General rules or principles that are stated mathematically are known as mathematical theorems.
What is theorem?A theorem is a statement or proposition in mathematics that can be proved using logic and previously established facts or principles. It is a statement that has been shown to be true through a logical and rigorous argument. A theorem is considered to be an important and fundamental concept in mathematics and plays a key role in the development and advancement of the subject. Many famous theorems, such as the Pythagorean Theorem and the Fundamental Theorem of Calculus, have had a profound impact on mathematics and other fields of science.
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Express the following argument mathematically and give the rule(s) that could be used to prove or disprove them. a. The children are sick. The doctors are not here. Therefore the doctors are not here and the children are sick. [2 marks]?
Answer:
Step-by-step explanation:
Let A represent "The children are sick."
Let B represent "The doctors are not here."
Argument: A and ¬B
Rule(s) used to prove or disprove: Conjunction (AND)
In each of the following statements, choose one word, parallelogram, rectangle, rhombus, trapezoid, kite, or square, so that the resulting sentence is true. If none of the words makes the sentence true, answer "none." a. A quadrilateral is a _____if, and only if, its diagonals are congruent and bisect each other. b. A quadrilateral is ______if, and only if, its diagonals are perpendicular and bisect each other. c. A quadrilateral is a _______ if, and only if, its diagonals are perpendicular bisectors of each other. d. A quadrilateral is a______ if, and only if, a pair of opposite sides are parallel and congruent.
Answer:
A. rhombus
B. square
C. rhombus
D. parallelogram
Simplify.
2 - 4 x 3 + 6 x 3
• 0
• 12
• 8
• -28
Answer:
8
Step-by-step explanation:
On a certain day, Miquel. had a credit of $75 in her checking account and spent $240. Which represents the total change in his account that day?
A. $315
B. $365
C. -$135
D. -$165
SHOW YOUR WORK!!
Answer:
B. $365
Step-by-step explanation:
The mean per capita daily water consumption in a village in Bangladesh is about 83 liters per person and the standard deviation is about 11.9 liters person. Random samples of size 50 are drawn from this population and the mean of each sample is determined . Probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person.
the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability theory is a branch of mathematics that deals with the study of random events and their probabilities
In the given question,
We are given that the population mean per capita daily water consumption is 83 liters and the standard deviation is 11.9 liters. We are also given that random samples of size 50 are drawn from this population and the mean of each sample is determined.
We can use the central limit theorem to approximate the distribution of the sample means. According to the central limit theorem, the distribution of the sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
So, for a sample size of 50, the standard deviation of the sample mean is:
standard deviation of sample mean = 11.9 / √(50) = 1.68
To find the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person, we need to find the z-scores corresponding to these values and use the standard normal distribution table or calculator to find the probability.
The z-score for 80 liters per person is:
z = (80 - 83) / 1.68 = -1.79
The z-score for 82 liters per person is:
z = (82 - 83) / 1.68 = -0.60
Using the standard normal distribution table or calculator, we can find that the probability of getting a z-score between -1.79 and -0.60 is 0.1271.
Therefore, the probability that the mean per capita daily water consumption for a given sample is between 80 and 82 liters per person is approximately 0.1271 or 12.71%
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The sum of the digits of a two digit number is 10. When the digits are reversed, the number increases by 18. Find original number.
Answer:
Step-by-step explanation:
10x+y=10y+x-18 multiply the tens digit by 10 and leave the one's digit alone
9x=9y-18 divide by 9
x=y-2
x-y=-2
x+y=10
add above two equations
2x=8 divide by 2
x=4
y=10-4=6
numbers are 46 and 64
64=46+18 4+6=10
Add the expressions.
the quantity negative 8 minus one fourth times p end quantity plus the quantity five eighths times p minus 7 end quantity
negative 3 over 12 times p plus negative 1
7 over 16 times p minus 1
3 over 8 times p minus 15
7 over 8 times p plus negative 15
Please help me and tell me what is did wrong I picked The second one
An addition of the quantity negative 8 minus one fourth times p end quantity plus the quantity five eighths times p minus 7 end quantity is: C. 3 over 8 times p minus 15.
What is an expression?In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Based on the information provided above, we have the following mathematical expressions:
Expression = -8 - 1/4(p)
Expression = 5/8(p) - 7
By adding the two expressions, we have:
Addition = -8 - 1/4(p) + 5/8(p) - 7
Addition = -8 - p/4 + 5p/8 - 7
Addition = -15 +(-p/4 + 5p/8)
Addition = -15 +(-2p + 5p)/8
Addition = -15 + (3p)/8
Addition = 3p/8 - 15
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A small company is selling a new product, and they need to know how many to produce in the future in order to make a profit and revenue.
After 12 months, they sold 4 thousand products; after 18 months, they sold 7 thousand products; and after 36 months, they sold 15 thousand products.
1. Based on this information, estimate the number of products sold after 48 months.
2. Is the number of products sold a function of the amount of months? Does this information show a linear function? Explain your thinking.
Answer:
1. To estimate the number of products sold after 48 months, we can assume that the sales follow a linear pattern over time. We can use the data given to find the rate of change (slope) of the line and then use that to predict the sales after 48 months.
Using the points (12, 4), (18, 7), and (36, 15), we can find the slope of the line that represents the sales:
slope = (15 - 7) / (36 - 18) = 8 / 18 = 4/9
Now we can use the point-slope form of a line to find the equation of the line:
y - 4 = (4/9)(x - 12)
where x is the number of months and y is the number of products sold.
To find the estimated number of products sold after 48 months, we can substitute x = 48 into the equation and solve for y:
y - 4 = (4/9)(48 - 12)
y - 4 = 16
y = 20
Therefore, we can estimate that the company will sell 20 thousand products after 48 months.
2. Yes, the number of products sold is a function of the amount of months. It is a linear function because the sales appear to follow a straight line over time, as we assumed in our calculation above. This means that for every increase of 1 month, the number of products sold increases by a constant rate of 4/9 thousand.
Step-by-step explanation:
Help plssssssssssssssss
Properties of rotation
I need help on this
The coordinates of the rotation are
Problem 5:
(4, 0), (0, -2), and (0, 0)
Problem 6:
(0, -4), (-2, 0), and (0, 0)
Describing each rotation
1. 90 degrees counterclockwise rotation about the origin
2. 90 degrees clockwise rotation about the origin
How to do the rotationsProblem 5: The transformation rule for 90 degrees clockwise rotation about the origin is
(x, y) becomes (y, -x)
preimage coordinates image coordinates
(0, 4) becomes (4, 0)
(2, 0) becomes (0, -2)
(0, 0) becomes (0, 0)
The image is plotted and attached
Problem 6: The transformation rule for 180 degrees counterclockwise rotation about the origin is
(x, y) becomes (-x, -y)
preimage coordinates image coordinates
(0, 4) becomes (0, -4)
(2, 0) becomes (-2, 0)
(0, 0) becomes (0, 0)
The image is plotted and attached
Describing each rotation
1. 90 degrees counterclockwise rotation about the origin
This can be likened to the rotation as in problem 6, the polygon moves in the counterclockwise direction and this is according to the rule:
(x, y) becomes (-y, x)
2. 90 degrees clockwise rotation about the origin
This is similar to the rotation as in problem 5, the polygon moves in the clockwise direction and this is according to the rule:
(x, y) becomes (y, -x)
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To make marbled paper, Shannon filled a rectangular 279/10cm by 178/10cm dish with water. Then they gently swirled paint on top of the water. let a represent the area of the dish.
Select 1 multiplication and 1 division equation to represent the relationship.
choose 2 answers
A) 178/10 x a = 279/10
B) 178/10 x 279/10 = a
C) 279/10 ÷ 178/10 = a
D) a ÷ 178/10 = 279/10
The area of the dish, a, can be represented by the product of its length and width. Thus, we can write:
a = (279/10) cm x (178/10) cm
Simplifying this expression, we get:
a = 4953/100 cm^2
So, the correct equations are:
B) 178/10 x 279/10 = a
and
D) a ÷ 178/10 = 279/10
Let a, b, and m be positive integers, where = a, and
4
=b. Which of the following numbers could be m?
The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.
What do you mean by term Integers?A whole number that can be either positive, negative, or zero is known as an integer. It is a number without a decimal or fractional component. Integer examples include: -3, -2, -1, 0, 1, 2, 3, etc
Lets check if 4 and 6 are divisible by both a and b and is a positive integer,
F. 124:
124/4 = 31, is a positive integer
124/6 = 20.6 is a not positive integer
Thus, 124 is not m.
G. 222:
222/4 = 55.5, is a not positive integer
Thus, 222 is not m.
H. 310:
310/4 = 77.5, is a not positive integer
Thus, 310 is not m.
J. 480:
480/4 = 120, is a positive integer
480/6 = 80 is a positive integer
Thus, 480 is m.
K. 544:
544/4 = 136, is a positive integer
544/6 = 90.6 is not a positive integer
Thus, 544 is not m.
Thus, The only number that could m is 480 as it is both divisible by 4 and 6. Thus, option J is correct.
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Complete question:
is 0.0505505550... a rational number?
The number "0.0505505550..." is an irrational number. The reason for it is that the number can't be expressed as the quotient of two integers. SInce it has the ellipsis (...) at the end, it indicates that the number isn't showing all its significant figures, therefore, can't be represented as the ratio of two integers. Thus, it is irrational.
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Answer:
No, it's not
Step-by-step explanation:
A rational number can be written in the form [tex]\sf{\dfrac{p}{q}}[/tex], where q ≠ 0.
While an irrational number cannot be written in such a form.
Well, not only can't we express 0.0505505550... as [tex]\sf{\dfrac{p}{q}}[/tex], we also see three dots in the end that indicate that the number goes on forever.
It's impossible to express a number that goes on for ever, as a fraction.
Therefore the number is irrational.
Write a mathematical expression to represent the following statement.
'Two less than a number plus twenty.'
Answer: (n - 2) + 20
Step-by-step explanation:
We will create a mathematical expression using the statement given. 'Less' implies subtraction, let n be a number.
'than a number' ➜ n
'Two less' ➜ - 2
'plus twenty.' ➜ + 20
'Two less than a number plus twenty.' ➜ (n - 2) + 20
On a map, 1 cm represents an actual distance of 200 m. Find the actual area, in square metres, represented by 1 cm2 on the map.
Answer:
80,000 [tex]meters^{2}[/tex]
Step-by-step explanation:
200 x 400 = 80,000
Helping in the name of Jesus.
A student is to be selected randomly from a group of students. For each classification of freshman and sophomore, there is a math major, an art major, and a biology major. The probability of each individual being selected is given in the following table: Math Art Biology Freshman 0.12 0.09 0.18 Sophomore 0.23 0.27 0.11 (a) Find the probability that a freshman is selected. (b) Find the probability that an art major is chosen. (c) Find the probability that a freshman math major or a sophomore biology major is chosen.
The probability that a freshman is selected is 0.39. the probability that an art major is chosen is 0.36. the probability that a freshman math major or a sophomore biology major is chosen is 0.23.
(a) To find the probability that a freshman is selected, we need to add up the probabilities of selecting any of the three types of majors among the freshman group. Thus:
Probability of selecting a freshman = Probability of selecting a freshman math major + Probability of selecting a freshman art major + Probability of selecting a freshman biology major
Probability of selecting a freshman = 0.12 + 0.09 + 0.18
Probability of selecting a freshman = 0.39
(b) To find the probability that an art major is chosen, we need to add up the probabilities of selecting an art major from both the freshman and sophomore groups. Thus:
Probability of selecting an art major = Probability of selecting a freshman art major + Probability of selecting a sophomore art major
Probability of selecting an art major = 0.09 + 0.27
Probability of selecting an art major = 0.36
(c) To find the probability that a freshman math major or a sophomore biology major is chosen, we need to add up the probabilities of selecting a freshman math major and a sophomore biology major. Thus:
Probability of selecting a freshman math major or a sophomore biology major = Probability of selecting a freshman math major + Probability of selecting a sophomore biology major
Probability of selecting a freshman math major or a sophomore biology major = 0.12 + 0.11
Probability of selecting a freshman math major or a sophomore biology major = 0.23
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Sample Response: I disagree. If each side of the equation is divided by 5, the result is x2 = 4. By the square root property of equality, x = -2 or x = 2. So x could be -2 instead of 2. Compare your response with the sample response presented here. Did your explanation mention the square root property? say that x could also be –2?
Using square root property,
Square root of 4 is 2 and -2.
Both 2 and -2 are square roots of 4 as:
2 × 2 = 4
also,
-2 × -2 =4
What is the square root property?The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, while the square root of a number can be found by looking for a number that, when squared, yields the original value.
It follows that a × a = b if "a" is the square root of "b." Every number has two square roots, one of a positive value and one of a negative value, because the square of any number is always a positive number.
In the given question,
Square root of 4 is 2 and -2.
Both 2 and -2 are square roots of 4 as:
2 × 2 = 4
also,
-2 × -2 =4
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which of the following statements is false 1) sin45=cos45 2)cos110=sin80 3)sin30=cos40 5) sin0=cos90
The false statement is 3)sin30=cos40.
This is because the sine of 30 degrees is 0.5, whereas the cosine of 40 degrees is approximately 0.766. These two values are not equal to each other.
The following claims, however, are accurate:
The sine of 45 degrees is equal to the cosine of 45 degrees (both are equal to approximately 0.707).The cosine of 110 degrees is equal to the sine of 80 degrees.The sine of 0 degrees (or any multiple of 360 degrees) is equal to 0, and the cosine of 90 degrees (or any odd multiple of 90 degrees) is also equal to 0.Therefore, the false statement is 3)sin30=cos40.
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The cost of a small business is given by the expression 3000 + 12x, where x is the number of units produced. The business will be profitable whenever its profit y exceeds its cost.
If the profit region is shaded in blue, which of the following graphs corresponds to the given situation?
The profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex] .
What is the profitable for all values?To determine which graph corresponds to the given situation, we need to understand the relationship between cost, profit, and revenue.
The revenue (R) of a small business is given by the product of the price per unit (p) and the number of units sold (x):
[tex]R = px[/tex]
The profit (P) of a small business is the difference between its revenue and cost (C):
[tex]P = R - C = px - (3000 + 12x) = (p - 12)x - 3000[/tex]
The profit will be positive when P > 0, which means that the revenue is greater than the cost:
[tex](p - 12)x > 3000[/tex]
[tex]x > 3000/(p - 12)[/tex]
This inequality tells us that the business will be profitable for all values of x greater than [tex]3000/(p - 12).[/tex]
Graph A: This graph shows a linear revenue function (R = 20x) and a linear cost function [tex](C = 3000 + 10x).[/tex] The profit function [tex](P = R - C)[/tex] is also linear.
To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex]. However, we cannot determine if this corresponds to the given situation without knowing the price per unit.
Graph B: This graph shows a linear revenue function [tex](R = 25x)[/tex] and a quadratic cost function [tex](C = 3000 + 15x + 0.5x^2).[/tex] The profit function [tex](P = R - C)[/tex] is also quadratic. To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex] .
We can solve for the roots of the quadratic equation [tex]P = 25x - (3000 + 15x + 0.5x^2) = -0.5x^2 + 10x - 3000[/tex] and find the interval of x-values for which [tex]P > 0.[/tex]
This corresponds to the range of x-values for which the graph of P is above the x-axis. We can see that this region is shaded in blue, so Graph B corresponds to the given situation.
Graph C: This graph shows a linear revenue function [tex](R = 15x)[/tex] and a linear cost function [tex](C = 3000 + 20x).[/tex]The profit function [tex](P = R - C)[/tex] is also linear.
To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex]. However, we can see that the profit function intersects the x-axis at [tex]x = 150.[/tex]
Therefore, the profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex].
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I NEED THIS ANSWER TO THIS QUESTION!!
a. The periodic deposit should be $643.28 (rounded to the nearest cent).
b. $15,438.72 of the $27,000 comes from deposits, and $11,561.28 comes from interest.
What is the future value of the annuity?a. To determine the periodic deposit, we can use the formula for the future value of an annuity:
FV = Pmt x [(1 + r)^n - 1] / r
where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods.
In this case, FV = $27,000, r = 8% / 4 = 2%, n = 6 x 4 = 24 (since there are 4 quarters in a year and the time period is 6 years).
Substituting these values into the formula, we get:
$27,000 = Pmt x [(1 + 0.02)^24 - 1] / 0.02
Solving for Pmt, we get:
Pmt = $643.28
b. The total amount contributed by deposits is:
$643.28 x 24 = $15,438.72
To find the amount of interest earned, we subtract the total deposits from the financial goal:
$27,000 - $15,438.72 = $11,561.28
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find the area 15, 8, 18
the area of the triangle is approximately 71.82 square units.
HOW TO SOLVE THE PROBLEM?
Using the Pythagorean theorem, we can find the length of the base of the right triangle:
Base² = Hypotenuse²- Perpendicular²
Base²= 18²- 15²
Base² = 324 - 225
Base² = 99
Taking the square root of both sides, we get:
Base = √99
Simplifying the square root of 99, we get:
Base = √(9 x 11)
Base = 3√11
Therefore, the length of the base of the right triangle is 3√11.
to find the area of the triangle 3√11-8=1.94
then we can find three side of triangles
which are 15,18,15.12
To find the area of a triangle when the lengths of its three sides are known, we can use Heron's formula:
Area = √[s(s-a)(s-b)(s-c)]
where s is the semiperimeter of the triangle, and a, b, and c are the lengths of its sides.
The semiperimeter s is half the perimeter of the triangle:
s = (15 + 18 + 15.14) / 2 = 24.57
Using this value for s, and plugging in the lengths of the sides a = 15, b = 18, and c = 15.14, we get:
Area = √[24.57(24.57-15)(24.57-18)(24.57-15.14)]
= √[24.57(9.57)(6.57)(9.43)]
= √5153.5853
= 71.82 (approx)
Therefore, the area of the triangle is approximately 71.82 square units.
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22-1x5-4 to the second
The value of a given arithmetic expression is 1.
We have given that an arithmetic expression -
22-(1×5)-4 to the seccond
So we can write it -
22-(1×5)-4²
we shall solve it with the help of the BODMASS rule
BODMAS Rule: The BODMAS Rule is a crucial mathematical tool for resolving issues. It is a technique for using an arithmetic expression to resolve mathematical problems. The abbreviation BODMAS stands for brackets, order of powers or roots, division, and multiplication. S indicates for subtraction, whereas A stands for addition.
according to BODMASS
first, solve the brackets and square,
=22-(5)-16
now subtract all
=22-21
=1
The complete question is
Solve the given arithmetic expression -
22-(1×5)-4 to the seccond
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How do you solve this?
27 cubic inches make up the volume of a cube.
Part A: The side length is 3 inches
Part B: The total surface area of the cube is 54 square inches
Part A:
The formula for the volume of a cube is V = s^3, where V is the volume and s is the side length.
We are given that the volume of the cube is 27 cubic inches, so we can plug this into the formula and solve for s:
27 = [tex]s^3[/tex]
By taking the cube root of both sides, we arrive at:
s = 3
Therefore, the side length of the cube is 3 inches.
Part B:
The formula for the surface area of a cube is A = 6[tex]s^2[/tex], where A is the surface area and s is the side length.
Plugging in the value we found for s in Part A, we get:
A = 6([tex]3^2[/tex])
A = 6(9)
A = 54
Therefore, the total surface area of the cube is 54 square inches.
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Evaluate the expression m^2+7m-6 when m=5
Answer:
54 =)
Step-by-step explanation:
m^2+7m-6
5^2+7(5)-6
25+35-6
Answer is 54
What is the answer?
Answer:?
The differentiation of the trigonometric function gives:
dy/dx = sin(x) - cos(x)
How to differentiate the function?Here we want to find dy/dx for:
y = sec⁻¹(x) + csc⁻¹(x)
Remember that these two are the inverses of the sine and cosine function, then we can write that just as:
y = cos(x) + sin(x)
Now the differentiation is part by part, we know that:
d(cos(x))/dx = -sin(x)
d(sin(x))/dx = cos(x)
Then:
dy/dx = sin(x) - cos(x)
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PLEASE HURRY
Given that YX is a diameter of circle V, find m
A. 32 degrees
B. 46 degrees
C. 70 degrees
D. 134 degrees
Answer:
B) 46 degrees
Solve for x. Round to the nearest tenth of a degree, if necessary.
E
2.6
F
to
3.4
G
The answer of the given question based on the triangle is the value of angle G or x is approximately 52.6° degrees (rounded to the nearest tenth of a degree).
What is Trigonometric function?Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). Trigonometric functions can be used to solve problems involving angles and sides of right triangles, as well as to model periodic phenomena such as waves and oscillations.
To find angle G, we need to use the trigonometric function tangent since we know the opposite and adjacent sides of angle G in the right triangle EFG.
Recall that the tangent of an angle is defined as the ratio of the opposite side to the adjacent side, i.e.,
tan(G) = opposite/adjacent = FG/EF
Substituting the given values, we get:
tan(G) = 3.4/2.6 = 1.3076
Using a calculator, we can find the inverse tangent of 1.3076, which gives us:
G ≈ [tex]tan^{-1}[/tex](1.3077) ≈ 52.6° degrees
Therefore, the value of angle G is approximately 52.6° degrees (rounded to the nearest tenth of a degree).
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Suppose that the functions h and g are defined as follows.
(a) The value of [h/g] function is h/g = (3x² - 4) / (-4x + 6).
(b) The domain of [h/g] is all real numbers except x = 3/2.
What is domain?In mathematics, the domain of a function is the set of all possible input values (usually denoted by x) for which the function is defined. It is the set of all values of the independent variable for which the function produces a valid output.
In the given question,
(a) To find h/g, we need to divide the function h(x) by the function g(x):
h/g = (3x² - 4) / (-4x + 6)
(b) To find the domain of [h/g], we need to determine which values of x would make the denominator equal to zero, since division by zero is undefined.
-4x + 6 = 0
-4x = -6
x = 6/4 = 3/2
So the only value that could make the denominator zero is x = 3/2. Therefore, the domain of [h/g] is all real numbers except x = 3/2.
[h/g] = (3x² - 4) / (-4x + 6), x ≠ 3/2.
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An urban planner collects data on how park trails are used by residents. The planner looks at two trails: one that winds
through an urban area and another in a suburban park. The table shows the number of users who walk, jog, or bike the
trail.
Type of Park
Urban
Suburban
Total
201
What proportion of suburban park users bike on the park trail?
O 0.1050
O 0.1728
0.6075
O 0.6461
Walk
A
76
125
Activity
Jog
58
76
134
Bike
23
42
65
Total
157
243
400
0.1728 proportion of suburban park users bike on the park trail .the answer is option O 0.1728.
what you mean by proportion?
Proportion refers to the relationship between a part and the whole. In statistics, a proportion is a measure that describes the size of a subset relative to the size of the entire set. It is usually expressed as a fraction or a percentage.
In the given question,
To find the proportion of suburban park users who bike on the park trail, we need to divide the number of suburban park users who bike by the total number of suburban park users.
From the table, we can see that the number of suburban park users who bike is 42 and the total number of suburban park users is 243.
So, the proportion of suburban park users who bike on the park trail is:
42/243 = 0.1728
Therefore, the answer is option O 0.1728.
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How many people can you allow on a
beach if the lifeguards want to have
30 sq ft per person and the beach is
1,000 ft long and 200 ft wide? Round
to a whole number.
Answer:
Rounding down to a whole number, we get:
6,666 people
Step-by-step explanation:
First, we need to calculate the total area of the beach:
1000 ft x 200 ft = 200,000 sq ft
Next, we divide the total area by the desired area per person:
200,000 sq ft ÷ 30 sq ft per person = 6,666.67 people