A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?
A. $0.60B. $0.70C. $0.80D. $0.90E. $1.00

Answer:

36.888

Step-by-step explanation:

you would just add them all up. 11.238 + 9.45 + 16.2 then you'll get your answer which is 36.888

Answer:

The answer to your question is: 10. 1 miles

Step-by-step explanation:

data

P = (-1, 3)

Q = (3, -3)

Formula

d = √((x2-x1)² + (y2-y1)²)

d = √)(3- -1)² + (-3-3))

d = √ (4² + -6²)

d = √ (16 + 36)

d = √ 52

d = 7.21 units

but

           1 units ----------------------- 1.4 miles

        7.21 units ---------------------     x

              x = 7.21 x 1.4/1 = 10.1 miles

Answer:12.5 seconds

Step-by-step explanation:hconsidering Runner 1 with a speed of 10m/s

and Runner 2 with a speed of 4 m/s

the equation of displacement for a uniform movement is

x=V*t

so x1=V1*t

and x2=V2*t

and the problem condition is x2=x1+75m

so we proceed to solve the equations.

from equation 2 t=x2/V2

substituting in equation 1 we have

x1=V1(x2/V2) and then the 3 equation

x1=V1((x1+75m)/v2

finally x1=75*(V1/(V2-V1)) =75*(10/(10-4))=125m

then t=(x1/v1)=125/10=12.5 seconds

Answer:

12.5 seconds

Step-by-step explanation:

Speed of the first person = 10 meter per second

Speed of the second person = 4 meter per second

Relative velocity of faster person = 10 - 4 = 6 meter per second

since distance between both the person is = 75 meter.

Therefore, time to cover this distance by faster person = [tex]\frac{Distance}{Speed}[/tex]

[tex]\frac{75}{6}[/tex]

= 12.5 seconds.

Faster runner catches the slower runner after 12.5 seconds.

Answer:

See the picture

Step-by-step explanation:

Interval   (-∞, 1] U (8, ∞)

On a number line the inequality x ≤ 1 shows all the numbers less than 1 and x>8 shows all the numbers greater than 8.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The graph of the two inequality is attached with the answer below where the inequality x ≤ 1 shows all the numbers less than 1 and x>8 shows all the numbers greater than 8.

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Answer:

  C = 18g +350

Step-by-step explanation:

The 2-point form of the equation of a line is useful for this. For points (x1, y1) and (x2, y2), the equation is ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

For points (25, 800) and (60, 1430), the line is ...

  y = (1430 -800)/(60 -25)(x -25) +800

  y = 630/35(x -25) +800

  y = 18x +350

Using the variables required by the problem statement, this is ...

  C = 18g +350

To find the probability that a middle-aged man with diabetes is very active, we need to use conditional probability. We calculate the probability of a middle-aged man being very active and the probability that a middle-aged man has diabetes. Then we use these probabilities to find the conditional probability of being very active given diabetes.

To find the probability that a middle-aged man with diabetes is very active, we need to use conditional probability. Let's first calculate the probability of a middle-aged man being very active:

P(very active) = 1/10

The remaining probability would be for men who are sedentary:

P(sedentary) = 1 - P(very active) = 9/10

Now we can calculate the probability that a middle-aged man with diabetes is very active using conditional probability:

P(very active | diabetes) = (P(very active) * P(diabetes | very active)) / P(diabetes)

Since the question states that men who are very active are a third as likely to develop diabetes compared to men who are sedentary, we can calculate:

P(diabetes | very active) = 202/5990

P(diabetes) = (202/5990 * 1/10) + (P(diabetes | sedentary) * 9/10)

Substituting the values, we can calculate the probability that a middle-aged man with diabetes is very active:

P(very active | diabetes) = (1/10 * 202/5990) / ((202/5990 * 1/10) + (P(diabetes | sedentary) * 9/10))

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The probability that a middle-aged man with diabetes is very active is:

[tex]\[ {0.0356} \][/tex].

Given data:

- [tex]\( P(A) = \frac{1}{10} = 0.1 \)[/tex](probability of being very active)

- [tex]\( P(S) = \frac{9}{10} = 0.9 \)[/tex] (probability of being sedentary)

- [tex]\( P(D | S) \)[/tex] (probability of developing diabetes given sedentary) is not directly given, but we can deduce it using the provided data and the fact that the risk of diabetes for active men is a third of that for sedentary men.

- Total probability of developing diabetes, [tex]\( P(D) = \frac{202}{5990} \approx 0.0337 \)[/tex]

First, we need to calculate [tex]\( P(D | A) \) and \( P(D | S) \)[/tex]:

Since active men are a third as likely to develop diabetes compared to sedentary men:

[tex]\[ P(D | A) = \frac{1}{3} P(D | S) \][/tex]

Using the law of total probability for  P(D) :

[tex]\[ P(D) = P(D | A)P(A) + P(D | S)P(S) \][/tex]

Substitute the given values and the relationship between  P(D | A) and  P(D | S):

[tex]\[ 0.0337 = \left( \frac{1}{3} P(D | S) \right)(0.1) + P(D | S)(0.9) \][/tex]

Solve for P(D | S) :

[tex]\[ 0.0337 = \frac{1}{30} P(D | S) + 0.9 P(D | S) \]\[ 0.0337 = 0.0333 P(D | S) + 0.9 P(D | S) \]\[ 0.0337 = (0.0333 + 0.9) P(D | S) \]\[ 0.0337 = 0.9333 P(D | S) \]\[ P(D | S) = \frac{0.0337}{0.9333} \approx 0.0361 \][/tex]

Now calculate  P(D | A) :

[tex]\[ P(D | A) = \frac{1}{3} P(D | S) = \frac{1}{3} \times 0.0361 \approx 0.0120 \][/tex]

Next, apply Bayes' theorem to find  P(A | D) :

[tex]\[ P(A | D) = \frac{P(D | A) P(A)}{P(D)} \]\[ P(A | D) = \frac{0.0120 \times 0.1}{0.0337} \]\[ P(A | D) = \frac{0.0012}{0.0337} \approx 0.0356 \][/tex]

Answer:

8,695

Step-by-step explanation:

The formula for compound interest is :

Money = C * (1+r)^n

Where

C is the money invested

r is the interest

n is the periods you are investing

Money is the money you will have at the end of the period

In this problem C is what you need to find, the interest is 3.5% (anually) and since it is compounded monthly you have to divide it by 12 months to know exactly the interest of each month:

3.5/12 = 0.2917

The number of periods invested is 4 years, and because the interest is monthly the exact number of periods is 48 ( 4* 12 )

Replacing and solving:

10000 = C * (1+0.002917)^48

C = 8,695

Answer:

8,695

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

1/3+1/4=7/12

7/12*24=12

24+12=26

Answer:

E)II and III only

Step-by-step explanation:

This can be seen with examples. Say a[0]=1 and and a[1]=2.

for I , the first line of code would be:

a[0]=a[1];

thus, we would get a new value for a[0]=2.

The second line of code

a[1]=a[0]; uses the new value of a[0], so we would get a[1]=2.

The end result is a[0]=2, and a[1]=2 which doesn't exchange the values of the first two elements.

For II the first line of code

int t= a[0]; saves the original value of a[0] to t, so we get t=1.

the second line of code

a[0]=a[1]; changes the value of a[0]  to that of a[1]. Thus, in our example a[0]=2.

the final line

a[1]=t; changes the value of a[1] to the original value of a[0], giving us a[1]=1 and a[0]=2, what we were looking for.

For III

the first line of code

a[0]=a[0]-a[1];

gives us

a[0]=1-2

the secon line

a[1]=a[1]+a[0];

takes the new value of a[0] and replaces it in the expression

a[1]= 2+(1-2)=1

the last line

a[0]=a[1]-a[0];

takes the new value of a[0] and a[1] and replaces the in the expression

a[0]=1-(1-2)=1-1+2=2

which exchanges the values needed.

So we can see that only II and III do what we require, giving us E as the answer.

[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-6)}}}\implies \cfrac{-8}{-3+6}\implies -\cfrac{8}{3}[/tex]

Check the picture below.

make sure your calculator is in Degree mode.

The angle that the ladder makes with the ground would be 66.42 degrees.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are given that  ladder is leaning against a building. The ladder is 10m long and it is sitting on the ground 4m out from the building.

The side adjacent to the angle is given, and the hypotenuse of the triangle is the unknown.

The cosine relation applies

 Cos = Adjacent/Hypotenuse

We are given the hypotenuse = ladder length

Cos (∅)= (4 )/10

Cos (∅)≈ 2/5

(∅)≈ [tex]Cos^{-1}[/tex]2/5

(∅) = 66.42

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Answer:

The answer is (d) "None of the these alternatives are correct"

Step-by-step explanation:

If two events A and B are independent, the probability of the intersection [tex]P(A\cap B)[/tex] is defined as:

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

Therefore, in the exercise:

[tex]P(A\cap B)=P(A)\cdot P(B)=0.5\cdot 0.5\\P(A\cap B)=0.25[/tex]

which give (d) "None of the these alternatives are correct"

For independent events A and B with P(A) = 0.5 and P(B) = 0.5, the probability of both events occurring, P(A ∩ B), is the product of their probabilities, which is 0.5 × 0.5 = 0.25. The correct answer is 'd. None of these alternatives are correct.'

The question revolves around the concept of independent events in probability. Since events A and B are independent, the probability of both events occurring together, P(A ∩ B), is the product of their individual probabilities. Thus, using the given probabilities P(A) = 0.5 and P(B) = 0.5, the probability of both A and B occurring is found by multiplying these probabilities together.

P(A ∩ B) = P(A) × P(B) = 0.5 × 0.5 = 0.25.

Therefore, the correct answer is not listed among the provided alternatives, so the correct choice would be 'd. None of these alternatives are correct.'

Answer:

The equation of the line is [tex]y=45.25t+545[/tex]

Step-by-step explanation:

The general for of a line is:

[tex]y=mt+n[/tex]       (1)

where:

[tex]m[/tex] is the slope of the line and [tex]m[/tex] is the intercept with the axis of the dependent variable, [tex]y[/tex] in this case.

In order to obtain the value of the slope ([tex]m[/tex]) we can use the corresponding slope formula:

[tex]m=\frac{y_{2}-y_1 }{t_2-t_1}[/tex]         (2)

where [tex]t_1, t_2, y_1[/tex] and [tex]y_2[/tex] are the corresponding coordinates of the given points. In this case:

[tex]t_1=0\\t_2=4\\y_1=545\\y_2=726\\[/tex]

Substituting these values in equation (2) we obtain:

[tex]m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25[/tex]

Hence, the line equation is now:

[tex]y=45.25t+n[/tex]     (3)

Now to obtain the value of [tex]n[/tex] you can follow two options:

Note that for this question, it is easier to select point A because of having the independent variable equals to zero [tex]t=0[/tex]. Hence, substituting point A in equation (3):

[tex]45.25*0+n=545\\n=545[/tex]

Therefore, the line equation is: [tex]y=45.25t+545[/tex]

The second option to find [tex]n[/tex] is to think of the meaning of the intercept. The intercept of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that [tex]n[/tex] is equal to [tex]545[/tex].

See the attachment for a plot of the line.

Final answer:

To derive the equation of the line through A(0, 545) and B(4, 726), calculate the slope (45.25) and use the point-slope form to get the final equation: [tex]\(y = 45.25t + 545\).[/tex]

Explanation:

To derive an equation of the line passing through points A(0, 545) and B(4, 726), first we need to find the slope of the line. The slope, usually represented as[tex]\(m\),[/tex] is given by the change in \(y\) over the change in \(x\), which is [tex]\(\Delta y / \Delta x\).[/tex]We use the formula [tex]\(m = (y_2 - y_1) / (x_2 - x_1)\).[/tex]

Substituting the given points into the formula:

[tex]\[m = \frac{726 - 545}{4 - 0} = \frac{181}{4} = 45.25\][/tex]

Now that we have the slope, we use the point-slope form of a line's equation, which is [tex]\(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\)[/tex]is a point on the line. Since one point we have is A(0, 545), we can substitute the values in:

[tex]\[y - 545 = 45.25 \cdot (x - 0)\][/tex]

Therefore, the equation simplifies to:

[tex]\[y = 45.25x + 545\][/tex]

This is the equation of the line in slope-intercept form, with \(t\) being the independent variable and \(y\) being the dependent variable.

Answer:

In this case study we have following groups:

1. Population: It had all the cars which passed the bicyclist. Out of which 3000 cars were taken.

2. Who:  Each instance of a car passing a rider, means the drivers passing by.

That is the 3000 cars which passed the researcher on his bicycle.

3. What: The distance at which cars pass the bicycle rider. The distance the drivers stayed away from his bike.

The subject of this question is the cars in the study.

The Who in this study refers to the cases under study. In this case, the cases under study are the cars. The researcher rigged his bicycle with an ultrasonic sensor to measure how close each car was that passed him, and he observed that when he wore a helmet, motorists passed closer to him compared to when his head was bare. Therefore, the cars are the subject of this study.

Answer:

A. [tex]150+75h>600[/tex]

B. More than 6 hours

Step-by-step explanation:

A plumber earns $50 for a repair job, so he will earn $150 for three repair jobs.

Let h be the number of hours the plumber worked on Tuesday. He earns $75 per hour worked, so he will earn $75h in h hours.

In total, the plumber earned $(150 + 75h)

A. On Tuesday, he completed 3 repair jobs and earned a total of more than $600. Thus

[tex]150+75h>600[/tex]

B. Solve this inequality. Subtract 150:

[tex]150+75h-150>600-150\\ \\75h>450[/tex]

Divide by 75:

[tex]h>\dfrac{450}{75}\\ \\h>6[/tex]

This means, the plumber worked more than 6 hours.

Answer:

D.8 inches

Step-by-step explanation:

Answer:

May

Step-by-step explanation:

Let x be the sales in January,

∵ Sales were 10% greater in February than in January,

So, the sales in February = (100 +10)% of x

= 110% of x

= [tex]\frac{110x}{100}[/tex]

= 1.1x

∵  it is 15% less in March than in Feb,

Sales in march = (100-15)% sales in February

= 85% of 1.1x

= 0.935x

∵ It is 20% greater in April than in March,

Sales in April = (100+20)% of sales in march

= 120% of 0.935x

= 1.122x,

∵ It is 10% less in May than in April

Sales in May = (100-10)% of sales in march

= 90% of 1.122x,

= 1.0098x,

∵ It is 5% greater in June than in May

Sales in June = (100+5)% of sales in march

= 105% of 1.0098x,

= 1.5147x

∵ 1.0098x is much closure to x than 1.1x, 0.935x, 1.122x and 1.5147x

Hence, the sales in May is closest to sales in January.

In order to get the answer to this question you will have to rearrange and solve the question step by step.

[tex]10=7-m[/tex]

Rearrange:

[tex]10-(7-m)=0[/tex]

[tex]10-7=3[/tex]

Rearrange once more:

[tex]m+3=0[/tex]

[tex]-3 -3[/tex]

[tex]m=-3[/tex]

Therefore the answer is "m=-3."

Hope this helps.

Answer:

P = 8x + 2

P = 98 when x = 12

Step-by-step explanation:

the perimeter is 2 times width + length

P = 2(w + l)

w = 2x - 5

l = 2x + 6

replacing both terms in the perimeter:

P = 2(2x - 5 + 2x + 6)

P = 2(4x + 1)

P = 8x + 2

Evaluating P for x = 12

P = 8(12) + 2

P = 98

Answer:

The answer is d) 297000

Step-by-step explanation:

The stockholders' equity of a company represents the amount of money that will be returned to the accionists if all the assests will be liquidated and the compan'y debt will be paid.  So to calculate the Swifty Corporation stockholders' equity at the end of the year you need to add all what enters to the company (assets and revenues) and substract all what goes out (liabilities, expenses and dividends).

- What enters?

Total incomes = $300.000 + $633.000 = $933.000

- What goes out?

Total expenses = $240.000 + $335.000 + $61.000 = $636.000

Stockholders' equity = Total income - Total expenses

Stockholders' equity = $933.000 - $636.000 = $297.000

In order to get the answer to this question you will have to multiply both sides by 8.75 and you will get your answer.

[tex]\frac{w}{8.75} =7[/tex]

[tex]\times8.75\times8.75[/tex]

[tex]7\times8.75=61.25[/tex]

[tex]w=61.25[/tex]

Therefore your answer is "w = 61.25."

Hope this helps.

Answer:

They are intersecting line segments ⇒ answer b

Step-by-step explanation:

* Lets explain the types of the lines

- Parallel lines lie in the same plane and never intersect each other

- Intersecting lines are lines that meet each other in exactly one point

- Skew lines are lines that are in different planes and never intersect

* Now lets solve the problem

- The line segments that cut sides of a wedge of apple pie

∵ The wage of apple pie could represent a plane

∵ The line segments cut the sides of the wedge

∴ The lines are in the same plane

∵ Skew lines are in different planes and never intersect

∴ The lines can not be skew

∵ The line segments that cut sides of the wage must be intersected

   at exactly one point

∵ Parallel lines never intersected

∴ The lines can not be parallel lines

∴ They are intersecting line segments

Answer:

A- for every animal, if the animal is a rabbit, the animal hops.

B- every animal is a rabbit and it hops.

C-there are animals that, if they are rabbits, they hop.

D-there are animals that are rabbits and they hop

Answer:

a) For every animal, if the animal is a rabbit, then the animal hops

b) For every animal, the animal is a rabbit and the animal hops

c) there are animals such that if they are rabbits then they hop

d) there are animals such that they are rabbits and they hop

Step-by-step explanation:

∀ For every

a⇒b  a then b

a∧b   a and b

∃ there are

Answer:

  24

Step-by-step explanation:

The greatest common divisor of 72 and 96 is 24. Robert can make any number of bags that is a divisor of 24. If he wants to make the largest number possible, then he can make 24 bags with 4 balloons and 3 pieces of candy in each one.

__

  72 = 2³·3²

  96 = 2⁵·3

The greatest common divisor is the product of the common factors: 2³·3 = 24.

Answer:

The statistical tests that researchers use to determine if there was a statisticallysignificant difference in levels of self-esteem between the boys and the girls were the T-test and Cohen's d.

Step-by-step explanation:

A statistical test is utilized to evaluate differences between groups (in this case, between boy and girls). The dependent variable was the self-esteem while the independent variable was the sex. A T-test is utilized to establish differences in the mean of two groups. The null hypothesis for a T-test is that means of the groups are the same; the statistical value is t. A Cohen's d test indicates standardized differences between the mean of both groups. It usually accompanies a T-test result; the statistical value is d.

Answer:

Option D. No solutions

Step-by-step explanation:

we have

[tex]3x+2y=1[/tex] -----> equation A

[tex]-9x-6y=3[/tex] ----> equation B

Multiply by -3 both sides equation A

[tex]-3(3x+2y)=-3(1)[/tex]

[tex]-9x-6y=-3[/tex] -----> equation C

Compare equation B and equation C

Equation B and equation C are parallel lines with different y-intercept

Verify

For x=0

Equation C

[tex]-9(0)-6y=-3[/tex] ----->[tex]y=0.5[/tex]

The y-intercept is the point (0,0.5)

Equation B

[tex]-9(0)-6y=3[/tex] ----->[tex]y=-0.5[/tex]

The y-intercept is the point (0,-0.5)

therefore

Lines do not intersect

The system has no solution

see the attached figure to better understand the problem

Final answer:

The system of equations has infinitely many solutions because the second equation is an exact multiple of the first, indicating that both equations are equivalent and represent the same line.

Explanation:

To determine how many solutions the system of equations has, we can look at the coefficients of the variables x and y in both equations.

The first equation is 3x + 2y = 1.

The second equation is -9x - 6y = 3. If we multiply the first equation by -3, we obtain -9x - 6y = -3.

We notice that the second equation is an exact multiple of the first equation after our manipulation. This means that the two equations are equivalent, and every solution to one equation is also a solution to the other. Thus, the system does not have a unique solution, but rather infinitely many solutions, as both lines represented by these equations would perfectly overlap on a graph.

The correct answer to the question is A. Infinitely many solutions.

Answer:

Perimeter at the big rectangle is 156 cm.

Step-by-step explanation:

Let's see how to calculate it.

1. First of all you know that perimeter in the blue one is 20cm, so imagine this:

L (long side); S (short side)

2L + 2S =20

and we consider that L = 4S

So, solving the equation:

2.4S + 2S =20

10S=20

S=20/10

S=2

L=8

2. Side at the gold square is 8, the same at the long side in the blue rectangle. So, if you see on the right side in the big one, we got 2 + 8 + 8 + (?). Take a look to the green. Green square is the gold + a short piece and you can understand the short piece as 2 short sides from the blue. If we give numbers we have 8 + 2 + 2, 12.

Now, 2+8+8+12 = 30cm

3. Let's go to the long side in the big one.

We have long side from blue (8) and as you see, side at the orange square must be side at the yellow + short at the blue, so 8+2 =10. We have four oranges square so 10+10+10+10=40, and +8 =48

4. Now that we have the two sides in the big one, let's find the perimeter with the rectangle formula:

2L + 2S =P

2.48 + 2.30 = 156 cm.

Answer:

27.32 m

Step-by-step explanation:

We are given that

Height of window from the ground=18 m

Height of rock  form the ground=2 m

Speed of thrown rock=30 m/s

We have to find the horizontal distance from the window from which rock was release.

Difference between window and rock=18-2=16 m

Initial vertical velocity component=[tex]30sin40^{\circ}=19.28 [/tex]m/s

Initial horizontal velocity component=[tex]30cos 40^{\circ}=22.98 m/s[/tex]

If the rock is reached to maximum height

Then, maximum height=[tex]\frac{v^2}{2g}=\frac{(19.28)^2}{2\times 9.8}=18.9731 m[/tex]

Time taken by rock to reach maximum height=[tex]\frac{v}{g}=\frac{19.28}{9.8}=1.96775 s[/tex]

Distance between window and maximum height at which rock reached=18.9731-16=2.973 m

Time to drop 2.973 m=[tex]\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\cdot 2.973}{9.8}}=0.77893 s[/tex]

Time to be at 16 m=1.96775-0.77893=1.189 s

Horizontal distance=[tex]1.189\times 22.98=27.32 m[/tex]

Hence, horizontal distance of rock from the window from which rock was released=27.32 m

The rock was released approximately 71.1 meters horizontally from the window. This calculation is based on the rock's initial speed of 30.0 m/s, launch angle of 40.0°, and the fact that it struck the window on its upward trajectory with no air resistance.

To solve this problem, we can use the kinematic equations of motion. We need to find the horizontal distance the rock was released from the window.

1. First, we can find the time it takes for the rock to reach its maximum height. We can use the following kinematic equation:

[tex]\[v_y = u_y + at\][/tex]

  Where:

  - [tex]\(v_y\)[/tex] is the final vertical velocity (0 m/s at the maximum height),

  - [tex]\(u_y\)[/tex] is the initial vertical velocity (30.0 m/s, since it's thrown vertically),

  - \(a\) is the vertical acceleration due to gravity (-9.81 m/s²),

  - \(t\) is the time.

  Rearrange the equation to solve for t:

 [tex]\[0 = 30 - 9.81t\]\\\\[/tex]

[tex]\[t = \frac{30}{9.81} \approx 3.06 \, \text{s}\][/tex]

2. Now, we can find the horizontal distance using the horizontal motion equation:

 [tex]\[d_x = u_x \cdot t\][/tex]

  Where:

  - [tex]\(d_x\)[/tex] is the horizontal distance we want to find.

  - [tex]\(u_x\)[/tex] is the horizontal component of the initial velocity                                    
[tex](30.0 m/s * cos(40°)).[/tex]

  - \(t\) is the time calculated in step 1.

  Plug in the values:

[tex]\[d_x = (30 \cdot \cos(40°)) \cdot 3.06 \approx 71.1 \, \text{m}\][/tex]

So, the rock was released approximately 71.1 meters horizontally from the window.

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The value of 5 in 5,476,807,139 is five billion, as it is positioned in the billions place. This is explained by the concept of place value.

The value of 5 in the number 5,476,807,139 refers to its place value in the numerical system. In this case, the 5 is in the billions place. This means that, in terms of place value, that 5 actually represents [5 × 1,000,000,000], which is 5,000,000,000 or five billion. The concept of place value is important in mathematics, it tells you how much each digit in a number is worth according to its position.

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