The area of the 125 degree sector for a circle with a radius of 12 m is approximately 158 square meters.
To find the area of a 125 degree sector of a circle with a radius of 12 m, we need to use the formula for the area of a sector:
Area of sector = (θ/360) x πr², where θ is the central angle of the sector, r is the radius of the circle, and π is a constant equal to approximately 3.14.
Substituting the given values, we get: Area of sector = (125/360) x π x 12² = (0.3472) x π x 144 = 158.03
Rounding to the nearest whole number, we get the area of the sector as 158 square meters. Therefore, the area of the 125 degree sector for a circle with a radius of 12 m is approximately 158 square meters.
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LQ - 10.4 Areas in Polar Coordinates Show all work and use proper notation for full credit. Find the area of the region enclosed by one loop of the curve. • Include a sketch of the entire curve. r = 4cos (20) LQ - 10.3 Polar Coordinates Show all work and use proper notation for full credit. Find the slope of the tangent line to the given polar curve at the point specified by the value of e. TT r = 1-2sine, =
The area of the region enclosed by one loop of the curve r = 4cos(θ) is 4 square units. The slope of the tangent line to the polar curve r=1 - 2sin(θ) at θ = π/4 is 2 + √2.
Area of region enclosed by one loop of the curve r = 4cos(2θ)
The curve r = 4cos(2θ) has two loops, and we need to find the area of one loop, which is from θ = 0 to θ = π/4.
To find the area, we use the formula for the area enclosed by a polar curve
A = (1/2) ∫[a,b] r^2 dθ
where r is the polar function, and a and b are the angles of the region we want to find the area for.
So, the area of one loop is
A = (1/2) ∫[0,π/4] (4cos(2θ))^2 dθ
= 8 ∫[0,π/4] cos^2(2θ) dθ
Using the identity cos(2θ) = (cos^2θ - sin^2θ), we can rewrite the integrand as
cos^2(2θ) = (cos^2θ - sin^2θ)^2
= cos^4θ - 2cos^2θsin^2θ + sin^4θ
= (1/2) (1 + cos(4θ)) - (1/2) sin^2(2θ)
So, the integral becomes
A = 8 ∫[0,π/4] [(1/2) (1 + cos(4θ)) - (1/2) sin^2(2θ)] dθ
= 4 [θ/2 + (1/8)sin(4θ) - (1/4)θ - (1/8)sin(2θ)]|[0,π/4]
= 1 + (2/π)
Therefore, the area of one loop of the curve r = 4cos(2θ) is 1 + (2/π).
Slope of tangent line to the polar curve r = 1-2sinθ at θ = π/4
To find the slope of the tangent line, we need to take the derivative of the polar function with respect to θ:
dr/dθ = -2cosθ
Then, we can use the formula for the slope of the tangent line in polar coordinates
dy/dx = (dy/dθ) / (dx/dθ) = (r sinθ) / (r cosθ) = tanθ + r dθ/dθ
At the point specified by θ = π/4, we have
r = 1 - 2sin(π/4) = 1 - √2/2 = (2 - √2)/2
dθ/dθ = 1
So, the slope of the tangent line is
dy/dx = tan(π/4) + r dθ/dθ
= 1 + (2 - √2)/2
= (4 + 2√2)/2
= 2 + √2
Therefore, the slope of the tangent line to the polar curve r = 1-2sinθ at θ = π/4 is 2 + √2.
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The gcf of 16mn and 24m
f(x) = x(x2 − 4) − 3x(x − 2)
To simplify the given function F(x) = x(x^2 - 4) - 3x(x - 2), we need to use the distributive property and combine like terms.
First, we distribute x in the first term, and we get:
F(x) = x^3 - 4x - 3x^2 + 6x
Next, we can combine like terms:
F(x) = x^3 - 3x^2 + 2x
Therefore, the simplified form of the given function F(x) = x(x^2 - 4) - 3x(x - 2) is F(x) = x^3 - 3x^2 + 2x.
The histogram shows the numbers of rebounds per game for a middle school basketball player in a season.
A vertical bar graph titled, Rebounds per Game. The vertical axis is labeled frequency and ranges from 0 to 7. The horizontal axis is labeled rebounds and has bin in the following intervals: For 0 to 1, the bar height is 3. For 2 to 3, the bar height is 6. For 4 to 5, the bar height is 2. For 6 to 7, the bar height is 1.
a. Which interval contains the most data values?
Responses
0–1 rebounds
0–1 rebounds
2–3 rebounds
2–3 rebounds
4–5 rebounds
4–5 rebounds
6–7 rebounds
6–7 rebounds
Question 2
b. How many games did the player play during the season?
The player played
games.
Question 3
c. In what percent of the games did the player have 4 or more rebounds?
The player had 4 or more rebounds in
% of the games.
Skip to navigation
a. Which interval contains the most data values?
2–3 rebounds
b. How many games did the player play during the season?
The player played 12 games.
c. In what percent of the games did the player have 4 or more rebounds?
The player had 4 or more rebounds in 25% of the games.
What is a Histogram?A depiction of frequency distribution is graphically manifested in a histogram where data identified as bars show the number of occurrences in a specific range or category.
The x-axis indicates value ranges, and the y-axis exhibits "counts" or "frequency". This statistical tool helps examine patterns and visualize different types of data variation by industry professionals such as financial analysts, economists, and social scientists across many fields, among others.
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Help I don't know what I did wrong.
[tex]4\sqrt{125} -2\sqrt{243} -3\sqrt{20}+5\sqrt{27}[/tex]
Given the system of inequalities: 4x – 5y < 1 one-halfy – x < 3 which shows the given inequalities in slope-intercept form? y < four-fifthsx – one-fifth y < 2x 6 y > four-fifthsx – one-fifths y < 2x 6 y > negative four-fifthsx one-fifth y > 2x 6
y < four-fifthsx - one-fifth
y < 2x + 6
How to express the given inequalities in slope-intercept form?The given system of inequalities can be represented in slope-intercept form as follows:
y < (4/5)x - 1/5
y < 2x + 6
To convert the given inequalities into slope-intercept form, we rearrange each equation to solve for y
In the first inequality, we add 5y to both sides and then divide by 4 to isolate y. This gives us:
4x - 5y < 1
-5y < -4x + 1
y > (4/5)x - 1/5
In the second inequality, we add x to both sides and then divide by -1/2 to isolate y. This gives us:
1/2y - x < 3
1/2y < x + 3
y > 2x + 6
Therefore, the given inequalities in slope-intercept form are:
y < (4/5)x - 1/5
y > 2x + 6
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Two cafés on opposite sides of an atrium in a shopping centre are respectively 10m and 15m above the ground floor. If the cafés are linked by a 20m escalator, find the horizontal distance (to the nearest metre) across the atrium, between the two cafés
The horizontal distance between the two cafes is approximately 19.36 meters.
To solve this problem, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the atrium can be considered as the base of a right-angled triangle, with the difference in height between the two cafes as the vertical side and the distance between them as the hypotenuse.
Let's call the horizontal distance we are looking for "x". Using the Pythagorean theorem, we have:
[tex]x^2 = 20^2 - (15 - 10)^2\\x^2 = 400 - 25\\x^2 = 375[/tex]
x ≈ 19.36
Therefore, the horizontal distance between the two cafes is approximately 19.36 meters.
In this problem, we can see that the height of the cafes above the ground floor is not directly relevant to finding the horizontal distance between them. Instead, the height difference is used as the vertical side of the right-angled triangle, while the distance between the cafes is the hypotenuse. By using the Pythagorean theorem, we can find the horizontal distance that we are looking for.
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Joel measures the heights of some plants. The heights of the plants, in feet, are
î
2
, 1, , $; , and 1. Which line plot correctly shows Joel's data?
Plant Heights
Plant Heights
Х
Х Х х
+ + +
X
x x x x x
A
Х
A
0
Height (feet)
Height (feet)
Plant Heights
Plant Heights
Х
Х
X
Х
A
Height (feet)
Height (feet)
In this line plot, the Xs represent the heights of the plants, and the A represents the number of plants with that height.
How to find the line plot that correctly shows Joel's data?The line plot that correctly shows Joel's data is:
Plant Heights
Х
Х
X
X
A
0
Height (feet)
In this line plot, the Xs represent the heights of the plants, and the A represents the number of plants with that height. According to the given data, there are two plants with a height of 1 foot, one plant with a height of 2 feet, and one plant with a height of 3 feet. Therefore, the correct line plot would have an X above the 2 and two As above it, an X above the 1 and one A above it, and an X above the 3 and one A above it. The other line plot shown does not correctly represent Joel's data.
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You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test your suspicion, you rolled the die in question 200 times and obtained the following frequencies for each of the six possible outcomes of the die:
Number Frequency 1 2 3 4 5 6 45 39 35 25 27 29
Can you conclude that the die is loaded? Use a 0. 05 as the significance level and perform a hypothesis test. Remember to state the null and alternative hypothesis
Based on the hypothesis test, with a significance level of 0.05, there is no evidence to suggest that the die is loaded, as the p-value is greater than the significance level. The null hypothesis that the die is fair is failed to rejected.
To determine if the die is loaded, we need to perform a hypothesis test.
Null Hypothesis (H0) The die is fair; all outcomes are equally likely.
Alternative Hypothesis (Ha) The die is loaded, and not all outcomes are equally likely.
We will use a significance level of 0.05.
To test the hypothesis, we can use a chi-square goodness-of-fit test.
First, we need to calculate the expected frequencies for each outcome, assuming that the die is fair. Since there are six possible outcomes, each with an expected frequency of 200/6 = 33.33.
Number Observed Frequency (O) Expected Frequency (E) (O - E)² / E
1 45 33.33 3.48
2 39 33.33 0.87
3 35 33.33 0.07
4 25 33.33 1.83
5 27 33.33 0.99
6 29 33.33 0.44
The test statistic is the sum of (O-E)² / E, which is 7.68.
The degrees of freedom for this test are (number of categories - 1) = 5.
Using a chi-square distribution table or calculator, we find that the p-value associated with a test statistic of 7.68 and 5 degrees of freedom is approximately 0.177.
Since the p-value is greater than our significance level of 0.05, we fail to reject the null hypothesis. We cannot conclude that the die is loaded based on this data alone.
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at a local farmers market a farmer pays $10 to rent a stall and $7 for every hour he stays there. if he pays $45 on saturday how many hours did he stay at the market
Answer: The answer is 5.
Step-by-step explanation:
You first set up the equation
10 + 7x = 45
You must put x because you don't know the number of hours he stays
You then subtract 10 from both sides of the numbers 10 and 45
That'll get you 7x = 35
To find out what x is you divide both sides by 7
7x divided by 7 is x
35 divided by 7 is 5
X = 5
a project has two activities a and b that must be carried out sequentially. the probability distributions of the times required to complete each of the activities a and b are uniformly distributed in intervals [1,6] and [3,7] respectively. find the total project completion time and run 6000 simulation trials in excel. a) what is the output of the simulations? b) what is the excel functions would properly generate a random number for the duration of activity a in the project described above? c) what is the standard deviation of the project completion time in the project described?
The project completion time is output of the simulations, option A, the EXCEL function used is (c) 1+4*RAND() and the standard deviation is
(b) 1.47.
1) In this simulation, we enter commands based on the way that activity durations are distributed (here uniformly with predetermined intervals). We determine the project completion time as an output based on the command we used and our calculations. This value will fluctuate (slightly) when the simulation is run, hence it is not fixed.
Hence, the "project completion time" is an (a) Output of the simulation.
2) Here, it is given that time required to complete activity A is uniformly distributed in an interval [1, 5].
So, we require random numbers starting from 1 with an interval of length 5-1=4.
We know, during simulation using usual Excel function RAND() we obtain random numbers in an interval [0, 1].
Thus if we multiply usual Excel function RAND() by 4 and thus use 4*RAND(), then we obtain random numbers in an interval [0*4, 1*4] i.e
[0, 4].
Adding 1 to this Excel function i.e. using Excel function 1+4*RAND() we obtain random numbers in an interval [0+1, 4+1] i.e [1, 5].
Hence, the Excel function to be used to generate random numbers for the duration of activity A is (c) 1+4*RAND().
3) For [tex]\tiny X\sim Unif\left ( a,b \right )[/tex], variance is given by
[tex]\tiny Var\left ( X \right )=\frac{\left ( b-a \right )^2}{12}[/tex]
Variance for activity A is given by
[tex]\tiny \frac{\left ( 5-1 \right )^2}{12}=\frac{4^2}{12}=1.333333[/tex]
Variance for activity B is given by
[tex]\tiny \frac{\left ( 3-2 \right )^2}{12}=\frac{1^2}{12}=0.083333[/tex]
Variance for activity C is given by
[tex]\tiny \frac{\left ( 6-3 \right )^2}{12}=\frac{3^2}{12}=0.75[/tex]
Variance of project completion time in the project is \tiny [tex]1.333333+0.083333+0.75= 2.166666[/tex]
So, standard deviation of project completion time in the project is [tex]\tiny \sqrt {2.166666}=1.47196\approx 1.47[/tex]
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Complete question:
A project has three activities A, B, and C that must be carried out sequentially. The probability distributions of the times required to complete each of the activities A, B, and C are uniformly distributed in intervals (1,5), (2,3) and (3,6) respectively. Find the total project completion time and run 1000 simulation trials in Excel. 7. The "project completion time" is a(n)... a. Output of the simulation b. Input of the simulation c. Decision variable in the simulation d. A fixed value in the simulation 8. Which of the following Excel functions would properly generate a random number for the duration of activity A in the project described above? a. 5* RANDO b. 1+5 * RANDO c. 1+4* RANDO d. NORM.INV(RAND(),1,5) e. NORM.INV(RAND(0,5,1) 9. The standard deviation of the project completion time in the project described above is cl a 2.83 b. 1.47 c. 1.15 d. 1.82 e. 1.63
what is the volume of a cylinder, in cubic feet, with. height of 7 inches and a base diameter of 18ft
148.35 cubic feet is the volume of a cylinder with height of 7 inches and a base diameter of 18ft
We have to find the volume of a cylinder
V=πr²h
h is the height of cylinder and r is radius of the base.
Given height is 7 inches which is 0.583333 feet
Diameter is 18 ft
Radius is 9 ft
Now plug in value of height and radius
Volume=π(9)²×0.5833
=3.14×81×0.5833
=148.35 cubic feet
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A culture of bacteria has an initial population of 65000 bacteria and doubles every 2
hours. Using the formula Pt = Po 2a, where Pt is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 13 hours, to the nearest whole number?
.
The population of bacteria in the culture after 13 hours is approximately 1,656,320.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
We have the initial population, Po = 65000, and the doubling time, d = 2 hours. To find the population after 13 hours, we need to use the formula:
[tex]Pt = Po * 2^{(t/d)[/tex]
where Pt is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.
Substituting the given values, we get:
Pt = 65000 x [tex]2^{(13/2)[/tex]
Pt ≈ 1,656,320
Rounding this to the nearest whole number, we get:
The population of bacteria in the culture after 13 hours is approximately 1,656,320.
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stressing outtt I need help its due in a few minuets
Identify the constant of proportionality in the situation
8. A plane travels 462.4 miles in 34 minutes.
Answer:
13.6 miles/minute
Step-by-step explanation:
We Know
A plane travels 462.4 miles in 34 minutes.
Identify the constant of proportionality in the situation..
We Take
462.4 / 34 = 13.6 miles/minute
So, the answer is 13.6 miles/minute
Katie Ledecky has become the first women ever to swim the 1,000 yard freestyle in under nine minutes (8:59.65 but let’s call it exactly 9 for our problem) While on vacation with her friends at Redleaf lake they bet her that she couldn’t make it from point A to point B in less then ten minutes. Assuming she can swim at her Olympic level pace should she take this bet? Justify your work.
Katie should be able to make it from point A to point B in less than ten minutes and win the bet.
What is minute?A minute is a unit of time equal to 60 seconds or one sixtieth of an hour. It is commonly used to measure short periods of time, such as the duration of a phone call or a meeting. The symbol for minute is "min".
According to given information:To determine whether Katie Ledecky can make it from point A to point B in less than ten minutes, we need to calculate the distance between the two points and compare it to her swimming speed.
From the given information, we can use the Law of Cosines to find the distance between points A and B:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
where c is the distance between points A and B, a is the distance from point A to point C, b is the distance from point B to point C, and C is the angle between sides a and b.
Plugging in the given values, we get:
[tex]c^2 = 620^2 + 455^2 - 2(620)(455) cos(150°)\\\\c^2 = 383,825[/tex]
c ≈ 619.5 yards
So the distance between points A and B is approximately 619.5 yards.
Now, we need to determine whether Katie Ledecky can swim this distance in less than ten minutes. We are given that she swam 1,000 yards in 8 minutes and 59.65 seconds, which is approximately 8.99 minutes. So her average speed for the 1,000 yard freestyle was:
speed = distance / time
speed = 1,000 yards / 8.99 minutes
speed ≈ 111.23 yards/minute
To swim the distance between points A and B in less than ten minutes, Katie would need to swim at an average speed of:
speed = distance / time
speed = 619.5 yards / 10 minutes
speed = 61.95 yards/minute
Katie's Olympic level swimming speed of 111.23 yards/minute is significantly faster than the required average speed of 61.95 yards/minute to swim from point A to point B in under ten minutes. Therefore, she should be able to make it from point A to point B in less than ten minutes and win the bet.
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PLEASE HELP ME ASSAP!!!!!!!!!
The slope of UF is 1/6
What is a slope of a line?The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
The slope is given = change in point on y axis/ change in point on x axis
slope = y2-y1/x2-x1
The cordinate of F = (-2,-3) and U ( 4, -2)
y1 = -3 and y2 = -2
x1 = -2 and x2 = 4
slope = -2-(-3)/4-(-2)
= -2+3/(4+2)
= 1/6
therefore the slope of UF is 1/6
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d – 10 – 2d + 7 = 8 + d – 10 – 3d
d = –5
d = –1
d = 1
d = 5
Answer:
d=1
Step-by-step explanation:
(i have to write this cuz i cant write less than 20 words)
1. What is the probability of rolling a # larger than 2 and drawing an Ace or 4? A 2 3 4 5
The probability of rolling a number larger than 2 and drawing an Ace or 4 is 2/39. There are 4 numbers larger than 2 and 2 Aces and 1 4 in a deck of 52 cards and a total of 6 outcomes that meet the criteria.
The probability of rolling a number larger than 2 is 4/6, which simplifies to 2/3. The probability of drawing an Ace or 4 is 4/52, which simplifies to 1/13. To find the probability of both events happening, you multiply the probabilities
P(rolling a number larger than 2 and drawing an Ace or 4) = P(rolling a number larger than 2) x P(drawing an Ace or 4)
= (2/3) x (1/13)
= 2/39
Therefore, the probability of number larger than 2 and drawing an Ace or 4 is 2/39.
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Melanie is making a piece of jewelry that is in the shape of a right triangle. The two shorter sides of the piece of jewelry are 4 mm and 3 mm. Find the perimeter of the piece of jewelry.
Therefore , the solution of the given problem of triangle comes out to be the jewellery's circumference is 12 mm.
What precisely is a triangle?If a polygon contains at least one more segment, it is a hexagon. It is a simple rectangle in shape. Anything like this can only be distinguished from a standard triangle form by edges A and B. Even if the edges are perfectly collinear, Euclidean geometry only creates a portion of the cube. A triangle is made up of a quadrilateral and three angles.
Here,
The lengths of all three sides must be added up in order to determine the jewellery's perimeter.
=> c²= a² + b²
where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.
=> A = 3mm, and B = 4mm.
Therefore, we can determine the length of the hypotenuse using the Pythagorean theorem:
=> c² = a²+ b²
=> c² = 3² + 4²
=> c² = 9 + 16
=> c² = 25
=> c = √25)
=> c = 5 mm
As a result, the hypotenuse is 5 mm long.
We total the lengths of all three sides to determine the jewellery's perimeter:
=> perimeter = 4mm, 3mm, and 5mm.
=> 12 mm is the diameter.
Therefore, the jewellery's circumference is 12 mm.
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A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent.
The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?
2 cm
2 StartRoot 2 EndRoot cm
4 cm
4 StartRoot 2 EndRoot cm
Answer:
The length of one leg of this right triangle is 4/√2 = 2√2 cm.
At the baby next checkup the baby weighed 11 pounds and four ounces how many ounces did the baby gain since the appointment mentioned in the first probloem
If at the previous appointment the baby weighed 10 pounds and 8 ounces, then the baby has gained 12 ounces since the last appointment.
To calculate this, we need to subtract the weight at the previous appointment from the weight at the current appointment:
11 pounds and 4 ounces - 10 pounds and 8 ounces = 12 ounces
So the baby has gained 12 ounces since the last appointment. It's important to keep track of a baby's weight gain, as it is an indicator of their growth and overall health.
It's also worth noting that the rate of weight gain can vary for each baby, so it's important to discuss any concerns or questions with a pediatrician. Additionally, other factors like height, head circumference, and developmental milestones should also be taken into consideration when evaluating a baby's growth.
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Find the exact location of all the relative and absolute extrema of the function. (Order your answers from smallest to largest x.) g(x) = 3x³ - 36x with domain [-4, 4] g has an absolute minimum at (x,y) =
We can see that the absolute minimum occurs at (x, y) = (2, -48).
To find the relative and absolute extrema of the function g(x) = 3x³ - 36x on the domain [-4, 4], we first need to find the critical points. We do this by finding the first derivative, setting it to zero, and solving for x.
g'(x) = d(3x³ - 36x)/dx = 9x² - 36
Setting g'(x) to 0:
0 = 9x² - 36
x² = 4
x = ±2
These are our critical points. To determine if these are minima, maxima, or neither, we use the second derivative test.
g''(x) = d(9x² - 36)/dx = 18x
At x = -2:
g''(-2) = -36 < 0, so it's a relative maximum.
At x = 2:
g''(2) = 36 > 0, so it's a relative minimum.
Now, we need to compare the function values at the critical points and endpoints of the domain to determine the absolute extrema.
g(-4) = 3(-4)³ - 36(-4) = -192
g(-2) = 3(-2)³ - 36(-2) = 48 (relative maximum)
g(2) = 3(2)³ - 36(2) = -48 (relative minimum)
g(4) = 3(4)³ - 36(4) = 192
From the above values, we can see that the absolute minimum occurs at (x, y) = (2, -48).
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The rate of change of the gender ratio for the United States during the twentieth century can be modeled as g(t) = (1. 68 · 10^−4)t^2 − 0. 02t − 0. 10
where output is measured in males/100 females per year and t is the number of years since 1900. In 1970, the gender ratio was 94. 8 males per 100 females.
(a) Write a specific antiderivative giving the gender ratio.
G(t) = _______________ males/100 females
(b) How is this specific antiderivative related to an accumulation function of g?
The specific antiderivative in part (a) is the formula for the accumulation function of g passing through (t, g) =
Answer:
(a) G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84
(b) A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 - 1900^2) - 0.10(t - 1900)
Step-by-step explanation:
(a) The antiderivative of g(t) can be found by integrating each term of the function with respect to t:
∫g(t) dt = ∫(1.68 × 10^-4)t^2 dt - ∫0.02t dt - ∫0.10 dt
= (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t + C
where C is the constant of integration.
To find the specific antiderivative G(t) that passes through the point (1970, 94.8), we can use this point to solve for C:
94.8 = (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970) + C
C = 94.8 + (1.68 × 10^-4) × (1/3) (1970)^3 - (0.02/2) (1970)^2 - 0.10(1970)
C ≈ -2445.84
Therefore, the specific antiderivative that gives the gender ratio is:
G(t) = (1.68 × 10^-4) × (1/3) t^3 - (0.02/2) t^2 - 0.10t - 2445.84
(b) The accumulation function of g is the integral of g with respect to t, or:
A(t) = ∫g(t) dt = G(t) + C
where C is the constant of integration. We can find the value of C using the initial condition given in the problem:
A(1900) = ∫g(t) dt ∣t=1900 = G(1900) + C = 0
Therefore, C = -G(1900), and the accumulation function of g is:
A(t) = G(t) - G(1900) = (1.68 × 10^-4) × (1/3) (t^3 - 1900^3) - (0.02/2) (t^2 - 1900^2) - 0.10(t - 1900)
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Explain me that excersice step by step please3x((2x3)^-1x1/2^3)^-1x(3x2^2)^-2
Answer:
Begin by simplifying the phrases within the brackets, beginning with the innermost brackets:
(2 x 3)^-1 = 1/6 (because 2 x 3 = 6, and the negative exponent flips the fraction)
1/2^3 = 1/8 (because 2^3 = 8)
So, (2x3)^-1x1/2^3 = 1/6 x 1/8 = 1/48
Next, simplify the expression outside the parentheses:
(3x2^2)^-2 = 1/(3x2^2)^2 = 1/(3^2 x 2^4) = 1/36 x 1/16 = 1/576
Now, substitute the simplified terms back into the original expression and simplify:
3x(1/48)x(1/576) = 1/768
So the final answer is 1/768.
2x + 7 = -1(3 - 2x) solve for X
This linear equation is invalid, the left and right sides are not equal, therefore there is no solution.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to be linear equations. axe+b = 0 is a one-variable example in which a and b are real numbers and x is the variable.
2x + -7 = -1(3 + -2x)
Reorder the terms:
-7 + 2x = -1(3 + -2x)
-7 + 2x = (3 * -1 + -2x * -1)
-7 + 2x = (-3 + 2x)
Add '-2x' to each side of the equation.
-7 + 2x + -2x = -3 + 2x + -2x
Combine like terms: 2x + -2x = 0
-7 + 0 = -3 + 2x + -2x
-7 = -3 + 2x + -2x
Combine like terms: 2x + -2x = 0
-7 = -3 + 0
-7 = -3
Solving
-7 = -3
Couldn't find a variable to solve for.
This equation is invalid, the left and right sides are not equal, therefore there is no solution.
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How do you do this problem?
Knowing that tan(x) = 3/5 and using a trigonometric identity, we will get that:
tan(2x) = 1.875
How to find the tangent of 2x?There is a trigonometric identity we can use for this, we know that:
[tex]tan(2x) = \frac{2tan(x)}{1 - tan^2(x)}[/tex]
So we only need to knos tan(x), which we already know that is equal to 3/5, then we can replace it in the formula above to get:
[tex]tan(2x) = \frac{2*3/5}{1 - (3/5)^2}\\\\tan(2x) = \frac{6/5}{1 - 9/25} \\tan(2x) = 1.875[/tex]
That is the value of the tangent of 2x.
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jack draw a number line on his paper jack drew a new point 45% of the distance from e to point j. between which two letters does the new point lie?
The two letters in which the new point lie include the following: C. between G and H.
What is a number line?In Geometry, a number line simply refers to a type of graph that is composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.
This ultimately implies that, all number lines would primarily increase in numerical value (number) towards the right from zero (0) and decrease in numerical value (number) towards the left from zero (0).
From the number line shown in the image attached below, we can logically deduce the following point:
|J - E| = 45% of x
|J - E| = 0.45x
|J - E| = GH
In conclusion, 45% is almost half way or 50% between E and J, which makes the distance between the two letters G and H, the new point.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
i need help please
20pts
Answer:
the answer is A
Step-by-step explanation:
√3 = Irrational
√12 = Irrational
but if
√3 × √ 12 = √36 = 6 = rational
The arrow on this spinner is equally likely to land on each section. the arrow is spun 72 times. how many times do you expect the arrow to land on 4?
we know that the spinner has an equal chance of landing on each section. Since there are a total of six sections on the spinner, we can assume that the probability of the arrow landing on any one section is 1/6 or approximately 0.1667.
Now, if the arrow is spun 72 times, we can use this probability to calculate the expected number of times the arrow will land on 4. To do this, we simply multiply the probability by the number of spins, as follows:
Expected number of times arrow lands on 4 = Probability of arrow landing on 4 x Number of spins
Expected number of times arrow lands on 4 = 0.1667 x 72
Expected number of times arrow lands on 4 = 12
So, we can expect the arrow to land on 4 approximately 12 times out of 72 spins. Of course, this is just an expected value, and the actual number of times the arrow lands on 4 may vary from this value due to random chance.
In summary, if we assume that the arrow on the spinner is equally likely to land on each section, and it is spun 72 times, we can expect the arrow to land on 4 approximately 12 times based on probability calculations.
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