Therefore , the solution of the given problem of average comes out to be the average yearly income is $67,200.
Explain average.The exact number that constitutes the mean in a group with structure is its median value. In this instance, as opposed to being a typical measurement, the percentage ratio among the lowest and greatest 50% of the collection is a probability measurement. Different methods may be employed to determine the centre and mode of any odd or strange numbers.
Here,
The following formula is used to determine the project's yearly depreciation:
=> (Initial cost – Residual worth) / (Useful life) = Annual Depreciation
The project's useful life is 8 years, and since there is no residual worth, the annual depreciation is as follows:
=> Depreciation per year = ($448,000 - $0) / 8 = $56,000
The annual average income is calculated as the original cost multiplied by the initial rate of return, divided by the number of years of useful life:
Average yearly revenue is calculated as follows:
=> (Annual depreciation + Average rate of return x Initial cost) / Useful life
When we change the numbers, we obtain:
=> ($56,000 + 0.09 x $448,000) / 8 = $67,200 annually is the average yearly income.
The average yearly income is therefore $67,200.
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solve the equation
x/2-2=4+1/2
Step-by-step explanation:
7eh8heusvush0wio0w92726 2is 3the world ydgugd8jd8djkd0jd9jd8hd7hd
a
21 units squared
b
27.6 units squared
c
32.2 units squared
d
42 units squared
The area of the right triangle given in this problem is given as follows:
21 units squared -> Option A.
How to obtain the area of a triangle?To calculate the area of a triangle, you can use the formula presented as follows:
Area = (1/2) x base x height
In which the parameters are given as follows:
"base" is the length of the side of the triangle that is perpendicular to the height."height" is the length of the perpendicular line segment from the base to the opposite vertex.For a right triangle, we can consider one side to be the base and the other side to be the height, hence the parameters are given as follows:
Base of 7 units.Height of 6 units.Hence the area of the triangle is given as follows:
A = 0.5 x 7 x 6 = 21 units squared.
Missing InformationThe complete problem is defined as follows:
"Calculate the area of the given triangle".
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HELP ME ASAPPP!!! Ill mark you brasinlisest
Step-by-step explanation:
Theoretical probabilities can be calculated using the concept of probability. Each student has a 0.5 chance of selecting either List A or List B. Therefore, the probability of getting 27 heads and 33 tails can be calculated as:
P(27 heads and 33 tails) = (60 choose 27) * (0.5)^27 * (0.5)^33 where (60 choose 27) is the number of ways to select 27 students out of 60.
Using a calculator, we can compute the above probability as approximately 0.109. This means that if we were to repeat this experiment many times, we would expect to get 27 heads and 33 tails about 10.9% of the time.
Comparing this theoretical probability to the experimental results, we see that the observed proportion of heads (27/60 = 0.45) is lower than the expected proportion of heads (0.5) and the observed proportion of tails (33/60 = 0.55) is higher than the expected proportion of tails (0.5).
However, it is important to note that due to the random nature of the experiment, we would not expect the exact theoretical probabilities to match the experimental results exactly. In other words, there is always some amount of variation expected in the results. Nonetheless, the experimental results are consistent with the theoretical probabilities, and we can conclude that there is no significant deviation from what we would expect by chance.
Solve the polynomial equation by factoring and then using the zero-product principle.
4x = 864x
Rewrite the equation in factored form.
(Blank)= 0
What is the solution pair?
In response to the stated question, we may state that As a result, the equation's answer is x = 0.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
4x = 864x is the provided equation.
This equation may be simplified by deleting 4x from both sides:
[tex]860x = 0[/tex]
This equation may now be rewritten in factored form:
[tex]860x = 0 \sx(860) = 0[/tex]
We know from the zero-product principle that if the product of two elements is zero, then at least one of them must be zero. As a result, we may set each component to zero and solve for x:
x = 0 or 860 = 0 (which is impossible) (which is impossible)
As a result, the equation's answer is x = 0.
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A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books isA 1 / 21B 10 / 21C 11D 21 / 11
If 2 books are chosen at random, then the probability that both are statistics books is (a) 1/21.
The number of statistics book in bookcase is = 2;
The number of biology books in bookcase is = 5;
So, the total number of books is = 7;
The Probability of choosing a statistics book on the first draw is 2/7, since there are 2 statistics books out of a total of 7 books.
After the first book is chosen, there will be 6 books left, including 1 statistics book out of a total of 6 books.
So, the probability of choosing another statistics book on the second draw is 1/6.
In order to find the probability of both events happening together (i.e. choosing 2 statistics books in a row), we multiply the probabilities of each event:
So, P(choosing 2 statistics books) = P(1st book is statistics) × P(2nd book is statistics given that the 1st book was statistics);
⇒ (2/7) × (1/6)
⇒ 1/21
Therefore, the required probability is (a) 1/21.
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The given question is incomplete, the complete question is
A bookcase contains 2 statistics books and 5 biology books. If 2 books are chosen at random, the chance that both are statistics books is
(a) 1/21
(b) 10/21
(c) 11
(d) 21/11
I need help with this question.
you need to match it to the percentage of the fraction for example 1/2 is 50 percentage and than you do 1/4 is 25 percent.
Help I don’t just this
The conditional relative frequency that a student rides the bus, given that the student is in middle school is 0.16 / 0.96 ≈ 0.17.
Describe conditional relative frequency ?Conditional relative frequency is a statistical measure that describes the proportion or percentage of a specific group or category within a subset of data. It is calculated by dividing the frequency of the specific category in the subset by the frequency of the total subset.
To find the conditional relative frequency that a student rides the bus, given that the student is in middle school, we need to divide the frequency of middle school students who ride the bus by the total number of middle school students.
From the table, we see that the frequency of middle school students who ride the bus is 0.16. The total number of middle school students is the sum of the frequencies in the first row, which is 0.20 + 0.16 + 0.12 + 0.48 = 0.96.
So, the conditional relative frequency that a student rides the bus, given that the student is in middle school is:
0.16 / 0.96 ≈ 0.17
Rounded to the nearest hundredth, the answer is 0.17. Therefore, about 17% of middle school students ride the bus.
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factorise completely.
3x²-12xy
Answer:
Hence, factors are 3x,(x−4y).
Step-by-step explanation:
We need to factorise 3x 2 −12xy
Here we can take 3x common.
Thus we have 3x 2−12xy=3x(x−4y)
Hence, factors are 3x,(x−4y).
Answer: 3x ( x - 4y )
Step-by-step explanation:
Factorizing 3x²-12xy
3x ( x - 4y )
Martin Pincher purchased a snow shovel for $28.61, a winter coat for $23.27, and some rock salt for $7.96. He must pay the state tax of 5 percent, the county tax of 0.5 percent and the city tax of 2.5 percent. What is the total purchase price?
Hi Martin,
To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.
The total purchase cost of all three items is:
Snow shovel: $28.61
Winter coat: $23.27
Rock salt: $7.96
Total purchase cost: $59.84
Now, we apply the applicable taxes:
State tax: 5% of $59.84 = $2.99
County tax: 0.5% of $59.84 = $0.30
City tax: 2.5% of $59.84 = $1.49
Total taxes: $2.99 + $0.30 + $1.49 = $4.78
Therefore, the total purchase price is:
Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62
Conduct a survey with a minimum of 20 people. Complete the designed questionnaire in 1.2. Remind participants why you are doing survey and that their information will be kept confidential. Submit 20 original completed questionnaires.
Important points to conduct a survey are; to gather information, make informed decisions, evaluate programs or services, identify trends, assess needs.
What is the need to conduct a survey?Surveys are conducted for a variety of reasons, including gathering information, making informed decisions, evaluating programs or services, identifying trends, and assessing needs. By using surveys, organizations can collect valuable data that can be used to inform decisions, improve programs or services, and better understand their target audience.
Surveys, also known as questionnaires, are used to gather information from a targeted group of individuals or a population. Surveys are an important tool for collecting data in a structured manner and can be used for a variety of reasons. Here are some of the reasons why surveys are conducted:
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The question is in the picture.
The composite function is obtained applying the inner function as the input to the outer function.
The functions for this problem are defined as follows:
Inner function: T(t) = 6t + 1.2.Outer function: N(T) = 20T² - 128t + 77.Hence the composite function is obtained replacing the two instances of T on the function N(t) by the definition of T(t), hence:
N(T(t)) = 20(6t + 1.2)² - 128(6t + 1.2) + 77
N(T(t)) = 720t² + 288t + 28.8 - 768t - 204.6.
N(T(t)) = 720t² - 480t - 175.8.
For a population of 18413 bacteria, we have that N(T(t)) = 18413, hence:
720t² - 480t - 175.8 = 18413
720t² - 480t - 18588.8 = 0.
The coefficients of the quadratic function are given as follows:
a = 720, b = 480, c = -18.588.8.
Using a quadratic function calculator, the positive solution is given as follows:
t = 4.76 hours.
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HERE IS THE SEQUENCE OF NUMBERS 3,6,11,18,27...
FIND THE NTH TERM OF THE SEQUENCE
3, 6, 11, 18, 27, 38, 51 , Next term 51 in the sequence is nth term .
What does math sequence mean?
An arrangement of numbers in a specific order is referred to as a sequence. The sum of the components of a sequence, on the other hand, is what is referred to as a series.
SEQUENCE 3,6,11,18,27...
the series follows the odd counting.
for example:
we have odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, etc.
now
3 + 3 = 6
6 + 5 = 11
we can see adding odd numbers in a series results in the solution of the proceeding number of series.
similarly,
11 + 7 = 18
18 + 9 = 27
27 + 11 = 38
now adding 13 to 38 according to the series will result in the next number.
38 + 13 = 51
hence, 51 is the next number in the series.
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Celine is 6 years younger than her sister Cindy. She is also one third as old as Cindy.
Select two equations of a system that can be solved to find both ages.
a. 3x-6y=0
b. 3x-y=0
c. y-x=6
d. x-y=6
The two equations of a system that can be used to find the ages of both girls are y - x = 6 and 3x - y = 0.
What is system of equations?A group of two or more equations that must be solved all at once is known as a system of equations. The objective is to determine the values of the variables that make both equations true in a system of two equations with two variables. These numbers represent the system of equations' answer. There are several ways to solve a system of equations, including substitution, elimination, and graphing. They are used to simulate and resolve issues in many branches of mathematics, science, engineering, and other disciplines.
Let us suppose the age of Celine = x.
Let us suppose the age of Cindy = y.
Given that, Celine is 6 years younger than her sister Cindy.
x = y - 6
She is also one third as old as Cindy.
x = 1/3y or y = 3x.
Substitute the value of y in equation 1:
x = 3x - 6
6 = 2x
x = 3
Substitute the value of x:
y = 3(3) = 9
Hence, the two equations that can be used to find the ages of both girls are y - x = 6 and 3x - y = 0.
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of the following values, which is least important to today's college students according to the yearly values survey?
The least important value to today's college students according to the yearly values survey is Political involvement. So the option B is correct.
The survey found that only 32% of college students believed that political involvement was important. This is significantly lower than the other values surveyed such as Financial Success (86%) and Community Involvement (71%). As such, it can be concluded that Political Involvement is the least important value to today's college students.
This may be due to a variety of factors, such as a lack of understanding of the political system, a lack of interest in politics, or a sense that individual political action will not make a difference.
It is important to recognize, however, that political involvement is still an important part of civic engagement and an essential part of the democratic process. As such, college students should strive to become more informed about politics and to find ways to get involved in the political process.
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The complete question is:
Which of the following values, which is least important to today's college students according to the yearly values survey?
A. Career success
B. Political involvement
C. Healthy lifestyle
D. Social media presence
The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 50 trials and got the following results.
(a) Assuming that the machine is fair, compute the theoretical probability of getting a 5 or 6 .
(b) From these results, compute the experimental probability of getting a 5 or 6 .
(c) Assuming that the machine is fair, choose the statement below that is true:
o With a large number of trials, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.
o With a large number of trials, there must be no difference between the experimental and theoretical probabilities.
o With a large number of trials, there must be a large difference between the experimental and theoretical probabilities.
(a) The theoretical probability of getting a 5 or 6 is 1/5
(b) The experimental probability of getting a 5 or 6 is 1/5
(c) The true statement is the first statement.
What is a probability?A subfield of statistics known as probability studies random events and their likelihood of happening. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes and is used to make predictions and estimate the likelihood of future events.
(a) Assuming that the machine is fair, the theoretical probability of getting a 5 or 6 is:
P(5 or 6) = P(5) + P(6) = 1/10 + 1/10 = 1/5
(b) From the results, we can see that out of the 50 trials, there were 10 trials where the machine output a 5 or a 6.
The experimental probability of getting a 5 or 6 is:
P(5 or 6) = 10/50 = 1/5
(c) A large number of trials, might be a difference between the experimental and theoretical probabilities, but the difference should be small. This is because the theoretical probability is based on the assumption of a fair machine, while the experimental probability is based on actual results.
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PLEASE HELP ASAP!! 25 POINTS AND BRAINLIEST
Answer: 62°
Step-by-step explanation:
All angles of a triangle add up to 180°.
So, add up all the other angles.
15 + 25 + 39 = 79
180 - 79 = 101
Then, to find x, subtract 39 from 101, to get 62!
What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←
Answer:
What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←
Step-by-step explanation:
To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.
We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.
To do this, we need to find the angle between these two vectors. Using the dot product, we have:
<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0
Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.
To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:
[0 -1]
[1 0]
Multiplying this matrix by the vector <4, -7>, we get:
[0 -1] [4] = [-7]
[1 0] [-7] [ 4]
which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.
Answer:
90° counterclockwise
Step-by-step explanation:
I am not sure if the picture helps or not. I am trying to show that I traced the point (4,-7). Then I have a plus sign at (0,0). I start rotating the tracing paper counterclockwise until I get to the point (7,4). I needed to turn one turn of the plus sign. That would be 90°
Helping in the name of Jesus.
he triangles below are similar. Triangle X Y Z. Side X Z has a length of 12, Z Y is 16, Y X is 14. Triangle R Q S. Side R Q is 3.5, Q S is 4, S R is 3. Which similarity statement expresses the relationship between the two triangles? Triangle X Y Z is similar to Triangle Q R S Triangle X Y Z is similar to Triangle R Q S Triangle Z X Y is similar to triangle Q S R Triangle Z X Y is similar to triangle Q R S
Answer:
Triangle XYZ is similar to Triangle RQS
Step-by-step explanation:
Triangle XYZ is similar to Triangle RQS
XZ/SR = 12/3 = 4
ZY/QS = 16/4 = 4
YX/RQ = 14/3.5 = 4
similar figures have all corresponding sides in the same ratio
he buys a 5kg lwisa samp and repacks the samp into 125g packets. determine how many packets will be able to get from one pack of 5kg samp?
Answer:5
Step-by-step explanation:5555555
A TRIANGLE HAS TWO SIDES OF LENTHS 6 AND 9. WHAT VALUE COULD THE LENGTH OF THE THIRD SIDE BE
Answer:
The value could be any length between 3 and 15
Step-by-step explanation:
9 - 6 = 3
and
9 + 6 = 15
Where i = sqrt(- 1) which of the following complex numbers is equal to (6 - 5i) - (4 - 3i) + (2 - 7i) ? A (4 - 9i)/25 B 4 - i C 9i - 4 D 4 - 9i E 4 + 9i
Answer: A) 4 - 9i/25
Step-by-step explanation:
We can simplify the expression (6 - 5i) - (4 - 3i) + (2 - 7i) by combining the real and imaginary parts separately:
Real part: (6 - 5i) - (4 - 3i) + (2 - 7i) = 6 - 4 + 2 - (-5i + 3i + 7i) = 4 - 5i
Imaginary part: 0
Therefore, the complex number equal to (6 - 5i) - (4 - 3i) + (2 - 7i) is 4 - 5i.
None of the answer choices matches this result exactly, but we can simplify 4 - 5i further:
(4 - 5i)/1 = (4 - 5i)/sqrt(1*1) [multiply the numerator and denominator by 1]
= (4/sqrt(1)) - (5/sqrt(1))i [divide the real and imaginary parts by 1]
= 4 - 5i
Therefore, the answer is A) (4 - 9i)/25. We can verify this by multiplying the numerator and denominator of this fraction by 25:
(4 - 9i)/25 = (4/25) - (9/25)i
Now, we can see that this is equivalent to 4 - 5i, which is the simplified form of the original expression.
SUPPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: Angle 1 = 32, Angle 2 = x + 29
COMPLEMENTARY ANGLE
Find the value of x. Answer only.
Given: 54 + x = 90
COMPLEMENTARY ANGLE Find the value of x. Answer only. Given: Angle 1 = x, Angle 2 = 24 + 2x
Answer:
Given: Angle 1 = 32, Angle 2 = x + 29 ----- Answer is x = 119°
Given: 54 + x = 90 ----- Answer is x = 36°
Given: Angle 1 = x, Angle 2 = 24 + 2x ----- Answer is x = 22°
Step-by-step explanation:
1. Supplementary angle = 180°
Angle 1 = 32° Angle 2 = x + 29
Angles 1 + 2 = 180°
32° + x + 29° = 180°
32° + x = 180° - 29°
32° + x = 151°
x = 151° - 32°
x = 119°
2. Complementary angle = 90°
Given: 54 + x = 90
90 - 54 = x
x = 36°
3. Complementary angle = 90°
Given: Angle 1 = x, Angle 2 = 24 + 2x
Angles 1 + 2 = 90°
x + 24 + 2x = 90°
3x + 24 = 90°
3x = 90° - 24
3x = 66°
x = 66°/3
x = 22°
Hope it helps!
Z decreased by 15%
Express as algebra
Answer:
Z-0.15Z
Step-by-step explanation:
multiply z by the decimal form of 15, but since it's decreased by z you need to include a way of subtracting the z
The algebraic expression for the given statement is 0.85Z
What is an algebraic expression?An algebraic expression is a mathematical expression that consists of variables, numbers and operations.
Given that, Z decreased by 15%, we need to convert it into an algebraic expression
Multiply z by the decimal form of 15, but since it's decreased by z we will subtract z from that,
So,
= Z - 15% of Z
= Z - 0.15Z
= Z(1-0.15)
= 0.85Z
Hence, the algebraic expression for the given statement is 0.85Z
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label each example with the type of variable that best represents it. labels can be used more than once.
Answer:
Step-by-step explanation:
A 16-ounce bottle of orange juice says it contains 200 milligrams of vitamin C, which is 250% of the daily recommended allowance of vitamin C for adults. Yoself drank 4 ounces of orange Juice. What percent of the daily recommended amount of Vitamin C is this ? Explain your thinking.
Step-by-step explanation:
'Yoself' drank 1/4 of 16 oz so he got 1/4 of 250%
1/4 * 250% = 62.5 %
Due today!! Pls helppp
if we that Abby spent 50% of her time on School, 30% on Work, and 20% on Sleep, we can estimate that she spent:
100% - (50% + 30% + 20%) = 100% - 100% = 0% on Other.
What do you mean by spending?If Abby divided her time into four categories (School, Work, Other, and Sleep), the percentage she spent on Other would be 100% less the sum of the percentages she spent on School, Work, and Sleep.
So, assuming Abby spending 50% of her time at school, 30% at work, and 20% sleeping, we can estimate she spent:
On Other, 100% - (50% + 30% + 20%) = 100% - 100% = 0%.
However, this is just a guess based on assumptions about how Abby spent her time. It's difficult to provide a more accurate estimate without more information.
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Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer
Answer: A positive whole number multiplied by any whole number will remain positive. In the case of the squares of 4, it will always end in a 6 which is a positive number.
Step-by-step explanation:
4^2= 16
16^2 = 256
256^2= 65,536
etc.
Does anyone know what x equals?
Answer:
X=18
Step-by-step explanation:
Answer:
x = 3.5 units (nearest tenth)
Step-by-step explanation:
The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.
A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.
Therefore, the formula for the ratio of the sides is x : x : x√2 where:
x is each side opposite the 45 degree angles (legs).x√2 is the side opposite the right angle (hypotenuse).As the hypotenuse of the given right triangle is 5 units:
[tex]\implies x\sqrt{2} = 5[/tex]
To find the measure of x, solve for x:
[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x =3.5355339...[/tex]
[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 3.5 units.
Twelve of the workers received the following salaries: three of them earn P12,500 a month, four of them earn P11,000; twoearn P10,500 and the rest earn P9,000 a month. What is the median salary of the workers?
The median salary of the workers is P11,000.
What is median?In statistics, the median is a measure of central tendency that represents the middle value of a data set when the data set is ordered from least to greatest (or vice versa). If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. The median is used as a measure of central tendency when the data set has outliers or is not normally distributed.
How to calculate median?To calculate the median of a set of numbers:
Put the numbers in order from lowest to highest.If the number of items in the list is odd, the median is the middle number. For example, if the list is 3, 5, 7, 9, 11, the median is 7.If the number of items in the list is even, the median is the average of the two middle numbers. For example, if the list is 4, 6, 8, 10, the median is (6 + 8)/2 = 7.In the given question,
To find the median salary of the workers, we need to arrange the salaries in order from lowest to highest.
The salaries are:
P9,000, P9,000, P10,500, P10,500, P11,000, P11,000, P11,000, P11,000, P12,500, P12,500, P12,500, P12,500
There are 12 workers, so the median salary will be the average of the 6th and 7th salaries when arranged in order.
Median salary = (P11,000 + P11,000)/2
= P11,000
Therefore, the median salary of the workers is P11,000.
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Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 92 people are called to jury duty and only 11 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection process? Again run a test using the PHANTOMS method to complete all parts of your problem.
Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.
To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.
First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.
The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.
We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:
z = (p - P) / sqrt(P(1-P)/n)
where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).
Plugging in the values, we get
z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39
Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.
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