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MAVERICK [17]
2 years ago
6

You earn $35 for washing 7 cars. How much do you earn for washing 4 cars?

Mathematics
1 answer:
Gre4nikov [31]2 years ago
5 0

Answer:

The earning by washing four cars is $20

Step-by-step explanation:

You earn $35 for washing 7 cars.

The following steps can be used in order to determine the earning by washing four cars:

Step 1 - The unitary method can be used in order to determine the earning by washing four cars.

Step 2 - According to the given data, the earning by washing seven cars is $35.

Step 3 - So, the earning for washing four cars is given by:

4/7 x 35

Step 4 - Simplify the above expression.

140/7

= $20

So, the earning by washing four cars is $20.

You might be interested in
A manufactured lot of buggy whips has 20 items, of which 5 are defective. A random sample of 5 items is chosen to be inspected.
dimulka [17.4K]

Answer:

a. 39.55%

b. 44.02%

Step-by-step explanation:

We have the following data:

n = 5

x = 1

p = 5/20 = 0.25

to. If the sampling is done with replacement.

We apply the binomial distribution formula, which is as follows:

P = nCx * (p ^ x) * ((1-p) ^ (n-x))

Where nCx, is a combination, and is equal to:

nCx = n! / x! * (n-x)!

replacing we have:

5C1 = 5! / 1! * 4! = 5

replacing in the main formula:

P = 5 * (0.25 ^ 1) * ((1- 0.25) ^ (5-1))

P = 0.3955

that is, without replacing the probability is 39.55%

b. if the sampling is done without replacement.

Here it is a little different from the previous one, but what you should do is calculate three cases,

the first was the one at point a, when n = 5 and x = 1

5C1 = 5! / 1! * 4! = 5

the second is when n = 20 and x = 5, this is all possible scenarios.

20C5 = 20! / 5! * 15! = 15504

and the third is when n = 15 (20-5) and x = 4 (5-1), which corresponds to the cases when none were damaged

15C4 = 15! / 4! * 11! = 1365

In the end, it would be:

P = (5C1 * 15C4) / 20C5

Replacing:

P = 5 * 1365/15504

P = 0.4402

Which means that without replacing the probability is 44.02%

7 0
3 years ago
I GIVVEEEEEE BRAINLILST
Wewaii [24]

Answer: 1/2?

Step-by-step explanation:

4 0
2 years ago
Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.
just olya [345]

Answer:

Find the answers below

Step-by-step explanation:

Using m<X as the reference angle

Opposite YZ = 7

Adjacent  XY = 10

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinX = opp/hyp

sinX =YZ/XZ

sinX = 7/√149

For cos X

cos X = adj/hyp

cos X =10/√149

Using m<Z as reference angle;

Opposite XY = 10

Adjacent  YZ = 7

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinZ = opp/hyp

sinZ =10/√149

sinZ = 7/√149

For cos Z

cosZ = 7/√149

7 0
2 years ago
Population growth is an example of _____________?
olga2289 [7]

Answer:

The answer is 1. an exponential pattern ,friend (:

4 0
3 years ago
What are the solutions of 4(x+6)^2=52
zysi [14]

ANSWER: 1.211 or 13.211

Step-by-step explanation:

STEP

1

:

1.1     Evaluate :  (x-6)2   =    x2-12x+36  

Trying to factor by splitting the middle term

1.2     Factoring  x2-12x-16  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -12x  its coefficient is  -12 .

The last term, "the constant", is  -16  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -16 = -16  

Step-2 : Find two factors of  -16  whose sum equals the coefficient of the middle term, which is   -12 .

     -16    +    1    =    -15  

     -8    +    2    =    -6  

     -4    +    4    =    0  

     -2    +    8    =    6  

     -1    +    16    =    15  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

1

:

 x2 - 12x - 16  = 0  

STEP

2

:

Parabola, Finding the Vertex

2.1      Find the Vertex of   y = x2-12x-16

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.  

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.  

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   6.0000  

Plugging into the parabola formula   6.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 6.00 * 6.00 - 12.0 * 6.00 - 16.0

or   y = -52.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-12x-16

Axis of Symmetry (dashed)  {x}={ 6.00}  

Vertex at  {x,y} = { 6.00,-52.00}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-1.21, 0.00}  

Root 2 at  {x,y} = {13.21, 0.00}  

Solve Quadratic Equation by Completing The Square

2.2     Solving   x2-12x-16 = 0 by Completing The Square .

Add  16  to both side of the equation :

  x2-12x = 16

Now the clever bit: Take the coefficient of  x , which is  12 , divide by two, giving  6 , and finally square it giving  36  

Add  36  to both sides of the equation :

 On the right hand side we have :

  16  +  36    or,  (16/1)+(36/1)  

 The common denominator of the two fractions is  1   Adding  (16/1)+(36/1)  gives  52/1  

 So adding to both sides we finally get :

  x2-12x+36 = 52

Adding  36  has completed the left hand side into a perfect square :

  x2-12x+36  =

  (x-6) • (x-6)  =

 (x-6)2

Things which are equal to the same thing are also equal to one another. Since

  x2-12x+36 = 52 and

  x2-12x+36 = (x-6)2

then, according to the law of transitivity,

  (x-6)2 = 52

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-6)2   is

  (x-6)2/2 =

 (x-6)1 =

  x-6

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x-6 = √ 52

Add  6  to both sides to obtain:

  x = 6 + √ 52

Since a square root has two values, one positive and the other negative

  x2 - 12x - 16 = 0

  has two solutions:

 x = 6 + √ 52

  or

 x = 6 - √ 52

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-12x-16 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =   -12

                     C   =  -16

Accordingly,  B2  -  4AC   =

                    144 - (-64) =

                    208

Applying the quadratic formula :

              12 ± √ 208

  x  =    ——————

                     2

Can  √ 208 be simplified ?

Yes!   The prime factorization of  208   is

  2•2•2•2•13  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 208   =  √ 2•2•2•2•13   =2•2•√ 13   =

               ±  4 • √ 13

 √ 13   , rounded to 4 decimal digits, is   3.6056

So now we are looking at:

          x  =  ( 12 ± 4 •  3.606 ) / 2

Two real solutions:

x =(12+√208)/2=6+2√ 13 = 13.211

or:

x =(12-√208)/2=6-2√ 13 = -1.211

6 0
3 years ago
Read 2 more answers
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