the length of a rectangle is 4 inches shorter than its width. the perimeter of the rectangle is 80 inches. what are the length and width of the rectangle?

Therefore , the solution of scatter plot is construct this fence, we multiply the IQR by 1.5, subtract Q1 from this result, and add Q3 to the result.

Taxes calculated in the manner above can be considered regular tax liabilities. tax calculated at 15% of book profit (plus any applicable surcharges and cess) (manner of computation of book profit is discussed in later part). The tax that is calculated by applying 15% (plus any applicable surcharge and cess) to book profit is known as MAT.

Here,

In bivariate data, a scatter plot is helpful for identifying outliers (data with two variables).

Because they will be separated from the majority of points on the scatter plot, the outliers are simple to identify.

We can compare each observation to the minimum and maximum fence posts as a result. Outliers are any observations that fall more than 1.5 IQR outside Q1 or rise more than 1.5 IQR outside Q3.

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Therefore ,as a result, the answer to the given circle problem is  

√ 1996/(√ 62)3 =0.0915, which is the curvature.

A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric the about center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.

Here,

Given: (7, 2t, 3t2) r'(t)

r''(t)= (0, 2, 6t) (0, 2, 6t)

r(t) x r(t) = (6t2, -42t, 14)

(36t4 + 1764t2 + 196) = sqrt (r'(t) x r"(t)

|r'(t)|= sqrt (49 + 4 T 2 + 9 T 4)

We know that t = 1 at (7,1,1), therefore sqrt (36 + 1764 + 196) = sqrt 1996 |r'(t)| = √ (49 + 4 + 9) = √ 62.

The curvature is then equal as√ 1996/(√ 62)3 =0.0915

Therefore ,as a result, the answer to the given circle problem is  √ 1996/(√ 62)3 =0.0915, which is the curvature.

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Answer:

1

Step-by-step explanation:

The measure of angle ∠CXA is 134°

What is the Isosceles triangle?

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Triangle ABC is an isosceles triangle where AB = BC

∵ AB = BC

- The base angles in the isosceles triangle are congruent

∴ m∠BAC = m∠BCA

∵ m∠ BCA = 46° ⇒ given

∴ m∠ BAC = 46°

- The sum of the measures of the interior angles in any triangle is 180°

∵ m∠BAC + m∠BCA + m∠ABC = 180°

- Substitute the values of angle BAC and BCA in the equation above

∴ 46 + 46 + m∠ABC = 180

∴ 92 + m∠ABC = 180

- Subtract 92 from both sides

∴ m∠ABC = 88°

- BF, AD, and CE are bisectors segments of angles B, A, and C and they are intersected at point X

∵ CE bisects ∠BCA

∵ X ∈ CE

∴ m∠XCA = 1/2 m∠BCA

∴ m∠XCA = 1/2 (46) = 23°

∵ AD bisects ∠BAC

∵ X ∈ AD

∴ m∠XAC = 1/2 m∠BAC

∴ m∠XAC = 1/2 (46) = 23°

- In Δ AXC

∵ m∠XAC = 23° ⇒ proved

∵ m∠XCA = 23° ⇒ proved

∵ m∠CXA + m∠XAC + m∠XCA = 180° ⇒ interior angles of Δ

Substitute the values of angles XAC and XCA

∴ m∠AXC + 23 + 23 = 180

∴ m∠CXA + 46 = 180

- Subtract 46 from both sides

∴ m∠CXA = 134°

Hence, The measure of angle ∠CXA is 134°.

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The complete question is:

Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X. triangle ABC with diagonals BF, AD, and EC that intersect at point X If segment BA is congruent to segment BC and m∠BCA = 46°, what is m∠CXA?

assuming a year is 365 days

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$19211.34\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]A = 19211.34\left(1+\frac{0.04}{365}\right)^{365\cdot 3} \implies \stackrel{balance}{\boxed{A \approx 21660.58}}~\hfill \underset{interest}{\stackrel{21660.58~~ - ~~19211.34}{\boxed{\approx 2449.24}}}[/tex]

A 45-45-90 triangle is a right and isosceles triangle, whose legs are congruent or equal, and have one right angle of 90°. Thus all the statements are correct.

A 45-45-90 triangle is a special kind of triangle, which has the following characteristics:

The attached picture gives a better understanding of these characteristics.

If we take a look at the given problem, we can conclude that all the given statements are correct.

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The probability of scoring a total of 6 is 1/36 and the probability of scoring a total greater than 10 is 25/36.

a) The possibility space for two spinners is all the possible combinations of numbers that the two spinners can produce. The possibilities for spinner A are 1, 2, 3, 4, 5, and 6, and for spinner B are also 1, 2, 3, 4, 5, and 6. Therefore, the possibility space is 1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 2x1, 2x2, 2x3, 2x4, 2x5, 2x6, 3x1, 3x2, 3x3, 3x4, 3x5, 3x6, 4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 5x1, 5x2, 5x3, 5x4, 5x5, 5x6, and 6x1, 6x2, 6x3, 6x4, 6x5, 6x6.

b) The probability of scoring a total of 6 is 1/36, since there is only one possibility (3x2) that produces a score of 6.

c) The probability of scoring a total greater than 10 is 25/36, since there are 25 combinations of numbers (4x3, 4x4, 4x5, 4x6, 5x2, 5x3, 5x4, 5x5, 5x6, 6x1, 6x2, 6x3, 6x4, 6x5, 6x6) that produce a score greater than 10.

The possibility space for two spinners is all the possible combinations of numbers that the two spinners can produce, which is 1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 2x1, 2x2, 2x3, 2x4, 2x5, 2x6, 3x1, 3x2, 3x3, 3x4, 3x5, 3x6, 4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 5x1, 5x2, 5x3, 5x4, 5x5, 5x6, and 6x1, 6x2, 6x3, 6x4, 6x5, 6x6. The probability of scoring a total of 6 is 1/36 and the probability of scoring a total greater than 10 is 25/36.

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Answer:

Please provide a question to be answered, as you have only given us the piecewise function that would be used to solve a problem.

N and f(n) is totally different by their own circumstances.

N is independent variables

And f(n) is dependent variable

These are the main difference about n and f(n),You can typically depend on f(n) to represent the value of the function f at n. fn might mean f(n), especially when the domain is natural numbers, but it usually denotes the nth function in a sequence of functions.

F(a,b) would mean that the function takes two values, a and b. Your function takes one argument, n.

For example, f(n) might be the number of eggs in n packages, where each package has a dozen eggs. That would be f(n) = 12n, so f(3) = 12 * 3 = 36.

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Answer: it is 0.05 m

Answer:

  $12300

Step-by-step explanation:

You want to know the amount loaned at 7% if $19000 loaned at 7% and 17% earns $2000 in one year.

The interest on an investment P at rate r for t years is ...

  I = Prt

The sum of the amounts of interest on a 7% investment of x and a 17% investment of (19000 -x) is given as 2000:

  0.07x +0.17(19000 -x) = 2000

  -0.10x +3230 = 2000 . . . simplify

  1230 = 0.10x . . . . . . . . . . add 0.10x -2000

  12300 = x . . . . . . . . . . . . divide by 0.10

The amount loaned at 7% was $12,300.

Mariela's purchase of a house located in the V Zone of an NFIP participating community means that the house is located in a high amount of risk flood zone and that she is required to purchase flood insurance if she has a mortgage. This insurance will help to protect her investment in the event of a flood.

Mariela must purchase flood insurance if she has a mortgage on her house, which is located in a high amount of risk flood zone in an NFIP participating community. This insurance will help to protect her investment in the event of a flood.

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This is a convenience sample as it is based on accessibility and availability of visitors.

What is average ?

The average, also known as the mean, is a measure of central tendency that is commonly used to summarize a set of numerical data. It is calculated by adding all of the values in a dataset and then dividing by the number of values in the dataset.

This is an example of a convenience sample ,

A convenience sample is a type of sample where the researcher selects participants based on accessibility and availability, rather than using a random selection method. In this case, the librarian is only collecting data on visitors who are checking out books at her specific check-out station in the children's section of the library, which is a subset of the total population of visitors to the library. The data may not be representative of the entire population of visitors to the library, as it only includes data from visitors who are checking out books in the children's section of the library.

This is a convenience sample as it is based on accessibility and availability of visitors.

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Answer:

Step-by-step explanation:

AB = √36 = 6 cm

Area of semicircle πr²/2 or 9π/2

Area of 4 semicircles = 18 π

Total area = 36 + 18 π ≈ 92.5 cm²

The equations ( x1+4x2 ) = 11 and ( 2x1+7x2 ) = 18 give the solution as x1 = -5 and x2 = 4.

In order to solve the equation using elementary row operation it is required to multiply the first equation with -2, so that the term with x1 is eliminated from both equations and the value of x2 can be found.

Now

-2. ( x1+4x2 ) = -2 . 11

(-2x1 - 8x2 ) = -22

Now, this equation is added to the second equation (the left-hand sides of both equations are added together and the right-hand side of the equations are added together).

(-2x1 - 8x2 ) + ( 2x1+7x2 ) = ( -22 + 18 )

-2x1 + 2x1  - 8x2  + 7x2  = -4

-x2 =  -4

(x2 = 4)

The value of x2 = 4 is now put in equation 1 to get the value of x1,

( x1 + 4x2 ) = 11

x1+ 4 (4) =  11

x1 + 16 = 11

x1 = (11 - 16)

(x1 = - 5)

So solution is x1 =  -5 and x2 = 4.

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The curves r1(t) = t, 2 − t, 35 + t2 and r2(s) = 7 − s, s − 5, s2 intersect at the point (2.5, -2.5).

An equation is a mathematical statement that asserts the equality of two expressions. It is usually written with an equals sign (=) and expresses the relationships between different variables and constants. Equations are often used to model or describe physical, biological, and chemical phenomena and relationships.

This can be seen by solving the system of equations formed by equating the two curves:

t = 7 − s
2 − t = s − 5
35 + t2 = s2

Solving the first two equations for t and s yields t = 7 − s and s = 2 − t. Plugging these equations into the third equation yields:

35 + (7 − s)2 = s2

By rearranging terms and solving, this equation can be solved for s, which yields s = 2.5. Plugging this value back into the first two equations yields t = 7 − 2.5 = 4.5 and s = 2 − 4.5 = -2.5. Thus, the two curves intersect at the point (2.5, -2.5).

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The points on the x-axis whose distance from the point (5, 0) is 13 units is given as follows:

(-8, 0) and (18,0).

The points on the y-axis whole distance from the point (5, 0) is 13 are given as follows:

(0, -12) and (0, 12).

The general coordinates of the two points are given as follows:

[tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

Hence the distance between them is of:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

A point on the x-axis has the coordinates given as follows:

(x,0).

For the distance of 13 units from point (5,0), the possible points are given as follows:

On the y-axis, the coordinates are given as follows:

(0,y).

Hence the possible values of y are obtained as follows:

[tex]13 = \sqrt{5^2 + y^2}[/tex]

Applying the square root to both sides, we have that:

25 + y² = 13²

y² = 144

y = -12 or y = 12.

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On solving the provided question, we can say that by unitary method 8 pints of apple juice does she need for 2 cups of cinnamon candy

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

Paula is brewing hot apple cider with cinnamon caramel and apple juice.

her recipe calls for = 0.5 cups of cinnamon

candy for every = 2 pints of apple juice

she need for 2 cups of cinnamon candy are -

for 1 = she need 2/0.5

for 2 = she needs  2/0.5 * 2 = 8

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Answer:

12.4

Step-by-step explanation:

The set of ordered pairs depicts the volume of water in the can in gallons (y) as a function of time in minutes (x), beginning with the first minute after the can begins distributing water and ending with {(1, 6.7) , (2, 6.4) , (3, 6.1)}.

An ordered pair is a pair of objects in mathematics. The order of the objects in the pair is important: the ordered pair differs from the ordered pair unless a = b. Ordered pairs are also known as 2-tuples or 2-length sequences. An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair's numeric values can be integers or fractions.

Here,

A watering can dispenses water at the rate of 0.3 gallon per minute.

The original volume of water in the can was 7 gallons.

If you plot a graph of volume of water in the can (gallons) against time (minutes),

The set of points on the graph will be:

After 1 minute: (1, 7 - 0.3) = (1, 6,7)

After 2 minutes: (2, 7 - 0.6) = (2, 6.4)

After 3 minutes: (3, 7 - 0.9) = (3, 6.1)

i.e the set {(1, 6.7) , (2, 6.4) , (3, 6.1)}

The set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after the can starts dispensing water is {(1, 6.7) , (2, 6.4) , (3, 6.1)}.

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The probability that the chosen coin is the two-headed one will be 1/16.

It should be noted that probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events.

In this situation, one coin in a collection of 16 coins has two heads, the rest being fair coins with a head and a tail each.

When a coin is chosen at random from the collection and tossed four times, coming up with a head on each of the four tosses, the probability that the chosen coin is the two-headed one will be:

= Number of two headed coins / Total coins

= 1/16

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Melissa's monthly payment is $450 if the down payment is $3,900.

To calculate the monthly payment, we first need to calculate the total amount financed. This is done by adding the list price of the car ($20,540), the sales tax (8.25% of $20,540 = $1,690.35), the registration fee ($995), and the documentation fee ($57) for a total of $23,282.35.

We then need to calculate the total amount of interest that Melissa will pay over the 5-year loan period. This is done by multiplying the interest rate (8.6%) by the total amount financed ($23,282.35) and multiplying that by the number of years (5).

This gives us a total interest payment of $7,634.84. We then add the total amount financed ($23,282.35) and the total interest payment ($7,634.84) and subtract the down payment ($3,900), which gives us the total amount that Melissa will pay over the 5-year loan period: $27,016.99.

We then divide this total amount by the number of months in the loan period (60) to get the monthly payment: of $450

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Solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.

We can easily identify the values of the independent variable x and the domain by solving the equation y = f(x). The range may then be found by solving for x.

For a relation, the domain and range are defined as sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively. For instance, if the relationship is R = (1, 2), (2, 2), (3, 3), and (4, 3), then

The collection of all x-coordinates with values 1, 2, 3, and 4 is known as the domain.Range is the set of all y-coordinates with values of 2, 3.

The elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values. Range, Function, and Domain.

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Answer:

1 mile is about 1.6 km

1 feet is 30cm.

Safe to say a mile is bigger.

Answer:

Miles are bigger than feet.

Step-by-step explanation:

In 1 mile, there are 5,280 feet. So miles would be 5,280 times bigger than feet.

The only option that represents the two possible transformations that together could have been used to create the image is; D. a translation of 6 units down followed by a reflection across the y axis

In geometry, a transformation is defined as an operation that moves, flips, or changes a shape that is called the preimage in order to create a new shape that is called the image. Some of the types of transformations includes; Translation, Reflection, Dilation e.t.c

Let us analyze each of the options;

A. This is not correct because the transformation rule for a reflection over the x -axis is (x, y) → (x, −y)  while the transformation rule for the reflection of point (x, y) across the y-axis is (-x, y). This will not correspond with the final transformation given.

B) This is not correct because it will not produce the complete match as the rotation given will not allow for proper mapping.

C) This is NOT correct just like is seen in option A above.

D) This is correct because after translation by 6 units downwards, when we reflect across the y-axis, it produces the final transformed image.

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Answer:

$17.08

Step-by-step explanation:

Ok, so we know it takes 61-23 = 38 minutes of call to change the credit from $22.24 to $17.68.

Basically, it takes 43 minutes to lose 22.24 - 17.68 = $4.56

38 minutes - $4.56

5 minutes - $4.56 x 5 /38 = 0.6

I took 5 minutes because 5 + 61 = 66

Now, we know it takes 61 minutes for the person to have $17.68 remaining.

So, if we had 5 minutes, it becomes 17.68 - 0.6 = $17.08 remaining.

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Therefore , the solution of the given problem of ratio comes out to be  the coordinate P = (7, 0.4).

A ratio as well as fraction in mathematics shows how frequently one value is present in another. For instance, if there are eight grapefruit and six lemons in a fruit plate, the ratio from oranges to citrus is eight to six, or 8:6, which is comparable to the ratios 4:3 or the decimal 1.333.

Here,

Ratios are a useful tool for segmenting lines into smaller units.

P's coordinate is P = (7, -0.4)

The criteria are as follows:

A = (8,0)\sB = (3,-2) (3,-2)

m: n=1:4

Using P = mx2+nx1 my2+ny

m+n

m+n, line ratio is computed.

The result is:

P 1x3+4x8 /1x-2+4x0 = 1+4 / 7

=> P = 35, 2

=>P = (7, -0.4) (7, -0.4)

1+4

P therefore has the coordinate P = (7, 0.4).

Therefore , the solution of the given problem of ratio comes out to be  the coordinate P = (7, 0.4).

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Answer:

3 = 1 + 1/2 + 2/2 + 1/2

The blank number is:

1

Step-by-step explanation:

2/2 = 1

1/2 + 1/2 = 2/2

3 = a + 1/2 + 2/2 + 1/2

3 = a + 1 + 1

3 = a + 2

3 - 2 = a

a = 1