how to calculate slope and y intercept online

The new coordinates of Rita's tent after a 90° clockwise rotation and dilation by a scale factor of 3 centered at the origin will be (-3y1, 3x1), (-3y2, 3x2), and (-3y3, 3x3)

What are the coordinates of plane?

A coordinate plane is a framework for graphing and describing points and lines. The coordinate plane is made up of a vertical (y) axis and a horizontal (x) axis. The coordinate plane is divided into four quadrants. The origin is the location where these lines meet (0, 0).

To find the new coordinates of Rita's tent after a 90° clockwise rotation and dilation by a scale factor of 3 centered at the origin, we need to perform the following steps:

Rotate the original coordinates 90° clockwise: To do this, we swap the x and y coordinates and negate the new x-coordinate. If the original coordinates of the vertices of the triangle are (x1, y1), (x2, y2), and (x3, y3), then the rotated coordinates will be (-y1, x1), (-y2, x2), and (-y3, x3).

Dilate the rotated coordinates: To dilate the rotated coordinates by a scale factor of 3 centered at the origin, we multiply each coordinate by the scale factor. If the rotated coordinates of the vertices of the triangle are (-y1, x1), (-y2, x2), and (-y3, x3), then the dilated coordinates will be (-3y1, 3x1), (-3y2, 3x2), and (-3y3, 3x3).

Therefore, the new coordinates of Rita's tent after a 90° clockwise rotation and dilation by a scale factor of 3 centered at the origin will be (-3y1, 3x1), (-3y2, 3x2), and (-3y3, 3x3), where (x1, y1), (x2, y2), and (x3, y3) are the original coordinates of the vertices of the triangle.

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When two companies have a correlation value of -0.95, there is less than zero covariance between their returns. So statement d is correct.

The correlation coefficient is an important measure that helps to establish a relationship between two variables. Its value is mostly between +1 to -1. Therefore, the value can be positive, negative, or zero. Based on this the types of correlation are positive correlation, negative correlation, and no relation.  This is calculated for the given condition using the below formula,

[tex]\text{correlation coefficient}=\frac{\text{covariance of security}}{\text{SD of security 1}\times\text{SD of security 2}}[/tex].

Here, the SD (standard deviation) is always positive, and the covariance value should be negative or less than zero so that the correlation coefficient of the two companies will be negative (as -0.95). From the given option, d is correct.

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Recognizing that sin(30º) = 1/2, the exact value of sin(120º) is √3/2.

The exact value of sin(120˚) can be found by using the double angle formula for sine. The formula is:
sin(2θ) = 2sinθcosθ

Since we are given that sin(30˚) = 1/2, we can substitute 30˚ for θ in the formula to find sin(120˚):
sin(120˚) = 2sin30˚cos30˚
sin(120˚) = 2(1/2)(√3/2)
sin(120˚) = √3/2

Therefore, the exact value of sin(120˚) is √3/2.

Note that to solve this type of problem it is crucial to know different types of trigonometric identities.

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Answer: 88 1/2

Step-by-step explanation:

easy

Answer:

89

Step-by-step explanation:

The value of the triple integral xy dV over the solid tetrahedron with vertices (0,0,0), (9,0,0), (0,8,0), and (0,0,6) is approximately 490.5. The limits of integration for x, y, and z are 0 to 9, 0 to 8 - (8/9)x, and 0 to 6 - (1/3)x - (1/4)y, respectively.

To evaluate the triple integral, we need to set up the limits of integration for the three variables x, y, and z. Since the solid is a tetrahedron with vertices at (0,0,0), (9,0,0), (0,8,0), and (0,0,6), we can write the limits of integration as follows:

0 ≤ x ≤ 9

0 ≤ y ≤ 8 - (8/9)x

0 ≤ z ≤ 6 - (1/3)x - (1/4)y

The limits of integration for x are straightforward, as x ranges from 0 to 9. For y, we need to consider that the solid is bounded by the x-axis (y=0), the y-axis (x=0), and two planes that intersect along the line x=9, y=8. The equation of the plane containing the points (0,8,0), (9,0,0), and (0,0,6) is given by 8x/9 + 6z/9 = 8, which simplifies to y = 8 - (8/9)x - (2/3)z. Solving for z, we get z = (3/2)(4 - (3/4)x - (3/4)y), so the limits of integration for z depend on both x and y.

With these limits of integration, we can set up the triple integral as follows:

∭E xy dV = ∫0⁹ ∫0(⁸-(⁸/⁹)ˣ) ∫0(⁶-(¹/³)ˣ-(¹/⁴)ʸ) xy dz dy dx

Evaluating the innermost integral with respect to z, we get:

∫0(⁶-(¹/³)ˣ-(¹/⁴)ʸ) xy dz = xyz |z=0 to z=(6-(1/3)x-(1/4)y) = x y (6 - (1/3)x - (1/4)y)

Substituting this expression back into the triple integral and evaluating the remaining integrals, we get:

∭E xy dV = ∫0⁹ ∫0(⁸-(⁸/⁹)ˣ) x y (6 - (1/3)x - (1/4)y) dy dx

= ∫0⁹ x [(3/4)y²(8/9 - (1/3)x) - (1/12)y³(8/9 - (1/3)x)] |y=0 to y=(8-(8/9)x) dx

= ∫0⁹ x [(3/4)(8/9 - (1/3)x)³ - (1/12)(8/9 - (1/3)x)⁴] dx

≈ 490.5

Therefore, the value of the triple integral is approximately 490.5

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The two equations that describe the time x, when 405 cells would be expected are:

To solve for x in the first equation, we can divide both sides by 5 to get:

3^x = 81

Then, we can take the log base 3 of both sides to get:

x = log3(81)

x = 4

To solve for x in the second equation, we can use the properties of logarithms to simplify:

log3(405/5) = log3(81)

x = log3(81)

x = 4

Both equations give us the same answer of x = 4, which means that after 4 hours, there would be 405 cells on the plate if the cell growth is exponential.

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So, in response to the above question, we can state that They gathered a total equation of s + 2s = 3s shells.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

In the case where Anna gathered s shells and her brother gathered twice as many, the brother gathered 2s shells.

They gathered a total of s + 2s = 3s shells.

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The proof for the given statements is as follows:

Statements:

1. overline AB || overline PQ

2. overline AP || overline BQ

3. overline BP || overline CQ

Reasons:

1. Since AB || PO, then AB || PQ

2. Since AP || BQ and AB || PQ, then AP || BQ

3. Since BP || CQ and AB || PQ, then BP || CQ

Therefore, by the properties of parallel lines, we can conclude that angle ABP congruent to angle BCQ and angle BAP congruent to angle CBO. Since angles ABP and BCQ are congruent, and angles BAP and CBO are congruent, this implies that angle ABP is congruent to angle QPB, and angle CBQ is congruent to angle PQB.

By the definition of similar triangles, two triangles are said to be similar if their corresponding angles are congruent. Therefore, triangle ABP is similar to triangle QPB, which is similar to triangle BCQ, proving the statement.

The converted values of 139 pounds to kilograms in standard form is equal to 63.0493 kilograms.

Scale factor used to convert pounds to kilograms is equal to :

One pounds is equal to 0.453592 kilograms.

Now convert pounds to kilogram by substituting the value in standard form we get,

⇒ 139 pounds = ( 139 ) multiply to ( 0.453592 ) kilograms

⇒ 139 pounds =  139 × 0.453592  kilograms

⇒ 139 pounds =  63.049288 kilograms

⇒ 139 pounds =  63.0493 kilograms

Therefore, the using standard scale factor to convert 139 pounds to kilograms is equal to 63.0493 kilograms.

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21% of 200 is going to be 42.

If you want this the simple way, multiply 21% to 200 and it will actually tell you the answer. :)

Answer:

42

Step-by-step explanation:

To find the percentage of a number, take the percent and change it to decimal form.

21% = .21

Multiply this by the number

.21 * 200

42

21% of 200 = 42

On graphing the given models we got a parabola as shown below

To graph the given equation, find the coordinate points using the given variables. In this problem, we have taken the values of t as 0, 1, and -1 from that find the values of 'h' and form the coordinate points. Now plot the resultant points as a graph.

Here we have

h = - 16t² + 12 represents the height that corn from the ground

Where t represents the time in sec

From given equation,

at t = 0 => h = 12

at t = 1 => h = - 4

at t = -1 => h = -4

Now take h = y and t = x

The coordinates we got are (0, 12) (1, -4) and (-1, -4)

Now use the above points to draw the graph as shown below  

Therefore,

On graphing the given models we got a parabola as shown below

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it will take them both 600 seconds to ice 35 cupcakes.

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

Here,  Ann can ice a cupcake in 30 seconds,

Then, the total number of cupcakes iced by Ann is,

t/30 cupcakes

Similarly, If Sarah can ice a cupcake in 40 seconds,

Then, the total number of cupcakes iced by Sarah is

t/40 cupcakes,

Hence, For them to ice 35 cupcakes together, then;

t/30 +  t/40 = 35

where t is the times taken by both of them to ice 35cupcakes

40t+30t/1200 = 35

70t/1200 = 35

7t/120 = 35

t/120 = 5

t = 600

Thus, This shows that it will take them both 600seconds to ice 35 cupcakes.

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One milliliter is equal to one cubic centimeter

To convert 1 milliliter to cubic centimeter , we can use the following formula:

1 mm = 1 cc

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The volume in cc = Conversion factor × The volume in ml

Substitute the values in the equation

The volume in cc = 1 × 1

Multiply the terms

= 1 cc

Therefore, one ml is 1 cc

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The average rate change of over the interval [-1,1] is 2.

What is an interval?

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific numbers are referred to as an interval. All actual numbers between those two are included in this range.

Given points on the graph is

x   -2     -1     0     1        

y   -4     -3     -1     3

The average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,

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

Here a = -1, b = 1, f(a) = -3, and f(b) = 3

The average rate is (3 - (-3))/ (1 - (-1)) = 2

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The sample means represented by the red lines below the curve do not include the actual population mean μ. Out of the 25 samples, 4 of them do not have the true proportion while 21 out of the 25 do have the true mean. This means that 84% of the samples contain the true mean. The closest confidence level is 80%.

The statement refers to a statistical concept where a sample mean is compared to the true population mean. The red lines under a curve represent sample means that do not include the actual population mean. Out of 25 samples, only 21 of them contain the true mean while 4 do not. This indicates that 84% of the samples have the true mean. The closest confidence level is 80%, which suggests that there is an 80% probability that the true mean falls within the interval estimate. This information is important in statistical analysis as it helps researchers understand the accuracy of their results and make more informed decisions.

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The distance of 7km in miles is 4.349597 miles.

It's important to note that kilometers are the primary unit of distance measurement in most countries, while miles are used primarily in the United States and a few other countries. To convert 7km to miles, we need to know the conversion factor between the two units.

By knowing how to convert between these two units is a useful skill when traveling internationally or when working with different units of measurement. Here, One kilometer is equal to 0.621371 miles.

Therefore, to convert 7km to miles, we simply multiply 7 by the conversion factor:

7km x 0.621371 miles/km = 4.349597 miles

So, 7km is equal to approximately 4.35 miles.

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Answer:

k < 24

Step-by-step explanation:

The phrase "k less than 24" can be written as an algebraic expression using the symbol "<" which means "less than."

So, "k less than 24" can be written as:

k < 24

This means that the value of "k" is smaller than 24. For example, if k = 20, then 20 is less than 24, so the statement "k < 24" is true.

If k = 30, then 30 is not less than 24, so the statement "k < 24" is false.

I hope this helps!

- Dante

A measure of variation that includes spread, variance, and spread from the mean is the standard deviation.

The skewness of the data is expressed as standard deviation. It measures how far each observation is from the mean. Approximately 95% of the values ​​in each distribution fall within 2 standard deviations of the mean.

Standard deviation is a measure of spread, variance, and deviation from the mean given spread.

The standard deviation represents the "typical" deviation from the mean. This is a popular measure of volatility because it preserves the original units of the data set.

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Answer:

1 ≤ x ≤ 9

Step-by-step explanation:

Answer:

93.6

Step-by-step explanation:

First, convert the time you have to work with to hours:

1 hour 15 minutes = 1.25 hours

required speed to cover 117 miles in 1.25 hours =

distance ÷ time = 117 miles ÷ 1.25 hours = 93.6 miles per hour (apprx.)

Answer:

2/3 gallons

Step-by-step explanation:

0.67 gallons or 2/3 gallons is used on the fence.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

Amount of gallons = 2 gallons

The amount used on a fence.
= 1/3 of 2 gallons

Now,

1/3 x 2 gallons

= 2/3 gallons

= 0.67 gallons

Thus,

0.67 gallons or 2/3 gallons is used on the fence.

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5:00 pm in military time is 1700 hours. Military time, also known as the 24-hour clock, is a system of timekeeping used by the military, emergency services, and other organizations around the world.

In this system, the day is divided into 24 hours, starting at midnight (0000 hours) and ending at midnight the following day (2400 hours).

To convert from standard time (AM/PM) to military time, you can simply add 12 hours to any time after 12:00 pm. For example, to convert 5:00 pm to military time, you would add 12 hours to 5:00 pm, which gives you 17:00 or 1700 hours.

Military time is commonly used in situations where time needs to be communicated clearly and without confusion, such as in aviation, transportation, and healthcare. It can also be useful in everyday life to avoid confusion and ensure accurate scheduling.

In summary, 5:00 pm in military time is equivalent to 1700 hours, and understanding how to convert between military time and standard time can be useful in a variety of contexts where clear and accurate timekeeping is important.

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Approximately 27% of the jerseys did not sell.

What is Percentage?

Percentage is a way of expressing a number as a fraction of 100. It is used to describe ratios, proportions, and changes in quantities in terms of a fraction of the whole.

Solution:

The school ordered 225 jerseys and sold 165, so the number of jerseys that did not sell is:

225 - 165 = 60

To find the percentage of jerseys that did not sell, we need to divide the number of unsold jerseys by the total number of jerseys ordered and then multiply by 100:

60 / 225 x 100% = 26.67%

Rounding this to the nearest percent gives: 27%

Therefore, approximately 27% of the jerseys did not sell.

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The method to convert mililitres to deciliter is by multiplying the quantity in mililitres with 0.01.

Firstly know the full form of units being used in the question. Here ml represents mililitres and dl represents deciliter. Now, we know that mililitres and deciliter are connected to each by the formula -

1 deciliter = 100 mililitres

So, 1 millilitre in deciliter will be = 1/100 deciliter

It can be written in decimal form as -

Quantity in deciliter = 0.01 deciliter

Let us say we have 1000 mililitres of milk which needs to be converted into deciliter.

So, Quantity in deciliter = 1000 × 0.01

Performing multiplication on Right Hand Side of the equation

Quantity of 1000 mililitres in deciliter = 10 deciliter.

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Answer:

D. X/3=1

Step-by-step explanation:

A. 8x = 28

8(3) = 28

24 = 28

Option A is wrong

B. x - 19 = 16

3 - 19 = 16

-16 = 16

Option B is wrong

C. 28 + 3 = 25

31 = 25

Option C is wrong

D. X/3=1

3/3 = 1

1 = 1

Option D is correct.

Since the rectangular prism holds exactly 24 unit cubes, the volume of the prism is equal to 24 cubic units.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

Generally speaking, the volume of a rectangular prism is directly proportional to the number of unit cubes. Based on the information provided above, we can reasonably infer and logically deduce that volume of this rectangular prism is equal to 24 cubic units because it holds exactly 24 unit cubes.

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Answer:

188 cm rounded to the nearest whole number.

Step-by-step explanation:

1 rotation = 2[tex]\pi[/tex]r

2[tex]\pi[/tex](15)  If the dimeter is 30, the radius is 15

2 rotations would be

2[2[tex]\pi[/tex](15)]

188.495559218

Answer:

188.5 cm

Step-by-step explanation:

Circumference of a circle = C = 2πr = πD

D = 30 cm

C = π(30 cm) = 94.25 cm

2 revs = 2C = 2(94.25) = 188.5 cm

Answer:

Michelle has 18.9 yards of string. She cuts the string into 5 pieces of equal length. How long is each piece?

18.9 ÷ 5

Step-by-step explanation:

You're welcome.

If 18,793 is multiplied by 1000, then the product of this arithmetic equation will be equal to 18,793,000.

The arithmetic equations are the mathematical problems which includes simple functions such as addition (summation), subtraction, multiplication and division. The function of multiplication is also called as repeated addition. In the given question, the multiplicand is 18,793 and the multiplier is 1000 and the result which we get that is 18,793,000 is called as product.

The multiplicand is always written first. When the multiple of 10 is multiplied to any number, the general rule says that there is simple addition of zeroes in the right hand side of the number if is not in decimal form. If the number is in decimal form, the decimal point shift to the right hand side as many times as there are zeroes in the multiplier.

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