In an election of a municipality two candidates A and B stood for the post of Mayor and 25000 people were in the voter list. Voters were supposed to cast the vote for a single candidate. 12000 people cast vote for A, 10000 people cast for B and 1000 people cast vote even for both. Show these informations in a Venn-diagram. How many people didn't cast vote ? Find it. How many votes were valid ? Find it.​

Answer: its not equal.

Step-by-step explanation:

-6y + 4 = 2 (-3y + 2)

|4y + 12| = 4 (y + 3)

Answer:

no it is not proportional...

Step-by-step explanation:

5 miles/40 minutes is 1/8

3 miles/27 minutes is 1/9...

Answer: -7/3≤t≤5/3

Step-by-step explanation:

|2t + 2/3|≤4

2t + 2/3≤4

(2t + 2/3≤4)*3

6t+2≤12

6t≤10

t≤10/6

t≤5/3

2t + 2/3>=-4

(2t + 2/3>=-4)*3

6t + 2>=-12

6t>=-14

t>=-14/6

t>=-7/3

-7/3≤t≤5/3

Using the relation between velocity, distance and time, the distances are given as follows:

A. d = 13/3 miles.

B. d = 4.25 miles.

C. d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).

Velocity is distance divided by time, that is:

v = d/t.

Hence the distance is:

d = vt.

In item a, considering the time in hours, we have that:

v = 13, t = 20/60 = 1/3.

Hence:

d = 13/3 miles.

In item b, we have different definitions, then:

d = 15 x 5/60(first five minutes) + 12 x 15/60(last 15 minutes).

d = 15/12 + 15/5

d = 4.25 miles.

For item c, we have that:

d = M x 5/60(first five minutes) + N x 15/60(last 15 minutes).

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The polynomial function with degree 5 is formed as:

f (x) = x (x + 2)³ (x - 2).

(-2) is derived from the factor (x + 2); because it has a multiplicity of three, you must account for that zero three times; thus, it is composed as (x + 2)³.

0 is derived from the factor x.

2 is derived from of the factor (x - 2).

The factored polynomial function is:

f (x) = x (x + 2)³ (x - 2)

Thus, the polynomial function with degree 5 is composed.

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Answer:

10°C

Step-by-step explanation:

F = 50

C = 5/9 * (F - 32) = 5/9 * (50 - 32) = 5/9 * 18 = 5 * 2 = 10

Answer:

946 gal

629 gal

Step-by-step explanation:

volume that evaporates = LWH

volume = (5.0 m × 100 cm/m × inch / 2.54 cm) × (12.0 m × 100 cm/m × inch / 2.54 cm) × 2.35 inch

volume = 218,550 in.³

volume = 218,550 in.³ × 1 gal / 231 in.³

volume = 946 gallons

You must add 946 gallons.

The loss to evaporation is 2.35 in.

The amount of rain is 20 mm

The net loss is

2.35 in. × 25.4 mm / inch - 20 mm = 39.69 mm

39.69 mm × 1 inch / 25.4 mm = 1.563 in.

The net loss now is 1.563 in. instead of 2.35 in.

We find the fraction of the the previous loss is the loss with rain and multiply by the previous loss.

1.563/2.35 × 946 gal = 629 gal

With rain, then 629 gallons of water must be added.

Answer:

Step-by-step explanation:

its ''C''

a) The slope of the line is 6 / 7.

b) The point-slope form of the equation of the line is y - 2 = (6 / 7) · (x - 4).

c) The slope-intercept form of the equation of the line is y = (6 / 7) · x - 17 / 7.

d) The point-slope form of the equation of the line is - 6 · x + 7 · y + 17 = 0.

There are three different forms of the equation of the line:

Point-slope

y - y' = m · (x - x')                     (1)

Slope-intercept

y = m · x + k                             (2)

Standard

a · x + b · x + c = 0                   (3)

Where:

a) The slope that passes through the two given points is found by secant line formula:

m = [8 - 2] / [11 - 4]

m = 6 / 7

b) The point-slope form of the equation of the line is:

y - 2 = (6 / 7) · (x - 4)

c) The slope-intercept form of the equation of the line is:

y - 2 = (6 / 7) · x - 24 / 7

y = (6 / 7) · x - 17 / 7

d) The standard form of the equation of the line is:

7 · y = 6 · x - 17

- 6 · x + 7 · y + 17 = 0

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Answer:

24 seconds

Step-by-step explanation:

Strand A: 3 × 8 secons =24 seconds

Strand B: 2 × 12 seconds= 24 seconds

Answer: 50

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

300(2) bcuz 300 guests and each person gets 2

600(12) bcuz 300(2) is 600 and a dozen is 12

=50

Answer:

x/7+12

Step-by-step explanation:

One seventh refers to 1/7.

Since we do not know what "a number" is it, it is written as "x."

Whenever you see the word "increased" think addition.

So in this case,

x / 7 + 12

Pentagon Question

The sides add to 63, so:

[tex]11+3x+11+x+2+2x+3=63 \\ \\ 6x+27=63 \\ \\ 6x=36 \\ \\ x=6 \\ \\ \implies AB=2(6)+3=15[/tex]

Rectangle Question

If the width is w, then the length is w+4.

This means that 2(w+w+4)=68.

[tex] 2(2w+4)=68 \\ \\ 2w+4=34 \\ \\ 2w=30 \\ \\ w=15[/tex]

So, the length is 19 and the width is 15.

Answer:

Hello,

Step-by-step explanation:

[tex]1 < x\leq 5 \ \\\Longrightarrow\ 4 < 4x \leq 20 \ \\\Longrightarrow\ -1 < 4x-5 \leq 15 \\\Longrightarrow\ -1 < f(x) \leq 15 \\\\range=]-1; 15][/tex]

The range of the function f(x) = 4x - 5 will range from -1 to 15.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given that the function f(x) = 4x – 5 and the interval is  1 < x ≤ 5. The range will be calculated as,

1 < x ≤ 5

4 < 4x ≤ 20

4-5<4x - 5< 20-5

-1 < 4x - 5 < 15

Therefore, the range of the function f(x) = 4x - 5 will range from -1 to 15.

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Another form of the given expression using associative property is 10y + (-3y -6y)

Associative property shows that if two or more property are added or multiplied, the result remains the same. For instance;

a +(b + c) = (a+b) + c

Given the expression below;

-3y - 6y + 10y

Group to have

(-3y - 6y) + 10y

10y - 3y - 6y

This can also be grouped as;

(10y - 3y) - 6y = 10y + (-3y -6y)

Hence another form of the given expression using associative property is 10y + (-3y -6y)

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Answer:

4/5 is the slope of the line

If you contribute $400 every quarter for 20 years, the amount of  interest you would  earn during the 20 years is $22,447.52

What future value formula is applicable in this case?

The applicable future value formula is that of an ordinary annuity which determines the future worth of $400 quarterly savings for 20 years bearing in mind that the quarterly interest rate is the annual interest rate divided by 4

FV=PMT*(1+r)^N-1/r

FV=worth of the annuity after 20 years=unknown

PMT=quarterly deposit=$400

r=quarterly interest rate=5%/4=1.25%

N=number of quarterly savings in 20 years=20*4=80

FV=$400*(1+0.0125)^80-1/0.0125

FV=$54,447.52

interest=$54,447.52-($400*80)

interest=$ 22,447.52

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The angle at which the shot was made should be 17.53° degrees.

Let C denote the point where the player attempts to put in a goal.

Let A and B denote the two goalposts.

We are given the posts of a hockey goal are 6 ft apart.

The distance between the player and one goalpost is 19 ft.

The distance between the player and the other goalpost is 24 ft.

Then, we have AC = 19 ft, BC = 24 ft, and AB= 6 ft.

Refer to the diagram.

Let θ be the angle made when trying to shoot the goal towards goalpost A.

Then we have tan(θ) = 6/19

⇒ θ = 17.53° degrees.

Therefore, the angle at which the shot was made should be 17.53° degrees.

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The investment in  Fund B is $2000.

To understand the given question we first have to understand the logic of percentage and how it affect the return on Investment.

If an investment fund returns a profit on an investment then the profit is calculated by multiplying the investment with the profit(in decimal form).

For Example: If the investment is A and profit is x % then the profit is calculated by:

Profit =A×([tex]\frac{x}{100}[/tex])

Now in the given problem, let us consider the amount of investment into the Fund B be x.

Profit in Fund B=10%

Profit in Fund A is 3%.

Investment in Fund A=$5000

Total profit from both investments=3% of 5000+10% of x

[tex]=\frac{3}{100}\times 5000 + \frac{10}{100}\times x\\ =150+0.1x[/tex]

Now the total investment=5000+x

The combined profit for both the Investments is 150+0.1x

But the combined profit is 5% for both investments.

profit=[tex]5\% of(5000+x)[/tex]

[tex]=\frac{5}{100}\times (5000+x)\\=0.05\times5000+0.05x\\=250+0.05x[/tex]

Now the profit is same, so if we equate both the expressions of profit we get a linear equation in x.

[tex]\therefore 250+0.05x=150+0.1x\\or,250-150=0.1x-0.05x\\or,100=0.05x\\or,x=2000[/tex]

Thus we can conclude that she invested $2000 in the Fund B.

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Answer:

2 groups of 3/8 are in one

Step-by-step explanation:

making up 6/8 because you can add another 3/8 to it.

The profit in 2012 must be 4.5(in hundreds of dollars) to break even.

Profit for a company is defined as the difference between the revenue and cost of a product.

Let us take an example to learn more about profit.

A company sells a product at a price of 'S' dollars and the company spends 'C' dollars to manufacture the product. Here C includes the cost of raw materials, labor cost, transport etc.. Now the net profit for the company for selling one unit of this particular product is given by

Profit=S-C

In the given chart it is shown the profit of the company is given as

2.5,1.75,-3.3 and -1.4 (in thousands of dollars) over 4 years.

Net profit over four years=[tex]2.5+1.75-3.3 -1.4=-0.45[/tex]

So over the past four years the company incurred a loss of

[tex]=0.45\times 1000\\[/tex]

[tex]=450[/tex] dollars

Now the company needs to break even in 2012.

So net profit must be zero over 5 years.

Therefore Profit in 2012=0-(-450)=450 dollars

Profit=4.5 (hundreds of dollars)

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Answer:

=

15/4

(Decimal: 3.75)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Joint variation equation:

Find the value of k by plugging in the given values:

The equation is:

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-2}x+8\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-2\implies \cfrac{-2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-2}\implies \cfrac{1}{2}}}[/tex]

so, we're really looking for the equation of a line whose slope is 1/2 and that it passes through (6 , -2)

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \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}{(-2)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{6}) \implies y +2= \cfrac{1}{2} (x -6) \\\\\\ y+2=\cfrac{1}{2}x-3\implies \LARGE \begin{array}{llll} y=\cfrac{1}{2}x-5 \end{array}[/tex]

Answer:

11

Step-by-step explanation:

2x-3=19

2x=22

x=11

Step-by-step explanation:

Factor of 225

= 3 × 3 × 5 × 5

Factor of 495

= 3 × 3 × 5 × 11

Factor of 810

= 3 × 3 × 3 × 3 × 2 × 5

Now ,

HCF = Common Factor

= 3 × 3 × 5

= 45

[tex]...[/tex]

☘️☘️☘️...

the expression of the variable for a = 2 and c = 3. 2a − (c + a)2

2a+b^2 2a +b2

2(-3) +(-2)^2 2(-3) + (-2)

-6 +4 -6 -4

-2 -10

An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6 .

Either the options are incorrect, or the problem is poorly written.

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Answer:

  B.  False

Step-by-step explanation:

You want to compare the lateral surface areas of a cone and cylinder, where the slant height of the cone is twice the height of the cylinder. Your proposition is that the cone's lateral area is half that of the cylinder.

Effectively, the lateral area of a cone is the area of a triangle whose base is the circumference of the cone, and whose height is the cone's slant height. The formula for the lateral area of a cone of radius r and slant-height s is ...

  A = πrs

For the given dimensions (s=2h), the lateral area is ...

  A = πr(2h) = 2πrh

The lateral area of a cylinder is the area of a rectangle whose base is the circumference of the cylinder, and whose height is the cylinder's height. The formula for the lateral area of a cylinder of radius r and height h is ...

  A = 2πrh

The lateral areas of the given figures are both 2πrh, so one is not half the other.

The proposition is False.