Match the equation to its description:
y=2x+3
2y=-3x-4
x--10
y-8
3y-2x+12

As per the concept of margin of error, the standard deviation increases as the margin of error increases.

The term margin of error is referred as the estimate of a small sample drawn from a relatively large population data.

Here the margin of error is usually governed by parameters such as standard deviation of population, sample size and desired confidence level.

Here we have given that for fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.

And we need to find the missing term in the statement.

Here let us consider that the following values are represented the given situation,

=> σ = Standard deviation for population

=> m = Margin of error

=> Z = Empirical value of Z-score at a given confidence level

Then the minimum sample size for a given confidence level is written as

=> (Z x σ)²/m²

Here from the above given formula it can be inferred that the minimum sample size is directly related to the population standard deviation. Therefore, the minimum sample size required would increase with the increase in population standard deviation.

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The equation of  the parabola will be y = -1/8[tex]x^{2}[/tex].

A right circular cone and a plane perpendicular to one of the cone's elements cross to form a parabola, also known as an open curve.

Y = a(x - h)2 + k or x = a(y - k)2 + h is the general equation of a parabola. The vertex is shown here as (h, k).

The parabola's y= value is provided to us.

When we mirror this parabola along the x-axis, we scale the resulting image vertically by a factor of 1/8.

Then we get y = -1/8[tex]x^{2}[/tex]

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Answer:

He has $185 left

Step-by-step explanation:

Subtract $220 from how much he spent

The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

From the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius, r = 3

Additionally, this line and the circle's center lies on the x-axis because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer: Statements 1, 3, and 4 are not true. The sum, difference, and quotient of two negative integers can be positive, negative, or zero, depending on the values of the two integers. For example, the sum of -5 and -7 is -12, which is a negative number. The difference of -5 and -7 is 2, which is a positive number. The quotient of -5 and -7 is -0.7142857142857143, which is a negative number.

Only statement 2 is true. The product of two negative integers is always a positive number. For example, the product of -5 and -7 is 35, which is a positive number. This is because the two negative signs "cancel out" when multiplying two numbers, resulting in a positive product.

Sarah completed reading for x = 18 minutes.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question

The number of pages Sarah will read in an hour is x. (this is "pages per hour" rate).

(10 minutes) / (3 pages) = (x pages) / (60 minutes)

cross-multiply:

10x = 3*60

x = 18

Hence, Sarah completed reading for x = 18 minutes.

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The system of inequalities is:

x + y ≤ 10

x*$1.25 + y*$1.50 ≥ $24

And the graph can be seen below, on the graph, we can see that there are no solutions.

So we need to start by defining the variables we will be using, these are:

First, we know that Larissa wants to make at most 10 loaves of bread, then we can start with the inequality:

x + y ≤ 10

We also know that each banana bread sells for $1.25 and each but bread sells for $1.50, and she wants to make at least $24, then:

x*$1.25 + y*$1.50 ≥ $24

So the system of inequalities is:

x + y ≤ 10

x*$1.25 + y*$1.50 ≥ $24

So to graph these inequalities, we need to shade the region abovce the first line:

x + y = 10

and below the second line:

1.25*x + 1.50*x = 24

The graph of that system of inequalities can be seen below. The graph shows that the system has no real solutions (only has solutions for negative values of x).

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Answer: 113 bananas

Step-by-step explanation:

The ratio is 6:19, with 6 papayas for every 19 bananas.

We have 36 papayas, which is 6 times, so we just need to get 19 times 6 = 113 bananas

Answer:

108

324

12

and 54

Step-by-step explanation:

Answer:

5 x 10⁰

Step-by-step explanation:

-15 / -3 = 5

5 in standard form is 5 x 10⁰

Answer: 5

Step-by-step explanation:

-15/-3

negative signs cancel out each other to make positive

⇒15/3

⇒5/1

⇒5 answer.

hope that helps...

Answer: B

Step-by-step explanation:

The 480 chairs were all finished by the employees in 4 days while maintaining a steady pace.

Time and work deals with the time taken by an individual or a group of individuals to complete a piece of work and the efficiency of the work done by each of them.

Work Done = Time Taken × Rate of Work.

Rate of Work = 1 / Time Taken.

Time Taken = 1 / Rate of Work.

If a piece of work is done in x number of days, then the work done in one day = 1/x.

Total Work Done = Number of Days × Efficiency.

Here,

Total number of chairs=480

Chairs left to work on=120

It took them 3 days to install 360 chairs which means if they were working at a constant rate they got 120 chairs installed daily.

With 120 chairs left that means in 1 days they will finish.

So overall, it took the workers 4 days to finish.

The workers took 4 days to complete all the 480 chairs from start to finish at a constant rate.

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Both Anorexia and Bulimia the rate of occurrence is high in females as compare to males so the choice is female to male ratio is 12  to 1.

Therefore, the rate of occurrence in females is much more than the males. Correct option is 12 to 1.

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Answer:

16[tex]\pi[/tex]

Step-by-step explanation:

Area = [tex]\frac{\pi r^{2} }{4}[/tex]  It is only 1/4 of a circle so we have to divide by 4

a = [tex]\frac{8^{2}\pi }{4}[/tex]

a = 16[tex]\pi[/tex]

Answer: To solve this system of inequalities graphically, we can plot the two inequalities on the same coordinate plane and find the region where they overlap.

First, let's consider the inequality that states that Tyshawn has at most 22 coins worth no less than $3.40 combined. We can represent this inequality as follows:

Quarters * $0.25 + Dimes * $0.10 ≥ $3.40

Next, we can consider the inequality that states that at most 16 of the coins are quarters. We can represent this inequality as follows:

Quarters ≤ 16

Finally, we can consider the inequality that states that a maximum of 6 of the coins are dimes. We can represent this inequality as follows:

Dimes ≤ 6

To solve the system of inequalities graphically, we can plot the three inequalities on the same coordinate plane and find the region where they overlap. The region where the three inequalities overlap represents all of the possible values of Quarters and Dimes that satisfy all three inequalities.

One possible solution to the system of inequalities is (Quarters = 12, Dimes = 10). This solution satisfies all three inequalities and is represented by a point within the region where the three inequalities overlap on the coordinate plane.

Answer:

Yes, you take the average value of the two numbers in the middle.

Step-by-step explanation:

Since there are TWO middle values, you always put 2 as a denominator.

Answer: x= 6/5

Step-by-step explanation:

Let an unknown number be x

5x - 2 = 4

5x = 6

x= 6/5

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Sam has 7/8 m of rope left.

What is fraction ?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

To derive a solution, you have to subtract the meter of rope that Sam has from the meter of rope he cut for a project.  

Therefore,

1½ - 5/8,  

Since the meter of rope Sam had is represent with a mixed fraction, we have to convert it to an improper fraction, and therefore 1½ can also be written as 3/2

Therefore, we have

3/2 – 5/8

To solve this fraction, you need to find the smallest number that can divide the denominator (2 and 8), which is 8.  

Now divide the denominators with 8 and multiply the answers you get by the numerators.

Therefore, we have

3/2 -5/8

= 12/8 – 5/8

= 7/8 m.

Therefore, Sam has 7/8 m of rope left.

The smallest number used to divide the denominators is also known as the lowest common denominator (LCD).

A fraction has 2 parts, which are numerator and denominator. The numerator is the number at the top in a fraction while the denominator is the number below in a fraction.  

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Answer:

Hi i'm wondering how to find the answer the answer is 3 over 2 (2k-8) > 1 over 3(k-9)

After 7 years  the laptop computer will be worth $200 or less.

In this question, we have been given a laptop computer is purchased for $1500 . Each year, its value is 75%  of its value the year before.

We need to find the number of years when laptop computer be worth $200  or less.

We can see that given situation represents exponential decay function with initial value 1500, decay rate = 0.75 and the final value = 200

We need to find period t.

For given situation we get an exponential function as,

1500 * (0.75)^t ≤  200

(0.75)^t  ≤ 2/15

t * ln(0.75) ≤ ln(2/15)

t * (-0.2877) ≤ -2.0149

t ≥ (-2.0149)/(-0.2877)

t ≥ 7

Therefore, the laptop computer will be worth $200 or less after 7 years.

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True , statistical measures that communicate the most information should be used with scales that contain the most information.

Given :

statistical measures that communicate the most information should be used with scales that contain the most information. true  or false .

we know that ,

What is statistical measures ?

The mean, median, mode, percentiles, range, variance, and standard deviation are the most commonly used numerical measures for quantitative data.

So the statistical measures that must communicate the most information should be used with scales that contain the most information for knowing the details of the given data .

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The probabilities are P(X = 2) = 0.14 and P(X ≥ 2) = 0.30

The mean and the standard deviation are 0.96 and 0.90

P(x = 2)

From the question, we have the following parameters that can be used in our computation:

X       0         1         2       3

P(X)   0.12    0.20   0.14  0.16

From the above table, we have

P(X = 2) = 0.14

P(x ≥  2)

From the question, we have the following parameters that can be used in our computation:

X       0         1         2       3

P(X)   0.12    0.20   0.14  0.16

From the above table, we have

P(X ≥ 2) = P(2) + P(3)

Substitute the known values in the above equation, so, we have the following representation

P(X ≥ 2) = 0.14 + 0.16

Evaluate the sum

P(X ≥ 2) = 0.30

The mean is calculated as

μx = sum of the products of x and P(x)

So, we have

μx = 0 * 0.12 + 1 *0.20 + 2 * 0.14 + 3 * 0.16

Evaluate

μx = 0.96

The standard deviation is calculated as

ox = the square root of sum of the products of x and P(x) * (1 - P(x)

So, we have

ox = √[(0 * 0.12 * 0.88) + (1 * 0.20 * 0.80) + (2 * 0.14 * 0.86) + (3 * 0.16 * 0.84)]

Evaluate

ox = 0.90

Hence, the standard deviation is 0.90

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Answer:

10626 different recital programs possible

Step-by-step explanation:

Since  there is no repetition we can tackle this problem in the following manner.

Out of the 23 pieces, the pianist can choose the first one in 23 ways

Out of the remaining 22 pieces she can choose the second one in 22 different ways

Out of the remaining 21 pieces she can choose the third one in 21 different ways

So total number of ways in which 3 pieces can be played without repetition is 23 x 22 x 21 = 10,626 ways

There is a formula for this kind of situation
If there are a total of n items and you want to choose r items from this, the number of possible ways to do this without repetition is given by the formula

[tex]_{n}P_{r} = \dfrac{n!}{(n-r)!}[/tex]

In this case, n = 23, r = 3 so we get
[tex]_{23}P_{3} = \dfrac{23!}{(23-3)!} = \dfrac{23!}{20!} = 23 \times 22 \times 21 = 10626[/tex]

Same as the above

To find the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x), you can use the following steps:

Set y equal to 0 and solve for x to find the x-intercepts of the graph.

Since the graph of y = cos(12x) + cos(16x) is periodic with period 2π/12 = π/6 and 2π/16 = π/8, respectively, you only need to consider x-intercepts in the interval [0,π/6).

Use the identity cos(a+b) = cos(a)cos(b) - sin(a)sin(b) to rewrite the equation y = cos(12x) + cos(16x) as:

y = 2cos(4x)cos(8x) - sin(4x)sin(8x)

Set y equal to 0 and solve for x to find the x-intercepts. This will give you the x-coordinates of all the x-intercepts of the graph.

Sort the x-coordinates in increasing order and take the first three smallest positive values to find the 3 smallest positive x-intercepts.

For example, if you set y equal to 0 and solve for x, you get:

0 = 2cos(4x)cos(8x) - sin(4x)sin(8x)

This equation can be rewritten as:

cos(4x)cos(8x) = sin(4x)sin(8x)

Using the identity cos(a) = sin(π/2 - a) and substituting this into the equation above, we get:

sin(4x)sin(8x) = sin(4x + π/2)sin(8x)

This equation simplifies to:

sin(4x)sin(8x) = sin(4x)cos(8x)

Dividing both sides by sin(4x) and rearranging, we get:

sin(8x) = cos(8x)

This equation holds for all values of x that satisfy sin(8x) = cos(8x), so we can find the x-intercepts by setting these two functions equal to each other and solving for x:

sin(8x) = cos(8x)

sin^2(8x) = cos^2(8x)

sin^2(8x) - cos^2(8x) = 0

1 - cos(16x) = 0

cos(16x) = 1

Thus, the x-intercepts of the graph are at x = 0, x = π/16, x = π/8, x = 3π/16, and so on. Since we are only interested in the 3 smallest positive x-intercepts, we can take the first three values in this list: x = 0, x = π/16, and x = π/8.

Therefore, the 3 smallest positive x-intercepts of the graph of y = cos(12x) + cos(16x) are [0, π/16, π/8].

The solution to the equations using the substitution method is x = - 2 and y = 0

The two equations given are known as system of equations. The equations have to be solved simultaneously to determine the required values.

y = 6x + 12 equation 1

y = 4x + 8 equation 2

Equate equation 1 and equation 2 together

6x + 12 = 4x + 8

6x - 4x = 8 - 12

2x = -4

x = -4 / 2

x = -2

Substitute for x in equation 1:

y = 4(-2) + 8

y = -8 + 8

Y = 0

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Answer:

Slope is 1, since we use rise over run which is expressed as 1/1

Answer:

Step-by-step explanation:

wait