Answer:
6 is not the solution. 7 is the solution.
Step-by-step explanation:
5(x -3) = x + 13 Substitute 6 for x
5(6 -3) = 6 + 13
5(3) = 19
15 ≠ 19
6 is not a solution because it results in a false statement. The two sides do not equal each other.
5(x - 3) = x + 13 Distribute the 5
5x -15 = x + 13 Subtract x from both sides
5x - x - 15 = x - x + 13
4x - 15 = 13 Add 15 to both sides
4x - 15 + 15 = 15 + 13
4x = 28 Divide both sides by 4
x = 7
7 is the solution to the equaion.
Pete is saving $0. 45 each week to buy a video game that cost $9. 0. How many weeks will he have to save?
If , Pete is saving $0. 45 each week to buy a video game that cost $9.0. Pete will have to save for 20 weeks to have enough money to buy the video game.
The problem asks us to find out how many weeks Pete will have to save to buy a video game that costs $9.0 if he is saving $0.45 each week. To solve this problem, we can use division to find out how many times $0.45 goes into $9.0.
We first divide the total cost of the game by the amount Pete saves each week, which gives us the number of weeks he will need to save.
In this case, the division of $9.0 by $0.45 yields 20, which means that Pete will have to save for 20 weeks to buy the video game. This calculation is important for Pete because it helps him plan his savings and gives him a goal to work towards. By saving $0.45 every week, he can keep track of his progress and stay motivated to reach his goal.
This problem highlights the importance of basic arithmetic skills, specifically division, in practical situations like budgeting and financial planning. By applying mathematical concepts to everyday situations, we can make informed decisions and manage our resources more effectively.
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In the graph, y represents a company's profit in thousands of dollars, and x represents the time in years.
(3,4)
(3,2)
per year
x1
At what rate is the company's profit changing?
The company profit is decreasing by 1/3 thousand dollars per year.
What is an equation?An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the initial value of y.
Let y represents a company's profit in thousands of dollars, and x represents the time in years.
From the graph, using the point (-3, 4) and (3, 2):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Substituting:
[tex]y-4=\frac{2-4}{3-(-3)} (x-(-3))\\\\y=-\frac{1}{3}x+3[/tex]
The company profit is decreasing by 1/3 thousand dollars per year.
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15. Miss Jackson wrote this number sentence on the board.
7x = 36
Which procedure could be used to find a value for x that will make the number
sentence true?
A. Subtract 7 from 7x, and subtract 7 from 36.
B. Multiply 7x by 7, and multiply 36 by 7.
C. Divide 7x by 7, and divide 36 by 7.
D. Add 7 to 7x, and add 7 to 36.
Find the circumference of each of the circle with the following radius. A. 10 cm
B. 2. 7 cm
C. 1. 2 mm
D. 9. 01 cm
A. 10 cm radius: 2 * pi * 10 cm = 62.83 cm
B. 2.7 cm radius: 2 * pi * 2.7 cm = 16.94 cm
C. 1.2 mm radius: 2 * pi * 1.2 mm = 7.54 mm
D. 9.01 cm radius: 2 * pi * 9.01 cm = 56.76 cm
A. The circumference of a circle with a radius of 10 cm is 62.83 cm.
B. The circumference of a circle with a radius of 2.7 cm is 16.94 cm.
C. The circumference of a circle with a radius of 1.2 mm is 7.54 mm.
D. The circumference of a circle with a radius of 9.01 cm is 56.76 cm.
The circumference of a circle is the distance around its edge. It can be calculated using the formula 2πr, where r is the radius of the circle. The radius is the distance from the center of the circle to any point on its edge. To find the circumference of a circle, we need to multiply the radius by 2 and then by pi (π), which is roughly 3.14.
For example, if the radius of the circle is 10 cm, then the circumference of the circle is 2πr = 2π x 10 cm = 62.83 cm. Similarly, if the radius of the circle is 2.7 cm, then the circumference of the circle is 2π x 2.7 cm = 16.94 cm. If the radius of the circle is 1.2 mm, then the circumference of the circle is 2π x 1.2 mm = 7.54 mm. Finally, if the radius of the circle is 9.01 cm, then the circumference of the circle is 2π x 9.01 cm = 56.76 cm.
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Combine like terms to create an equivalent expression.
−
3.6
−
1.9
�
+
1.2
+
5.1
�
−3.6−1.9t+1.2+5.1tminus, 3, point, 6, minus, 1, point, 9, t, plus, 1, point, 2, plus, 5, point, 1, t
The equivalent expression with combined like terms is -5.5t + 6.3.
What is Equivalent expression?
Equivalent equations are algebraic equations with the same roots or solutions. We get an analogous equation by adding or subtracting the same number or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same non-zero value.
To combine like terms, we can group the terms with the variable t together, and group the constant terms together:
(-3.6t) + (-1.9t) + (1.2 + 5.1)
We can simplify the constant terms:
(-3.6t) + (-1.9t) + 6.3
Finally, we can combine the terms with the same variable by adding their coefficients:
-5.5t + 6.3
Therefore, the equivalent expression with combined like terms is -5.5t + 6.3.
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The student can combine like terms in the given expression by adding and subtracting the corresponding pairs. This gives the equivalent expression as 3.2t - 2.4.
Explanation:To combine like terms in the equation -3.6 - 1.9t + 1.2 + 5.1t, you need to group together the like terms. The two like terms we have are the terms with the variable t, -1.9t and +5.1t, and the two constant terms -3.6 and +1.2 without the variable t.
When you add and subtract these pairs accordingly, you get:
-1.9t + 5.1t = 3.2t
-3.6 + 1.2 = -2.4
So, the equivalent expression that combines these like terms is: 3.2t - 2.4.
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The above figure shows the market for DVDs. The government decides that all citizens deserve to watch affordable DVDs so a price ceiling of $12 per DVD is placed on DVDs. After this price ceiling is in effect, producer surplus equals ________.
$1,800,000
$900,000
$400,000
$200,000
$100,000
Option B : The market for DVDs is described by a downward sloping demand curve and an upward sloping supply curve. The price ceiling of $12 per DVD will result in a shortage of DVDs.
In a competitive market, the market price of a good will be set at the intersection of the demand curve and the supply curve. This is the point where the quantity of the good that consumers are willing to buy at a given price is equal to the quantity that producers are willing to sell. At this market price, producer surplus is equal to the area above the supply curve and below the market price, up to the quantity supplied.
In this scenario, the producer surplus will be equal to the area between the supply curve and the price ceiling, up to the quantity that is supplied. Based on the diagram, the producer surplus will be equal to $900,000.
So, the answer to the question is $900,000.
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The above figure shows the market for DVDs. The government decides that all citizens deserve to watch affordable DVDs so a price ceiling of $12 per DVD is placed on DVDs. After this price ceiling is in effect, producer surplus equals ________.
A. $1,800,000
B. $900,000
C. $400,000
D. $200,000
E. $100,000
how quarts are equivalent to 14 liters? Round your answer to the nearest tenth.
Answer:
14.737
Step-by-step explanation:14 divided by .95 = 14.7368… then rounded to nearest hundred is 14.737
€100 was invested in a savings account. After 10 years, there is
€300 in the account.
Work out how much money would have been in the account after
only 5 years if it had been gathering
a) annual simple interest.
b) annual compound interest.
Give each of your answers to the nearest €1.
c) Will the savings account have more money in it after 15 years if
it is gathering annual simple interest or annual compound interest?
Answer:
Simple Interest
SI=PRT/100
P=€100
SI=€300-€100 = €200
T=10 years
rate = unknown
Rate = SIx100/(pxt)
Rate = 200x100/(100x10)
= 20%
b)Compound interest
CI = P(1+i)ⁿ
CI= €300
P =€100
n = 10
€300 = €100(1+i)¹⁰
take the tenth root of both sides
€1.77 = €1.58(1+i)
divide both sides by 1.58
1.12 = 1 + i
i = 1.12 - 1
i = 12%
c)si=prt/100
=(100x20x15)/100
= €300
total = 300+100
€400
CI = P(1+i)ⁿ
= 100(1+0.12)¹⁵
=€547.35
It is gathering more money with annual compound interest
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i wasnt here when we did this, please help?
Answer:
25°
Step-by-step explanation:
look at the picture, that's the ans
Answer:
x = 25.4
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
139° is an exterior angle of the triangle, then
5x - 25 + 37 = 139
5x + 12 = 139 ( subtract 12 from both sides )
5x = 127 ( divide both sides by 5 )
x = 25.4
LA Galaxy have won 36%of their soccer matches .If they have played 50 matches ,how many have they won ?
If LA Galaxy has won 36% of their soccer matches, this means that they have won 36/100 * 50 = 18 matches.
So, they have won 18 matches out of 50.
Step-by-step explanation:
percentage of soccer matches won = 36%
total matches = 50
matches won = 36/100 * 50
=18
Joe and Martha shared 56 books joe had 2 more books than Martha how many did Martha have
Answer:
26
Step-by-step explanation:
56/2 -2
What are the coordinates of(D0.25∘rx-axis)(ABCD) for A(2, 6), B(0, 0), C(-5, 8), and D(-2, 10)?
(express ordered pairs as decimal)
Answer: The coordinates of the image of a figure after a rotation of 0.25 degrees about the x-axis can be found using the following formulas:
x' = x
y' = y * cos(θ) - z * sin(θ)
z' = y * sin(θ) + z * cos(θ)
where (x, y, z) are the original coordinates and (x', y', z') are the new coordinates. In this case, we only need to find the y' coordinate because the rotation is about the x-axis and the x coordinate will not change.
For each point, we can use the formula to find the y' coordinate:
A (2, 6) -> y' = 6 * cos(0.25) - 0 * sin(0.25) = 5.99911... ~ 6
B (0, 0) -> y' = 0 * cos(0.25) - 0 * sin(0.25) = 0
C (-5, 8) -> y' = 8 * cos(0.25) - 0 * sin(0.25) = 7.99823... ~ 8
D (-2, 10) -> y' = 10 * cos(0.25) - 0 * sin(0.25) = 9.99649... ~ 10
So, the new coordinates after rotating 0.25 degrees about the x-axis are:
A (2, 6) -> (2, 6)
B (0, 0) -> (0, 0)
C (-5, 8) -> (-5, 8)
D (-2, 10) -> (-2, 10)
The coordinates of the points have not changed after the rotation because the rotation angle is very small.
Step-by-step explanation:
There were 50 guests in a marriage ceremony. 30 were from the groom's family and 20 were from the brides's family. There's a tradition of giving hugs among the groom's family although there's no such traditions in the bride's family. They only shake hands. what's the number of total handshakes?
Note that the members from the bride's family will shake hands with the groom's family too.
Answer:
1020 handshakes including the bride and the groom. 980 excluding the groom and the bride.
Step-by-step explanation:
(20*19) twenty people on the brides side shake hands with the other 19 people (19 because you can't really shake your own hand).
+(20*30) twenty people on the brides side shake hand with 30 people on the grooms side.
+(20*2) twenty people on the brides side shake hands with the bride and the groom.
this equalssss......
1020!!!!
Since the grooms family does hugs instead of handshakes, you'd only calculate how many the brides side does.
Hello can somebody please explain thank you
The correct option is C which is out of 30000 there will be 27000 deaths.
What is the percentage?According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.
Given, according to the website, 90% of the 30,000 deaths caused by unsafe water and filthy living conditions that occur every week around the world involve children under the age of five. All of the following interpretations of this statistic are accurate.
The percentage of deaths will be calculated as:-
Percentage = 30000 x 90%
Percentage = 30000 x 0.9
Percentage = 27000
Therefore, the number of deaths will be 27000.
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The quadrilateral is a trapezoid. What is the value of x?454825
The value of x for the trapezoid quadrilateral is equal to 5.
The quadrilateral is an isosceles trapezoid, with a line parallel to both opposing lines splitting the other two unparallelly going lines into equal halves. Hence, according to normal relations, the mid length is 5x-1.
The lengths of the opposing sides are 21 and 27 respectively. As a result, we may write 2(5x - 1) = 21 + 27.
Growing further, 10x - 2 = 48
10x = 48 + 2
10x = 50
Divide all sides by ten.
x = 50/10
x = 5
As a result, the value of x is 5.
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Los 2/5 de los ingresos de una comunidad de vecinos
se emplean en combustible; 1/8 en electricidad, 1/12
en recogida de basuras, 1/4 en mantenimiento del
edificio y el resto se emplea en limpieza.
¿Qué fracción de los ingresos se emplea en limpieza?
The fraction of income spent on cleaning is 71/50.
What is fraction?A fraction is represented by the ratio in the form -
{x} : {y} = {x}/{y}
In terms of numbers, we can write -
2 : 3 = 2/3
Given is that 2/5 of the income of a community of neighbors they are used in fuel, 1/8 in electricity, 1/12 in garbage collection, 1/4 in maintenance of the building and the rest is used for cleaning.
Assume the fraction to be {x}. Then, we can write -
2/5 + 1/8 + 1/12 + 1/4 + x = 1
0.4 + 0.125 + 0.083 + 0.25 + x = 1
x = 0.142
x = 142/100
x = 71/50
Therefore, the fraction of income spent on cleaning is 71/50.
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{Question in english -
2/5 of the income of a community of neighbors
they are used in fuel; 1/8 in electricity, 1/12
in garbage collection, 1/4 in maintenance of the
building and the rest is used for cleaning.
What fraction of the income is spent on cleaning?}
How much money in dollars and cents did Julie have to spend after buying the chair?
How are lim p(x) and lim p(x) calculated if p is a polynomial function?
Limits function lim p(x) can be calculated if p is a polynomial function by:
Identify the degree of the polynomial.Substitute the defined limits with xSimplify and solve the limits function.To calculate the limits of a polynomial function, p(x), first identify the degree of the polynomial. Then, use the formula Lim p(x) = aₙ xⁿ + aₙ₋₁ xⁿ⁻¹ + ... + a₀, where an is the leading coefficient. For example, if the polynomial is of degree 3, then the formula would be:
Lim p(x) = a₃ x³ + a₂ x² + a₁ x + a₀.
Next, we need to subtitute the variable x with the defined limits. For example, if the defined limit of the function is 2, then the limit function would be:
Lim p(2) = a₃ (2)³ + a₂ (2)² + a₁ (2) + a₀
Then, we just need to simplify our finding:
Lim p(2) = 8a₃ + 4a₂ + 2a₁ + a₀
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the probability distribution for the random variable follows. 200.20 250.15 300.25 350.40 a. is this probability distribution valid? explain.
The given probability distribution for the random variables is valid
The probability is the ratio of the number of favorable outcomes to the total number of outcomes
The equation will be
The probability = Number of favorable outcomes / Total number of outcomes
The probability distribution is the probabilities of the each random event
From the table we can see that the probability distribution of each random events are
0.20, 0.15, 0.25, 0.40
Add the probability distributions of each random events
= 0.20 + 0.15 + 0.25 + 0.40
= 1
Here the sum of the probability distribution of the random events is 1
Therefore, the probability distribution is valid
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an analyst has a sample of 28 observations of the weekly return of an index portfolio that includes 50 stocks. the weekly returns are approximately normally distributed, and the sample mean and sample variance are 1.2% and 0.00175. a 90% confidence interval for a weekly return is closest to:
We are 90% confident that the true weekly return of the index portfolio is between 1.186% and 1.214%.
One important concept in statistics is a confidence interval, which is a range of values that is likely to contain the true value of a parameter, such as a population mean or proportion.
The analyst has a sample of 28 observations of the weekly return, which is assumed to be normally distributed. The sample mean is 1.2% and the sample variance is 0.00175. With this information, we can calculate the standard error of the mean, which measures the variability of the sample mean from one sample to another. The formula for the standard error is:
standard error = sample standard deviation / square root of sample size
In this case, the sample standard deviation is the square root of the sample variance, which is approximately 0.0418%. The square root of the sample size is 5.2915. Therefore, the standard error of the mean is:
standard error = 0.0418 / 5.2915 = 0.0079%
To construct a 90% confidence interval for the weekly return, we need to use the t-distribution, which is a probability distribution that takes into account the sample size and the level of confidence. The t-distribution has more variability than the normal distribution, which results in wider confidence intervals for smaller sample sizes.
The formula for a t-confidence interval is:
sample mean ± t-value x standard error
The t-value depends on the sample size and the level of confidence. For a sample size of 28 and a 90% confidence level, the t-value is 1.699. Therefore, the confidence interval is:
1.2 ± 1.699 x 0.0079 = [1.186%, 1.214%]
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Which cylinder has a volume of 45% cm³?
Answer:
Right cylinder
Step-by-step explanation:
Right cylinder
A haiku is a poem with three lines: the first line contains 5 syllables, the second line 7 syllables, and the last line 5 syllables. If each word in each list shown is used at most once, how many different haiku can be made with these words?
2 syllable words:
UNKNOWN
MEASURE
COUNTING
LOGIC
3 syllable words:
ALGEBRA
TRIANGLE
REASONING
There will be 350 different haiku that can be made with the given words.
How to calculate the valueIn this case, there are 5 syllables in the first line, 7 syllables in the second line, and 5 syllables in the last line, so the number of different haiku is given by the number of combinations of 3 elements taken from the set containing 5 elements (for the first and last lines) and 7 elements (for the second line), respectively.
This can be calculated as:
C(5,3) * C(7,3) = 10 * 35
= 350
So, there are 350 different haiku that can be made with the given words.
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Find X then find angle PSQ
The value of angle PSQ is 136. 9 degrees
How to determine the valueIt is important to note the following;
Supplementary angles sum up to 180 degreesAngles on a straight are equivalent to 180 degreesThen, we have that;
30x + 6 + 11x - 5 = 180 degrees
Now, let's collect the like terms
30x + 11x + 6 - 5 = 180
add or subtract the like terms
41x = 180 - 1
41x = 179
Divide the values, we get;
x = 4. 36
Then,
PSQ = 30x + 6
PSQ = 136. 9 degrees
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a school superintendent must make a decision whether or not to cancel school because of a threatening snow storm. what would the results be of type i and type ii errors for the null hypothesis: the weather will remain dry?
Type I error would be weather remains dry, but school is needlessly canceled. Type II error would be don't cancel school, but the snow storm hits. The correct option is B.
In hypothesis testing, the null hypothesis is the default assumption that is being tested. In this case, the null hypothesis is that the weather will remain dry. The school superintendent must decide whether to reject or accept this null hypothesis based on the evidence available.
There are two types of errors that can occur in hypothesis testing: Type I and Type II errors.
Type I error occurs when the null hypothesis is rejected, even though it is actually true. In other words, the school superintendent decides to cancel school due to a snowstorm, but the weather remains dry. This can result in unnecessary school closures, which can disrupt students, teachers, and parents' schedules.
Type II error occurs when the null hypothesis is accepted, even though it is actually false. In other words, the school superintendent decides not to cancel school because of the assumption that the weather will remain dry, but a snowstorm hits. This can put students, teachers, and parents in danger as they try to commute to school in hazardous conditions.
The consequences of a Type I error and a Type II error can be significant in this scenario. The school superintendent must weigh the potential risks of making each type of error to make the best decision for the safety and well-being of the school community.
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Complete question is:
A school superintendent must make a decision whether or not to cancel school because of a threatening snow storm. What would the results be of Type I and Type II errors for the null hypothesis: The weather will remain dry?
A. Type I error: don't cancel school, but the snow storm hits.
Type II error: weather remains dry, but school is needlessly canceled.
B. Type I error: weather remains dry, but school is needlessly canceled.
Type II error: don't cancel school, but the snow storm hits.
C. Type I error: cancel school, and the storm hits.
Type II error: don't cancel school, and weather remains dry.
D. Type I error: don't cancel school, and snow storm hits.
Type II error: don't cancel school, and weather remains dry.
E. Type I error: don't cancel school, but the snow storm hits.
Type II error: cancel school, and the storm hits.
A tree that is 18 feet tall is growing at a rate of 2 feet each year. A different tree that is 20.5 feet tall is growing at a rate of
3/4
feet each year. At this rate, when will the trees be the same height? What will
the height of the trees be?
The trees will be the same height in 2 years and the height of these trees will be 22 ft.
Linear Expression
A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=x+10. Where:
m= the slope.
b= the constant term that represents the y-intercept
For the given example: m=1 and b=10.
For solving the question you should convert the given text into an algebraic expression.
Tree01= 18+2*y
Tree02= 20.5+0.75*y (Note that 3/4=0.75)
y= number of years
Therefore,
18+2*y=20.5+0.75*y
2y-0.75*y=20.5-18
1.25y=2,5
y=2
Thus, at 2 years the trees will be the same height.
When y=2, you have:
Tree01= 18+2*y= 18+2*2=18+4=22
Tree02= 20.5+0.75*y =20.5+1.5=22
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Please help me it’s a drag and drop
Darnell solved a system of equations by graphing. When he graphed the lines,
he saw that the two lines intersected. What should Darnell conclude about the
solution to this system of equations?
There are infinitely many solutions.
There is exactly one solution.
There are exactly two solutions.
There are no solutions.
The point of intersection of two lines implies a system has one solution, therefore, Darnell should conclude that: B. there is exactly one solution to the system of equations.
What is the Solution of a System by Graphing?If the two lines in a system of equations intersect when graphed, then there is exactly one solution to the system of equations. This is because the point of intersection represents the values of the variables that satisfy both equations simultaneously.
If the two lines in a system of equations are parallel and do not intersect when graphed, then there are no solutions to the system of equations. If the two lines are the same and coincide when graphed, then there are infinitely many solutions to the system of equations.
Therefore, Darnell should conclude that: B. there is exactly one solution to the system of equations.
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Solve for system of equation 2 equations 6x+3y=8 and 8x+4y=-1
The solution of the given system of equations 6x+3y=8 and 8x+4y=-1 is x=0 and y==-8/9
What is system of equations?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system. (5, 4) is a solution of the first equation, but not the second.
We are given that;
The equation 1; 6x+3y=8
The equation 2; 8x+4y=-1
Now,
In equation 1
6x=8-3y
x=(8-3y)/6
Substituting the value of x in equation 2
8((8-3y)/6)+4y=-1
4((8-3y)/3)+4y=-1
(8-3y)/3)+4y=-1/4
8-3y+12y=-3/4
8+9y=-3/4
9y=-3/4-8
9y=-3-32/4
9y=-35/4
y=-32/36=-8/9
Putting the value of y in equation 1
6x+3(-8/9)=8
54x-8=8
x=0
Therefore, the solution of the equations will be x=0, y=-8/9.
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I don’t understand this can someone help
The ordered pair (2,10) means that the cost to feed 200 animals is of $10,000.
How to interpret the ordered pair?The general format of an ordered pair is given as follows:
(x,y).
The meaning of an ordered pair (x,y) is that y = f(x), meaning that the numeric value of the function at the value of x is of y.
The variables for this problem are given as follows:
x -> number of animals, in hundreds, hence x = 2 means that there are 200 animals.y -> cost to feed the animals, in thousands, hence y = 10 means that the cost is of $10,000.More can be learned about ordered pairs at brainly.com/question/1528681
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the food marketing institute shows that of households spend more than per week on groceries. assume the population proportion is and a simple random sample of households will be selected from the population. use the z-table.
a) The sampling distribution of p can be approximated as a normal distribution with mean μp = .17 and standard deviation σp = .0203.
b) The probability that the sample proportion will be within ±.02 of the population proportion is 0.6778
In statistics, sampling distribution plays a crucial role in estimating the parameters of a population. The sampling distribution helps us to understand the probability distribution of sample statistics that we obtain by taking random samples from a population.
a) In this case, we are interested in the proportion of households that spend more than $100 per week on groceries, denoted by p. We know that the population proportion is p = .17, and a sample of 800 households will be selected from the population.
The central limit theorem states that if the sample size is large enough (in this case, n = 800), then the sampling distribution of p will be approximately normal with a mean of p and a standard deviation of:
σp = √(p(1-p)/n)
where p is the population proportion, and n is the sample size. Plugging in the values, we get:
σp = √(.17(1-.17)/800) = .0203
b) Now, we want to find the probability that the sample proportion will be within ±.02 of the population proportion. That is, we want to find P(.15 ≤ p ≤ .19).
To calculate this probability, we need to standardize the distribution using the z-score formula:
z = (p - μp) / σp
Plugging in the values, we get:
z = (.15 - .17) / .0203 = -0.9867
z = (.19 - .17) / .0203 = 0.9867
Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:
P(z ≤ -0.9867) = 0.1611
P(z ≤ 0.9867) = 0.8389
Therefore, the probability that the sample proportion will be within ±.02 of the population proportion is:
P(.15 ≤ p ≤ .19) = P(z ≤ 0.9867) - P(z ≤ -0.9867) = 0.8389 - 0.1611 = 0.6778
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Complete Question:
The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population.
a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries.
b. What is the probability that the sample proportion will be within ±.02 of the population proportion?
