£410 is divided between Gordon, Malachy & Paul so that Gordon gets twice as much as Malachy, and Malachy gets three times as much as Paul. How much does Malachy get?​

Answer:

15$

Step-by-step explanation:

The value of the x, y, and z for the given system of equations are; x =  -2/3, y = -1/2, and z = 1.

First, let us understand the equation:

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given the system of equations;

3x − 4y + z = 2                ...........equation 1

−9x + 12y − 3z = − 6       ...........equation 2

4x − 2y − z = -16             ...........equation 3

Add equation 1 to equation 3, we will get;

(3x − 4y + z ) + (4x − 2y − z ) =  2 -16

7x - 6y = -14  ...........equation 4

Multiply equation 3 by 3 and subtract from equation 2, we will get;

3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6

12x - 6y - 3z + 9x - 12y + 3z = 42

21x  - 18y = 42   ...........equation 5

Multiply equation 4 by 3 and add it to equation 4, we will get;

3(-3x + 3z) + (9x + 4z) = 5×3 - 2

-9x + 9z + 9x + 4z = 15 -2

13z = 13

z = 1

Put z = 1 in equation 5, we will get;

-3x + 3×1 = 5

-3x + 3 = 5

-3x = 5 - 3

x = -2/3

y = -1/2

Thus, the value of the x, y, and z for the given system of equations are; x =  -2/3, y = -1/2, and z = 1.

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Answer:

3/5=w

Step-by-step explanation:

the 2 onthe numerator and the 2 on the denominator cancel each other out leaving w byitself.

Answer:

16/5

Step-by-step explanation:

10x3/5=10x w-2/2

list <- value, value, value, value

x<-value

FOR EACH item IN the list

{

             IF item=x

                display "found"

}

Pseudocode is an informal manner of programming description that does not require any strict programming language syntax or underlying era concerns. it is used for growing an outline or a rough draft of a program. Pseudocode summarizes an application's flow but excludes underlying info.

Pseudocode is a synthetic and casual language that facilitates programmers' to increase algorithms. Pseudocode is a "text-primarily based totally" element (algorithmic) layout device. The policies of Pseudocode are fairly straightforward. All statements showing "dependency" are to be indented. the Python pseudocode is a syntax-loose representation of code. So, the Python pseudocode no longer involves any code in it. The Python pseudocode should be a very near illustration of algorithmic good judgment.

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The money A has is #150 and the money B has is #125.

According to the question,

We have the following information:

Half of A's money plus one-fifth of B's makes #100. Two-thirds of A's money plus two-fifth of B's makes # 150.

So, we will convert these verbal phrases into expression.

Now, let's take the amount of A to be #x and the amount of B to be #y.

x/2 + y/5 = 100

Using the least common factor of 2 and 5:

5x+2y = 1000

5x = 1000-2y ...(1)

2x/3 + 2y/5 = 150

Adding the fractions using the least common multiple of 3 and 5:

(10x+6y)/15 = 150

Using the cross multiplication method:

10x+6y = 2250

Now, putting the value of 5x from equation 1:

2(1000-2y)+6y = 2250

2000-4y+6y = 2250

2y = 2250-2000

2y = 250

y = 250/2

y = #125

Now, putting this value of y in equation 1:

5x = 1000-2y

5x = 1000-2*125

5x = 1000-250

5x = 750

x = 750/5

x = #150

Hence, the money A has is #150 and the money B has is #125.

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We have that the data is: (x₁ =–9.3, y₁=3) and (x₂=– 9.3, y₂=–7.5). The formula to calculate two distance between two points is:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(x_1-x_2)^2+(y_1-Y_2)^2 } } \end{gathered}$}}[/tex]

When we calculate the distance between two points, we solve what goes inside the parentheses, then it is calculated to the power of 2, and we continue adding the two numbers of the previous results, and finally the square root is calculated.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(-9.3-(-9.3))^2+(-7.5-3)^2 } } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(0)^2+(-10.5)^2 } } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{0+110.25 } } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{110.25 } } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=10.5 } \end{gathered}$}}}[/tex]

Answer:

20

Step-by-step explanation:

3-point shots made : 3-point shots attempted = 2 : 5

If the team made 24 points out of 3-point baskets, then since 24/3 = 8, it made 8 3-point baskets.

Proportion:

8 made is to 2 as x attempted is to 5

8/2 = x/5

2x = 40

x = 20

The standard form of quadratic function is f(x) = 1(x-2)2 - 6

A quadratic function is a two-degree function. A parabola is the graph of a quadratic function. A quadratic function has the general form f(x)=ax2+bx+c, where a, b, and c are real numbers and a0. A quadratic function has the standard form f(x)=a(xh)2+k. The vertex (h,k) has the coordinates h=-b2a,k=f(h)=f(b2a).

Given points (5,3) and (2,-6)

We know that the General form of a quadratic function is

f(x) = ax2+bx+c

Standard form = a(x-h)2 + k

Here point(x,y) = (5,3) and vertex (h,k) = (2,-6)

y =  a(x-h)2 + k

3 = a(5-2)2 – 6

3 = a(3)2 – 6

3 + 6 =9a2

9= 9a2

a2 = 9/9

a2=1

a=1

Now substitute a value in standard form

f(x) = 1(x-2)2 – 6

Therefore the standard form of quadratic function is f(x) = 1(x-2)2 – 6

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Answer:

The area of the circle would be 113.04

Step-by-step explanation:

If you plug the radius into the formula for finding the area of a circle (π·r²), or (3.14 · r²) then you'll get 113.04

Hope this helps! :D

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The starting term of the function  f(x) = 300 (1.16)^x is 300

This is a type of function that are of 3 main parts

Considering the given problem,  f(x) = 300(1.16)^x

the starting = 300

the base = 1.16

the exponents = x

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.

The base is what determines exponential growth or decay

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Answer:

Step-by-step explanation:

3 * 4 = 12 3 * 5 = 15 List of the First 5 Multiples of 3: 3, 6, 9, 12, 15 Notes: The listed multiples are the First 5 Multiples of 3 that are positive (greater than 0) The sum of the digits in Multiples of 3 are divisible by 3

Answer:

the number is 24 good luck :)

Answer:

24

Step-by-step explanation:

1) Break down the question

We are told that a number increased by 6 is 30 meaning a number added to 6 will get 30.

2) Work you way backwards to get your answer

To find the answer to this question we have to subtract 30 from 6.

This is because we are told that a number is added to get 30 so we should subtract to find our number!

3) Check you answer

Every question that you may be unsure of or had been struggling with should always be checked.

To check our answer we have to go backwards and see if the numbers match

As we can see the numbers match together and are correct in our equation

Hope this helps, have a great day!

Answer:

9l^5n-8l-3<15

Step-by-step explanation:

The correct expression to determine the amount of time is 45 times startfraction 4 over 9 endfraction times three-fifths.

Sal has finished = 5/9 of 45 maths problems

So, the remaining number of maths problems = 1 - 5/9

The remaining number of maths problem = (9 - 5)/9

The remaining number of maths problem = 4/9 of 45

Amount of time to solve 1 problem = 3/5 of a minute

Amount of time to solve 4/9 problems = 45×4/9 × 3/5 of a minute.

Hence, 45 times startfraction 4 over 9 endfraction times three-fifths is the correct expression to find the time.

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The Answer is : 64

I took the test and it showed this is the correct answer, hope this helped :)

Answer:

11r+2

Step-by-step explanation:

combine the two numbers with the same variable and then leave the 2 by itself, that would be 4r+7r=11r and then bring the 2 down that makes 11r+2

According to the the concept of hypothesis testing, there is no evidence that the proportion of Americans who are afraid to fly has decreased.

Hypothesis testing:

Basically, in math hypothesis, it test the population on the basis of the sample data taken from the population using a simple random sampling.

Given,

According to a study conducted by an​ organization, the proportion of Americans who were afraid to fly in 2006 was 0. 10. A random sample of 1300  Americans results in 117 indicating that they are afraid to fly.

Now, we need to explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has.

While we looking into the given question,

Sample size, n = 1300

Number of Americans who were afraid to fly, x = 117

Now, we have to computing the sample proportion of Americans who afraid to fly,

Therefore, p = 117 / 1300 = 0.09

Then the Formulation of Hypotheses is written as,

Here the Null Hypothesis: H0: p≥0.10

And the alternative Hypothesis: Ha: p<0.10

Then the Left-tailed test of Test statistic is written as,

Here Let us assume that the level of significance, α = 0.05.

Then the Critical value, z≈−1.645

And the Decision rule is written as

If the value of  |z|<|z0.05|≈1.645: Do not reject the null hypothesis.

Otherwise If value of  |z|≥|z0.05|≈1.645: Reject the null hypothesis.

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The equation that best represents this relationship given in the table is y = 56x.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have a table below that shows the number of hours the Carrera family has been driving and the number of miles they’ve driven.  

We can find the slope of the line from the table as follows -

m = (168 - 84)/(3 - 1.5)

m = 56

Now, we can write -

y = 56x + c

84 = 56 x 1.5 + c

c = 0

So, the equation would be -

y = 56x

Therefore, the equation that best represents this relationship given in the table is y = 56x.

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For the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including  28 free songs is equal to 54 songs.

As given in the question,

Total free download songs is equal to 28

Let us consider variable 'x' to represent  the number of downloaded songs at the rate of $0.59

Total monthly bill of downloaded songs = $15.34

Equation formed :

0.59x = $15.34

⇒ x = 15.34 / 0.59

⇒ x = 26 songs

Total number of downloaded songs including 28 free songs

= 26 + 28

= 54 songs

Therefore, for the given data, 1 free download song and cost of each additional download song is $0.59 ,then total downloaded songs in $15.34 including  28 free songs is equal to 54 songs.

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With annual growth rate of 1.2% per year, the projected world population in 2044 is 10.5 billion

The formula for the exponential growth model is:

X(t) = Xo (1 + r)^t

Where:

X(t) = value of X at time t

Xo = initial value

t = time interval

r = growth rate

Parameters given:

Xo = 7 billion = 7 x 10⁹

t = 2044 - 2010 = 34

r = 1.2% = 0.012

Hence,

X(t) =  7 x 10⁹ (1 + 0.012)³⁴

X(t) = 10.5 x 10⁹ = 10.5 billion

Therefore,

The projected world population in 2044 = 10.5 billion

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Answer:

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

The slope- intercept form:

Use two points on the graph to find the slope:

Find the slope:

The y-intercept is b = - 4.

The equation is:

The linear model that predicts the population, y, of Florida (in millions) in terms of x, the number of years since 2010 is y = 17.4+0.22x.

According to the question,

We have the following information:

The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2015.

Now, y is the population.

So, we will have the total population in 2010 and 0.22 times the number of years.

So, the expression will be:

y = 17.4+0.22x

Hence, the correct option is C.

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Answer:

4 7/12

Step-by-step explanation:

Answer:

Hence, the value of y = b^2 = (-3/2)^2 = 9/4 is your answer

Step-by-step explanation:

only if your answers are
A) 3/2

B) 9/4

C) 6

D) 9

The solution of the inequality is x>2 and the graph is attached below.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. When two values are compared, an inequality shows whether one is higher, lower, or simply not equal to the other.

The given inequality is 2x - (3-x) > x + 1,

Now, solving the inequality by opening the bracket,

2x - (3-x) > x + 1

[tex]2x - 3 + x > x + 1[/tex]

3x - 3 > x + 1

Subtracting x from both sides and  adding 3 on both sides,

2x > 4

x > 2

So, the graph is attached below and Option D is correct.

Therefore, after solving the given inequality, we get x > 2 and the graph is attached below.

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Answer:

B, or y - 1 = 1/2(x + 2)

Step-by-step explanation:

when you solve B, you get y = 1/2x + 2, which is the equation being shown on the graph.

Answer: y=x+4

Step-by-step explanation:

The formula for slope-intercept form is y=mx+b where

m is the slope and b is the y-intercept.

Formula for working out the slope: y2-y1/x2-x1

Put the values in the equation: 4-3/0-(-1). Answer is 1/1 which is 1.

y-intercept: put one of the x and y values from the graph into the equation y=mx+b. Here, I'm going to choose the point (0,4).

The equation is now 4=1(0) + b

Working out for equation:

4=0+b

4=b

The final equation is y=x+4.

You can also use the graph to help you find the y-intercept! First, look at the y-axis. Then the point that passes it is your y-intercept!(Remember it's the y value not the x)

Answer:

Step-by-step explanation:

Angles f and g are congruent as opposite sides are congruent. Therefore:

Angles h, 76°, g and the right angle all together form 360°: