Please answer the 5 questions and number them when you have answered them
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The value of m on solving the equation 6 1/9m+ 3 1/3m = 28 1/3 is 3

We need to solve the equation

6 1/9m+ 3 1/3m = 28 1/3 for m

converting mixed fractions into improper fractions

55/9 m + 10/3 m = 85/3

Upon taking L.C.M.

55/9 m + 10x3/3x3 m = 85/3

(55 + 30)m/9 = 85/3

3 x 85m = 85 x 9

m = 3

Therefore, the value of m on solving the equation 6 1/9m+ 3 1/3m = 28 1/3 is 3

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Answer:

0.5

Step-by-step explanation:

2/4

= 1/2

Multiply 5 to both numerator and denominator.

= 1/2 x 5/5

= ( 1 x 5 )/( 2 x 5 )

= 5/10

= 0.5

A total of 81 apples and 72 spears are there in total.

Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -

A : B ∷ C : D

AND

A x D = B x C

Product of extremes equal to product of means.

Given is in a Petri café they discovered that as many apples as pears are rotten, ⅔ of all apples are rotten and that ¾ of all pears are rotten.

Assume that there are [x] apples and [y] pears in total.

Then, rotten apples = 2x/3

rotten paears = 3y/4

Since, they are equal, we get -

2x/3 = 3y/4

2x (4) = 3y (3)

8x = 9y

The whole number coordinates satisfying the equation are - (81, 72). Refer to the graph attached.

Therefore, a total of 81 apples and 72 spears are there in total.

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The equation of the line is y = 2 and is parallel to the x-axis.

The equation of the line is [tex]y = 2[/tex]  and is parallel to the x-axis.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

As per the given graph, the equation of line which is parallel to the x-axis is [tex]y=2[/tex].

Draw the graph

Hence, the equation of line which is parallel to the x-axis is [tex]y=2[/tex].

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[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-\frac{3}{4}})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{\frac{5}{4}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{5}{4}}-\stackrel{y1}{\left( -\frac{3}{4} \right)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{~~ \frac{5 }{4 }+\frac{3}{4} ~~}{-2} \\\\\\ \cfrac{~~ \frac{ 5+3}{ 4} ~~}{-2}\implies \cfrac{~~ \frac{8 }{4 } ~~}{-2}\implies \cfrac{2}{-2}\implies -1\qquad \impliedby m[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{\left(-\frac{3}{4} \right)}=\stackrel{m}{-1}(x-\stackrel{x_1}{4})\implies {\large \begin{array}{llll} y+\cfrac{3}{4}=-(x-4) \end{array}}[/tex]

The interval notation of the compound inequality (x < 1) and [x > (-5)] is

[(-5) < x < 1], and the graph of it's solution set is a straight line lying on the x-axis from 1 to (-5).

As per the question statement, we are provided with a compound inequality (x < 1) and [x > (-5)],

And we are required to determine the interval notation of the above mentioned compound inequality, and graph it's solution set.

Now, the interval notation of a compound inequality is simply the combination of the separate inequalities, that is, the interval notation of the compound inequality (x < 1) and [x > (-5)] is [(-5) < x < 1].

And since "x" is less than 1, but greater than (-5), the values in the solution set of [(-5) < x < 1] are (0, -1, -2, -3, -4), and the graph of these values is a straight line lying on the x-axis from 1 to (-5).

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Answer:

x=50 y=140

Step-by-step explanation:

Since l and m are parallel, all you have to do is add 40 and y.

Because a straight line has a 180-degree angle, you can subtract 40 from 180 you can find y.

180-40=140

Now we know that 3x-10=140 so we just have to solve.

First, add 10 to each side

3x=150

Then divide by 3

x=50

Answer: y < 3 - 2x

Step-by-step explanation:

6x + 3y < 9

3y < 9 - 6x (after subtracting both sides by 6x)

y < 3 - 2x (after dividing both sides by 3)

I forgot how to do this stuff

Answer: It has to be between 0.1 to 0.3

Step-by-step explanation:

The time taken to cover Suva to Sigatoka is 2 Hours and 30 Minutes.

We know that, Time taken = (Distance Covered)/(Average Speed)

Given that the car travelled from Suva to Sigatoka and travelled 125 Km.

Average speed is = 50 km/hr

So the time taken to cover the distance = 125/50 = 5/2 hr = 2 hours and 30 minutes.

Hence the time taken to cover Suva to Sigatoka is 2 Hours and 30 Minutes.

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The slope of the best least squares line through the three points (-2, 4), (0, 3), (2, 0) is -1.

Given:

Three points (-2, 4), (0, 3), (2, 0).

    x      y      x^2      xy

   -2     4        4       -8

    0     3        0        0

    2     0        4        0

∑   0     7        8       -8

[tex]SS_{xx}[/tex] = ∑[tex]x^{2}[/tex] - 1/n(∑x)^2

= 8 - 1/3(0)^2

= 8 - 1/3*0

= 8 - 0

= 8

[tex]SS_{xy}[/tex] = ∑xy - 1/n(∑x)(∑y)

= -8 - 1/3(0)(7)

= -8 - 1/3*0

= -8 - 0

= -8

slope m = [tex]SS_{xy} /SS_{xx}[/tex]

= -8/8

= -1

Therefore the slope of the best least squares line through the three points (-2, 4), (0, 3), (2, 0) is -1.

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Answer: 26%

Step-by-step explanation: 50 x 0.14 = 7. 12 + 8 + 10 + 7 = 37, 37÷50=0.26 so 26%

The percentage of blue skittles is 26%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total number of skittles = 50

Red skittles = 12

Yellow skittles = 8

Green skittles = 10

Orange skittles = 14%

This means,

= 14/100 x 50

=  7

Blue skittles.

= 50 - (12 + 8 + 10 + 7)

= 50 - 37

= 13

The percentage of blue skittles.

= 13/50 x 100

= 1300/50

= 26%

Thus,

26% of blue skittles.

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Answer:

SSS means Side-Side-Side. SAS means Side-Angle-Side. ASA means Angle-Side-Angle. AAS means Angle-Angle-Side.

Hopes this helps! :)

⇒The shape in the picture is a pentagon because it has five sides.

⇒ The sum of the interior angles of a pentagon is 540°

meaning:

[tex]4x+(3x+3)+(5x-2)+103+100=540\\[/tex]

⇒As a results you can see above we have an equation that can enable us to solve for x.

⇒Solving for x we have

[tex]4x+3x+5x+3-2+103+100=540\\[/tex]

⇒Now let us simplify like terms since we have grouped them already.

[tex]12x+204=540\\12x=540-204\\12x=336\\\frac{12x}{12} =\frac{336}{12} \\x=28[/tex]

∴ x=28°

Note I have written the equation above, as the first step.

Answer:

Step-by-step explanation:

Let the initial number of books be x.

Set equation:

Answer:

50 books

Step-by-step explanation:

Forming the equation,

→ x + ((x/100) × 12) = x + 6

Now the value of x will be,

→ x + ((x/100) × 12) = x + 6

→ x - x + (12x/100) = 6

→ 0.12x = 6

→ x = 6/0.12

→ [ x = 50 books ]

Hence, answer is 50 books.

Eight people skiing downhill in a race can finish in 40,320 different orders.

Calculating probabilities for a set of possibilities keeping in account the order they are in is called permutation ([tex]{n}_P_{r}[/tex]).

If we overlook the order, it becomes a problem of combination ([tex]{n}_C_{r}[/tex]).

Permutation plays an important role in probability problems where the order of the possible outcomes is concerned. It does not allow repetition of outcomes.

Mathematically, permutation can be represented as:

[tex]{n}_P_{r}=\frac{n!}{(n-r)!}[/tex]

where 'n' represents the total objects/values/instances and 'r' represents our selected number of objects/values/instances.

In this case, we have total 8 drivers (n=8) and 8 positions we are selecting i.e. the order skiing people finish in (r=8);

[tex]{n}_P_{r}=\frac{8!}{(8-8)!}=\frac{8!}{0!}=\frac{40320}{1}[/tex]

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The state income tax owed on a $60,000 per year salary.

is tax = $2850.

A percentage is a figure or a ratio that is expressed as a fraction of 100. The percentage sign, "%," is used to denote it. The percentage is denoted by the abbreviations "pct" or "pc." In other words, the percentage is measured in terms of 100 and is defined as the proportion of one quantity that is made up of another.

The % has no boundaries. It implies that they are dimensionless numbers. When we state a number is 60% of something, we are implying that it is 60% of everything. Even fractional versions, like 0.56% or 0.87%, can be used to express it. Students' exam scores in any subject are calculated as a percentage. For instance, Pooja received a 78% on his exam.

Tax slab is as follows:-

0 - 10,000                  =   3%

10,001 - 50,000         =    5%

50,001 - 100,000       =   5.5%

So total salary = $60000

Till $10000 tax deduction will be 3%

So, $10000 * 0.03 = $300

Then from $10,001 - $50,000 tax deduction will be 5%

Hence, the tax deduction will be $40000 * 0.05 = $2000

And from $50,001 - $100,000 tax deduction will be 5.5%

Only $10000 will be available for tax deduction

so, $10000 * 0.055 = 550

Hence total tax deduction will be $2850.

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The area of the rhombus is 50[tex]\sqrt{3}[/tex] .

Given:

In a rhombus, all the side lengths are $10,$ and one of the angles is equal to $120^\circ.

If angle = 120 the its half is 60 which forms a right angled triangle.

sin 60 = Height / 10

[tex]\sqrt{3}[/tex]/2 *10 = height

height = 5[tex]\sqrt{3}[/tex].

Area of rhombus = base * height

= 10*5[tex]\sqrt{3}[/tex]

= 50[tex]\sqrt{3}[/tex] .

Therefore the area of the rhombus is 50[tex]\sqrt{3}[/tex] .

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Equation:

a) 4 + 3x = 3x- 7 has no solution.

b) 5.4x + 12 = 2(2.7x - 9 ) has no solution

c) 6 + 2.5x = 0.5x - 8 has one solution.

A formula that expresses the connection between two expressions on each side of a sign is called equation. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 2.

Given,

Equations:

a) 4 + 3x = 3x- 7

3x - 3x = -7 -4

0

4 + 3x = 3x- 7 has no solution.

b) 5.4x + 12 = 2(2.7x - 9 )

5.4x + 12 = 5.4x - 18

0

b) 5.4x + 12 = 2(2.7x - 9 ) has no solution

c) 6 + 2.5x = 0.5x - 8

2.5x - 0.5x = -8 -6

2x = -14

x = -7

c) 6 + 2.5x = 0.5x - 8 has one solution.

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Answer:

3.45 hours. The closest answer option to this value would be (10/3), which is technically 3.3333 hours, but it is the closest correct option, by far.  3.333 hours would suggest the distance was 250 miles, not 259 (250/75) = 3.33333)

Step-by-step explanation:

Distance, D, is found by multiplying the speed (75 mph) times the time, x (in hours.  If distance is 259 miles, we can write:

   259 miles = (75 miles/hr)*x

Rearrange to find x  [divide both sides by (75 miles/hr):

x = (259 miles/(75 miles/hr)

Note the units:  miles cancel and hours moves to the top, leaving only hours, which is what we want.

(259 hours)/75 = 3.45 hours

Segments that are congruent are same in length. Collinear points are those that share a line. A mathematical claim that can be supported by evidence is called a theorem. A segment's midpoint is the point at which it is divided into two congruent segments.

What are congruent segments?

What is an example of congruent segments?

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The image of the point (-3,0) after the given transformation is (0,5) and this can be determined by using the rules of transformation.

The following steps can be used to determine the image of the point after transformation:

As per the given data translate the point (-3,0) by (3,5).

[tex]( x, y )[/tex]  =  [tex]( x + 3, y+ 5)[/tex]  = (0, 5)

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The cost of the coffee beans per pounds is 1.6 pounds.

Given that,

Coffee beans are available in stores for $8 per bag.

We have to find the price of coffee beans per pound if a bag weighs 5 pounds.

one lb is one pound.

To convert it from pounds to kilogram's, increase it by 1. (or just change the unit). This shows that the number of pounds is exactly the same.

Let us take the cost as x.

We get,

5x=8

x=8/5

x=1.6

Therefore, The cost of the coffee beans per pounds is 1.6 pounds.

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The amount she should try to sell the rare vase to make profit of 15% would be = £1,081.

Profit amount is defined as the amount of money received by an individual that is an extra amount gained when compared with the cost price of the item.

The cost price of the rare vase = £940

The percentage profit seeked for = 15% of cost price.

That is;

15/100 × 940

= 14,100/100

= £141

The profit Christa seeks= £141 additionally.

Therefore, she should attempt to sell it at a price of 940 + 141 = £1,081.

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Answer: A. (5³) x (5³) x (5³) x (5³)

B. (-9²) x (-9²) x (-9²) x (-9²) x (-9²)

Step-by-step explanation: 5x5x5=5³ we have four 5³

9x9=9² we have five 9²

The inequality that would represent the possible values for the number of hours walking dogs is 9d + 8c ≥ 130

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let number of hours walking dogs = d

Let number of hours clearing tables = c

The appropriate inequality is 9d + 8c ≥ 130.

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Total sum that Bill owe the bank is $36

Given,

The overdraft fee charged by the bank = $27.50

The charge for using an ATM out of network = $3.50

The amount in the checking account = $25

The amount for check clearing = $50

ATM debit amount added = $80

We have to find the money Bill owe the bank;

Overdraft;-

A bank will grant a customer an overdraft when their account balance is 0 so they may pay their payments and other expenses.

Here,

Total sum in bank = 25 + 50 - 80

Total sum in bank = -5

Then,

Total Sum he owe = 5 + 27.5 + 3.5

Total sum he owe = $36

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Quadratic function for the given properties is [tex]y=-4x^{2} +24x-28[/tex].

The roots are [tex]3+\sqrt{2}[/tex] and [tex]3-\sqrt{2}[/tex]; that means the axis of symmetry is x=3; which means the vertex has x coordinate 3. Then the vertex form of the equation is

[tex]y = a(x-3)^{2}+k[/tex]

Then since y is 0 when x is [tex]3+\sqrt{2}[/tex],

[tex]0=a(\sqrt{2} )^{2} +k[/tex]

[tex]0=2a+k[/tex]                    (1)

And when x = 1, y = -8,

[tex]-8 = a(-2)^{2}+k[/tex]

[tex]-8=4a+k[/tex]                (2)

Then from equations (1) and (2)

[tex]-8=2a[/tex]

[tex]a = -4[/tex]

And then from either equation (1) or (2), k = 8.

So the equation is

[tex]y = -4(x-3)^{2}+8[/tex]

[tex]y=-4(x^{2} -6x+9)+8[/tex]

[tex]y=-4x^{2} +24x-28[/tex]

Solving this equation using the quadratic formula verifies that the roots are  [tex]3+\sqrt{2}[/tex] and [tex]3-\sqrt{2}[/tex]; evaluating the expression for x=1 verifies that the y value is -8.

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The geom_jitter() function is the function creates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier to find

Given that,

In order to make the points in the plot easier to find, function first creates a scatterplot and then adds a small amount of random noise to each point in the plot.

Generally, To make the points in the scatterplot easier to find, the geom jitter() method first builds a scatterplot and then adds a little amount of random noise to each point in the plot.

What is the purpose of the Geom jitter () function? Description. The geom point (position = "jitter") shortcut is the jitter geom. It is a practical method of managing overplotting brought on by discreteness in smaller datasets by adding a little degree of random variation to the location of each point.

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The geom_jitter() function is a funcreates a scatterplot and then adds a small amount of random noise to each point in the plot to make the points easier

Given that,

Function first makes a scatterplot, then adds a small amount of random noise to each point in the plot to make the points in the field easier to find.

The geom jitter() method often produces a scatterplot first, then adds a small amount of random noise to each point in the plot to make the points in the field easier to find.

What does the Geom jitter () function do? The jitter geom is the shortcut geom point with a position equal to "jitter". It is a helpful technique for controlling overplotting caused by discreteness in smaller datasets by giving each point's location a small amount of random variation.

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