From the graphing utility, we get the value of the integral as, Integral = 0.7206 Comparing the values of the integrals obtained from Trapezoidal rule, Simpson's rule and graphing utility, we find that the integral value obtained from the graphing utility is closest to the Simpson's rule.
We are given the definite integral ∫31ln(x)dx and we are required to approximate the integral using the trapezoidal rule and Simpson's rule. Also, we are supposed to compare these results with the approximation of the integral using a graphing utility using n=4.Trapezoidal Rule. The trapezoidal rule for numerical integration is a method to approximate the definite integral using linear interpolation.
This rule approximates the definite integral by dividing the total area into trapezoids. The formula for trapezoidal rule is given by:(Image attached)Here, a = 3 and b = 1The value of h can be calculated as follows;h=(b−a)/nh=(3−1)/4=0.5We need to calculate the values of f(1), f(1.5), f(2), f(2.5), f(3) using n = 4(Image attached)The value of integral using the trapezoidal rule is,Integral = 0.7201.
Simpson's rule is used to approximate the value of definite integral. Simpson's rule involves approximating the integral under the curve using the parabolic shape. This is done by dividing the area under the curve into small sections and then approximating each section with a parabolic shape. The formula for Simpson's rule is given as:(Image attached)Here, a = 3 and b = 1
The value of h can be calculated as follows;h=(b−a)/nh=(3−1)/4=0.5We need to calculate the values of f(1), f(1.5), f(2), f(2.5), f(3) using n = 4(Image attached)The value of integral using the Simpson's rule is,Integral = 0.7200Comparing with Graphing UtilityIntegral = 0.7201 (from Trapezoidal rule)Integral = 0.7200 (from Simpson's rule).
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i need help with this aleks assignment
The correct answer to this question is OU=13.7. This answer can be determined by using the Pythagorean Theorem.
What is Pythagorean Theorem?This states that the sum of the squares of the lengths of the two shorter sides of a right triangle will always equal the square of the length of the longest side, or the hypotenuse.
In this problem, the triangle created by points O, U, and V is a right triangle as OV and UW are tangent to the circle at point O. Therefore, the Pythagorean Theorem can be used to solve for OU.
OV is 6.5 and UW is 7.2. This is done by taking the square of the two legs and adding them together. (6.5)2 + (7.2)2 = OU2. Simplifying this equation, OU2 = 73.04. Taking the square root of both sides of this equation yields OU = 13.7
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The answer can be determined by using the Pythagorean Theorem which is OU=9.7.
What is Pythagorean Theorem?This states that the sum of the squares of the lengths of the two shorter sides of a right triangle will always equal the square of the length of the longest side, or the hypotenuse.
In this problem, the triangle created by points O, U, and V is a right triangle as OV and UW are tangent to the circle at point O.
Therefore, the Pythagorean Theorem can be used to solve for OU.
OV= 6.5
UW= 7.2.
(6.5)² + (7.2)² = OU²
Simplifying this equation,
OU² = 94.09.
Taking the square root of both sides of this equation yields
OU = 9.7
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NEED HELP PLEASE HELP
*CORRECT AND FASTEST ANSWER GETS BRAINLIEST!!!*
A greengrocer buys fruit and vegetables from the market and sells them at a 25% mark up. On one particular moring her fruit and vegetables cost her €500. If she sells all of her produce, find:
A) her profit
B) her total income
Answer: Below :)
Step-by-step explanation:
A) To find the profit, we first need to calculate the cost of the produce plus the 25% markup.
The markup is 25% of the cost, which is 0.25 * 500 = €125.
So the total cost of the produce plus markup is €500 + €125 = €625.
Now, if the greengrocer sells all the produce, the total revenue will be 100% plus the 25% markup, which is 125% of the original cost.
125% of €500 is 1.25 * 500 = €625, which is the same as the cost plus markup.
Therefore, the profit is the markup, which is €125.
B) To find the total income, we add the profit to the total cost:
Total income = €500 + €125 = €625
Answer:
A) €125
B) €625
If the GM between √2 and 2√2 is a find the value of a.
Answer:
If the GM between √2 and 2√2 is a find the value of a.
Step-by-step explanation:
To find the geometric mean between two numbers, we simply take the square root of their product.
In this case, we want to find the geometric mean between √2 and 2√2.
Their product is:
√2 * 2√2 = 2√4 = 2*2 = 4
So, the geometric mean between √2 and 2√2 is the square root of 4, which is:
√4 = 2
Therefore, the value of a is 2.
Solve the inequality and write the solution in set-builder notation. b+2≥ 4
Answer:
B ≥ 2
Step-by-step explanation:
b + 2 ≥ 4
b ≥ 4 - 2
b ≥ 2
Hope this helps <3
Pablo's is a popular Mexican restaurant, known especially for its homemade salsa. During dinner last night at Pablo's, 7 tables of people ordered chips and salsa for every 2 tables that did not.
Answer: =84
Step-by-step explanation:
you are dealt one card from a standard 52-card deck. playing cards find the probability of being dealt a three and an ace. the probability of being dealt a three and an ace is . (type an integer or a fraction.)
The probability of getting an ace and a three is (4/52) × (3/51) = 12/2652 which simplifies to 1/221.
There are 4 aces and 4 threes in a deck of 52 standard cards.
The probability of getting an ace on your first draw is 4/52.
Once you have the ace, there are 51 cards left in the deck, 3 of which are threes.
Therefore, the probability of drawing a three is 3/51.
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HELP PLEASE !!
Use the information given in the figure to find the length RV.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
5
13
R
T
11
15
0
The length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.
What is the Pythagoras rule?The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
so by Pythagoras rule we can evaluate for the length RV by considering the following right triangles:
For ∆TVU:
13² = 5² + TV²
TV = √(13² - 5²) {make TV the subject}
TV = √(169 - 25)
TV = √144
TV = 12
For ∆TVS:
15² = 12² + SV²
SV = √(15² - 12²) {make SV the subject}
SV = √(225 - 44)
SV = √81
SV = 9
For ∆RVS:
11² = 9² + RV²
RV = √(11² - 9²) {make RV the subject}
RV = √(121 - 81)
RV = √49
RV = 6.3246
Therefore, the length of RV for the right triangle is equal to 6 to the nearest whole number using the Pythagoras rule.
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HELPPPPPPP PLEASEEEEEEEEEEEEEEE
y=mx+b
The required equation of straight line is y = 0.03x + 20.
What is an equation?
A mathematical equation states that two quantities or values are identical. Equations are used when more than one factor has to be examined in order to fully understand or explain a situation.
The general form of an equation is y = mx + b, where m is the slope of equation and b is a constant.
From the given graph we get 2 points.
i.e., (0, 20) and (2000, 80)
Slope of the line is
[tex]m=\frac{80-20}{2000-0}\\\ \ = \frac{60}{2000}\\ = \frac{6}{200} \\= \frac{3}{100}[/tex]
Then the equation will be
[tex]y-20=\frac{3}{100}(x-0)\\\Rightarrow y-20=0.03x\\\Rightarrow y-0.03x-20=0\\\Rightarrow y = 0.03x+20[/tex]
Therefore, the required equation is y = 0.03x + 20, calculating with the help of given graph.
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In one year 120 students enrolled at a community college. This was 3/5 of the number of students accepted. How many of those accepted did not enroll
The number of students who did not enroll in the college given that only 3/5th of the total students accepted the admission is equal to 80 students.
Let us consider that the total number of students who enrolled for the process is equal to x. Since it is given that three-fifth of the total students who enrolled positively are equal to 120, this means that 3/5*x = 120.
Thus value of x can be calculated by cross multiplication as follows:
3/5*x = 120
x = 120 * 5/3 = 200
Now, since two third of the students didn't respond/ enroll, then this number can be calculated as the difference between the total numbers who joined and the number of students who accepted the enrollment process.
Number of students who accepted but did not enroll = 200 - 120 = 80
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Environment An accident at an oil drilling platform is causing a circular oil slick. The slick is 0.08 foot thick, and when the radius of the slick is 150 feet, the radius is increasing at the rate of 0.5 foot per minute. At what rate (in cubic feet per minute) is oil flowing from the site of the accident?
The rate of oil flowing from the site of the accident is 47123.74 cubic feet per minute.
To find the rate at which oil is flowing from the site of the accident, we need to determine the rate of change of the volume of oil in the slick with respect to time.
We know that the slick is circular with a thickness of 0.08 feet and a radius that is increasing at a rate of 0.5 feet per minute. Let's call the radius of the slick at time t "r" and the volume of oil in the slick at time t "V".
The volume of a cylinder (which the slick approximates) is given by the formula V = πr^2h, where π is the constant pi and h is the height or thickness of the cylinder.
Differentiating both sides with respect to time, we get:
dV/dt = 2πrh(dr/dt) + πr^2(dh/dt)
We know that the thickness of the slick is constant at 0.08 feet, so dh/dt = 0. We also know that the radius is increasing at a rate of 0.5 feet per minute, so dr/dt = 0.5. Finally, we know that the radius of the slick is currently 150 feet, so r = 150.
Substituting these values into the formula, we get:
dV/dt = 2π(150)(0.5) + π(150)^2(0)
dV/dt = 47123.74 cubic feet per minute
Therefore, the rate at which oil is flowing from the site of the accident is approximately 47123.74 cubic feet per minute.
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What is the value of x? X = X-38° O X X-33°
Answer:
Step-by-step explanation:
Caris has a carton of 12 eggs, two of which have brown shells while the rest have white shells. Caris randomly chooses a brown egg from the carton. Which of the following statements is true? If she rejects this egg, returns it to the carton, and randomly picks again, these will be dependent events. If she uses this egg in a recipe and picks another one from the carton, these will be dependent events. Whether or not these are dependent or independent events depends on what color egg Caris chooses next. If she uses this egg in a recipe and picks another one from the carton, these will be independent events.
Answer:
Step-by-step explanation:
i think you have to times it
A pharmaceutical company produces caffeine pills that are each supposed to contain 200mg of caffeine. A plant that produces thousands of these pills per batch took an SRS of 15 pills from their latest batch to see if they contained the proper amount of caffeine. The sample data had a mean of 200.4mg of caffeine per pill with a standard deviation of 0.8mg. The amounts were roughly symmetric with no outliers. Based on this sample, which of the following is a 95% confidence interval for the mean amount of caffeine (in mg) per pill in this batch?
options
200.4±1.96(0.8)
200±1.96(0.8/sqrt(15))
200.4±1.96(0.8/sqrt(15))
200.4±2.145(0.8/sqrt(15))
200±2.145(0.8/sqrt(15))
The correct answer is 200.4 + 2.145(0.8/sqrt(15)).
We may use the following calculation to determine the confidence interval for the average caffeine content per tablet in this batch:
Confidence interval = sample mean + (critical value) x (standard error)
The crucial number in this situation is 1.96 since we want a 95% confidence interval. Since the sample size is 15, and the standard deviation is 0.8, the standard error is 0.8/sqrt(15). Here is what we get after entering these values:
Confidence interval = 200.4 + 1.96(0.8/sqrt(15))
The result of computing this expression is:
Confidence interval = 200.4 + 0.347
We achieve by simplifying:
Confidence interval = 200.4 + 2.145(0.8/sqrt(15))
As a result, the right response is 200.4 + 2.145(0.8/sqrt(15)).
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Answer:
Step-by-step explanation:
10) When Perry Person got a paycheck, Perry went shopping. He spent $26 on a shirt and twice as much on jeans. Then he spent half of what he had left on a snack. On his way home, he found $10 and ended up with $ 24. How much was Perry's paycheck ?
Perry's paycheck was $100. To find Perry's paycheck, we can work backward from the final amount he had after finding $10 and ending up with $24.
Let's denote Perry's paycheck as "x". After buying the shirt and jeans, he spent a total of $26 + $52 = $78. So he had "x" - $78 left. He then spent half of what he had left on a snack, leaving him with 1/2 * ("x" - $78) = 1/2*x - $39.
When he found $10, he ended up with $24, so we can set up the equation:
1/2*x - $39 + $10 = $24
Simplifying this equation gives us:
1/2*x = $53
Multiplying both sides by 2, we get:
x = $106
Therefore, Perry's paycheck was $100.
In summary, we used a series of calculations to work backward from the final amount Perry had to determine his original paycheck. We accounted for the amount he spent on a shirt, jeans, and a snack, as well as the amount he found on his way home.
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b) If Keira has burned 640 calories cycling, how many miles has she cycled? Give any decimal answers to 2 d.p. x distance cycled Number of calories burned against distance cycled calories burned Calories burned 400 350 300 250 200 150 100 50 0 2 6 8 10 12 14 16 4 Distance cycled (miles)
Using the slope we know that the distance Keira traveled is 32 miles.
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise).
Find the difference between these two points' x-coordinates (run).
Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
So, in the given situation:
c is calories burned and d is the distance.
Then,
x = kd
k is the slope = 200/10 = 20
Calories burned = 20 * distance cycled
When, c = 640:
640 = 20*distance
distance = 640/20
distance = 32 miles
Therefore, using the slope we know that the distance Keira traveled is 32 miles.
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Al's car travels 40 miles on a gallon of gas the car's gas tank has a capacity of 10 gallons the distance out control was shown on the graph before his trips Al stops at the gas station where 10 gallons of gas cost $27 his tank already 2/5 full and he spends $13.50 on gas what is the maximum distance I'll can travel with the gas he has now in his tank
The maximum distance that can be traveled is given as follows:
360 miles.
How to obtain the maximum distance?The maximum distance that can be traveled is obtained applying the proportions in the context of the problem.
The amount of gas on the tank of Al's car is given as follows:
2/5 full = 2/5 x 10 = 4 gallons.10 gallons of gas cost $27, he spends $13.50, hence he put 5 gallons on the tank.Then he has 9 gallons of gas in the tank, and the car has a rate of 40 miles per gallon, hence the maximum distance that can be traveled is given as follows:
9 x 40 = 360 miles.
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An inequality is shown.
2x - 5 < 33
Select all the values that are solutions to this inequality.
A.28
B.26
C.19
D.18
E.12
Answer:
To solve the inequality 2x - 5 < 33, we can add 5 to both sides to isolate the variable:
2x - 5 + 5 < 33 + 5
2x < 38
Next, we divide both sides by 2 to obtain the value of x:
2x/2 < 38/2
x < 19
Therefore, any value of x that is less than 19 is a solution to this inequality. Among the given values, only 12 and 18 are less than 19. So, the solutions to the inequality are:
E. 12
D. 18
. An Estate dealer sells houses and makes a commission of GHc3750 for the first house sold. He receives GHc500 increase in commission for each additional house sold. How many houses must she sell to reach a total commission of GHc6500?
Answer: Let's denote the number of additional houses sold after the first one as "x".
Since the commission for the first house sold is GHc3750, the commission for selling x additional houses is GHc500x.
Therefore, the total commission earned by selling x additional houses is:
GHc3750 + GHc500x
We want to find the value of x that makes the total commission equal to GHc6500. Setting up an equation and solving for x, we get:
GHc3750 + GHc500x = GHc6500
GHc500x = GHc2750
x = 5.5
Since we can't sell half of a house, we round up to the nearest whole number. Therefore, the estate dealer must sell a total of 6 houses (including the first one) to reach a total commission of GHc6500.
Step-by-step explanation:
The owner of a sports complex wants to carpet a hallway connecting two buildings. The carpet costs $2.50 per square foot. How much does it cost to carpet the hallway?
Therefore, it will cost $510 to carpet the hallway.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width. The concept of area is used in many fields, including mathematics, geometry, engineering, and architecture. It is an important measure for determining the amount of material needed to cover a surface, such as carpet or paint, and is used in a wide variety of real-world applications.
Here,
To find the cost of carpeting the hallway, we need to know the total area of both trapezoids in square feet. Let's assume that the trapezoids have parallel sides of length 16 and 18 feet, and a height of 6 feet.
The area of each trapezoid is given by the formula:
Area = (1/2) x (sum of parallel sides) x height
For the first trapezoid, the sum of parallel sides is 16 + 18 = 34 feet. Therefore, the area of the first trapezoid is:
Area1 = (1/2) x (16 + 18) x 6
Area1 = 102 square feet
For the second trapezoid, the sum of parallel sides is also 16 + 18 = 34 feet. Therefore, the area of the second trapezoid is:
Area2 = (1/2) x (16 + 18) x 6
Area2 = 102 square feet
The total area of both trapezoids is:
Total Area = Area1 + Area2
Total Area = 102 square feet + 102 square feet
Total Area = 204 square feet
Now that we know the area of the hallway, we can calculate the cost of carpeting it. We're told that the carpet costs $2.50 per square foot, so we can multiply the area of the hallway by the cost per square foot to find the total cost:
Total Cost = Area x Cost per square foot
Total Cost = 204 square feet x $2.50 per square foot
Total Cost = $510
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Simplify this expression.
1/4 + 4/5 (3/4 x - 1 1/9).
The answer is (x^2)*(a)/28 I just need the if condition
The value of the given expression is x²a/28.
What is an expression?Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. An absolute numerical number is referred to as a constant.
Variable: A variable is a marker with no fixed value.
Term: A term might be a single constant, a single variable, or a mix of a variable and a constant paired with multiplication or division.
The given expression is:
4x² + 2x³/7a³ ÷ 16 + 8x/a⁴
The expression can be written using multiplication as follows:
4x² + 2x³/7a³ × a⁴/16 + 8x
Take the common terms out:
2x²(2+ x)/7a³ × a⁴/8(2 + x)
Cancel the like terms:
x²a/28
Hence, the value of the given expression is x²a/28.
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Hi please help me thank you
The value of the r in following triangle is 29.
How to find r ?[tex]65° + (4r - 1) ^ 0 = 180°[/tex]
Angles on a straight line ddd up to 180 deg
therefore
65°+ 4r - 1 = 180°
4r - 1 = 180° - 65°
4r - 1 = 115°
4r = 115 + 1
4r = 116
r = 116/4
r = 29.
A triangle is a three-sided polygon with three angles. It is a simple closed shape and one of the fundamental geometric shapes. Triangles are classified based on the length of their sides and the angle measurement.
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What are the zeros of g(x) = x3 + 6x2 − 9x − 54?
Answer:
Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.
What are the key features of the graphs of the trigonometric functions?
Select all correct trigonometric functions.The function's period is 2π.
f(x)=sinx
f(x)=cosx
The function's asymptotes are πunits apart.
f(x)=tanx
The function has a maximum value of 1.
f(x)=sinx
f(x)=cosx
The function's period is 2π: f(x)=sinx , f(x)=cosx.
The function has a maximum value of 1: f(x)=sinx
The function's asymptotes are π units apart: f(x)=tanx.
The function's period is 2π:
The period of a trigonometric function is the distance between two consecutive repetitions of its pattern.
For the functions f(x) = sin(x) and f(x) = cos(x), the period is indeed 2π. This means that the graph of these functions repeats its pattern every 2π units along the x-axis.
The function has a maximum value of 1:
The function f(x) = sin(x) has a maximum value of 1.
As you go through the sine wave, it reaches its highest point at 1 and then starts decreasing.
The function's asymptotes are π units apart:
An asymptote is a line that a graph approaches but never quite reaches. The function f(x) = tan(x) has vertical asymptotes that are π units apart.
These asymptotes occur at regular intervals along the x-axis, specifically at x = π/2, x = 3π/2, x = 5π/2, and so on.
The tangent function has a repeating pattern of asymptotes separated by π units.
Hence, The function's period is 2π: f(x)=sinx , f(x)=cosx.
The function has a maximum value of 1: f(x)=sinx
The function's asymptotes are π units apart: f(x)=tanx.
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Complete question:
What are the key features of the graphs of the trigonometric functions?
Select all correct trigonometric functions.
The function's period is 2π.
f(x)=sinx
f(x)=cosx
f(x)=tanx
The function's asymptotes are π units apart.
f(x)=sinx
f(x)=cosx
f(x)=tanx
The function has a maximum value of 1.
f(x)=sinx
f(x)=cosx
f(x)=tanx
3. A double coconut can grow for 10 years and have a mass of 20. 0 kg. If a 20. 0 kg double coconut oscillates on a spring 42. 7 times each minutewhat is the spring constant of the spring?
If a 20. 0 kg double coconut oscillates on a spring 42. 7 times each minute, then the spring constant of the spring is 689 N/m.
The spring constant, also known as the force constant or stiffness, is a measure of the elasticity of a spring or any other elastic object. It is defined as the force required to stretch or compress a spring by a unit distance.
The period of oscillation of the coconut can be calculated as:
[tex]T = \frac{60}{42.7} = 1.405[/tex] seconds
The mass of the coconut is 20.0 kg, so we can use the formula for the period of oscillation of a mass on a spring:
[tex]T=2\pi \sqrt{\frac{m}{k}}[/tex]
where m is the mass of the coconut and k is the spring constant.
Rearranging this formula gives:
[tex]k = (2\pi)^2 *(\frac{m}{T})^2[/tex]
Substituting the values we have:
[tex]k = (2\pi)^2 *(\frac{20.0}{1.405})^2[/tex]
k = 689 N/m (to three significant figures)
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Round the answers to three decimal places Part 1 of2 (a) Find P(5) P(5)- Part 2 of2 (b) Find P(More than 3) P(More than 3)
(a) n = 10, p = 1/4, and x = 5. Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)
(b) P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)
Here n = 10, p = 1/4, and x = 5.Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)
Find P(More than 3)For this, we need to calculate P(4), P(5), P(6),...,P(10) and add them.Using the formula of binomial probability function,P(4) = 10C4 * (1/4)^4 * (3/4)^6 = 0.2503 (rounded to three decimal places)P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)P(6) = 10C6 * (1/4)^6 * (3/4)^4≈ 0.0014 (rounded to three decimal places)P(7) = 10C7 * (1/4)^7 * (3/4)^3≈ 0.0001 (rounded to three decimal places)P(8) = 10C8 * (1/4)^8 * (3/4)^2≈ 0.0000 (rounded to three decimal places)P(9) = 10C9 * (1/4)^9 * (3/4)^1≈ 0.0000 (rounded to three decimal places)P(10) = 10C10 * (1/4)^10 * (3/4)^0≈ 0.0000 (rounded to three decimal places)P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)
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I need some help with this
the solid is really just a right-cylinder missing a chunk.
so a full circle is 360°, now from the one in the picture above we're missing 90°, that means the cylinder is only using 270°, 360-90=270.
Well, 270° is just 3/4 of a full circle, and since the circle extends all the way down the solid cylinder, we can also say that's 3/4 of the volume of the cylinder, so hmmm let's just get the full volume of the cylinder with a radius of 6 and a height of 12 and then only grab 3/4 of it.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2(12)\implies V=432\pi \\\\\\ \stackrel{\textit{now let's just grab }\frac{3}{4}}{432\pi \cdot \cfrac{3}{4}}\implies 324\pi ~~ \approx ~~ \text{\LARGE 1017.88}[/tex]
Write an equation for the line on the graph below.
Pleaseee Helppp I'm sick and my brain cells are dying.
Answer: y = 4, hope you feel better
Step-by-step explanation:
AP STATS
Burping (also known as "belching" or "eructation") is one way the human body expels excess gas in your digestive system. It occurs when your stomach fills with air, which can be caused by swallowing food and liquids. Drinking carbonated beverages, such as soda, is known to increase burping because its bubbles have tiny amounts of carbon dioxide in them.
As an avid soda drinker and statistics student, you notice you tend to burp more after drinking root beer than you do after drinking cola. You decide to determine whether there is a difference between the number of burps while drinking a root beer and while drinking a cola. To determine this, you select 20 students at random from high school, have each drink both types of beverages, and record the number of burps. You randomize which beverage each participant drinks first by flipping a coin. Both beverages contain 12 fluid ounces. Here are the results:
Part A: Based on these results, what should you report about the difference between the number of burps from drinking root beer and those from drinking cola? Give appropriate statistical evidence to support your response at the α = 0.05 significance level.
Part B: How much of a difference is there when an individual burps from drinking root beer than from drinking cola? Construct and interpret a 95% confidence interval.
Part C: Describe the conclusion about the mean difference between the number of burps that might be drawn from the interval. How does this relate to your conclusion in part A?"
The mean number of burps after drinking root beer is between 0.66 and 4.24 burps fewer than after drinking cola.
What is the definition of a mean number?Mean: The "average" number obtained by adding all data points and dividing the total number of data points by the total number of data points.
Part A: A paired t-test can be used to see if there is a significant difference in the number of burps after drinking root beer versus cola. The null hypothesis states that there is no difference in the mean number of burps between the two beverages, whereas the alternative hypothesis states that there is. Using a two-tailed test with a significance level of = 0.05, we find that the t-value is -3.365 and the p-value is 0.003. We reject the null hypothesis because the p-value is less than the significance level and conclude that there is a significant difference in the mean number of burps between root beer and cola.
Part B: We can use the paired t-test formula to generate a 95% confidence interval for the difference in the mean number of burps between root beer and cola:
(xd - d) / (sd / n) t
where xd represents the sample mean difference, d represents the hypothesised population mean difference (which is 0), sd represents the sample standard deviation of the differences, and n represents the sample size.
We calculate the sample mean difference to be -2.45 and the sample standard deviation of the differences to be 2.69 using the data in the table. We get a t-value of -3.365 with 19 degrees of freedom after plugging in these values. The critical t-value for a 95% confidence interval with 19 degrees of freedom is 2.093, according to a t-distribution table.
As a result, the 95% CI for the true difference in the mean number of burps between root beer and cola is (-4.24, -0.66). This means that we are 95% certain that the true population mean difference is within this range.
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