To determine whether there is a minimum or maximum value to the quadratic function h(t) = -8t² + 4t - 1 and find the minimum or maximum value of h, one has to follow the steps given below. So, the minimum or maximum value of h = -1/2.
Step 1: Write the quadratic function in standard form.
The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.
h(t) = -8t² + 4t - 1 ... (1)
Step 2: Calculate the axis of symmetry of the parabola.
The axis of symmetry of the parabola is given by x = -b/2a, where a and b are the coefficients of x² and x, respectively. Therefore, the axis of symmetry of the parabola given by h(t) = -8t² + 4t - 1 is given by: t = -b/2a = -4/(2 * (-8)) = 4/16 = 1/4
Step 3: Calculate the vertex of the parabola.
The vertex of the parabola is given by (h, k), where h and k are the coordinates of the vertex. Therefore, the coordinates of the vertex of the parabola given by h(t) = -8t² + 4t - 1 are given by: (1/4, h(1/4))
Substituting t = 1/4 in Equation (1), we have: h(1/4) = -8(1/4)² + 4(1/4) - 1h(1/4) = -8/16 + 4/4 - 1h(1/4) = -1/2 + 1 - 1h(1/4) = -1/2
Therefore, the vertex of the parabola given by h(t) = -8t² + 4t - 1 is given by the point(1/4, -1/2)
Step 4: Determine the nature of the extrema of the functionThe coefficient of the x² term in Equation (1) is -8, which is negative. Therefore, the parabola is downward-facing and the vertex represents a maximum value. Thus, the maximum value of the function h(t) = -8t² + 4t - 1 is given by h(1/4) = -1/2. Answer: Thus, the minimum or maximum value of h = -1/2.
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Please answer ASAP I will brainlist
Answer:
-x + 20(8) = 147 -x + 10(8) = 67
-x + 160 = 147 -x + 80 = 67
x = 13 x = 13
A. The system has exactly one solution. The solution is (13, 8).
B. All three colonies had a population of 8 thousand people in 2013.
For a project in statistics class, a pair of students decided to invest in two companies, one that produces software and one that does biotechnology research. Sally purchased 7 shares in the software company and 87 shares in the biotech firm, which cost a total of $8,315. At the same time, Katle invested a total of $7,338 in 84 shares in the software company and 50 shares in the biotech firm. How much did each share cost?
The cost of one share in the software company (x) is $32, and the cost of one share in the biotech company (y) is approximately $93.
Let's denote the cost of one share in the software company as 'x' dollars and the cost of one share in the biotech company as 'y' dollars.
According to the given information, Sally purchased 7 shares in the software company and 87 shares in the biotech company, which cost a total of $8,315. We can express this as the following equation:
7x + 87y = 8315 ----(Equation 1)
Similarly, Katle invested a total of $7,338 in 84 shares in the software company and 50 shares in the biotech company. This can be represented as the following equation:
84x + 50y = 7338 ----(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method.
Multiply Equation 1 by 50 and Equation 2 by 87 to eliminate the 'y' terms:
350x + 4350y = 415750 ----(Equation 3)
7308x + 4350y = 638526 ----(Equation 4)
Now, subtract Equation 3 from Equation 4:
(7308x + 4350y) - (350x + 4350y) = 638526 - 415750
Simplifying the equation:
7308x - 350x = 222776
6958x = 222776
Divide both sides of the equation by 6958:
x = 222776 / 6958
x = 32
Now that we have the value of 'x', we can substitute it back into either Equation 1 or Equation 2 to solve for 'y'. Let's substitute it into Equation 1:
7(32) + 87y = 8315
224 + 87y = 8315
87y = 8315 - 224
87y = 8091
Divide both sides of the equation by 87:
y = 8091 / 87
y ≈ 93
Therefore, the cost of one share in the software company (x) is $32, and the cost of one share in the biotech company (y) is approximately $93.
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Ian took out a $19,000 personal loan to pay for his home renovations. He will not make a payment for 5 years and there is a 15% interest rate. How much will be owed in 5 years with monthly compounding?
Round your answer to the nearest cent.
Do NOT round until your final answer.
The amount owed in 5 years with monthly compounding, considering a $19,000 personal loan with a 15% interest rate, will be $34,558.52.
1. Convert the interest rate to a decimal: 15% = 0.15.
2. Determine the number of compounding periods: Since the loan compounds monthly, multiply the number of years by 12. In this case, 5 years * 12 months/year = 60 months.
3. Calculate the monthly interest rate: Divide the annual interest rate by 12. In this case, 0.15 / 12 = 0.0125.
4. Use the compound interest formula to calculate the future value:
Future Value = Principal * (1 + Monthly Interest Rate)^(Number of Compounding Periods)
Future Value = $19,000 * (1 + 0.0[tex]125)^{(60[/tex])
5. Evaluate the expression inside the parentheses: (1 + 0.0[tex]125)^{(60[/tex]) ≈ 1.954503.
6. Multiply the principal by the evaluated expression: $19,000 * 1.954503 = $37,133.57 (unrounded).
7. Round the final answer to the nearest cent: $34,558.52.
Therefore, in 5 years with monthly compounding, the amount owed on the $19,000 personal loan will be approximately $34,558.52.
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Which of the following is equal to the fraction below? (7/4)11
Answer:
It's A
Step-by-step explanation:
Use the following models to show the equivalence of the fractions 35 and 610 a) Set model
Use the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set model
A camera sensor with a fixed size of 720 × 680 is used in the system described in the article. For a sensor of these dimensions, calculate
i.the resolution in pixels in scientific notation to 4 significant figures
ii.the resolution in megapixels, rounded to the nearest thousandth of a megapixel
iii.the aspect ratio of the sensor, cancelled down to its lowest terms
The pixel resolution is 4.896 x 10^5 pixels; in megapixels, it's approximately 0.490; and the aspect ratio is 18:17.
Explanation:First, let's calculate the resolution in pixels: Resolution is simply the width times the height of the sensor. Specifically for this question, multiply 720 by 680. This gives us 489600 pixels for the resolution - in scientific notation to 4 significant figures we have 4.896 x 10^5.
Next, to calculate the resolution in megapixels, we need to divide the resolution by 1 million (since one megapixel is equal to 1 million pixels). So, 489600/1,000,000 is approximately 0.490 megapixels when rounded to the nearest thousandth of a megapixel.
Finally, the aspect ratio is the relationship of the width to the height of an image or screen. For a 720 x 680 sensor, if we divide 720 by 680, the result would be approximately 1.0588. However, we want this ratio in its simplest form, so we should use the greatest common divisor (GCD). In this case, the GCD of 720 and 680 is 40, so by dividing both dimensions by 40, we get an aspect ratio of 18:17.
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ecorded the sizes of the shoes in her family's cupboa
the modal size?
8, 7, 8, 8.5, 7, 8.5, 7
The modal sizes of shoes in the family's cupboard are 8 and 7.
To determine the modal size of shoes in the family's cupboard, we need to find the shoe size that appears most frequently in the given data. Let's analyze the sizes:
8, 7, 8, 8.5, 7, 8.5, 7
To find the mode, we can create a frequency table by counting the number of occurrences for each shoe size:
8 | 3
7 | 3
8.5 | 2
From the frequency table, we can see that both size 8 and size 7 appear three times each, while size 8.5 appears two times. Since both size 8 and size 7 have the highest frequency of occurrence (3), they are considered modal sizes. In this case, there is more than one mode, and we refer to it as a bimodal distribution.
To determine the mode, we performed a frequency count of each shoe size in the given data. We counted the number of occurrences for sizes 8, 7, and 8.5. Based on the frequency counts, we identified the sizes with the highest frequency, which turned out to be 8 and 7, both occurring three times. Thus, they are the modal sizes in the data set.
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If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?
Answer:
39°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
let the other angle be x , then
x + 54° + 87° = 180°
x + 141° = 180° ( subtract 141° from both sides )
x = 39°
that is the other angle is 39°
In a triangle, the sum of all angles is always 180°. To find the third angle in a scalene triangle where two angles are known, subtract the known angles from 180°. In this case, subtracting 54° and 87° from 180° gives a third angle of 39°.
Explanation:The question refers to finding the third angle in a scalene triangle, where we know two of the angles. A scalene triangle is a triangle where all three sides are of a different length, and therefore all three angles are also different. The sum of the angles in any triangle is always 180°.
To find the third angle in the triangle, you can use the equation: Angle C = 180° - Angle A - Angle B.
So, we subtract the known angles from 180°: Angle C = 180° - 54° - 87° = 39°.
Therefore, the third angle in this scalene triangle is 39°.
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Which function is graphed ?
Please answer ASAP I will brainlist
There is just one solution to this system. The answer is (460/7), (-13/7), and (-24/7). The correct answer is option A.
Given the system of equations as X+ y- z=63x- y+ z=2x- 4y+ 2z-34.We have to use row operations to solve this system of equations. Let us start by writing down the augmented matrix of the given system of equations. [1, 1, -1 | 6][3, -1, 1 | 2][1, -4, 2 | -34]
The first step is to change the first element of the second row to zero. For that, we subtract three times the first row from the second row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][1, -4, 2 | -34]
Now, we need to change the first element of the third row to zero. For that, we subtract the first row from the third-row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][0, -5, 3 | -40]
The next step is to change the second element of the third row to zero. For that, we add 5/4 times the second row to the third row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][0, 0, 7 | -24]
Now, we solve the system of equations using back-substitution. We have 7z = -24 ⇒ z = -24/7
Substituting this value of z in the second equation, we get -4y = 4 - z = 4 + 24/7 = 52/7⇒ y = -13/7
Substituting these values of y and z in the first equation, we get x = 63 - y + z = 63 + 13/7 - 24/7 = 460/7Thus, the solution of the given system of equations is (x, y, z) = (460/7, -13/7, -24/7). Therefore, the correct choice is A. This system has exactly one solution. The solution is (460/7, -13/7, -24/7).
The given system of equations is solved using row operations. It is found that this system has exactly one solution which is (460/7, -13/7, -24/7). Therefore, the correct choice is A. This system has exactly one solution. The solution is (460/7, -13/7, -24/7).
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Which of the following graphs shows a pair of lines that represents the equations with the solution (4, −1)?
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 1 unit to the right and 4 units down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 4 units to the right and 1 unit down.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 4 units to the left and 1 unit up.
A coordinate grid is shown from negative 8 to positive 8 on the x axis and also on the y axis. A pair of lines is shown intersecting on ordered pair 1 unit to the left and 4 units up.
The graph that shows a pair of lines representing the equations with the solution (4, -1) is option D.
To determine which graph represents the equations with the solution (4, -1), we need to check if the given point lies on the lines represented by each graph.
Let's examine each option:
A) The lines intersect 1 unit to the right and 4 units down. This does not match the given solution of (4, -1), so option A can be eliminated.
B) The lines intersect 4 units to the right and 1 unit down. Again, this does not match the given solution of (4, -1), so option B can be eliminated.
C) The lines intersect 4 units to the left and 1 unit up. This is the exact opposite of the given solution (4, -1), so option C can be eliminated.
D) The lines intersect 1 unit to the left and 4 units up. This matches the given solution of (4, -1), where the x-coordinate is 1 unit to the left and the y-coordinate is 4 units up. Therefore, option D represents the equations with the solution (4, -1).
In conclusion, the graph that shows a pair of lines representing the equations with the solution (4, -1) is option D.
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Help please
The box plot represents the scores on quizzes in a science class. A box plot uses a number line from 70 to 86 with tick marks every one-half unit. The box extends from 76 to 80.5 on the number line. A line in the box is at 79. The lines outside the box end at 72 and 84. The graph is titled Science Quizzes, and the line is labeled Scores On Quizzes. Determine which of the following is the five-number summary of the data. Min: 72, Q1: 79, Median: 80, Q3: 82, Max: 84 Min: 75, Q1: 77.5, Median: 80, Q3: 81.5, Max: 85 Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84 Min: 73, Q1: 77, Median: 78, Q3: 80.5, Max: 85
Answer:
The five-number summary of the data represented by the given box plot is: Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84. Therefore, the correct option is: Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84.
Step-by-step explanation:
Find the perimeter of a sector whose radius is 4 unit and arc length is 16π
Answer:
perimeter ≈ 58.3 units
Step-by-step explanation:
the perimeter of the sector includes 2 radii and the arc
perimeter = 4 + 4 + 16π = 8 + 16π ≈ 58.3 ( to 1 decimal place )
Escriba el tipo de variable y nivel de medición para la siguiente grupo de variables : A) tipo de medallas a prueba olímpica. B) Volumen de agua en un tanque
The type of medals is a categorical nominal variable, while the volume of water is a numerical continuous variable.
How can these variables be classified?Type of medals in an Olympic event: This is a categorical nominal variable as there are fixed categories for the medals such as gold and silver and they do not have an inherent order The volume of water in a tank: This is a numerical and continuous variable which means it is measured with numbers. Moreover, it is continuous as it is obtained by measuring.Note: This question is in Spanish, here is the question in English:
Write the type of variable and level of measurement for the following group of variables: A) type of medals at Olympic test. B) Volume of water in a tank
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Calc II Question
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y axis.
Y = e^(-x^2)
Y = 0
X = 0
X = 1
Correct answer is pi (1 - (1/e))
I'm just not sure how to get to that answer
Answer:
[tex]\displaystyle \pi\biggr(1-\frac{1}{e}\biggr)[/tex]
Step-by-step explanation:
Shell Method (Vertical Axis)
[tex]\displaystyle V=2\pi\int^b_ar(x)h(x)\,dx[/tex]
Radius: [tex]r(x)=x[/tex]
Height: [tex]h(x)=e^{-x^2}[/tex]
Bounds: [tex][a,b]=[0,1][/tex]
Set up and evaluate integral
[tex]\displaystyle V=2\pi\int^1_0xe^{-x^2}\,dx[/tex]
Let [tex]u=-x^2[/tex] and [tex]du=-2x\,dx[/tex] so that [tex]-\frac{1}{2}\,du=x\,dx[/tex]Bounds become [tex]u=-0^2=0[/tex] and [tex]u=-1^2=-1[/tex][tex]\displaystyle V= -\frac{1}{2}\cdot2\pi\int^{-1}_0e^u\,du\\\\V= -\pi\int^{-1}_0e^u\,du\\\\V=\pi\int^0_{-1}e^u\,du\\\\V=\pi e^u\biggr|^0_{-1}\\\\V=\pi e^0-\pi e^{-1}\\\\V=\pi-\frac{\pi}{e}\\\\V=\pi\biggr(1-\frac{1}{e}\biggr)[/tex]
Anna volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday, 382 people went to The Youth Wing, 461 people went to Social Issues, and 355 went to Fiction and Literature. On Sunday, the library had 800 total visitors. Based on what Anna had recorded on Saturday, about how many people should be expected to go to The Youth Wing? Round your answer to the nearest whole number.
Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.
Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:
[tex]\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}[/tex]
Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}[/tex]
Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:
[tex]\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}[/tex]
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800[/tex]
Calculating the proportion:
[tex]\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}[/tex]
Calculating the estimated number of visitors to The Youth Wing on Sunday:
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800[/tex]
Simplifying the equation:
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}[/tex]
Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254[/tex]
Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
If
Answer:
I pass my classes.
Step-by-step explanation:
I had to add this sentence or else it wouldnt allow me to send it.
Answer:
In math, the word "if" can be used for piecewise functions. In piecewise functions, you can see equations where f(x) = x+3 IF x>0 and f(x) = -x IF x<0.
NO LINKS!! URGENT HELP PLEASE PLEASE!!!
Answer:
[tex]\textsf{12)} \quad \text{a.}\;\;m \angle 1 = 107^{\circ}, \quad \text{b.}\;\;m \angle 2 = 107^{\circ}, \quad \text{c.}\;\;m \angle 3 = 73^{\circ}[/tex]
[tex]\textsf{13)} \quad EC = 6[/tex]
[tex]\textf{14)}\quad \text{a.}\;\;x = 33, \quad \text{b.}\;\; x = 8[/tex]
Step-by-step explanation:
Question 12As the base angles of an isosceles trapezoid are congruent, the measures of angles E and J are the same. Therefore:
[tex]m\angle 3 = 73^{\circ}[/tex]
The opposite angles of an isosceles trapezoid sum to 180°. Therefore:
[tex]\implies m\angle 1 + m\angle 3 = 180^{\circ}[/tex]
[tex]\implies m\angle 1 + 73^{\circ} = 180^{\circ}[/tex]
[tex]\implies m\angle 1 = 107^{\circ}[/tex]
Since the base angles of an isosceles trapezoid are congruent, the measures of angles A and N are the same. Therefore:
[tex]m\angle 2 = 107^{\circ}[/tex]
[tex]\hrulefill[/tex]
Question 13The diagonals of isosceles trapezoid ABCD are AC and BD.
Point E is the point of intersection of the diagonals. Therefore:
[tex]BE + ED = BD[/tex]
[tex]AE + EC = AC[/tex]
As the diagonals of an isosceles trapezoid are the same length, BD = AC. Therefore:
[tex]AE + EC = BD[/tex]
Given BD = 20 and AE = 14:
[tex]\implies AE + EC = BD[/tex]
[tex]\implies 14 + EC = 20[/tex]
[tex]\implies 14 + EC - 14 = 20 - 14[/tex]
[tex]\implies EC = 6[/tex]
[tex]\hrulefill[/tex]
Question 14The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides (legs) of the trapezoid.
The formula for the midsegment of a trapezoid is:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Midsegment of a trapezoid}\\\\$M=\dfrac{1}{2}(a+b)$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the midsegment.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides.\\\end{minipage}}[/tex]
a) From inspection of the given trapezoid:
M = xa = 18b = 48Substitute these values into the midsegment formula and solve for x:
[tex]x=\dfrac{1}{2}(18+48)[/tex]
[tex]x=\dfrac{1}{2}(66)[/tex]
[tex]x=33[/tex]
Therefore, the value of x is 33.
b) From inspection of the given trapezoid:
M = 15a = 22b = xSubstitute these values into the midsegment formula and solve for x:
[tex]15=\dfrac{1}{2}(22+x)[/tex]
[tex]30=22+x[/tex]
[tex]x=8[/tex]
Therefore, the value of x is 8.
If the left-hand limit of is equal to the right-hand limit of as x approaches 10, the limit of as x approaches 10 is and the value of k is .
The limit of f(x) as x approaches 10 is 315 and The value of k is 250.
The function f(x) is a piecewise function, so we need to evaluate it separately for x < 10 and x >= 10.
[tex]f(x)= { \frac{(0.1x(2)+20x+15,x < 10)}{(0.25x(3)+k,x > 10)}[/tex]
For x < 10, the function is equal to 0.1x^2 + 20x + 15. So the left-hand limit of f(x) as x approaches 10 is equal to 0.1(10)^2 + 20(10) + 15 = 315.
For x >= 10, the function is equal to 0.25x^3 + k. So the right-hand limit of f(x) as x approaches 10 is equal to 0.25(10)^3 + k = 250 + k.
Since the left-hand limit and the right-hand limit are equal, the limit of f(x) as x approaches 10 is also equal to 315, and the value of k is equal to 250.
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Two roll of electric wire contain 80m 20cm and 86m 56cm of wire respectively. what is the total length of electric wire of both the roll? Express the Result in metres
The total length of electric wire in both rolls is 166.76 meters.
To find the total length of electric wire in both rolls, we need to add the lengths of the two rolls together.
The first roll contains 80m 20cm of wire. We can convert this to meters by noting that 1 meter is equal to 100 centimeters. Therefore, the length of the first roll is:
80m 20cm = 80 meters + (20 centimeters / 100) meters
= 80 meters + 0.20 meters
= 80.20 meters
Similarly, the second roll contains 86m 56cm of wire. Converting this to meters:
86m 56cm = 86 meters + (56 centimeters / 100) meters
= 86 meters + 0.56 meters
= 86.56 meters
To find the total length, we add the lengths of both rolls:
Total length = 80.20 meters + 86.56 meters
= 166.76 meters
Therefore, the total length of electric wire in both rolls is 166.76 meters.
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A sample of gas stored at ST has a volume of 3.56 L. The gas is heated to 400 K and has a pressure of 125 kPa. What is the volume of the gas after it is heated?
The volume of the gas after it is heated is approximately 0.0417 liters.
To find the volume of the gas after it is heated, we can use the combined gas law, which relates the initial and final conditions of a gas sample. The combined gas law is expressed as:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures of the gas (in kPa)
V₁ and V₂ are the initial and final volumes of the gas (in liters)
T₁ and T₂ are the initial and final temperatures of the gas (in Kelvin)
Given:
Initial volume (V₁) = 3.56 L
Initial temperature (T₁) = ST (which is typically 273.15 K)
Final temperature (T₂) = 400 K
Final pressure (P₂) = 125 kPa
Now we can plug these values into the combined gas law equation and solve for V₂:
(P₁V₁) / T₁ = (P₂V₂) / T₂
(1 * 3.56) / 273.15 = (125 * V₂) / 400
(3.56 / 273.15) = (125 * V₂) / 400
Cross-multiplying and solving for V₂:
3.56 * 400 = 273.15 * 125 * V₂
1424 = 34143.75 * V₂
V₂ = 1424 / 34143.75
V₂ ≈ 0.0417 L
As a result, the heated gas has a volume of approximately 0.0417 litres.
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Let X_1,…,X_n be a random sample. For S(X_1,…,X_n )=1/(1/n ∑_(i=1)^n▒〖(x_i-c)〗^2 ) , find its asymptotic distribution where EX^k=α_k.
The asymptotic distribution of the estimator S(X₁, ..., Xₙ) is a standard normal distribution, denoted as N(0, 1).
To find the asymptotic distribution of the estimator S(X₁, ..., Xₙ), we can use the Central Limit Theorem (CLT). However, we need some additional assumptions to apply the CLT, such as the finite variance of the random variables.
Given that E(Xᵢ^k) = αₖ for all k, we can assume that the random variables Xᵢ have a finite variance. Let's denote the variance of Xᵢ as Var(Xᵢ) = σ².
First, let's simplify the estimator S(X₁, ..., Xₙ):
S(X₁, ..., Xₙ) = 1 / (1/n ∑ᵢ (Xᵢ - c)²)
Notice that the numerator is a constant and doesn't affect the asymptotic distribution. So, we can focus on analyzing the denominator.
Let's calculate the expected value and variance of the denominator:
E[1/n ∑ᵢ (Xᵢ - c)²] = 1/n ∑ᵢ E[(Xᵢ - c)²] = 1/n ∑ᵢ (Var(Xᵢ) + E[Xᵢ]² - 2cE[Xᵢ] + c²)
= 1/n (nσ² + α₁ - 2cα₁ + c²) (using the fact that E[Xᵢ] = α₁ for all i)
Var[1/n ∑ᵢ (Xᵢ - c)²] = 1/n² ∑ᵢ Var[(Xᵢ - c)²] = 1/n² ∑ᵢ (Var(Xᵢ - c)²) = 1/n² ∑ᵢ (Var(Xᵢ))
= 1/n² (nσ²) = σ²/n
Now, let's apply the CLT. According to the CLT, if we have a sequence of independent and identically distributed random variables with a finite mean (μ) and a finite variance (σ²), the sample mean (in this case, our denominator) converges in distribution to a standard normal distribution as the sample size approaches infinity.
Therefore, as n approaches infinity, the asymptotic distribution of S(X₁, ..., Xₙ) will follow a standard normal distribution.
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determine the value of x
The hypotenuse (x) of the right triangle is 10 units
Finding the hypotenuse of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse (x) of the right triangle can be calculated using the following sine equation
sin(30) = 5/x
Using the above as a guide, we have the following:
x = 5/sin(30)
Evaluate
x = 10
Hence, the hypotenuse of the right triangle is 10
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on #5
Find the measure of the indicated are.
90°
80°
100°
70°
H
40°
The measure of the Intercepted arc having an inscribed angle of 40 degrees is 80 degrees.
What is the measure of the intercepted arc?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the figure:
Inscribed angle = 40 degrees
Intercepted arc = ?
Plug the given value into the above formula and solve for the arc:
Inscribed angle = 1/2 × intercepted arc.
40 = 1/2 × intercepted arc
Multiply both sides by 2:
40 × 2 = 2 × 1/2 × intercepted arc
40 × 2 = intercepted arc
Intercepted arc = 80°
Therefoore, the Intercepted arc is 80 degrees.
Option B) 80° is the correct answer.
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What’s equivalent to 6 to the -3 power
Currency exchange rates are based on______.
A.each country’s economy
B. The gold standard
C.current bartering
D.one-for-one exchange
Currency exchange rates are primarily based on each country's economy.
The exchange rate of a currency is influenced by various factors, such as inflation rates, interest rates, political stability, economic performance, trade balances, and market supply and demand.
These factors reflect the overall strength or weakness of a country's economy and play a significant role in determining the value of its currency relative to other currencies in the foreign exchange market.
While historical exchange rate systems, such as the gold standard, had an impact on currency values in the past, the modern exchange rate regime is primarily determined by market forces and economic fundamentals.
Bartering and one-for-one exchange are not directly related to currency exchange rates in the context of global currency markets, as exchange rates involve the relative value of one currency against another.
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If the manager of a bottled water distributor wants to estimate, 95% confidence, the mean amount of water in a 1-gallon bottle to within ±0.006 gallons and also assumes that the standard deviation is 0.003 gallons, what sample size is needed?
If a light bulb manufacturing company wants to estimate, with 95% confidence, the mean life of compact fluorescent light bulbs to within ±250 hours and also assumes that the population standard deviation is 900 hours, how many compact fluorescent light bulbs need to be selected?
If the inspection division of a county weighs and measures department wants to estimate the mean amount of soft drink fill in 2-liter bottles to within ± 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.08 liters, what sample size is needed?
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 52 minutes. What sample size is needed if the executive wants to be 95% confident of being correct to within ±5 minutes?
Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
The dependent variable is t.
When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155."
The dependent variable is f(t).
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t.
The independent variable
The correct statements are
The dependent variable is t.
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t. Option A,D,E,F.
Let's analyze each statement to understand why it is true:
A) The dependent variable is t: In the given function, f(t), the value of f depends on the value of t. Therefore, t is the independent variable, and f is the dependent variable.
D) When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced": Here, the value of t is 2, representing the year 2002, and the value of f(t) is 1,323, representing the amount of garbage produced in tons.
E) When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced": Similar to statement D, the value of t is 4, representing the year 2004, and the value of f(t) is 1,458.6, representing the amount of garbage produced in tons.
F) The independent variable is t: As mentioned in statement A, t is the independent variable in the given function. It is the variable that we can change or manipulate, and the value of f depends on the value of t.
Statements B, C, and G are incorrect:
B) When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155": This statement is incorrect because in the given function, t represents the time in years after 2000, not the amount of garbage produced.
C) The dependent variable is f(t): This statement is incorrect because, as mentioned earlier, t is the independent variable, and f is the dependent variable.
G) The independent variable f(t): This statement is incorrect because f(t) represents the amount of garbage produced, which is the dependent variable in the given function.
So Option A,D.E.F. Are correct.
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Note the complete question is
Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
A.) The dependent variable is t.
B.) When f(12) = 2,155, 12 represents "12 tons of garbage produced," and 2,155 represents "the year 2155."
C.) The dependent variable is f(t).
D.) When f(2) = 1,323, 2 represents "the year 2002," and 1,323 represents "1,323 tons of garbage produced."
E.) When f(4) = 1,458.6, 4 represents "the year 2004," and 1,458.6 represents "1,458.6 tons of garbage produced."
F.) The independent variable is t.
G.) The independent variable f(t)
Graph the ellipse, Plot the foci of the ellipse 100pts
Answer:
Step-by-step explanation:
The general equation for an ellipse with center (h, k) is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
If a > b, the ellipse is horizontal.
If b > a, the ellipse is vertical.
Given equation:
[tex]\dfrac{(x-5)^2}{4}+\dfrac{(y+5)^2}{9}=1[/tex]
As b > a, the ellipse is vertical. Therefore:
b is the major radius and 2b is the major axis.a is the minor radius and 2a is the minor axis.Vertices = (h, k±b)Co-vertices = (h±a, k)Foci = (h, k±c) where c² = b² - a²Comparing the given equation with the standard form, we get:
[tex]h = 5[/tex][tex]k = -5[/tex][tex]a^2=4 \implies a=2[/tex][tex]b^2=9 \implies b=3[/tex]Therefore:
[tex]\textsf{Center}= (5, -5)[/tex][tex]\textsf{Major axis}=2 \cdot 3 = 6[/tex][tex]\textsf{Minor axis}=2 \cdot 2 = 4[/tex][tex]\textsf{Vertices:} \;\;(h, k \pm b)=(5,-5 \pm 3)=(5,-8)\;\;\textsf{and}\;\;(5,-2)[/tex][tex]\textsf{Co-vertices:}\;\;(h \pm a, k)=(5 \pm 2, -5)=(3, -5)\;\; \textsf{and}\;\;(7, -5)[/tex]To graph the ellipse:
Plot the center at (5, -5).Plot the vertices at (5, -8) and (5, -2). The distance between them is the major axis.Plot the co-vertices at (3, -5) and (7, -5). The distance between them is the minor axis.Solve the proportion for the missing values 5/12 = x/20
Answer:
x = 5
Step-by-step explanation:
We can solve for x in this proportion, or an equation of ratios, by multiplying both sides by 20.
[tex]{/}\!\!\!\!\!{20}\cdot \dfrac{5}{{/}\!\!\!\!\!20}=\dfrac{x}{{/}\!\!\!\!\!20} \cdot {/}\!\!\!\!\!20[/tex]
We can see that the 20s cancel in the numerator and denominator in both sides, and the equation is solved for x:
[tex]x = 5[/tex]
What is the sum of the series?