(b)


A sum of money was shared between Aziz and Ahmad in the ratio 3 : 7.


Aziz received $32 less than Ahmad. Find the sum of money shared by both of them.



HELPP MEEEE PLSS

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Explanation:

Point T is at (-2,1)

When we reflect it over the line x = 0, aka the y axis, we use the rule \((x,y) \to (-x,y)\) so T(-2,1) becomes T ' (2, 1). The x coordinate flipped in sign, while the y coordinate stays the same.

Then the final transformation is reflecting over y = -x using the rule \((x,y) \to (-y, -x)\). Therefore, the point (2,1) moves to (-1, -2) which is where T'' is located in the diagram.

You apply the same two transformations for the points R and S to get R'' and S'' respectively.

Note: A composition of two reflections, where the lines of reflection aren't parallel, form a rotation. In this case, we have a 90 degree counterclockwise rotation when going from triangle RST to triangle R''S''T''.

The temperature measure 92 is warmer than 40 by a measure of; 52.

It follows from the task content that it is required to be determined, how much warmer is 92 than 40.

Since the greater temperature measure is; 92 while the lesser is 40.

It can be concluded that the temperature difference is; 92 - 40 = 52.

Ultimately, the measure 92 is 52 warmer than 40.

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The decrease in the number of pirates in the world correlates with an increase in mean global temperature is an example of a spurious correlation.

While there might be a statistical relationship between these two variables, it is not a causative one, and the correlation is likely coincidental.This is the importance of distinguishing between correlation and causation. In this case, the decrease in the number of pirates and the increase in mean global temperature are unrelated factors that happen to show a correlation when observed over time.

This is often used humorously to demonstrate the fallacy of assuming causation based solely on a correlation. It underscores the need for careful analysis and consideration of other relevant factors before making conclusions about causal relationships. In reality, factors such as greenhouse gas emissions, deforestation, and industrialization have a more significant impact on global temperature trends than the number of pirates in the world.

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Answer:

3

Step-by-step explanation:

The distribution of Y is a poisson distribution with parameter λ = λ1 + λ2.

To find the distribution of Y = X1 + X2, we can use the moment-generating functions (MGFs) of X1 and X2.

The moment-generating function (MGF) of a random variable X is defined as:

\(M_X(t) = E(e^(^t^X^))\)

Given that X1 and X2 have Poisson distributions with parameters λ1 and λ2, respectively, their MGFs can be determined as follows:

For X₁:

\(M_X_1(t) = E(e^(^t^X^_1))\)

\(M_x(t)= \sum[x=0 to \infty] e^(^t^x^) * P(X1 = x)\\M_x(t) = \sum[x=0 to \infty] e^(^t^x^) * (e^(^-^\lambda^1) * (\lambda^1^x) / x!)\\M_x(t)= e^(^-^\lambda1) * \sum[x=0 to \infty] (e^(^t^) * \lambda1)^x / x!\\M_x(t)= e^(^-^\lambda1) * e^(e^(^t^) *\lambda_1)\\M_x(t) = e^(^\lambda^1 * (e^(^t^) - 1))\\\)      

Similarly, for X2:

\(M_X2(t) = e^(^\lambda^2 * (e^(^t^) - 1))\)

To find the MGF of Y = X1 + X2, we can use the property that the MGF of the sum of independent random variables is the product of their individual MGFs:

\(M_Y(t) = M_X_1(t) * M_X_2(t)\\M_Y(t)= e^(^\lambda1 * (e^(^t^) - 1)) * e^(^\lambda_2 * (e^(^t^) - 1))\\M_Y(t)= e^(^(^\lambda^1 + \lambda^2^) * (e^(^t^) - 1))\)

The MGF of Y is in the form of a Poisson distribution with parameter λ = λ1 + λ2. T

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Answer:

Adam's share is £590

Step-by-step explanation:

Given

Return Ticket = £1460

Accommodation = £720

Car Hire = £180

Required

Determine Adam's share

First, we need to determine the total cost.

Total = Return Ticket + Accommodation + Car Hire

Total = £1460 + £720 + £180

Total = £2360

Next, is to determine the average.

\(Average = Total/4\)

\(Average = 2360/4\)

\(Average = 590\)

Hence;

Adam's share is £590

The value of tn–1,α/2 for constructing a 90% confidence interval with a sample size of 12 is approximately 1.796.

To find the value of tn–1,α/2 for a 90% confidence interval with a sample size of 12, we can use a t-distribution table or a calculator.

Using a t-distribution table with 11 degrees of freedom (12-1=11) and a 5% significance level (since we want a 90% confidence interval), we can find the value of tn–1,α/2 to be approximately 1.796.

Rounding this value to three decimal places, we get tn–1,α/2 = 1.796.

Therefore, to construct a 90% confidence interval with a sample size of 12, we would use the formula:

sample mean ± tn–1,α/2 * (sample standard deviation / sqrt(sample size))

where tn–1,α/2 = 1.796 and the sample mean and sample standard deviation are calculated from the data.

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The 7 rules of logarithms are as: 

1. Rule of product.

2. Rule of division.

3. The Power/Exponential Rule.

4. A new fundamental rule.

5. Rule of the base swap.

6. Log derivative.

7. Log integral.

The alternate format for writing exponents is with logarithms. A number appears base-based logarithm is approximately equivalent to another number. A logarithm performs exponentiation's exact opposite function.

1. Rule of product: According to this rule, adding the individual logarithms of two logarithmic values results in the multiplication of those values.

\(Log_b (mn)= log_b m + log_b n\)

2. Rule of division: The difference between each logarithm is equivalent to the division of two logarithmic values.

\(Log_b \left(\frac{m}{n}\right)= log_b m - log_b n\)

3. The Power/Exponential Rule: According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.

\(Log_b (m^n) = n log_b m\)

4. A new fundamental rule:

\(Log_b m =\frac{log_a m}{log_a b}\)

5. Rule of the base swap:

\(log_b (a) = \frac{1}{log_a (b)}\)

6. Log derivative: If f (x) = \(log_b (x)\), then the derivative of f(x) is given by;

\(f'(x) = \frac{1}{(x ln(b))}\)

7. Log integral:

\(\int{log_b(x)dx} = x\left(log_b(x) - \frac{1}{ln(b)}\right) + C\)

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Answer:

El perímetro es de 1.2 cm

Step-by-step explanation:

La formula del perímetro de un triángulo rectángulo es:

p = cateto1 + cateto2 + hipotenusa

Para determinar el valor de la hipotenusa usamos el Teorema de Pitágoras:

hipotenusa² = cateto1² + cateto2²

hipotenusa² = 0.4² + 0.3²

hipotenusa² = 0.16 + 0.09

hipotenusa² = 0.25

√hipotenusa² = √0.25

hipotenusa = 0.5

entonces, el perímetro es:

p = 0.4 + 0.3 + 0.5

p = 1.2cm

por tanto

Micaela tiene razón, el perímetro es de:

1.2 cm

The vector parametrization for the equation of line passing through points (2,5,3) and (6,9,6) is: r(t)= (2i + 5j + 3k) + μ(6i + 9j + 6K).

WE know that parameterization of the a curve is provided by each vector-valued function.

Since the pair of equations x = x (t) and y = y (t) that express the coordinates of a point along a curve in terms of such a parameter is known as a parameterization of a curve.

Given passing points:

(2,5,3) and (6,9,6)

In vector form;

Let vector a = 2i + 5j + 3k

Let vector b = 6i + 9j + 6K

Let μ be any constant.

Then, using the vector parametrization:

The equation of line in vector form for the given points is;

r(t)= a + μb

r(t)= (2i + 5j + 3k) + μ(6i + 9j + 6K)

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Correct question:

Find the vector parametrization for equation of the line that passes through the points (2,5,3) and (6,9,6). (Give your answer in the form 〈∗,∗,∗〉. Express numbers in exact form. Use symbolic notation and fractions where needed.)

r(t)=?

A 24-hour collection provides a more comprehensive and reliable assessment of certain values.

A 24-hour collection is a better indicator of some values than a random specimen because it provides a more comprehensive and representative sample of the specific substance or parameter being measured.

It captures variations in levels throughout the day and allows for the detection of fluctuations that may not be captured by a single random specimen.

A 24-hour collection involves collecting samples over a full day, typically for substances such as urine or hormones. This method provides a more accurate representation of the average levels of the substance being measured. It takes into account the diurnal rhythm or cyclical variations that may occur throughout the day.

For example, hormone levels often fluctuate throughout the day, with different peaks and troughs at specific times.

By collecting samples at regular intervals over a 24-hour period, a more accurate picture of the average hormone levels can be obtained, allowing for a better assessment of hormonal imbalances or abnormalities.

In contrast, a random specimen may only capture a snapshot of the substance's level at a specific moment, which may not be representative of the overall pattern.

Fluctuations in levels throughout the day can be missed, leading to potential inaccuracies or misinterpretation of the data.

Therefore, a 24-hour collection provides a more comprehensive and reliable assessment of certain values by capturing variations and trends over time, making it a better indicator than a single random specimen.

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Answer:

A ≈ 28.5

Step-by-step explanation:

a, b, c

P = a + b + c

Semiperimeter s = \(\frac{a+b+c}{2}\)

A = \(\sqrt{s(s-a)(s-b)(s-c)}\)

~~~~~~~~~~~~~~~

\(P_{ABC}\) = 4.3 + 2.89 + 6.81 = 14

s = 14 ÷ 2 = 7

\(A_{ABC}\) = \(\sqrt{7(7-4.3)(7-2.89)(7-6.81)}\) = √14.75901 ≈ 3.84

\(P_{BCD}\) = 8.59 + 7.58 + 6.81 = 22.98

s = 22.98 ÷ 2 = 11.49

\(A_{BCD}\) = \(\sqrt{11.49(11.49-8.59)(11.49-7.58)(11.49-6.81)}\) = √609.7343148 ≈ 24.6928

\(A_{ABCD}\) = 3.84 + 24.6928 ≈ 28.5

No. Since the limit as x approaches 3 from both sides of f(x) equals 6, f(x) will have a hole at x equals 3 and not a vertical asymptote.

A vertical asymptote is a vertical line on a graph that the function approaches but never touches as the input values approach a certain value. In other words, it is a value of the independent variable for which the function approaches infinity or negative infinity as the independent variable approaches that value.

It is often found in rational functions, where the denominator becomes zero at some value, causing the function to become undefined at that point.

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Answer:

$2,898.00

Step-by-step explanation:

FV=2500(1.03)^5

FV=2500(1.159274)

FV=$2,898.00

The expression is simplified to give 2(9x + 2√3x - 5)

First, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms

From the information given, we have that;

(2√3x - 2)(3√3x + 5)

expand the bracket, we get;

6√9x² + 5(2√3x) - 6√3x - 10

Find the square root factor

6(3x)  + 10√3x - 6√3x - 10

collect the like terms, we have;

18x + 4√3x - 10

Factorize the expression, we have;

2(9x + 2√3x - 5)

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The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.

a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.

b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.

c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.

d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.

Therefore, the number of different spanning trees for each graph is:

a) K3: 1

b) K4: 4

c) K2,2: 2

d) C5: 5  

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Step-by-step explanation:

the gradient of the line = 2 units/ 3 units = 2/3

Answer:

50

Step-by-step explanation:

Answer:

314 cm

Step-by-step explanation:

If Keith's height is 15x and his nephew's height is 7x, we can write the following equation:

1.16 * 15x = 34 + 7x * 2 -- (We get the 1.16 from the 16% increase)

17.4x = 34 + 14x

3.4x = 34

x = 10 so Keith's current height is 1.16 * 15 * 10 = 174 cm and his nephew's height is 174 - 34 = 140 cm for a total current height of 174 + 140 = 314 cm.

Answer:

m=2

Step-by-step explanation:

(x+1).2

y=2x+2

m=2

The value of the equation is y = x² + 2x + 1

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

y = ( x + 1 )²   be equation (1)

On simplifying the equation , we get

y = ( x + 1 ) ( x + 1 )

Taking the product of the terms , we get

y = x² + x + x + 1

y = x² + 2x + 1

Therefore , the value of y = x² + 2x + 1

Hence , the equation is y = x² + 2x + 1

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With 8 candidates and 2 janitorial jobs, the number of possible job assignments can be calculated using combinations. With 8 candidates and 2 jobs (one CEO and one secretary), the number of possible job assignments can be calculated using permutations.

In the first scenario, where there are 8 candidates and 2 janitorial jobs available, we need to determine the number of possible job assignments. Since the order of assignment does not matter (both jobs are identical), we can use combinations to calculate this. Using the formula for combinations, we can find the number of ways to select 2 candidates out of 8, which is given by C(8, 2) = 28. Therefore, there are 28 possible job assignments for the 2 janitorial positions.

In the second scenario, there are 8 candidates and 2 jobs available, one being a CEO position and the other a secretary position. Since the roles are distinct (CEO and secretary), we need to use permutations to calculate the number of possible job assignments. Using the formula for permutations, we can find the number of ways to select one candidate for the CEO position (8 options) and another candidate for the secretary position (7 options). This gives us P(8, 2) = 56 possible job assignments. Therefore, there are 56 different ways to assign the 2 jobs, considering the distinction between CEO and secretary.

The explanation provides a clear understanding of how to calculate the number of possible job assignments in each scenario, using either combinations or permutations. It explains the concept of combinations and permutations and applies them to the given situations.

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Answer:

1 : 2

Step-by-step explanation:

The original ratio would be 3 : 6, so now you need to simplify it.

To simplify ratios, you divide the number on each side by their greatest common factor. The GCF(greatest common factor) for 3 and 6 would be 3, so divide 3 by 3 =1 and divide 6 by 3 =2, so then your simplified ratio of circles to triangles would be 1 : 2

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The amount of Interest Tristan pays is $955.2

Given:

Tristan borrows $4000 at an interest rate of 7.4% with a loan term of 3 years.

we are asked to determine the interest Tristan pays for it:

we know:

P = $4000

r = 7.4%

t = 3 years.

Evaluate :

I = 4000(1+7.4%)³ - 4000

I = 4000(1+0.074)³ - 4000

I = 4000(1.074)³ - 4000

I = 4000(1.2388) - 4000

I = 4955.2 - 4000

I = 955.2

Hence we get the required interest as $955.2

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Answer:

Step-by-step explanation:

25,584km

Answer:

Step-by-step explanation:

we have

\(y=2x2-8x+9\)

Group terms that contain the same variable, and move the constant to the opposite side of the equation

\(y-9=2x2-8x\)

\(y-9=2(x2-4x)\)

\(y-9+8=2(x2-4x+4)\)

\(y-1=2(x2-4x+4)\)

\(y-1=2(x-2)2\)

\(y=2(x-2)2+1\)

the answer is the option C

\(y=2(x-2)2+1\)

The equation  y = 2x² – 8(x + 9) can be rewritten in vertex form as y = 2(x – 2)² + 1 option (C) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

It is given that:

The equation is:

y = 2x² – 8(x + 9)

y = 2x² - 8x + 8 + 1

y = 2(x² - 4x + 4) + 1

y = 2(x – 2)² + 1

Thus, the equation  y = 2x² – 8(x + 9) can be rewritten in vertex form as y = 2(x – 2)² + 1 option (C) is correct.

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Answer:

25% and 5% im pretty sure

Given expression:  \(\frac{9x^2 - 1}{12x^2 - 12x} \div \frac{9x^2 + 12x + 3}{3x^2 - 6x + 3}\) . We can simplify the given expression by multiplying the numerator and denominator of the first fraction by (3x-1) and then factorise. So, the simplified expression is \($\frac{3(x-1)^2}{4x(3x+1)(x+1)}$\).

In the second fraction, we can factorise the quadratic expression in the numerator.

=  \(\frac{9x^2 - 1}{12x^2 - 12x} \cdot \frac{3x^2 - 6x + 3}{9x^2 + 12x + 3}\)

= \(\frac{(3x-1)(3x+1)}{12x(x-1)} \cdot \frac{3(x^2 - 2x + 1)}{3(3x^2 + 4x + 1)}\)

Simplify the expression.

= \(\frac{(3x-1)(x-1)}{4x(x-1)} \cdot \frac{(x-1)^2}{(3x+1)(x+1)}\)

= \(\frac{3(x-1)}{4x} \cdot \frac{(x-1)}{(3x+1)(x+1)}\)

= \(\frac{3(x-1)^2}{4x(3x+1)(x+1)}\) . Thus, the simplified expression is \($\frac{3(x-1)^2}{4x(3x+1)(x+1)}$\).

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