The correct form of the expression is x² -9
How to find the rewrite the expression?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is y = (x − 3)(x + 3) =
This can be done by opening the brackets
x²+3x-3x-9
⇒x²-9
Therefore, the correct form of the equation is x²-9
The x-intercept = 1 and the y intercept is -9
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1522 customers at a major retailer were surveyed whether or not they made a purchase and were satisfied with the service they received. The table below organizes the responses.
Satisfied with Service
Not Satisfied with Service
Total
Made a Purchase
130
494
624
Did Not Make a Purchase
715
183
898
Total
845
677
1522
What are the odds that a shopper selected at random was satisfied with the service they received?
Probability that the shopper selected at random was satisfied with the service they received is 845 / 1522.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Total number of customers = 1522
Out of these,
Number of customers made a purchase = 624
Number of customers not made a purchase = 898
Number of customers who purchased satisfied with the service = 130
Number of customers who does not purchase satisfied with the service = 715
Total number of customers who are satisfied with the service = 130 + 715 = 845
Probability that the randomly selected shopper satisfied with the service = 845 / 1522
Hence the probability is 845 / 1522.
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If the terminal side of angle A goes through the point (−24/25,7/25) on the unit circle, then what is sin(A)?
The value of sin A is, 7/25.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
The terminal side of angle A goes through the point (−24/25,7/25) on the unit circle.
Now, By definition we get;
⇒ cos A = - 24/25
⇒ Sin A = 7/25
Thus, The value of sin A is, 7/25.
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what is the correlation between the amount of rain (mm) in the summer and the amount of water (m2) used for watering the lawn
The correlation between the amount of rain (mm) in the summer and the amount of water (m2) used for watering the lawn is directly proportion to each other
The classification of rainBased on the grain size, the classification of rain is divided into four, namely:
Drizzle is a small amount of rain precipitation that can even be called light, which generally has a diameter of less than 0.5 mm. Drizzle is caused by small stratus clouds and stratocumulus clouds. Snowfall or snow is rain from small crystals of water that turn into ice and have temperatures below freezing. Hail hailstones are ice cubes that fall from clouds that have temperatures below 0° degrees Celsius which occur in hot weather Heavy rain is an outpouring of water that has grains of approximately 7 millimeters and comes from clouds that have temperatures above 0°.Learn more about amount of rain at https://brainly.com/question/30487357
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47) A convention manager finds that she has $1370, made up of twenties and fifties. She has a total of 46 bills. How many fifty-dollar bills does the manager have?
The number of fifty dollars with the manager are 31.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a convention manager finds that she has $1370, made up of twenties and fifties.
20x+50y=1370
She has a total of 46 bills.
x+y=46
x=46-y
Now we have to plug in x value in equation 1
20(46-y)+50y=1370
920-20y+50y=1370
920+30y=1370
Subtract 920 on both sides
30y=450
Divide both sides by 30
y=15
Now plug in y value in x+y=46
x+15=46
Subtract 15 on both sides
x=46-15
x=31
Hence, the number of fifty dollars with the manager are 31.
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Help pic is included y(x^2+1)=1
Answer:
C.
Step-by-step explanation:
The answer is C (-1, 1/2)
Find the equation of the line through the point (7,-9) with slope -5/7 The equation is (Be sure to enter your answer as an equation)
Required the equation of the line is y = -5/7 *x -4.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
the line through the point (7,-9) with slope -5/7
so, m= -5/7
now, y= mx+c
solving with the given values we get,
c= -9 +5
= -4
Hence, Required the equation of the line is y = -5/7 *x -4.
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8/10 of 3/9 is what?
From IXL
Answer:
7/15
Step-by-step explanation:
Select the correct answer.
Where does the graph of y= sin x from x = 0 to x = 277 start?
OA.
OB.
O C.
O D.
at its minimum
at an x-intercept
at its maximum
between an x-intercept and its maximum
Answer:
At an x-intercept
Step-by-step explanation:
y = sin x
y = sin 0
y = 0
(0,0) is an x-intercept but not it's maximum or minimum.
12x - 3у = -3
6x + y = 1
Use elimination
Pls hurry I need it now
The solution of the system of equations is (0, 1).
How to solve the system of equations?Here we want to solve the system of equations:
12x - 3y = -3
6x + y = 1
To use the elimination method, we can take the difference between the first equation and two times the second one, then we will get:
12x - 3y - 2*(6x + y) = -3 - 2*1
12x - 3y - 12x - 2y = -5
-5y = -5
y = -5/-5 = 1
Now we know the value of y, we can replace it in one of the equations ot find the value of x.
6x + y = 1
6x + 1 = 1
6x = 1 - 1 = 0
x = 0
The solution is (0, 1)
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Han wants to buy a $30 ticket to a game, but the pre-order tickets are sold out. He knows there will be more tickets sold of the day of the game, with a markup of 200%. How much should Han expect to pay for the ticket if he buys it the days of the game?
Han should expect to pay $90 for the ticket if he buys it the day of the game.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Han should expect to pay $90 for the ticket if he buys it the day of the game
The current ticket fee = $30
The markup = 200%
The markup = 200% of the current price
Markup = 200/100 ×30
= $60
The ticket fee on the game day = The current fee + The markup
The ticket fee on the game day = $30 + $60
The ticket fee on the game day = $90
Hence, Han should expect to pay $90 for the ticket if he buys it the day of the game.
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what is the value of the expression hurry please!
Answer:
50
Step-by-step explanation:
Seth owns a printing shop that makes customized T-shirts. The cost to make T-shirts is proportional to the number of T-shirts he makes. Seth graphs a line that shows the cost per customized T-shirt. Two points on the line are (2, 8) and (4, 16). What does the slope of the line mean in this situation?
Group of answer choices
a. The cost is $4 per T-shirt.
b. The cost is $2 per T-shirt.
c. The cost is $0.25 per T-shirt.
d. The cost is $8 per T-shirt.
the slope of the line means in this situation "a. The cost is $4 per T-shirt".
What is a Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given, Seth owns a printing shop that makes customized T-shirts.
Since The cost to make T-shirts is proportional to the number of T-shirts he makes.
Thus,
The y-intercept of the line will be 0 cause the line is passing through the origin point.
The general formula of the equation of a line:
y=mx+b,
where m is the slope
b is the y-intercept
since, slope = (y - y')/(x -x')
In our case,
b = 0
m = (8 - 4)(2-1)
m = 4
And m represents The cost is $4 per T-shirt.
therefore, the slope of the line means in this situation "a. The cost is $4 per T-shirt".
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On his sixth birthday, a boy inherits $6000 which is to be used for his college education. The money is deposited into a trust fund that will pay him
R dollars on his 18th, 19th, 20th, and 21st birthdays. Find R if the money earns 8% interest compounded annually.
The money deposited will pay the boy $ on his 18th, 19th, 20th and 21st birthdays.
(Round the final apower to the nearest cent as needed Round all intermediate values to six decimal places as needed.)
On solving the provided question, we can say that by solving the interest the amount after his 21st birthday = $ 10,806
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.
P = $6000
Rate= 4 %
Time, t= 12 years
Formula of Compound Interest
[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{12}\\A = 9606.19332[/tex]
On his 19 th birthday
[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{13}\\A = 9990. 44106[/tex]
After 21st year S. I is
S. I = 10390.058700 × 4/100
S. I = 415.602348
A= 415.602348 + 10390.058700
A = $ 10,805.661.
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Choose the justification for each step in the solution to the given equation.
- division property of equality
- simplification
- multiplication property of equality
-Addition property of equality
-Subtraction property of equality
The properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation
What are the properties of equality?
The "division property of equality" states that if you divide both sides of an equation by the same non-zero number, the two sides will remain equal.
The "simplification" step is used to simplify an expression by combining like terms, reducing fractions, or performing other operations to simplify the expression.
The "multiplication property of equality" states that if you multiply both sides of an equation by the same non-zero number, the two sides will remain equal.
The "addition property of equality" states that if you add the same number to both sides of an equation, the two sides will remain equal.
The "subtraction property of equality" states that if you subtract the same number from both sides of an equation, the two sides will remain equal.
These properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation.
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An amount is divided among A, B and
C in the ratio 2:5:7 respectively. B
gets R30.
How much does A get?
On solving the provided question, we can say that ratio is = 2:5:7 => 2x + 5x + 7x = 84 => x = 6 and A gets = 2x = 12 rs.
what is ratio?Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.
ratio is = 2:5:7
2x + 5x + 7x = 84
14x = 84
x = 84/14 = 6
a gets = 2x = 12 rs.
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PLEASE YALL HELP ME WITH THIS I NEED IT FOR RN
The piecewise function for the Tax due on an income of x dollars are:
T(x) = 0.035x; if 0 < x ≤ $15,000T(x) = 525 + 0.0625 (x- 15,000); if 15,000 < x ≤ 30,000 T(x) = 1462.50 + 0.068 (x - 30,000); if 30,000 < xFrom the case, we know that there are 3 scenariois for filling tax due based on an individual's income, where:
Between $0 until $15,000 is taxed 3.5% of taxable incomeBetween $15,000 until $30,000 is taxed $525 plus 6.25% of excess over $15,000Over $30,000 is taxed $1462.50 plus 6.8% of excess over $30,000.To construct the piecewise function for the Tax due, we need to translate the given conditions into mathematical formulation.
We assume that:
T(x) = tax due
x = $ amount of taxable income
For taxable income between $0 until $15,000, the tax is 3.5% of taxable income; then:
T(x) = 3.5% x
T(x) = 0.035x
For taxable income between $15,000 until $30,000, the tax is $525 plus 6.25% of excess over $15,000. Then:
T(x) = 525 + 6.25% (x - 15,000)
T(x) = 525 + 0.0625 (x- 15,000)
Please note that the additional 6.25% only will be counted based on the remaining of the taxable income deducted by $15,000.
For taxable income over than $30,000, the tax is $1462.50 plus 6.8% of excess over $30,000. Then:
T(x) = 1462.50 + 6.8% (x - 30,000)
T(x) = 1462.50 + 0.068 (x - 30,000)
Please note that the additional 6.8% only will be counted based on the remaining of the taxable income deducted by $30,000.
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3. Determine the cost to lay down pebbel in the seating area one bag of pebbels covers 5 ft² and costs $8.99
The total amount to lay down the pebbles in the seating area would be - ${(A/5) x 8.99}.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that one bag of pebbles covers 5 ft² and costs $8.99.
Assume that the area of the seating place is A ft². Now -
1 bag will cover - 5 ft²
1 ft² will be covered in (1/5) bags
A ft² will be covered in (A/5) bags
The total cost of laying the pebbles -
(A/5) x 8.99
Therefore, the total amount to lay down the pebbles in the seating area would be - ${(A/5) x 8.99}.
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A rectangular garden has a walkway around it. The area of the garden is 6(4.5x + 2.5). The combined area of the garden
and the walkway is 6.5(6x + 6). Find the area of the walkway around the garden as the sum of two terms.
Answer:
2w^2.
Step-by-step explanation:
Let "w" be the width of the walkway. Then, the length of the garden is 6.5(6x + 6) - 2w and the width of the garden is 6.5(6x + 6) - 2w.
The area of the garden is 6(4.5x + 2.5) = 6 * 4.5 * x + 6 * 2.5 = 27x + 15
The area of the garden and walkway is (6.5(6x + 6) - 2w)^2 = 27x + 15 + 2w^2
Equating the two expressions for the area of the garden:
27x + 15 = 27x + 15 + 2w^2
Thus, the area of the walkway is:
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Savvas Realize
Jamilas mom wants to make a size 10 dress and jacket. About how much yards of fabric does she need?
Answer:
[tex]2\frac{7}{8}[/tex]
Step-by-step explanation:
size 10 dress requires 2 1/4 yards of fabric while a jacket requires 1 5/8 yards so we add them
2 1/4+1 5/8
we make similar fractions and turn the denominator to 8
2 2/8+ 1 5/8
and now we can add the whole numbers first
2+1=3
now the fractions
2/8+5/8
7/8
final answer is 2 7/8
hopes this helps
Reid found 6 coins that totaled 61c in all. What coins did the find?
Answer:
1 quarter, 3 dimes, 1 nickel, 1 penny
Step-by-step explanation:
25c + 10c+10c+10c+5c+1c =61c
An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet tall and has a base with a circumference of 26.376 feet, what is the volume of the sculpture? Use 3.14 for 1.
The volume of the sculpture is 92.316 feet³.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is (1/3)πr²h.
We have,
Cone-shaped sculpture:
Height = 5 feet
Base circumference = 26.376
This means,
2πr = 26.376
r = 26.376/(2 x 3.14)
r = 4.2 feet
Now,
The volume of the sculpture.
= 1/3 x 3.14 x 4.2 x 4.2 x 5
= 92.316 feet³.
Thus,
92.316 feet³ is the volume of the sculpture.
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6. In a market economy
a. an individual consumer has a great influence on the price of goods and services.
b. consumers do not influence the price of goods and services.
c. all consumers collectively have a great influence on the price of goods and services
d. all consumers collectively have no influence on the price of goods and services.
nomic terms?
In a market economy, option C. all consumers collectively have a great influence on the price of goods and services.
What is a market economy?A market economy is an economic system in which goods and services are traded in a market, and prices are determined by supply and demand. The decisions of individual consumers and producers, operating through the market mechanism, determine what goods and services are produced and how they are distributed.
Therefore, the correct answer is as given above. It could be concluded that market economy allow individuals to influence the price of goods and services
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Which of these numbers is NOT divisible by 3?
300
321
241
8.910
Answer: 241
300 / 3 = 100
321 / 3 = 107
241 / 3 = 80.333
8.910 / 3 = 2.97
(100 POINTS!) What is the sum of 6 of the interior angles of a regular octagon?
[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=8 \end{cases}\implies S=180(8-2)\implies S=1080 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{just one angle is}}{\cfrac{1080}{8}\implies 135^o}\hspace{5em}\stackrel{\textit{for six angles}}{(6)(135)\implies \boxed{810^o}}[/tex]
Work out the following sheet,please
a) The measure of <ABC is 131 degree.
What is Angle sum property?According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle.
The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.
Given:
a) As <ACD= 90
and Triangle BCD is an equilateral triangle then each of its angle measure 60 degree.
So, <ACD= 90
<ACB + <BCD = 90
<ACB = 90 - 60
<ACB = 30
and, <BAC = 19
Using Angle sum property in Triangle ACB
19 + <ABC + 30 = 180
<ABC = 180 - 49
<ABC = 131 degree.
b) Bow, In Triangle HEF using Angle sum property
<E + <F + <EHF = 180
<EHF = 180 - (69+ 40)
<EHF = 71 degree.
Then, <GHE + <EHF + <FHI
= 72 + 71 + 37
= 180, which forms on straight line.
Thus, GHI is a straight line.
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Physics shows that when an object is thrown upward with an initial velocity of v_0, then its approximate height is given by this quadratic function.
s = -4.9t^2 + v_0^t + h
A ball is thrown upward from the top of a building 15 meters high, at a velocity of 3.1m/sec. Answer the following questions. Be sure to show and explain all work.
A. Find the maximum height and the time in which it was attained (round to 3 decimal places)
B. When does it reach the ground? (round to 3 decimal places)
C. Sketch a graph to illustrate your answers.
The answers to each part is given above.
Explain Maxima and Minima in mathematics?Maxima and Minima are known as the extrema of a function. Maxima and minima are the maximum or the minimum value of a function within the given set of ranges. For the function, under the entire range, the maximum value of the function is known as the absolute maxima and the minimum value is known as the absolute minima.Local Maxima : A point x = b is a point of local maximum for f(x) if in the neighborhood of b i.e in (b−, b+) where can be made arbitrarily small, f(x) < f(b) for all x ∈ (b−, b+)∖{b}. This simply means that if we consider a small region (interval) around x = b, f(b) should be the maximum in that interval.Local Minima : A point x = a is a point of local minimum for f(x) if in the neighbourhood of a, i.e. in (a−,a+), (where can have arbitrarily small values), f(x) > f(a) for all x ∈ (a−,a+)∖{a}. This means that if we consider a small interval around x = a, f(a) should be the minimum in that interval.Given is that when an object is thrown upward with an initial velocity of v{0}, then its approximate height is given by this quadratic function -
S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h
The approximate height is given by this quadratic function -
S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h
{ 1 } - For the maximum height :
dS/dt = 0 ... Eq{ 1 }
dS/dt = -9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 0 = 0
- 9.8t + [tex]$3.1^{t}[/tex] log(3.1) = 0
Refer to the graph attached. At t = 3.8 {possible value}, the function is 0.
So we get -
t = 3.8 s ... Eq{ 2 }
Maximum height achieved -
h{max} = - 9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 15
h{max} = - 9.8 x 3.8 + [tex]$3.1^{3.8}[/tex] log(3.1) + 15
h{max} = - 37.24 + 73.65 x 0.50 + 15
h{max} = 14.585 m
{ 2 } -
0 = 3.1 t + 9.8/2 t²
0 = 3.1 t + 4.9 t²
Solving graphically, we get -
|t| = 0.6 s
Total time taken to reach ground -
T = 2 x 3.8 + 0.6
T = 8.2 seconds ... Eq{ 3 }
Therefore, the answers to each part is given above.
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Write a story problem that can be solved using 1 3/4 / 1/2. Drraw a picture to match your story and Illustrate the answer.
Answer: A baker needs to make a dessert for a party. The recipe calls for 1 3/4 cups of sugar, but the baker only has 1/2 cup measuring cups. How many measuring cups does the baker need to measure out the sugar for the recipe?
We can start by converting the mixed number 1 3/4 into an improper fraction: 1 3/4 = 7/4. Then, we can divide 7/4 by 1/2:
7/4 ÷ 1/2 = 7/4 * 2/1 = 14/4 = 3 1/4
The baker needs 3 1/4 measuring cups to measure out the sugar for the recipe.
[Image: Three and a quarter measuring cups filled with sugar]
Step-by-step explanation:
Math on the Spot An arcade deducts 3.5 points from
a 50-point game card for each game played. The linear
equation y= -3.5x + 50 represents the number of
points y on a card after x games played. Graph the
equation using the slope and y-intercept.
For the linear equation y = -3.5x + 50 the graph is plotted with points (0,50) and (14.28,0).
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The linear equation is y = -3.5x + 50.
An arcade deducts 3.5 points from a 50-point game card for each game played.
The graph will represent the x axis as number of games played.
The graph will represent the y axis as points earned.
Substitute the value x = 0 in the equation -
y = -3.5(0) + 50
y = 50
The coordinate point is (0,50).
Substitute the value y = 0 in the equation -
0 = -3.5x + 50
-50 = -3.5x
x = 14.28
The coordinate point is (14.28,0).
Plot both the coordinate points and join the line.
Therefore, the graph is plotted for the linear equation.
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6x6 foot area. Use this value to estimate the size of a crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route.
22000
44000
4800
8400
The size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, the size of a crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route,
The number of people that can fit comfortably in a 6 feet by 6 feet area = 10
The ratio of the number of people per unit area = 10/(6 × 6) = 10/36
The area, A, occupied by the crowd = 5 feet × 3 mile × 2
3 miles = 15840 feet
∴ A = 5 feet × 15840 feet × 2 = 158400 ft²
We then have;
Number of people / 158400 = 10/36
Number of people = 44000
Hence, the size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.
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Julie purchased a bottle of vegetable oil for $4.58. The cashier gave Julie $2.82 in change. How much money did Julie give the cashier?
Answer:
7.40
Step-by-step explanation:
4.58+2.82 = 7.40