Line A contains the points (2, 6) and (4, 10). Line B contains the
points (-2, 3) and (3, 13).
1. Are the lines parallel? Explain your reasoning.

Standard deviation of the sampling distribution of the sample mean is 50.

We were asked to determine the mean of the sampling distribution of the sample mean. The mean score for a standardized exam is 400, the standard deviation is 50, and we have a random sample of 25 students. You take a sample of 25 students in total. You will obtain a sample average of X after averaging that sample. Take 70 student samples, then compute the mean.

The sampling distribution of the sample mean is the term used to describe how the mean varies from sample to sample. The question being posed here is, what is the mean of the sampling distribution of sample means?

Regardless of how the population distribution is shaped, the mean of sample averages is always the same as the mean of the population.

The sample mean is 400.

The spread of a data distribution is measured by standard deviation. The average distance between each data point and the mean is measured. Whether the data is being treated as a population unto itself or as a sample of a larger population will affect the standard deviation calculation formula.

So standard deviation of sample mean is also same as it is for random sample that is 50.

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Positive Rational Numbers, Negative Rational Numbers, Whole Numbers, Fractions are the 4 types of rational numbers.

1. Positive Rational Numbers: These are numbers that are greater than zero, such as 1/2, 3/4, and 5/6.

2. Negative Rational Numbers: These are numbers that are less than zero, such as -1/2, -3/4, and -5/6.

3. Whole Numbers: These are numbers that are greater than or equal to zero, such as 0, 1, 2, 3, and so on.

4. Fractions: These are numbers that are represented as a ratio of two integers, such as 1/2, 3/4, and 5/6.

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The total number of frogs in the reservoir are 160.

What is Reservoir?

An enlarged lake behind a dam is a reservoir. Such a dam could be a man-made structure created to hold freshwater or it could be a natural formation.

Given:

Elanor wants to estimate the number of frogs in a reservoir.

She catches 90 frogs from the reservoir and marks them with a non-harmful dye.

Elanor then returns the frogs to the reservoir.

The next day she catches another 80 frogs and 10 of these are marked with the dye.

So on the first day the total frogs are 90.

On second day total frogs are 80 but 10 of them are dye, so the remaining are 70.

Therefore, the total frogs are 90 + 70 = 160.

Hence, the total number of frogs in the reservoir are 160.

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Draw a drawing in the scale factor of 5 / 1 then drawn drawing is said to be in ratio and get enlarge 5 times to the scale drawing.

As given in the question,

Given scale ratio is equal to 5 / 1.

Let us consider scale drawing is in the scale ratio of 1cm  : 3m

It means we have

Therefore, scale factor of 5 / 1 used to draw a drawing is said to be in ratio to  enlarge or small the given picture.

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Answer:could you get a better picure

Thank you :)

Various linear equations in different forms are : horizontal and vertical line equations, An equation for a line in point-slope form, Linear equation in two-point form, the line's slope-intercept form equation, intercept form 

and standard form.

1) Equation of a Vertical Line : x = k , where k is a constant.

2) Equation of a Horizontal Line: y = k , where k is a constant.

3) Form of a Point Slope: y - y1 = m (x - x1).

If the slope m and a point (x1, y1) through which the line travels are known, the point-slope form is helpful.

4) Form of the slope-intercept, y = mx + b

If the slope m and the y-intercept (0, b) are known, the slope-intercept form is helpful.

5) Standard form: a x + b y = c , where a, b and c are constants.

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Answer:

( -4 , 1 )

Step-by-step explanation:

Answer: -4

(Hope I'm correct :D )

Step-by-step explanation:

Easy, let's start with what we know to find the slope. To find the slope you do:

(y2-y1)/(x2-x1)

For this equation then, we do:

(-2 - 2)/ (-5 - (-6)) Which simplifies to:

-4/1

= -4

So the slope is -4.

Dale and his dog walk for 5 miles.

What is distance?

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Given:

Dale and his dog walked for 1.25 hours at a speed of 4 miles per hour.

Since,

Distance = Speed x time

Here, speed = 4 miles per hour and

time is 1.25 hours

So,

Distance = 4 x 1.25

Distance = 5 miles

Hence, Dale and his dog walk for 5 miles.

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Answer:Child ticket sold = 30

Adult ticket sold = 50

Total ticket sold = 80

Step-by-step explanation:

If we want to be 90% confident that the sample mean is within 17 kernels of the true population mean then the minimum sample size that should be taken is 83.

Given:

the population standard deviation for the number of corn kernels on an ear of corn is 94 kernels.

if we want to be 90% confident that the sample mean is within 17 kernels of the true population mean

what is the minimum sample size that should be taken = ?

population standard deviation (σ) = 94

margin of error (E) = 17

for 90% confidence interval Zα/2 = 1.645

formula:

sample size (n) = [ zα/2 × σ/E]²

sample size (n) = [1.645×94/17]²

sample size (n) = 82.7

sample size (n) ≈ 83

Hence we get the required answer.

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Answer:

A’ (5,2) B’ (2,1) and C’ (1,3)

Step-by-step explanation:

When we reflect a point (x,y) over x-axis, we get (x,-y)

A ( 2,5) becomes (2,-5)

B (1,2) becomes (1,-2)

C ( 3,1) becomes (3,-1)

Then we proceed to rotate 90 degrees counterclockwise about the origin

(x,y) becomes (-y,x)

(2,-5) becomes (5,2)

(1,-2) becomes (2,1)

(3,-1) becomes (1,3)

Answer: 8

Step-by-step explanation:

128 divided by 16 = 8 baseball cards on each page

8 Baseball card if the page takes the same number of baseball cards

Step-by-step explanation:

If the album as 16pages, and there are 128 baseball cards to share in each pages "equally", then it's going to be 128/16 which equals 8 in each pages

Answer: the volume of the figure is 792 ft³

Step-by-step explanation:

The volume of a shape V consists of the volume of a prism V1 and

the volume of the pyramid V2

9²+12²=15²

81+144=225

225≡225

Hence, figure base is а right triangle

So, V=V1+V2

[tex]\displaystyle\\V1=\frac{12*9}{2} *10\\\\V1=6(9)(10)\\\\V1=540\ ft^3\\[/tex]

[tex]\displaystyle\\V2=\frac{1}{3}(\frac{12*9}{2} )(24-10) \\\\V2=\frac{12(9)(14)}{6} \\\\V2=252\ ft^3[/tex]

[tex]V=540+252\\\\V=792\ ft^3[/tex]

A 20 year old has height below 3.7 feet and above 7.9 feet then 20 year old be considered abnormal.

The average height means that the given population determined by the interaction between the environment in which it lives and the resources it commands.

Abnormal means diffrent from what is normal or usual, in a way that worries you or that is unplesant.

We have given that average height is 5.8 feet.

And abnormal height a 20 year old must be 2.1 feet below average height or 2.1 feet above average height.

Therefore 5.8 - 2.1 = 3.7 feet

                 5.8 + 2.1 = 7.9 feet

Hence height below 3.7 feet abd above 7.9 feet is considered to be abnormal.

That means [-∞ , 3.7] and [7.9,∞] is considered to be abnormal height for 20 year old man.

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There are an infinite number of solutions to the system of equations 2x + 5y = - 2 and 4x - 10y = 4.

The intersection locations of all the aforementioned equations can be found using graphic solutions to a system of equations.

Only when the equations have an intersection point can a system of two or more equations be solved.

According to the given information

A set of equations including

4x - 10y = 4 and 2x + 5y = - 2... (ii).

Now, when we multiply equation(i) by 2, we get

- 4x + 10y = - 4. (iii).

Adding (ii) and (iii) now gives us,

0x + 0y = 0.

Since 0 = 0, these coincident lines have an infinite number of solutions.

There are an infinite number of solutions to the system of equations 2x + 5y = - 2 and 4x - 10y = 4.

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The equation to find the value of x is x² - x - 4 = 0

The dimension of a sand box can be represented as (x + 2) inches and (x + 1) inches. The value of the area in square inches of the sandbox is equal to the value of the perimeter of the sandbox in inches.

Therefore, the equation that can be used to find the value of x can be express as follows:

Hence,

area of the sandbox = (x + 2)(x + 1)

area of the sandbox = x² + x + 2x + 2

area of the sandbox = x² + 3x + 2

Perimeter of the sandbox = 2(x + 2 + x + 1)

Perimeter of the sandbox =2(2x + 3)

Perimeter of the sandbox = 4x + 6

Therefore,

x² + 3x + 2 =  4x + 6

x² + 3x - 4x + 2 - 6 = 0

Hence, the equation is  x² - x - 4 = 0

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The required simplified value of the function when t= 3  is y = 36.8.

To Identify the initial amount a and the rate of decay r (as a percent) of the exponential functionⁿ.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given expression,
[tex]y=575(1-0.6)^t[/tex]
put t = 3
y=575(1-0.6)³
y = 36.8

Thus, the required simplified value of the function when t= 3  is y = 36.8.

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Point-slope form: y - 13= -3(x + 8)

Slope-intercept form: y = -3x - 11

Her height is 48 inches

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The distance jump = 13.2 inches

The percentage of the distance jump = 27.5% of her height.

This means,

Height = x

x = 100%

Now,

13.2 inches = 27.5%

Multiply 100/27.5 on both sides.

100/27.5 x 13.2 inches = 100%

48 inches - 100%

Thus,

The height is 48 inches.

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Answer:

4x+14

Step-by-step explanation:

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By replacing the value of x by 4 the answer to the given Algebraic Expression is 10

What is an Algebraic Expression?

The concept of algebraic expressions is to represent numbers using letters or alphabets without providing their real values. In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

Solution:

All we have to do to solve the following problem is to replace x by 4

3(4+4)(4+1)/(4+2)(4-2)

(3*8*5)/(6*2)

10

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Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

The image of (- 4, 4) by rotation is equal to (4, - 4).

In this problem we get the coordinates of the point and we are asked to find the coordinates of its image by rotation about the origin. The rotation rule is described below:

x' = x · cos θ - y · sin θ

y' = x · sin θ + y · cos θ

Where:

First, write the coordinates of the point:

P(x, y) = (- 4, 4)

Second, use the rotation formula to find its image:

x' = - 4 · cos 180° - 4 · sin 180°

x' = 4

y' = - 4 · sin 180° + 4 · cos 180°

y' = - 4

The point (4, - 4) is the image by rotation of the point (- 4, 4).

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Add the scale factor to the x- and y-coordinates of a point on a coordinate plane with the center of dilatation at the origin.

Given,

Dilation;

Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.

We have to dilate a figure with a center of dilation;

Dilations centered at the origin;

On the coordinate plane, figures can be enlarged. The centre of dilatation is frequently used to be the origin. The points in the picture can be found by multiplying the coordinates of the preimage's points by the scale factor when distorting a figure that is centered at the origin.

That is,

On a coordinate plane with the center of dilatation at the origin, multiply the point's x and y coordinates by the scale factor.

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The Square-1 is a Cubic twisty puzzle.

It is similar to the 3x3 Rubik's cube, but due to the way the pieces are cut and designed can shapeshift. It is even governed by the WCA, and uniquely the only shapeshifting puzzle in the WCA.

It's probably the hardest WCA puzzle to learn how to solve due to the restrictions in its turning and its unique design.Square-1 became an official WCA event in 2007. It is a shape-shifting puzzle with a middle slice that you can use to interchange pieces.

X-Man Volt has long been the best square-1 on the market. However, Yu-Xin has rolled out a new budget square-1, which is fully magnetic.

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The temperature was 42°C this afternoon. If the temperature dropped 9°C, The temperature is now 33°C.

In order to calibrate thermometers, a variety of temperature scales with distinct reference points and thermometric materials are used.The Celsius scale (°C), formerly known as centigrade, with the unit symbol °C, is the most commonly used scale, followed by the Fahrenheit scale (°F) and the Kelvin scale (K), which is mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).

42°C - 9°C = 33°C

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Answer: The area is 12

Step-by-step explanation:

P=2l+2w

We are given, 

P=40in

l=2w-4

Plug these into the first formula and solve for the dimensions,

length and width, of the rectangle:

 40=2(2w-4)+2w       Simplify

40=4w-8+2w

40=6w-8

48=6w

8=w OR the width is 8 in, therefore, 

the length is

l=2(8)-4

l=12 sq in

l= area

Answer:

256

Step-by-step explanation:

Answer:

[tex]\sf a. \quad Scale\;factor=\dfrac{10}{9}[/tex]

b.    Enlargement.

Step-by-step explanation:

The original figure is called the "pre-image".

The new, transformed figure is called the "image" and is usually indicated by the addition of ' after the name.

Therefore:

To find the scale factor of dilation, divide the dimension of the image by the dimension of the pre-image.

[tex]\implies \sf Scale\;factor=\dfrac{CP'}{CP}=\dfrac{20}{18}=\dfrac{10}{9}[/tex]

As the image is larger than the pre-image (and the scale factor is larger than 1), the dilation is an enlargement.

Answer:

C

Step-by-step explanation:

y=mx+b m=slope b=y-intercept, y-int: 4 slope: 3/1 but can just be put as 3. y=3x+4 bc it's a positive slope with a positive y-int.