To be 95% confident that the true proportion is calculated to within 2%, 62 voters must be questioned.
Given,
A pollster wishes to estimate the true proportion of US. voters who oppose capital punishment.
We have to find the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%
Here,
To obtain the sample size,
n = z² pq / ME²
Where,
P is the proportion of voters
M. E is the margin of error.
q is the proportion of non-voters
z is the corresponding z score
The z score for the 95% confidence interval is 1.96.
n = 1.96² pq / 0.05²
n = 1536.64 pq
If 0.2 is the proportion of voters, then 0.2 is the fraction of non-voters.
n = 1536.64 pq = 61.42
≈ 62 voters
Therefore,
62 voters can be surveyed in order to be 95% confident that the true proportion is estimated to within 2%
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a general term for a sample selected in accordance with probability theory, which ensures that every person in the population has an equal chance of being selected for the sample, is known as
A general term for a sample selected in accordance with probability theory, which ensures that every person in the population has an equal chance of being selected for the sample, is known as Probability sampling.
A probability sampling method is an any method of sampling that utilizes some from of random selection. Probability sampling refers to the selection of a sample from a population, when the selection is based on the principle of randomization, that is random selection or chance.
In simple random sampling each sampling unit of a population has an equal chance of being included in the sample. Consequently, each possible sample also has an equal chance of being selected.
The advantage of simple random sampling is that it does not require any information on the survey frame other than the complete list of units of the survey population along with contact information. In a simple random sample, every number of the population has an equal chance of being selected.
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Taylor Swift is having 2 concerts at the same venue on Friday and
Saturday nights. On Friday, the ratio of the number of tickets sold to the
number of tickets still available is 5 to 3. On Saturday night, the ratio of the
number of tickets that were sold to the number of tickets available was
7:1. If 1,300 tickets were still available for the Saturday night concert, How
many tickets were sold for the Friday night concert?
Answer:
When using raitos you want to do P=2 +2+2+2
P=8
when L equals Ochoa
what will the answer be?
B2 + 62 + 25 gives us 169 - 25 and that gives us C Ronaldo
Step-by-step explanation:
Hope this helped! :)
determine if the following functions are increasing or decreasing 
Answer:
D both are decreasing
Step-by-step explanation:
In both, as x is increasing, y is decreasing.
Alan and Jorge are selling popcorn to earn money for a school trip.
Alan's popcorn sales can be represented by the equation y=2x, where x is the number of bags of popcorn sold and y is the amount of money raised.
Jorge's popcorn sales can be represented by this graph.If both boys sell the same amount of popcorn, who will raise the most money? Why?
Select the answer that is entirely correct.
Responses
Jorge will raise more money because he is selling the popcorn for $3 per bag, and Alan is selling the popcorn for $2 per bag.
Jorge will raise more money because he is selling the popcorn for 3 dollars per bag, and Alan is selling the popcorn for 2 dollars per bag.
Alan will raise more money because he is selling the popcorn for $3 per bag, and Jorge is selling the popcorn for $2 per bag.
Alan will raise more money because he is selling the popcorn for 3 dollars per bag, and Jorge is selling the popcorn for 2 dollars per bag.
Jorge will raise more money because he is selling the popcorn at 2 bags for a $1, and Alan is selling the popcorn at 3 bags for $1.Jorge will raise more money because he is selling the popcorn at 2 bags for a 1 dollars and Alan is selling the popcorn at 3 bags for
Alan will raise more money because he is selling the popcorn at 2 bags for a $1, and Jorge is selling the popcorn at 3 bags for $1.Alan will raise more money because he is selling the popcorn at 2 bags for a 1 dollars and Jorge is selling the popcorn at 3 bags for
The answer that is entirely correct based on the sales of popcorn is;
A: Jorge will raise more money because he is selling the popcorn for $3 per bag, and Alan is selling the popcorn for $2 per bag.
How to interpret Linear Equations?
The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, For Alan, we are told that her popcorn sales can be represented by the equation; y = 2x
where;
x is the number of bags of popcorn sold.
y is the amount of money raised.
Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $2
Now, for Jorge, looking at the graph, we can see that;
y -intercept = 0
Slope = (15 - 6)/(5 - 2)
Slope = 3
Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $3.
Looking at the options, the correct one are Options A,
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Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x=98.13, y=100.6, r=0.904, P-value=0.000, ŷ=14.68+0.88x, where x represents the IQ score of the twin born first. Find the best predicted value of ModifyingAbove y with caret given that the twin born first has an IQ of 104? Use a significance level of 0.05.
The predicted value of the twin born first has an IQ of 104 is 106.2..
We have given that,
sample size n = 10
x = 98.13
y = 100.6
r = 0.904
p-value = 0.000
y'= 14.68 + 0.88x
significance level = 0.05
and we have to find predicted value of the twin born first has an IQ of 104.
We know that x represents the IQ score of the twin born first.
Therefore value of x is 104.
Hence the predicted value P will be,
P = 14.68 + 0.88(104)
= 14.68 + 91.52
P = 106.2
Therefore the best predicted value of the twin born first has an IQ of 104 is 106.2.
The positive predicted value is the probability that a test gives result for a true statistic. The negative predictive value is the probability that a test gives a false result for a false statistic.
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how many numbers less than 2017 are both the sum of two consecutive positive integers, and the sum of five consecutive positive integers?
201 numbers are less than 2017
If and only if it is odd, a number is the sum of two successive integers.
Only if it is a multiple of 5 is a number considered to be the sum of 5 consecutive integers. If you have any doubts, remember that the product of five consecutive integers equals five times the integer in the middle (this remains true if instead of 5 you put in any odd positive integer).
Consequently, you are seeking odd multiples of 5 below 2017. There are 403 multiples of 5 immediately below 2017, or 2015/5. Of those, 202 are odd. It is necessary to eliminate the number 5 because it is not completely positive when expressed as the sum of its successive integers, which is (-1)+0+1+2+3.
There are 201 numbers left.
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Find the gradient vector field of f. f(x, y) =xe9xy
The gradient vector field of function f(x,y) is given as follows:
grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.
The gradient vector field of a function
Suppose that a function defined as follows:
f(x,y).
The gradient function is defined considering the partial derivatives of function f(x,y), as follows:
grad(f(x,y)) = fx(x,y) i + fy(x,y) j.
The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.
In which:
fx(x,y) is the partial derivative of f relative to variable x.
fy(x,y) is the partial derivative of f relative to variable y.
The function in this problem is defined as follows:
f(x,y) = xe^(9xy).
The partial derivative relative to x as follows:
fx(x,y) = e^(9xy) + 9xye^(9xy) = (1 + 9xy)e^(9xy).
The partial derivative relative to y as follows:
fy(x,y) = 9x²e^(9xy).
Hence the gradient vector field of the function is defined as follows:
grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.
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Y is inversely proportional to the square of x. If Y = 3 when x = 2, find Y, when x is 1.
Answer:
Y=K1/x
K=6
Y=6
that's the process the answer is 6
HELP MEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!
find formula for growth of city
y intercept of 300,000 because the function starts here
the slope is 1.08 because it grows by 8 percent each year
population at x year = 300,000(1.08)^x
you can better understand why the x is in the exponent by this example
in one year, it grows 8 percent
300,000 * 1.08 = 324,000
the next year, that previous year grows 8 percent
324,000 * 1.08 = 349,920
300,000 * 1.08 * 1.08 =349,920
300,000 * 1.08^2 = 349,920
in 2 years it grows to that
just do it to the 14th power now
300,000 * 1.08^14 = 881,158
hope this helps :)
if you got any questions just comment
Overview
Question Progress
Here is a list of numbers.
-45 -21
-16
12 33 40
11
a) Write down two numbers from the list that add up to -9.
c) Work out the sum of all the numbers in the list.
12 13 14
b) Write down two numbers from the list that have a difference of 29.
-21 + 12
Answer:
Step-by-step explanation:
fly
the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal. what is the square of the ratio of the short side to the long side of this rectangle?
As per the Pythagoras theorem, the ratio of the short side to the long side of this rectangle is (√5 - 1)/ 2
In math Pythagoras theorem is defined as the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
Here we have given that the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal.
And we need to find is the square of the ratio of the short side to the long side of this rectangle
While we looking into the given question we have identified that the short side of the rectangle be a and let the long side of the rectangle be b.
Therefore, the diagonal, according to the Pythagorean Theorem, is
√(a²+b²)
Now we can write the equation:
a / b = b /√ a² + b²
Then we have to find the square of the ratio of a to b.
Let us consider the answer, be k.
When we squaring the above equation,
a²/ b² = b² / a² + b² = k
When we solve this one then we get the value of k = 1.
Now we have to Multiply each side of the equation by k,
=> k² = 1 - k.
And then adding each side by k,
k² + k − 1 = 0.
Now, we have to Solving for k using the Quadratic Formula,
= > k = -1 ± √[1² − 4(1)(−1)] / 2
=> k = -1±√5/2
As we know that the ratio of lengths and diagonals of a rectangle cannot be negative.
Therefore, the resulting value is √5 - 1/2
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write the coordinate of the x-intercept and y-intercept for each linear relationship
To find y-intercept: set x = 0 and solve for y. The point will be (0, y).
To find x-intercept: set y = 0 and solve for x. The point will be (x, 0)
What is slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be shown as
tan θ = Δy/Δx
So, the slope of a line is tan.
When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.
To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.
When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.
To find y-intercept: set x = 0 and solve for y. The point will be (0, y).
To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).
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Find the general solution of the given differential equation.
(x + 1) dy/dx + (x + 2)y = 2xe?x
y=
Give the largest interval I over which the general solution is defined. (Think about the implications of any singular points.)
(??, ?)
(0, 1)
(?1, ?)
(0, ?)
(??, 1)
The general solution of the given differential equation is y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2) and the largest interval is (-infinity, -2) U (-1, infinity).
The general solution of the mentioned differential equation will be calculated as follows -
Firstly rewriting the differential equation in standard form:
(x+1) dy/dx + (x+2)y = 2x[tex] {e}^{(xy)} [/tex]
Calculating the integrating factor to make the LHS as a total derivative:
As known, formula for integrating factor is:
mu = [tex] {e}^{(integral of (x+2)/(x+1) dx)} [/tex]
= [tex] {e}^{(ln(x+1) + ln(x+2))} [/tex]
= (x+1)(x+2)
Now multiplying both sides of the equation by the integrating factor:
(x+1)(x+2) × (x+1) dy/dx + (x+1)(x+2) × (x+2)y = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)
LHS will be a total derivative. Rearrange the equation for the same -
d/dx((x+1)(x+2)y) = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)
Integrating both sides of the equation:
(x+1)(x+2)y = integral of 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2) dx
= 2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C
Now find the equation for y:
y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2)
Equation for y is the general solution of the differential equation where constant C is the arbitrary constant of integration.
The general solution is not defined at the position x=-1 and x=-2. Hence, the largest interval over which the general solution is defined is (-infinity, -2) U (-1, infinity).
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how much do national football league players weigh on aerage in a random sample of 50 nfl players the average weight is 244.4 pounds
This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.
This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.
In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.
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Which of the following are the roots of the quadratic equation 3x^2 + 7x + 2 = 0?
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words.
Multiply the expressions.
Answer:
[tex]$\frac{x^{2}+12x-27}{x^{2}-x-6}$[/tex]
Step-by-step explanation:
See picture below :)
let s 5 {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s. must there be two integers whose sum is 15? why?
The given set have two integers whose sum is 15 because if we selcet the element from the given set then there sum is equal to 15.
In the given question, let s = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s.
We have to check there be two integers whose sum is 15.
As we know that,
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The letter Z or the chalkboard Z is frequently used to represent the set of integers in mathematical terminology.
There are total 10 elements.
We have to choose two element from the given set which sum is equal to 15.
If we choose 3 and 12 then there sum is 15.
Similarly, if select (5,10), (6,9), (7,8) the sum of all these selection is 15.
So the given set have two integers whose sum is 15.
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the+population+of+a+town+is+2500+and+is+decreasing+at+a+rate+of+3%+per+year+5+years
2,092.1 is the population of the town after 5 years, and P(t)=2500*(1-0.035)^t is the exponential function.
What is the exponential decay function?In mathematics, exponential decay defines the process of diminishing an amount by a consistent percentage rate over a period of time.
It can be stated by the formula y=a(1-b)x wherein y is the total form and is the initial money, b is the decay factor, and x is the quantity of time that has passed.
So, we got:
r = 3.5%/100% = 0.035
We have our exponential function:
P(t) = 2500*(1 - 0.035)^t
The number after 5 years is provided by substituting t = 5, we will get:
P(5) = 2500*(1 - 0.035)^5 = 2,092.1
Therefore, 2,092.1 is the population of the town after 5 years, and P(t) = 2500*(1 - 0.035)^t is the exponential function.
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Correct question:
The population of the town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential decay function to find the population of the town after 5 years
$32.75. Find the total cost if the tax is 9.25% and you want to leave an 18% tip.
Answer:About 155 results (0.47 seconds)
Tax and Tip - Illustrative Math Taskshttps://tasks.illustrativemathematics.org
Step-by-step explanation:
this may help
Bryan estimate the cost of a vacation to be $730. The actual cost of the vacation is $850. Find the percent error. Round to the nearest whole percent if necessary. Is the percent positive or negative? Explain.
Answer: 14%
The percentage is positive because the actual cost is a result of the estimated cost increased by 14%
Step-by-step explanation:
Formula
Subtract the actual value from the estimated value
850-730=120
Divide the results from step 1 by the real value
120/850= 0.14117647058*100
Multiply the results by 100 to find the total percentage
0.14117647058*100=14.1176
Round
14%
A particular fungal cell weighs 0.0009 gram. If this weight, in grams, is written in scientific notation as 9 x 10^q , what is the value of q?
Answer:
q = -4
Step-by-step explanation:
0.0009 = 9 × 10^(-4)
q = -4
the ratio 1:4 os equivalent to
Answer:
2/8, 3/12, 4/16 and etc
Step-by-step explanation:
Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number
An object was launched off the top of a building.
The function f(x) = −16x² + 48x + 64
represents the height of the object above the
ground, in feet, a seconds after being launched.
Find and interpret the given function values and
determine an appropriate domain for the
function.
f(-1) =
launched, the object was
above the ground. This interpretation
the problem.
f(0.5)
seconds after the object was
=
meaning that
the problem.
feet
in the context of
, meaning that
seconds after the object was
launched, the object was
above the ground. This interpretation
feet
in the context of
The function f(x) = −16x² + 48x + 64 represents the height of an object above the ground in feet, x seconds after being launched.
How to find f(-1)?To find f(-1), we plug -1 into the function:
f(-1) = −16(-1)² + 48(-1) + 64
= 16 - 48 + 64
= 32
This means that 1 second after the object was launched, it was 32 feet above the ground.
To find f(0.5), we plug 0.5 into the function:
f(0.5) = −16(0.5)² + 48(0.5) + 64
= −16(0.25) + 24 + 64
= −4 + 24 + 64
= 84
This means that 0.5 seconds after the object was launched, it was 84 feet above the ground.
Since the function represents the height of the object above the ground, the domain of the function would be the set of all real numbers x such that x represents the number of seconds after the object was launched.
This would include all positive and negative values of x, since the object could have been launched at any time in the past or future. However, if the problem specifies a specific range of time, then the domain would be limited to that range.
Therefore, the correct answer is as given above
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the sample mean is the point estimator of
the sample mean is the point estimator of μ
Sample Mean:
The Sample Mean is the average mathematical value of a sample’s values. It is a statistical indicator used to analyze various variables over time. Statisticians and researchers obtain it by dividing the total sum of values of all data fragments and then dividing it by the total number of data sets.
Point Estimate:
p=x/
p is the point estimate for the population proportion, x is the number of
successes, n is the sample size
p= + /2
for the population proportion
x= + /2
for the population mean
= − /2
is the margin of error
the sample mean is the point estimator of μ
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In 200920092009, Usain Bolt set the world record for sprinting 100 \text{ m}100 m100, start text, space, m, end text in approximately 9\dfrac359
5
3
9, start fraction, 3, divided by, 5, end fraction seconds.
Find his average speed in meters per second.
Average speed of Usain Bolt is 10.41 m/s.
What is Speed?The distance travelled by an object in relation to the amount of time it takes to travel that distance can be used to define speed. In plainer terms, it is a gauge of how quickly an object moves.
Average speed = (Total distance travelled)/(Total time required)
SI unit of speed is m/s.
Distance Travelled by Usain Bolt = 100m
Time required to travel this distance = [tex]9\frac{3}{5}[/tex] = 48 ⁄ (5 sec)
Average speed = (Total distance travelled)/ (Total time required)
Average speed = 100/ (48/5)
= 500/48
= 10.41 m/s
Therefore, average speed of Usain Bolt is 10.41 m/s.
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describe the relationship between the variables in terms of direction (positive or negative slope), form (a straight line or a curve), and strength (how much the points deviate from a straight line).
The relationship between the variables in terms of direction form and strength.
Given :
the relationship of between the variables in terms of direction ( positive or negative slope ) , form (a straight line or a curve), and strength.
The straight line form with variables is :
y = mx + b is a straight line equation
here x and y are variables
m = slope
b = y - intercept
example :
y = 3x + 3
m = + 3 is a positive slope
y = -2x + 4
here
m = - 2 is a negative slope
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Can someone please help me to convert 2,8hours to hours, minutes and seconds ?
convert 2.8hours to hours, minutes and seconds is 2.8 hours = 2 hours 48 minutes 0 seconds
The conversion of 2.8 hours into hours, minutes and seconds is relatively simple. To begin, we must first convert 2.8 hours into minutes. To do this, we multiply 2.8 by 60, which equals 168 minutes. Now, we need to convert those minutes into hours and seconds. To do this, we divide the 168 minutes by 60, which gives us 2 hours. We then take the remainder, which is 48 minutes, and divide it by 60, which gives us 0 seconds. Therefore, 2.8 hours is equivalent to 2 hours 48 minutes 0 seconds.
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write log7t as a base 2 logarithm. note: if you are using log you need to type it in and use the subscript button on the keyboard. there is no log button.
By using logarithm principles, log₇t in base 2 logarithm equals log₂t/log₂7.
What is logarithm?The most frequent logarithms are common logarithms with a base of 10, binary logarithms with a base of 2, and natural logarithms with a base of e 2.71828. A logarithm is the number of powers that a number must be raised to in order to acquire another number (see Section 3 of this Math Review for more about exponents). The base ten logarithm of 100, for example, is 2, because ten raised to the power of two equals 100: log 100 = 2.
Here,
logₓy=logₐy/logₐx
log₇t=log₂t/log₂7
log₇t in base 2 logarithm is log₂t/log₂7 by the help of properties of logarithm applied.
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a steep mountain is inclined 80 degrees from the horizontal and rises 3400 vertical feet above the surrounding plain. a cable car is to be installed that will travel from a point 990 ft from the base of the mountain to the top. find the shortest length of cable needed.
Answer:
3753.20 ft
Step-by-step explanation:
tan 80° = 3400 ft/x
x = 599.51 ft = distance at ground level from point directly below mountain peek to edge of mountain.
599.51 ft + 990 ft = 1589.51 ft = horizontal distance at ground level from where cable is attached to the ground to the center of the mountain. This is a leg of a right triangle.
3400 ft is another leg of a right triangle.
(1589.51 ft)² + (3400 ft)² = y²
The hypotenuse, y, is the length of the cable.
y = 3753.20 ft
elise buys only soft drinks at the higher price. her demand curve is linear. what is the appropriate compensation?
Elise only purchases the more expensive soft drinks. There is a linear demand curve. The relation is directly proportional is then the suitable compensation.
Explain the relation of directly proportional?The relationship between two values where their ratio equals a constant number is known as a direct proportion and direct variation.It is symbolized by the proportional sign (∝).When the ratio x:y is constant, two values, x and y, are seen to be directly proportional to one another.Linear demand curve
A line reflecting the relationship between both the demand for a good or service and its price is called a linear demand curve. Everyone is aware that sales are inversely correlated with price: the higher the price you ask for an item, and fewer you may anticipate selling.Elise only purchases the more expensive soft drinks. Her supply curve is straight.
Thus, the relation is directly proportional is then the suitable compensation.
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