The population grew to 5650 in 13.48 years .
Given,
Population of town in 1940 is a function given by:
P= 1304 + 300t
Now,
Let total number of population after certain years be 5650.
Let t1 be the year in which the population reached a count of 5650. Solve for t1:
5650= 1304 + 300t1
t1 = 13.48 years
The population grew to the number 5650 in 13.48 years past 1940, approximately 1954 .
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Triangle ABC - triangle DEF. Use the image to answer the question. Determine the measurement of DF.
A. DF=3.3
B. DF=2.37
C. DF=2.28
D. DF=1.1
The measure of DF is 2.28.
We have,
Triangle ABC ≅ Triangle DEF
So,
The ratio of the corresponding sides is equal.
Now,
BA/ED = AC/DF
Substitute the values.
11/3.3 = 7.6/DF
DF = (7.6 x 3.3) / 11
DF = 7.6 x 0.3
DF = 2.28
Thus,
The measure of DF is 2.28.
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Amy opened a savings account and deposited $300.00. The account earns 2% interest, compounded continuously. If she wants to use the money to buy a new bicycle in 1 year, how much will she be able to spend on the bike?
Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.
The final amount is $2203. 2
How to determine the valueFrom the information given, the formula for finding the amount is expressed as;
A=Pert
Such that the parameters are;
A is the balance (final amount), P is the principal (starting amount) e is the base of natural logarithms (≈2.71828) r is the interest rate expressed as a decimal t is the time in years.Substitute the values, we have;
A = 300 × [tex]2.71^(^2^*^1^)[/tex]
Multiply the exponents, we have;
A = 300 × [tex]2.71^2[/tex]
Find the square value and multiply, we get;
A = $2203. 2
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WC is tangent to circle O at point W. If the radius of the circle is 32, and the tangent segment WC = 27, what is the length of CO? Round your answer to two decimal places.
The length of CO is approximately 41.89 units, rounded to two decimal places.
We have a circle O with radius 32. WC is a tangent segment to the circle at point W, and its length is 27. We are required to find the length of CO.
Since WC is tangent to the circle, it is perpendicular to the radius drawn from the center of the circle to the point of tangency (W). Let's label the center of the circle as point C.
We can use the Pythagorean theorem to find the length of CO. According to the theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, CO is the hypotenuse, and WC and OW are the other two sides of the right triangle.
Using the Pythagorean theorem, we have:
CO^2 = WC^2 + OW^2
CO^2 = 27^2 + 32^2
CO^2 = 729 + 1024
CO^2 = 1753
Taking the square root of both sides, we get:
[tex]CO ≈ √1753[/tex]
CO ≈ 41.89
Therefore, the length of CO is approximately 41.89 units, rounded to two decimal places.6
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I NEED HELP WITH STATISTICS
a.) The null hypothesis states that the number of hours worked by the software developers is not related to the mean number of hours.
The alternate hypothesis states that the number of hours worked by the software developers is related to the mean number of hours.
b.) The source of error we may be making when null hypothesis is rejected is that the mean hours will remain 44 hours.
What is alternate and null hypothesis?Alternate hypothesis is the type of hypothesis that is used to statistically test a result of a research and it is used to disprove the null hypothesis.
The null hypothesis is used to show that there is not relationship between two variables that are used in a research problem.
When a null hypothesis is rejected, it means that there is a relationship between the two variables of the research question.
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please help if you can answer any it’s helpful thanks so much
Answer:quantom physics x=y
Step-by-step explanation:
need to get oxygen
Somraj had ₹1,78,500 in his bank account and after one year, he withdrew the amount completely along with the interest of 20,489. He bought a laptop for his son worth 36,725, a dining table worth 8,800, a bike worth 56,725 and deposited the rest in his wife's account. a. What is the total cost of the bike and the dining table? Which is costlier, the bike or the dining table? b. c. What is the amount that he deposited in his wife's account?
Answer:
Step-by-step explanation:
Let's calculate the total cost of the bike and the dining table first.
The cost of the bike is ₹56,725.
The cost of the dining table is ₹8,800.
To find the total cost, we add the cost of the bike and the cost of the dining table:
₹56,725 + ₹8,800 = ₹65,525
So, the total cost of the bike and the dining table is ₹65,525.
To determine which item is costlier, we compare the costs of the bike and the dining table. In this case, the bike is costlier as it costs ₹56,725, while the dining table costs ₹8,800.
Now, let's calculate the amount that Somraj deposited in his wife's account.
He initially had ₹1,78,500 in his bank account and withdrew the entire amount along with the interest of ₹20,489. Therefore, the total amount withdrawn is:
₹1,78,500 + ₹20,489 = ₹1,98,989
From this amount, he spent ₹36,725 on the laptop, ₹8,800 on the dining table, and ₹56,725 on the bike. So, the total amount spent on these items is:
₹36,725 + ₹8,800 + ₹56,725 = ₹1,02,250
To find the amount deposited in his wife's account, we subtract the total amount spent from the total amount withdrawn:
₹1,98,989 - ₹1,02,250 = ₹96,739
Therefore, Somraj deposited ₹96,739 in his wife's account.
Answer:
a. 65,525
b. bike
c. 96,739
Step-by-step explanation:
a.
total cost of the bike and the dining table,
= 56,725 + 8,800
= 65,525
b.
bike is costlier than the dining table.
c.
total amount somraj received from bank
= 1,78,500 + 20,489
= 198,989
total expenditures
= 36,725 + 8,800 + 56,725
= 102,250
amount he saved to deposit in his wife's account
= 198,989 - 102,250
= 96,739
HELP QUICK PLS, For each of the figures, write Absolute Value equation in the form
|x−c=d|, where c and d are some numbers, to satisfy the given solution set.
pls answer!
x = -8; x = -4
The absolute value equation for x = -4 can be written as:
|x - (-2)| = 2
We have,
For x = -8, the absolute value equation can be written as:
|x - c| = d
Substituting x = -8 into the equation, we have:
|-8 - c| = d
To satisfy the given solution set, we need to determine the values of c and d that make the equation true.
Since x = -8, the absolute value of -8 minus c should be equal to d.
For x = -8, a suitable choice of c would be -12 and d would be 4.
This gives us:
|-8 - (-12)| = 4
|4| = 4
Therefore, the absolute value equation for x = -8 can be written as:
|x - (-12)| = 4
Similarly, for x = -4, the absolute value equation can be written as:
|x - c| = d
Substituting x = -4 into the equation, we have:
|-4 - c| = d
To satisfy the given solution set, we need to determine the values of c and d that make the equation true.
Since x = -4, the absolute value of -4 minus c should be equal to d.
For x = -4, a suitable choice of c would be -2 and d would be 2. This gives us:
|-4 - (-2)| = 2
|-2| = 2
Therefore,
The absolute value equation for x = -4 can be written as:
|x - (-2)| = 2
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An investor was afraid that he would become like King Lear in his retirement and beg hospitality from his children, so he purchased grain "tithes," or shares in farm output, for 800 pounds. The tithes paid him 78 pounds per year for 30 years. What interest rate did the he receive on this investment?
as far as I can read it, he bought £800 in shares, who knows how many, is irrelevant in this case, however we also know that he got £78 for 30 years, what was the rate?
well, we can nevermind the 30 years part and keep an eye that every year his earned interest was £78 flat, so we're looking at a simple interest rate, since it's not compounding, so let's reword all that
with an initial investment of £800 yielding £78 per year, what's the interest rate?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \pounds 78\\ P=\textit{original amount deposited}\dotfill & \pounds 800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 78 = (800)(\frac{r}{100})(1) \implies 78=8r\implies \cfrac{78}{8}=r\implies \stackrel{ \% }{9.75}=r[/tex]
A cylinder has a base diameter of 20 inches and a height of 2 inches. What is its volume in cubic inches, to the nearest tenths place?
Answer:
628.3 cubic inches
Step-by-step explanation:
Since the base diameter of the cylinder is d=20 inches, so its radius r is:
[tex]r=\frac{d}{2}=\frac{20}{2}=10[/tex]
Then, the volume V of the cylinder with radius r=10 inches and height h=2 inches is:
[tex]V=\pi r^{2} h=\pi\times 10^{2}\times 2=628.3[/tex]
Answer:
To find the volume of a cylinder, we need to use the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height. Since we are given the diameter of the base, which is 20 inches, we can find the radius by dividing it by 2. So, r = 20 / 2 = 10 inches. The height is given as 2 inches. Plugging these values into the formula, we get:
V = π(10)^2(2)
V = π(100)(2)
V = 200π
To get the volume in cubic inches, we need to multiply this by the conversion factor of 1 cubic inch per cubic inch. This does not change the value, but it gives us the correct units. So,
V = 200π cubic inches
To round this to the nearest tenths place, we need to look at the hundredths digit. If it is 5 or more, we round up; if it is less than 5, we round down. Using a calculator, we can approximate π as 3.14. So,
V ≈ 200(3.14) cubic inches
V ≈ 628 cubic inches
The hundredths digit is 0, which is less than 5. So we round down and keep the tenths digit as it is. Therefore,
V ≈ 628.0 cubic inches
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NEED HELP ASAP! Can otter enclosure has a cuboid shaped pool with dimensions 4m by 18m by 7m. a zookeeper decides that there should be at least 30m3 of space in the pool for every otter living in the enclosure. use this information to workout the maximum number of otters that can live in the enclosure
Answer: 16
Step-by-step explanation:
Given:
Enclosure is 4 m x 18 m x 7 m
Find:
How many 30 m³ spaces can you make in the enclosure. This will tell you how many otters can live
Solution:
Cuboid is same as cube
Volume for cube = Length x width x height
Volume for cube = 4 x 18 x 7
Volume for cube = 504 m³
Divide 504 by 30 to find the number of spaces the enclosure can hold
Can hold = 540/30
Can hold = 16.8
You cannot hold 16.8 otters because you cannot have a portion of an otter so you round down to 16.
16 is your answer
Find the volume
1.Cone whose radius is 10cm and the height is 5cm.
2.Sphere whose radius is 5m.
3.Cone whose radius is 6m and the height is 20m.
Answer:
The answers are all in 2d.p
1)523.81cm³
2)166.67m³
3)754.29m³
Step-by-step explanation:
1)V=1/3pir²h
V=1/3×10²×5×22/7
V=523.81cm³
2)V=4/3pir³
V=4/3×5³
V=166.67m³
3)V=1/3pir²h
V=1/3×22/7×6²×20
V=754.29m³
(q13) You invest in a fund and it is expected to generate $3,000 per year for the next 5 years. Find the present value of the investment if the interest rate is 4% per year compounded continuously.
The present value of the investment in the fund is $2,455.32.
In order to calculate the present value of the investment in a fund, which is expected to generate $3,000 per year for the next 5 years with an interest rate of 4% per year compounded continuously,
we can use the formula for the present value of an annuity:
PV = A / r,
where PV is the present value, A is the annuity payment, and r is the interest rate.
However, since the interest rate is compounded continuously, we need to use the formula PV = A / e^(rt),
where e is the constant 2.71828, t is the time period in years, and r is the interest rate.
In this case, A = $3,000, r = 4%, and t = 5 years.
Therefore, the present value of the investment is:
PV = $3,000 / e^(0.04 x 5)
= $3,000 / e^(0.2)
= $3,000 / 1.2214
= $2,455.32 (rounded to the nearest cent).
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
The probability of landing on purple to the nearest hundredth: 0.15
How to solveThe total number of spins is 84, and the probability of landing on purple is 13/84 = 0.15476.
Rounding to the nearest hundredth, this is 0.15.
Elaborating:
Number of times the spinner landed on purple: 13
Total number of spins: 84
Probability of landing on purple: (13/84) = 0.15476
Probability of landing on purple to the nearest hundredth: 0.15
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The Complete Question
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 18
Blue 15
Green 20
Yellow 18
Purple 13
Based on these results, express the probability that the next spin will land on purple as a decimal to the nearest hundredth.
Selina claims single having one exemption. Her state tax deduction is 21% of her federal tax contribution. Calculate the amount of state tax Selina owes if her gross pay for two weeks is $840.
The following federal tax table is for biweekly earnings of a single person.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
a.
$16.17
b.
$16.80
c.
$32.34
d.
$33.60
The amount of state tax Selina owes is $77.42.
To calculate the amount of state tax Selina owes, we need to follow the given information.
Selina's gross pay for two weeks is $840. We need to determine her federal tax contribution based on the provided tax table.
Looking at the federal tax table, we find that for a gross pay of $840, the federal tax withheld for 0 withholding allowances is $98.
Next, we calculate the state tax deduction, which is 21% of the federal tax contribution:
State tax deduction = 21% of $98
State tax deduction = 0.21 * $98
State tax deduction = $20.58
Finally, we subtract the state tax deduction from the federal tax contribution to find the amount of state tax Selina owes:
State tax owed = Federal tax contribution - State tax deduction
State tax owed = $98 - $20.58
State tax owed = $77.42
Therefore, the amount of state tax Selina owes is $77.42.
None of the provided options (a, b, c, d) match the calculated amount.
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Answer:
B. $16.56
Step-by-step explanation:
Got it right on edge 2023
Help me plssss 5 stars to whoever answers
Answer:
f = 65
s = 144
t = 144
u = 77
Step-by-step explanation:
the sum of a triangles angles will always be 180
so we can subtract 37 and 78 from 180 to find f which is 65
in regards to s and t, the sum of those 4 angles will be 360, and we can assume the opposite sides of the angles are the same.
so the other side of the 36 angle will also be 36, so we subtract 36 and 36 from from 380 which gives us 288
then we divide it by 2 because we have 2 unknown angles that are the same size, then we get 144 for s and 144 for t
the sum of the angles of a polygon will always be 360
so we can subtract 86 and 53 and t (which we now know is 144) from 360 to find u
so u = 77
Use cramer's rule to solve this system: 8x+5y= 2x - 4y = - 10
The solution to the system of equations using Cramer's rule is x = -1 and y = 2.
To solve the system of equations using Cramer's rule, we'll need to determine the values of x and y by calculating the determinants of various matrices.
The given system of equations is:
8x + 5y = 2 (Equation 1)
2x - 4y = -10 (Equation 2)
First, let's calculate the determinant of the coefficient matrix, D:
D = |8 5|
|2 -4|
D = (8 * -4) - (5 * 2)
D = -32 - 10
D = -42
Next, we'll calculate the determinant of the matrix formed by replacing the x coefficients with the constants from the right side of the equations, Dx:
Dx = |2 5|
|-10 -4|
Dx = (2 * -4) - (5 * -10)
Dx = -8 + 50
Dx = 42
Similarly, we'll calculate the determinant of the matrix formed by replacing the y coefficients with the constants, Dy:
Dy = |8 2|
|2 -10|
Dy = (8 * -10) - (2 * 2)
Dy = -80 - 4
Dy = -84
Now, we can find the values of x and y:
x = Dx / D
x = 42 / -42
x = -1
y = Dy / D
y = -84 / -42
y = 2
Therefore, the solution to the system of equations is x = -1 and y = 2.
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Convert the following: i. 6 feet into cm
The measurement of the length of 6 feet is 182.88 cm after unit conversion.
Given data ,
To convert feet to centimeters, we need to know the conversion factor between the two units.
In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
1 foot is equal to 30.48 centimeters.
To convert 6 feet to centimeters, we can use the conversion factor:
A = 6 feet x 30.48 centimeters/foot
On simplifying the equation , we get
A = 182.88 centimeters.
Therefore , the value of A is A = 182.88 cm
Hence , 6 feet is equal to 182.88 centimeters.
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A steel manufacturer wants to produce a container in the shape of a rectangular solid with volume 84 m3 . The manufacturer wants the length of the container to be one meter longer than the width, and the height to be one meter greater than twice the width. What should the dimensions of the container be?
Answer:
Step-by-step explanation:
Vanilla Ice cream comes in 2 sizes. The 48 oz box costs $1.97. The 128 oz costs $5.87. Which size is the better buy?
Answer: The 128 oz box is the better buy.
What is the co-interior angle x in the drawing below? Type in numerical answer only
Answer:
[tex]58 + x = 180[/tex]
[tex]x = 122[/tex]
Angle x measures 122°.
5/6x - 1/3 > 1 1/3
Solve for x
Answer:
First subtract (4) and (3x) from each side of the equation to isolate the x ... 5x-4=3x-8 One solution was found : x = -2 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
Step-by-step explanation:
Answer:
x > 2
Step-by-step explanation:
To solve for x, we will first simplify the left side of the inequality by finding a common denominator for the fractions:
5/6x - 1/3 > 4/3
Multiplying both sides by 6 to eliminate the fractions, we get:
5x - 2 > 8
Adding 2 to both sides, we have:
5x > 10
Dividing both sides by 5, the final answer is:
x > 2
Hope this helps!
given cos theta=4/5 and theta is in the 1st quadrant. find the angle equivalent to theta between 0 and 360 degrees. (give answer to 2. dp)
The angle equivalent to θ between 0 and 360 degrees is approximately 36.87 degrees.
We have,
To find the angle equivalent to θ between 0 and 360 degrees, we can use the inverse cosine function [tex](cos^{-1}).[/tex]
The given value of cos θ = 4/5 represents the cosine of an angle in the first quadrant. In the first quadrant, all trigonometric functions are positive, including cosine.
Taking the inverse cosine [tex](cos^{-1})[/tex] of both sides of the equation, we get:
θ =[tex]cos^{-1}(4/5)[/tex]
The inverse cosine function returns the angle whose cosine is equal to the given value.
Evaluating [tex]cos^{-1}(4/5)[/tex] using a calculator or trigonometric tables, we find the value to be approximately 36.87 degrees.
Therefore,
The angle equivalent to θ between 0 and 360 degrees is approximately 36.87 degrees.
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in aright prism,all the lateral faces are rectangles. true or false
True. In a right prism, all the lateral faces are indeed rectangles.
Given data ,
A right prism is a three-dimensional solid with congruent polygonal bases and rectangular lateral faces that connect the corresponding sides of the bases.
Bases: A right prism has two parallel polygonal bases that are congruent. The bases can be any polygon, such as a triangle, rectangle, square, pentagon, etc. The shape of the bases determines the overall shape of the prism.
Height: The height of a right prism is the perpendicular distance between the two bases. It is the length of the lateral edges connecting the corresponding vertices of the bases.
Lateral Faces: The lateral faces of a right prism are rectangular in shape. They are perpendicular to the bases and connect the corresponding edges of the bases. The lateral faces are always parallelograms, and their opposite sides are equal in length.
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simplify and write in usual form ((5.5 * 10 ^ - 4)(6 * 10 ^ 7))/((3.3 * 10 ^ - 6) * (2 * 10 ^ 4) ^ 2)
Step-by-step explanation:
Expand the given 10 n and multiply it by the given number. 2. Then the result will be in the usual form.
if i were to make 126 dollars a week and i were to work for one year, how much money would i have when the year is over? please hurry
What is the angle of o in the drawing below? Type in numerical answer only
Answer:
[tex]52 + o = 180[/tex]
[tex]o = 128[/tex]
Angle o measures 128°.
A 13 km 13km13, start text, k, m, end text stretch of road needs repairs. Workers can repair 3 1 2 km 3 2 1 km3, start fraction, 1, divided by, 2, end fraction, start text, k, m, end text of road per week. How many weeks will it take to repair this stretch of road?
you can start by dividing the total length of the road by the distance that can be repaired per week:
13 km ÷ 3 1/2 km/week = 3.71 weeks
Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.
Write each expression in factored form. If it is not possible, write “not possible.”
a2−36
49−25b2
c2+9
10081−16d2
64+121b2
Expression in factored form
a² - 36 = (a + 6)(a - 6)
49 - 25b² = (7 - 5b)(7 + 5b)
c² + 9 = Not possible (sum of squares)
10081 - 16d² = (101 - 4d)(101 + 4d)
64 + 121b² = Not possible (sum of squares)
Let's factorize each expression:
a² - 36:
This expression is a difference of squares, as it can be written as (a + 6)(a - 6). Therefore, the factored form is (a + 6)(a - 6).
49 - 25b²:
This expression is also a difference of squares. It can be factored as (7 - 5b)(7 + 5b).
c² + 9:
This expression is not factorable because it is a sum of squares. The factored form is not possible.
10081 - 16d²:
This expression is a difference of squares. It can be factored as (101 - 4d)(101 + 4d).
64 + 121b²:
This expression is not factorable because it is a sum of squares. The factored form is not possible.
To summarize:
a² - 36 = (a + 6)(a - 6)
49 - 25b² = (7 - 5b)(7 + 5b)
c² + 9 = Not possible (sum of squares)
10081 - 16d² = (101 - 4d)(101 + 4d)
64 + 121b² = Not possible (sum of squares)
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A spinner with three equal size sections labeled red, green, and yellow is
spun once. Then a coin is tossed, and one of two cards labeled with a 1 or
a 2 is selected. What is the probability of spinning yellow, tossing heads,
and selecting the number 2?
FASTTT (ASAPPP!)
a racer is traveling 150 miles per hour how many feet dose it travel in 5 seconds
150 miles is the same as 150*5280 = 792000 feet, and one hour is equivalent to 60*60 = 3600 seconds. Now we divide 792000 feet by 3600 seconds to get the equivalent rate: 792000 ft/3600 sec = 220 ft/second. Now, we multiply the rate by 5 and get 1100 feet per 5 seconds. So, our answer is 1100 feet.
