Step-by-step explanation:
The equation of a circle is usually in the form: [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h, k) is the center and r is the radius. With the information you provided you would have the equation: [tex](x+3)^2+(y-4)^2=16[/tex]. I'm a bit confused by "solve the equation of a circle" do you mean solve for y? if so you would just do
Original Equation:
[tex](x+3)^2+(y-4)^2=16[/tex]
Subtract (x+3)^2 from both sides
[tex](y-4)^2=-(x+3)^2+16[/tex]
Take the square root of both sides
[tex]y-4 = \pm\sqrt{-(x+3)^2+16}[/tex]
add 4 to both sides
[tex]y=\pm(\sqrt{-(x+3)^2+16})+4[/tex]
and then just change the sign to negative or positive depending on what half of the circle you want
Let's take this problem step-by-step:
I will assume that you want the standard form of the equation of the circle:
⇒ standard form: [tex](x-h)^2 +(y-k)^2=r^2[/tex]
(h,k) --> coordinate of circle's center --> (-3,4)r --> length of radius --> 4LEt's plug in the known values
[tex](x-(-3))^2+(y-4)^2 = 4^2\\(x+3)^2+(y-4)^2=16[/tex]
Answer: (x+3)² + (y-4)² = 16
Hope that helps!
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CNA SOMEONE HELP ME
measure of
angle C = 48 degrees, a = 5, b = 9. What is the length
of c to the nearest tenth?
Answer: 6.8
Step-by-step explanation:
By the Law of Cosines,
[tex]c^2 = 5^2 + 9^2 - 2(5)(9)\cos 48^{\circ}\\\\c=\sqrt{5^2 + 9^2 - 2(5)(9)\cos 48^{\circ}}\\\\c \approx 6.8[/tex]
Describe the transformations necessary to transform the blue graph of f(x) into the red graph of g(x)
Transformation is a process that involves either increasing, or decreasing the size of a given object, or changing its orientation to produce an image.
The required transformations are:
i. For graph a - translation.
ii. For graph b - dilation.
Rigid transformation involves a change in the orientation of a given object or resizing of a given object to produce an image. The types of transformation are reflection, translation, rotation, and dilation.
i. Reflection is a type of transformation that requires flipping a given object about a reference point or line.
ii. Translation is a type of transformation that involves moving an object in a particular direction without a change in its size and orientation.
iii. Rotation is a type of transformation that involves turning an object at a given angle about a reference point.
iv. Dilation is a type of transformation that require increasing or decreasing the size of the object using a given factor.
Therefore the necessary transformation to transform the blue graph of f(x) into the red graph of g(x) is:
a. For graph a is translation.
b. For graph b is dilaton.
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What is the area of this polygon? Enter your answer in the box. units?
Answer:
45units^2
Step-by-step explanation:
Break the polygon into two shapes. A rectangle and a triangle.
The area formula for a rectangle is A=L•W or
Area = Length x Width. Counting the units for length and width is 9 x 2. Which would equal 18units.
Now for the triangle, the formula is A=1/2 (b•h)
The base is 9 and Height is 6.
9 • 6 = 54
Since a triangle is half the area of a rectangle you divide 54 by 2. Area for triangle is 27.
Now add the rectangle area and triangle area.
18+27=45
Area=45 units ^2
There are 24 boys and serveral girls in a class.They sit in pairs so that exactly one fourth of the boys sit with a girl and exactly one half of the girls sit with a boy. How many students in the class?
Please explain it step-by-step. I will give you a brainlist!
Answer:
36 total students in the class
Step-by-step explanation:
Analyze the boysThere are 24 boys in the class.
Since they sit in pairs, and exactly 1/4 of the boys sit with a girl, then one-quarter of the 24 boys sits with a girl.
1/4 * 24 = 6, so 6 of the boys sit with a girl. Reflexively, 6 girls sit with a boy.
Analyze the girls
Since the problem states that exactly half of the girls sit with a boy, then half of the total number of girls is 6 (since we know that exactly 6 girls were sitting with a boy).
1/2 * x = 6
Multiplying both sides by 2...
x=12
So there are 12 girls total in the class, half (6) of whom sit with a boy.
Find the totalThere are 24 boys total in the class, one-quarter (6) of whom sit with a girl. The rest of the boys (18) sit in pairs with another boy (9 pairs), and the rest of the girls (6) sit with another girl (3 pairs).
Since there are 12 girls total and 24 boys total in the class, the total number of students is the sum of 12 and 24
12+24 =36 total students in the class
A car insurance company has determined that 9% of all drivers were involved in a car accident last year. among 14 drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?
a) 0.094.
b) 0.906.
c) 0.126.
d) 0.393.
The probability of getting 3 or more who were involved in a car accident last year is 0.126.
Given 9% of the drivers were involved in a car accident last year.
We have to find the probability of getting 3 or more who were involved in a car accident last year if 14 were selected randomly.
We have to use binomial theorem which is as under:
n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex]
where p is the probability an r is the number of trials.
Probability that 3 or more involved in a car accident last year if 14 are randomly selected=1-[P(X=0)+P(X=1)+P(X=2)]
=1-{[tex]14C_{0}0.9^{0} (0.1)^{14} +14C_{1} (0.9)^{1} (0.1)^{13} +14C_{2} (0.9)^{2} (0.1)^{12}[/tex]}
=1-{1*0.2670+14!/13!*0.9*0.29+14!/2!12!*0.0081*0.2358}
=1-{0.2670+0.3654+0.2358}
=1-0.8682
=0.1318
Among the options given the nearest is 0.126.
Hence the probability that 3 or more are involved in the accident is 0.126.
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6+x= 34 how do you solve for x?
What is the smallest natural number in which its digits are only 1's and 2's and which is divisible by 3 and 8?
Look at the multiples of lcm(3, 8) = 24, each of which are divisible by both 3 and 8. Naturally, the number we're looking for must have at least two digits.
The last/ones digit of a number [tex]n[/tex] can be computed by evaluating [tex]n \pmod{10}[/tex]. Suppose the ones digit is 1. Then
[tex]n \equiv 24k \equiv 20k + 4k \equiv 4k \equiv 1 \pmod{10}[/tex]
but this has no solution since no multiple of 4 ends in 1. So our number ends with a 2.
If our number has two digits, then in order for it to be divisible by 3, the first digit must be 1, since 1 + 2 = 3. But 12 is not divisible by 24.
If our number has three digits, then it's either 111 (with digital sum 1 + 1 + 1 = 3) or 222 (digital sum 2 + 2 + 2 = 6), since no other triplet of 1s and 2s sums to a multiple of 3. But 111 = 3×37 and 222 = 2×111, so neither are divisible by 24.
Now suppose [tex]n[/tex] has four digits. Also suppose that the tens digit is 2. Then our number must be 1122 to uphold divisibility by 3, but 1122 = 2×3×11×17 is not divisible by 8. So the tens digit must be 1. This in turn leaves two remaining candidates, 1212 and 2112. We have 1212 = 12×(100 + 1) not divisible by 8, so our number must be [tex]\boxed{n=2112}[/tex]. And it is, since 2112 = 24×88.
An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0).
Which equation represents this ellipse?
[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex] is the equation of the ellipse.
What is the equation of an Ellipse ?The equation of an ellipse is given by
[tex]\rm \dfrac{ (x-h)^2 }{a^2} + \dfrac{ (y-k)^2}{b^2} = 1[/tex]
here
(h,k) is the center
c = is the distance between center to focus
c = [tex]\rm \sqrt{a ^2 - b^2}[/tex]
as the a = 10 , component length
and c = 8
8 = [tex]\rm \sqrt{10 ^2 - b^2}[/tex]
8² = 10² -b²
b² = 36
b = 6
h = 0 ,k = 0
Substituting the values given
[tex]\rm \dfrac{ (x-0)^2 }{10^2} + \dfrac{ (y-0)^2}{6^2} = 1[/tex]
[tex]\rm \dfrac{ x^2 }{100} + \dfrac{ y^2}{36} = 1[/tex]
Therefore the equation of the ellipse has been determined.
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if −x+5y=7 is a true equation, what would be the value of -2(-x+5y)
Answer:
-14
Step-by-step explanation:
Given -x+5y=7
Now we substitute x+5y into -2(-x+5y)
-2(-x+5y) = (-2)(7)
= - 14
statements and reasons please
The lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.
What are the properties of a parallelogram?Properties of a parallelogram include;
Opposite sides are equalOpposite angels are equalThe angles are supplementary to each other The diagonals of a parallelogram bisect each otherFrom the figure, we have that lines YZ and WZ are equivalent because the diagonal bisects the parallelogram to two four of which they are of equal lengths.
Thus, the lines YZ and WZ are equivalent because the diagonal bisects the parallelogram into two parts of which are equal.
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Maina is thrice old as her daughter seven years ago the ratio of their ages was 5:1 Find the daughters age in six years
The daughter's age in 6 years time is 20
How to determine their ages?Let their current age be x and y
So, we have:
x = 3y
7 years ago, we have:
x - 7 : y - 7 = 5 : 1
Express as fraction
[tex]\frac{x - 7}{y - 7} = \frac 51[/tex]
Cross multiply
x - 7 = 5y - 35
This gives
x = 5y - 28
Substitute x = 3y in x = 5y - 28
3y = 5y - 28
Evaluate the like terms
2y = 28
Divide by 2
y = 14
In 6 years time, we have:
y + 6 = 20
Hence, the daughter's age in 6 years time is 20
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What would x be? (giving 50 points!)
Using the following image, solve for x.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = -3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: CD + DE = CE[/tex]
[tex]\qquad \tt \rightarrow \: x + 10 + x + 4 = 8[/tex]
[tex]\qquad \tt \rightarrow \: 2x + 14 = 8[/tex]
[tex]\qquad \tt \rightarrow \: 2x =8 - 14[/tex]
[tex]\qquad \tt \rightarrow \: 2x = - 6[/tex]
[tex]\qquad \tt \rightarrow \: x = - 3[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
[tex]\huge \boxed{\sf x=-3}\\\\\\\displaystyle \sf CD+DE=8 \\\\x+10+x+4=8\\\\2x+14=8\\\\Subtracting\ 14\ from\ each\ side\\\\ 2x+14-14=8-14\\\\2x=-6\\\\ Dividing\ each\ side\ by\ 2 \\\\ \frac{2x}{2} =\frac{-6}{2} \\\\x=-3[/tex]
What is the area of a rectangle with side lengths of 6/8 meter and 4/10 meter?
Enter your answer as a fraction in simplest form by filling in the boxes.
$$
m²
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is,
Area of rectangle = 6/8 meter × 4/10 meter
= 24 / 80 meters²
= 6 /20 meters²
= 0.3 meters²
Hence, The area of a rectangle with side lengths of 6/8 meter and 4/10 meter is 0.3 meters².
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Solve the following
2(x+6)-10=12
⊰________________________________________________________⊱
Answer:
x=5
Step-by-step explanation:
Apply the distributive property,
2(x+6)-10=12
2x+12-10=12
Collect a few like terms
2x+2=12
Subtract 2 from both sides
2x=10
Divide the equation by 2.
x=5
Done!!
⊱______________________________________________________⊰
2(x+6) - 10 = 12
2(x+6) = 22
x+6 = 11
x = 11 - 6 = 5
x = 5
The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. Last year, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are
The appropriate hypothesis which is used to test the dropout rate are [tex]H_{0}:p > =0.081\\[/tex] and [tex]H_{1}: p < 0.081[/tex].
Given Drop out rate through 24 year old who are not enrolled is 8.1%, sample size=1000 and we have to find the hypothesis to test the drop out rate of the school.
The variable which needs to be studied is X=Number of individuals with age between 16 and 24 years old that are high school dropouts.
The parameter of interest is the proportion to high school drop outs is p.
Sample proportion=[tex]p^{1}[/tex]=0.065
The hypothesis can be formed as under:
[tex]H_{0}:p > =0.081[/tex] (null hypothesis)
[tex]H_{1}:p < 0.081[/tex] ( alternate hypothesis)
Null hypothesis is a hypothesis which is tested for its validity and alternate hypothesis is hypothesis which is opposite of null hypothesis means if null hypothesis is rejected then the alternate hypothesis will be true.
[tex]Z_{H_{0} }=(p^{1}-p)/\sqrt{p*(1-p)/n}[/tex]
=[tex]0.065-0.081/\sqrt{(0.081*0.0919)/1000}[/tex]
=-1.85
Hence the appropriate hypothesis are [tex]H_{0}:p > =0.081[/tex] and [tex]H_{1}:p < 0.081[/tex].
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You are planning your week-end schedule. You can spend at most 8 hours playing video games and doing homework. You want to spend less than 2 hours pla
video games. You must spend at least 1.5hours on homework. Which of the following is the system of equations that would represent this situation? Let v-
number of hours spent playing video games and let h- the number of hours spent on homework.
The system of inequalities is:
v + h ≤ 8
v < 2
h ≥ 1.5
Which system of equations represents this situation?
Let's define the variables:
v = number of hours playing video games.h = number of hours spent on homework.The maximum time that you can spend on both activities is 8 hours, then:
v + h ≤ 8
You want to spend less than 2 hours on video games, so:
v < 2
You want to spend at least, 1.5 hours on homework, so:
h ≥ 1.5
Then the system of inequalities is:
v + h ≤ 8
v < 2
h ≥ 1.5
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It will take 29.4 years for the population of Africa to be two times what it is today. This reflects:
It will take 29.4 years for the population of Africa to be two times what it is today. This reflects: doubling time.
Doubling time is the time it takes for a particular amount of size or value to double at a given growth rate. By applying the 70 rules, we can find the doubling time of the exponentially increasing population. To do this, divide 70 by the growth rate (r).
Rule of 70 is a simplified way to determine the doubling time using the equation doubling time = 70 / r. Where r is the percentage growth rate of the population. For example, if the population of 10 species increases by 2 individuals per year, the r value will be 20%.
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please help me answer this!!
The value of x from the given expression is 5/6
Expansion of equation
Given the expression to expand expressed as:
15 = 3/5(6x + 20)
We are to determine the value of x
15(5) = 3(6x + 20)
Expand
75 = 18x +60
Collect like terms
18x = 75 - 60
18x = 15
x = 15/18
x = 5/6
Hence the value of x from the given expression is 5/6
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huang bought 12 boxes of floor tiles that weight 288 pounds each. how much is this in kilograms
[tex]in \: pounds \\ 12 \times 288 = 3456 \: pounds[/tex]
[tex]1 \: kilo = 2.2046 \: pounds[/tex]
[tex]x \: kilos = 3456 \: pounds[/tex]
[tex]x = \frac{3456}{2.2046} = 1567.61 \: kilos[/tex]
what is the rule of the reflection?
The rule of reflection in the image shown is: (x, -y).
What is Reflection?Reflection is a transformation which creates a new image by flipping over a line of reflection. The new image is congruent to the original image after reflection. The rule of reflection over an x-axis is given as, (x, -y).
In the image given we can see that rotating triangle LMN over the x-axis gave us:
M(-5, 4) → M'(-5, -4)
L(-4, 2) → L'(-4, -2)
N(-2, 3) → N'(-2, -3)
Therefore, the rule of reflection is: (x, -y).
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please help!!! (if you can explain the answer that would be great too)
Answer:
Option A
Step-by-step explanation:
Equation of line:[tex]\sf Slope=\dfrac{Change \ in \ y}{Change \ in \ x}=\dfrac{rise}{run}[/tex]
We can find the equation of line, by comparing the slope of line segment AC and slope of AE.
Slope of AC = Slope of AE
[tex]\sf \dfrac{4}{3}=\dfrac{y +2}{x}[/tex]
Cross multiply
4*x = 3*(y +2)
4x = 3y + 3*2
4x = 3y + 6
Equation of the line in standard form:
4x - 3y - 6= 0
If triangle PQR is an obtuse triangle and angle P is obtuse, then angle Q must be
Answer:
Angle Q is acute.
Step-by-step explanation:
In an obtuse triangle, there is one obtuse angle and the other two angles are acute.
tion
If a soccer team made 19 penalty shots out of 100, what fraction and what
percentage of penalty shots did the team miss? Choose two answers.
A.
B. 19%
C.
19
100
D.
81
100
80
100
E. 81%
OF. 0.19%
A number in a fraction implies the part of a number in another given number. While percentage relates a given number to 100%. Thus the answers to the given question are:
a. a fraction of penalty shots that the team missed = [tex]\frac{81}{100}[/tex]
b. percentage of penalty shots missed = [tex]\frac{81}{100}[/tex] x 100%
= 81%
A fraction is a part of a given number stated in a quotient form. Generally, all numbers can be expressed in form of fractions, even whole numbers.
The percentage is an expression that shows the part of a number in a given number with respect to 100%. An example is 10%([tex]\frac{10}{100}[/tex]).
From the given question, let;
n, number of penalty shots made = 19
T, the total number of penalties taken = 100
Thus, the number of penalties missed = T - n
= 100 - 19
= 81
Thus,
i. a fraction of penalty shots that the team missed = [tex]\frac{81}{100}[/tex]
ii. percentage of penalty shots missed = [tex]\frac{81}{100}[/tex] x 100%
= 81%
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Find two consecutive even numbers such that the sum of 3 times the smaller and 5 times thelarger is106.
Answer:
12 and 14
Step-by-step explanation:
The first number can be assigned x, the second will be assigned x+2 so that it will be even.
3(x)+5(x+2) = 106
3x+5x+10 = 106
8x = 96
x = 12
x+2 = 14
The two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.
We are given two consecutive even numbers, thus the larger number will be two more than the smaller one, as consecutive even numbers differ by two.
We assume the smaller number to be x.
Thus, the larger number = x + 2.
We have been given that three times the smaller number summed with five times the larger number results in 106.
This can be shown by the linear equation in one variable:
3x + 5(x + 2) = 106.
To find the numbers, we need to solve this linear equation in one variable as follows:
3x + 5(x + 2) = 106,
or 3x + 5x + 10 = 106 {Simplifying},
or, 8x + 10 = 106 {Simplifying},
or, 8x + 10 - 10 = 106 - 10 {Subtracting 10 from both sides of the equation},
or, 8x = 96 {Simplifying},
or, 8x/8 = 96/8 {Dividing both sides of the equation by 8},
or, x = 12 {Simplifying}.
Thus the smaller number, x = 12.
The larger number, x + 2 = 12 + 2 = 14.
Thus, the two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.
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Write the phrase as a mathematical expression. Use x as the variable.
4 times the sum of 2 times a number and 7
Answer:
4(2x+7) which is equal to 8x+28
sabbir arrived at dhaka train station at 9 30 pm write this time using the 24hr clock
Okay so a 24hr clock is very simple. We usually turn to "PM" when its 12:00 (day time).
In the 24hr clock we do not, we don't use PM or AM but its crucial to know when converting a standard clock time to military time (aka. 24hr).
9:30 PM in 24hr clock is 12:00 + 9:30 because 9:30 is past that first 12 hours.
So in 24hr clock time it is 21:30. You can also count backwards from midnight to figure it out, for example 12:00 AM (midnight), minus 9:30 is 2:30. Therefore 24:00-2:30=21:30.
Hopefully it helps, heart will help me alot too!
Answer:
21:30
Step-by-step explanation:
The 24hour clock uses 0:00 for midnite. 1am through noon are just 1:00 - 12:00. But the pm hours continue counting up, 13 - 23.
For example, 1pm is 13:00 and 2pm is 14:00.
To change to 24 hour clock, for pm hours, ADD 12.
So for your problem, 9:30 is:
9:30 + 12
= 21:30
find the sine of y. write your answer in simplified, rationalized form. do not round.
Answer:
[tex]\frac{\sqrt{61} }{\sqrt{97} }[/tex]
Step-by-step explanation:
Sin(y) = opposite over hypotenuse
opposite side is [tex]\sqrt{61}[/tex]
hypotenuse is [tex]\sqrt{97}[/tex]
Select the correct answer from each drop-down menu.
Trapezoid PQRS
4650
be inscribed in a circle because the
Reset
115⁰
Next
65°
Based on the inscribed quadrilateral conjecture: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.
What is the Inscribed Quadrilateral Conjecture?The inscribed quadrilateral conjecture states that the opposite angle of any inscribed quadrilateral are supplementary to each other. That is, they have a sum of 180 degrees.
From the diagram given, the opposite angles in the trapezoid, 115 + 65 = 180 degrees.
Therefore, we can conclude that: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.
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Maya, lute and aran are cousins. maya's age is 1/3 of lute's and aran is 1/4 of lute's age. if the sum of their agaes is 38, find the ages of each cousin
The ages of Lute, Maya and Aran are respectively; 24, 8 and 6 years old.
How to solve algebra problems?Let Lute's age be x
Thus;
Maya's age = ¹/₃x
Aran's age = ¹/₄x
We are told the sum of their ages is 38. Thus;
x + ¹/₃x + ¹/₄x = 38
Multiply through by 12 to get;
12x + 4x + 3x = 456
19x = 456
x = 456/19
x = 24
Maya's age = ¹/₃ * 24 = 8 years
Aran's age = ¹/₄ * 24 = 6 years
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A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 98% confidence if
The sample size required is 1725.
(A) Sample size calculation
p=0.15
For 98%, z=2.326
d=0.02
Sample size = (z^2*p*(1-p))/d^2
= (2.326^2*0.15*0.85)/0.02^2
=1724.5
The sample size required= 1725
(B) Sample size calculation
p=0.5
For 98%, z=2.326
d=0.02
Sample size = (z^2*p*(1-p))/d^2
= (2.326^2*0.5*0.5)/0.02^2
= 3381.4
The sample size required= 3382
In records, the pattern size is the degree of the variety of character samples utilized in a test. For example, if we're testing 50 samples of folks that watch television in a town, then the pattern length is 50.
Sample size willpower is the act of selecting the range of observations or replicates to consist of in a statistical pattern. The sample size is a crucial function of any empirical look at in which the intention is to make inferences about a populace from a sample.
Your question is incomplete. Please find the complete question below.
A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with98% confidence if
(a) Does he use a 2006 estimate of 15% obtained from a Coinstar National Currency Poll?
(b) he does not use any prior estimate?
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