A rectangular parking lot with a perimeter of 440 feet is to have an area of at least 8000 square feet. Within what bounds must the length of the rectangle lie?
Answers
The length of a rectangular parking lot, given its perimeter and minimum required area, is determined by finding the bounds within which the length must lie. The length of the rectangle must lie within L ≤ 20 or L ≥ 200.
Let's denote the length of the rectangle as L and the width as W. The perimeter of a rectangle is given by the formula P = 2L + 2W, and the area is given by the formula A = L * W.
In this case, we are given that the perimeter is 440 feet and the minimum required area is 8000 square feet. Using the perimeter equation, we can express the width in terms of the length: W = (440 - 2L) / 2 = 220 - L.
Substituting this value of W into the area equation, we get A = L * (220 - L) = 220L - \(L^2\).
To find the bounds for the length, we need to consider the minimum and maximum values of L that satisfy the given conditions. Since the area must be at least 8000 square feet, we can set up the inequality: 220L - \(L^2\) ≥ 8000.
Simplifying the inequality, we have -\(L^2\) + 220L - 8000 ≥ 0. To solve this quadratic inequality, we can factor it: (L - 20)(L - 200) ≥ 0.
The roots of the equation are L = 20 and L = 200. The inequality holds true when L ≤ 20 or L ≥ 200.
Therefore, the length of the rectangle must lie within the bounds of L ≤ 20 or L ≥ 200.
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Related Questions
Circle theorem. Find the following angles.
Answers
The measure of the angle ∠CDE in the cyclic quadrilateral AEDC and the angle ∠BFC indicates;
(a) \(G\widehat{A}E\) = 38°
(b) \(A \widehat{E}B\) = 63°
What is a cyclic quadrilateral?A cyclic quadrilateral is an inscribed quadrilateral of a circle.
(a) The quadrilateral ACDE is a cyclic quadrilateral, therefore;
∠CDE and ∠AEF are supplementary angles
m∠CDE + m∠AEF = 180° (Definition of supplementary angles
m∠CDE = 128°
Therefore; m∠EAF = 180° - 128° = 52°
AC is a diameter of the circle, therefore FA is a radius of the circle and ∠GAF is a right angle (90°) (Properties of a tangent to a circle)
∠GAF = ∠GAE + ∠EAF (Angle addition postulate)
m∠GAE = m∠GAF - m∠EAF
m∠GAE = 90° - 52° = 38°
Angle \(G\widehat{A}E\) = 38°
(b) Angle AEB, angle AFE and angle EAF are the interior angles of the triangle AEF, therefore;
m∠AEB + m∠AFE + m∠EAF = 180° (Angle sum property of a triangle)
m∠AEB = 180° - (m∠EAF + m∠AFE)
m∠AEB = 180° - (52° + m∠AFE)
∠AFE and ∠BFC are vertical angles, therefore;
m∠AFE = m∠BFC = 65°
m∠AEB = 180° - (52° + 65°) = 63°
\(A\widehat{E}B\) = 63°
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Find the range of {(45.5, 65.5), (48.2, 68), (41.8, 62.2), (46, 66), (50.4, 70)}.
Answers
Answer:
range = biggest - smallest
65.5-45.5= 29
68 -48.2 =19.8
62.2-41.8 = 20.4
66-46= 20
70-50.4=19.6
Select the correct answer. rational functions v and w both have a point of discontinuity at x = 7. which equation could represent function w? a. w(x) = v(x − 7) b. w(x) = v(x 7) c. w(x) = v(x − 7) 7 d. w(x) = v(x) 7
Answers
The following equation could be used to represent a function w:
= w(x)=v(x-7)+7
According to the information provided,
The point of discontinuity of rational functions is at x=7.
When a rational function has a point of discontinuity, it generally occurs when,
q(x) = r(x-a), where x = a
In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)
If we know that a=7 and k=7.
The equation which can represent w is as follows,
w(x) = v ( x-7 ) + 7
A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.
Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.
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Jesse Pinkman throws out $3 million through his car window. If each band of money is worth $10,000 dollars, how much bands of money did Pinkman throw out?
Answers
Answer: 300 bands
Step-by-step explanation: 3 million divided by 10 thousand is 300.
The current student population of memphis is 1800. if the population decreases at a rate of 12% each year. what will the student population be in 6 years? write an exponential growth model for the future population p where x is in years:
Answers
The student population of Memphis will be approx 1,011.45 in 6 years. Hence, 6 years is the required answer.
To model future population growth, we can use an exponential decay model since the population decreases at a rate of 12% each year. The general form of an exponential decay model is given by:
P(x) = P₀ * (1 - r)^x
Where P(x) represents the population after x years, P₀ is the initial population, r is the decay rate (expressed as a decimal), and x is the number of years.
In this case, the initial population (P₀) is 1800 and the decay rate (r) is 0.12 (12% expressed as a decimal). Plugging in these values into the exponential decay model, we have:
P(x) = 1800 * (1 - 0.12)^x
To find the population after 6 years (P(6)), we substitute x = 6 into the equation:
P(6) = 1800 * (1 - 0.12)^6
Simplifying the equation, we get:
P(6) ≈ 1800 * (0.88)^6 ≈ 1,011.45
Therefore, the student population of Memphis will be approximately 1,011.45 in 6 years based on the given exponential decay model.
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X+6=6+x is it a one solution, infinite solutions or no solutions
Answers
Answer:
infinite solutions
Step-by-step explanation:
The revenue and operating cost of a car wash facility are given by () = 13 − 0.72 and() = 2.5 + 3.5, where x represents the number of cars washed. What is the profit when 10 cars are washed?
Answers
EXPLANATION:
Given;
We are given the revenue and cost function of a car wash facility as follows;
\(\begin{gathered} Revenue: \\ R(x)=13x-0.7x^2 \\ Cost: \\ C(x)=2.5x+3.5 \end{gathered}\)Also, we are told that in this function, x represents the number of cars washed.
Required;
We are required to calculate the profit when 10 cars are washed.
Step-by-step solution;
To begin, we will take note that the profit function is given as;
\(Profit=Revenue-Cost\)Therefore, to determine the profit at any level of input x, we would have;
\(P(x)=R(x)-C(x)\)We now substitute the values given;
\(P(x)=(13x-0.7x^2)-(2.5x+3.5)\)\(P(x)=13x-0.7x^2-2.5x-3.5\)Notice how the negative sign is distributed among the two values in the right parenthesis.
\(P(x)=10.5x-0.7x^2-3.5\)We can now determine the profit when 10 cars are washed, that is, when x = 10.
\(P(10)=10.5(10)-0.7(10)^2-3.5\)\(P(10)=105-0.7(100)-3.5\)\(P(10)=105-70-3.5\)\(P(10)=31.5\)ANSWER:
The profit from washing 10 cars therefore will be $31.5
How do I write a phrase in words as an algebraic expression for 8/d?
Answers
Answer:
The quotient of 8 and d.
Step-by-step explanation:
I hope this helps you have a wonderful day! :D
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which scatter plot is incorrect and what is wrong with it
ill give 50 points
Answers
Answer:
is there any more information
Given a collection of 2023 closed squares of total area 4, prove that they can be arranged to cover a unit square (overlaps are allowed)
Answers
We can arrange the 2023 squares to cover the unit square, with overlaps allowed.
We can prove that a collection of 2023 closed squares of total area 4 can be arranged to cover a unit square by using the pigeonhole principle. Since the total area of the squares is 4, the average area of each square is 4/2023. Let's take a unit square and divide it into 2023 smaller squares of area (1/2023) each. By the pigeonhole principle, we can assign one of the 2023 squares to each of the smaller squares. Since the average area of each square is 4/2023, each of the assigned squares will overlap with at most 4 other squares. Therefore, we can arrange the 2023 squares to cover the unit square, with overlaps allowed.
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Determine all solutions of the given equation. Express your answer(s) using radian measure.
2 tan2 x + sec2 x - 2 = 0 Ox= 1/3 + πk, where k is any integer 0x = π/6 + πk, where k is any integer x = 2n/3 + k, where k is any integer Ox= 5/6 + nk, where k is any integer
Answers
The equation 2tan^2(x) + sec^2(x) - 2 = 0 has solutions x = (1/3 + πk), x = (π/6 + πk), x = (2n/3 + k), and x = (5/6 + nk), where k is any integer and n is any integer multiple of 3.
To determine the solutions of the equation 2tan^2(x) + sec^2(x) - 2 = 0, we can use trigonometric identities to simplify and find the values of x. Firstly, we rewrite tan^2(x) in terms of sec^2(x) using the identity tan^2(x) = sec^2(x) - 1. Substituting this identity into the equation, we get:
2(sec^2(x) - 1) + sec^2(x) - 2 = 0
3sec^2(x) - 4 = 0
Simplifying further, we have sec^2(x) = 4/3. Taking the square root of both sides, we obtain sec(x) = ±√(4/3).
Using the definition of sec(x) as 1/cos(x), we find that cos(x) = ±√(3/4). This implies that x is an angle where the cosine is equal to ±√(3/4).
From the unit circle, we know that the cosine of π/6, π/3, 5π/6, and 7π/6 is √(3/4). Hence, we have x = π/6 + πk and x = 5π/6 + πk as solutions.
Since sec(x) is positive, we also have x = 1/3 + πk and x = 2/3 + πk as solutions.
Furthermore, x = 2n/3 + k, where n is any integer multiple of 3, and x = 5/6 + nk, where k is any integer, are additional solutions to the equation.
These solutions cover all possible values of x that satisfy the given equation, expressed in radian measure.
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list the elements of the Sets (1) (AnB)' UC (ii) (AUC) 'n B (iii) (AUBUC)'
Answers
Answer:
(i) The complement of the intersection of Sets A and B, denoted by (A∩B)', is the set of all elements that are not in the intersection of Sets A and B. It can be found by taking the union of the complements of Sets A and B, denoted by A' and B'. Hence, (AnB)' = A' U B'.
(ii) The complement of the union of Sets A and C, denoted by (A U C)', is the set of all elements that are not in the union of Sets A and C. It can be found by taking the intersection of the complements of Sets A and C. Hence, (A U C)' = A' ∩ C'.
(iii) The complement of the union of Sets A, B, and C, denoted by (A U B U C)', is the set of all elements that are not in the union of Sets A, B, and C. It can be found by taking the intersection of the complements of Sets A, B, and C. Hence, (A U B U C)' = A' ∩ B' ∩ C'.
The sale price of every item in a store is 85% of its usual price. Find the price of the following items given their usual price. The usual price of a soccer ball is $19.80, what
is its sale price?
Answers
Answer:
$16.83
Step-by-step explanation:
If the usual price is $19.80 and they are on sale for 85% of the usual price, you can set this up in the form of a proportion.
\(\frac{85}{100} = \frac{x}{19.80}\)
With this, you first multiply 85*19.80 and then you divide that answer by 100 to solve for x, the sale price.
Another way you can approach it is by changing 85% into it's decimal form (.85) and multiplying this by the original price (19.80).
If f(x) and g(x) are polynomial functions, use the table of values for f(x) and g(x) to complete the table of values for (f o g)(x)
.
x g(x)
-2 4
-1 1
0 0
1 1
2 4
x f(x)
0 3
1 4
2 5
3 6
4 7
Answers
The table of values for the composition (f o g)(x) for polynomial functions f(x) and g(x) is:
x (f o g)(x)
-2 7
-1 4
0 3
1 4
2 7
To find the values of (f o g)(x), we need to substitute the values of g(x) into f(x). The composition (f o g)(x) means that we first apply g(x) to x, and then apply f(x) to the result.
Using the table of values for g(x):
x g(x)
-2 4
-1 1
0 0
1 1
2 4
We substitute these values into f(x):
x f(x)
0 3
1 4
2 5
3 6
4 7
Calculating (f o g)(x):
For x = -2:
(f o g)(-2) = f(g(-2)) = f(4) = 7
For x = -1:
(f o g)(-1) = f(g(-1)) = f(1) = 4
For x = 0:
(f o g)(0) = f(g(0)) = f(0) = 3
For x = 1:
(f o g)(1) = f(g(1)) = f(1) = 4
For x = 2:
(f o g)(2) = f(g(2)) = f(4) = 7
Completing the table of values for (f o g)(x):
x (f o g)(x)
-2 7
-1 4
0 3
1 4
2 7
Therefore, the completed table of values for (f o g)(x) is as shown above.
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Question 1
The expression (-4a3b)2 is equivalent to
16a6b2
16a5b2
8a6b2
-16a6b2
Answers
In your initial ocular visit to the site, you measured the radius of the curved path that is 40 meters. Complete the table below.
Answers
The table for the coefficient of friction and velocity speed square when the radius of the curved path is 40 meters.
Coefficient of static friction 0.1 0.2 0.3 0.4 0.5
(Velocity speed)² ( m²/s² ) 40 80 120 140 200
The radius of the curved path is 40 meters.
To provide the friction force necessary for an automobile moving at speed v to navigate a flat curve of radius r, consider the coefficient of static friction of v² = μrg.
When the coefficient of static friction between tires and pavement is μ, the fastest curve of radius r can be traveled is at this speed.
Here g is the acceleration due to gravity g = 10 m/s².
When μ = 0.1,
v² = 0.1 × 40 × 10 = 40 m²/s²
When μ = 0.2,
v² = 0.2 × 40 × 10 = 80 m²/s²
When μ = 0.3,
v² = 0.3 × 40 × 10 = 120 m²/s²
When μ = 0.5,
v² = 0.5 × 40 × 10 = 200 m²/s²
Hence, the complete table is:
Coefficient of static friction 0.1 0.2 0.3 0.4 0.5
(Velocity speed)² ( m²/s² ) 40 80 120 140 200
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Please Help!! Brainliest Answer!! Thank you!
Answers
Answer:
B
Step-by-step explanation:
sine = opposite/hypotenuse
sin45 = x/4
sin45/1 = x/4
cross multiply
1 × x = 4 × sin45
x = 4sin45
x = 2.828427125
x = 2 × square root of 2 = 2.828427125
Answer:
B ) 2\(\sqrt{2}\)
Steps:
α = 90°, β = 45°, a = 4: b = 2.82842. . .
β = 45°
a = 4
α = 90°
b = \(\frac{4sin(45)}{sin(90)}\)
b = 2.82842. . .
2\(\sqrt{2}\) = 2.82842. . .
to calculate the cpi, the bureau of labor statistics uses
Answers
The CPI uses data from the Consumer Expenditure (CE) survey to determine the weights of the different categories of goods and services in the CPI. The CE survey collects data on the out-of-pocket expenses spent to acquire all consumer products and services.
CPI price data are collected via two surveys: one survey collects prices for commodities and services and the other survey collects prices for rent. The CPI survey collects about 94,000 prices per month to compute indexes for commodities and services.
The U.S. Consumer Price Index (CPI) is a collection of consumer price indices determined by the U.S. Bureau of Labor Statistics (BLS). To be specific, the BLS routinely calculates many distinctive CPIs that is practiced for several purposes.
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The given question is incomplete, So, take the similar question:
How does the Bureau of Labor Statistics calculate the CPI?
Mary creates a stack of 10 of piece M and a stack of 8 of piece N. Both stacks have equal volumes
Answers
True or False? A circle could be circumscribed about the quadrilateral below.
Answers
Answer:
false
Step-by-step explanation:
Because the length of the sides are not the same
Find the mean for the number of yards gained by Roger during his seven carries in thefootball game: {2, 6, 20, 11, 8, 12, 4}.A 08B 09C 63D 07
Answers
The answer is option B) 09. To find the mean (average) of the yards gained by Roger during his seven carries, we need to add up all the yards gained and divide the sum by the number of carries.
So, for the given data set {2, 6, 20, 11, 8, 12, 4}, the total yards gained is:
2 + 6 + 20 + 11 + 8 + 12 + 4 = 63
The number of carries is 7.
Therefore, the mean yards gained per carry is:
Mean = Total yards gained / Number of carries
= 63 / 7
= 9
Hence, the answer is option B) 09.
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A family reduced the consumption of sugar from 10 kg to 8kg per month due to increase in price. Find the percentage decrease in consumption.
Answers
Answer:
20%
Step-by-step explanation:
Step 1: Find the decrease in consumption
10kg - 8kg = 2kg
So the family decrease their consumption of sugar by 2kg
Step 2: We have to find what percent did the family reduce their sugar consumption
We can divide how much they reduced by with the original amount
2kg/10kg = 1/5 kg or 20%
Therefore the family reduced the consumption of sugar by 20$
Translate the following phrase to an expression: the difference between twenty and twice a number. Evaluate the expression for n = 3.
Answers
Answer:
22-2n or 22-2(3)
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
Rewritten as an expression it would be 20 - n^2, and with the variable substituted and multiplied, it will become 20 - 6.
20 - 6 = 14
Find the coordinates of the midpoint of the segment connecting points \((9,5)\) and \((-1,-7)\). In your final answer, include the formula and calculations that you used to find the midpoint.
Answers
The coordinates of the midpoint of the segment connecting points are (4,-1).
What are coordinates?Coordinates are two integers (Cartesian coordinates) or a letter and a number that point to a specific place on a grid known as a coordinate plane. A coordinate plane has four quadrants and two axes: x (horizontal) and y (vertical) (vertical).To find the coordinates of the midpoint of the segment:
Given points -
(9, 5) and (-1, -7)Formula = (x₁ + x₂)/2, (y₁ + y₂)/2Now, add the respective values in the formula:
(9 + (-1))/2, (5 + (-7))/2(4, -1)Therefore, the coordinates of the midpoint of the segment connecting points are (4, -1).
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Let P(n) be the statement that 13 + 23+….n3 = (n(n + 1) / 2)² for the positiveinteger n. a.) What is the statement P(1)? b.) Showthat P(1), completing the basis step of theproof?
Answers
Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.
a.) The statement P(1) is obtained by substituting n=1 into the equation. So, P(1) would be: 1³ = (1(1 + 1) / 2)²
b.) To show that P(1) is true, we need to prove that both sides of the equation are equal:
Left side: 1³ = 1
Right side: (1(1 + 1) / 2)² = (1(2) / 2)² = (2 / 2)² = 1² = 1
Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.
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a) The equation is not true for n = 1, so P(1) is false.
b) The positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1
a) To find P(1), we substitute n = 1 into the equation given:
13 = (1(1 + 1) / 2)²
13 = (1 / 2)²
13 = 1/4
The equation is not true for n = 1, so P(1) is false.
b) To complete the basic step of the proof, we need to show that P(1) is true.
However, we have just shown that P(1) is false.
This means that the statement "for the positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1.
Therefore, the proof cannot proceed and is incomplete.
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find the greatist common factor of 18 and 35
1
3
18
7
Answers
35: 1, 5, 7, 45
———————————
GCF is 1
Answer:
GCF = 1
Step-by-step explanation:
factors of 18 = 1, 2, 3, 6, 9, 18
factors of 35 = 1, 5, 7, 35
the common factor to both is 1 only
then the GCF of 18 and 35 is 1
what does the slope of a beer's law plot represent
Answers
The slope of a beer's law plot represents that one can quantitatively determine the molar absorptivity of a substance, which is essential for accurately determining concentrations of unknown samples using spectrophotometric methods.
In Beer's law, the relationship between the concentration of a substance and its absorbance is described by the equation A = εbc, where A is the absorbance, ε is the molar absorptivity (also known as the molar absorptivity coefficient), b is the path length of the sample, and c is the concentration of the substance.
When plotting a graph of absorbance versus concentration, the slope of the line represents the molar absorptivity (ε). The molar absorptivity is a constant that reflects the substance's ability to absorb light at a specific wavelength. A higher molar absorptivity indicates that the substance has a greater tendency to absorb light and is more sensitive to changes in concentration.
Conversely, a lower molar absorptivity indicates weaker absorption characteristics.
In summary, by measuring the slope of the Beer's law plot, one can quantitatively determine the molar absorptivity of a substance.
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Matt wants to purchase 3.5 pounds of Swiss cheese for a party. Each pound costs $4.95. How much will Matt pay for the Swiss cheese, rounded to the nearest whole cent?
Answers
Answer:
$17.33
Step-by-step explanation:
3.5×4.95
=17.325
= $17.33
the marketing club at school is opening a student store. they randomly survey 50 students about how much money they spend on lunch each day. what is the expected value for a student to spend on lunch each day? student lunch surveynumber of studentsdollars spent onlunch each day2$101$812$623$58$44$3$2.59$5.11$5.18$9.07
Answers
The expected value for a student to spend on lunch each day is $7.09.
To calculate the expected value for a student to spend on lunch each day based on the survey data,
we need to find the average amount spent by each student.
We can calculate the expected value by summing up the products of the number of students and the amount spent on lunch for each category, and then dividing by the total number of students:
Expected value = \((2 * 10 + 1 * 8 + 2 * 6 + 3 * 5 + 8 * 4 + 11 * 3 + 10 * 2.59 + 13 * 5.11 + 10 * 5.18 + 10 * 9.07) / 50\)
Expected value = \((20 + 8 + 12 + 15 + 32 + 33 + 25.9 + 55.21 + 51.8 + 90.7) / 50\)
Expected value = $354.71 / 50
Expected value ≈ $7.09
Therefore, based on the survey data, the expected value for a student to spend on lunch each day is approximately $7.09.
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A bee hummingbird, the world's smallest bird, has a mass of 1.836 grams. a new united states nickel has a mass of 5 grams. what is the difference in grams between the mass of a nickel and the mass of a bee hummingbird?
Answers
The difference in grams between the mass of a nickel and the mass of a bee hummingbird is 3.164 grams.
A nickel has a mass of 5 grams. On the other hand, a bee hummingbird, known as the world's smallest bird, has a mass of 1.836 grams. To find the difference between their masses, we subtract the mass of the bee hummingbird from the mass of the nickel.
5 grams (mass of a nickel) - 1.836 grams (mass of a bee hummingbird) = 3.164 grams.
Therefore, the difference in grams between the mass of a nickel and the mass of a bee hummingbird is 3.164 grams. This means that a nickel weighs approximately 3.164 grams more than a bee hummingbird.
In conclusion, the mass difference between a nickel and a bee hummingbird is 3.164 grams. The comparison highlights the vast contrast in size and weight between these two objects, emphasizing the incredibly small mass of the bee hummingbird.
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