = (1/4) x + 4

because the y intercept is still (0,4)

Let's check it's through (4,5)

(1/4) (4) + 4 = 5 check

Answer:

Choice d.

Step-by-step explanation:

Consistent means the linear functions will have at least one solution.

Independent means the it will just that one solution.

Dependent means the system will have infinitely many solutions.

So we are looking for a pair of equations that consist of the same line.

y=mx+b is slope-intercept form where m is the slope and b is the y-intercept.

If m and b are the same amongst the pair, then that pair is the same line and the system is consistent and dependent.

If m is the same and b is different amongst the pair, then they are parallel and the system will be inconsistent (have no solution).

If m is different, then the pair will have one solution and will be consistent and independent.

---------------------------

Choice A:

First line has m=1 and b=4.

Second line has m=1 and b=-4.

These lines are parallel.

This system is inconsistent.

Choice B:

First line is x+y=4 and it isn't in y=mx+b form.

Second line is 2x+2y=6 and it isn't in y=mx+b form.

These lines do have the same form though. This is actually standard form.

If you divide second equation by 2 on both sides you get:  x+y=3

The lines are not the same.

We are looking for the same line.

Now we could go ahead and determine to call this system.

If x+y has value 4 then how could x+y have value 3.  It is not possible. There is no solution. These lines are parallel.

Need more convincing. Let's put them into slope-intercept form.

x+y=4

Subtract x on both sides:

y=-x+4

m=-1 and b=4

x+y=3

Subtract x on both sides:

y=-x+3

m=-1 and b=3.

The system is inconsistent because they are parallel.

Choice c:

I'm going to go ahead in put them both in slope-intercept form:

3x+y=3

Subtract 3x on both sides:

y=-3x+3

So m=-3 and b=3

2y=6x+6

Divide both sides by 2:

y=3x+3

So m=3 and b=3

The m's are different so this system will by consistent and independent.

Choice d:

The goal is the same. Put them in slope-intercept form.

4x-2y=6

Divide both sides by -2:

-2x+y=-3

Add 2x on both sides:

y=2x-3

m=2 and b=-3

6x-3y=9

Divide both sides by -3:

-2x+y=-3

Add 2x on btoh sides:

y=2x-3

m=2 and b=-3

These are the same line because they have the same m and the same b.

This system is consistent and dependent.

Answer:

D

Step-by-step explanation:

15-x=4

Subtract 15 from both sides

leaves you with

-x=-11

x=11

Hey there! :)

15 - x = 4

Subtract 15 from both sides.

-x = 4 - 15

Simplify.

-x = -11

Divide both sides by -1.

-x ÷ -1 = -11 ÷ -1

x = 11

Therefore, your answer is D. 11

~Hope I helped! :)

The total number of phone numbers that can be made is 1,200,000.

To find the number of possible phone numbers given the conditions:

We can calculate as follows:

Therefore, the total number of phone numbers that can be made is [tex]1 x 3 x 4 x 10^7[/tex] = 1,200,000.

Answer:

If plants infested with aphids are sprayed with diluted coffee then the aphids will die.

Step-by-step explanation:

"Aphids sprayed with diluted coffee will not infest the plants" doesn't explain what happens to the aphids. (For example: they die, etc.)

"Plant sprayed with diluted coffee will not be infested by aphids" doesn't explain why it will not be infested by aphids.

"If plants with bug infestations are sprayed with diluted coffee then the bugs will die" doesn't say what type of bug, not all bugs will die from diluted coffee on plants.

The hypothesis best suited for Amy's test is 'If plants infested with aphids are sprayed with diluted coffee then the aphids will die', because it directly tests the claim Amy read online and is measurable through an experiment.

The appropriate hypothesis for Amy to test in order to determine whether spraying plants with diluted coffee will kill aphids is: 'If plants infested with aphids are sprayed with diluted coffee then the aphids will die'.

This hypothesis directly addresses the question Amy has and can be tested through an experiment where plants infested with aphids are sprayed with a diluted coffee solution. If the aphids die after being sprayed, the hypothesis would be supported. Conversely, if the aphids do not die, the hypothesis would need to be revised.

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x = amount of liters of the 15% OJ

y = amount of liters of the 5% OJ

let's recall that

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}[/tex]

so then, the amount of juice in the 15% solution will be (15/100)*x, or 0.15x

and the amount of juice in the 5% solution will be (5/100)*y or 0.05y.

we know our mixture must be 10 liters at 14% or namely 14/100, which will give in juice (14/100)*10 or 1.4 liters or pure juice in the solution with water making the OJ.

[tex]\bf \begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of }}{juice}&\stackrel{\textit{liters of }}{juice}\\ \cline{2-4}&\\ \textit{15\% OJ}&x&0.15&0.15x\\ \textit{5\% OJ}&y&0.05&0.05y\\ \cline{2-4}&\\ mixture&10&0.14&1.4 \end{array}~\hfill \begin{cases} x+y=10\\ \boxed{y}=10-x\\ \cline{1-1} 0.15x+0.05y=1.4 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{substituting on the 2nd equation}}{0.15x+0.05\left( \boxed{10-x} \right)}=1.4\implies 0.15x+0.5-0.05x=1.4 \\\\\\ 0.10x+0.5=1.4\implies 0.10x=0.9\implies x=\cfrac{0.9}{0.10}\implies \blacktriangleright x = 9 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y=10-9\implies \blacktriangleright y=1 \blacktriangleleft[/tex]

Answer:

By continuing my education I increased my earning potential from $21,484 to $39,746 a year. That's a difference of $18262 a year.

If the additional education costs $18,000, then in one year it will pay for itself.

Answer:

The answer is 1 year.

Step-by-step explanation:

You increased your yearly earning potential from $21,484 to $39,746.

The difference is : [tex]39746-21484=18262[/tex] dollars

This difference is in a year.

So, if the additional education costs $18,000, then in about 1 year it will pay for itself.

Hence, the answer is 1 year.

The correct answer is C. on edg

Answer:

The correct answer is C. on edg

Step-bexplanation:

Answer:

x² + y² = 42.25

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ← r is the radius

here r = 6.5, hence

x² + y² = 6.5², that is

x² + y² = 42.25 ← equation of circle

Answer: [tex]x^2 + y^2 = 42.25[/tex]

Step-by-step explanation:

The equation of a circle in center-radius form is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

Given the circle with radius 6.5 and centered at the origin, you can identify that:

 [tex]h=0\\y=0\\r=6.5[/tex]

Then, substituting values into [tex](x - h)^2 + (y - k)^2 = r^2[/tex], you get:

[tex](x - 0)^2 + (y - 0)^2 = (6.25)^2[/tex]

[tex]x^2 + y^2 = 42.25[/tex]

Answer:

B 1 1/7

Step-by-step explanation:

- 9 2/7 - ( -10 3/7)

We know subtracting a negative is like adding

- 9 2/7 +10 3/7

10 3/7 - 9 2/7

Putting this vertical

10  3/7

-9  2/7

-----------------

1   1/7

Answer:

1/17

Step-by-step explanation:

Using the principle of odds representation in probability, the odds that a card chosen is not spade ls 3 : 1

Not spade = (total number of cards - number of spades)

Not spade = (52 - 13) = 39

The odds of not picking a spade can be represented thus :

Therefore, the odds of not choosing a spade is 3 : 1

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In a deck of 52 cards, the odds of not drawing a spade are 3:1, meaning that for every three times one pulls a non-spade card, one time will yield a spade.

In a standard deck of 52 playing cards, there are 13 spades. Hence, the number of successful outcomes for picking a non-spade card is 52 - 13 = 39. The number of unsuccessful outcomes for not picking a spade is 13. So, the odds of not picking a spade (successful outcome) to picking a spade (unsuccessful outcome) are 39:13, which can be reduced to a simpler ratio of 3:1. Therefore, for every three times one pulls a non-spade card, one time will yield a spade.

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Rounded to the nearest hundredth of a percent, the probability that both chosen people own a dog is approximately 1.44%.

We have,

The probability of the first person owning a dog is 12%, or 0.12.

Given that the first person owns a dog, the probability of the second person also owning a dog (assuming independence) remains 12%, or 0.12.

To find the probability that both of them own a dog, you multiply these probabilities:

Probability = 0.12 * 0.12 = 0.0144

To express this as a percentage, multiply by 100:

Probability = 0.0144 * 100 = 1.44%

Thus,

Rounded to the nearest hundredth of a percent, the probability that both chosen people own a dog is approximately 1.44%.

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The probability that both randomly chosen people own a dog is 1.44%.

To find the probability that both randomly chosen people own a dog, we multiply the probability that the first person owns a dog by the probability that the second person also owns a dog.

Given:

- Probability that a person owns a dog [tex]\( P(\text{dog}) = 12\% = 0.12 \)[/tex]

Since the events (ownership of dogs by two different people) are independent, we use the multiplication rule for independent events.

[tex]\[ P(\text{both own a dog}) = P(\text{person 1 owns a dog}) \times P(\text{person 2 owns a dog}) \][/tex]

[tex]\[ P(\text{both own a dog}) = 0.12 \times 0.12 \][/tex]

[tex]\[ P(\text{both own a dog}) = 0.0144 \][/tex]

Now, convert the decimal to a percentage:

[tex]\[ P(\text{both own a dog}) = 0.0144 \times 100\% = 1.44\% \][/tex]

Answer:

First problem: a (2,0)

Second problem: b. none of these; the answer is (4, 5/3) which is not listed.

Third problem: b. none of the above; there are no holes period.

Step-by-step explanation:

First problem:  The hole is going to make both the bottom and the top zero.

So I start at the bottom first.

[tex]x^2-3x+2=0[/tex]

The left hand expression is factorable.

Since the coefficient of [tex]x^2[/tex] is 1, you are looking for two numbers that multiply to be 2 and add to be -3.

Those numbers are -2 and -1 since (-2)(-1)=2 and -2+(-1)=-3.

The factored form of the equation is:

[tex](x-2)(x-1)=0[/tex].

This means x-2=0 or x-1=0.

We have to solve both equations here.

x-2=0

Add 2 on both sides:

x=2

x-1=0

Add 1 on both sides:

x=1

Now to determine if x=2 or x=1 is a hole, we have to see if it makes the top 0.

If the top is zero when you replace in 2 for x, then x=2 is a hole.

If the top is zero when you replace in 1 for x, then x=1 is a hole.

Let's do that.

[tex]x^2-4x+4[/tex]

x=2

[tex]2^2-4(2)+4[/tex]

[tex]4-8+4[/tex]

[tex]-4+4[/tex]

[tex]0[/tex]

So we have a hole at x=2.

[tex]x^2-4x+4[/tex]

x=1

[tex]1^2-4(1)+4[/tex]

[tex]1-4+4[/tex]

[tex]-3+4[/tex]

[tex]1[/tex]

So x=1 is not a hole, it is a vertical asymptote.  We know it is a vertical asymptote instead of a hole because the numerator wasn't 0 when we plugged in the x=1.

So anyways to find the point for which we have the hole, we will cancel out the factor that makes us have 0/0.

So let's factor the denominator now.

Since the coefficient of [tex]x^2[/tex] is 1, all we have to do is find two numbers that multiply to be 4 and add up to be -4.

Those numbers are -2 and -2 because -2(-2)=4 and -2+(-2)=-4.

[tex]f(x)=\frac{(x-2)(x-2)}{(x-2)(x-1)}=\frac{x-2}{x-1}[/tex]

So now let's plug in 2 into the simplified version:

[tex]f(2)=\frac{2-2}{2-1}=\frac{0}{1}=0[/tex].

So the hole is at x=2 and the point for which the hole is at is (2,0).

a. (2,0)

Problem 2:

So these quadratics are the same kind of the ones before. They all have coefficient of [tex]x^2[/tex] being 1.

I'm going to start with the factored forms this time:

The factored form of [tex]x^2-3x-4[/tex] is [tex](x-4)(x+1)[/tex] because -4(1)=-3 and -4+1=-3.

The factored form of [tex]x^2-5x+4[/tex] is [tex](x-4)(x-1)[/tex] because -4(-1)=4 and -4+(-1)=-5.

Look at [tex]\frac{(x-4)(x+1)}{(x-4)(x-1)}[/tex].

The hole is going to be when you have 0/0.

This happens at x=4 because x-4 is 0 when x=4.

The hole is at x=4.

Let's find the point now. It is (4,something).

So let's cancel out the (x-4)'s now.

[tex]\frac{x+1}{x-1}[/tex]

Plug in x=4 to find the corresponding y:

[tex]\frac{4+1}{4-1}{/tex]

[tex]\frac{5}{3}[/tex]

The hole is at (4, 5/3).

Third problem:

[tex]x^2-4x+4[/tex] has factored form [tex](x-2)(x-2)[/tex] because (-2)(-2)=4 and -2+(-2)=-4.

[tex]x^2-5x+4[/tex] has factored form [tex](x-4)(x-1)[/tex] because (-4)(-1)=4 and -4+(-1)=-5.

There are no common factors on top and bottom.  You aren't going to have a hole.  There is no value of x that gives you 0/0.

Answer with explanation:

Total number of Children = x Children

Total number of chocolates distributed = y Chocolates

If there are x children, then total number of chocolate got by children= 5 x Chocolate

Number of chocolate got by Adults= 20

Let total number of adults be z.

Expressing the statement in terms of Equation

 y = 5 x + 20 z

[tex]z=\frac{y-5 x}{20}[/tex]

⇒Number of Adults =z

       [tex]=\frac{y-5 x}{20}[/tex]

Answer:

Step-by-step explanation:

a) 189 km/h = (189 km/h)(1 h/(3600 s))(1000 m/km) = 189/3.6 m/s = 52.5 m/s

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b) In 5 seconds, the parachutist will fall ...

  (5 s)(52.5 m/s) = 262.5 m