Alexander said: "All primes are odd,
except the number 2. Therefore, all odd numbers are prime numbers.
prime." Do you agree with Alexander? Explain your answer.

To determine the minimum sample size required to estimate the population proportion with the given margin of error and confidence level, we need to use the formula:

n = (\(Z^2\) * p * q) / \(E^2\)

where:

n = minimum sample size

Z = Z-score corresponding to the desired confidence level (96% confidence level corresponds to a Z-score of approximately 1.96)

p = estimated proportion of the population (since it is unknown, we can assume p = 0.5, which provides the maximum sample size needed)

q = 1 - p (complement of p)

E = margin of error

Substituting the given values into the formula, we have:

n = \((1.96^2\) * 0.5 * 0.5) / \((0.005^2)\)

Calculating this expression:

n = (3.8416 * 0.25) / 0.000025

n = 96,040

Therefore, the minimum sample size required to estimate the population proportion is 96,040.

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Answer:

1 remainder 13

Step-by-step explanation:

:)

Answer:

I believe it is a 25% increase

Answer:

11.1111% increase fee for an accounting course,

5.55555% per each semester.

Step-by-step explanation:

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!

The time Billy should get up to be right on time for school is 6:52 am.

The formula to calculate the time Billy should get up to be right on time for school is as follows: Time Billy Should Get Up = School Start Time - (Time to Get Dressed + Time to Eat Breakfast + Time to Walk to School). In this case, the formula is: Time Billy Should Get Up = 8:35 am - (32 minutes + 13 minutes + 17 minutes). In order to solve this equation, first we must convert the minutes to hours. 32 minutes is equal to 0.53 hours and 13 minutes is equal to 0.22 hours. 17 minutes is equal to 0.28 hours. Thus, the formula is: Time Billy Should Get Up = 8:35 am - (0.53 hours + 0.22 hours + 0.28 hours). Now, we can solve for the time Billy should get up. 8:35 am minus 0.53 hours is 7:42 am. Then, 7:42 am minus 0.22 hours is 7:20 am. Finally, 7:20 am minus 0.28 hours is 6:52 am. Therefore, the time Billy should get up to be right on time for school is 6:52 am.

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Answer:

9 cans

Step-by-step explanation:

45/30=1.5

1.5*6=9

Answer:

9 Cans of dog food

Step-by-step explanation:

You have to divide 45 the amount of cans within the 30 days. 45/30=1.5.And you have to multiply this by 6 days. 1.5×6=9

Answer:

15cm

Step-by-step explanation:

Given parameters:

Area of the square = 225cm²

Unknown:

Base  = ?

Solution:

A square is a figure with equal sides.

Area of a square  = L²

L is the side length

    225cm²  = L²

       L = √225

       L = 15cm

The base of the square is 15cm

Step-by-step explanation:

answer .................

Given parameters:

   Expression;

                        6¹²

Identify the exponent and the base in the expression;

                         6¹²

An exponent is a power to which a number or variable is raised.

Generally, it signifies the number of times a number should be repeatedly multiplied.

The base is the number that is being multiplied.

So, in this problem, exponent is 12 and base is 6.

Step-by-step explanation:

2(a + 2ab) + 4 - ab

= 2a + 4ab + 4 - ab

= 3ab + 2a + 4.

When a = 4 and b = -2,

we have 3ab + 2a + 4

= 3(4)(-2) + 2(4) + 4 = -24 + 8 + 4 = -12.

Answer:

1

Step-by-step explanation:

3.2/0.4=8

8×2=16

16×0.4=6.4

6.4÷0.1=64

Answer:

x = 15

Step-by-step explanation:

Given that,

The length of the base of an isosceles triangle is x.

The length of a leg is 3x-4.

Perimeter, P = 97

An isosceles triangle has one base. The perimeter of a triangle is given by :

97=x+3x-4+3x-4

97 = 7x-8

97+8=7x

105 = 7x

x = 15

So, the value of x is 15.

Answer:

y=30

x=3

Step-by-step explanation:

~may it help you~

Answer:

  95°

Step-by-step explanation:

  ∠SRW is a vertical angle with respect to the one marked 95°. As such, it will have the same measure: 95°.

  m∠SRW = 95°

The best approximation for the solution of the system of equations is (0.88,0.65).

Given a system of equations is y=-(2/5)x+1 and y=3x-2.

A system of linear equations consists of two or more equations, and one attempts to solve the equations together.

To find the best approximation solution solve the system of equations.

The given system of equations are

y=-(2/5)x+1     .......(1)

y=3x-2           .......(2)

Firstly, substitute the value of y into equation (1) to find the value of x, we get

3x-2=-(2/5)x+1

Now, we will add (2/5)x in both sides, we get

3x-2+(2/5)x=-(2/5)x+1+(2/5)x

3x-2+(2/5)x=1

Further, we will add 2 on both sides, we get

3x-2+(2/5)x+2=1+2

3x+(2/5)x=3

17x/5=3

Furthermore, we will multiply both sides with 5, we get

5×(17x/5)=3×5

17x=15

Now, divide both sides with 17, we get

17x/17=15/17

x=0.88

Further, we will find the value of y by substituting the value of x in equation (2), we get

y=3(0.88)-2

y=2.65-2

y=0.65

Hence, the best approximation for the solution of the system of equations y=-(2/5)x+1 and y=3x-2 is (0.88,0.65).

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Answer:

therefore he will pay $12,264

Answer:

$1,379.37

Step-by-step explanation:

to solve we do \(12000(1.022)^5\) then subtract 12000.

Please rate and mark as brainlest. hope this helps!

(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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The profit per bag is approximately $2.50  and the total profit is approximately is $36 , the correct option is (c) .

In the question ,

a graph of relation of price and quantity is given .

Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost

that means P = MC .

price is given as = $8 ,

Form the graph ATC = $5.5

per unit profit can be calculated using the formula ,

Per unit profit = Price - ATC

per unit profit = 8 - 5.5

= $2.5

From the graph , the quantity is Q = 14.4 (approximately)

Total profit is calculated using the formula

Total Profit = (profit per unit) × (quantity)

Total Profit = 2.5 × 14.4

= $36

Therefore , The profit per bag is approximately $2.50  and the total profit is approximately is $36 .

The given question is incomplete , the complete question is

This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is      and the total profit is       .

(a) $5.50 , $78

(b) $5.00 , $60

(c) $2.50 , $36

(d) $8.00 , $114

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Adam Vinatieri made 14 field goals and 7 extra points.

Given that,

a field goal is 3 points and the field goal after a touchdown is only 1 point.

Adam Vinatieri made 21 field goals and extra point kicks for 49 points.

Let x be the number of field goals and y be the extra point kicks.

So we get,

x + y = 21 -------------(1)

3x + y = 49 -----------(2)

Subtracting equation (1) from equation (2),

2x = 28

 x = 14

putting the value of x in equation (1),

14 + y = 21

       y = 7

Therefore Adam Vinatieri made 14 field goals and 7 extra points.

Field goal means a score of three points in football made by drop kicking or placekicking the ball over the crossbar from ordinary play. A field goal is a successful kick of the ball by a kicker through the goalpost. It is an offensive play that can score three points for a team.

Adam Vinatieri is an American former football placekicker who played in the National Football League.

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Answer: A

Step-by-step explanation:

Answer:

The equation of the perpendicular bisector of the segment QR (with endpoints Q(-2,0) and R(6,12) is... \(y=-\frac{2}{3}x+\frac{22}{3}\) 

Step-by-step explanation:

01. Review what we know:

We are told that the endpoints of the segment QR is Q(-2,0) and R(6,12).

02. Find the midpoint:

We need to find the coordinates of the midpoint of the segment. The formula for this is \((\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2})\)

We can do \((\frac{-2+6}{2} ,\frac{0+12}{2})\), which would become \((\frac{4}{2} ,\frac{12}{2})\). This is equal to (2,6), so we know that the midpoint of the segment is at (2,6).

03. Find the slope:

Now, to find the slope of the segment, we must use the formula \(\frac{(y_2-y_1)}{(x_2-x_1)}\)

Using this, we can input the coordinates of Q and R to find the slope.

\(\frac{(0-12)}{(-2-6)}\) would become \(\frac{(-12)}{(-8)}\), which can be simplified to \(\frac{(3)}{(2)}\)

04. Find the slope of the perpendicular bisector:

Whenever we need to find the slope of something perpendicular to the original, we need to take the original slope and find the opposite reciprocal. To find the reciprocal, we would flip the fraction, and to make it opposite, we would make it positive if the original was negative, or negative if the original was positive.

In this case, we would flip \(\frac{3}{2}\) to \(\frac{2}{3}\), and because the original was positive, we would make \(\frac{2}{3}\) negative, into \(-\frac{2}{3}\).

So the slope of the perpendicular bisector is \(-\frac{2}{3}\).

05. Plug in our information to begin to write the equation:

Now, we have all the information we need to begin to form our equation.

Our equation needs to be in the format of y=mx+b, also known as slope-intercept form (m is our slope, b is our y-intercept, and x and y represent the coordinates).

Plugging in our new slope for the perpendicular bisector, we would have \(y=-\frac{2}{3} x+b\)

However, we need to find the y-intercept in order to complete the equation!

06. Finding our y-intercept (aka "b"):

We can do this by plugging in the midpoint coordinates into x and y and solving for b!

We can plug in 2 and 6 into x and y, respectively.

That would give us \(6=-\frac{2}{3} (2)+b\)

Through basic algebra, we can solve this equation.

First we need to multiply \(-\frac{2}{3}\) and \((2)\), which gives us \(-\frac{4}{3}\)

Then, we need to isolate b, which we can do by adding \(\frac{4}{3}\) on both sides of the equation.

\(6=-\frac{4}{3}+b\\+\frac{4}{3}+\frac{4}{3}\\\) (<-- like this)

This would cancel \(-\frac{4}{3}\) out on the right side and move it to the left side, giving us \(6+\frac{4}{3}=b\)

Now, we need to add \(6+\frac{4}{3}\), which we can do by finding the common denominator of both. \(6=\frac{6}{1}\), and \(\frac{6}{1} *3=\frac{18}{3}\)

Now they share the same denominator, and we can add them together. \(\frac{4}{3} +\frac{18}{3}=\frac{22}{3}\), so the y-intercept, or "b," is \(\frac{22}{3}\)

07. Add the y-intercept to the equation:

Now that we have our y-intercept, we can finalize our equation!

\(y=-\frac{2}{3} x+b\) becomes \(y=-\frac{2}{3} x+\frac{22}{3}\) when we add in the y-intercept.

Now we have our equation for the perpendicular bisector of QR! Our answer is \(y=-\frac{2}{3} x+\frac{22}{3}\)

Key Words:

perpendicular bisector

opposite reciprocal

slope-intercept form

y-intercept

slope

midpoint

Formulas:

midpoint formula: \((\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2})\)

slope formula: \frac{(y_2-y_1)}{(x_2-x_1)}

slope-intercept form: \(y=mx+b\)

Variables:

slope: "m"

y-intercept: "b"

(x,y) coordinates: x and y

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\((2x + 3x + 4x) = 180 \\ 9x = 18 \\ \frac{9x}{9} = \frac{180}{9} \\ x = 20\)

ATTACHED IS THE SOLUTION with the steps.

Answer:

The answer is A.

Step-by-step explanation:

Took it on Edge (:

By using the formula for sample size with a 95% confidence interval and a proportion of 0.6 we find that bound of 0.08 on the error of estimation, the industry should sample at least 558 plants.

In Exercise 8.8, the sample size was 2500, and the proportion of employees in favor of the policy was 0.64. We need to estimate the sample size required to have a bound of 0.08 on the error of estimation. Using the formula for the margin of error, we get:

ME = z * sqrt(p * q / n)

0.08 = z * sqrt(0.64 * 0.36 / n)

Assuming a 95% confidence interval, we have z = 1.96. Solving for n, we get:

n = (z / ME)^2 * p * q

n = (1.96 / 0.08)^2 * 0.64 * 0.36

n ≈ 558. So, we need to sample at least 558 plants to have a bound of 0.08 on the error of estimation.

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ANSWER:

10^11 * 14818

Expand: factor out 10^11: 10^11 (15800-982) = 10^11 * 14818

Answer:

1/3

Step-by-step explanation:

let x = 0.333.....(1)

10x = 3.333......(2)

Subtract (1) from (2)

\(10x = 3.333 \\ x = 0.333\)

9x = 3

X = 3/9

\(x = \frac{1}{3} \)

The statement "Relationships between two categorical variables are less evident when the data is expressed in counts rather than percentages" is false. Categorical variables are those that divide a population into groups. These groups can be classified into one of two categories: nominal or ordinal. The nominal category does not have an intrinsic order, whereas the ordinal category does.

Categorical data is a data type that is collected from observations that are grouped into categories with numerical figures. These variables are frequently defined in nominal terms. The data is expressed in percentages or proportions in a categorical data table instead of counts. When analyzing categorical data, it is best to use percentages, as these provide a better picture of the underlying relationship.

Therefore, relationships between two categorical variables are more evident when data is expressed in percentages rather than counts. When percentages are utilized, it is more straightforward to understand the relationship between two categorical variables. An example of categorical data is the top 150 movies of all time.

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The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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Answer:

2 quarts .

Step-by-step explanation:

4 quarts make a gallon but two is already added

Answer:

2 quarts

Step-by-step explanation:

Answer: \(y=\frac{5}{6}(x-2)(x+3)(x-4)\)

Step-by-step explanation:

Assuming this is a cubic polynomial, the equation in factored form is:

\(y=a(x-2)(x+3)(x-4)\)

Using the point \((1, 10)\) to solve for \(a\),

\(10=a(1-2)(1+3)(1-4)\\\\10=12a\\ \\ a=\frac{5}{6}\\\\\therefore y=\frac{5}{6}(x-2)(x+3)(x-4)\)