If your monthly income is $5,000 and your rent is $2,000, what percentage of your
income is used to pay rent?
20%
30%
40%
50%

Answer:

Step-by-step explanation:

A = 600 x 120 = 72 000 cm^2

Area of a paving stone = 30^2 = 900 cm^2

number of paving stone = 72 000 : 900 = 720 : 9 = 80

Total cost = 2.50 * 80 = £200.00

Answer:

if it stopped repeating yes , if no , no

Step-by-step explanation:

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The combination of 6 are total samples (without replacement) of size five can be selected from this population

What is permutation and combination?

           ⁿCr = n!/( n-r)! r!

r = 5

total samples

⁶C₅ = 6!/(6-5)!5!

       = 6!/1!5!

      = 6 * 5!/1*5!

      = 6

Hence, there are 6 ways

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Answer:

Area of triangle = ½ × b × h

Step-by-step explanation:

Now we have to,

→ write formula of area of triangle.

Formula we use,

→ A = ½ × b × h

Hence, this is the formula.

Answer: Use the formula

Step-by-step explanation:

Answer: 12

Step-by-step explanation:  7 1/2 divided by 5/8 equals 12.

Answer:

12

Step-by-step explanation:

7 1/2 = 15/2

15/2 divided by 5/8 = 12

Hope this helps

Answer:

-330°

Step-by-step explanation:

just gotta trust it i guess

Answer:

38

Step-by-step explanation:

the sum of the interior angles of a triangle is 180

2c + 3c -48 +2c -38 = 180  Combine like terms

7c + -86 = 180  Add 86 to both sides

7x = 266  Divide both sides by 7

x = 38

Answer: c = 38

Step-by-step explanation:

      We know that a triangle's angles add up to 180 degrees. We will write an equation and solve it by combining like terms and then using inverse operations.

   Given:

(2c)° + (2c - 38)° + (3c - 48)° = 180°

   Distribute it out:

2c° + 2c° - 38° + 3c° - 48° = 180°

   Combine like terms:

7c° - 86° = 180°

   Add 86 to both sides:

7c° = 266°

   Divide both sides by 7:

c = 38

There would be 150 students enrolled in the school, according to estimates, in 2001.

468 students are projected to be enrolled in the school in the academic year 2018

We have the equation as

[tex]y = 123.1(1.069)^x[/tex]

where we have x to be the difference in the number of years

2001 - 1998 = 3

y = 123.1(1.069)³

y = 123.1 * 1.2216115

y = 150.4

The estimated number of persons that would be studying in the school in the year 2001 would be 150.

b. 2018

We have to take the difference

x = 2018 - 1998 = 20

y = 123.1(1.069)²⁰

y = 123.1 * 3.798

y = 467.5

y ~ 468

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Answer:3200 m²

Step-by-step explanation: length times width so 80*40

Answer: 3,200 meters

Step-by-step explanation:

Area of a rectangle = length times width

A=lw

A=80(40)

A=3,200 meters

The engagement score in 4 months ago would be 7.69.

Future worth is the value of an asset in the future. It estimates the nominal amount of money that a certain quantity of money will be "worth" at a specified moment in the future under the assumption of a particular interest rate and is calculated by multiplying the present value by the accumulation function.

In four months, we must determine the future value of the engagement score.

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value = 4.89  

R = rate of increase = 12%

N = number of months = 4

4.89 ( 1.12)^4 = 7.69

Therefore the engagement score in 4 months ago would be 7.69.

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Answer:   m∡Ɪ  = 41.8 °

___

Step-by-step explanation:

Use the following mnemonic for right triangles:
 SOH  CAH  TOA ;

in which:
sin   =  opposite/ hypotenuse ;

cos  =  adjacent/ hypotenuse ;

tan =  opposite/adjacent ;

___
We shall solve for the unknown " m∡Ɪ " ;
 that is:  "the measure of Angle Ɪ ".

From looking at the image attached:
 Let's take at  ∡Ɪ .

  We see that the opposite side = 6 ; and that the hypotenuse = 9 ;
So, from the mnemonic mentioned ^above.

We use the SOH component:
    sin Ɪ = opposite /adjacent ;

             = 6/9 ;

      which can be reduced:
             " 6/9 =  (6÷3)/(9÷3) = (2/3) ."

So:  sin Ɪ = (2/3) ;

To solve for  Ɪ ;  

  We use a calculator; to take the (arcsin) of Each Side of the equation:

     [(arcsin) sin Ɪ ]  = (arcsin) ( [tex]\frac{2}{3}[/tex] ) ;

 to get:  Ɪ = 41.810314895779 ;
      [Source used:  Web2.0 Online Scientific Calculator].

Now, we shall round this calculated decimal number to the nearest tenth;  that is;  to the nearest single decimal point that appears after the non-decimal value.
    We have: 41.81... ;

So:  41.8 ? Or: 41.9 ?  If the digit in the hundredth place [that is, the next occurring decimal] is "4 or lesser" [i.e. "0, 1, 2, 3, or 4"] ; then we round down.  

  If the digit in the hundredth place [that is, the next occurring decimal] is "5 or greater" [i.e. "5, 6, 7, 8, or 9"] ; then we round down.

   In our case, we have:  "41.81..." ;
 →  As such, we round down to "41.8" .

  The correct answer is  " m∡Ɪ  = 41.8 °

___
I hope this answer and explanation are helpful to you!

  Best wishes!
___

The equation to model the population is P = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30

Here the population P of a small town, measured in hundreds, is modeled by the inverse of the function,P−1(t) = 20ln(40t − 1200)

where t is measured in years.

We need to find an equation to model the population.

let y = [tex]p^{-1}[/tex](t)

where t is measured in years.

We need to find an equation to model the population.

20[tex]ln[/tex](40y - 1200) = t

[tex]ln[/tex](40y - 1200) = t/20

[tex]e^{ln(40y - 1200)}[/tex] = [tex]e^{0.05t}[/tex]

(40y - 1200) = [tex]e^{0.05t}[/tex]

40y = [tex]e^{0.05t}[/tex] + 1200

y = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30

Now, we determine the initial value.

P(0) = [tex]\frac{1}{40}[/tex] + 30

P(0) = 30

The equation to model the population is P = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30

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The original amount of the bill exists $ 90.

What is the Gratuity amount?

A gratuity exists as a totality of money customarily provided by a customer to specific service sector workers such as hospitality for the service they have executed, in addition to the basic expense of the service.

Gratuity on a restaurant bill = $18 and tip = 20%.

To find the original amount of the bill.

The tip exists directly proportional to the total cost = $ 90

18/(20%)

=(18/(20/100))

=$90

Therefore, the original amount of the bill exists as $ 90.

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The equation of the line passes through (-2, -1) and parallel to y = -1/3x - 5 is y = - 1 / 3 x - 5 / 3

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

The equation of the line passes through (-2, -1) and parallel to y = -1/3x - 5

Therefore, the slope of the line is - 1 / 3.

Parallel lines have the same slopes.

Therefore, let's find the y-intercept using (-2, -1)

y = - 1 / 3 x + b

-1  = - 1 / 3 (-2) + b

b = -1 - 2 / 3

b =  -3 - 2/ 3

b = - 5 / 3

Therefore, the equation is y = - 1 / 3 x - 5 / 3

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The answer to the given question is Yes, we can. We can conclude that there are two distinct subsets of the 14 3-digit numbers in the list which have the same sum.

There are [tex]2^{14}[/tex] = 16384 subsets. Since each number goes in the range from 0 through 999 and there are at most 14 3-digit numbers in a subset, the sum of any subset of the numbers will be in the range from 0 through 14 x 1000.

So, there are at most 14001 possible values for the sum of a subset of the 3-digit numbers. Since 16384 > 14001, if each subset is plotted to the value of its sum, then there need to be at least two different subsets which are plotted on to the same value.

For that reason, there are at least two different subsets whose numbers sum to the same value.

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B) m is the independent variable and p is the dependent variable.

Its given in question,

The number of people they will be able to serve depends on the number of meals they prepare. p = the number of people Florence and Anna will be able to serve m = the number of meals Florence and Anna prepare.

Which means people served depends on the meals prepared.

Therefore, p depends on m.

Hence, m is the independent variable and p is the dependent variable.

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Answer:

it hi

Step-by-step explanation:

The vertex of y=|2x+4|+5 is (-2, 5) and Range of the y=|2x+4|+5 is 5≤y<∞

A relation is a function if it has only one y-value for each x-value.

We need to find the vertex and range of y=|2x+4|+5

f(x)=2x+4

f of x is equal to zero

2x+4=0

Subtract 4 from both sides

2x=-4

Divide both sides by 2

x=-2

y=|2x+4|+5

=|2(-2)+4|+5=|-4+4|+5=5

Hence vertex is (-2, 5)

The range of the y=|2x+4|+5 is 5≤y<∞

Hence vertex is (-2, 5) and Range of the y=|2x+4|+5 is 5≤y<∞

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In the word hawks, it is possible to rearrange the letters if none repeat and the letter w must go last as follows,

In the word “HAWKS” there are 24 possible ways to rearrange the letters so that no letter can be repeated and letter ‘w’ must go last.

It can be solved using Factorial concept.

Given word = “HAWKS”

Number of letters in Hawks = 5

There is a condition that W must be the last letter. So according to that we are now left with the 4 letters that we have to place so that no letter should be repeated.

By using the Factorial concept, (solve the numbers of letters left)! which is 4!

4! = 4x3x2x1

    = 24

By this way we can say that there are 24 possible ways to rearrange the letters of “Hawks” by fulfilling all the conditions.

Hence there are 24 possible ways to rearrange the letters of Hawks.

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Answer:

77.6 m

Step-by-step explanation:

Angle of Depression

If a person stands at a point and looks down at an object, the angle between their horizontal line of sight and the object is called the angle of depression.

To find how far the bridge is from the front of the boat, model as a right triangle and solve using the tan trigonometric ratio.

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given information:

As the teenagers' line of sight is 1.8 m above the bridge, the side of the right triangle opposite the angle of depression is:

Therefore:

[tex]\implies \sf \tan21^{\circ}=\dfrac{29.8}{A}[/tex]

[tex]\implies \sf A=\dfrac{29.8}{\tan21^{\circ}}[/tex]

[tex]\implies \sf A=77.6\;m\;\;(nearest\;tenth)[/tex]

Answer:

  ∆APQ is isosceles, so sides AP, AQ are congruent

Step-by-step explanation:

You want to show that AP≅AQ in the given figure.

The Angles of Intersecting Chords Theorem tells you that the angle where chords cross is half the sum of the intercepted arcs. Here, that means ...

  ∠APY = (arc BX +arc AY)/2

  ∠AQX = (arc AX +arc CY)/2

Given that arc AX ≅ arc BX, and arc AY ≅ arc CY, we can substitute for BX and CY to get ...

  ∠APY = (arc AX +arc AY)/2

  ∠AQX = (arc AX +arc AY)/2

Two angles equal to the same thing are equal (substitution property), so ...

  ∠APY ≅ ∠AQX

These are base angles in the isosceles triangle APQ, so their opposite sides, AQ and AP, respectively, are congruent.

  AP ≅ AQ

The range is (-∞,∞),{y∣y∈R}

The range is the set of all valid y values. Using the graph to find the range.

Interval Notation:  (-∞,∞)

Range: (-∞,∞),{y∣y∈R}

Graph:

In mathematics, a graph is a logical visual representation of any data. The graph shows the relationship between the values of the variables. In graph theory, a group of objects that are related in some way are represented by a graph. In essence, the edges of the objects are representations of the connections between the vertices, or nodes, of the objects. Numerous graph types are employed in mathematics and statistics to visually display data. The field of graph theory is concerned with the study of points and lines. It is a subfield of mathematics with a graph analysis emphasis.

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The cubic polynomial for the given function in question can be written as:  x³ -2x² - 16x+ 32 = 0.

What is polynomial?

All the exponents of an algebraic expression called a polynomial must be whole numbers. Any polynomial must have non-negative integer variable exponents. We cannot divide a polynomial by a variable even though it contains variables and constants.

From the table given, we can see the function f(x) = 0 when, x = -4, 2, 4

It means, x+4 = 0, x-4 = 0, x-2 = 0

Multiplying these equations,

(x+4)(x-4)(x-2) = 0

(x²-4x+4x-16)(x-2) = 0

x³- 16x -2x² + 32 = 0

Therefore the cubic polynomial for the given function is:

x³ -2x² - 16x+ 32 = 0

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After t=1 or t=4 seconds, the ball will reach 20 meters high.

The ball will go up to 31.25 meters high.

After 4.5 seconds, the ball will be at a height of 11.25 meters.

What is a quadratic equation?

A quadratic equation is any equation in algebra that can be rearranged in standard form as ax²+bx+c=0, where x is an unknown value and a, b, and c are known numbers.

For 19)

The given equation is h = 25t - 5t²

Now the height of the ball is 20 meters, so put h = 20, so the equation will become,

               20 = 25t - 5t²

         ⇒ 5t² -25t + 20 = 0

         ⇒ t² - 5t + 4 = 0

       finding factors, we get

              t² - 4t - t + 4 = 0

              t (t - 4) - 1(t - 4) = 0

                    (t - 4)(t - 1) = 0

                t = 4 seconds  (or) t = 1 second.

For 20)

To find the maximum height, we have to differentiate the given function with respect to the 't'

so differentiating 'h' with respect to 't', we get

 dh/dt = 25 - 10t

dh/dt = velocity.

  v = 25 - 10t,

The maximum height will attain at v = 0,

  25 - 10t = 0

   ⇒ t = 2.5 seconds

so at t = 2.5 seconds, the ball will achieve its maximum height.

put t = 2.5 in the given function, we get

         h = 25(2.5) - 5(2.5)²

         h = 62.5 - 31.25

         h = 31.25 meters.

For 21)

        Put t = 4.5 seconds,

         h = 25(4.5) - 5(4.5)²

         h = 112.5 - 101.25

         h = 11.25 meters.

Hence,

After t=1 or t=4 seconds, the ball will reach 20 meters high.

The ball will go up to 31.25 meters high.

After 4.5 seconds, the ball will be at a height of 11.25 meters.

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The value of x = 6 cm

The hypotenuse of a right triangle is its longest side. In other words, the hypotenuse is the side opposite the right angle.

Given that

Adjacent side = 12cm

Angle = 26

We must determine the value of x.

Here we have to use the tan ratio to find the value of x.

tan θ = opposite side/adjacent side

tan 26 = x / 12

Now Multiplying both sides by 12, we get

x = 12 tan 26               [tan 35 = 0.7]

x = 12 x 0.5

x = 6

Therefore, the value of x = 6 cm

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Answer:

37.5

Step-by-step explanation:

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Answer:

Total cost for her new boots is $71.74!

Step-by-step explanation:

The range of possible values of X are X>12.5

In mathematics, the range of a function can refer to one of two closely related concepts:

1. The function's codomain

2. The function's image

In mathematics, a function is an expression, rule, or law that explains a relationship between one variable (the independent variable) and another variable (the dependent variable).

A function is a sort of rule that generates a single output for a single input. In mathematics, a function is an expression, rule, or law that explains a relationship between one variable and another variable.  A good example is Y=X². You will only get one output for y if you enter anything for x. We can say that y is a function of X because X represents the input value.

By using Hin-ges theorem,

(4X-10) > 40

4X > 50

X > 12.5

The range of possible values of X are X>12.5

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