The distance covered by second cyclist is, 9 + (3/4)b miles.
What is speed?
Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).
Given: Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions.
The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.
Speed of first cyclist = 12 miles per hour.
Speed of second cyclist = 12 + b miles per hour.
Since, distance = speed x time
The distance covered by the second cyclist in 45 minutes is,
45 minutes = 45/60 = 3/4 hour.
Therefore, distance covered by second cyclist is,
= (12 + b) x 3/4 = 9 + 3b/4 miles.
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ABCD is a square. If LABC = (6x - 12)° and CD= (x + 15). Find the length of AD.
Answer:
AD = 32
Step-by-step explanation:
You want the length of side AD of square ABCD, when CD = (x+15) and angle ABC is (6x-12)°.
Value of xThe value of x can be found by recognizing that the measure of any angle in a square is 90°.
(6x -12)° = 90°
6x = 102 . . . . . . . . divide by °, add 12
x = 17
Measure of ADThe sides of a square are congruent, so ...
AD = CD = (x +15) = 17 +15 = 32
The length of AD is 32 units.
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
t =2.45s
Step-by-step explanation:
H=-16t2+96t
then, -16t2= -96t
divide both sides by 16
-16t2/16 = -96t/16
-t2 = -6
t2=6
t=√6
t=2.45
Julie obtained an installment loan of $4,600 to have some trees removed from her
yard. The APR is 13 percent. The loan is to be repaid in 36 months. What is the
finance charge (Use the table on page 799 for monthly payment)?
O $2,432.02
A
O $12,870.00
B
O $16.15
C
O $980.72
D
The finance charge for Julie's installment loan of $4,600 at 13% for 36 months is D. $979.64.
What is the finance charge?The finance charge represents the interest and other administrative charges for granting a loan to an individual or organization.
The finance charge is always described in terms of the APR (annual percentage rate) that accrues on the loan, depending on the amount and the period.
N (# of periods) = 36 months (3 years x 12)
I/Y (Interest per year) = 13%
PV (Present Value) = $4,600
FV (Future Value) = $0
Results:
PMT = $154.99
Sum of all periodic payments = $5,579.64
Total Interest = $979.64
Thus, Julie will pay a finance charge of $979.64.
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Question Completion:Option D. $979.64
-2(4 + 3y) = -2(4 + y)
Answer:
Step-by-step explanation:
-8-6y=-8-2y
+2y +2y
-8-4y=-8
+8 +8
-4y=0
Y=0
→
Enter a formula using k to connect the two
variables.
y is proportional to x³
Directly proportional to x.
What is propotionality?In algebra, proportionality is the equality of two ratios. A and B are in the same ratio as C and D in the formula a/b = c/d. When one of a proportion's four quantities is unknown, a proportion is often built up to resolve the word problem. By multiplying one numerator by the opposing denominator and equating the result to that of the other numerator and denominator, the equation can be solved. Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.Acc to our question-
If two variables' ratios (yx)(x and y) have the same value as a constant (k=yx)therefore the ratio's variable (y) in the numerator is the sum of the other variable and the constant (y=k:x).With a proportionality constant of k, it is claimed that y is directly proportional to x in this instance.Hence,Directly proportional to x.
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Write The recursive formula for the sequence 18,22,26,30?
The recursive formula is an = a(n-1) +4. A recursive formula is one that defines each term in a sequence by using the term before it (s)
What is recursive formula?A recursive formula is one that defines each term in a sequence by using the term before it (s). The following parameters are defined by the recursive formulas: The sequence's first term. The pattern rule for obtaining any term from its preceding term. A recursive formula is composed of two parts: a statement of the first term and a statement of the formula that connects successive terms. The sequence is as follows: 10, 15, 20, 25, 30, 35,... Look for a recursive formula. This is an arithmetic sequence (the same number, 5, is added to each term to get to the next term).The sequence's first term
The pattern rule for obtaining any term from its preceding term
Recursive Arithmetic Sequence Formula
To find the nth term of an arithmetic sequence, use the recursive formula:
an = an-1 + d for n ≥ 2
Where
an is the nth term of a A.P.
d is the common difference.
Given:
14, 18, 22, 26, 30, …
a1 = 14
and, d = 18-14
d = 4
a2 = a1 + 4
a2 = 14 + 4 = 18
Similarly, going this way
an = a(n-1) +4
Hence, the recursive formula is an = a(n-1) +4
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18. Richard measured a house and its lot and made a scale drawing. The scale of the drawing was 1 inch: 2 feet. The backyard is 74 feet long in real life. How long is the yard in the drawing?
The length of backyard in drawing is 37 inch when 74 feet long in real life and scale of drawing is 1 inch: 2 feet.
What is proportion?A proportion is a form of ratio in which the denominator also contains the numerator. For example, the fraction of male deaths would be deaths to men divided by deaths to males + deaths to females (i.e. the total population). A population proportion is a percentage of the population that possesses a specific feature. Assume you have 1,000 persons in your population, with 237 of them having blue eyes. Blue eyes account for 237 of every 1,000 persons, or 237/1000.
Here,
as the given scale is 1 inch: 2 feet.
actual length of backyard=74 feet
length of backyard in drawing is x inch,
1/2=x/74
2x=74
x=37 inch
The length of the backyard in the drawing is 37 inches, although it is 74 feet long in real life, and the scale of the drawing is 1 inch: 2 feet.
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Given that 27 ^-1/3 = 9^1/4÷ 3^x+1
find the exact value of x.
Answer:
decimal form> -4.87577494
Exact form> -In(212)/In(3)
which OF THE Following have infinitely many solutions? Choose all answers that apply, A -76x+76=-76x+76 B 76x+76=76x+76 C76x+76=-76x+76 D -76x+76=76x+76. please really need help
The equation which has infinitely many solutions from the given answer choices is; Choice A: -76x+76=-76x+76 and Choice B: 76x + 76 = 76x + 76.
Equations with infinitely many solutions.It follows from the task content the the equation with infinitely many solutions among the given answer choices is to be determined.
An equation of the type; a(1)x + b(1) = a(2)x + b(2) is said to have infinitely many solutions if; a(1) = a(2) and b(1) = b(2).
Hence, the equations which have infinitely many solutions among the given answer choices are; Choice A: -76x+76=-76x+76 and Choice B: 76x + 76 = 76x + 76.
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which equation represents the graph below?
y = −1/5x − 3y
y = 5x − 3y
y = −1/5x + 3
Answer:
y=-1/5x+3
Step-by-step explanation:
I think this the answer
Answer:
y = -1/5x - 3
Step-by-step explanation:
→ Find the x intercept
( - 15 , 0 )
→ Find y intercept
( 0 , -3 )
→ Find gradient
y = -1/5x + c
→ Substitute coordinate pair in
y = -1/5x - 3
x+3y+z=-8
2x+y-6z+20
x-2y+z=-13
please help me with this
The solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line in point slope form can be also written as-
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
We have the following set of equations -
x+3y+z=-8 ..[1]
2x+y-6z=20 ..[2]
x-2y+z=-13 ..[3]
We can write eq [3] as -
z = - 13 - x + 2y
So, eq [1] and [2], will become -
x + 3y + (-13 - x + 2y) = -8
x + 3y - 13 - x + 2y = -8
5y = - 8 + 13
5y = 5
y = 1 ..Eq[4]
AND
2x + y - 6z = 20
2x + y - 6(- 13 - x + 2y) = 20
2x + y + 78 + 6x - 12y = 20
2x + 1 + 78 + 6x - 12 = 20
8x = 47
x = 5.875 ..Eq[5]
Now -
x - 2y + z = -13
5.875 - 2 + z = - 13
z = 16.875
Therefore, the solution for the system of equations -
x+3y+z=-8
2x+y-6z=20
x-2y+z=-13
is x = 5.875, y = 1, z = 16.875.
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using the formula for calculating the number of communication channels, how many channels would five people require?
The number of communication channels, 10 channels would five people require.
To find number of communication channels, we use;
On the other hand, it might be a sign of the scope and intensity of the project communication management needed in huge projects and so-called megaprojects. This could, for example, entail allocating specific resources to project communication responsibilities in accordance to the number of available channels for communication. These factors may be especially important for teams working on sensitive projects and projects where information flow may be unclear or even fraudulent.
Number of potential communication channels = n x (n-1)/2
Given n = 5;
→ x = 5*(5 - 1)/2
= 5*2
= 10
The number of communication channels, 10 channels would five people require.
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in a certain industrial facility, accidents occur infrequently. it is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other. what is the probability that in any given period of 400 days there will be an accident on one day? use binomial approximation to poisson distribution.
The probability that in any given period of 400 days there will be an accident on one day is 0.2707
Given that;
In a certain industrial facility, accidents occur infrequently. it is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other.
n = 400, p = 0.005
Poisson distribution is given by;
e P(x) = (λˣe^λ ) / x!
Here, Mean(λ) = np
= 400*0.005
=2
The probability that there will be an accident on one day;
(P(x = 1)) = (λxe-λ)/x!
= 2*e-2
= 0.2707
The probability that in any given period of 400 days there will be an accident on one day is 0.2707
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what is the area of the figure?
The area of the figure is 1875 sq.in.
In this question, we need to find the area of the given figure.
the area of the figure = area of rectangle + area of two triangles.
For rectangle,
length = 50 inch and width = 30 in.
Using the formula for the area of rectangle,
A1 = length * width
A1 = 50 * 30
A1 = 1500 sq.in.
For triangle,
base = 1/2 * length of rectangle
so, base = 25 in and height = 15 inch
Using the formula for the area of triangle,
A2 = 1/2 * base * height
A2 = 1/2 * 25 * 15
A2 = 187.5 sq.in.
so, the area of the figure would be,
A = A1 + (2 * A2)
A = 1500 + (2 * 187.5)
A = 1875 sq.in.
Therefore, the area of the figure is 1875 sq.in.
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4. Round the number 39,944 to the nearest hundred.
Answer:
39.94
Step-by-step explanation:
Ask? :)
Answer:40,000 porque dice que redondees a la centecima mas cercana
The dimensions of a rectangle can be expressed as x+4 and x-3. If the area of the rectangle is 60 inches squared, find the dimensions of the rectangle
Step-by-step explanation:
length(l)=x+4
breadth(b)=x-3
Area of rectangle(A)=l×b
60=(x+4)×(x-3)
60=x^2-3x+4x-12
60=x^2+x-12
x^2+x-12-60=0
x^2+x-72=0
x^2+9x-8x-72=0
x(x+9)-8(x+9)=0
(x+9)(x-8)=0
equating equation
x+9=0.....eq(i)
x=-9 it is not possible
x-8=0.....eq(ii)
x=8
Then,length(l)=x+4
=8+4=12
breadth(b)=x-3
=8-3=5
Step up an inequality for this situation below. Define your variable, but do not solve. (2 points – 1 defined variable, 1 point correct inequality).
Mr. Bass charges his music students $25 per lesson plus a recital fee of $50. How many lessons can a student take if they pay no more than $175?
The lessons can a student take if they pay no more than $175 is 25x + 50 < 175.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
In the 12U Softball division, Olivia gets chosen. What is Olivia's age? Olivia's age is unknown to you because the word "equals" is missing. However, since you are aware that she should be under or equal to 12, you can write Olivia's Age 12. This is a real-world example of an inequality.
given:
Per lesson charges= $25
Recital f= $50
Total money can be spend= $175
let the number of lessons taken be x.
So, the inequality is
25x + 50 < 175
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Hola, me ayudan a despejar X - 8 = -2
Answer:
x=6
Step-by-step explanation:
x-8=-2
x=-2+8
x=6
Answer:
x = 6
Step-by-step explanation:
x - 8 = -2
x - 8 + 8 = -2 + 8
x + 0 = 6
x = 6
Check:
6 - 8 = -2
Each year, the Department of Water Works measures the chloride concentration level in the water. The first year, they found the chloride concentration changed by −1.6 mg/L−1.6 mg/L . It is estimated that the chloride concentration will change −2.2 mg/L−2.2 mg/L the next year. What is the total change that will likely occur in 2 years? Enter your answer in the box.
Answer:
L
Step-by-step explanation:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Considering a circle whose equation is x² + y² – 2x – 8 = 0. The statements that are true about it is as follows
The radius of the circle is 3 unitsThe center of the circle lies on the y-axisThe standard form of the equation is (x – 1)² + y² = 3How to determine the equation the circleInformation given in the question
a circle whose equation is x² + y² – 2x – 8 = 0
Equation of a circle is given as
(x - h)² (y - k)² = r²
The equation of the circle is written in standard form by completing the square of each of the quadratic equation involved
x² + y² – 2x – 8 = 0
x² - 2x + 1 + y² + 0 = 8 + 1
(x – 1)² + (y - 0)² = 3²
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Can someone pls help me with this and show your work it would mean a lot
Using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.
What is the angle of elevation?The angular relationship between the horizontal plane and the line of sight for an object above the horizontal.The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.You may calculate the angle of elevation, for instance, by standing on the ground and looking up at the peak of a mountain.So, the distance of the building from John and Fred is:
Let, the height of the building be QR and the distance between the building and John and Fred be PR and SR.Now, we get the formula:
Tanθ = QR/PRTanθ = QR/SRCalculate as follows:
John's distance:
Tanθ = QR/PR25 = 30/PRPR25 = 30PR = 30/25PR = 6/5Fred's distance:
Tanθ = QR/SR18 = 30/SRSR18 = 30SR = 30/18SR = 15/9SR = 1.67mTherefore, using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.
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Does the following relation represent a function? {(16,7), (7,26), (15,16), (-7,15), (-8,26)} ?
Yes, No, There is not enough information to answer this question
there are 5 major sea islands in the queen elizabeth islands of canada that you are interested in visiting. there are 12 major lakes in saskatchewan, canada that you would also like to visit. (a) if you are planning a trip to visit one of these islands, followed by one of these lakes, how many different trips could you make?
The person can make 60 trips.
Let us say that A indicates the major sea Islands and B indicates the major lakes. Taking both the cases as events, we will use multiplication principle. Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.
Thus, A × B = 5 × 12
Performing multiplication on Right Hand Side of the equation to find the number of trips
Total number of trips = 60
Hence, there are 60 trips that could be made.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length of the rectangular area is 800 yards and width is 800 yards
The perimeter of the rectangular area = 3200 yards
The perimeter of the rectangle = 2 (l + w)
Then the equation will be
2(l + w) = 3200
l + w = 3200 / 2
l + w = 1600 yards
w = 1600 - l
The area of the rectangular area = l × w
= l(1600 - l)
Since the area is maximizing the the rate of change of area will be zero
l × w = 0
1600 - 2l = 0
2l = 1600
l = 1600/2
l = 800 yards
Then
w = 1600 - l
Substitute the value of l in the equation
w = 1600 - 800
w = 800 yards
Hence, the length of the rectangular area is 800 yards and width is 800 yards
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Which conversion factors are used to multiply to 12 m/s to get kilometers per minute?
Select each correct answer.
1min60 s
1 min over 60 s
60 s1 min
60 s over 1 min
1000 m1 km
1000 m over 1 km
1 km1000 m
PLEASE HELP
To convert 12 m/s to get a kilometer per minute, we will need to multiply 12m/s by 1000 km/60 m.
1000 m over 1km 1 min over 60 sWhat are Unit Conversion and Conversion Factors?Unit conversion is the expression of the same function in a new unit of measurement. Time, for example, can be stated in minutes rather than hours, and distance can be translated from miles to kilometers/feet, or another length measurement. A conversion factor is a numerical equation that allows for the equal conversion of feet to another dimensional analysis unit.
A conversion factor is a number that is used to multiply or divide one set of units into another. When converting to an equivalent value, the proper conversion factor must be utilized. For example, to translate inches to feet, the correct conversion value is 12 inches equals 1 foot. The converting value for minutes to hours is 60 minutes equals 1 hour.
From the information given:
To convert 12 m/s to get a kilometer per minute, we will need to multiply 12m/s by 1000 km/60 m.
The conversion factors are:
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A right triangle's hypotenuse is 1 cm longer than twice the length of the shortest side.
The third side is 1 cm less than twice the shortest side.
Find the length (in cm) of the hypotenuse.
Answer:
17 cm
Step-by-step explanation:
You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.
Pythagorean theoremThe relation between the side lengths in the right triangle is ...
a² +b² = c²
ApplicationSubstituting the given relations, we have ...
a² +(2a-1)² = (2a+1)²
a² +4a² -4a +1 = 4a² +4a +1
a² -8a = 0 . . . . . . write in standard form
a(a -8) = 0 . . . . . . factor
a = 0 or a = 8
We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...
c = 2(8) +1 = 17
The hypotenuse is 17 cm.
__
Additional comment
You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point D is at -3, and point E is at 6. The point F lies on segment DE . The ratio of DF to FE is 2 : 3. Where does point F lie on the number line? Point F is at on the number line.
Using the section formula, point F lie on 3/5 in the number line.
In the given question,
On a number line, point D is at -3, and point E is at 6.
The point F lies on segment DE .
The ratio of DF to FE is 2 : 3.
We have to find where point F lie on the number line.
Since point D lies is at -3 at x axis so the point should be ( -3,0).
Point E lies is at 6 at x axis so the point should be ( 6,0).
F lies on segment DE. So let the point of F is (X, Y)
The ratio is 2:3.
Now firstly finding the value of X using section formula
X = [tex]\frac{mx_{2}+nx_{1}}{m+n}[/tex]
where [tex]x_{1}[/tex]= -3, [tex]x_{2}[/tex]= 6, m= 2 and n=3
Now putting the value
X = {2×6+(-3)3}/(2+3)
Simplifying
X = (12-9)/5
X = 3/5
Now firstly finding the value of Y using section formula
Y = [tex]\frac{my_{2}+ny_{1}}{m+n}[/tex]
where [tex]y_{1}[/tex]= 0, [tex]y_{2}[/tex]= 0, m= 2 and n=3
Now putting the value
Y = (2×0+3×0}/(2+3)
Y = 0/5
Y = 0
Hence, point F lie on 3/5 in the number line.
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Use the "Insert Line" Tool to construct the line
showing the given distance. If you need to extend
the line outside the shape, use a dotted line.
(100 points for brainliest answer)
The distance from B to AC can be constructed as shown in the figure.
The distance from G to EF can be constructed as shown in the figure.
The distance from Q to SR can be constructed as shown in the figure.
What is the distance of a line from a point?
A point-to-line distance is the shortest distance from a point to any point on an infinite line. This is the perpendicular distance from the point to the line and the length of the line segment connecting the point to the nearest point on the line.
For the figure 1, the distance from B to AC, will be the perpendicular line through point B on side AC, so side BD will be the distance.
For the figure 2, the distance from G to EF, will be the perpendicular line through point G on side EF, so side GH will be the distance.
For the figure 1, the distance from Q to SR, will be the perpendicular line through point Q on side SR, so side QT will be the distance.
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Add. Write your answer as a fraction or as a whole or mixed number.
2 8/9 + 5 5/9 =
The required answer in mixed number for a given operation is [tex]8\frac{4}{9}[/tex]
What are mixed numbers?
A whole number and a proper fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it.
Given, [tex]2\frac{8}{9} + 5\frac{5}{9}[/tex]
[tex]= \frac{(2*9)+8}{9} +\frac{(5*9)+5}{9}[/tex]
[tex]= \frac{18+8}{9} +\frac{45+5}{9}[/tex]
[tex]= \frac{26}{9} +\frac{50}{9}[/tex]
[tex]= \frac{26+50}{9} = \frac{76}{9} = 8\frac{4}{9}[/tex]
Hence, the required answer for the given term is [tex]8\frac{4}{9}[/tex] .
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There is no prior information about the proportion of Americans who support free
trade in 2019. If we want to estimate a 98% confidence interval for the true
proportion of Americans who support free trade in 2019 with a 0.21 margin of error,
how many randomly selected Americans must be surveyed? Answer: (Round up your
answer to nearest whole number, do not include any decimals)
31 Americans should be surveyed by Z mean.
What does critical value of Z mean?
The Z-score will show you how far a specific data point is from your sample's mean. This kind of critical value will inform you of the amount of standard deviations above or below the population mean for your sample.If the prior population proportion is unavailable then the formula to find the sample size is given by
n = 0.25[tex](\frac{z^{*} }{E} )^{2}[/tex]
where z* = Critical z-value
E = margin of error
Given, Confidence level = 98%
The critical z-value for 98% confidence interval is 2.326 ( BY z-table)
Margin of error : E= 0.21
n = 0.25 [tex](\frac{2.326}{0.21})^{2}[/tex]
n = 0.25 * ( 11 .07)²
n = 0.25 * 122.5449
n = 30.363225 ≈ 31
Hence, 31 Americans should be surveyed.
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