Solve for the following systems using the algebraic method.

1. 3x + 4y = 12; 2x – 3y = 6

2. x + y = 3; x – y = 5

3. 3x + 2y – z = 4; 2x – y + 3z = 4; x + y + 2z = 4

4. x – y + 5z = -4; 4x – 2y + 3z = 1; 3x – 2y + 6z = 6

5. x2 + y2 = 13; 2x – 3y = -5

6. 5x2 + y2 = 14; 3x2 – 2y2 = -15

7. 2x2 + 5x – 4y = 3; 3x2 – 3x + 2y2 = 2

The equation of the parabola is  y² = 900x

We know that  the equation of the parabola is y² = 4ax

Since the arch has a span of 360 meters and a maximum height of 36 feet.

The coordinates of the ends of the parabola would be  (36, ±180)

So, equation of becomes,

180² = 4 × a × 36

⇒ a = 32400/144

⇒ a = 225

So, the equation of the parabola:

y² = 4(225)x

y² = 900x

This is the required equation.

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The complete question is:

An arch is in the shape of a parabola. It has a span of 360 meters and a maximum height of 36 feet. Find the equation of the parabola.

The hundredth interval of the number line in which √(84) is between 9.16 and 9.17

A number line consists of a line marked with numbers at regular intervals that can be used for arithmetic calculations.

The hundredths interval n the number line in which √(84) can be located is found as follows;

√(84) = 2·√(21) ≈ 9.165

A hundredth is a value expressed to two decimal places, therefore, the hundredth on the number line in which the value 9.165 is located are the values larger than 0.16 but less than 0.17.

Therefore √(84) lies in between 9.16 and 9.17 on the number line

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When the depth of water in the vase is 9 cm, there are 81 mL of water in the vase.

Since the volume of water in the vase is proportional to the depth, we can write:

The volume of water in the vase = constant x depth of water

Let's call the constant of proportionality "k". Then we have:

The volume of water in the vase = k x depth of water

To find the value of "k", we can use the information given in the problem. When there are 63 mL of water in the vase, the depth is 7 cm. So we have:

63 mL = k × 7 cm

Solving for "k", we get:

k = 63/7  = 9 mL/cm

Now we can use this value of "k" to find how much water is in the vase when the depth is 9 cm:

The volume of water in the vase = k × depth of water

Volume of water in vase = 9 × 9

The volume of water in the vase = 81 mL

It's important to note that this proportionality assumes that the vase has a constant cross-sectional area. If the shape of the vase changes with depth, the relationship between volume and depth will not be proportional.

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Answer: 206

360 (full circle/angle) - 64 = 296

296 - 42 = 254

254 - 48 = 206

x = 206*  GUYS THE ANSWER IS 206 not 360

The sum of squares of the real roots of p(x) = x³ - x² - 18x +18 is 37 for k= 18.

The cubic equation is given as,

p(x) = x³ - x² - 18x +k

To find the real roots of the cubic equation p(x) we can equate p(x) =0 , we get,

x³ - x² - 18x +k = 0

⇒ x² (x -1) - 18(x - k/18) = 0

For factoring the equation we can equate  (x -1) = (x - k/18) by comparing it with solving of general equations.

That is by arranging the cubic equation after equating (x -1) = (x - k/18)  we will get,

(x-1)(x² -18) =0

Thus we get,

(x -1) = (x - k/18)

⇒ k/18 =1

⇒ k =18

The cubic equation which will give us real roots will become,

p(x) = x³ - x² - 18x +18

By factoring we can find the real roots as,

x³ - x² - 18x +18 =0

⇒ (x² -18)(x -1) =0

⇒x= 1 , x = 3√2 and x= -3√2

Let us say, a = 1 , b = 3√2 and c = -3√2 are the required real roots.

The square of real roots are as follows,

a² = 1

b² = 18

c² = 18

Thus, the sum of squares of the real roots of p(x) = x³ - x² - 18x +18 is

= a² + b²+ c²

= 1 + 18 + 18

= 37

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Each floor is 3 meter high.

We have,

A building is 57 metres high.

If this building has 19 floors.

Then, the height of each floor

= 57/ 19

= 3 m

Thus, Each floor is 3 meter high.

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We can say with 99% confidence that the true mean length of all Hollywood movies made in the last 10 years is between 107.2 and 116.0 minutes.

We are given:

Sample size (n) = 45

Sample mean (x) = 111.6 minutes

Sample standard deviation (s) = 14.3 minutes

Confidence level = 99%

To construct the confidence interval, we can use the formula:

Confidence interval = x ± zα/2 * (s/√n)

Where:

x = sample mean

zα/2 = the z-score associated with the desired confidence level (in this case, 99% corresponds to a z-score of 2.576)

s = sample standard deviation

n = sample size

Substituting the given values, we get:

Confidence interval = 111.6 ± 2.576 * (14.3/√45)

Confidence interval = 111.6 ± 4.36

Confidence interval = (107.2, 116.0)

Therefore, we can say with 99% confidence that the true mean length of all Hollywood movies made in the last 10 years is between 107.2 and 116.0 minutes.

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(a) In the equation of a straight line, y = bx + a, where b is equal to +5,

The relationship between the two variables, x and y, is a positive linear relationship. Since b is positive (+5), as the value of x increases, the value of y will also increase proportionally. The slope of the straight line is 5, indicating that for every unit increase in x, y will increase by 5 units.

(b) The statement is false.

A very strong correlation between two variables means the correlation coefficient is close to -1 or +1. If the correlation coefficient is near 0, it indicates that there is little to no correlation between the two variables.

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The A value from the given equation is CE = (io^0.118)/10.

To find the A value from the equation 0.242 = log of  CRnx CF ICF Rn= 1.334X10 CE=?, we need to isolate the variable A on one side of the equation. We can start by using the definition of logarithms, which states that log of CRnx CF ICF Rn= A is equivalent to CRnx CF ICF Rn= io^A.

Substituting the given values, we get:

1.334X10 CE= io^A

Taking the logarithm of both sides with base 10, we get:

logio (1.334X10 CE) = logio (io^A)

Using the logarithmic identity logio (a^b) = b*logio (a), we can simplify the left-hand side to:

logio (1.334X10 CE) = logio (1.334) + logio (10 CE)

Now we can substitute the given value of logio CRnx CF ICF Rn= 0.242:

0.242 = logio (1.334) + logio (10 CE)

Solving for logio (10 CE), we get:

logio (10 CE) = 0.242 - logio (1.334)

logio (10 CE) = 0.242 - 0.124

logio (10 CE) = 0.118

Finally, we can solve for CE by exponentiating both sides with base 10:

10 CE = io^0.118

CE = (io^0.118)/10

Therefore, the A value from the given equation is CE = (io^0.118)/10.

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The economic order quantity for Zhou Bicycle Company's Airwing bicycle is approximately 68. The answer is (b) 68.

To calculate the economic order quantity (EOQ) for Zhou Bicycle Company's Airwing bicycle, we need to use the following formula:

EOQ = √((2DS)/H)

where:

D = annual demand

S = cost of placing one order

H = holding cost per unit per year

First, we need to calculate the annual demand for Airwing bicycles. The table provided shows the sales data for the past two years:

Year 1: 300 Airwing bicycles sold

Year 2: 350 Airwing bicycles sold

Average annual demand = (300 + 350) / 2 = 325

Next, we need to calculate the cost of placing one order. The question states that each time an order is placed, ZBC incurs a cost of $65. Therefore, S = $65.

Finally, we must compute the annual holding cost per unit. According to the question, ZBC's inventory carrying cost is 1% per month (12% per year) of the purchase price. ZBC paid 60% of the suggested retail price of $170 for the purchase. Therefore, the purchase price paid by ZBC is 0.6 x $170 = $102.

Holding cost per unit per year = 12% x $102 = $12.24

Now we can plug these values into the EOQ formula:

EOQ = √((2 x 325 x $65)/$12.24) ≈ 68

Therefore, the economic order quantity for Zhou Bicycle Company's Airwing bicycle is approximately 68.

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Complete question:

Zhou Bicycle Company​ (ZBC), located in​ Seattle, is a wholesale distributor of bicycles and bicycle parts. Formed in 1981 by University of Washington Professor​ Yong-Pin Zhou, the​ firm’s primary retail outlets are located within a​ 400-mile radius of the distribution center. These retail outlets receive the order from ZBC within 2 days after notifying the distribution​ center, provided that the stock is available.​ However, if an order is not fulfilled by the​ company, no backorder is​ placed; the retailers arrange to get their shipment from other​ distributors, and ZBC loses that amount of business.

The company distributes a wide variety of bicycles. The most popular​ model, and the major source of revenue to the​ company, is the Airwing. ZBC receives all the models from a single manufacturer in​ China, and shipment takes as long as 4 weeks from the time an order is placed. With the cost of​ communication, paperwork, and customs clearance​ included, ZBC estimates that each time an order is​ placed, it incurs a cost of​ $65. The purchase price paid by​ ZBC, per​ bicycle, is roughly​ 60% of the suggested retail price for all the styles​ available, and the inventory carrying cost is​ 1% per month​ (12% per​ year) of the purchase price paid by ZBC. The retail price​ (paid by the​ customers) for the Airwing is​ $170 per bicycle.

ZBC is interested in making an inventory plan for 2019. The firm wants to maintain a​ 95% service level with its customers to minimize the losses on the lost orders. The data collected for the past 2 years are summarized in the following table. A forecast for Airwing model sales in 2019 has been developed and will be used to make an inventory plan for ZBC.

The point-slope form of the line with slope −14 that passes through the point (−2, 9) include the following: A. y - 9 = -14(x + 2), y minus 9 equals negative 1 fourth left parenthesis x plus 2 right parenthesis.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (-2, 9) and a slope of -14, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 9 = -14(x - (-2))  

y - 9 = -14(x + 2)

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The length of MN is 12 inches,  total surface area in square inches of the wooden blocks to be painted is 80400 square inches and

The formula for volume of a cuboid is:

Volume = Length× Width × Height

Thus 427 = (MN × 7× 3) + (5 × 5 × 7)

427 = 21MN + 175

21MN = 252

MN = 252/21

MN = 12

2) Surface area of entire object is:

TSA = 2(12 × 3) + 2(12×7) - (5 × 7) + 2(7×3) + 3(5 × 7) + 2(5 ×5)

= 402 in²

For 200 blocks:

TSA = 200× 402 = 80400 in²

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With a 3% annual inflation rate, the predicted cost of the fence after four years is $28,138.75.

The inflation rate is the percentage by which a currency devalues over time. The fact that the consumer price index (CPI) rises over this period demonstrates the devaluation. In other words, it is the pace at which the currency is devalued, leading overall consumer prices to rise compared to the change in currency value.

To calculate the projected cost of the fence after 4 years with an annual inflation rate of 3%, we can use the following formula:

[tex]Projected Cost = Current Cost * (1 + Inflation Rate)^{Number of Years[/tex]

Plugging in the given values, we get:

Projected Cost = $25,000 x (1 + 0.03)⁴

Projected Cost = $25,000 x 1.1255

Projected Cost = $28,138.75

Therefore, the projected cost of the fence after 4 years with an annual inflation rate of 3% is $28,138.75.

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Answer: (-1, 2)

Step-by-step explanation:

I really hope its right I'm sorry if it's wrong

The three approaches for prevention (primary, secondary, and tertiary) for the COVID-19 infection.

1. Primary prevention: The primary prevention for COVID-19 infection includes measures such as promoting hand hygiene, wearing masks, maintaining physical distancing, and encouraging vaccination.

2. Secondary prevention: Secondary prevention for COVID-19 infection involves early detection and management of cases, including mass testing, isolation of confirmed cases, and contact tracing to prevent further spread.

3. Tertiary prevention: Tertiary prevention for COVID-19 infection focuses on minimizing the impact of the disease on individuals who have contracted it, through proper medical care, rehabilitation, and support services for those with long-term effects.

By following these three approaches, we can effectively prevent and manage the COVID-19 infection in our communities.

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A survey does not help capture:

(b) Everything a population knows.

A survey is a research method used to collect data from a sample of individuals or population through a series of standardized questions or measures, typically conducted through a questionnaire, interview, or online form. Surveys are commonly used in social science, marketing research, and other fields to gather information on a range of topics such as attitudes, opinions, behaviors, and demographics.

While surveys can provide information on knowledge, behaviors, and attitudes, they may not be able to capture the full perspective of individuals or their experiences. Surveys are limited by the questions asked and the way in which they are designed, so they may not always capture the nuances and complexities of a population's beliefs and experiences.

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When the popularity of grapefruits increases, it leads to a higher demand for them in the market. Consequently, the price of grapefruits rises due to this increased demand. In response to the price increase, several changes occur in the market for grapefruits.

Firstly, as the price of grapefruits increases, the quantity demanded by consumers will likely decrease, as some individuals might be deterred by the higher cost. This is in accordance with the law of demand, which states that as the price of a good increases, the quantity demanded decreases, and vice versa.

Secondly, the higher price of grapefruits may encourage producers to increase their supply to take advantage of the increased revenue potential. As a result, the quantity supplied in the market will likely rise, following the law of supply, which states that as the price of a good increases, the quantity supplied increases, and vice versa.

In the long run, the market will seek to achieve equilibrium, where the quantity demanded equals the quantity supplied. This process will involve adjustments in both supply and demand until a new equilibrium price and quantity are established. The ultimate outcome will depend on the elasticity of both supply and demand for grapefruits, which determine how responsive they are to price changes.

In conclusion, an increase in the popularity of grapefruits resulting in a higher price leads to changes in the market, including decreased quantity demanded, increased quantity supplied, and eventually, a new market equilibrium.

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Samantha uses 3.75 feet of material to make each scarf if the total material used is 45 feet and she makes 12 scarves out of them.

Samantha has the total amount of material to make scarves is 45 feet. The total number of scarves made out of the material is 12. To calculate the material for one scarf we calculate it by dividing the total material by the number of scarves produced

Thus, Total material used = 45 feet

Number of scarves made = 12

Material for one scarf = 45 ÷ 12 = 3.75 feet

Thus, one scarf requires 3.75 feet of material.

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When a polynomial function f is divided by x-c, the remainder is given by the value of the polynomial function f evaluated at the value c. This result is known as the Remainder Theorem.

The result of dividing a polynomial function f(x) by x-c equals f(c), according to the theorem. Numerous branches of mathematics, such as algebra, calculus, and number theory, can benefit from this theorem.

It offers a straightforward and effective technique for computing remainders and comprehending how polynomial functions behave. The Remainder Theorem can be used to factor polynomials, factor complicated calculations, and solve equations with polynomial functions.

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Hi! To determine which data set is less variable, we can compare their ranges. The range is calculated by subtracting the minimum value from the maximum value in the data set.

a. 4 - 1 = 3
b. 8 - 1 = 7
c. 1 - (-1) = 2
e. 4.5 - 1 = 3.5
f. 8 - 1 = 7

The data set with the least variability is option C, with a range of 2.

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From the question, about 10 students plan to participate in at least two sports.

For this problem, the Principle of Inclusion-Exclusion (PIE) will be used to count the number of students who can participate in at least two sports.

Note that from the question:

So the Number of students participate in at least two sports:

= 20 + 6 + 8 - 2 x (12)

= 20 + 6 + 8 - 24

= 10

Therefore, 10 students plan to participate in at least two sports.

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The probability of 3 dying of SIDS in this situation is approximately 0.000227. The number of SIDS cases in this hospital is significantly higher than the expected rate.

a. The probability of 3 infants dying of SIDS in this situation can be calculated using the binomial probability formula:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of k successes (SIDS cases) in n trials (infants),
C(n,k) is the number of combinations of n items taken k at a time,
p is the probability of SIDS (0.0001),
n = 100 infants,
k = 3 SIDS cases.
P(3 SIDS cases in 100 infants) = C(100,3) * (0.0001)^3 * (1-0.0001)^(100-3)
After calculating, the probability is approximately 0.000227.

b. In this situation, it is alarming that many infants died of SIDS, as the probability of 3 deaths in 100 infants is very low (0.000227), much lower than the prevalence of 0.01%. This indicates that the number of SIDS cases in this hospital is significantly higher than the expected rate.

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Answer:

Step-by-step explanation:

(x - 2)²/16 - (y - 1)²/4 = 1

(x - 2)² - 4(y - 1)² = 16

x² + 4 - 4x - 4(y² + 1 - 2y) = 16

x² + 4 - 4x - 4y² - 4 + 8y = 16

x² - 4x + 8y - 4y² = 16

x² - 4x = 16  ,  -4y² + 8y = 16

x(x - 4) = 16  ,  4y(-y + 2) = 16

x = 16, x = 20,  y = 4, y = -14

The probability of p(placebo and improvement) is 7.6%.

Here, we have,

Given that

Participants in a study of a new medication received either medication A or a placebo.

We have to find

The probability of P(placebo and improvement).

According to the question

Participants in a study of a new medication received either medication A or a placebo.

Let Probability that participants received medication A = P(M) = 0.80

Probability that participants received placebo = P(P) = 1 - P(M) = 1 - 0.80 = 0.20.

Because there are only two cases either medication A or a placebo.

Let I = event that there is an improvement.

Also, the Probability that participants reported improvement given that they had received medication A = P(I/M) = 0.76

The probability that participants reported no improvement given that they had received placebo = P(I'/P) = 0.62

So, Probability that participants reported improvement given that they had received placebo is,

=  P(I / P) = 1 - P(I' / P) = 1 - 0.62 = 0.38

Now, Probability of (placebo and improvement) = Probability that participants received placebo times Probability that participants reported improvement given that they had received placebo.

P(placebo and improvement) =  P(P)  times  P(I / P)  

P(placebo and improvement) =  0.20 times 0.38  =  0.076  or  7.6%

Therefore, the required probability of p(placebo and improvement) is 7.6%.

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The loan you can take is : Solid Savings & Loan at 9% interest for 4 years.

To determine which loan you can take, you need to calculate the monthly payments for each option.

For the loan from Solid Savings & Loan, the total interest over 4 years would be $3,600 ($10,000 x 0.09 x 4). This means that the total amount you would need to repay over 4 years would be $13,600 ($10,000 + $3,600). Divided by 48 months, your monthly payment would be $283.33 ($13,600 / 48).

For the loan from Fifth Federal Bank & Trust, the total interest over 3 years would be $2,100 ($10,000 x 0.07 x 3). This means that the total amount you would need to repay over 3 years would be $12,100 ($10,000 + $2,100). Divided by 36 months, your monthly payment would be $336.11 ($12,100 / 36).

Since you can afford to pay $250 per month, you cannot take the loan from Fifth Federal Bank & Trust as the monthly payment is higher than what you can afford. However, you can take the loan from Solid Savings & Loan as the monthly payment is $250. Therefore, the loan you can take is from Solid Savings & Loan at 9% interest for 4 years.

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The statement that is true about the 2 functions, in which the relationship between the x and y-values in the table of values for both functions is a linear relationship is that The y-intercept of the graph of A is equal to the y-intercept of the graph of B

The equation representing the relationship in function A in point-slope form is therefore;

y - 12 = 6·(x - 2)

y - 12 = 6·x - 12

y = 6·x - 12 + 12 = 6·x

The equation in slope-intercept form, y = m·x + c, where c is the y-intercept is therefore; y = 6·x

The true statement is therefore; The y-intercept of the graph of A is less than the y-intercept of the graph of B

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The integral has a value of 27.

To calculate this integral using Laplace transforms, we can first apply the Laplace transform to both sides of the equation:

L{0∫[infinity] t[tex]e^{(-54t)}[/tex] sin(t) dt} = L{0}

Using the property of Laplace transform for integration, we get:

[tex]L{te^{(-54t)} sin(t)} = -F'(s)[/tex]

where F(s) is the Laplace transform of sin(t).

Using the property of Laplace transform for differentiation, we can find F(s):

F(s) = L{sin(t)} = 1 / (s² + 1)

Now we can differentiate F(s) to find -F'(s):

-F'(s) = L{t [tex]e^{(-54t)[/tex] sin(t)} = (s² + 54) / (s² + 1)²

Finally, we can apply the inverse Laplace transform to get the solution:

0∫[infinity] [tex]te^{(-54t)[/tex] sin(t) dt = [tex]L^{-1}{(s^2 + 54) / (s^2 + 1)^2}[/tex]

Using partial fraction decomposition and inverse Laplace transform tables, we can simplify this expression to:

0∫[infinity] [tex]te^{(-54t)[/tex] sin(t) dt = (1/2) [cos(t) - 54 sin(t)] from 0 to infinity

Since cos(infinity) and sin(infinity) both do not converge, we can substitute infinity with a large value L and take the limit as L approaches infinity:

0∫[infinity] [tex]te^{(-54t)[/tex] sin(t) dt = (1/2) [cos(0) - cos(L) - 54(sin(0) - sin(L))] = 27

Therefore, the value of the integral is 27.

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There will always be at least two blue balls that are adjacent to each other.

To show that no matter how the balls are arranged, after they are painted, there will always be at least two blue balls that are adjacent to each other, we can use the Pigeonhole Principle.

First, let's consider the worst-case scenario, which is when the blue balls are arranged such that they are as spread out as possible. In this case, we can imagine that the 15 white balls are arranged in a straight line, with 7 blue balls and 8 green balls interspersed in such a way that there are no two blue balls that are adjacent to each other.

Now, let's place each of the 7 blue balls in a pigeonhole that corresponds to their position in the line. Specifically, the first blue ball goes in the first pigeonhole, the second blue ball goes in the second pigeonhole, and so on, until the seventh blue ball goes in the seventh pigeonhole.

Since there are only 7 pigeonholes and 7 blue balls, at least one pigeonhole must contain two blue balls. And since the only way for two blue balls to be in the same pigeonhole is for them to be adjacent to each other in the line, we have shown that no matter how the balls are arranged, after they are painted, there will always be at least two blue balls that are adjacent to each other.

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At the .005 significance level with a one-tailed test, the critical z-value is 2.33. Since our calculated z-value (2.58) is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to support the claim that the proportion of men who own cats is larger than 90% at the .005 significance level.

To test the claim that the proportion of men who own cats is larger than 90% at the .005 significance level, we can conduct a one-tailed hypothesis test. Our null hypothesis (H0) is that the proportion of men who own cats is less than or equal to 90%, while our alternative hypothesis (Ha) is that the proportion is greater than 90%.

We can use a z-test for proportions to calculate the test statistic and p-value. Let's assume we sample 200 men and find that 186 own cats. This gives us a sample proportion of 0.93.

Using the formula for the z-test for proportions, we get:

z = (0.93 - 0.9) / sqrt(0.9 * 0.1 / 200) = 2.58

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