a. The proportion of students have scores less than 380 is 11.51%.
b. The proportion of students have scores greater than 639 is 8.23%.
What is the proportion with SAT scores below 380 and above 639?1. Using the z-score formula:
We can calculate that score of 380 corresponds to a z-score of -1.2 since z = (x - μ) / σ.
Using a standard normal distribution table, we find that:
The proportion of students with scores less than 380 is 0.1151.2. Similarly, a score of 639 corresponds to a z-score of 1.39.
Using a standard normal distribution table, we find that:
The proportion of students with scores greater than 639 is approximately 0.0823.Read more about distribution
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What is the value of the shaded area of the total diagram?(both squares). Please see attached image.
A.0.148
B.0.148 repeated
C. 0.3
D.0.3 repeated
Supplementary angles
The angle that is supplementary to <DEA is DEC
How to determine the angleTo determine the angle that is supplementary to <DEA , we need to consider the following;
Supplementary angles are described as angles that sum up to 180 degreesIt is described as the pair of angles on a straight lineSum of angles on a straight line is 180 degreesThe supplementary angles must be pairTangent lines forms supplementary anglesFrom the information given, we have that;
<DEA is supplementary to <DEC that is sum of angles on a straight line.
Then,
<DEA + <DEC = 180 degrees
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A pool measuring 18 meters by 30 meters is surrounded by a path of uniform width, as shown in the
figure. If the area of the pool and the path combined is 1900 square meters, what is the width of
the path?
The width of the path is approximately 7.45 meters.
What is meant by width?
The width refers to the measurement of something from side to side, typically in a direction perpendicular to its length or height, such as the width of a door or the width of a piece of paper.
What is meant by meters?
Meters are a unit of measurement used to measure the length in the metric system. One meter is equal to 100 centimetres or approximately 3.28 feet. It is commonly used to measure distances, heights, and lengths.
According to the given information
The area of the pool is given by the product of its length and width:
18 × 30 = 540 square meters
The area of the entire region, including the pool and the path, is given by the product of the length and width of the outer rectangle:
(18 + 2x) × (30 + 2x)
Expanding this expression, we get:
540 + 36x + 60x + 4x²
Simplifying, we get:
4x² + 96x + 540
We are given that the area of the entire region is 1900 square meters:
4x² + 96x + 540 = 1900
Subtracting 1900 from both sides, we get:
4x² + 96x - 1360 = 0
Dividing both sides by 4, we get:
x² + 24x - 340 = 0
We can use the quadratic formula to solve for x:
x = (-24 ± √(24² - 4 × 1 × (-340))) / (2 × 1)
Simplifying, we get:
x = (-24 ± √(1216)) / 2
x ≈ -17.45 or x ≈ 7.45
Since the width of the path cannot be negative, we can ignore the negative solution.
Therefore, the width of the path is approximately 7.45 meters.
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If the sides of a square are increased by 11, the area becomes 400. What is the length of the original side?
Answer: The length of the original side of the square is 22 units.
Step-by-step explanation:
Let x be the length of the original side of the square.
If the sides are increased by 11, the new side length is x + 11.
The area of the new square is given as 400, so we have:
(x + 11)^2 = 400
Expanding the left side: x^2 + 22x + 121 = 400
Subtracting 400 from both sides: x^2 + 22x - 279 = 0
Using the quadratic formula:
x = (-22 ± sqrt(22^2 - 41(-279))) / (2*1)
x = (-22 ± sqrt(12100)) / 2
x = (-22 ± 110) / 2
Taking the positive solution:
x = (-22 + 110) / 2
x = 44 / 2
x = 22
On Friday, three friends shared how much they read during the week
Barbara read the first 100 pages from a 320-page in the last 4 days
Judy read the first 54 pages from a 260-page book in the last 3 days.
Nancy read the first 160 pages from a 480-page book in the last 5 days
Order the friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book(Show all work)
The friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book is given by the order Nancy > Barbara > Judy
Given data ,
The total number of pages in each friend's book as follows:
Barbara's book: 320 pages
Judy's book: 260 pages
Nancy's book: 480 pages
Now, we can calculate their reading rates as pages read per day:
Barbara's reading rate: 100 pages / 4 days = 25 pages/day
Judy's reading rate: 54 pages / 3 days = 18 pages/day
Nancy's reading rate: 160 pages / 5 days = 32 pages/day
Hence , the descending order is Nancy > Barbara > Judy
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Practice: Tell and Write Time-Practice-Level C
Determine if each statement describes the time shown on the clock.
i-Ready
......................
10
9
8
12
11
76
1
5
2
4
3:
(16 minutes before 10:00
»44 minutes after 9:00
Yes
(47 minutes after 8:00
No
» 13 minutes before 10:00 O
13 minutes before 9:00
O
O
00
O
O
O
O
7:76 - This is not a valid time. There are only 60 minutes in an hour, so the minutes place cannot be 76.
What is time?Time is a measurable and non-spatial quantity used to describe or quantify the sequence, duration, or occurrence of events. It is a concept used to understand the order in which events occur and to measure the duration of those events.
According to question:10:44 - Yes, the statement is true. The time is 44 minutes after 10:00.
9:47 - No, the statement is false. The time is 13 minutes before 10:00.
12:13 - Yes, the statement is true. The time is 13 minutes after 12:00.
11:00 - Yes, the statement is true. The time is exactly 11:00.
7:76 - This is not a valid time. There are only 60 minutes in an hour, so the minutes place cannot be 76.
1:05 - Yes, the statement is true. The time is 5 minutes after 1:00.
5:02 - No information is provided about this time on the clock.
2:00 - Yes, the statement is true. The time is exactly 2:00.
4:00 - Yes, the statement is true. The time is exactly 4:00.
3:00 - Yes, the statement is true. The time is exactly 3:00.
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You want to buy a $12,000 car. The company is offering a 2% interest rate for 48 months (4 years). What
will your monthly payments be?
Answer:
240
Step-by-step explanation:
Answer the following questions.
Answer:
A=60
B=27
Step-by-step explanation:
Two partner a and b agree to divide 30% of the total profits equally between than a and the balance in the ratio 3:4.if the profits is rs 30000 find a,s share of the profits.
well, let's first find out how much is 30% of 30000
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 30000}}{\left( \cfrac{30}{100} \right)30000}\implies 9000[/tex]
ok, that means if we split that down the middle, each will get 4500.
so the remaining is 21000, and that's split on a 3:4 ratio, assuming from A to B, so let's simply divide the total 21000 by (3 + 4) and distribute accordingly.
[tex]\stackrel{A}{3}~~ : ~~\stackrel{B}{4} ~~ \implies ~~ \stackrel{A}{3\cdot \frac{21000}{3+4}}~~ : ~~\stackrel{B}{4\cdot \frac{21000}{3+4}}\implies \stackrel{A}{3\cdot 3000}~~ : ~~\stackrel{B}{4\cdot 3000} \\\\\\ \stackrel{A}{9000}~~ : ~~\stackrel{B}{12000}\hspace{9em}\underset{ \textit{share for A} }{\stackrel{ 4500~~ + ~~9000 }{\text{\LARGE 13500}}}[/tex]
Each graph below was obtained by transformation(s) of the graph of the cubic function. Write the equation for the function each graph represents.
Correct answer gets brainliest !
The cubic equation graphed have the functions as follows
3/40(x + 5)^3 - 7 y = 2 - 2/5(x + 0.5)^3How to write the equation of the functionsGraph of cubic function
The equation of cubic function is
y = a(x - h)^3 + k
For horizontal inflection at (-5, -7)
y = a(x + 5)^3 - 7
passing through point (-1, -3.8)
-3.8 = a(-1 + 5)^3 - 7
4.8 = -64a
a = 4.8/64 = 3/40
hence the equation is: y = 3/40(x + 5)^3 - 7
Graph of cubic function
The equation of cubic function is
y = k - a(x - h)^3
For horizontal inflection at (-0.5, 2)
y = 2 - a(x + 0.5)^3
passing through point (-5, 38.45)
38.45 = 2 - a(-5 + 0.5)^3
38.45 -2 = -a(-4.5)^3
a = -36.45/(-4.5)^3 = 2/5
hence the equation is: y = 2 - 2/5(x + 0.5)^3
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Felicia is deciding on her schedule for next semester. She must take each of the following classes: English 102, Spanish 102, History 102, and College Algebra. If there are 15 sections of English 102, 9 sections of Spanish 102, 12 sections of History 102, and 13 sections of College Algebra, how many different possible schedules are there for Felicia to choose from? Assume there are no time conflicts between the different classes.
Okay, here are the steps to solve this problem:
* There are 15 sections of English 102 to choose from
* There are 9 sections of Spanish 102 to choose from
* There are 12 sections of History 102 to choose from
* There are 13 sections of College Algebra to choose from
So for English 102 Felicia has 15 options, for Spanish 102 she has 9 options, for History 102 she has 12 options, and for College Algebra she has 13 options.
By the Fundamental Principle of Counting, the total number of possible schedules is:
15 * 9 * 12 * 13 = 16,920
Therefore, the total number of possible schedules for Felicia is 16,920
Please see the attached
a. Monthly payment for the bank's car loan is $407.67
b. Monthly payment for the savings and loan association's car loan is $315.99
c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.
What is interest rate?The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.
(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:
[tex]PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }[/tex]
putting the given values,
⇒ [tex]21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }[/tex]
Solving for PMT, we get:
PMT = $407.67
Therefore, the monthly payment for the bank's car loan is $407.67
(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:
where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.
putting the given values,
[tex]21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }[/tex]
Solving for PMT, we get:
PMT = $315.99
Therefore, the monthly payment for the savings and loan association's car loan is $315.99.
(c) Bank's car loan: $407.67 x 60 = $24,460.20
Savings and loan association's car loan: $315.99 x 84 = $26,495.16
Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96
Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.
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When Caroline runs the 400 meter dash, her finishing times are normally distributed with a mean of 68 seconds and a standard deviation of 1.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 99.7% of her finishing times in the 400 meter race.
The interval of times that represents the middle 99.7% of Caroline's finishing times is (63.5, 72.5) seconds
How to calculate the intervalIn this case, we are looking for the interval of times that represents the middle 99.7% of Caroline's finishing times.
The middle 99.7% of the data corresponds to three standard deviations from the mean in both directions
Three standard deviations from the mean is 3 x 1.5 = 4.5 seconds.
Therefore, the interval of times that represents the middle 99.7% of Caroline's finishing times is (68 - 4.5, 68 + 4.5) = (63.5, 72.5) seconds
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Review the information given based on a principal balance of $8,000 to answer the question:
FICO Score Simple Interest Rate Total # of Payments Total Amount Paid
800–850 12% 29 $9,256.00
740–799 15% 33 $9,812.00
670–739 18% 38 $10,554.00
580–669 21% 48 $11,891.00
300–579 28% 60 $14,945.00
Calculate how much more a household with a credit score of 525 will pay compared to a household with a credit score of 675.
a household with a credit score of 525 would pay $4,280.82 more than a household with a credit score of 675 for a principal balance of $8,000.
what is principal balance ?
Principal balance refers to the amount of money that you still owe on a loan or debt, not including any interest or fees that have accrued. When you make a payment towards your loan or debt, a portion of the payment goes towards paying down the principal balance,
In the given question,
To calculate the difference in payment between a household with a credit score of 525 and one with a score of 675, we need to compare the total amount paid for each score range.
For a principal balance of $8,000, based on the given information:
A household with a credit score of 525 would have a simple interest rate of 28%, and would make 60 payments of $249.08 each, for a total amount paid of $14,945.00.
A household with a credit score of 675 would have a simple interest rate of 18%, and would make 38 payments of $280.61 each, for a total amount paid of $10,664.18.
The difference in payment between these two scores would be:
$14,945.00 - $10,664.18 = $4,280.82
Therefore, a household with a credit score of 525 would pay $4,280.82 more than a household with a credit score of 675 for a principal balance of $8,000.
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a random sample of 50 employees at a large firm has 22 females and 28 males. if the company has 1300 workers, what is the expected number of male workers?
Step-by-step explanation:
We can use the proportion of males in the sample to estimate the proportion of males in the population, and then use that proportion to find the expected number of male workers.
The proportion of males in the sample is:
p = 28/50 = 0.56
We can use this proportion to estimate the proportion of males in the population:
p' = 0.56
The expected number of male workers is then:
E(X) = n * p'
where n is the total number of workers in the population:
E(X) = 1300 * 0.56
E(X) = 728
Therefore, we would expect there to be approximately 728 male workers in the company.
I NEED HELP WITH THIS TRIG QUESTION
The angle of elevation from the player's eyes to the center of the rim is approximately 16.2 degrees.
What is unit circle in trigonometry?A circle having a radius of 1 that is centred at the origin of a coordinate plane is known as the unit circle. The sine, cosine, and tangent values for every angle in the unit circle are frequently defined in trigonometry.
A radian-measured angle that begins at the positive x-axis and rotates anticlockwise around the circle can be used to represent each point on the unit circle. (Cos, Sin) are the coordinates of the point on the unit circle that corresponds to the angle.
For the given triangle first determine the value of the height from, the player to the top of the baseball pole as follows:
10 - 5.8 = 4.2 units
Now, using the trigonometric identity of tangent we have:
tan θ = opposite / adjacent
tan θ = 4.2 / 15
θ = tan⁻¹(4.2 / 15)
Hence, the angle of elevation from the player's eyes to the center of the rim is approximately 16.2 degrees.
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HELP PLS ASAPPP!!!
algebra problem; solving linear inequalities !!! :)
Answer: x = -3/2
Step-by-step explanation:
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
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The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
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Exercise
find the truth set of the
1.5(3x-5)-2(x-7)=11
Can someone please help me
The height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.
How to solveThe height of point A on the Ferris Wheel can be calculated using the sine function, as it is the vertical component of the point's position. The center of the Ferris Wheel is 100 feet off the ground, and its radius is 85 feet.
Let's denote the height of point A as h_A, which is the vertical distance from the center of the Ferris Wheel to point A.
Since point A is at the 0 radian position, it is at the highest point on the Ferris Wheel. At this point, the height of point A is equal to the sum of the radius and the center's height:
h_A = radius + center's height
h_A = 85 + 100
h_A = 185 feet
So, the height of point A off the ground is 185 feet.
To estimate the value of h_A using the sine function, we can use the fact that at any given angle θ on the unit circle, the height of the point on the circle is given by the sine of that angle multiplied by the radius. In this case, since point A is at the highest point on the Ferris Wheel, we can use the sine of 0 radians (which is 0) to estimate the height of point A:
h_A = radius * sin(0)
h_A = 85 * 0
h_A = 0
So, using the sine function, we estimate that the height of point A is 0 feet. However, this is not the actual height of point A, as it is at the highest point on the Ferris Wheel, which is 185 feet as calculated previously.
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1. (i) Find the first 3 terms in the expansion of (2 - y)^5 in ascending powers of y.
(ii) Use the result in part (i) to find the coefficient of x² in the expansion of (2 − (2x - x²))^5.
1) The first three terms in the expansion of [tex](2 - y)^{5}[/tex] in ascending powers of y are as follows:
32, -80y, and [tex]80y^2[/tex]
2)The [tex]x^{2}[/tex] coefficient in the expansion of (2 (2x - [tex]x^{2}[/tex]))5 is 80.
What is the binomial theorem?As the power increases, the expansion gets more difficult to compute. The Binomial Theorem can be used to easily calculate a binomial statement that has been raised to very big power.
(i) Using the binomial theorem, we can expand [tex](2 - y)^{5}[/tex] as follows:
[tex](2 - y)^{5}[/tex] = [tex]2^{5} - 5(24)y^{1} + 10(23)y^{2} + 10(23)y^{3} + 5(2)y^{4} - y^{5}[/tex]
By combining the powers of two and simplifying, we get:
[tex]32 - 80y + 80y^{2} - 40y^3 + 10y^4 - y^5[/tex]
As a result, the first three terms in the expansion of [tex](2 - y)^{5}[/tex] in ascending powers of y are as follows:
32, -80y, and [tex]80y^2[/tex]
(ii) Using the result of section (i), we can expand [tex](2 - (2x - x^{2} ))^{5}[/tex] by substituting y with 2x - x2:
[tex](2 - (2x - x^2))^5 = 2^5 - 5(2^4)(2x - x^2) + 10(2^3)(2x - x^2)^2 - 10(2^2)(2x - x^2)^3 + 5(2)(2x - x^2)^4 - (2x - x^2)^5[/tex]
By combining the powers of two and simplifying, we get:
[tex]32 - 80x + 80x^2 - 40x^3 + 10x^4 - x^5[/tex]
As a result, the [tex]x^{2}[/tex] coefficient in the expansion of (2 (2x - [tex]x^{2}[/tex]))5 is 80.
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Using these sets, find the following: (D NE) UF=
D = {b, a, c, k}
• E = {t, a, s, k}
. F = {b, a, t, h}
Using the information regarding the set, it should be noted that (D NE) UF will be {b, a, t, h, s, t}
How to explain the informationD U E = {b, a, c, k} U {t, a, s, k}
= {b, a, c, k, t, s}
Next, we need to find the complement of set D with respect to set E, which is denoted as D NE. This is the set of all elements in E that are not in D: D NE = E \ D = {t, s}
(D NE) UF = {t, s} U {b, a, t, h}
= {b, a, t, h, s, t}
In conclusion, Using the information regarding the set, it should be noted that (D NE) UF will be {b, a, t, h, s, t}
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I need to know the order asap
The inverse of the function f(x) = 3 · x / (8 + x) is f⁻¹(x) = 8 · x / (3 - x).
How to find the inverse of a function
In this problem we must determine the inverse of a function, this can be done by means of algebra properties. First, write the entire function:
f(x) = 3 · x / (8 + x) (Step 0)
y = 3 · x / (8 + x) (Step 1)
Second, use the following substitutions:
x → y
y → x
x = 3 · y / (8 + y) (Step 2)
Third, clear y within the expression:
x · (8 + y) = 3 · y (Step 3)
8 · x + x · y = 3 · y
8 · x = 3 · y - x · y (Step 4)
8 · x = y · (3 - x)
y = 8 · x / (3 - x)
Fourth, use final notation:
f⁻¹(x) = 8 · x / (3 - x) (Step 5)
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An archaeologist found a fossil whose length is489.44 in.
Consult the conversion table to calculate the length of the fossil infeet.
Round your answer to the nearest tenth.
If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.
What is the conversion table?The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions
For instance, the conversion table shows that 12 inches equal 1 foot.
The length of the fossil = 489.44 inches
12 inches = 1 foot
489.44 inches = 40.8 feet (489.44 ÷ 12)
Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.
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Supplementary angles
Answer: ∠EAI and/or ∠EDG (More listed below lol)
Step-by-step explanation:
Starting Angle: ∠ADE
Possible Supplements: ∠EAI, ∠EDG, ∠DAH, ∠DEC, ∠ADF, and ∠AEB
please help me!!!!!!
Answer:2nd one
Step-by-step explanation:
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 12 15 4 31
Female 9 8 16 33
Total 21 23 20 64
If one student is chosen at random, find the probability that the student was male GIVEN they got a 'C':
Answer: [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Males who got a C = 4
Total amount of people who got a C = 20
[tex]\frac{4}{20}[/tex]
[tex]\frac{4}{20}[/tex] simplifies to [tex]\frac{1}{5}[/tex]
A hiker travels 6 mph, which is 3/11 of the rate of a cyclist.Suppose the hiker and cyclist are traveling toward each other.How fast does the distance between them decrease?
Answer:
28 mph
Step-by-step explanation:
let x= rate of cyclist
3/11(x)=6
x=66/3=22 mph
22mph+ 6mph=28 mph
they move towards each other with a relative speed of 28 mph
K
The eccentricity of an ellipse is defined as e = c/a. For an ellipse, 0
5
Find an equation of an ellipse with vertices (0,-6) and (0,6) and e=
6
The equation of an ellipse which satisfies the given conditions is
(Type your answer in standard form.)
close to 0, an ellipse
The equation of the ellipse is y² = 35 (1 - x²)
How did we get this ?The given ellipse has vertices at ( 0, -6) and ( 0 , 6), which lie on the y - axis.
The distance between the centr of the ellipse (which also lies on the y - axis) and each vertex is 6 units. So since we hve
c = 6
and the eccentricity of the ellipse is also given as e = 6
we can use the r elationship between e, a, and c to find the value of a....
e = c/a
6 = 6/a
a = 1
Using the value of A and C, we find the equation of the ellipse, we can use the standard form
( x² / a²) + (y² / b²) = 1
Since the center of the ellipse is at the origin, know that
x / a² + y² / b ² = 1
Substituting a and c, ......
x² / 1² + y² / b² = 1
y² / b² = 1 - x²
y² = b² (1 - x²)
We need to find the value of b. We know that the distance between the center and each co-vertex of the ellipse is 5 units. So we state this as
b² = c² - a²
b² = 6² - 1 ²
b² = 35
Substituting the value of b² in the equation we got earlier, we get
y² = 35( 1 - x²)
Therefore, the equation of the ellipse is:
y² = 35 (1 - x² )
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A teacher asks her students to find an expression for the number of tiles needed to
surround such a square pool, and sees the following responses from her students:
4(s+1)
s²
4s+4
2s+2(s+2)
4s
Is each mathematical model correct or incorrect? How do you know?
The correct mathematical expression to find the number of tiles needed to surround a square pool would depend on how the tiles are arranged and how the dimensions of the pool and the tiles are related.
4(s+1): This expression appears to be correct if we assume that each side of the square pool is surrounded by a row of tiles, and each corner requires an additional tile.
So, the expression can be simplified to 4s+4. This is a valid expression for the number of tiles needed to surround the pool.
s²: This expression does not appear to be correct, as it only gives the area of the square pool, and does not take into account the dimensions of the tiles or the need to surround the pool.
4s+4: This expression is the same as the first expression, 4(s+1), and is a valid expression for the number of tiles needed to surround the pool.
2s+2(s+2): This expression appears to be incorrect, as it gives the total perimeter of the pool plus an additional 4 units, but does not take into account the size of the tiles or the need to surround the pool.
4s: This expression is incorrect, as it only gives the perimeter of the pool and does not take into account the need to surround the pool with tiles.
Thus, two of the given expressions (4(s+1) and 4s+4) are correct, one expression (s²) is incomplete, and two expressions (2s+2(s+2) and 4s) are incorrect.
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