the perimeter of a rectangular paper is 120 cm. If the breadth is 20 cm, find its length. Also find the area​

Answer:

36 cm²

Step-by-step explanation:

Area of a triangle = 1/2bh = 1/2(9)(8) = 36

Answer:

  (c)  y -2 = 6/5(x -1)

Step-by-step explanation:

The equations are all in point-slope form with a slope of 6/5. The points used are (-1, -2), (-2, -1), and (1, 2). It seems point (1, 2) best matches a point on the graphed line. Choice C is the best. (In the attached graph, choice C is the red line.)

_____

Additional comment

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

__

The equation might be easier to see if the point chosen were one at a grid intersection, such as (-4, -4) or (6, 8).

The height of the cone in terms of Y is as follows:

The cylinder and the cone have the same volume.  The cylinder has a radius of X and a height of Y.

Therefore,

volume of a cylinder = πr²h

volume of the cylinder = π × X² × Y

volume of a cylinder = X²Yπ  unit cube

The cone has radius 1/2X. The height of the cone can be found as follows:

Recall the volumes of the cylinder and cones are the same.

Therefore,

volume of a cone = 1 / 3 πr²h

X²Yπ = 1 / 3 π (1 / 2 X)²h

1 / 3 π × 1 / 4 X² h =  X²Yπ

divide both sides by π

1 / 3 × 1 / 4 X² h = X²Y

divide both sides by X²

1 / 12 h = Y

cross multiply

h = 12Y units

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Answer:

Step-by-step explanation:

The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.

A. No solution

y = 1/4x+5

x - 4y = 4

You can simplify the second equation into y = 1/4x - 1

Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.

Company 1 would need to invest $1,000,000 to reduce its CM from 40% to 25%, assuming Company 2 does not support it.

To calculate the profits that each company would make, you would need more information such as the total revenue and total cost of each company.

Without this information, it is not possible to calculate the profits that each company would make.

Regarding the second part of the question, to calculate how much Company 1 would be willing to invest to reduce its CM from 40 to 25, assuming.

Company 2 does not support it, you can use the formula:

Amount of investment = (Current CM - Desired CM) / CM ratio

Where CM ratio = Contribution Margin / Total Sales

Assuming that Company 1's current CM ratio is 40%, and it wants to reduce its CM to 25%,

The CM ratio would be (40% - 25%) = 15%.

Let's say Company 1 has total sales of $1,000,000.

To calculate the amount of investment required to reduce the CM from 40% to 25%, we can use the formula:

Amount of investment = (0.4 - 0.25) / 0.15 * $1,000,000
Amount of investment = $1,000,000

Therefore,

Company 1 would need to invest $1,000,000 to reduce its CM from 40% to 25%, assuming.

Company 2 does not support it.

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Answer:

4th graph

Step-by-step explanation:

I believe that they are just saying f(x) and then adding 2 to each of the corrdnants to x+2 y+2

Answer:

See below ~

Step-by-step explanation:

The +2 in the equation : f(x) + 2, indicates the y-intercept of the graph lies at (0, 2). The 4th graph (attached below) is the correct answer.

1 to 500000

to solve this we need to know the equivalence

The scale ratio of a model represents the proportional ratio of a linear dimension of the model to the same feature of the original.

so

Step 1

a)Let

b) now, replace

therefore, the scale factor is

1 to 500000

I hope this helps you

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:To divide 15a^6b^4 by 5a^2b, we can divide the coefficients and then divide the variables using the quotient rule of exponents, which states that when dividing two exponential terms with the same base, you can subtract the exponents.

So we have:

(15a^6b^4) / (5a^2b) = (15/5) * (a^6/a^2) * (b^4/b)

= 3a^(6-2)b^(4-1)

= 3a^4b^3

Therefore, the simplified result of dividing 15a^6b^4 by 5a^2b is 3a^4b^3

Step-by-step explanation:

The solution to the division is 3a⁴b³.

Given that we need to divide the expression (15a⁶b⁴) by (5a²b),

To divide the expression (15a⁶b⁴) by (5a²b), you need to apply the rules of division with variables and exponents.

Here's how you can simplify the expression:

When dividing with the same base, you subtract the exponents. In this case, the base is "a" and the exponents are 6 and 2.

Subtracting the exponents gives us a⁶ - a² = a⁶⁻² = a⁴.

Similarly, for the variable "b," the exponents are 4 and 1.

Subtracting the exponents gives us b⁴ - b¹ = b⁴⁻¹ = b³.

Now, let's simplify the coefficients. The coefficient 15 divided by 5 is 3.

Putting it all together, the expression (15a⁶b⁴) / (5a²b) simplifies to:

3a⁴b³

Hence the solution to the division is 3a⁴b³.

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Answer:   b = 10 is correct

I don't know how your teacher got 12.

========================================================

Explanation:

The point (-1,2) means x = -1 and y = 2 pair up together.

Plug those points into the template ax+by = 16 to get -a+2b = 16

We'll come back to this later.

Do the same for the point (4,0) to get 4a+0b = 16 which solves to a = 4

Then plug this value into the other equation and solve for b.

-a+2b = 16

-4+2b = 16

2b = 16+4

2b = 20

b = 20/2

b = 10

The inequality which represents the given situation will be 2.25x + 2y ≤ 25.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

Suppose the cost of an apple is x and the cost of one mango is y.

2.25x + 2y = total cost

2.25x + 2y ≤ 25

Hence "The inequality which represents the given situation will be 2.25x + 2y ≤ 25".

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Answer:

ΔCFG is an isosceles triangle.

Step-by-step explanation:

From the picture attached,

From ΔABF and ΔEDG,

Conditions for ΔABF and ΔEDG by SSS property of congruence,

1). AB ≅ DE [Given]

2). (BC + CF) = (DF + CG)

CF = CG [Given → BC = DF]

3). FA ≅ EG

(AG + GF) ≅ (EF + GF)

AG ≅ EF

Since, two sides of ΔCFG are equal in measure

ΔCFG is an isosceles triangle.

This can be determined by property of congruency. Hence, \(\bold{2^{nd}}\)option i.e. ΔCFG is an isosceles triangle is most appropriate.

Given :

From figure ΔABF and ΔEDG  are congruence by SSS property.

Proof:

From ΔABF and ΔEDG in figure,

Conditions for ΔABF and ΔEDG by SSS property of congruence,

1). AB ≅ DE [Given]

   (BC + CF) = (DC + CG)

2). BF≅DG

     CF = CG [Given → BC = CD]

3). FA ≅ EG

     (AG + GF) ≅ (EF + GF)

    AG ≅ EF

Therefore, two sides of ΔCFG are equal in measure.

Thus,ΔCFG is an isosceles triangle.

Hence, \(\bold{2^{nd}}\) option i.e. ΔCFG is an isosceles triangle is most appropriate.

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The correct option is Fail to reject the null hypothesis.

The statistical decision is "Fail to reject the null hypothesis".What is a hypothesis?In research, a hypothesis is a proposition or explanation that is put forward as a preliminary premise to be tested or demonstrated through research. In scientific research, hypotheses are critical because they assist researchers to establish study goals and design appropriate studies. Hypotheses, in turn, offer a framework for researchers to develop research questions that they can use to explore phenomena and relationships between variables.What is a statistical hypothesis?In statistics, hypotheses are typically about population parameters that we can only estimate from samples. Statistical hypotheses refer to assumptions about the parameters of a statistical model and the statistical significance of the difference between two or more groups of data.In most cases, the null hypothesis, H0, is the hypothesis that researchers wish to refute. On the other hand, the alternative hypothesis, Ha, is the hypothesis that researchers wish to establish. The research hypothesis, which is another term for the alternative hypothesis, is the statement that you want to test. As a result, it's crucial to define the null and alternative hypotheses precisely in advance of the study, as well as the statistical significance level, to avoid confusion and attain accurate results.What is a statistical decision?A statistical decision is a decision made by a researcher based on the statistical analysis of data. The statistical decision is based on a statistical test of the data that is conducted to determine if there is evidence that supports the alternative hypothesis or not. Based on the outcome of the statistical test, the researcher can make a statistical decision to either reject the null hypothesis, fail to reject the null hypothesis, or conclude that the test is inconclusive.In conclusion, the statistical decision is "Fail to reject the null hypothesis".  This decision is made when the statistical evidence is insufficient to refute the null hypothesis.

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The required simplified value of the given expression using the distributive property is 8a + 32.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The distributive property is defined as,
a(b + c) = ab + ac

From the above property,
8(a + 4) = 8a + 32

Thus, the required simplified value of the given expression using the distributive property is 8a + 32.

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The statement is true.

To prove this, we will use a proof by contradiction.

Assume that all of the sets {ai lie i} are finite. Then, for each set ai, there exists a finite number of elements in that set. Therefore, the union of all of these sets will also be finite.

However, we are given that the union of all the sets is countably infinite. This means that there exists a countable list of elements in the union.

Let's construct this list:
- First, list all of the elements in a1.
- Then, list all of the elements in a2 that are not already in the list.
- Continue this process for all of the remaining sets.

Since the union is countably infinite, this process will never terminate and we will always have elements to add to our list.

But this contradicts the fact that each set is finite. If each set has a finite number of elements, then there can only be a finite number of unique elements in the union.

Therefore, our assumption that all of the sets are finite must be false. At least one of the sets must be countably infinite.

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Answer:

36

Step-by-step explanation:

Answer:

Solution,

X = 16 [ Given]

Now,

\(x - ( - 20)\)

Plugging the value of X

\(16 - ( - 20)\)

\( = 16 + 20\)

\( = 36\)

Hope this helps..

Good luck on your assignment..

Sasha should use 2 desired outcomes in her probability calculation to determine that she has a 1/3 chance of winning the game.

To calculate Sasha's probability of winning, we need to determine how many desired outcomes she has. In this game, Sasha needs to spin a number higher than both of her friends' spins, which means she needs to spin a number greater than 1 and 4.

Let's analyze the spinner pictured. From the image, we can see that the spinner has numbers ranging from 1 to 6. Since Sasha needs to spin a number higher than 4, she has two options: 5 or 6.

Now, let's consider the desired outcomes. Sasha has two desired outcomes, which are spinning a 5 or spinning a 6. If she spins either of these numbers, she will have a number higher than both of her friends and win the game.

To calculate Sasha's probability of winning, we need to divide the number of desired outcomes by the total number of possible outcomes. In this case, the total number of possible outcomes is the number of sections on the spinner, which is 6.

Sasha's probability of winning is 2 desired outcomes divided by 6 total outcomes, which simplifies to 1/3.

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.

Answer:

(4, 0)

Step-by-step explanation:

3x + 4y = 12

2x - y = 8

8x - 4y = 32

11x = 44

x = 4

y = 0

Answer: the ordered pair is (4,0)

Step-by-step explanation:

Answer:

Random samples are more likely to contain data that can be used to make predictions about a whole population. The size of a sample influences the strength of the inference about the population.

Step-by-step explanation:

The sequence is  converges.

To obtain the first five terms of the sequence, we plug in n = 1, 2, 3, 4, and 5 into the given formula:
- First term: (1 + p)(1 + 2p) / (1 + p²) = (1 + p + 2p + 2p²) / (1 + p²) = (2p² + 3p + 1) / (p² + 1)
- Second term: (2 + p)(2 + 2p) / (4 + p) = (4 + 6p + 2p²) / (4 + p) = (2p² + 6p + 4) / (p + 4)
- Third term: (3 + p)(3 + 2p) / (9 + p) = (9 + 9p + 2p²) / (9 + p) = (2p² + 9p + 9) / (p + 9)
- Fourth term: (4 + p)(4 + 2p) / (16 + p) = (16 + 12p + 2p²) / (16 + p) = (2p² + 12p + 16) / (p + 16)
- Fifth term: (5 + p)(5 + 2p) / (25 + p) = (25 + 15p + 2p²) / (25 + p) = (2p² + 15p + 25) / (p + 25)

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Answer:

B) 24

Step-by-step explanation:

This angle adds to 90 degrees, so to solve for x you need this equation:

(2x) + 42 = 90

Subtract 42 from both sides to get:

2x = 48

Divide 2 from both sides to get:

x = 24

Hope it helps!!!

Answer:

b) 1.82n

Step-by-step explanation:

n + n - 0.18n

2n - 0.18n (combine like terms)

1.82n

Hope this helps!

The 98% confidence interval for the proportion of delinquent mortgages in Maryland is between 7.9% and 16.2%.

1. Calculate the sample proportion:

Divide the number of delinquent mortgages (14) by the total number of mortgages in the sample (130) to get 0.1077.

2. Find the standard error:

Calculate the standard error by taking the square root of (0.1077 * (1 - 0.1077) / 130), which is approximately 0.0296.

3. Determine the margin of error:

Multiply the standard error by the critical value for a 98% confidence level, which is approximately 2.33. The margin of error is approximately 0.0688.

4. Calculate the confidence interval:

Subtract the margin of error from the sample proportion to get the lower bound (0.1077 - 0.0688 = 0.0389), and add the margin of error to the sample proportion to get the upper bound (0.1077 + 0.0688 = 0.1765).

Therefore, the 98% confidence interval for the proportion of delinquent mortgages in Maryland is between 0.0389 (3.89%) and 0.1765 (17.65%).

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We can be 98% confident that the true proportion of delinquent mortgages in the state of Maryland falls between 0.0361 and 0.1793.

The 98% confidence interval for the proportion of delinquent mortgages in the state of Maryland, based on the given sample, can be calculated using the formula:

Confidence Interval = Sample Proportion ± Margin of Error

Step 1: Calculate the sample proportion:
Sample Proportion = Number of delinquent mortgages / Total number of mortgages
Sample Proportion = 14 / 130
Sample Proportion ≈ 0.1077

Step 2: Calculate the margin of error:
Margin of Error = Critical value * Standard Error
To find the critical value, we need to determine the z-score associated with a 98% confidence level.

The z-score can be found using a standard normal distribution table or a calculator. For a 98% confidence level, the z-score is approximately 2.326.

Standard Error = √(Sample Proportion * (1 - Sample Proportion) / Sample Size)
Standard Error = √(0.1077 * (1 - 0.1077) / 130)
Standard Error ≈ 0.0308

Margin of Error = 2.326 * 0.0308
Margin of Error ≈ 0.0716

Step 3: Calculate the confidence interval:
Confidence Interval = Sample Proportion ± Margin of Error
Confidence Interval = 0.1077 ± 0.0716

Finally, the 98% confidence interval for the proportion of delinquent mortgages in the state of Maryland, based on the given sample, is approximately:
0.0361 ≤ Proportion ≤ 0.1793

Therefore, we can be 98% confident that the true proportion of delinquent mortgages in the state of Maryland falls between 0.0361 and 0.1793.

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1/2 gallons of water rush down the slide each seconds.

For the given question-

Rate of running water = 1 half gallon every 3 seconds.

Rate of running water = 1 1/2 = 3/2 gallon every 3 seconds.

It means-

In every 3 seconds ----> 3/2 gallons water flows.

Thus for 1 sec, divide both side by 3.

1 seconds ----> 1/2 gallons water flows.

Therefore, 1/2 gallons of water rush down the slide each seconds.

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Answer:

y = -3x + 5

Step-by-step explanation:

slope-intercept form means it should look like

y = mx + b

9x + 3y – 15 = 0

3y = -9x + 15

y = -3x + 5

Answer:

  (B)  a = $0.50, b = $0.25

Step-by-step explanation:

Answer choice B is the only one in which an apple costs twice as much as a banana.

__

It helps to see if the answer choices match the requirements of the problem statement.

Answer:

12

Step-by-step explanation:

21-9

12

Answer:

The answer is 12

Step-by-step explanation:

|21| = just 21

|-9| = positive 9

so take that into this:

21 - 9 = 12

Answer: 41$

Step-by-step explanation:

This is because 5x6=30 (To find how much money is made)

then 11+30=41 (add both amounts)

The sum of x and y i.e (x+y) is equal to 23

When two diagonals of a parallelogram bisect each other. Each diagonal bisects the parallelogram into two congruent triangles. The Sum of the square of all the sides of a parallelogram is equal to the sum of the square of its diagonals.

This implies that line uz = wz, and vz= tz

therefore 3y+6= 2x equation 1

since vt = 78

5y-1= 78-(5y-1) equation 2

5y-1= 78-5y+1

collecting like terms,

5y+5y= 78+1+1

10y= 80

divide both sides by 10

y= 80/10

y= 8

substituting 8 for y in equation 1

3×8+6= 2x

24+6= 2x

30= 2x

divide both sides by 2

x= 30/2= 15

therefore the sum of x and y = 15+8= 23

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Answer:

b=2

Step-by-step explanation: