which inequality is less than the quadratic function with zero -7 and 1 and includes the point (2,27/2) on the boundary?
Answers
The second inequality, y < (3/2)x² + 9x -21/2, is less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
What is a quadratic equation?The equation of the form ax² + bx +c is known as a quadratic equation.
Given that, the zeros of the quadratic function are -7 and 1 and include the point (2,27/2).
Substitute x = 1 into the given inequality to check whether any of them becomes less than 0 or not:
From the first inequality:
y < -3/2 + 9 + 21/2
y < 18
From the second inequality:
y < 3/2 + 9 -21/2
y < 0
Since the inequality is less than 0, it is also less than the quadratic function at x = 1.
Similarly, checking the third inequality also gives y < 0, but the fourth doesn't.
Now, from the second and the third inequality, check which one is less than 27/2 for x = 2:
From the second inequality:
y < 6 + 18 -21/2
y < 27/2
From the third inequality:
y < -6-9+21/2
y < -27/2
Since the second inequality, y < (3/2)x² + 9x -21/2, is less than 0 at x =1 and less than 27/2 at x=2, it is also less than the quadratic function whose zeros are -7 and 1 and includes the point (2,27/2).
Hence, the second inequality, y < (3/2)x² + 9x -21/2, is less than the quadratic function with zero -7 and 1 and includes the point (2, 27/2).
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Answer:
it’s B took the test
Step-by-step explanation:
Related Questions
The owner of a landscaping business wants to know how much time, on average, his workers spend mowing one lawn. Which is the most appropriate rate with which to calculate an answer to his question?
lawns per employee
hours per lawn
employee per lawn
lawns per day
Answers
The mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1. It can be solved by rate of work.
The rate lawns per employee gives the lawns mowed by one employee.
The rate hours per lawn gives the number of hours required to mow one lawn.
The rate employee per lawn gives how many employees are required to mow one lawn.
The rate lawns per day gives the number of lawn mow in one day.
Since the mowing takes hours hence, the best rate is hours per lawn. Hence the correct option is option 1.
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what would 10 possibly be? please help me thank u :)
- have a wonderful day/ night <3
Answers
The distance is 244.56 feet, in feet, between point K and point L.
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Recall the Pythagorean theorem formula:
a² + b² = c²
Given that Kim is standing on the deck, point k, which is 140.75 feet above ground level.
Louise point L, is standing 200ft from the base of the lighthouse directly below Kim’s position.
Thus the distance, in feet, between point K and point L
Replacing by the values we have;
200 ² + 140.75² = KL²
KL² = 59810.56
KL = 244.56
The distance is 244.56 feet, in feet, between point K and point L.
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Find the missing number so that the equation has infinitely many solutions.
–2x + 8= __x + 8
a
3
b
-4
c
8
d
-2
Answers
Answer:
-2
Step-by-step explanation:
If both sides are identical, there will be infinitely many solutions.
Rahim is saving for a new bike which will cost $1600. Rahim earns $3000 per month. Rahim spends his money on bills, food and extras in the ratio 6:4:2. Of the money he spends on extras, and puts 20% into his savings account to buy his bike. How long will it take rahim to save for his new bike
Answers
Answer:
it will take rahim 16 months
Step-by-step explanation:
6:4:2
3000÷12=250
1500:1000:500
20% 100
100×16=1600
A mason is a person who builds structures with bricks, stone, cement block, or wee. A mason usually uses, mortar to hold the bricks together. A general rule of thumb in masonry is that 2 1/2 bags of mortar are needed for every 100 cement blocks. Use a double number line to determine each answer.
Answers
By using the concept of unitary method, it can be calculated that
a) For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required
b) For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required
What is unitary method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, unitary method will be used
The double number line has been shown below-
a) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required
For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required
For 350 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 350[/tex] bags of mortar are required
For 350 blocks of cement, [tex]\frac{35}{4}[/tex] bags of mortar are required
For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required
b) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required
For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required
For 50 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 50[/tex] bags of mortar are required
For 50 blocks of cement, [tex]\frac{5}{4}[/tex] bags of mortar are required
For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required
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Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using first two then four rectangles.f(x)=x^3 between x=0 and x=1
Answers
The area under the graph using the first two and then four rectangles = 0.221 unit square
According to the graphs given in the below figure,
Given in the question,
f(x) = [tex]x^{3}[/tex] when x = 0 and x = 1
The first rectangle of the first graph goes from 0 to 0 .6,
Width = 0.6
Height measured from the middle point = 0.3
f( 0.3) = [tex]( 0.3)^{3}[/tex]
f(0.3) = 0.027 units.
Area of first rectangle = 0.6 x 0.027 = 0.0162 unit square
Now taking the second rectangle of the first part,
It is going from 0.6 to 1.0,
Width = 0.4 units
height = 0.8 units
Height measured from the middle-
f(0.8) = [tex](0.8)^{3}[/tex] = 0.512
Area of the second part of the rectangle = 0.512 x 0.4
= 0.2048 unit square
Final area = 0.2048 + 0.0162 = 0.221 square units
Therefore, the same could be done with the second part rectangle of 4
For the given first part of four rectangles = width = 0.6 units and height = 0.1 unit
so f(0.1) = [tex]0.1^{3}[/tex]
= 0.001 units
Therefore, the area under the graph using the first two and then four rectangles = 0.221 unit square
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Solve the system using substitution.
5x + 3y = -4
y - 2x = 6
([?], [ ])
Answers
Y=2x+6
Now we can input this and substitute for equation 1
5x+3(2x+6)=-4
So we distribute to get
6x+ 18 within the parentheses
We add or subtract like terms such as 5x +6x to get 11x
-4-18=-22
Now we have 11x=-22
Divide by 11
X= -2
Now we plug this into equation 2 to solve for y
Y-2(-2)=6
Y+4=6
Subtract 4
Y=2
So
(-2,2) is the answer
Hope this helped
PLEASEEEEE HELP MEEEEEE!
Answers
$9/1lb
Jason drops a tennis ball outside of his hotel balcony. He is standing 52 feet above the street. If the ball hits the hotel canopy 12 feet above street-level, how long after Jason releases the ball will it hit the canopy. Use the function h(t) = -16t2 + 52. Round your answer to the nearest tenth.
Jason drops a tennis ball outside of his hotel balcony. He is standing 52 feet above the street. If the ball hits the hotel canopy 12 feet above street-level, how long after Jason releases the ball will it hit the canopy. Use the function h(t) = -16t2 + 52. Round your answer to the nearest tenth.
1.6 seconds
2.0 seconds
0.4 seconds
4.0 seconds
Answers
1.6 seconds. The ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.
How to find time ?To find the time it takes for the ball to hit the canopy, we need to solve the equation h(t) = 12 for t.
The given equation for h(t) is h(t) = -16t^2 + 52, so we can substitute this into the equation h(t) = 12 to get:
12 = -16t^2 + 52
To solve this equation, we can move all the terms to one side of the equation to get:
-16t^2 + 40 = 0
We can then divide both sides of the equation by -16 to get:
t^2 - 2.5 = 0
We can then use the quadratic formula to solve for t:
t = +/- sqrt(2.5)
t = +/- 1.58
Thus, the ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.
Rounding this answer to the nearest tenth gives us 1.6 seconds, so the correct answer is 1.6 seconds.
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twice the number of x
Answers
If the ratio of perimeters is 2:9, then the ratio of areas is?
Group of answer choices
2:9
5:21
4:81
8:729
Answers
Answer:
4:81
Step-by-step explanation:
κμΛζΖυ
The ratio of area of squares is 4:81. Therefore, option C is the correct answer.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of perimeters of a squares is 2:9.
We know that, perimeter of square is 4a, where a is side of a square
Now, 4x/4y =2/9
x/y =2/9
As we know area of square is a², where a is side of a square
So, x²/y² =2²/9²
x²/y² =4/81
The ratio of area of squares is 4:81. Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
If the ratio of perimeters of a squares is 2:9, then the ratio of their areas is
A) 2:9
B) 5:21
C) 4:81
D) 8:729
Pls help what this is
Stem-and-leaf plots
Answers
Answer:
C is the answer
Step-by-step explanation:
Stem and leaf plots were also confusing to me at first, but once you understand they are actually easy!
Look at the first column where it says 2,3,4,5 and 6. Those are the tens place. The columns next to it with 2,3,8,9,etc are the ones place. For example, the first column has two, so we know that the number has a two in the tens place.
2_
Look at the numbers next to it, there's 2,3, and 8.
Since there's 3 numbers, that means that there are three numbers that have a two in the ones place. 2,3 and 8 are the numbers that go in the ones place.
So in the graph there is 22,23 and 28.
If you look at your choices, you can find all of them except 38, since on the row with the 3, next to it is the number 9 and not the number 8.
Factor a²+4 b² completely.
a²+4b²=_____
Answers
Answer: The expression a²+4b² can be factored in the following way:
a²+4b² = (a² + 2ab + 2ab + 4b²)
= (a+b)²
In general, the square of a binomial (a+b) can be written as (a+b)² = a² + 2ab + b². This is known as the "square of a sum" formula. In this case, we can apply this formula to the binomial a+b to obtain a² + 2ab + b² = (a+b)². We can then use the fact that the square of a binomial can be written as the square of each term plus twice the product of the two terms. This allows us to write the expression as (a+b)² = a² + 2ab + b² = a² + 2ab + 2ab + 4b² = (a² + 2ab + 2ab + 4b²) = (a²+4b²). Therefore, the fully factored form of a²+4b² is (a+b)².
The corner convenience store sells candy in 20 c, 30 c, and 50 c packages, List all the ways in which Waylon can spend exactly $3.00 on candy.
Answers
The possible ways the corner convenience store can sell candy packages to spend at least $3.00 is
How to solve equations?An equation is a mathematical model showing the equality of two opposite sides or an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given parameters are
20c, 30c and 50c
Least cost =$3
Let the possible ways be x
20x+30x+50x=3.00
Solving the equation we have:
100x=3.00
make x the subject
100x=3
x=3/100
This can be expressed in decimal as 0.03
In conclusion, he can sell it in 3/100 or 0.03 ways to spend at least $3.00 on a candy.
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A water tank initially contained 111 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
How many minutes have passed, m, when the tank contains 194 liters? Round to the nearest hundredth.
Answers
Answer:
9.22 minutes
Step-by-step explanation:
You could use the form y=mx + b to find this equation
y will represent the total liters
x will represent the total number of minutes
b will represent the initial number of liters in the beginning
1. Plug 194 in for y, plug 9 in for m, put 111 in place of b
The equation should look be: [tex]194 = 9x + 111[/tex]
2. Solve the equation
3. Subtract 111 on both sides. The equation would now be: [tex]83 = 9x[/tex]
4. Divide both sides by 9 (to get x by itself). [tex]\frac{83}{9} = 9.22222222[/tex]
5. Round to the nearest hundredth place to get 9. 22 minutes
A teacher gives students independent reading 1/2 time for 1 hour,three times a week.Represent the total amount of reading time for a week as a mixed number and an improper fraction.
Answers
The reading time calculated to be
1 1/2 represented as mixed fraction3/2 represented as improper fractionHow to determine the the reading timeThe problem involves multiplication of fractions
The fraction required are:
let the reading time be x
1/2 time for 1 hour = 1/2 * x = x/2
three times a week
= x/2 * 3
= 3x/2
The reading time is 3/2 improper fraction and 1 1/2 mixed fraction
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if 3 -letter words'' are formed using the letters a, b, c, d, e, f, g, how many such words are possible for each of the following conditions:
Answers
The possible number of 3 -letter words that can be formed with given conditions.
(a) No condition is imposed: 343
(b) No letter can be repeated in a word: 210
(c) Each word must begin with the letter 'a' : 49
(d) The letter 'c' must be at the end: 49
(e) The second letter must be a vowel: 98
In this question we have been given that 3 -letter words' are formed using the letters a, b, c, d, e, f, g.
We need to find the possible number of 3 -letter words that can be formed with given conditions.
(a) No condition is imposed.
the possible number of 3 letters words would be,
7³ = 343
(b) No letter can be repeated in a word.
Using the formula of Permutation,
^{7}P_3 = 7!/(7 - 3)!
= 210
(c) Each word must begin with the letter a.
If each word begins with letter 'a' there would be possible combinations of remaining 6 letters at 2nd and 3rd position of 3-letter word.
So, the possible number of 3 letters words would be,
7² = 49
(d) The letter c must be at the end.
If each word ends with letter c there would be possible combinations of remaining 6 letters at 1st and 2nd position of 3-letter word.
So, the possible number of 3 letters words would be,
7² = 49
(e) The second letter must be a vowel.
In the 3 letter word, the second letter must be vowel which is either a or e.
So, the possible number of 3 letters words would be,
49 + 49 = 98
Therefore, the possible number of words would be (a) No condition is imposed: 343
(b) No letter can be repeated in a word: 210
(c) Each word must begin with the letter 'a' : 49
(d) The letter 'c' must be at the end: 49
(e) The second letter must be a vowel: 98
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The complete question is:
3 -letter words'' are formed using the letters a, b, c, d, e, f, g. How many such words are possible for each of the following conditions?
(a) No condition is imposed.
(b) No letter can be repeated in a word.
(c) Each word must begin with the letter a.
(d) The letter c must be at the end.
(e) The second letter must be a vowel.
Find the area of the circle with a diameter of 6.1
Answers
59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find: (round to 4 decimal places where possible)
Answers
The probability that a resident own a cat or a dog is 48%
How to determine the probability a resident own a cat or a dogFrom the question, we have the following parameters that can be used in our computation:
P(Own a cat) = 70%
P(Own a dog) = 59%
P(Own a cat and a dog) = 42%
The probability a resident own a cat or a dog is then calculated as
Probability a resident own a cat or a dog = P(Own a cat) + P(Own a dog) - P(Own a cat and a dog)
Substitute the known values in the above equation, so, we have the following representation
Probability a resident own a cat or a dog = 70% + 59% - 42%
Evaluate the sum and the difference
Probability a resident own a cat or a dog = 48%
Hence, the probability is 48%
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Complete question
59% of all the town's residents own a dog and 70% own a cat. Of the dog owners 42% also own a cat. If a town resident is chosen at random find:
the probability a resident own a cat or a dog
(round to 4 decimal places where possible)
The arts & crafts club is selling candles to raise money. It costs $100 to rent a booth to sell the candles in. Materials to decorate the booth cost $32.50. The candles cost $2.50 each to make and the club sells them for $5 each. How many candles must be sold to break even?
Answers
We know that we need to sell out 53 candles to break even using mathematical operations.
What are mathematical operations?
The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).
So, the total expense of the shop:
$100 + $32.50 = $132.50
No, the candle costs $2.50.
The selling price of a candle is $5.
Profit in each candle is: 5 - 2.50 = $2.50
A number of candles that we need to sell to break even are:
132.50/2.50
53
Therefore, we know that we need to sell out 53 candles to break even using mathematical operations.
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6. Mrs. Ramirez' groceries cost $50 before tax, and the total including sales tax was $55. What is
the sales tax rate that Mrs. Ramirez paid?
Answers
Answer:sales tax rate would be 0.1
using the formula
Sales tax rate = Sales tax percent / 100
What is the rate of change of the function y=-5x+3
Answers
Answer:
-5
Step-by-step explanation:
The rate of change, also known as slope, would be -5.
Slope can be found with two points and the formula y minus y divided by x minus x or the change of y divided by the change in x.
To identify the slope on the equation is easy since this is slope-intercept form.
y=mx+b
where m is the slope
m in this case is -5, so -5 is your answer
For the functions f(x)=2x3 and g(x)=3x3−2, find (f∘g)(1) and (g∘f)(1).
Answers
Value of composite function (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
What is composite function?
Function composition is associate operation ∘ that takes 2 performs f and g, and produces a perform h = g ∘ f such h(x) = g. during this operation, the perform g is applied to the results of applying the perform f to x
Main body:
according to question;
f(x) = 2x³
g(x) = 3x³ -2
we need to find composite function:
f o g (x) = 2(3x³-2)
{to find composite function , we replace one function as value of x in another}
f o g(x) = 6x³ -4
= 6x³ -4
f o g(1) = 6*1 -
= 2
g o f(x) = 3(2x³)-2
g o f(x) = 6x³ -2
= 6x -2
g o f(1) = 6*1 -2
= 5
Hence value of (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.
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A phone company offers two monthly plans plan a cost $19 plus an additional $0.11 for each minute of calls plan b has no initial fee but costs $0.15 for each minute of costs For what amount of calling do the two plans cost the same? What is the cost when the two plans cost the same?
Answers
When the costs of the two plans are equal, plan A will cost $37.81, whereas plan B will cost $25.65.
To find the number of calls at which the two plans cost the same, we need to set the costs equal to each other and solve for the number of minutes. The cost of plan A is $19 + $0.11 per minute, and the cost of plan B is $0.15 per minute. Setting these equal to each other, we get:
$19 + $0.11 per minute = $0.15 per minute
We can then solve for the number of minutes by dividing both sides by the per-minute cost:
$19 / $0.11 per minute = $0.15 per minute / $0.11 per minute
This simplifies to:
171 minutes = 135 minutes
Therefore, the two plans cost the same at 171 minutes of calling.
To find the cost at this point, we can substitute 171 minutes back into either of the original cost equations:
Plan A: $19 + $0.11 per minute × 171 minutes = $19 + $18.81 = $37.81
Plan B: $0.15 per minute × 171 minutes = $25.65
Thus, the cost when the two plans cost the same is $37.81 for plan A and $25.65 for plan B.
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Line p passes through points (8, 7) and (4, 4). Line q is parallel to line p. What is the slope of line q?
Answers
Answer:
slope of line q = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
calculate the slope of line p using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 7 ) and (x₂, y₂ ) = (4, 4 )
m = [tex]\frac{4-7}{4-8}[/tex] = [tex]\frac{-3}{-4}[/tex] = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes
then slope of line q = [tex]\frac{3}{4}[/tex]
The ratio of top dogs to fat cats was 24 to 19. if they were 152 fat cats, how many top dogs were there?
Answers
The ratio shows how many times one value is contained in another value.
The number of top dogs is 192.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of top dogs to fat cats was 24 to 19.
if they were 152 fat cats.
This means,
Number of top dogs = 24x
Number of fat cats = 19x
Now,
Number of fat cats = 152
This means,
152 = 19x
x = 8
Now,
Number of top dogs = 24x
= 24x
= 24 x 8
= 192
Thus,
The number of top dogs is 192.
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Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modeled by the function y=3.5x+5 where y is the total miles jogged and x is the number of hours Shirley continues to jog. Identify the rate of change and the initial value of the function. Express your answers as decimals if necessary.
Answers
The rate of change of the modelled equation is 3.5 and the initial value is 5.
How to find the rate of change in a slope intercept equation?Linear equation can be represented in different form such as slope intercept form, point slope form, general form and standard form.
Equation in slope intercept form is as follows:
y = mx + b
where
m = slope = rate of changeb = y-intercept = initial valueTherefore, Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modelled by the function y = 3.5x + 5 where y is the total miles jogged and x is the number of hours.
The equation is modelled in slope intercept form.
Therefore,
rate of change = 3.5
initial value = 5
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Mark and Aly were selling slices of pizza for a school event. Mark had 2 1/3
of a pizza pie left over. Aly had 1 5/9 left.
Together, how much pizza did Mark and Aly have left?
Answers
Answer:
11/9
Step-by-step explanation:
If this is an addition question then this is your answer.
9. ΔRWS ≅ ΔTUV
Find the values of x and y
Answers
[tex]VT=SR \implies 3y+7=25 \implies \boxed{y=6} \\ \\ \\ ○\ m\angle UTV=180^{\circ}-90^{\circ}-29^{\circ}=61^{\circ} \\ \\ \angle WRS \cong \angle UTV \implies 8x-27=61 \implies \boxed{x=11}[/tex]
Suppose 41% of the registered voters in a country are Republican. If a sample of 488 voters is selected, what is the probability that the sample proportion of Republicans will be greater than 44%?
Answers
The probability that the sample's Republican percentage will be higher than 44% is 0.089.
What is probability?Probability is a metric used to express the possibility or chance that a particular event will occur.
Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.
To determine the probability of a sample proportion, the normal probability is used as the z-test statistic of one sample proportion.
When the sample size is big, the z-test statistic, a normal test statistic, is employed.
So, the probability will be:
We know that the sample size is n = 488 and the proportion is p = 0.41.
Now, obtain P(p > 0.44) as follows:
[tex]\begin{aligned}& P(\hat{p} > 0.44)=1-P\left(\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} \leq \frac{0.44-p}{\sqrt{\frac{p(1-p)}{n}}}\right) \\& P(\hat{p} > 0.44)=1-P\left(Z \leq \frac{0.44-0.41}{\sqrt{\frac{0.41(1-0.41)}{488}}}\right) \\& P(\hat{p} > 0.44)=1-P(Z \leq 1.347)\end{aligned}[/tex]
Excel function for the p-value:
P(p > 0.44) = 1 - 0.911
P(p > 0.44) = 0.089
Therefore, the probability that the sample's Republican percentage will be higher than 44% is 0.089.
Know more about probability here:
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