when the finite population correction factor is applied to the sample mean, the resulting standard error for the sample mean is equal to

Answer:

O I, II & III

Step-by-step explanation:

(2, 3) and (1, 1)

m = (3 - 1)/(2 - 1) = 2

y = 2x + b

1 = 2(1) + b

b = -1

The equation of the line is

y = 2x - 1

I) y = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1   Yes

II) y = 2x - 1   Yes

III) y = 2(x - 1) + 1 = 2x - 2 + 1 = 2x - 1   Yes

Answer: O I, II & III

it will take approximately 22.56 years for the amount to triple.

The given information for this problem is that there is an initial investment of $600 in an account with an annual interest rate of 4%. The task is to determine after how many years the amount will triple.Using the compound interest formula, we can find the amount in the account after t years:A = P(1 + r/n)nt Where,A = final amount in the account, P = initial amount in the account r = annual interest rate ,n = number of times the interest is compounded per year ,t = time in years.

From the problem statement, we know that the initial amount, P, is $600 and the annual interest rate, r, is 4%. Let's assume that the interest is compounded annually, i.e., n = 1.Substituting these values in the formula, we get:A = $600(1 + 0.04/1)1t Simplifying this expression,A = $600(1.04)t.

Taking the ratio of the final amount to the initial amount, we get: 3P = $600 × 3 = $1800. Therefore,A/P = 3 = (1.04)t.Dividing both sides by P, we get:3 = (1.04)t ln(3) = ln(1.04)t. Using the logarithmic property, we can bring down the exponent to the front:ln(3) / ln(1.04) = t Using a calculator, we get ≈ 22.56. Therefore, it will take approximately 22.56 years for the amount to triple.

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Therefore, the expression that would give the total number of elements in the array list is n*m.

The Student question is given below :Assume that Item is some class available to the code below and that n and m are two integer variables correctly initialized. Consider the following array declaration and initialization.

[tex]Item[][] list= new Item[n][m];[/tex]

What expression would give the total number of elements in the array list?

The expression that would give the total number of elements in the array list is n*m. The given array declaration and initialization is Item[][] list= new Item[n][m]; This declaration and initialization signify that the array list is a 2D array with n rows and m columns. The total number of elements in this array can be determined by computing the product of the total number of rows (n) and the total number of columns (m).

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The recursively defined function has a first term equal to 10 and a common difference of 4 is f(n) = 6 + 4n.

When a recursive procedure gets repeated, it's called recursion. A recursive is a type of function or expression stating some conception or property of one or further variables, which is specified by a procedure that yields values or cases of that function by constantly applying a given relation or routine operation to known values of the function.

We have first term = a = 10

And the common difference of d = 4

We have the formula for the t terms of a as 10 and d as 4

f(n) = a + (n - 1)d

f(n) = 10 + (n-1) x 4

f(n) = 10 + 4n - 4

f(n) = 6 + 4n

So, the defined function is f(n) = 6 + 4n.

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The cost to ship a box containing 5 laptops, weighing a total of 11 kg (including the empty box), is $58.90, with a cost of $40.00 for the first 5 kg and $3.15 for each additional kilogram.

The total mass of the packed shipping box can be found by adding the mass of the laptops (5 * 1.65 kg = 8.25 kg) to the mass of the empty box (2.75 kg) for a total mass of 11 kg.

Since the cost to ship the box is $40.00 for the first 5 kg and $3.15 for each additional kilogram over 5 kg, we can split the total mass into two parts: the first 5 kg and the additional weight above 5 kg.

The cost to ship the first 5 kg is $40.00, and the remaining weight is 11 kg - 5 kg = 6 kg.

The cost to ship the additional 6 kg is $3.15 per kilogram, so the total cost to ship the packed box is:

$40.00 + $3.15 * 6 kg = $58.90

Therefore, the cost to ship the packed box is $58.90.

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Variable b represents the number of hours Kevin spends watching television each week.

A statement proving the equality of two mathematical expressions is known as an equation.

Given equation a + b = 15 relates the number of hours.

If here Kevin spends doing homework each week (represented by the variable "a") and the number of hours he spends watching television each week (represented by the variable "b").

Since the total number of hours Kevin spends doing homework and watching television each week is 15, we can write:

homework + watching television = 15 hours

a + b = 15

To find out what b represents, we can rearrange the equation to solve for b:

b = 15 - a

This means that b represents the number of hours Kevin spends watching television each week, given that he spends a hours doing homework each week and the total number of hours spent on both activities is 15.

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Complete question-

The equation is a + b = 15

The graph of the function f given by f(Θ) = 2 sin(Θ) is attached below the sum,

Use the form

a sin(bx−c)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift.

a=2

b=1

c=0

d=0

Find the amplitude |a|.

Amplitude: 2

Find the period of 2 sin(x).

Its 2π.

List the properties of the trigonometric function.

Amplitude: 2

Period: 2π

Phase Shift: None

Vertical Shift: None

x      y

0     0

[tex]\frac{\pi }{2}[/tex]     2

[tex]\pi[/tex]     0

[tex]\frac{3\pi }{2}[/tex]    -2

[tex]2\pi[/tex]    0

Then we can plot the according to the given function f(Θ) = 2 sin(Θ).

Hence the graph is attached below.

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Answer:

√1.5

Step-by-step explanation:

As a fraction, the square root of 3/2 can be expressed as √1.51 or just as √1.5.

The following conditions must be met to conduct a two-proportion significance test:

the populations are independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.

The two-proportion significance test is a hypothesis test that compares the proportions of two independent populations.

To conduct the two-proportion significance test, the following conditions must be met:

Populations must be independent.

Sample sizes are greater than 30.

The probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population.

The sample size should be large enough so that the sampling distribution of the sample proportion is nearly normal. The sample sizes should be large enough so that the central limit theorem can be applied.

In short, to conduct a two-proportion significance test, the populations must be independent, the probabilities of success multiplied by the sample sizes are greater than or equal to 10 and the probabilities of failure multiplied by the sample sizes are greater than or equal to 10 for each population, and the sample sizes are greater than 30.


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Answer: 1250 miles

Step-by-step explanation:

50 miles in 1/5 of an hour = 250 miles in 1 hour = 1250 miles in 5 hours

Answer:

1,250

Step-by-step explanation:

50 divided by 1/5 equals 250.

Multiply 250 by 5.

250*5= 1,250

Total number of  cups of berries does the school cafeteria have is 600

Addition is a basic mathematical operation that involves combining two or more numbers or quantities to find a total or sum. In other words, it is the process of finding the total amount when two or more numbers are added together.

To find the total number of cups of berries in the school cafeteria, you can add the number of cups of strawberries and blackberries.

The school cafeteria has 150 cups of strawberries and 450 cups of blackberries, so

Total cups of berries = cups of strawberries + cups of blackberries

Total cups of berries = 150 + 450

Total cups of berries = 600

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The associative property works with expressions that use multiplication and addition. The correct option is (D).

The associative property is a rule in mathematics that allows us to change the grouping of the numbers or variables in an expression without changing the result. This property only applies to addition and multiplication, and not to subtraction and division.

The associative property of addition tells us that we can add a group of numbers in any order, and the result will be the same. For example, (2 + 3) + 4 is the same as 2 + (3 + 4). The associative property of multiplication tells us that we can multiply a group of numbers in any order, and the result will be the same. For example, (2 × 3) × 4 is the same as 2 × (3 × 4).

However, the associative property does not work with subtraction and division. For example, (10 - 3) - 2 is not the same as 10 - (3 - 2). Similarly, (12 ÷ 2) ÷ 3 is not the same as 12 ÷ (2 ÷ 3). Therefore, the correct answer to the question is D - the associative property works with expressions that use multiplication and addition.

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To estimate a population proportion with a margin of error of 1% and a 99% confidence interval, we would need a sample size of at least 6644 individuals.

The formula to calculate the sample size is:

n = [z² x p(1-p)] / e²

where:

n is the sample size

z is the z-score corresponding to the desired confidence level (in this case, 2.576 for a 99% confidence level)

p is the planning value for the population proportion, which we don't know in this case, so we will assume the worst-case scenario of p=0.5 (which gives us the maximum sample size needed)

e is the desired margin of error

Plugging in the values, we get:

n = [(2.576)² x 0.5(1-0.5)] / (0.01)²

n = 6643.04

Since we need to round up to the next whole number, the minimum sample size needed is 6644.

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Answer:

  y = csc(3x)

Step-by-step explanation:

You want an equation for a cosecant curve with vertical asymptotes at multiples of π/3.

The vertical asymptotes of the parent cosecant function are at multiples of π. Putting them at multiples of π/3 means compressing the graph horizontally by a factor of 3.

That compression means x will be replaced by 3x in the equation. You want ...

  y = csc(3x)

The algebraic expression for the particle's velocity vₓ at a later time t is v(t) = ct²/2m +v₀ₓ.

Given that,

c = speed of light

t = time

v₀ₓ = initial velocity of particle

m = mass of particle

Velocity and acceleration are related through time. Acceleration is the rate of change of velocity, which is represented graphically as the slope of the velocity vs. time line. Velocity can be represented as the area underneath an acceleration vs. time line.

Newton's second law declares that an object having mass m will accelerate due to a net force (F) will accelerate at a rate of:

α = F/m

Therefore, the function that describes the acceleration at any point in time of the particle is:

α(t)=ct/m

The velocity function is the integral of the acceleration function, so we get:

v(t)= ∫ct/m dt

= ct²/2m +C

where the constant C is the initial velocity of the particle at time t=0. Therefore, the velocity function representing the velocity at any point in time is:

v(t) = ct²/2m +v₀ₓ

Therefore, the algebraic expression for the particle's velocity vₓ at a later time t is v(t) = ct²/2m +v₀ₓ.

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Yes

The logarithm function is continuous for all x>0. Its derivative is 1/x and r12 ln x dx = x ln x - x + c.

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The probability that 2 red balls and 2 blue balls are taken from the box is 3/7. This can be expressed mathematically as [tex](8C2 * 8C2) / (16C4) = 3/7[/tex].

To better understand this probability, let's look at an example. Say there are 8 red balls and 8 blue balls in the box. This can be represented as:

R = 8, B = 8

We want to determine the probability of taking 2 red balls and 2 blue balls out of the box. To do this, we need to calculate the total number of ways of selecting 4 balls from the box (16 balls in total) and then calculate the total number of ways of selecting 2 red and 2 blue balls out of the box.

The total number of ways of selecting 4 balls from the box can be expressed as (16C4). This is calculated by dividing the number of ways of selecting 4 balls out of 16 (16!) by the number of ways of arranging those 4 balls in any order (4!):

[tex](16C4) = 16! / 4! = 1820[/tex]

The total number of ways of selecting 2 red and 2 blue balls out of the box can be expressed as (8C2 * 8C2). This is calculated by multiplying the number of ways of selecting 2 red balls out of 8 (8C2) by the number of ways of selecting 2 blue balls out of 8 (8C2):

[tex](8C2 * 8C2) = 8C2 * 8C2 = 28[/tex]

The probability of taking 2 red balls and 2 blue balls out of the box is then the ratio of the number of ways of selecting 2 red and 2 blue balls out of the box (28) to the total number of ways of selecting 4 balls from the box (1820):

P(2 red balls, 2 blue balls) = 28 / 1820 = 3/7

In conclusion, the probability of taking 2 red balls and 2 blue balls out of a box containing 8 red balls and 8 blue balls is 3/7.

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The height is either 10 cm,12 cm,14 cm.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The base of the parallelogram has a length of 10 cm.

Here, area is not given so the height may be anything.

suppose h = 10

Hence, We get;

Area = base * height

      = 10 * 10

       = 100 cm²

if h = 12

area = 10 * 12

       = 120 cm²

if h = 14

area = 10 * 14

        = 140 cm²

Therefore, the height is either 10 cm,12 cm,14 cm.

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To visually display the trends in net profits over a period of four years, you should use a line chart

Explanation:

A line chart is a type of chart used to show information as a series of data points connected by straight line segments. A line chart is a basic type of chart that is often used in data analysis. It is also known as a line graph or a curve chart. This type of chart is commonly used to display trends in data over time.

                  In the given question, it has been asked to visually display the trends in net profits over a period of four years. To visually display the trends in net profits, a line chart is the best choice. Therefore, the correct answer is option C, a line chart.

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Answer:

(5x+40)+x+2(2x+20)=360

5x+40+x+4x+40=360

10x+80=360

10x=360-80

10x=280

x=28°

substitute x=28° into (5x+40)

=140+40= 180

therefore line Ac is the diameter of a he circle because a diameter divides a circle into 2 equal part and the angle on the line is 180° showing that the circle is on a straight line

Using the volume formula it is obtained that the least number of bags Martin should buy is Option C: 13.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

First, we need to convert the height of the cylinder from inches to feet -

6 inches = 6/12 feet = 0.5 feet

The volume of the cylinder can be calculated as -

V = πr²h

where r is the radius and h is the height.

Substituting the given values, we get -

V = 3.14 x 2² x 0.5

V = 6.28 cubic feet

Since each bag contains 0.5 cubic feet of sand, we can find the number of bags needed by dividing the total volume by the volume of each bag -

n = V / 0.5

n = 6.28 / 0.5

n = 12.56

Since we can't buy a fractional number of bags, we must round up to the nearest whole number.

Therefore, Martin needs to buy at least 13 bags of sand.

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The average rate of change of the function as x varies from 2 to 5 is 22.

Given function: g(x) = 1 – 2x + [tex]3x^2[/tex]

To find the average rate of change of the function as x varies from 2 to 5.

Solution: We are given a function: g(x) = 1 – 2x + [tex]3x^2[/tex]

The average rate of change of the function as x varies from a to b is given by:

Average rate of change = f(b) - f(a) / b - a

Let a = 2 and b = 5

We have to find the average rate of change of g(x) as x varies from 2 to 5.

So, the average rate of change of g(x) is given by:

Average rate of change = g(5) - g(2) / 5 - 2

= [1 - 2(5) + 3([tex]5^2[/tex])] - [1 - 2(2) + 3([tex]2^2[/tex])] / 3

= [1 - 10 + 75] - [1 - 4 + 12] / 3= 66 / 3= 22

Therefore, the average rate of change of the function as x varies from 2 to 5 is 22.

An average rate of change is the amount that the function changes on average over a specified interval.

The formula for average rate of change is given as the change in the function value divided by the change in x value for two distinct points on the function.

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The amount of work done when winding up a 50-foot long cable with a weight density of 8 pounds per foot is 14 feet is 5600 foot-pounds.

To explain this answer in more detail, work is a measure of energy and is calculated by multiplying force and distance. In this case, the force is the weight-density of the cable, which is 8 pounds per foot. The distance is the amount of cable that was wound up, which is 14 feet. Multiplying 8 and 14 together gives us the force of 112 pounds. Multiplying 112 by the total length of the cable, which is 50 feet, gives us the answer of 5600 foot-pounds.

To further explain, it is important to remember that 1 foot-pound is equal to 1 pound-foot. That means that 1 pound of force must be applied to move an object 1 foot in order to do 1 foot-pound of work. When this is applied to the example above, we can see that 8 pounds of force must be applied to the cable in order to move it 1 foot. Multiplying this by the length of the cable (50 feet) and the amount of cable wound up (14 feet) gives us the total amount of work done, which is 5600 foot-pounds.

In summary, the amount of work done when winding up a 50-foot long cable with a weight density of 8 pounds per foot is 14 feet is 14 x 8 x 50 = 5600 foot-pounds.

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Answer: The speed of light is approximately 89,100 times faster than the speed of sound.

Step-by-step explanation: To find out how many times faster the speed of light is than the speed of sound, we need to divide the speed of light by the speed of sound:

Speed of light / Speed of sound = (6.710610^7) / (7.5410^2)

Simplifying this calculation gives us:

Speed of light / Speed of sound = 8.91*10^4

This means that the speed of light is approximately 89,100 times faster than the speed of sound.

Hope this helps, and have a great day!

Answer:

30 feet

Step-by-step explanation:

Coordinates of Ann: (-4,3)

Coordinates of bottle caps: (4,-10)

Distance from Ann to bottle caps can be found out using the distance formula:
[tex]x_2=4, x_1=-4\\y_2=-3,y_1=-10\\Distance=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2 } \\=\sqrt{(4-(-4))^2 + ((-10)-3)^2} \\=15.26\\15\text{ is the answer}[/tex]

To increase £88 by 14%, we can use the multiplication method, which involves multiplying the original amount by the decimal equivalent of the percentage increase.

The multiplication method is a mathematical technique used to solve problems involving multiplication. It involves breaking down numbers into their constituent parts and then multiplying those parts together to arrive at the final answer.

To find the decimal equivalent of 14%, we divide the percentage by 100:

14% ÷ 100 = 0.14

This tells us that a 14% increase is equivalent to multiplying the original amount by 1.14 (1 + 0.14).

To increase £88 by 14%, we can multiply it by 1.14:

£88 x 1.14 = £100.32

Therefore, the increased amount is £100.32.

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We can solve the system by elimination without multiplying first only when, [tex]$a = 8$[/tex].

To solve the system by elimination, we want to eliminate one of the variables, either x or y, from one of the equations. To do this, we need to find a multiple of one equation that cancels out one of the variables in the other equation.

We can eliminate x by multiplying the first equation by -4 and adding it to the second equation:

[tex]-4(ax+3y) + (4x+5y) &=\\ -4(7) + 15\(-4a+4)x + (5-12)y &=\\ -13\ (4-4a)x - 7y &= -13[/tex]

By adding the first equation to the second equation and multiplying it by -4, we can get rid of x:

[tex](4-4a)x-7y=13\\4x+5y=15[/tex]

We can eliminate y by multiplying the second equation by 7 and subtracting it from the first equation:

[tex](4-4a)x - 7y &=\\ -13-28x - 35y &=\\ -105[/tex]

Simplifying this last equation, we get:

[tex](4a-4)x &= 28x\\4a &= 32\\a &= 8[/tex]

Therefore, we can solve the system by elimination without multiplying first only when, [tex]$a = 8$[/tex].

For any other value of a, we need to multiply one or both equations by a constant before we can eliminate a variable.

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The class intervals are given as:

0 - 15   15-30  30-45

2            3          2

A histogram is a graphical representation of the distribution of numerical data. It is a way of summarizing the shape and spread of a set of continuous data values into a series of bins or intervals.

The histogram is a bar graph-like representation of the data, where the data is grouped into intervals or bins on the horizontal axis and the frequency or count of observations falling into each bin is represented by the height of the bar on the vertical axis.

Each value is grouped into one of three ranges, 0-15, 15-30, 30-45, once we know how many values are in each group, we can graph it.

The class intervals are given as:

0 - 15   15-30  30-45

2            3          2

The histogram is provided below:

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Answer: what do you mean? I need more info-

Step-by-step explanation:

I can answer it with more info :)