What happens to the margin of error as you increase the confidence level?.

Let's use x to represent the cost of one orange and y to represent the cost of one lemon. We can then set up a system of two equations:16x + 13y = 9.29 19x + 6y = 9.05 These equations represent the total cost of buying a certain number of oranges and lemons in two different scenarios.

To understand why we need two equations, let's consider the first equation: 16x + 13y = 9.29

This equation tells us that if we buy 16 oranges and 13 lemons, the total cost will be $9.29. But we don't know the individual prices of oranges and lemons yet. That's where the second equation comes in: 19x + 6y = 9.05

This equation tells us that if we buy 19 oranges and 6 lemons, the total cost will be $9.05. Again, we don't know the individual prices yet.

By setting up a system of equations, we can solve for x and y, which represent the prices of oranges and lemons, respectively.

One way to solve this system is by elimination. We can multiply the first equation by 19 and the second equation by -16, which will allow us to eliminate y:

304x + 247y = 176.51
-304x - 96y = -144.8

Adding these two equations together gives: 151y = 31.71
Dividing both sides by 151, we get: y = 0.21
Now we can substitute this value of y into one of the original equations to solve for x. Let's use the first equation:
16x + 13(0.21) = 9.29
16x + 2.73 = 9.29
16x = 6.56
x = 0.41

So the cost of one orange is $0.41 and the cost of one lemon is $0.21.

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31.9

1) In this problem

10 x 3. 19 = 31.9

For decimal numbers, in a multiplication just move to the right the dot as many tenths or zeros you are multiplying. That' why we move it to the right and have 31.9

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (called the "legs") is equal to the square of the longest side (called the "hypotenuse").

In other words, if we let $a$ and $b$ be the lengths of the two legs, and $c$ be the length of the hypotenuse, we have:

$a^2 + b^2 = c^2$

In this case, we know that the hypotenuse has length 39 units, so we can write:

$a^2 + b^2 = 39^2 = 1521$

We also know that $a$ and $b$ are both integers, since they are the lengths of sides of a triangle. We can use this information to try out different values of $a$ and see if any of them result in a value of $b$ that is also an integer.

One way to do this is to start with $a=1$ and see what value of $b$ makes the equation $a^2 + b^2 = 1521$ true. We can rewrite this equation as:

$b^2 = 1521 - a^2$

If we plug in $a=1$, we get:

$b^2 = 1521 - 1^2 = 1520$

Now we need to find a perfect square that is less than or equal to 1520, since that will give us a value of $b$ that is an integer. The largest perfect square that is less than or equal to 1520 is $36^2 = 1296$, so we can try plugging in $b=36$:

$36^2 = 1296$

$1^2 + 36^2 = 1297$

This is close, but not quite right – we need the sum of the squares to be 1521, not 1297. We can try again with a larger value of $a$, and keep going until we find a value that works. This process can be a bit tedious, but fortunately there is a shortcut – we can use the fact that $a$ and $b$ must be the lengths of sides of a triangle to narrow down our choices.

Specifically, we know that in a triangle, the length of any side must be less than the sum of the lengths of the other two sides. In this case, we have a right triangle with hypotenuse length 39, so the length of each leg must be less than 39. This means that $a$ and $b$ must both be less than 39.

We can use this fact to quickly eliminate many of the possibilities. For example, if $a=1$, we know that $b^2 = 1520$, which means that $b$ must be greater than 39 (since $6^2 = 36$ and $7^2 = 49$). This tells us that $a$ must be at least 7 in order for there to be any hope of finding a value of $b$ that works.

Using this approach, we can quickly narrow down the possibilities and find that the only value of $a$ that works is 15. If we plug in $a=15$, we get:

$b^2 = 1521 - 15^2 = 216$

$b = \sqrt{216} = 6\sqrt{6}$

So the length of the shorter leg is $\boxed{15}$ units.

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Answer:

A)

Step-by-step explanation:

Incenter is the point where all of the angle bisectores meet in the triangle

The incenter is the point where all of the angle bisectors meet in the triangle. It is not necessarily the center of the triangle.

Step-by-step explanation:

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The equilibrium level of income (Y), interest rate (i), consumption (C), investments (I), and budget surplus can be calculated using the given equations and information. When G increases by 100, the new values for investments and budget surplus can be determined. The crowding out effect resulting from the increase in G can also be evaluated. Additionally, if the increase in G is accompanied by an increase in M/P by 100, the equilibrium level of Y and r, as well as the crowding out effect, can be determined and explained.

To calculate the equilibrium level of income (Y), we set the total income (Y) equal to total expenditures (C + I + G), solve the equation, and find the value of Y that satisfies it. Similarly, the equilibrium interest rate (i) can be determined by equating the demand for money (L) with the money supply (M/P). Consumption (C), investments (I), and budget surplus can be calculated using the respective equations provided.

When G increases by 100, we can recalculate the new values for investments and budget surplus by substituting the updated value of G into the equation. The crowding out effect can be assessed by comparing the initial and new values of investments.

If the increase in G is accompanied by an increase in M/P by 100, the equilibrium level of Y and r can be calculated by simultaneously solving the equations for total income (Y) and the interest rate (i). The crowding out effect in this case refers to the reduction in investments resulting from the increase in government spending (G) and its impact on the interest rate (r), which influences private sector investment decisions.

Overall, by analyzing the given equations and their relationships, we can determine the equilibrium levels of various economic variables, evaluate the effects of changes in government spending, and understand the concept of crowding out.

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Answer:

The answer is C. As the risk of an investment increases its, market value increases.

Step-by-step explanation:

Based on the amount of Nacho cheese corn chips and the calories per gram, the calories per party bag is 1,094.6 calories

First, convert ounces to grams:

= 1 ounce is 28.3495 grams

Party bag in grams:

= 15 x 28.3495

= 425.243 grams

The amount of calories is:

= 425.243 x 28.6% x 9

= 1,094.6 calories

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Answer:

I will try it :)

Step-by-step explanation:

thanks for the points.

Answer: The answer is B.3

The calculation; (9.04-8.23+21.954+81.0) * 3.1416 should have three significant figures.

To determine the number of significant figures in a calculation, we follow these rules:

1. When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.

2. When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

Let's calculate the expression:

(9.04 - 8.23 + 21.954 + 81.0) * 3.1416

First, perform the addition and subtraction:

(0.81 + 21.954 + 81.0) * 3.1416

= 103.764 * 3.1416

Next, perform the multiplication:

325.8512544

To determine the number of significant figures, we look at the original numbers involved in the calculation.

9.04 has three significant figures.

8.23 has three significant figures.

21.954 has five significant figures.

81.0 has three significant figures.

3.1416 has five significant figures.

Among these numbers, the number with the fewest significant figures is 81.0 with three significant figures.

Therefore, the result of the calculation, 325.8512544, should have three significant figures to match the least precise value.

In scientific notation, the result would be expressed as 3.26 x 10^2.

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The given calculation would yield a result with five significant figures because we base our significant digits off of the least precise term within the parentheses, which is 81.0. The result is then rounded according to this rule.

In the case of the calculation (9.04-8.23+21.954+81.0) * 3.1416, it's important to first consider the rule for significant figures in calculations - the result should be reported with the smallest number of decimal places in the numbers used in the calculation. The number 81.0 has two numbers after the decimal point, therefore, our final answer should have two numbers after the decimal point. When you calculate the inside of the parentheses, the result is 103.764. Multiplying that by 3.1416 would approximately yield 325.854. Rounding this to the least precise measurement (which is to two decimal places due to 81.0) would give us 325.85 which has five significant figures, effectively limiting our calculated value to five significant figures.

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The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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The equivalent expression to the complex number (3 + 4i) + (3-5i) is option C: 6 - i.

What is complex number?

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively.

The complex number expression is -

(3 + 4i) + (3 - 5i)

= 3 + 4i + 3 - 5i

= 3 + 3 + 4i - 5i

= 6 - i

Therefore, the value for the expression is 6 - i.

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Answer:

54

Step-by-step explanation:

Answer:

C. x-intercept = (-6, 0)

y-intercept = (0, -48/5)

Step-by-step explanation:

as you can see, x-intercept means y = 0.

and y-intercept means x = 0.

so, for x = 0 we have

5y = -48

y = -48/5

for y = 0 we have

8x = -48

x = -48/8 = -6

Answer:

1/32

Step-by-step explanation:

A unit fraction is a fraction that has a numerator value of one

300 + (200)r is the proper expression for sales if the number of units expected to be sold is uniformly distributed between 300 and 500. If r is a random number between 0 and 1.

What is a random number?

a random number is a number chosen by chance -- i.e., randomly, from a set of numbers. All the numbers in a specified distribution have equal probability of being chosen randomly.

Given that r is a random number between 0 and 1.  it is uniformly distributed between 300 and 500 will be done by using the formula of 300+200r.

If r = 0, 300+200r will result in the output as 300

If r = 0.5, 300+200r will result in the output as 400

If r= 1, 300+200r will result in the output as 500

Hence ,the proper expression for sales is 300+200r

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Answer:

The answer is A

Step-by-step explanation:

Answer:

0.24+n*pi and 1.33+n*pi

Step-by-step explanation:

First you add three to both sides to get:

13sin(2x)=6

Then you divide by thirteen to both sides to get:

sin(2x)= 6/13

Next, you use a calculator to perform the inverse of sine to both sides, which is arcsin, and cancels out the sin.

arcsin(sin(2x))= arcsin(6/13) -> 2x= arcsin(6/13)

Arcsin(6/13)= approximately 0.48. But besides 0.48, there is another solution, because the y value of 6/13 can have two possible x values, both in quadrant one and two. We found the quadrant one value. The quadrant two value is just pi-0.48=2.66.

So, if we add two pi (360 degrees) to both of these solutions for n amount of times, then on a graph, we would end up on the same point every time. Each of those revolutions around the graph is one solution. These are the solutions:

2x= 0.48+n*2pi ->       0.24+n*pi

2x=2.66+n*2pi ->          1.33+n*pi

Answer:

24.6

Step-by-step explanation:

4(4)+8.6

16+8.6=24.6

Answer:

4² + 8.6 = 24.6

Step-by-step explanation:

Just add.

16 + 8.6 = 24.6

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The correct interpretation of the interval (0.196, 0.320) is that it is 95% confident that the difference in the proportions of young people and senior citizens who use the internet as a news source lies between 0.196 and 0.320.

In addition, we can say that the interval (0.196, 0.320) is a measure of precision or uncertainty regarding the true difference in the proportions of young people and senior citizens who use the internet as a news source.

What is a confidence interval?

A confidence interval is a range of values that we use to estimate an unknown population parameter. It is calculated from a sample and provides a measure of the precision or uncertainty of our estimate. A confidence interval consists of a point estimate (e.g., a sample mean or proportion) and a margin of error (e.g., plus or minus some number of standard errors).

Senior citizens are elderly people who have reached the age of retirement or have been given special legal status as such. Senior citizens may be retirees or active in the workforce.

Complete question: A 95% confidence interval for the difference in proportions of young people and senior citizens who use the internet as a news source was found to be (.196, .320). which statements give a correct/appropriate interpretation of this interval?

a) The proportions of young people and senior citizens who use the internet as a news source lies between 0.196 and 0.320.

b)The proportions of young people and senior citizens who use the internet as a news source lies between 0.196 and 0.320.

c) Both a and b

d) None of the above

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Binomial is the name for an algebraic expression with only two terms. In mathematics the formula for a binomial is axᵐ + bxⁿ.

What is a binomial?

Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is sometimes referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form.

A binomial is a two-term algebraic expression that includes a constant, exponents, a variable, and a coefficient.

A binomial can be written as a single indeterminate as follows -

axᵐ + bxⁿ

Where m and n are non-negative distinct integers and a and b are the numbers. X can be a variable or be indefinite.

Binomials are stated in the same way in Laurent polynomials; the main distinction is that m and n may have negative exponents. Consequently, they are expressed as -

ax⁻ᵐ + bx⁻ⁿ

An example of a binomial polynomial is x² + 4x.

Therefore, binomial formula is axᵐ + bxⁿ.

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Length = 11.89 ft, Width = 3.5 ft, Height = 11.89 ft.

To find the dimensions of a box with volume 25 cubic feet that has minimum cost, the following formula can be used:
Volume of Box = Length x Width x Height
25 = L x W x H
Let L = length, W = width, H = height
25 = L x W x H
Since the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is $0.40 per square foot, the equation can be modified as:
0.2LW + 0.4LW = 25
0.6LW = 25
LW = 25/0.6
LW = 41.67
To find the dimensions of the box, we need to find the factors of 41.67.
Factors of 41.67 are: 1, 41.67, 3.5, 11.89
The possible dimensions of the box are:
Length = 3.5 ft, Width = 11.89 ft, Height = 11.89 ft
OR
Length = 11.89 ft, Width = 3.5 ft, Height = 11.89 ft.

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The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

1. Place the graduated pipet on a flat surface and make sure it is level

2. Draw the liquid up until the meniscus is level with the etched line that corresponds to the desired volume

3. Make sure the liquid is not touching the etched line above it

4. Observe the bottom of the meniscus and take the reading at the point where the liquid level is between the two etched lines

The volume is measured at the bottom of the meniscus when the liquid level is between the two etched marks on the pipet.

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Answer:

3

Step-by-step explanation:

An a=0.1 smoothing constant provides the most accurate forecast using MSE, MAE, and MAPE measures of forecast accuracy.
For this question, we need to find exponential smoothing forecasts using α = 0.1, and α = 0.2 and then find out which smoothing constant provides the most accurate forecast. The table for gasoline sales time series is given below:

To calculate the exponential smoothing forecasts, we use the following formula:

Ft+1 = α * At + (1- α) * Ft, where,

At = actual value at time t, and

Ft = forecasted value at time t, and

α is the smoothing constant.

For α = 0.1,

using the above formula, we get:

F2 = 0.1 * 18 + (1 - 0.1) * 18

= 18

F3 = 0.1 * 22 + (1 - 0.1) * 18

= 18.4

F4 = 0.1 * 15 + (1 - 0.1) * 18.4

= 18.36

F5 = 0.1 * 24 + (1 - 0.1) * 18.36

= 19.076

F6 = 0.1 * 18 + (1 - 0.1) * 19.076

= 18.7684

F7 = 0.1 * 15 + (1 - 0.1) * 18.7684

= 18.29156

F8 = 0.1 * 21 + (1 - 0.1) * 18.29156

= 18.862404

F9 = 0.1 * 19 + (1 - 0.1) * 18.862404

= 18.876164

F10 = 0.1 * 21 + (1 - 0.1) * 18.876164

= 19.061547

F11 = 0.1 * 20 + (1 - 0.1) * 19.061547

= 19.155392

F12 = 0.1 * 16 + (1 - 0.1) * 19.155392

= 18.940853

For α = 0.2, using the above formula, we get:

F2 = 0.2 * 18 + (1 - 0.2) * 18

= 18

F3 = 0.2 * 22 + (1 - 0.2) * 18

= 19.6

F4 = 0.2 * 15 + (1 - 0.2) * 19.6

= 17.68

F5 = 0.2 * 24 + (1 - 0.2) * 17.68

= 19.744

F6 = 0.2 * 18 + (1 - 0.2) * 19.744

= 18.9952

F7 = 0.2 * 15 + (1 - 0.2) * 18.9952

= 18.19616

F8 = 0.2 * 21 + (1 - 0.2) * 18.19616

= 18.956928

F9 = 0.2 * 19 + (1 - 0.2) * 18.956928

= 18.765543F10 = 0.2 * 21 + (1 - 0.2) * 18.765543

= 19.012434

F11 = 0.2 * 20 + (1 - 0.2) * 19.012434

= 19.009947

F12 = 0.2 * 16 + (1 - 0.2) * 19.009947

= 18.007958

(b) MSE measure of forecast accuracy is given by:

MSE = (1/n) Σ (At - Ft)^2, where n is the number of periods, At is the actual value, and Ft is the forecasted value. Using the above formula, we calculate MSE for α = 0.1 and α = 0.2 and compare which is more accurate.

An a=0.1 smoothing constant provides the most accurate forecast using MSE, MAE, and MAPE measures of forecast accuracy.

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The balanced nuclear fusion reaction is:
238 92 U → 234 90 Th + 4 2 He

The first reaction given is:
226 88 Ra → X + 4 2 He
Here, X represents the element that is formed as a result of the fusion reaction. To balance the equation, we need to find the atomic number of X. We can do this by subtracting the atomic number of helium (2) from the atomic number of radium (88):
88 - 2 = 86
Therefore, the balanced nuclear fusion reaction is:
226 88 Ra → 222 86 Rn + 4 2 He
Similarly, for the second reaction:
238 92 U → X + 4 2 He
Again, we need to find the atomic number of X to balance the equation. This can be done by subtracting the atomic number of helium (2) from the atomic number of uranium (92):
92 - 2 = 90
Therefore, the balanced nuclear fusion reaction is:
238 92 U → 234 90 Th + 4 2 He

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Answer:

I would say A cause I think that that is the closest answer

Step-by-step explanation:

I am so so so sorry if this is wrong I'm not that great at math myself.

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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