Pairs of twins are numbered 1, 1, 2, 2, 3, 3, and so on. They are seated
in a circle so that the least number of gaps between two twins always
equals their assigned number. This is called a twin circle. Note that this
means there is no person between the twins numbered 1 and 1, there is
just one person between the twins numbered 2 and 2, and so on.
Reflections (flips) and rotations (turns) of a twin circle are regarded as
the same. For example, the following are the same twin circles for 4
pairs of twins
Answers
a) Two different twin circles for five pair of twins are ( 5,2,4,2,3,5,4,3,1,1,3) and ( 3,1,1,3,4,5,3,2,4,2,5).
b) No twin circles in 3 pair of twins because any of arrangement of them cannot fulfil the condition of twin circle.
c) The partial twin circle ( third circle) present in above figure can't be completed because 4 positions are fixed there and after that number of persons more than seats.
We have a pair twins are numbered 1, 1, 2, 2, 3, 3, and so on. They all seated in a circle so that the least number of gaps between two twins always
equals their assigned number. This is called a twin circle. That is Number of persons between 1 and 1 twins = 0
Number of persons between 2 and 2 twins = 1,
so on.. Reflections (flips) and rotations (turns) of a twin circle are regarded as the same.
a) We have to make two twin circles for five pair twins. The arrangement of pair twins in two different ways with the satisfaction of conditions. So, first arrangement is ( 5,2,4,2,3,5,4,3,1,1,3) and
other arrangement is ( 3,1,1,3,4,5,3,2,4,2,5).
b) There is no twin circle between the arrangement of 3 twin pairs. Because in case of 3 twin pair total members = 3×2 = 6 and number of members can be seat between pairs are 3( 1+2+0). As we know, it is fixed that no person between (1,1). So, we cannot be arrange the 2 pairs with desirable 3 gaps that is 1 person between (2,2) and 2 persons between (3,3).
c) There is total 12 positions to seat in circles. The position of 6 and 1 is fixed. According to above scenario, position next to 1 is for 1 (clockwise) and 5th position from given 1 position in (clockwise) is other member of twin 6. Now, four positions are fixed. Eight positions are left and 4 twin pairs (2,2) , (3,3), (4,4),(5,5). Number of persons seat between 4 pairs are 10 in counts ( greater than position ) so, no such arrangement is possible. Hence, this partial circle can't be completed.
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Complete question:
The above figure complete question.
Pairs of twins are numbered 1, 1, 2, 2, 3, 3, and so on. They are seated in a circle so that the least number of gaps between two twins always
equals their assigned number. This is called a twin circle. Note that this means there is no person between the twins numbered 1 and 1, there is just one person between the twins numbered 2 and 2, and so on. Reflections (flips) and rotations (turns) of a twin circle are regarded as the same. For example, the following are the same twin circles for 4 pairs of twin.
a) Find two twin circles for five pairs of twin
b) Explain why no twin circles in 3 pairs of twin
c) explain why this partial twin circle can't be completed ? ( third circle)
Related Questions
Use this data set, which shows how many miles Tisha ran each week for 10 weeks
4,9,8,6,14,8,16,12
Find the statistical measures that you need tomake a box plot of Tisha's running distances.
(what’s a statistical measure)
Answers
Statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.
A statistical measure is a numerical value that provides information about a specific aspect of a dataset's distribution, such as its central tendency, spread, or variability. Box plots require several statistical measures to be constructed, including:
Minimum: The smallest value in the dataset. In this case, the minimum value is 4.
Maximum: The largest value in the dataset. In this case, the maximum value is 16.
Median: The middle value of the dataset when it is arranged in numerical order. In this case, the median is the average of the two middle values, which are 8 and 9. The median is therefore (8 + 9) / 2 = 8.5.
First Quartile (Q1): The value below which 25% of the data falls. In this case, the first quartile is the median of the first half of the data, which is 6.
Third Quartile (Q3): The value below which 75% of the data falls. In this case, the third quartile is the median of the second half of the data, which is 14.
With these statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.
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the operation manager at a tire manufacturing company believes that the mean mileage of a tire is 37,014 miles, with a standard deviation of 4617 miles. what is the probability that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires if the manager is correct? round your answer to four decimal places.
Answers
Probability or p-vale that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires is equals to zero if the manager is correct.
We have data of an operation manager at a tire manufacturing company.
Mean mileage of a tire, [tex] \mu[/tex]
= 37,014 miles
standard deviation, [tex] \sigma[/tex]
= 4617 miles.
Sample size, n = 56
We have to determine the probability that the sample mean would differ from the population mean by less than 221 miles. Using Z-score formula in normal distribution, [tex]\small z= \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}},[/tex]
Plugging all known values in above formula, [tex]z = \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}[/tex]
= 59.634
[tex]P( \bar x < 221) = P ( \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}} < \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}) \\ [/tex]
=> P ( z < 59.63) = P( \bar x < 221)
Using the Z-distribution table, probability value is equals to 0. Hence, required probability is zero.
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An arithmetic sequence K starts 4,13. Explain how would you calculate the value of the 5,000th term
Answers
The value of the [tex]5000^{th}[/tex] term in the given arithmetic sequence K is 44995.
The sequence that is given in the question is said to be an arithmetic sequence which means the consecutive elements in the series will have common differences.
To find any term in the series first, we need to find the first term and the common difference that the series follows.
Here we know that the first and the second term of the series are 4 and 13 so from this we can find the common difference which is:
13-4=9
so the first term (a) = 4
the common difference (d) = 9
To find the [tex]n^{th}[/tex] term of the series we can use the formula:
[tex]a_n=a_1+(n-1)*d[/tex]
where [tex]a_n[/tex] is the nth term in the sequence, [tex]a_1[/tex] is the first term of the series, n is the no.of term, and d is the common difference.
So to find the 5000th term in the series
[tex]a_{5000}=4+(5000-1)*9\\a_{5000}=4+(4999*9)\\a_{5000}=4+ 44991\\a_{5000}= 44995\\[/tex]
The value of the [tex]5000^{th}[/tex] term is 44995
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Consider the line segment defined by the points A(0, 1) and B(4,6). How does a
reflection across the x-axis affect AB?
Select all that apply.
A. The x-values of the reflection are the opposite values of the x-values of the
original segment.
B. The y-values of the endpoints become their opposites.
C• The length of the reflection of AB is greater than the length of AB.
DThe length of the reflection of AB is less than the length of AB.
E. The length of the reflection of AB is the same as the length of AB.
Answers
Considering "line-segment" defined by points A(0, 1) and B(4,6), then effects of reflection across the "x-axis" are :
(b) The "y-coordinate" of "end-points" become opposites in sign.
(e) The length of reflection of AB is same as length of line-segment AB.
When reflecting a line segment across the x-axis, the x-coordinates of all points remain the same, but the y-coordinates become their opposites.
So, for the line segment AB, the x-coordinate of point A remains 0, and the x-coordinate of point B remains 4. However, the y-coordinate of point A becomes -1, and the y-coordinate of point B becomes -6. This results in a new line segment A'(0, -1) and B'(4, -6).
Since the reflection is across a horizontal line, the length of the reflection is the same as the length of the original segment.
Therefore, the correct options are (b) and (e).
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Given the diagonals of square ABCD intersect at M. If the measure of
Answers
The value of x is 17.5 when the given diagonals of square ABCD points intersect at M and the measure 0f <MAD = 6x-15.
The diagonals are perpendicular bisectors of each other in a square and they intersect at the center of the square. By using diagonals we can divide the square into four congruent right triangles and assume that diagonals are all right angles (90 degrees).
let us consider the angle MAD as one of these angles. we can find the value of x by using the equation
6x - 15 = 90
6x = 105
x = 105/6
= 17.5.
Therefore, the value of the x is 17.5.
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The complete question is,
Given the diagonals of square ABCD points intersect at M: If the measure 0f <MAD = 6x-15, find the value of x Show the work that justifies your answer: M B Your answer
Peter had to solve a puzzle.which mathematical symbol can be placed between 5 and 9, to get a numbergreater than 5, but less than 9?
Answers
To get a number greater than 5,but less than 0, Peter can use the mathematical symbol of a decimal point (.) to solve this puzzle.
If Peter places decimal point between 5 and 9, he can get a number like 5.1, 5.2, 5.3... up to 8.9, which meets the conditions of being greater than 5 but less than 9.
A decimal point (.) is a mathematical symbol. When this decimal point is placed in between two numbers, suppose x and y, then x.y means x.y is greater than x and less than y.
So to solve the puzzle, Peter can use decimal point.
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The Rialto Theater sells balcony seats for $10 and main floor seats for
$25. One afternoon performance made $6250. The number of balcony
seats sold was 20 more than 3 times the number of main floor seats. Write
the system of equations to determine the number of main floor and
balcony seats.
Answers
The system of equations is:
Revenue from balcony seats = $10 × B
Revenue from main floor seats = $25 × M
Total revenue = $6250
B = 3M + 20
Let's define the following variables:
B = number of balcony seats sold
M = number of main floor seats sold
We know that the price of a balcony seat is $10 and the price of a main floor seat is $25.
From the given information, we can create the following equations:
The total revenue from balcony seats sold (B) is given by: Revenue from balcony seats = $10 × B
The total revenue from main floor seats sold (M) is given by: Revenue from main floor seats = $25 × M
The total revenue from the afternoon performance is $6250: Total revenue = Revenue from balcony seats + Revenue from main floor seats
The number of balcony seats sold (B) is 20 more than 3 times the number of main floor seats (M): B = 3M + 20
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Reema and Quinton both babysit for extra money. Reema charges $10 per hour and
Quinton charges based on the equation m= 5h + 25. Where h is the number of hours
worked and m is the total amount of money charged. Who would make more money if
they both worked 4 hours?
o Quinton would make $10 more than Reema
O Quinton would make $5 more than Reema
o Reema would make $10 more than Quinton
O Reema would make $5 more than Quinton
Answers
On babysitting for four hours, the differently earned money will be Quinton would make $5 more than Reema.
Reema's charge for babysitting for four hours = 10 × 4
Reema's charge = $40
For Quinton, keep the value of hours in expression -
Quinton's charge = 5 (4) + 25
Quinton's charge = 20 + 25
Quinton's charge = $45
As Quinton's charge is greater than Reema, she makes more money.
Amount of more money made by Quinton = 45 - 40
Subtract to find the difference
Amount of more money made by Quinton = $5
Hence, correct answer is Quinton would make $5 more than Reema.
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Kevin needs 2/3 of a yard to make a pillow. He has 3 1/3 yards of fabric. How many pillows can he make? A). 2 2/9 B. ) 3 2/3 C. ) 5 D. ) 6
Answers
The number of pillows requiring [tex]\frac{2}{3}[/tex] yards that can be made from [tex]3\frac{1}{3}[/tex] yards is 5. Thus the right answer to the given question is C.
Material required for making one pillow = [tex]\frac{2}{3}[/tex] yards
Total material = [tex]3\frac{1}{3}[/tex] yards
To find the number of pillows made we have to divide the material required for one pillow by the total material available to Kevin for making pillows
Number of pillows = [tex]3\frac{1}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex]
= [tex]\frac{10}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex]
To divide two fractions, we take the reciprocal of the second number and multiply it by the first number.
= [tex]\frac{10}{3}[/tex] * [tex]\frac{3}{2}[/tex]
= 5
Thus, the number of pillows made is 5.
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In a group of 20 people, 13 people like tea, 12 people like coffee and 3 people like neither tea nor coffee. How many people like tea but not coffee?
Answers
Answer:
8 people
Step-by-step explanation:
Tea- 13 people
Coffee- 12 people
Neither- 3 people
20 - 3 = 17
12 + 13 = 25
25 - 17 = 8
I’m having trouble with this
Answers
(x, y, z) = (3, 2, 1)
*x = 3; y = 2; z = 1.
Check point:
2*3 - 2 + 3*1 = 7
3*3 + 2 - 1 = 10
5*3 - 2*1 = 13
7=7
10=10
13=13
I will give brainlyist to who ever answers it.
A family with travel 475 miles on the Road trip which inequality can be used to find all possible values of T the time it would take to reach their destination if they travel in an average speed of at least in miles per hour
Answers
The inequality that can be used to find all possible values of T, the time it would take to reach their destination if they travel at an average speed of at least "r" miles per hour, can be expressed as:
T ≤ 475 / r
This inequality states that the time taken (T) should be less than or equal to the distance traveled (475 miles) divided by the average speed (r miles per hour). By dividing the total distance by the average speed, we obtain the maximum time it would take to reach the destination. Any time less than or equal to this value would satisfy the condition of traveling at an average speed of at least "r" miles per hour.
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La rueda de una bicicleta mide 62.2 cm de diámetro, ¿cuál es el perímetro de la rueda?
Answers
Answer:
"Querido hijo, estás despedido" es una novela juvenil escrita por Jordi Sierra i Fabra que se divide en 17 capítulos. A continuación, se presenta un breve resumen de cada uno de ellos:
Capítulo 1: El protagonista, Leo, es un adolescente que vive en un hogar en el que sus padres son muy estrictos y le exigen que saque buenas notas en la escuela.
Capítulo 2: Leo tiene una discusión con su padre, quien le dice que si no mejora sus notas, lo echará de casa.
Capítulo 3: Leo tiene un accidente de bicicleta y es atendido por la enfermera del colegio, la señorita Rovira.
Capítulo 4: Leo recibe la noticia de que su padre ha muerto en un accidente de tráfico.
Capítulo 5: En el funeral de su padre, Leo se siente alejado de su familia y amigos.
Capítulo 6: Leo recibe una carta de su padre en la que le explica que ha dejado un testamento y que su hermana mayor, Berta, será la administradora de la herencia.
Capítulo 7: Berta le comunica a Leo que su padre le ha dejado una empresa de limpieza y que él será el encargado de dirigirla.
Capítulo 8: Leo descubre que la empresa está en quiebra y que tendrá que tomar medidas drásticas para salvarla.
Capítulo 9: Leo empieza a tomar el control de la empresa y a hacer cambios en su funcionamiento.
Capítulo 10: Leo contrata a un joven llamado Iván, quien se convierte en su mano derecha en la empresa.
Capítulo 11: Leo se encuentra con la señorita Rovira, quien lo ayuda a tomar una importante decisión en la empresa.
Capítulo 12: Leo tiene una reunión con los trabajadores de la empresa y les comunica los cambios que va a hacer.
Capítulo 13: Leo se siente muy presionado por las exigencias de la empresa y se desahoga con su amigo Santi.
Capítulo 14: Leo tiene un encontronazo con su hermana Berta, quien intenta influir en la gestión de la empresa.
Capítulo 15: Leo descubre que Iván le ha estado robando dinero a la empresa y tiene que tomar medidas para solucionar el problema.
Capítulo 16: Leo consigue salvar la empresa y hace balance de lo que ha aprendido en el proceso.
Capítulo 17: La historia termina con Leo en paz consigo mismo y con su familia, habiendo aprendido importantes lecciones sobre la vida y el trabajo.
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Find the slope of the line through points 6,3 and 12,7
Answers
The slope of the line through points (6,3) and (12,7) is 2/3.
To find the slope of a line, we use the formula:
Slope = (y2 - y1) / (x2 - x1)
In this case, we have two points: (6, 3) and (12, 7). We can label them as follows:
x1 = 6
y1 = 3
x2 = 12
y2 = 7
Now we can plug these values into the formula:
Slope = (y2 - y1) / (x2 - x1)
Slope = (7 - 3) / (12 - 6)
Slope = 4 / 6
Slope = 2/3
Therefore, the slope of the line through the points (6, 3) and (12, 7) is 2/3.
The slope of a line tells us how steep it is. A positive slope means the line goes up as you move from left to right, while a negative slope means the line goes down. In this case, since the slope is positive (2/3), we know that the line goes up as we move from left to right.
The slope also tells us how much the y-value changes for every one unit of x-value. In this case, for every one unit we move to the right, the y-value goes up by 2/3.
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Kyla has a concrete patio in the shape of a semi-circle. What is the area of the patio? Use 3. 14 for π. It’s s i circle and is 6. 75 ft and in squared
Answers
The area of the semi-circle patio is approximately 17.91 square feet.
To find the area of the semi-circle patio, we need to use the formula for the area of a circle, which is A = πr^2, where π is 3.14 and r is the radius of the circle.
However, since we only have a semi-circle, we need to divide the result by 2 to get the area of the half-circle.
In this case, the radius of the semi-circle is half of the diameter, which is given as 6.75 feet. So, the radius is 6.75/2 = 3.375 feet.
Now, we can plug this value into the formula:
A = (π)(3.375)^2 / 2
A = (3.14)(11.390625) / 2
A = 35.81765625 / 2
A = 17.908828125 square feet
Therefore, the area of the semi-circle patio is approximately 17.91 square feet.
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Penny decided to travel to Palawan. The airplane flew at an average rate of 300 miles per hour and covered 1500 miles. How long will the flight will take? *
A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours
Answers
The time it will take the flight is C) 5 hours.
To solve this problem, we can use the formula: distance = rate x time. In this case, we know that the distance is 1500 miles and the rate (or speed) is 300 miles per hour. We can rearrange the formula to solve for time: time = distance / rate. Plugging in the values we have, we get:
time = 1500 miles / 300 miles per hour
time = 5 hours
Therefore, the correct answer is C. It will take Penny 5 hours to fly from her starting point to Palawan at an average speed of 300 miles per hour. This calculation assumes that the plane maintains a constant speed throughout the entire flight, which may not be the case due to factors such as wind and turbulence.
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Can someone help me asap? It’s due today!! Show work! I will give brainliest if it’s correct and has work
Make a probability table!
Answers
The probability of choosing randomly with replacement an H or P in either selection is derived to be equal to 0.16 which makes the last option correct.
What is probabilityThe probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.
The total possible outcome = 5
the event of selecting H = 1
probability of selecting H= 1/5
the event of selecting P = 2
probability of selecting H= 2/5
probability of choosing an H or P in either selection = 1/5 × 2/5 + 2/5 × 1/5
probability of choosing an H or P in either selection = 4/25
probability of choosing an H or P in either selection = 0.16
Therefore, the probability of choosing randomly with replacement an H or P in either selection is derived to be equal to 0.16
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Graph: 3y = 6
-
-6 -4 -2
6
4
2
-2
त्र
-6
y
2 4
st
Click or tap the graph to plot a point.
6
X
४
Draw
y
Answers
Make 20 questions subtraction and addition of fractions only like this
e. G saina ,anika and mercy got some money saina got 1/6 and mercy got 3/4 and anka got the rest
a. Caculate the fraction of saina and mercy
b. What is anika s share in fractions
c. How much was the money
you can use money,fruits or any thing
due 24/04/22
Answers
20 questions subtraction and addition of fractions only like this:
A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?
John had 3/4 of a pizza and gave 1/3 of it to his friend. What fraction of the pizza does John have left?If 2/5 of a cake is chocolate and 1/5 is vanilla, what fraction of the cake is another flavor?If Tom can run 5/6 of a mile in 4 minutes, how many minutes will it take him to run 1 mile?If 3/8 of a bag of apples is rotten, what fraction of the bag is not rotten?A store had 5/6 of its shelves stocked with books. If 1/4 of the books were science books, what fraction of the shelves were stocked with science books?If Maria has 3/8 of a tank of gas and she uses 1/4 of it to drive to work, what fraction of the tank is left when she arrives at work?A recipe calls for 1/3 cup of sugar and 1/4 cup of butter. What is the total amount of sugar and butter needed in fraction?If 2/3 of a box of crayons is blue and 1/4 of the box is red, what fraction of the box is another color?If a recipe calls for 3/4 cup of milk and you have only 1/2 cup, what fraction of milk do you need to buy to have enough?If a school has 7/8 of its students enrolled in math and 3/4 of those enrolled in math are also enrolled in science, what fraction of the school is enrolled in both math and science?A store had 1/2 of its apples on sale for 1/4 off. What fraction of the original price did a customer pay for a discounted apple?If a train travels 1/2 of a mile in 2 minutes, how long will it take to travel 1 mile?A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?If a recipe calls for 3/4 cup of oil and you have only 1/3 cup, what fraction of oil do you need to buy to have enough?If 3/8 of a class is girls and 2/5 of the girls have brown hair, what fraction of the class is girls with brown hair?If a recipe calls for 1/2 cup of brown sugar and 1/4 cup of white sugar, what is the total amount of sugar needed in fraction?If a store sells 3/4 of a bag of apples and has 2/3 of a bag left, what fraction of the original bag is left?If a car travels 3/4 of a mile in 2 minutes, how long will it take to travel 1 mile?If a recipe calls for 1/3 cup of butter and you have only 1/6 cup, what fraction of butter do you need to buy to have enough?If a recipe calls for 1/4 cup of honey and 1/3 cup of sugar, what is the total amount of honey and sugar needed in fraction?To know more about fractions, refer to the link below:
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All-star trinkets estimates its monthly profits using a quadratic function. the table shows the total profit as a function of the number of trinkets produced. which function can be used to model the monthly profit for x trinkets produced? f(x) = –4(x – 50)(x – 250) f(x) = (x – 50)(x – 250) f(x) = 28(x 50)(x 250) f(x) = (x 50)(x 250)
Answers
The function used to model the monthly profit for x trinkets produced are f(x) = -4(x - 50)(x - 250). The maximum profit occurs when 150 trinkets are produced.
The quadratic function that can be used to model the monthly profit for x trinkets produced is:
f(x) = -4(x - 50)(x - 250)
This is because the function is in the form of a quadratic equation, which is y = ax² + bx + c. In this case, a = -4, b = 1200, and c = 0. When we expand and simplify the equation, we get:
f(x) = -4x² + 1200x
This equation represents a parabola with a maximum value at x = 150. Therefore, the maximum profit occurs when 150 trinkets are produced.
The other answer choices are not correct because they are not quadratic functions. For example, f(x) = (x - 50)(x - 250) is a product of linear factors, and f(x) = 28(x - 50)(x + 250) and f(x) = (x + 50)(x + 250) have a coefficient of x² that is not equal to -4.
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25 acres of a forest is covered by coniferous trees. The remaining are shrubs and bushes which constitutes 42% of the total area of the forest. What is the total area of under the forest?
Answers
Therefore, the total area of the forest is approximately 43.10 acres.
What is area?Area is the measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters (m²) or square feet (ft²). The area of a shape can be calculated by multiplying the length and the width of the shape. Different shapes have different formulas for calculating their area, such as the formula for the area of a rectangle, which is length x width, or the formula for the area of a circle, which is πr², where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14159.
Here,
Let's call the total area of the forest "T".
We know that 25 acres of the forest is covered by coniferous trees. Therefore, the remaining area of the forest is:
T - 25
We also know that the shrubs and bushes constitute 42% of the total area of the forest. This means that:
0.42 x T = area covered by shrubs and bushes
Putting it all together, we can set up the following equation:
T = 25 + (0.42 x T)
Simplifying, we can solve for T:
0.58 x T = 25
T = 25 / 0.58
T = 43.10 acres (rounded to two decimal places)
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Question 3
CLASS PRESIDENT In a poll for senior class president, 68 of the 145 male students said they planned to vote for Santiago. Out of 139
female students, 89 planned to vote for his opponent, Measha.
Construct a conditional relative frequency table based on voter preference. Show your calculations on a separate sheet of paper. Round to
the nearest whole percent if necessary
Answers
The given data is tabulated for conditional relative frequency table as follows.
Total male = 145, Total female = 139
Total male votes for Santiago = 68, Total female votes for Measha = 89
Total female votes for Santiago = 50, Total male votes for Measha = 77
Now total votes for Santiago = 68+50=118
Total votes for Measha = 166
Total votes casted = 284
The above data is formulated in tables attached below.
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A cuboid has a square base of side (2 + √3)m. the area of one side is (2√3 - 3)m². find the height of the cuboid in the form (a+ b√3)m, where a and b are integers.
Answers
The height of the cuboid, after calculations, in the form (a+ b√3)m, is (6√3 - 9)/47 meters.
Let the height of the cuboid be h meters. The area of the square base is given by:
(2 + √3)² = 4 + 4√3 + 3 = 7 + 4√3 m²
The total surface area of the cuboid is the sum of the areas of the six rectangular faces. Since the base is a square, the area of each of the four vertical rectangular faces is also (2 + √3) × h = (2h + h√3) m². Therefore, we have:
Total surface area = 4(7 + 4√3) + 2(2h + h√3)(2 + √3) = 8h + 26 + (22 + 16√3)h
Since we know that one of the sides has area (2√3 - 3) m², we can set up another equation:
(2h + h√3)(2 + √3) = 2√3 - 3
Expanding the left side and simplifying, we get:
(2h + h√3)(2 + √3) = 2√3 - 3
4h + 7h√3 = 2√3 - 3
h(4 + 7√3) = 2√3 - 3
h = (2√3 - 3)/(4 + 7√3)
We can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:
h = [(2√3 - 3)/(4 + 7√3)] × [(4 - 7√3)/(4 - 7√3)]
h = (8√3 - 12 - 14√3 + 21)/(16 - 63)
h = (9 - 6√3)/(-47)
h = (6√3 - 9)/(47)
Therefore, the height of the cuboid is (6√3 - 9)/47 meters.
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1) harriett has a cylindrical pool with a diameter of 11 feet and a height of 2 feet.
the inside of the pool is lined with a plastic material. how many square feet of plastic material does the pool have? use 3.14 for pi. round your answer to the nearest tenth.
please help me because i really need with this question <3
Answers
The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.+
To calculate the surface area of the pool that is lined with plastic material, we need to find the area of the curved part and the area of the top and bottom circles.
First, let's find the radius of the pool, which is half of the diameter:
radius = 11 feet / 2 = 5.5 feet
The curved part of the pool is a cylinder with a height of 2 feet and a circumference of [tex]2 * π *radius:[/tex]
curved area = height * circumference
[tex]curved area = 2 feet * 2 * 3.14 * 5.5 feet[/tex]
[tex]curved area = 68.2 square feet[/tex]
The top and bottom of the pool are two circles with a radius of 5.5 feet:
circle area = π * radius²
[tex]circle area = 3.14 * 5.5 square feet[/tex]
[tex]circle area = 95.0 square feet[/tex]
To find the total surface area of the pool that is lined with plastic material, we add the area of the curved part and the area of the top and bottom circles:
Total area = curved area + 2 * circle area
Total area = 68.2 square feet + 2 * 95.0 square feet
Total area = 258.2 square feet
The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.
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Chord eg measures 8 inches and the distance from the center of j to the chord is 3 inches
Answers
The length of chord segment EG = 6 inches and the length of FG = √23 inches.
Given, chord EG = 8 inches and the distance from the center of J to the chord is 3 inches.
We can draw a diagram as follows:
J
/ \
/ \
/ \
/ \
E-----------G
|
|
|
|
|
F
Here, OJ is perpendicular to chord EG at point F.
As per the theorem, the length of the perpendicular from the center of the circle to a chord is half the length of the diameter intersecting the chord.
So, we can find the length of the diameter intersecting chord EG and then use it to find the radius of the circle.
Length of chord EG = 8 inches
Length of OJ = 3 inches
Using Pythagorean theorem in right triangle OFG, we get:
OG² = OF² + FG²
Let x be the length of FG
We know that OF = OJ = 3 inches
OG = radius of the circle
So, we have:
radius of circle = OG = √(OF² + FG²) = √(3² + x²)
The diameter of the circle = 2(radius) = 2√(3² + x²)
Now, using the theorem mentioned above, we can say:
Length of perpendicular from the center of the circle to chord EG = OF = 3 inches
Length of diameter intersecting chord EG = 2√(3² + x²)
So, we get:
Length of chord segment EG = 2 * length of perpendicular
= 2 * 3 inches
= 6 inches
Now, we know that the chord segment EG divides the diameter intersecting it into two equal parts.
So, we have:
Length of one part of the diameter = (2√(3² + x²))/2 = √(3² + x²)
Using Pythagorean theorem in right triangle OJF, we get:
OJ² + JF² = OF²
3² + JF² = 8²
JF² = 8² - 3² = 55
JF = √55
Using Pythagorean theorem in right triangle JFG, we get:
JG² + FG² = JF²
(√(3² + x²))² + x² = 55
9 + x² + x² = 55
2x² = 46
x² = 23
x = √23
Therefore, the length of chord segment EG = 6 inches and the length of FG = √23 inches.
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algebra 2 PLEASE if you know
Answers
The system of inequalities that has a solution set that is a line is [x + y ≥ 3; x + y ≤ 3]; option A
What is a system of inequalities?A system of inequalities is a set of two or more inequalities that are solved simultaneously to find the values of variables that satisfy all the inequalities in the system.
Considering the given system of inequalities:
The system of inequalities that has a solution set that is a line is:
[x + y = 3;]
This is because the solution set of this equation is a line with slope -1 passing through the point (3, 0) and (0, 3).
Therefore, the system of inequalities [x + y ≥ 3; x + y ≤ 3] has a solution set that is a line.
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Meg has 3/10 liter of juice left in her bottle, Ines has 3 times as much juice in her bottle as Meg has How much juice, in liters, does Ines have?
Answers
Ines has 9/10 liter of juice, if Meg has 3/10 liter of juice left in her bottle and Ines has 3 times as much juice in her bottle as Meg has .
It is need to find how much juice does Ines have.To calculate it, it is need to know how much liter of juice does Meg have. Meg have 3/10 liter of juice left in her bottle, and Ines has 3 times as much juice her bottle as Meg has.
That is Ines has 3 times means multiplying how much juice meg have by 3.
That is Juice left in bottle of Ines = juice left in bottle of Meg * 3 = 3/10 liter x 3 = 9/10 liter. Therefore, Ines has 9/10 liter of juice in her bottle.
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From a Word Problem
An online camera store charges $3 for every
8x10 picture that you order. The
shipping cost is $8. Write an equation to
model this situation. How much will it cost to
get 5 pictures printed?
Answers
3 is the $3 per every picture and x is the number of pictures printed. The 8 and the $8 added for shipping.
To find for 5 pictures printed, plug in 5 for x.
3(5)+8=y
15+8=y
23=y
To get 5 pictures printed, it will be $23.
ANALYZE In Europe, fuel economy is measured in liters per 100 kilometers. On a 2500 km road trip a car used 150 liters of fuel. The car used an average of how many liters per 100 km?
Answers
To find out the car's average fuel consumption in liters per 100 kilometers, we need to use the following formula:
Fuel consumption (liters per 100 km) = (Total fuel used / Total distance traveled) x 100
Using the information given, we know that the car traveled 2500 km and used 150 liters of fuel. Plugging these values into the formula, we get:
Fuel consumption (liters per 100 km) = (150 / 2500) x 100 = 6
Therefore, the car used an average of 6 liters of fuel per 100 kilometers on its 2500 km road trip.
It is important to note that fuel economy is an important factor in Europe, where fuel prices are generally higher than in other parts of the world.
By measuring fuel consumption in liters per 100 kilometers, European consumers can easily compare the fuel efficiency of different vehicles and make more informed purchasing decisions.
Additionally, analyzing fuel consumption data can help drivers identify ways to improve their fuel efficiency, such as reducing their speed, maintaining proper tire pressure, and avoiding excessive idling.
This not only saves money on fuel costs, but also reduces carbon emissions and contributes to a more sustainable transportation system.
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If f(x) = x2 − 6x − 4 and g(x) = 5x + 3, what is (f + g)(−3)? (1 point)
41
35
11
−35
Answers
The value of (f + g)(−3) given the functions f(x) = x² − 6x − 4 and g(x) = 5x + 3 is 11.
To find (f + g)(-3), we first need to add the functions f(x) and g(x) together, and then evaluate the resulting function at x = -3.
f(x) = x² - 6x - 4
g(x) = 5x + 3
Now, let's add f(x) and g(x):
(f + g)(x) = (x² - 6x - 4) + (5x + 3) = x² - x - 1
Now that we have the combined function, we can evaluate it at x = -3:
(f + g)(-3) = (-3)² - (-3) - 1 = 9 + 3 - 1 = 11
So, (f + g)(-3) = 11.
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