Solve for x - Remember to multiply both sides by the reciprocal 2/3 x = 12 *

Answer:$68.43

Step-by-step explanation:

Answer:

Geometric.

Step-by-step explanation:

It is Geometric because there is a common ratio between the terms.

50p/100p = 1/2

25p/50p = 1/2

The common ratio is 1/2.

Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.

The sample space is 18. The probability of getting a 2 or a b is 8/18 = 4/9.

The sample space is the set of all possible outcomes of the experiment. In this case, the sample space is all the possible combinations of a die being tossed and a spinner being spun.

There are 6 possible outcomes for the die (1,2,3,4,5,6) and 3 possible outcomes for the spinner (a,b,c). Therefore, the sample space consists of 6x3=18 possible outcomes.

Now, to calculate the probability of getting a 2 or a b, we can count the number of outcomes in which this occurs. There are 4 outcomes that satisfy this condition (2a, 2b, 2c, b). Therefore, the probability of getting a 2 or a b is 4/18 = 8/18 = 4/9.

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Answer:

C.

Step-by-step explanation:

Answer:

$31.104

Step-by-step explanation:

Given :

Regular price = $36

Discount on sale = 20%

Discounted price = (100-20)%*36=0.8*36 = $28.8

Sales tax rate = 8% ;

Tax on sale = 8% * $28.8 = 2.304

Final amount that will have to be paid :

Discounted price + tax on sale

$28.8 + $2.304

= $31.104

The correct answer is d. 11 = 11 0 +11 and option (a). This equation is produced as a step when using the Euclidean algorithm to find the greatest common divisor (gcd) of the given integers (11,1).

In this step, we divide 11 by 1 and get a quotient of 11 with a remainder of 0, represented by the equation 11 = 11(1) + 0. This means that 11 is the gcd of 11 and 1. The Euclidean algorithm finds the greatest common divisor (GCD) of two given integers. In this case, the integers are 11 and 1. Here's the step-by-step explanation:
1. Divide the larger integer (11) by the smaller integer (1).
2. Check the remainder. If the remainder is 0, the smaller integer (1) is the GCD.
3. If the remainder is not 0, repeat the process with the smaller integer (1) and the remainder.

Since 1 is a divisor of every integer, the GCD of (11, 1) is 1. The equation that represents this step in the Euclidean algorithm is:
a. 1 = 1 * 0 + 1
So, the correct answer is an option (a).

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Answer:

(-2,-36)

Step-by-step explanation:

\(y=(x-4)(x+8)\)

1) Find the zeros of the parabola

The zero-product property states that any value, when multiplied by 0 will equal 0. Therefore, to make y=0, either (x-4)=0 OR (x+8)=0.

Therefore, x=4 and x=-8.

2) Find the x-coordinate of the vertex

To do this, we take the average of our zeros.

\(\frac{4+(-8)}{2} \\=\frac{-4}{2} \\=-2\)

Therefore, the x-coordinate of the vertex is -2.

3) Find the y-coordinate of the vertex

Plug the x-coordinate back into the original equation

\(y=(-2-4)(-2+8)\\y=(-6)(6)\\y=-36\)

Therefore, the y-coordinate of the vertex is -36.

Therefore, the vertex of the parabola is (-2,-36).

I hope this helps!

It would take 220 minutes for Angela's and Benjamin's monthly bills be the same

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let y represent the cost after x minutes, hence:

For angela:

y = 0.15x + 49

The y intercept is $49 and the rate of change is $0.15 per minute

For Benjamin:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-60=\frac{80-60}{200-0} (x-0)\\\\y=0.1x+60\)

The y intercept is $60 and the rate of change is $0.10 per minute

For 200 minutes:

Angela: y = 0.15(200) + 49 = $79

Benjamin: y = 0.10(200) + 60 = $80

To be the same:

0.15x + 49 = 0.1x + 60

x = 220 minutes

It would take 220 minutes for Angela's and Benjamin's monthly bills be the same

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x=9/34 that's the answer

The expressions that equal 36 is:

E) 53 − (2. 5 × 30) − 20

Evaluated the mathematical expressions in each response to see if they equal 36.

A. (14⋅32)2−28 = (448)² - 28 = 14⁴ - 28 = 2016 - 28 = 1988, not equal to 36.

B. 23 + (58−54)2 + 122 = 23 + (4)² + 12 = 23 + 16 + 12 = 51, not equal to 36.

C. 92 − (43 + 32) + 30050 = 9² - (7 + 3) + 30050 = 81 - 10 + 30050 = 30021, not equal to 36.

D. 124 + (82 − 42) − 99 = 124 + (64 - 16) - 99 = 124 + 48 - 99 = 73, not equal to 36.

Thus, only the expressions listed in my previous answer equal 36.

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Answer:

x = 4

Step-by-step explanation:

1. 8x+1 = 33 and the 4x together

2. 8x = 32 subtract 1 from each side

3. x = 4 Divide both sides by 8

Answer:

x=4

Step-by-step explanation:

4x+4x+1=33

Combine like (similar) terms:

8x+1=33

Rearrange terms to solve for x:

8x=33-1

8x=32

\(\frac{8x}{8} =\frac{32}{8}\)

x=4

Therefore, x=4.

Answer:

Is A

Step-by-step explanation:

(2-4)/(-2--6) = -1/2

And the only answer that has -1/2 as the slope is A

Answer:

\(x^2+y^2=9\)

Step-by-step explanation:

Equation of a circle (when centred at the origin):

\(x^2+y^2=r^2\) where r is the radius of the circle

Plug in the point (0,3) to solve for the radius squared

\(0^2+3^2=r^2\\9=r^2\)

Plug r² back into the original equation

\(x^2+y^2=9\)

I hope this helps!

The equation of the exponential function is\(4 * 3^{x}\).

What is exponential function?

An exponential function is  of the form:

\(f(x) = a^{x}\)

here "a" is a constant called the base, and "x" is the variable. The base "a" is typically a positive real number, but it can also be a negative number or a complex number. The function is called exponential because the variable "x" appears in the exponent.

We can see that as "x" increases by 1, "y" is multiplied by a constant factor of 3. This suggests that the exponential function has a base of 3. To find the equation, we can use the general form of an exponential function:

\(y = a * b^{x}\)

where "a" is the initial value or y-intercept, and "b" is the base.

We can use the given values of (x,y) to form a system of equations:

\(a * 3^{0} = 4\)

\(a * 3^{1} = 12\)

\(a * 3^{2} = 36\)

\(a * 3^{3} = 108\)

Simplifying each equation, we get:

a = 4

3a = 12

9a = 36

27a = 108

Solving for "a", we get:

a = 4

Substituting this value of "a" into the equation, we get:

\(y = 4 * 3^{x}\)

So the equation of the exponential function represented by the table is y \(= 4 * 3^{x}.\)

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No, it is not safe to assume that the sampling distribution of the sample means is about normal given the sample size.

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Answer:

Slope = -2/5 new points (5/2,1) and (5,0)

Step-by-step explanation:

Standard point slope equation:

y = mx + b   where m is the slope and b is the y-intercept.

First find the slope between the given points.

Slope = rise/run

m = (y1 - y2) / (x1 - x2)

   = (4 - 0)/(-5 - 5)

   = 4/-10 = -2/5 then

y = (-2/5)x + b then one point (I picked (-5,4) to find b

4 = (-2/5)(-5) + b

4 = 2 + b

b = 2

y = (-2/5)x + 2 then pick an x and find y for additional points.

x = 5/2

y = (-2/5)(5/2) + 2

y = -1 + 2

y = 1 so the point is (5/2,1) and let x = 5

y = (-2/5)(5) + 2

y = -2 + 2

y = 0 so the point is (5,0)

Suppose that :

A = ( 5 , 0 )

B = ( - 5 , 4 )

Then we have :

Slope = [ y(B) - y(A) ] ÷ [ x(B) - x(A) ]

Slope = [ 4 - 0 ] ÷ [ -5 - 5 ]

Slope = 4 ÷ ( - 10 )

Slope = - 4/10

Slope = - 2/5

________________________________

It's time to find the formula of this linear function using following formula :

y - y ( A or B ) = Slope × ( x - x ( A or B ) )

I'm gonna using point A but u can do it with point B which will gave the same answer :

y - 0 = - 2/5 × ( x - 5 )

y = - 2/5 x + 2

_______________________________

We have the formula of the function now thus it's time to find two more points that line passe through ;

To do that we just have to put two desired values of x instead of it and find the y to have the coordinate of those points that line passes through :

I'm gonna use x = - 10 and x = 15 :

x = - 10 x = 15

y = - 2/5 × ( -10 ) + 2 y = -2/5 × ( 15 ) + 2

y = 4 + 2 y = - 6 + 2

y = 6 y = - 4

________________________________

Thus ( -10 , 6 ) & ( 15 , - 4 ) are two other points that line passes through.

A. x1, x2, x3, s1, s2 ≥ 0

B. New table au:

x1 x2 x3 s1 s2 RHS

x2 | 0 1 4/7 3/14 -1/14 1/2

s2 | 1 0 3/7 -1/14 3/14 3/2

Z | 0

a) Writing the problem in equation form and adding slack variables:

Maximize Z = 3x1 + 2x2 + x3

Subject to:

3x1 - 3x2 + 2x3 + s1 = 3

-x1 + 2x2 + x3 + s2 = 6

x1, x2, x3, s1, s2 ≥ 0

b) Solving the problem using the simplex method:

Step 1: Convert the problem into canonical form (standard form):

Maximize Z = 3x1 + 2x2 + x3 + 0s1 + 0s2

Subject to:

3x1 - 3x2 + 2x3 + s1 = 3

-x1 + 2x2 + x3 + s2 = 6

x1, x2, x3, s1, s2 ≥ 0

Step 2: Create the initial tableau:

x1 x2 x3 s1 s2 RHS

s1 | 3 -3 2 1 0 3

s2 | -1 2 1 0 1 6

Z | 3 2 1 0 0 0

Step 3: Perform the simplex method iterations:

Iteration 1:

Pivot column: x1 (lowest ratio = 3/1 = 3)

Pivot row: s2 (lowest ratio = 6/2 = 3)

Perform row operations to make the pivot element equal to 1 and other elements in the pivot column equal to 0:

s2 = -s2/3

x2 = x2 + (2/3)s2

x3 = x3 - (1/3)s2

s1 = s1 - (1/3)s2

Z = Z - (3/3)s2

New tableau:

x1 x2 x3 s1 s2 RHS

x1 | 1 -2/3 -1/3 0 1/3 2

s2 | 0 7/3 4/3 1 -1/3 2

Z | 0 2/3 2/3 0 -1/3 2

Iteration 2:

Pivot column: x2 (lowest ratio = 2/7)

Pivot row: x1 (lowest ratio = 2/(-2/3) = -3)

Perform row operations to make the pivot element equal to 1 and other elements in the pivot column equal to 0:

x1 = -3x1/2

x2 = x2/2 + (1/7)x1

x3 = x3/2 + (4/7)x1

s1 = s1/2 - (1/7)x1

Z = Z/2 - (2/7)x1

New tableau:

x1 x2 x3 s1 s2 RHS

x2 | 0 1 4/7 3/14 -1/14 1/2

s2 | 1 0 3/7 -1/14 3/14 3/2

Z | 0

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Answer:

3 and -2

Step-by-step explanation:

3+(-2) = 1

3*(-2) = -6

Answer:

3  and -2

Step-by-step explanation:

Thesis Proposal: Mathematical Modelling of Pollutants in Tano River in Ghana- Background to the Study,  Statement of the Problem, Research Questions,   Literature Review, Research design,  Theoretical model,  Empirical Model.

a. Background to the Study:

The Tano River in Ghana is a vital water resource that supports various ecological systems and provides water for domestic, agricultural, and industrial purposes. However, the river is facing pollution challenges due to human activities, such as industrial waste discharge, agricultural runoff, and improper waste management. The accumulation of pollutants in the Tano River poses a significant threat to aquatic life and the overall environmental health of the region. Therefore, it is crucial to develop a comprehensive understanding of pollutant dynamics in the Tano River to implement effective pollution management strategies.

b. Statement of the Problem:

The pollution levels in the Tano River are increasing, which has detrimental effects on the river's water quality and ecosystem. Traditional monitoring and assessment methods have limitations in providing a complete understanding of the pollutant dynamics. Therefore, there is a need to employ mathematical modelling techniques, specifically ordinary differential equations (ODEs), to develop a quantitative framework for predicting and analyzing pollutant concentrations in the Tano River.

c. Research Questions:

What are the primary sources of pollutants in the Tano River?

How do pollutants disperse and transport in the river system?

What are the factors influencing pollutant degradation and removal processes in the river?

Can mathematical modelling using ODEs accurately predict pollutant concentrations in the Tano River?

d. Literature Review:

The literature review will explore existing studies on pollution in river systems, particularly focusing on mathematical modelling approaches using ODEs. It will examine relevant research on pollutant sources, transport mechanisms, degradation processes, and their application in predicting pollutant concentrations. Additionally, it will review studies that have employed mathematical modelling in similar river systems to gain insights into their methodologies, limitations, and key findings.

e. Research Design:

The research will involve collecting water samples from various locations along the Tano River and analyzing them for pollutant concentrations. Data on pollutant sources, hydrological parameters, and environmental factors will also be collected. The collected data will be used to calibrate and validate the mathematical model. The research design will include field measurements, laboratory analysis, data collection, and model development and validation.

f. Theoretical Model:

The theoretical model will be based on ordinary differential equations to describe the pollutant dynamics in the Tano River. The model will incorporate factors such as pollutant sources, transport mechanisms (advection and dispersion), degradation processes, and removal mechanisms. The model will be formulated based on the mass balance principle and relevant reaction kinetics.

g. Empirical Model:

The empirical model will be developed by calibrating and validating the theoretical model using the collected data. Statistical techniques and optimization algorithms will be employed to estimate model parameters and assess the model's performance in predicting pollutant concentrations. The empirical model will serve as a tool for simulating pollutant dynamics and conducting scenario analysis to evaluate the effectiveness of potential pollution management strategies.

In conclusion, this thesis proposal aims to develop a mathematical model using ordinary differential equations to understand and predict the dynamics of pollutants in the Tano River in Ghana. The research will contribute to the field of environmental science and provide valuable insights for policymakers and stakeholders in implementing effective pollution management strategies to safeguard the Tano River's ecosystem and ensure sustainable water resources.

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If a logical vector z has at least one entry TRUE, the function all(!z) will always be false.

If a logical vector contains only TRUE items, the all() method returns FALSE; otherwise, it returns TRUE.

The any() function, on the other hand, gives a result of TRUE if a logical vector has at least one element that is TRUE and FALSE otherwise.

any(z) will always be TRUE if z contains at least one TRUE element since there is at least one TRUE element. On the other hand, depending on whether all of the components of z are TRUE, all(z) may or may not be TRUE.

any(!z) will always return FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.

Additionally, all(!z) will always return FALSE if any element is FALSE since if z has at least one TRUE element, then!z must include at least one FALSE element.

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Putting forecast errors into perspective is best done using MAPE and MAD. These are two common measures of forecast accuracy that can help evaluate the performance of a forecasting model and put forecast errors into perspective.

MAPE (Mean Absolute Percentage Error) measures the average absolute percentage difference between actual and forecasted values. This metric is useful because it expresses forecast accuracy in relative terms, allowing us to compare forecast errors across different data sets and time periods. However, it can be sensitive to extreme values and can be misleading when dealing with small or negative actual values. MAD (Mean Absolute Deviation) measures the average absolute difference between actual and forecasted values, without regard for direction. This metric is more robust to extreme values and is easier to interpret than MAPE, making it a popular choice for evaluating forecast accuracy. Using MAPE and MAD, we can identify areas where the forecasting model is performing well and where it needs improvement. By putting forecast errors into perspective, we can make informed decisions about how to adjust our forecasting approach to improve accuracy and reliability.

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Given, the height \($h=6$, the base $b_1=9$ and $b_2=12$.\)

The area of the trapezoid is given by the formula,

\(\[A = \frac{1}{2}h(b_1+b_2)\]\)

Substitute the given values,  

\(\[A = \frac{1}{2} \times 6 \times (9+12)\]\\\)

Simplifying the above expression,

\(\[A = 45 \text{ square feet}\]\)

Therefore, the area of the trapezoid is $45$ square feet.

The perimeter of a two-dimensional geometric shape is the entire length of the boundary or outer edge. It is the sum of the lengths of all the shape's sides or edges.

The perimeter of a square, for example, is calculated by adding the lengths of all four sides of the square.

Similarly, to find the perimeter of a rectangle, sum the lengths of two adjacent sides and then double the result because there are two pairs of adjacent sides.

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Answer:

A

Step-by-step explanation:

We are told that the number at the unit place is 3 less than the number at the tens place.

So if the number at the units place is b, then the number at the tens place is 10(b+ 3)

So the number is thus;

10(b + 3) + b

= 10b + 30 + b = 11b + 30

There are several observations that refute the null hypothesis that the Irish monoculture of the lumper potato did not significantly change the overall resistance of the potato crop in Ireland to diseases.

Firstly, the lumper potato was highly susceptible to potato blight, which caused the devastating potato famine in the mid-19th century. This suggests that the monoculture of the lumper potato made the potato crop more vulnerable to diseases.
Secondly, the lack of genetic diversity in the lumper potato meant that there were no natural defenses against diseases. This made the potato crop more vulnerable to diseases and pests, which could quickly spread and destroy entire crops.
Finally, the monoculture of the lumper potato led to a lack of agricultural diversity in Ireland, which made the country more dependent on the potato crop. This meant that when the potato crop failed due to diseases, the consequences were severe and widespread.
Taken together, these observations strongly suggest that the Irish monoculture of the lumper potato did indeed significantly change the overall resistance of the potato crop in Ireland to diseases.

To refute the null hypothesis that the Irish monoculture of the Lumper potato did not significantly change the overall resistance of the potato crop in Ireland to diseases, you can consider the following observations:
1. The Irish monoculture of the Lumper potato led to a lack of genetic diversity among the potato crops, making them more susceptible to diseases.
2. The Great Famine in Ireland (1845-1849) was a direct result of the Lumper potato's vulnerability to the potato blight (Phytophthora infestans), a disease that rapidly destroyed the potato crops due to their uniform genetic makeup.
3. The widespread cultivation of the Lumper potato in Ireland resulted in an increased reliance on this single crop, which intensified the consequences of its susceptibility to diseases.
These observations demonstrate that the Irish monoculture of the Lumper potato did, in fact, change the overall resistance of the potato crop in Ireland to diseases, making them more susceptible to devastation caused by potato blight.

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Answer:

32.6193819

Step-by-step explanation:

calulater never lies XD

Answer:

The answer should be: x=2,-12

which on your answer should backwards: {-12,2}

Step-by-step explanation:

The simplified expression for each problems after rationalizing the denominator are:

Let's work on each problems we have:

1. \(\frac{2\sqrt{x} -3\sqrt{y} }{\sqrt{x} +\sqrt{y} }\)

The denominator should be rationalized by its conjugate: \(\frac{\sqrt{x} -\sqrt{y} }{\sqrt{x} -\sqrt{y} }\)

The simplified expression would be:

\(\frac{2\sqrt{x} -3\sqrt{y} }{\sqrt{x} +\sqrt{y} } = \frac{2\sqrt{x} -3\sqrt{y} }{\sqrt{x} +\sqrt{y} } .\frac{\sqrt{x} -\sqrt{y} }{\sqrt{x} -\sqrt{y} }\)

\(\frac{2\sqrt{x} -3\sqrt{y} }{\sqrt{x} +\sqrt{y} } = \frac{2(x)-2\sqrt{xy}-3\sqrt{xy}+3(y)}{x-y}\)

\(\frac{2\sqrt{x} -3\sqrt{y} }{\sqrt{x} +\sqrt{y} } =\frac{2x-5\sqrt{xy}+3y}{x-y}\)

2. \(\frac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2} }\)

The denominator should be rationalized by its conjugate: \(\frac{4\sqrt{6}+3\sqrt{2}}{4\sqrt{6}+3\sqrt{2} }\)

The simplified expression would be:

\(\frac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2} } =\frac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2} } .\frac{4\sqrt{6}+3\sqrt{2}}{4\sqrt{6}+3\sqrt{2} }\)

\(\frac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2} } = \frac{12(6)+9\sqrt{12}+20\sqrt{12}+15(2)}{16(6)-9(2)}\)

\(\frac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2} } =\frac{72+29\sqrt{12}+30 }{96-18}\)

\(\frac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2} } = \frac{102+58\sqrt{3}}{78}\)

\(\frac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2} } =\frac{51+29\sqrt{3}}{39}\)

3. \(\frac{\sqrt{a+1}-2 }{\sqrt{a+1}+2}\)

The denominator should be rationalized by its conjugate: \(\frac{\sqrt{a+1}-2 }{\sqrt{a+1}-2}\)

he simplified expression would be:

\(\frac{\sqrt{a+1}-2 }{\sqrt{a+1}+2} =\frac{\sqrt{a+1}-2 }{\sqrt{a+1}+2} .\frac{\sqrt{a+1}-2 }{\sqrt{a+1}-2}\)

\(\frac{\sqrt{a+1}-2 }{\sqrt{a+1}+2} =\frac{(a+1)-2(2)(\sqrt{a+1})+4 }{(a+1)-4}\)

\(\frac{\sqrt{a+1}-2 }{\sqrt{a+1}+2} =\frac{a+1-4\sqrt{a+1}+4 }{a-3}\)

\(\frac{\sqrt{a+1}-2 }{\sqrt{a+1}+2} =\frac{a+5-4\sqrt{a+1} }{a-3}\)

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Answer:

4:5

Step-by-step explanation:

8:10 = 4  : 5

Answer:

4:5

Step-by-step explanation: