An equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment is y = 9.65x + 2.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (50.25 - 2)/(5 - 0)
Slope (m) = 48.25/5
Slope (m) = 9.65.
At data point (0, 2) and a slope of 9.65, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 2 = 9.65(x - 0)
y = 9.65x + 2
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solve all four parts
The rocket will hit the ground after 19.09 seconds.
How to calculate projectilea) The height of the rocket can be describe as:
h(t) = -16t² + 210t + 75
where
t = time in seconds
h(t) = height of the rocket in feet
b) To find the time at which the rocket reaches its maximum height, we need to find the vertex of the parabolic function. The vertex is given by the formula:
t = -b/(2a)
where
a = -16
b = 210
Substituting these values, we get:
t = -210/(2(-16)) = 6.5625 seconds
To find the maximum height, we substitute this value of t back into the equation for h(t):
h(6.5625) = -16(6.5625)² + 210(6.5625) + 75 = 690.625 feet
This means that the rocket reaches its maximum height of 690.625 feet after 6.5625 seconds.
c) We need to find the time interval during which the height of the rocket is greater than 721 feet. We set the height function h(t) greater than 721 and solve for t:
-16t² + 210t + 75 > 721
-16t² + 210t - 646 > 0
Solving for t using the quadratic formula, we get:
t < 2.975 or t > 14.038
Therefore, the rocket will be more than 721 feet above ground level between 0 and 2.975 seconds, and between 14.038 and infinity seconds.
d) To find the time at which the rocket hits the ground, we set h(t) equal to 0 and solve for t:
-16t² + 210t + 75 = 0
Solving for t using the quadratic formula, we get:
t = [tex]\frac{-b \± \sqrt{b^{2} - 4ac } }{2a}[/tex]
a = -16, b = 210, c = 75
t = [tex]\frac{-210 \± \sqrt{210^{2} - 4(16)(75) } }{2(-16)}[/tex]
t = [tex]\frac{-210 \± \sqrt{22225} }{-32}[/tex]
t = [tex]\frac{-210 \± 149}{-32}[/tex]
t = 2.53125 or t = 13.53125
Since the rocket was launched from the top of a 75-foot building, it will hit the ground after an additional time of:
t + 2.53125 = 5.09375 seconds or t + 13.53125 = 19.09375 seconds
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Which function does the dotted line represent explain how do you know
Answer:
Step-by-step explanation:
An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
Electronics store reduced price of tv From $900 to $837
The percentage decrease of the TV from $900 to $837 is 7%
Percentage decreaseOriginal price of TV = $900New price of TV = $837Percentage decrease = Difference in price / original price × 100
[tex]=\dfrac{(900-837)}{900} \times 100[/tex]
[tex]=\dfrac{63}{900} \times 100[/tex]
[tex]= 0.07 \times 100[/tex]
[tex]= 7\%[/tex]
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Complete question-
An electronics store reduced the price of a TV from $900 to $837. What was the percent of decrease?
Find the length of the third side. if necessary, round to the nearest tenth of 1 and 3
Using the Pythagorean theorem we know that the third side is 15 units.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b², are equal to the squares on the legs.
To determine c, use the Pythagorean Theorem as follows:
a² + b² = c²
9² + 12² = c²
81 + 144 = c²
225 = c
c² = 225
c = √(225)
c = 15
Therefore, using the Pythagorean theorem we know that the third side is 15 units.
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Correct question:
Find the length of the third side. If necessary, round to the nearest tenth.
12 and 9
. A and B completed a work together in 5 days. Had A worked at twice the speed and B at half the
speed, it would have taken them four days to complete the job. How much time would it take for
A alone to do the work
So it would take A 10 days to do the whole job alone.
What is equation?An equation is a statement that asserts the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in a variety of mathematical contexts, including algebra, calculus, and geometry, as well as in physics, engineering, and many other fields.
Here,
Let's denote A's speed as "a" and B's speed as "b" (in units of work per day). Then, we know that:
In 5 days, A and B together completed the job, so we can write: 5(a + b) = 1 (where 1 represents the whole job).
If A worked at twice the speed (2a) and B worked at half the speed (0.5b), then they would complete the job in 4 days, so we can write: 4(2a + 0.5b) = 1.
We can simplify the second equation by multiplying out the brackets and collecting like terms:
8a + 2b = 1
Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other, and substitute the result into the other equation to find the value of the remaining variable. Let's solve for "b" in terms of "a" from the first equation:
5(a + b) = 1
5b = 1 - 5a
b = (1/5) - a
Now we can substitute this expression for "b" into the second equation:
8a + 2b = 1
8a + 2((1/5) - a) = 1
8a + (2/5) - 2a = 1
6a = (3/5)
a = (1/10)
So A can do 1/10 of the job in one day. To find out how long it would take A to do the whole job alone, we can use the formula:
time = amount of work / rate
Since A can do the whole job alone, the amount of work is 1, and A's rate is 1/10. Therefore:
time = 1 / (1/10)
= 10 days
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In the diagram, AB, BC and CD are three sides of a regular polygon F
A
a) Work out the size of angle y.
square polygon P
B
D
square
regular 12-sided polygon
y z
b) Work out the size of angle z.
c) What is the name of polygon P?
Answer:
Step-by-step explanation:
The size of each interior angle of the polygon is 4x+28 °
The value of x is 34 degree and y is 56 degree.
What is a Tangent?Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.
here, we have,
We have, BOA is an isosceles triangle.
< CBO = 90°
So, < DBO = 90 - 56
<DBO = 34
and, <ODB = 34°
Now, let the angle ODB be x
As, from the figure < EBD is also 90°
So, <y = 180 - (90+34) (Angle sum property)
<y = 56
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complete question:
Work out the size of angle x and work out the size of angle y
Water flows from the bottom of a storage tank. After t minutes, the water is flowing at a rate of r(t)=200-4t liters per
minute, where 0≤t<50. Find the amount of water (in liters) that flows from the tank between the 7 minute mark and the
37 minute mark.
The total amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark is 720 liters.
What is rate of flow?The amount of fluid that moves through a pipe or other container over a given amount of time.
The amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark can be calculated using the equation for the rate at which the water is flowing.
Given that the rate at which the water is flowing at time t is r(t)=200-4t liters per minute and that 0≤t<50, the total amount of water that flows from the storage tank between the 7 minute mark and the 37 minute mark can be calculated as follows:
Total amount of water = ∫r(t)dt
= ∫(200 - 4t)dt
= (200t - 4t²)
= (200(37) - 4(37²)) - (200(7) - 4(7²))
= 1924 - 1204
= 720 liters
The rate of flow decreases linearly with time, which means that the total amount of water flowing from the tank at any given time is equal to the area under the graph of the rate of flow.
This means that the total amount of water that flows from the tank between the 7 minute mark and the 37 minute mark can be calculated by integrating the rate of flow function over the given time interval.
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Suppose that the function h is defined as follows.
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the five definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = -3 between x = -2.5 and x = -1.5.y = -2 between x = -1.5 and x = -0.5.y = -1 between x = -0.5 and x = 0.5.y = 0 between x = 0.5 and x = 1.5.y = 1 between x = 1.5 and x = 2.5.More can be learned about piece-wise functions at brainly.com/question/19358926
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N Heracio's Computer Time Shopping Research 10% Videos 15% Homework 20% Games 20% Social dia 25% Heracio used the computer a total of 40 hours last week. How many more hours did Heracio use the computer to do homework than shop online?
Heracio used the computer 4 more hours to do homework than shop online.
How to solve the proportionTo find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.
Let's start by calculating the number of hours Heracio spent on each activity:
Shopping: 10% of 40 hours = 4 hours
Videos: 15% of 40 hours = 6 hours
Homework: 20% of 40 hours = 8 hours
Games: 20% of 40 hours = 8 hours
Social media: 25% of 40 hours = 10 hours
Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:
8 hours (homework) - 4 hours (shopping) = 4 hours
Therefore, Heracio used the computer 4 more hours to do homework than shop online.
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Where will X be after a rotation 90° clockwise about (-5,-1)?
Click on the grid to place the point.
The image point of the coordinate X after the rotation is (-1, 5).
Calculating the image point of the coordinate XWhen a point is rotated 90° clockwise around the origin, the new point will be formed by switching the x and y-coordinates and then negating the new x-coordinate.
So for point X (-5, -1), the new x-coordinate will be -1, and the new y-coordinate will be -(-5) = 5, giving the new point (-1, 5).
Therefore, after a rotation of 90° clockwise, point X (-5, -1) will be at the new location (-1, 5).
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A movie theater considers upgrading to offer luxury seating. The manager randomly surveys 1,200 resident who live within 10 miles of the theater. What is the sample in the situation
Please it’s due in 2min
In this circumstance, the sample consists of 1,200 inhabitants living within a ten-mile radius of the movie theater that were selected for random deliberation by the overseer.
What is a sample?Samples are frequently utilized to gain information concerning a larger population through the study of a single set of individuals or objects. The aim of selecting a sample is to inspect the populace by delving into a representative, relatively small group.
Surveys, polls, and experiments often utilize samples to make evidence-based inferences regarding the target population. For exact and dependable results, an instance should be randomly chosen, accurately mirroring those present in the whole population so as to reduce prejudice and fully optimize the evaluation.
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the probability of rolling a 4 or an even number of the die is thrown 2 times. (6 sided dice)
The probability of rolling a 4 on a single throw of a fair 6-sided die is 1/6, since there is only one way to roll a 4 and there are 6 equally likely outcomes in total.
The probability of rolling an even number on a single throw of a fair 6-sided die is 3/6, or 1/2, since there are three even numbers (2, 4, and 6) out of six possible outcomes.
To find the probability of rolling a 4 or an even number on a single throw, we can add the probabilities of these two events:
P(4 or even) = P(4) + P(even) - P(4 and even)
where P(4 and even) is the probability of rolling a 4 and an even number on the same throw. Since there is only one outcome (rolling a 4), which is not even, this probability is 0.
Therefore:
P(4 or even) = P(4) + P(even) - P(4 and even)
= 1/6 + 1/2 - 0
= 2/3
So the probability of rolling a 4 or an even number on a single throw of a 6-sided die is 2/3.
If the die is thrown 2 times, the probability of rolling a 4 or an even number on both throws is the product of the probabilities of rolling a 4 or an even number on each throw:
P(4 or even on both throws) = P(4 or even) × P(4 or even)
= (2/3) × (2/3)
= 4/9
Therefore, the probability of rolling a 4 or an even number on both throws of a 6-sided die is 4/9.
Which fraction is a multiple of 1/9?
Unit fractions are the fraction in which the value of numerator is 1. The multiple of the given fraction are,
1/9 = 2/9, 3/9, 4/9,5/9 ......so on.
Here, we have,
To find the multiple of the fraction 1/9 we need to know about the multiple of fraction.
We have,
Multiple of fraction is the number which is n times of the original function. Here can be any whole or fraction number.
The given number in the problem is the fraction number which is,
The above number is the unit fraction.
Unit fraction-
Unit fractions are the fraction in which the value of numerator is 1.
The multiple of unit fraction is in times the original function. For the given fraction the multiple fraction can be given as,
1/9 = 2/9, 3/9, 4/9,5/9 .......so on.
Hence the multiple of the given fraction are,
1/9 = 2/9, 3/9, 4/9,5/9 ......so on.
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helpppp helppppp helppppp
Answer:
No, i do not believe i have learned this yet so good luck bestiee
Graph the linear equation y=-3x-1
Answer:
Step-by-step explanation:
y=-3x-1
format for formula:
y=mx+b
b=1 that is your y-intercept. where it hits the y-axis
m= -3 this is your slope [tex]\frac{rise}{run} =\frac{-3}{1}[/tex]
from a point you have, the y-intercept, you go down 3 (because of the negative in front of it), this is your rise,
and to the right 1, this is your run
If someone wants to call Havana, Cuba from the United States (US) begins with US three-digit exit code 011 followed the two-digit country code for Cuba is 53, followed by the county code of Havana is 7 and finally by seven-digit local telephone numbers. But this seven-digit local telephone numbers cannot begin with 0. How many different telephone numbers are possible?
Answer:
9000000 different numbers---------------------------
The number is basically a combination in the form of:
abcdefg, where a can't be zero but the rest of the digits have no restrictionsHence the possible digits:
a = 9, b,c,d,e,f,g = 10So possible telephone number combinations:
9*10⁶ = 9000000Help please
Expand the logarithm as much as possible
logy^10
Answer: 2.303
Explanation: In image
-(9-6)+(-1-2)-(3+4)+(5-6)=
Answer:
Step-by-step explanation:
-9+6-1-2-3-4+5-6
-3-3-7-1
-6-8
-14
Answer:
The answer is -14.
Step-by-step explanation:
-(9 - 6) + (-1 -2) - (3 + 4) + (5 - 6)
Subtract 6 from 9 to get 3.
-3 -1 -2 - (3 + 4) + 5 - 6
Subtract 1 from -3 to get -4.
-4 - 2 - (3 + 4) + 5 - 6
Subtract 2 from -4 to get -6.
-6 - (3 + 4) + 5 - 6
Add 3 and 4 to get 7.
-6 - 7 + 5 - 6
Subtract 7 from -6 to get -13.
-13 + 5 - 6
Add -13 and 5 to get -8.
-8 - 6
Subtract 6 from -8 to get -14.
-14.
WILL AWARD BRAINLIEST!!
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm
Answer:
351 cm^3
Step-by-step explanation:
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm
ChatGPT
Let AB = BC = x be the base of the isosceles triangle ABC. Then, the third side AC is:
AC = 2x * sin(35°)
Using the sine rule in triangle ABA, we have:
AB / sin(50°) = 18 / sin(80°)
Solving for AB, we get:
AB = 18 * sin(50°) / sin(80°)
The height of the prism is AB * cos(35°). Therefore, the volume of the prism is:
V = (1/2) * x^2 * 2x * sin(35°) * AB * cos(35°)
Substituting the values we have calculated, we get:
V = (1/2) * x^2 * 2x * sin(35°) * [18 * sin(50°) / sin(80°)] * cos(35°)
V ≈ 351 cm^3
Therefore, the volume of the prism is approximately 351 cubic centimeters.
The components of v = 210i + 300i represent the respective number of gallons of regular and premium gas sold at a station. The components of w = 2.8i + 2.99i represent the respective prices per gallon for each kind of gas. Find Vw and describe what the answer means in practical terms.
The station earned $1485 in revenue from selling the gas.
In this problem, we are given two vectors, v and w, representing the number of gallons of gas sold at a station and the corresponding prices per gallon, respectively. We are asked to find the dot product of these two vectors, which is a scalar quantity known as the "Vw". We will then interpret the meaning of this dot product in practical terms.
To find the dot product of v and w, we will use the formula:
Vw = v . w = (210)(2.8) + (300)(2.99)
Vw = 588 + 897 = 1485
Therefore, the value of Vw is 1485.
Practical terms: The dot product of two vectors is a scalar quantity that represents the "projection" of one vector onto the other. In this case, the dot product Vw represents the total revenue earned by selling regular and premium gasoline at the given station.
The components of v represent the number of gallons of regular and premium gas sold, while the components of w represent the respective prices per gallon for each kind of gas. Multiplying the number of gallons sold by the price per gallon gives the total revenue earned for each type of gas. Adding these two values together gives the total revenue earned for both types of gas.
Therefore, the dot product Vw represents the total revenue earned by selling all the gas at the given station. In practical terms, this means that the station earned $1485 in revenue from selling the gas.
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Select all equations that have infinitely many solutions
2nd and 4th is correct. Hope you got it!
Part 1
For the experiment of rolling a single fair die, find the probability of being even or divisible by 3.
The probability of rolling an even or divisible by 3 numbers is 2/3
When a single fair die is rolled, there are six possible outcomes:
1, 2, 3, 4, 5, or 6.
Of these outcomes, three are even (2, 4, and 6) and two are divisible by 3 (3 and 6). However, since the number 6 is both even and divisible by 3, we must count it only once to avoid overcounting. Thus, four outcomes are either even or divisible by 3: 2, 3, 4, and 6.
The probability of rolling an even or divisible by 3 number is the sum of the probabilities of these four outcomes, which is:
P(even or divisible by 3) = P(2) + P(3) + P(4) + P(6)
= 1/6 + 1/6 + 1/6 + 1/6
= 4/6
= 2/3
Therefore, the probability of rolling an even or divisible by 3 numbers is 2/3
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find the area of the shaded region
The area of the shaded region is 51.75 in².
From the figure
Radius of semicircle = √25² - 20²
=√625- 400 = 15 inch
Now, Area of Trapezium = 1/02 ( a +b ) h
= 1/2 (17 + 37) x 15
= 1/2 (54) x 15
= 27 x 15
= 405 in²
Then, Area of Shaded region
= Area of Trapezium - Area of semicircle
= (405 - πr²)
= 405 - 353.25
= 51.75 in²
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How do you find area?
The area of a shape is calculated by calculating the amount of space on the shape
How do you find area?By definitinon, the area of a shape is the amount of space on the shape
using the above as a guide, we have the following:
Area of rectangle = Length * WidthArea of square = Length²Area of triangle = 1/2 * base * heightArea of circle = π * radius²Area of parallelogram = base * heightThere are several formulas to calculate area
The formula to use is dependent on the shape whose area is being calculated
This means that the area of trapezoid cannot be calculated using the area of parallelogram
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Suppose the probability density function of a random variable X is
f(x)=[tex]\left \{ {{cx^{2}, 1\leq x\leq 2 } \atop {0, else}} \right.[/tex]
a. Find the value of constant c
b. Find the value of P(X>3/2)
The value of,
constant c is 3/7 andP(x>3/2) is 27/18Given function f(x) = cx for 1 ≤ x ≤ 2
a) To find the value of constant x, we have to use the following p.d.f condition as shown below,
[tex]\int\limits^a_b {x} \, dx =1[/tex]
here, a is -∞ and b is ∞.
From the above condition to find the value of c,
[tex]\int\limits^2_1{cx^2} \, dx[/tex] = 1
c * [[tex]\frac{x^3}{3}[/tex]]²₁ = 1
c * [8/3 - 1/3] = 1
c * 7/3 = 1
c = 3/7.
b) To find the value of P(x>3/2) we have to substitute the value of 3/2 in the given expression of f(x) = 3/7 * x²
f(3/2) = 3/7 * (3/2)²
= 3/7 * 9/4
= 27/28.
From the above solution, we solved both problems.
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Element X decays radioactivity with a half-life in 10 minutes if there are 660 g of element X how long to the nearest 10th of a minute would it take for the element to decay to 58 g
Step-by-step explanation:
58 g = 660 g * ( 1/2)^n
58 / 660 = (1/2) ^n LOG both sides
-1.056 = n log 1/2
n = 3.508 half lives
3. 508 x 10 min = ~ 35.1 min
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill & 58\\ P=\textit{initial amount}\dotfill &660\\ t=minutes\dotfill &t\\ h=\textit{half-life}\dotfill &10 \end{cases} \\\\\\ 58 = 660\left( \cfrac{1}{2} \right)^{\frac{t}{10}} \implies \cfrac{58}{660}=\left( \cfrac{1}{2} \right)^{\frac{t}{10}}\implies \cfrac{29}{330}=\left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t}[/tex]
[tex]\log\left( \cfrac{29}{330} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t} \right]\implies \log\left( \cfrac{29}{330} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}} \right] \\\\\\ \cfrac{ ~~ \log\left( \frac{29}{330} \right) ~~ }{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{10}} \right]}=t\implies 35.1\approx t[/tex]
In congress, each of the 50 states is represented by 2 senators. If you choose a senator randomly, what is the probability that you will choose a senator that represents Georgia, South Carolina, and Florida?
The probability of picking a senator from at least one out of Georgia, South Carolina, or Florida is equal to 3/50 or 0.06.
How to find the probabilityDetermining the probability of selecting a senator from either Georgia, South Carolina, or Florida is merely a summation of the individual probabilities of drawing one from each state.
There are 100 senators in all and two representatives from each region, thus resulting in an addition of 2 x 50 which equals to 100 senators altogether.
Subsequently, selecting a senator from Georgia has a chance of 1/50,
1/50 + 1/50 + 1/50 = 3/50
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Jerome buys 4 pints of milk for the baby goats and has pint of milk left from yesterday. If each baby goat gets pint of milk, how many goats can Jerome
feed?
Jerome can feed (blank) baby goats.
Answer:
5 baby goats
Step-by-step explanation:
4 + 1 = 5 pints total
each baby goat gets 1 pint
The National Academy of Science reported in a 1997 study that 40% of research in mathematics is published by U.S. authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 40%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 130 recent articles published by reputable mathematics research journals and finds that 62 of these articles have U.S. authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 40%? Use a 0.05 level of significance.
There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
How to test for the evidenceTo test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.
Let p be the true proportion of mathematics research published by U.S. authors.
The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).
sample proportion, x/n = 62/130 = 0.477
The test statistic for a two-tailed test is given by:
z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)
= 2.41
Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.
Since 0.016 < 0.05
, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
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Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 109, x = 65; 88% confidence
Rounding to three decimal places, the confidence interval is (0.419, 0.574).
How can a confidence interval for a sample proportion be created?The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.
Confidence interval=proportion±margin of error
CI = p ± ME
The proportion is:
p = x / n
p = 55/110
p = 0.5
Margin of error=critical value × standard error
ME = CV × SE
n > 30, so we can approximate CV with a normal distribution.
At P=88%, CV=1.55.
SE = √(pq / n)
SE = √(0.5 (1−0.5)/110)
SE = 0.048
So the margin of error is:
ME = 1.55 × 0.048
ME = 0.074
So the confidence interval is:
CI = 0.5 ± 0.074
CI = (0.426, 0.574)
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Question:
Use the given degree of confidence and Sample data to construct income confidence interval for the population proportion p. n=110, x=55; 88% confidence
A) 0.426 B)0.442 C)0.425 D)0.421