solving systems by eliminations; finding the coeficients
please write all the problems down, 5 points for each problem, and Brainliest

The profit made as of investor borrows $100 is $25.

Investing in foreign currencies can be a profitable venture, but it comes with a certain level of risk.

If an investor borrows $100, converts it to pesos, and invests the pesos in Mexico for one year, the profit made is $25.

This is calculated by borrowing $100 and converting it to 625 pesos at the spot rate of 6.25 pesos per dollar.

The 625 pesos are then invested in Mexico for a year at a 45% interest rate, resulting in 281.25 pesos.

The 281.25 pesos are then converted back to dollars at the forward rate of 7.25 pesos per dollar, resulting in $38.75.

The resulting profit is $38.75 - $100 = -$61.25.

Investing in foreign currencies is not without its risks.

When investing in foreign currencies, the exchange rate can change drastically over short periods of time, resulting in losses or gains.

Additionally,

The interest rate in the country of investment can also change, resulting in different levels of returns.

The profit made if an investor borrows $100, converts to pesos and invests in Mexico for a year is $25.

The calculation is as follows:

Borrow $100 and convert to pesos:

100 x 6.25 = 625 pesos

Invest 625 pesos in Mexico for one year:

625 x 45% = 281.25 pesos

Convert 281.25 pesos back to dollars at the forward rate:

281.25 / 7.25 = $38.75

Profit = $38.75 - $100 = -$61.25

For similar question on profit:

https://brainly.com/question/50981379

#SPJ11

If Mary needs to have $9,000 in 9 years at 4% interest compounded quarterly, she should deposit $208.93 in a sinking fund at the end of each quarter.

Compound interest refers to the system that charges interest on both the accumulated interest and the principal at the end of each period.

The compounding period may vary from annual, quarter, and monthly to daily.

N (# of periods) = 36 quarters (9 years x 4)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

FV (Future Value) = $9,000

Results:

Periodic (Quarterly) Deposit (PMT) = $208.93

The sum of all periodic payments = $7,521.44

Total Interest = $1,478.56

Thus, Mary needs to deposit $208.93 each quarter.

Learn more about compound interest and periodic deposits at https://brainly.com/question/3989769.

#SPJ1

Por lo tanto, el ciclomotor tardaría 6 horas en recorrer la misma distancia que el automóvil que tarda 3 horas a una velocidad de 90 km/h. ¡Espero que esto te ayude!

Para calcular el tiempo que tarda un ciclomotor a una velocidad de 45 km/h en realizar el mismo trayecto que un automóvil que circula a 90 km/h y tarda 3 horas en llegar a su destino, necesitamos utilizar la fórmula de la velocidad media.
La velocidad media se calcula dividiendo la distancia recorrida por el tiempo que tarda en recorrerla.

Sabemos que el automóvil tarda 3 horas en llegar a su destino y circula a una velocidad de 90 km/h.

Por lo tanto, podemos calcular la distancia que recorre utilizando la fórmula de la distancia:
Distancia = Velocidad x Tiempo
Distancia = 90 km/h x 3 h
Distancia = 270 km
Ahora que sabemos que el automóvil recorre una distancia de 270 km, podemos calcular el tiempo que tardaría el ciclomotor en recorrer la misma distancia a una velocidad de 45 km/h utilizando la fórmula de la velocidad media:
Velocidad media = Distancia / Tiempo
Tiempo = Distancia / Velocidad media
Tiempo = 270 km / 45 km/h
Tiempo = 6 horas

For similar questions on Velocided

https://brainly.com/question/31240188

#SPJ11

The greatest number of songs downloaded is 10."

"What is the greatest number of songs downloaded?" is:

A dot plot is a graphical representation of data using dots. In this case, the dot plot shows the number of songs Carly downloaded over 15 successive weekends. Each dot represents the number of songs downloaded during a particular weekend

To find the greatest number of songs downloaded, we need to identify the highest point on the dot plot. This can be done by visually examining the dot plot and looking for the highest dot.

Once we identify the highest dot, we can see the number of songs downloaded during that particular weekend, which is the greatest number of songs downloaded over the 15 successive weekends.

if the highest dot on the dot plot represents 10 songs downloaded, then the answer to the question would be "The greatest number of songs downloaded is 10."

Learn more about Dot plot

brainly.com/question/21862696

#SPJ11

When the width of the rectangle is 4 in, the length is 6 in.

Let's call the length of the rectangle "L" and the width "W". The problem states that the area of the rectangle is constant, so we can write:

LW = A

where A is some constant. We are also told that the length varies inversely with the width, which means that if the width increases, the length must decrease proportionally to keep the area constant. Mathematically, this means

L ∝ 1/W

or

L = k/W

where k is some constant of proportionality. We can find k by using the information given in the problem. We are told that when the width is 3 in, the length is 8 in

8 = k/3

Multiplying both sides by 3 gives:

24 = k

Now we can use this value of k to find the length when the width is 4 in:

L = k/W = 24/4 = 6 inches

When the width of the rectangle is 4 in, the length is 6 in, where the length and width of the rectangle are related by the inverse proportion L = k/W, with k = 24.

Learn more about inverse proportion here

brainly.com/question/16173480

#SPJ4

True. When calculating the process capacity of a specific process, it is important to consider the order in which a stage occurs when determining its stage capacity.

This statement is true. Considering the order of stages helps to accurately identify bottlenecks and ensures an efficient process flow. This is because the capacity of a stage can be affected by the preceding stages and the flow of the process. The stage capacity will also determine the overall capacity of the process.

To learn more about capacity visit;

https://brainly.com/question/31196313

#SPJ11

Answer:

To find the volume of a figure, we need to know the shape of the figure. Without this information, I cannot provide an answer. Please provide more details about the shape of the figure.

Using additional ink that is not necessary to convey information reduces the data-ink ratio, which should be maximized in order to effectively convey essential information in a table or chart.

Using additional ink that is not necessary to convey information reduces the data-ink ratio. The goal of maximizing the data-ink ratio is to ensure that the ink used in the visual representation of data is used only to convey the necessary information, without cluttering or distracting from the main message.

When unnecessary ink is used, it increases the amount of ink used overall, reducing the proportion of ink used for conveying information, and thus reducing the data-ink ratio. Therefore, to maximize the effectiveness of a table or chart, it's important to minimize the use of non-data ink and focus on the essential information.

Learn more about data-ink ratio here

brainly.com/question/30668721

#SPJ4

The number of people that would consume  alcoholic beverages is 34.85 people out of the given sample of fifty 18-20 years old.

Let us  take  a random sample of fifty 18-20 year olds

now, it is given to us that 69.7% of 18-20 year olds consumed alcoholic beverages in 2008,

We can utilize this information to evaluate the probability that any one person in the sample of fifty has consumed alcoholic beverages = 0.697.

Now to expected number of individual who have consumed alcoholic beverages in the sample,

Therefore, multiply the probability by the sample size: 0.697 x 50

= 34.85.

The number of people that would consume  alcoholic beverages is 34.85 people out of the given sample of fifty 18-20 years old.

To learn more about probability,

https://brainly.com/question/13604758

#SPJ4

the total consumption of oil in the United States from January 1, 1980, to January 1, 1990 is approximately 596,533.7 billion barrels.

To find the total consumption of oil in the United States from January 1, 1980 to January 1, 1990, we need to integrate the given function[tex]C(t) = 27.08e^t[/tex]with respect to time t, over the interval [0, 10], where t is measured in years.

The integral of the function is:
∫[tex](27.08e^t) dt[/tex]

To solve this integral, we use the fact that the integral of[tex]e^t[/tex] is [tex]e^t[/tex]itself. Thus, we get:
27.08∫[tex]e^t dt = 27.08e^t[/tex]
Now, we need to evaluate the definite integral over the interval [0, 10]:
[tex]27.08e^t[/tex]| from 0 to 10 =[tex]27.08(e^{10} - e^0)[/tex]

As e^0 = 1, the expression simplifies to:
[tex]27.08(e^{10} - 1)[/tex]
Now, we can calculate the value of the expression:
[tex]27.08(e^{10} - 1) =27.08(22026.47 - 1) = 27.08 * 22025.47 =596533.7[/tex]
Thus, the total consumption of oil in the United States from January 1, 1980, to January 1, 1990 is approximately 596,533.7 billion barrels.

learn more about integral

https://brainly.com/question/18125359

#SPJ11

Answer: the same as or equal to

Step-by-step explanation: The shapes are the same one's just stretched

Answer:

A square is a special kind of a rectangle

Step-by-step explanation:

Every Square is a rectangle but not every rectangle is a square.

The percentage of gain made by the trader is 390.9 percent (approximately).

The trader bought 40 shirts for Birr 220.

That is, each shirt was bought for Birr (220/40) =  Birr 5.5

The trader sold each shirt for Birr 27.

Thus total revenue he or she earned from selling 40 shirts is =  Birr (27)(40) = Birr 1080

Clearly, purchasing price is less than selling price.

Thus the trader has gained.

Gain = total selling price - initial price

= Birr (1080 - 220)

= Birr 860

Thus the percentage of  gain is = { (gain)/ (purchasing price) } 100

= (860/ 220) 100

= 390.9 percent (approximately)

Hence the trader has made a profit of 390.9 percent.

To know more about loss and gain percentage here

https://brainly.com/question/19709576

#SPJ4

The height of the parabolic balloon arch for the prom is 12.25 feet.

Using these assumptions, we can find the equation of the parabola that the arch follows as x = a(y-k)² + h, where (h,k) is the vertex and a is a constant that determines the shape of the parabola. We can find the value of a by using one of the points that the arch passes through, say (3,0):

3 = a(0-k)² + h h = 3 - a(k²)

Similarly, using the other point that the arch passes through, say (7,0):

7 = a(0-k)² + h h = 7 - a(k²)

Equating the expressions for h, we get:

3 - a(k²) = 7 - a(k²) a = -1/4

Substituting this value of a into one of the equations for h, say h = 7 - a(k²), we get:

h = 7 + 1/4(k²)

So the vertex of the parabola is at (h,k) = (7,0), and the equation of the parabola is x = -1/4(y² - 28y + 49).

To find the height of the arch, we need to find the y-coordinate of the vertex, which is k = 0. So the height of the arch is given by the distance between the vertex and the lowest point of the arch, which is the x-intercept of the parabola. To find the x-intercept, we set y = 0 in the equation of the parabola:

x = -1/4(0² - 28(0) + 49)

x = -1/4(49) = -12.25

However, since we are dealing with a physical object, the height cannot be negative. Therefore, we take the absolute value of the x-intercept, which gives us:

| -12.25 | = 12.25 feet

To know more about height here

https://brainly.com/question/10726356

#SPJ4

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Answer:

The rewritten function by completing the square is:

[tex]f(x)=(x-4)^2-18[/tex]

The solutions of the function are:

[tex]x=4+3\sqrt{2},\;x=4-3\sqrt{2}[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2-8x-2[/tex]

To rewrite the function by completing the square, begin by adding and subtracting the square of half the coefficient of the term in x. (Place these between the term in x and the constant).

[tex]f(x)=x^2-8x+\left(\dfrac{-8}{2}\right)^2-\left(\dfrac{-8}{2}\right)^2-2[/tex]

Simplify:

[tex]f(x)=x^2-8x+\left(-4\right)^2-\left(-4\right)^2-2[/tex]

[tex]f(x)=x^2-8x+16-16-2[/tex]

We have now created a perfect square trinomial from the first three terms: x² - 8x + 16.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{\sf \large Perfect Square Trinomial}\\\\\sf A perfect square trinomial is a polynomial of the form $a^2 + 2ab + b^2$ or $a^2 - 2ab + b^2$, where $a$ and $b$ are constants. \\\\When factored, a perfect square trinomial becomes the square of a binomial: $(a + b)^2$ or $(a - b)^2$. \\\end{minipage}}[/tex]

Factor the perfect square trinomial x² - 8x + 16.

[tex]f(x)=(x-4)^2-16-2[/tex]

Simplify by subtracting the numbers outside the parentheses:

[tex]f(x)=(x-4)^2-18[/tex]

Therefore, the given function rewritten by completing the square is:

The solutions to a quadratic function are the x-values which satisfy the equation f(x) = 0. Therefore, to find the solutions, set the function equal to zero and solve for x.

[tex]\begin{aligned}f(x)&=0\\\implies (x-4)^2-18&=0\\(x-4)^2-18+18&=0+18\\(x-4)^2&=18\\\sqrt{(x-4)^2}&=\sqrt{18}\\x-4&=\pm\sqrt{18}\\x-4+4&=\pm\sqrt{18}+4\\x&=4\pm\sqrt{18}\\x&=4\pm\sqrt{3^2 \cdot 2}\\x&=4\pm\sqrt{3^2} \sqrt{2}\\x&=4\pm3 \sqrt{2}\end{aligned}[/tex]

Therefore, the solutions of the function are:

[tex]x=4+3\sqrt{2},\;x=4-3\sqrt{2}[/tex]

By solving the probability, the possible outcomes for 5 rolls of dice is 1048576 and the number of outcomes in which the 5 rolls produce five different numbers is 524160. Also the probability that at least 2 of the rolls are the same is 0.5314

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

(a) Since each roll can produce one of 16 possible outcomes, there are 16^5 = 1048576 possible outcomes for these 5 rolls.

(b) To count the number of outcomes in which the 5 rolls produce five different numbers, we need to use the principle of permutations. The first roll can produce any of the 16 possible outcomes, the second roll can produce any of the remaining 15 outcomes, the third roll can produce any of the remaining 14 outcomes, and so on. Therefore, the number of outcomes in which the 5 rolls produce five different numbers is:

16 x 15 x 14 x 13 x 12 = 524160

(c) To calculate the probability that at least 2 of the rolls are the same, we can use the complement rule: the probability of at least 2 rolls being the same is 1 minus the probability that all 5 rolls produce different numbers.

The probability that the first roll produces a unique number is 16/16 = 1. The probability that the second roll produces a number different from the first is 15/16, the probability that the third roll produces a number different from the first two is 14/16, and so on. Therefore, the probability that all 5 rolls produce different numbers is:

(16/16) x (15/16) x (14/16) x (13/16) x (12/16) = 0.4686

So, the probability that at least 2 of the rolls are the same is:

1 - 0.4686 = 0.5314 (rounded to 4 decimal places)

Learn more about probability here:

https://brainly.com/question/25870256

#SPJ1

Jordan would take 22 hours to drive 1,188 miles at the same speed he drove 378 miles in 7 hours.

We can use the formula:

time = distance / speed

where speed is constant, to find the time it would take Jordan to drive 1,188 miles.

The speed at which Jordan drove can be calculated as:

speed = distance / time

where distance is 378 miles and time is 7 hours.

speed = 378 / 7 = 54 miles per hour

Now, we can use the speed to find the time it would take to drive 1,188 miles:

time = distance / speed = 1,188 / 54 = 22 hours

Therefore, if Jordan can maintain the same pace, it would take him 22 hours to drive 1,188 miles.

Learn more about Constant

https://brainly.com/question/1597456?referrer=searchResults

#SPJ11

If the expressions given, only C) if( x == 1) is always true.

In the given code fragment, the value of x is read from the user using the scanf() function. The value of x can be any integer value, depending on what the user enters. After the value of x is read, the program checks the value of x using a conditional statement (if statement) and executes the code inside the if statement only if the condition is true.

Expression A) if( x = 1) assigns the value 1 to x and then checks if x is true. This means that the condition is always true, because the assignment operation (=) returns the assigned value (in this case, 1), which is a non-zero value and therefore considered true in C programming.

Expression B) if( x < 3) checks if x is less than 3. This expression is not always true, as x can be any value greater than or equal to 3, in which case the condition would be false.

Expression C) if( x == 1) checks if x is equal to 1. This expression is always true if the user enters the value 1 for x.

Expression D) if((x/3) > 1) checks if the integer division of x by 3 is greater than 1. This expression is not always true, as x can be any value less than or equal to 3, in which case the result of the integer division by 3 would be 1 or less, in which case the condition would be false.

Learn more about  expressions

https://brainly.com/question/14083225

#SPJ4

the only expression that is always true in this code fragment is option C) if( x == 1).

The expression that is always true in this code fragment is option C) if( x == 1).

Option A) if( x = 1) is not always true because it is an assignment statement instead of a comparison statement. It assigns the value 1 to x instead of checking if x is equal to 1.

Option B) if( x < 3) is also not always true because x could be any number less than 3.

Option D) if((x/3) > 1) is not always true because x could be any number less than or equal to 3, in which case the expression would evaluate to false.

Therefore, the only expression that is always true in this code fragment is option C) if( x == 1).

learn more about code fragment

https://brainly.com/question/31133611

#SPJ11

a. The hypotenuse of the right angled triangle is 8

b. The leg of the right angled triangle is 4√2

The hypotenuse of a right angled triangle is its longest side

a. Given the triangle in the figure we see that the longest side facing the right angle is 8.

So, the hypotenuse is 8.

b. To find the leg of the right angle triangle x, using the trigonometric ratio

sinФ = opposite/hypotenuse

= x/H

Making x subject of the formula, we have that

x = H sinФ

Given that

Substituting the values of the variables into the equation, we have that

x = H sinФ

x = 8sin 45°

= 8 × 1/√2

= 8/√2

Rationalizing the denominator, we have that

x = 8/√2 × √2/√2

= 8 × √2/(√2)²

= 8√2/2

= 4√2

So, the leg is 4√2

Learn more about hypotenuse of right angled triangle here:

https://brainly.com/question/30949583

#SPJ1

3. The area of the shaded region is 5x² + 2x - 3

4. The area of the shaded region is 18x² + 21x + 6

From the question, we are to determine the area of the shaded region in the given diagrams.

3.

Area of the shaded region = {[(x - 1) + (2x - 1)] × [(x + 1) + (x + 1)]} - (x + 1)(x - 1)

Area of the shaded region = [(x - 1 + 2x - 1) × (x + 1 + x + 1)] - (x + 1)(x - 1)

Area of the shaded region = [(3x - 2) × (2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = [(3x - 2)(2x + 2)] - [(x + 1)(x - 1)]

Area of the shaded region = (6x² + 6x - 4x - 4) - (x² - x + x -1)

Area of the shaded region = 6x² + 6x - 4x - 4 - x² + x - x + 1

Area of the shaded region = 6x² + 2x - 4 - x² + 1

Area of the shaded region = 6x² - x² + 2x - 4  + 1

Area of the shaded region = 5x² + 2x - 3

4.

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2(1/2(6x +4) × (4x + 2))]

Area of the shaded region = [(6x + 4)(4x + 2)] - [1/2((3x + 2)(4x + 2))]

Area of the shaded region = [24x² + 12x + 16x + 8] - [1/2(12x² + 6x + 8x + 4)]

Area of the shaded region = (24x² + 12x + 16x + 8) - (6x² + 3x + 4x + 2)

Area of the shaded region = (24x² + 28x + 8) - (6x² + 7x + 2)

Area of the shaded region = 24x² + 28x + 8 - 6x² - 7x - 2

Area of the shaded region = 24x² - 6x² + 28x - 7x + 8 - 2

Area of the shaded region = 18x² + 21x + 6

Hence, the area is 18x² + 21x + 6

Learn more on Calculating Area of Shaded part here: https://brainly.com/question/14989383

#SPJ1

2 ounces of clay left in the bucket.

If Gina has used 3/10 of the bucket, then Joey has used,

1 - 3/10 = 7/10 of the bucket

Similarly, if Joey has used 3/5 of the bucket, then Gina has used,

1 - 3/5 = 2/5 of the bucket

The total amount of clay used by both of them is,

3/10 + 3/5 = 9/10

Therefore, the amount of clay left in the bucket is,

1 - 9/10 = 1/10

Since the bucket contains 20 ounces of clay, the amount of clay left in the bucket is,

(1/10) x 20 ounces = 2 ounces

So, there are 2 ounces of clay left in the bucket.

To learn more about clay here:

https://brainly.com/question/23857396

#SPJ4

The actual distance between the two towns is 337.5 miles.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it has only magnitude and no direction.

If 1/2 inch on the map represents 75 miles in reality, then 1 inch on the map would represent 150 miles (twice the distance of 1/2 inch).

So, to find the actual distance between the two towns, we need to multiply the distance on the map (2 1/4 inches) by the conversion factor (150 miles per inch):

2 1/4 inches * 150 miles per inch = (9/4) inches * 150 miles per inch

Simplifying:

(9/4) inches * 150 miles per inch = 337.5 miles

Therefore, the actual distance between the two towns is 337.5 miles.

To learn more about distance from the given link:

https://brainly.com/question/30923151

#SPJ1

The value of the expression, -0.4·(3·x - 2) + (2·x + 4)/3 when x = 4 is 0

-0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3 = 0

A mathematical expression comprises, variables, and or numbers, which could include indices, joined together by mathematical operators.

The value of the expression -0.4·(3·x - 2) + (2·x + 4)/3 for x = 4 can be found by plugging in x = 4 into the expression as follows;

Where; x = 4

-0.4·(3·x - 2) + (2·x + 4)/3 =  -0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3

-0.4 × (3 × 4 - 2) + (2 × 4 + 4)/3 = -0.4 × (12 - 2) + (8 + 4)/3

-0.4 × (12 - 2) + (8 + 4)/3 = -0.4 × 10 + 12/3 = -4 + 4 = 0

Therefore;

The value of the expression, -0.4·(3·x - 2) + (2·x + 4)/3 for x = 4 is zero

Learn more on evaluating mathematical expressions here: https://brainly.com/question/551090

#SPJ1

The sampling method used by the principal is Stratified sampling.

Stratified sampling is a sampling method where the population is divided into non-overlapping subgroups, called strata, based on certain characteristics or attributes, and then a random sample is drawn from each stratum.

In this case, the principal organized the school's population by grade level, which created four strata: freshman, sophomore, junior, and senior classes. The principal then randomly sampled fifty students from each of these four strata to collect data on their preferred elective course. This approach ensures that each grade level is represented in the sample, which can provide a more accurate and representative picture of the preferences of students in each grade level, compared to other sampling methods.

Learn more about Stratified sampling here: https://brainly.com/question/20544692

#SPJ1

The degrees of freedom associated with within treatments are 12 within the variation sum of squares degrees of freedom mean square f between treatments 64 within treatments (error) 96.

The ANOVA table divides the overall variance into variation between treatments and variation within treatments. Each source of variation's degrees of freedom (DF) is also provided.

According to the information provided, there are three treatments and a total of 15 observations. As a result, the total degrees of freedom is:

[tex]DF_{total}[/tex] = n - 1

where n is the number of observations

[tex]DF_{total}[/tex]= 15 - 1 = 14

The degrees of freedom between treatments are equal to the number of treatments minus one:

[tex]DF_{between}[/tex] = k - 1

where k is the number of groups being compared

[tex]DF_{between}[/tex]= 3 - 1 = 2

The number of treatments minus one equals the degrees of freedom between treatments, that is 2

We may use the following formula to calculate the degrees of freedom within treatments:

[tex]DF_{within}[/tex] = [tex]DF_{total} - DF_{between}[/tex]

Substituting the values we have:

[tex]DF_{within}[/tex] = 14 - 2 = 12

[tex]DF_{within}[/tex] = 12

As a result, the answer is 12. The degrees of freedom associated with within treatments are 12.

Learn more about ANOVA:

https://brainly.com/question/15084465

#SPJ4

A random sample of approximately 1067 registered voters is needed to estimate the proportion of voters planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

To estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a

margin of error no greater than 0.03, we need to determine the sample size. We can use the following formula for

sample size calculation:

[tex]n = (Z^2 × p × (1-p)) / E^2[/tex]
Where:
- n is the sample size
- Z is the Z-score (1.96 for 95% confidence)
- p is the estimated proportion of voters planning to vote for Chavez
- E is the margin of error (0.03 in this case)

Since we don't know the true proportion of voters planning to vote for Chavez, we can use the most conservative

estimate (p = 0.5) to ensure the required margin of error:

[tex]n = (1.96^2 × 0.5 × (1-0.5)) / 0.03^2[/tex]
n = (3.8416 × 0.25) / 0.0009
n = 0.9604 / 0.0009
n ≈ 1067

Therefore, a random sample of approximately 1067 registered voters is needed to estimate the proportion of voters

planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

for such more question on  random sample

https://brainly.com/question/24466382

#SPJ11

Value of the z-test statistic is 1.20.

To find the value of the z-test statistic, we need to calculate the sample proportion and the standard error of the proportion.

The sample proportion is:

p⁻ = 92/400 = 0.23

The standard error of the proportion is:

SE = √[(pq)/n] = √[(0.20.8)/400] = 0.025

where p = 0.2 and q = 0.8.

Now we can calculate the z-test statistic:

z = (p⁻ - p)/SE = (0.23 - 0.2)/0.025 = 1.2

Therefore, the value of the z-test statistic is 1.20.

Learn more about z-test statistic.

brainly.com/question/30577860

#SPJ11