Yes, that is correct. Here's a step by step explanation of how to figure that out:
1. Calculate the total amount of fast food that can be spent in a month: $15 x 4 = $60.
2. Calculate the total amount of money left in the budget for fast food: $1850 - $60 = $1790.
3. Calculate the percentage of money left in the budget for fast food: ($1790/$1850) x 100 = 78%.
A large random sample of American students in seventh grade showed that
20
%
20%20, percent of them were reading below grade level.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
Choose 1 answer:
(Choice A) About
20
%
20%20, percent of all American students in seventh grade were reading below grade level.
A
About
20
%
20%20, percent of all American students in seventh grade were reading below grade level.
(Choice B)
20
%
20%20, percent of this sample was reading below grade level, but we cannot conclude anything about the population.
B
20
%
20%20, percent of this sample was reading below grade level, but we cannot conclude anything about the population.
(Choice C) About
20
%
20%20, percent of all American students were reading below grade level.
C
About
20
%
20%20, percent of all American students were reading below grade level.
The appropriate inference from the data is (B) Since [tex]20%[/tex] of this group read below grade level, we cannot draw any generalizations about the population. Thus, option B is correct.
What is the percent of the sample?A representative sample is a subset of data, often drawn from a wider population, that can show qualities that are similar.
Because the data produced contains more manageable, smaller representations of the larger group, representative sampling aids in the analysis of bigger groups.
Although the sample may be representative of seventh-grade American students, it is not necessarily representative of all seventh-graders or all American children. Hence, without additional data or research, we cannot extrapolate the sample's results to the overall population.
Therefore, 20%20, percent of all American students in seventh grade were reading below grade level.
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Find X using the picture below.
Answer: 37.5
Step-by-step explanation:
75 - 180 = 105
105 degrees = the obtuse angle, bottom triangle.
75/2= 37.5 (since both sides of the bottom triangle are equal angles)
Find the measure of the angle A for the triangle shown!
Answer:
The value of A is 34 degrees angles on the right angle triangle are equal to 180 degrees
Need Help!
A commuter railway has 800 passengers per day and charges each one two dollars per day. For each 4 cents that the fare is increased, 5 fewer people will go by train.
What is the greatest profit that can be earned?
Greatest profit = $_____
Answer:
Step-by-step explanation:
To find the greatest profit, we need to determine the fare that will maximize revenue, while also considering the decrease in ridership due to the fare increase.
Let's assume the initial fare is $2, and the number of passengers is 800 per day. So, the initial revenue is:
$2 x 800 = $1600 per day
Now, let's say we increase the fare by 4 cents to $2.04. According to the problem, for each 4 cents increase in fare, there will be 5 fewer passengers. So, the number of passengers will decrease to:
800 - (5 x 4) = 780 passengers per day
The new revenue at this fare will be:
$2.04 x 780 = $1591.20 per day
By increasing the fare, the revenue decreased. This means that we may have increased the fare too much. Let's try another fare.
If we increase the fare by 2 cents to $2.02, the number of passengers will decrease by:
800 - (5 x 2) = 790 passengers per day
The new revenue at this fare will be:
$2.02 x 790 = $1595.80 per day
This is more revenue than the initial fare of $2 per person. Let's continue this process:
If we increase the fare by another 2 cents to $2.04, the number of passengers will decrease by:
790 - (5 x 2) = 780 passengers per day
The new revenue at this fare will be:
$2.04 x 780 = $1591.20 per day
This is less revenue than the $2.02 fare, so we can stop here.
Therefore, the greatest profit can be earned by charging $2.02 per person per day, and the maximum revenue will be:
$2.02 x 790 = $1595.80 per day
This is a bit less than the initial daily revenue of $1600, but it is the most revenue we can get by increasing the fare without causing a significant reduction in ridership.
Answer:
$2205
Step-by-step explanation:
You want the greatest profit that can be earned by a commuter railway that has 800 passengers per day at a fare of $2, and 5 fewer for each 4¢ increase in the fare.
Ridership functionThe number of riders (q) as a function of price (p) can be described by ...
q = 800 -5(p -2)/0.04
q = 1050 -125p . . . . . . . simplified
Revenue functionThe daily revenue is the product of price and the number of riders who pay that price.
r = pq
r = p(1050 -125p)
r = 125p(8.40 -p)
Maximum revenueThis function describes a parabola that opens downward. It has zeros at p=0 and p=8.40. The vertex of the parabola is on the line of symmetry, halfway between the zeros:
pmax = (0 +8.40)/2 = 4.20
The maximum revenue is ...
r(4.20) = 125·4.20(8.40 -4.20) = 125(4.20²) = 2205
The maximum revenue that can be earned is $2205.
__
Additional comment
The ridership at that fare is 125(4.20) = 525.
Profit is the difference between revenue and cost. Here, we have no information about the cost function, so we cannot predict the maximum profit. The question seems to assume that profit is equal to revenue.
Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
Answer:
x = 52.2
Step-by-step explanation:
Add 4x - 4y^2 = 36 and x + 2y^2 = 225
x + 2y^2 + 4x - 4y^2 = 225 + 36
5x = 261
x = 261/5=52.2
Shawn drinks 350 mL of milk every day. How many liters of milk does she drink in a week?
Answer:
The answer is 2.45 litres in one week.
Answer:
2.45 liters
Step-by-step explanation:
1 days - 350 ml of Milk
We know that, there are 7 days per week.
Therefore,
To find the milliliters of milk that she drinks in a week,
multiply milliliters of milk she drinks for a day by 7 ( number of days in a week).
Let us find it now.
350 ml × 7 = 2450 ml
And now to convert your answer into litres divide it by 1000.
2450ml ÷ 1000 = 2.45 liters
Can someone please help me
The volume of the composite figure is 837.33 cubic units.
What is volume of a cone?The area or capacity of a cone is determined by its volume. A cone's circular base tapers from a flat base to a point known as the apex or vertex in three dimensions. A cone is made up of a collection of line segments, half-lines, or lines that link the apex—the common point—to each point on the base, which is on a plane without the apex. A cone may be thought of as a collection of irregularly shaped circular discs placed on top of one another with the ratio of their radii remaining constant.
The volume of any composite figure is the addition of the volume of all the shapes present in the figure.
Here, the composite solid is made of 2 cones and a cylinder.
The volume of cone is:
V = 1/3(πr²h)
For cone with height 12 and r= 4:
V = 1/3(π)(4)²(12)
V = 200.96 cubic units.
For cone with h = 8 and r = 4:
V = 1/3(π)(4)²(8)
V = 133.97
The volume of cylinder is:
V = πr²h
V = (3.14)(4)²(10)
V = 502.4 cubic units.
The volume of the composite solid is:
Total volume = 200.96 + 133.97 + 502.4
Total volume = 837.33 cubic units.
Hence, the volume of the composite figure is 837.33 cubic units.
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Mr. Ross had been classifying fuel costs as Delivery Expense but has found that the amount paid each month for gasoline has become a major expense. He has decided to use a separate account, Gasoline Expense. Also, a new account, Water Expense, is to be added to the chart of accounts. Account number _ should be assigned to Gasoline Expense, and account number _ should be assigned to Water Expense.
For Gasoline Expense, the account number may be something like 4540 (4 for expenses, 5 for operating expenses, and 40 for the specific account number). For Water Expense, the account number may be something like 4550 (4 for expenses, 5 for utility expenses, and 50 for the specific account number
How to assign account number?
To add new accounts to the chart of accounts, Mr. Ross should first determine the account type and the appropriate category. In this case, Gasoline Expense would be classified as an operating expense account, while Water Expense would be classified as a utility expense account.
Once the account types have been identified, Mr. Ross should then determine the account number for each account. The account numbering system may vary depending on the accounting system in use, but generally, account numbers are structured hierarchically based on the account category and type.
For example, if the account numbering system uses a four-digit code, the first digit may represent the account category (e.g., 1 for assets, 2 for liabilities, 3 for equity, 4 for revenues, and 5 for expenses), the second digit may represent the specific account type (e.g., 4 for operating expenses and 5 for utility expenses), and the last two digits may be assigned sequentially to each account within that category and type.
So, for Gasoline Expense, the account number may be something like 4540 (4 for expenses, 5 for operating expenses, and 40 for the specific account number). For Water Expense, the account number may be something like 4550 (4 for expenses, 5 for utility expenses, and 50 for the specific account number).
However, the specific account numbering system used may vary depending on the accounting system in use, so Mr. Ross should consult with his accountant or accounting software provider for guidance on how to properly create and assign account numbers in his specific system.
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QUESTION THREE (30 Marks) a) For a group of 100 Kiondo weavers of Kitui, the median and quartile earnings per week are KSHs. 88.6, 86.0 and 91.8 respectively. The earnings for the group range between KShs. 80-100. Ten per cent of the group earn under KSHs. 84 per week, 13 per cent earn KSHs 94 and over and 6 per cent KShs. 96 and over. i. Put these data into the form of a frequency distribution and obtain an estimate of the mean wage. 15 Marks
Answer:
the answer would be 100 I guess
It is known that the area of a triangle can be calculated by multiplying the measure of the base by the measure of the height. Let the triangle measure 5m, 12m and 13m. Determine your area
The area of this triangle is 30 m².
What area?Area is a surface measure, that is, it is the amount of space that a geometric figure occupies on a flat surface.
To calculate the area of a triangle, we can use the formula:
Area = (base x height) / 2
In the case of the given triangle, we can choose the measure of 5m as the base and the measure of 12m as the height, since the height forms a right angle with the base and is perpendicular to it.
So, we have:
Area = (b*h)/2
Area = (5m * 12m) / 2
Area = 30m²
write a verbal expression for each algebraic expression
9a2
Answer:
Step-by-step explanation:
Assuming you mean [tex]9a^2[/tex]:
Multiply nine by a squared.
OR
Times nine by a squared.
If you mean 9a^2:
Multiply nine by a number squared
or
Multiply a number squared by nine
What is the height of the building shown below? Round to the nearest tenth if necessary.
62.9 feet
132 feet
123.5 feet
77.7 feet
Answer:
77.7
Step-by-step explanation:
if you know, you know. laso make sure your calculator is on degrees and not radians
d. A quantity increases by 25% each year for 3 years. How much is the combined percentage growth p over the three-year period?
When a quantity increases by 25%, the new quantity becomes 100% + 25% = 125% of the original quantity.
After the first year, the quantity has increased to 125% of its original value. After the second year, it increases an additional 25%, making the new value 125% + (25% of 125%) = 156.25% of the original value. Finally, after the third year, it increases by another 25%, making the new value 156.25% + (25% of 156.25%) = 195.3125% of the original value.
So the quantity has increased by 195.3125% - 100% = 95.3125% over the three-year period. Therefore, the combined percentage growth p over the three-year period is 95.3125%.
The sum of the ages of father and son at present is 45 years. If both live on until the son's age becomes equal to the father's present age, the sum of their ages then will be 95 years. Find their present ages.
Answer:
father age 45 son age 0 this is answer
300 students attend Ridgewood Junior High School. 4% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
On Thursday, 12 students brought their lunch at school.
Define the term percentage?Using a number out of 100, a percentage is a technique to indicate a fraction or piece of a total. The word "percent" means "per hundred."
If 4% of the students bring their lunch to school every day, we can find the number of students who brought their lunch on Thursday by multiplying the total number of students by the percentage that brought their lunch:
Number of students who brought their lunch = (4/100) x 300
Number of students who brought their lunch = 12
Therefore, On Thursday, 12 students brought their lunch at school.
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Find the equation for the circle with a diameter whose endpoints are (3,1) and (-2,3)
Answer:
Step-by-step explanation:
The center of the circle is the midpoint of the diameter. To find the midpoint, we use the midpoint formula:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the diameter.
Midpoint = [(3 + (-2))/2, (1 + 3)/2]
Midpoint = [1/2, 2]
So, the center of the circle is (1/2, 2).
The radius of the circle is half the length of the diameter. To find the length of the diameter, we use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the diameter.
Distance = sqrt((-2 - 3)^2 + (3 - 1)^2)
Distance = sqrt(25 + 4)
Distance = sqrt(29)
So, the length of the diameter is sqrt(29).
The radius of the circle is half of sqrt(29), which is sqrt(29)/2.
Therefore, the equation of the circle is:
(x - 1/2)^2 + (y - 2)^2 = (sqrt(29)/2)^2
Simplifying this equation, we get:
(x - 1/2)^2 + (y - 2)^2 = 29/4
So, the equation of the circle with a diameter whose endpoints are (3, 1) and (-2, 3) is (x - 1/2)^2 + (y - 2)^2 = 29/4.
In a group, there are 10 women, 8 blondes and 3 blonde women. How many people are either blonde or a woman?
Answer:
18. 10 women, 8 blondes. the 3 blonde women have already fallen into the previous categories.
TERM 1 ASSIGNMENT GRADE 7 Question 3 3.1. Calculate the following WITHOUT using a calculator; 3.1.1 6234 ×32
Answer: 6234 × 32 = 199488.
Step by step:
To calculate 6234 × 32 without using a calculator, you can use the traditional multiplication method as follows:
6234
x 32
-------
12468 (2 x 6234)
+ 62340 (3 x 6234 with a zero added)
--------
199488
fine the exact value of sin(45-30)
3 g(n) = 80 . (-) 4 O Complete the recursive formula of g(n). g(1) = g(n) = g(n − 1). -
Answer:
Based on the given information, we know that:
g(n) = 80 - 4g(n-1)
Also, we have the initial condition:
g(1) = g(n) = g(n-1)
Putting everything together, we can write the recursive formula for g(n) as follows:
g(1) = g(n) = g(n-1) (initial condition)
g(n) = 80 - 4g(n-1) (recursive formula)
where n > 1.
(please mark my answer as brainliest)
valuate the
expression
12 - 3y
2
+
√²v=4] for y = 3.
2y -
The result of the formula [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is [tex]-29/2[/tex] .
What are the ways to analyse an algebraic expression?When [tex]y = 3[/tex] is used, the value of the expression [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] has a value of [tex]-29/2[/tex] .
To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.
If [tex]y = 3[/tex] , we can insert it into the expression & simplify as follows to evaluate [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for [tex]y = 3[/tex] .
[tex]12 - 3(3)^2 + (√4) / (2(3) - 2)[/tex] (y = 3 replacement)
[tex]12 - 27 + 2 / 4\s-15 + 1/2\s-29/2[/tex]
Therefore, The result of the formula [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is [tex]-29/2[/tex] .
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I need help with this
The angle congruent to angle FYE is angle EYD.
What is a bisector?A line known as a bisector splits an angle or a line into two equally sized segments. A segment's midpoint is always contained in the segment's bisector. Based on the geometric shape that they bisect, there are two different sorts of bisectors. An angle is divided into equal angles by an angle bisector. The line segment is split into two equal halves by a line segment bisector. It travels through the line segment's centre.
Given that, YE bisects the angle FYD.
That is, the segment YE divides the angle FYD into two equal parts.
Thus, the angle congruent to angle FYE is angle EYD.
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The toll T charged for driving on a certain stretch of a toll road is $5 except during rush hours (between 7 AM and 10 AM and between 4 PM and 7 PM) when the toll is $7.
The toll calculation for driving on a certain stretch of a toll road is $5 except during rush hours when the toll is $7, depending on the time the driver uses the toll road.
To compute the toll for driving on the toll road during non-rush hours, simply add $5 to the total. During rush hour, however, the toll is $7.
To compute the toll for driving during rush hour, you must first determine when the driver intends to utilize the toll road. If the period is between 7 AM and 10 AM or 4 PM and 7 PM, the toll is $7.
For instance, if a vehicle expects to use the toll road at 8 a.m., the toll is $7. If the vehicle intends to use the toll road at 2 p.m., the toll is $5.
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se spherical coordinates to evaluate the triple integral where is the region bounded by the spheres and .
The value of the triple integral[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex] by using spherical coordinates [tex]2\pi(e^{-1}-e^{-9})[/tex].
Given that the triple integral is-
[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]
E is the region bounded by the spheres which are,
[tex]x^2+y^2+z^2=1\\\\x^2+y^2+z^2=9[/tex]
In spherical coordinates we have,
x = r cosθ sin ∅
y = r sinθ sin∅
z = r cos∅
dV = r²sin∅ dr dθ d∅
E contains two spheres of radius 1 and 3 () respectively, the bounds will be like this,
1 ≤ r ≤ 3
0 ≤ θ ≤ 2π
0 ≤ ∅ ≤ π
Then
[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]
[tex]\int\int\int _{E} \frac{e^{-r^2}}{r}r^2Sin\phi drd\phi d\theta\\\\2\pi \int_{0}^{\pi} \int_1^3 re^{-r^2} dr d\phi\\\\2\pi \int_1^3 re^{-r^2} dr\\\\2\pi(e^{-1}-e^{-9})[/tex]
The complete question is-
Use spherical coordinates to evaluate the triple integral ∭ee−(x2 y2 z2)x2 y2 z2−−−−−−−−−−√dv, where e is the region bounded by the spheres x2 y2 z2=1 and x2 y2 z2=9.
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Find the area of the surface obtained by rotating the curve about the x-axis. y = x^2/4 - ln x/2.
The area of the surface obtained by rotating the curve about the x-axis.
y = X²⁾⁴- ln x is 2.8.
The area of a sphere is defined as the area covered by its outer surface in three-dimensional space. A sphere is a three-dimensional solid that is circular in shape, like a circle.
Based on the Question:
Knowing the area of a solid obtained by rotating a curve governed by the function f(x) around the y-axis, where a ≤ x ≤ b, is represented by a single integral given below:
Surface Area = [tex]2\pi \int\limits^b_a {f(x)\sqrt{1+f(x')^2} } \, dx[/tex]
Consider the curve equation y(x) where 1 ≤ x ≤ 2 is shown below.
[tex]y(x) = \frac{x^2}{4} -\frac{ln x}{2}[/tex]
Now,
Derivations the above equation:
[tex]y'(x) =\frac{d}{dx} {\frac{x^2}{4} -\frac{ln x}{2} }[/tex]
⇒ [tex]y'(x)=\frac{x}{2} -\frac{1}{2x}[/tex]
⇒ [tex]y'(x) = \frac{x^2-1}{2x}[/tex]
Calculate the numerical value of the obtained area value to obtain the desired result.
Surface area = 5.30144 - 2.55493
= 2.74651 ≈ 2.8
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Consider the following algebraic statements and determine the values of x for which each statement is true. On a number line, show the set of all points corresponding to the values of x.
4=|-2x|
Your question is incomplete. The complete question is: Consider the following algebraic statements and determine the values of x for which each statement is true. On a number line, show the set of all points corresponding to the values of x.
|x| = 7
4=|-2x|
The values of x for which each statement is true are:
|x| = 7: x = -7 or x = 7
4 = |-2x|: x = -2 or x = 2
How to determine the values of x for which each statement is true?a) |x| = 7
-x = 7 or x = 7
x = -7 or x = 7
This statement is true for two values of x:
x = -7 and x = 7.
b) 4 = |-2x|
4 = -2x or 4 = 2x
x = -2 or x = 2
This statement is true for two values of x:
x = -2 and x = 2.
The number line is shown in the image attached.
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A bicycle wheel is 63m in diameter. how many metres does the bicycle travel for 100 revolutions of the wheel. (pie=²²/⁷
Answer:
19782m
Step-by-step explanation:
1 revolution = circumference
circumference = π * diameter
π = 3.1416
Then
circumference = 3.1416 * 63
= 197.92m
1 revolution = 197.82m
100 revolutions = 100*197.82m
= 19782m
Answer:
19.8 km
Step-by-step explanation:
To find:-
The distance travelled in 100 revolutions .Answer:-
We are here given that,
diameter = 63mWe can first find the circumference of the wheel using the formula,
[tex]:\implies \sf C = 2\pi r \\[/tex]
Here radius will be 63/2 as radius is half of diameter. So on substituting the respective values, we have;
[tex]:\implies \sf C = 2\times \dfrac{22}{7}\times \dfrac{63}{2} \ m \\[/tex]
[tex]:\implies \sf C = 198\ m \\[/tex]
Now in one revolution , the cycle will cover a distance of 198m . So in 100 revolutions it will cover,
[tex]:\implies \sf Distance= 198(100)m\\[/tex]
[tex]:\implies \sf Distance = 19800 m \\[/tex]
[tex]:\implies \sf Distance = 19.8 \ km\\[/tex]
Hence the bicycle would cover 19.8 km in 100 revolutions.
A 5-year swap contract can be viewed as a portfolio of 5 forward contracts with maturities of 1, 2, 3, 4 and 5 years. One important exception is that Multiple Choice O the forward price is the same for the swap contract but not for the forward contracts. the swap contract will have daily resettlement the forward contracts will have resettlement risk.
If a 5-year swap contract can be viewed as a portfolio of 5 forward contracts with maturities of 1, 2, 3, 4 and 5 years. One important exception is option (a) the forward price is the same for the swap contract but not for the forward contracts
In a swap contract, the fixed rate is agreed upon at the beginning of the contract, and the floating rate is determined by a reference rate such as LIBOR. The swap contract's value is based on the difference between the fixed and floating rates at each settlement date. In contrast, forward contracts involve an agreement to buy or sell an asset at a specified price on a specific future date. The forward price is determined at the time the contract is entered into and is based on the spot price of the underlying asset, the time to maturity of the contract, and the cost of carry.
Therefore, the forward price will be different for each forward contract in the swap portfolio, whereas the forward price for the swap contract will be the same throughout the contract's life. The other options mentioned are not true for swap or forward contracts.
Therefore, the correct option is (a) the forward price is the same for the swap contract but not for the forward contracts
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A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens, as shown in the figure. 4x + 3y = 100 (a) Write the area of the enclosed region as a function of x. 8 2 200 A(x) = + 3 -2 3 (b) Use a graphing utility to generate additional rows of the table. (Round your answers to one decimal place.) X y Area 2 92 3 30.7 368 3 122.7 4 28 224 6 25.3 > 304 8 22.7 362.7 10 | 20 400 12 17.3 416 14 || 14.7 410.7 Use the table to estimate the dimensions that will produce a maximum area. (Round your answers to one decimal place.) longer side 2x = 24 shorter side y = 173 m (c) Use the graphing utility to graph the area function. A(X) A(X) 400 400 300 300 200 200) 100 100 LUL X 5 10 15 20 25 o 5 10 15 20 25 A(X) A(X) 400 400) 300 300 200 200 100) 100 5 10 15 20 х 25 5 10 15 20 25 Use the graph to estimate the dimensions that will produce a maximum area. (Round your answers to one decimal place.) longer side 2x = 25 m shorter side y = 16.7 (d) Use the graph to approximate the dimensions such that the enclosed area is 336 square meters. (Round your answers to one decimal place.) Smaller value of x: longer side y = 23.3 m shorter side 2x = 15 X m Larger value of x: longer side 2x = 35 shorter side y = 10 m X m (e) Find the required dimensions of part (d) algebraically. (Round your answers to one decimal place.) Smaller value of x: longer side m shorter side 2x = 15 x m y = 23.3 Larger value of x: longer side 2x = 35 shorter side EE y = 10 x m
The area of enclosed region as a function of x is A(x) = 8x^2/3 + (200/3)x - 2x. Using a table, the estimated dimensions that produce maximum area are longer side x = 12 and shorter side y = 17.3 m. Using a graph, the estimated dimensions that produce maximum area are longer side 2x = 25 m and shorter side y = 16.7 m. The dimensions for an enclosed area of 336 square meters are smaller value of x: longer side y = 23.3 m, shorter side 2x = 15 x m and larger value of x: longer side 2x = 35 m, shorter side y = 10 x m.
The area of the enclosed region can be written as a function of x as follows.
A(x) = 2xy
Substituting y = (100 - 4x)/3, we get
A(x) = 2x(100 - 4x)/3 = (200x - 8x^2)/3 = 66.7x - 2.67x^2
Using a graphing utility, we can generate additional rows of the table as follows.
xy Area
2 92 368
3 122.7 367.1
4 128 512
5 116.7 583.3
6 100.7 604.2
7 80.0 560.0
8 65.3 522.7
9 56.0 504.0
10 51.3 513.0
11 51.0 561.0
12 54.7 656.7
13 62.0 806.2
14 72.7 1003.3
From the table, we can see that the maximum area occurs when x = 12 and y = 17.3.
The graph of the area function is shown.
From the graph, we can estimate that the dimensions that will produce a maximum area are x ≈ 12.5 and y ≈ 16.7.
From the graph, we can estimate that the smaller value of x for an area of 336 square meters is x ≈ 7.5 and the larger value of x is x ≈ 17.5. Substituting these values in the equation for y, we get:
For the smaller value of x:
y = (100 - 4(7.5))/3 ≈ 23.3
So, the required dimensions are longer side = 15 m and shorter side = 2(7.5) = 15 m.
For the larger value of x:
y = (100 - 4(17.5))/3 ≈ 10.0
So, the required dimensions are longer side = 2(17.5) = 35 m and shorter side = 10 m.
To find the required dimensions algebraically, we need to solve the equation A(x) = 336. We already have the expression for A(x) as:
A(x) = 8x(50 - 4x)
Substituting 336 for A(x), we get:
8x(50 - 4x) = 336
Dividing both sides by 8, we get:
x(50 - 4x) = 42
Expanding the left side, we get:
50x - 4x^2 = 42
Rearranging and simplifying, we get a quadratic equation:
4x^2 - 50x + 42 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 4, b = -50, and c = 42.
Substituting these values, we get:
x = (50 ± sqrt(50^2 - 4(4)(42))) / 2(4)
Simplifying, we get:
x = (50 ± sqrt(196)) / 8
x = (50 ± 14) / 8
So, the two possible values of x are:
x = 7 or x = 1.25
For x = 7, the corresponding dimensions are:
longer side 2x = 14 m
shorter side y = (50 - 4x) = 22 m
For x = 1.25, the corresponding dimensions are:
longer side 2x = 2.5 m
shorter side y = (50 - 4x) = 32.5 m
Therefore, the required dimensions for an enclosed area of 336 square meters are:
Smaller value of x: longer side 2x = 2.5 m, shorter side y = 32.5 m
Larger value of x: longer side 2x = 14 m, shorter side y = 22 m
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question in what quadrant does the terminal ray of the angle lie? select quadrant i, quadrant ii, quadrant iii, or quadrant iv.
, [tex]\frac{-21 \pi}{8}[/tex] lies in 3rd quadrant, ,[tex]\frac{-5 \pi }{9}[/tex] lies in 3rd quadrant,t, [tex]\frac{5 \pi}{6}[/tex] radian lies in 2nd quadrant and [tex]\frac{35 \pi}{4}[/tex] lies in 1st quadrant.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To determine the quadrant in which the angle -21π/8 lies
Convert, [tex]\frac{-21 \pi}{8}[/tex] to number
-21×180/8
-472.5 degrees lies in which quadrant we have to check.
The value is negative
Quadrant IV = 0 to -90°
Quadrant III = -90° to -180°
Quadrant II = -180° to -270°
Quadrant I = -270° to -360°
-21π/8 lies in 3rd quadrant
-5π/9=-100 which lies in 3rd quadrant
5π/6=150 which is positive so it lies in 2nd quadrant
35π÷4=1575 which is positive so it lies in 1st quadrant
Hence, [tex]\frac{-21 \pi}{8}[/tex] lies in 3rd quadrant,[tex]\frac{-5 \pi }{9}[/tex]lies in the 3rd quadrant, [tex]\frac{5 \pi}{6}[/tex] lies in 2nd quadrant and [tex]\frac{35 \pi}{4}[/tex] lies in 1st quadrant.
The complete question is-
In what quadrant does the terminal ray of the angle lie?
Select Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
Angle measure Quadrant I Quadrant II Quadrant III Quadrant IV
−21π8
Quadrant , I – negative fraction numerator 21 pi over denominator 8 end fraction
Quadrant , I I – negative fraction numerator 21 pi over denominator 8 end fraction
Quadrant , , I I I, – negative fraction numerator 21 pi over denominator 8 end fraction
Quadrant , I V – negative fraction numerator 21 pi over denominator 8 end fraction
−5π9
Quadrant , I – negative fraction numerator 5 pi over denominator 9 end fraction
Quadrant , I I – negative fraction numerator 5 pi over denominator 9 end fraction
Quadrant , , I I I, – negative fraction numerator 5 pi over denominator 9 end fraction
Quadrant , I V – negative fraction numerator 5 pi over denominator 9 end fraction
5π6
Quadrant , I – fraction numerator 5 pi over denominator 6 end fraction
Quadrant , I I – fraction numerator 5 pi over denominator 6 end fraction
Quadrant , , I I I, – fraction numerator 5 pi over denominator 6 end fraction
Quadrant , I V – fraction numerator 5 pi over denominator 6 end fraction
35π4
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