Given that the commuter used public transportation, find the probability that the commuter had a commute of 60 or more minutes.

Answer:

x=-60/24 or -5/2

Step-by-step explanation:

u have to find X

2/4x - 1/2 = 1/3 + 5/6x

subtract 2/4x from both sides

to do that u need to have common denominator

2/4= 6/12

5/6=10/12

-1/2=1/3+4/12x

subtract 1/3 on both sides and u need common denominator

-1/2=-3/6

1/3=2/6

-5/6=4/12x

multiply 12/4 on both sides

x=-60/24

Answer:

x=-5/2

Step-by-step explanation:

2/4x-1/2=1/3+5/6x

-5/6x           -5/6x

2/4x-5/6x-1/2 =1/3

+1/2                  +1/2

6/12x-10/12x=2/6+3/6

-4/12x=5/6

x=5/6:(-4/12)=5/6*(-12/4)=-5/2

x=-5/2

Answer:

Step-by-step explanation:

18 degrees

Answer:

2989.12

Step-by-step explanation:

238.00+232.50+54.88+236.00= 760.88

3750-760.88=2989.12

Answer:

36 minutes past 1, or 1:36

Step-by-step explanation:

A watch normally has an hour hand that does one revolution in 12 hours.

It takes 1 hour to go from the 1 o'clock position to the 2 o'clock position.

Since 1 hour equals 60 minutes, it takes 60 minutes to go from the 1 o'clock position to the 2 o'clock position.

The hour hand is 3/5 of the way from 1 to 2, so the number of minutes past 1 o'clock is 3/5 of 60 minutes.

3/5 of 60 minutes =

= 3/5 * 60 minutes

= 3/5 * 60/1 minutes

= 180/5 minutes

= 36 minutes

The time is 36 minutes past 1, or 1:36

Answer:

8:24

Step-by-step explanation:

dont ask me

Answer:

x =(7-√217)/2=-3.865

x =(7+√217)/2=10.865 mark brainliest please

Step-by-step explanation:

   Factoring  x2-7x-42

The first term is,  x2  its coefficient is  1 .

The middle term is,  -7x  its coefficient is  -7 .

The last term, "the constant", is  -42

Step-1 : Multiply the coefficient of the first term by the constant   1 • -42 = -42

Step-2 : Find two factors of  -42  whose sum equals the coefficient of the middle term, which is   -7 .

     -42    +    1    =    -41

     -21    +    2    =    -19

     -14    +    3    =    -11

     -7    +    6    =    -1

     -6    +    7    =    1

     -3    +    14    =    11

     -2    +    21    =    19

     -1    +    42    =    41

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  1  :

 x2 - 7x - 42  = 0

Step  2  :

Parabola, Finding the Vertex :

2.1      Find the Vertex of   y = x2-7x-42

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   3.5000  

Plugging into the parabola formula   3.5000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 3.50 * 3.50 - 7.0 * 3.50 - 42.0

or   y = -54.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-7x-42

Axis of Symmetry (dashed)  {x}={ 3.50}

Vertex at  {x,y} = { 3.50,-54.25}

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-3.87, 0.00}

Root 2 at  {x,y} = {10.87, 0.00}

Solve Quadratic Equation by Completing The Square

2.2     Solving   x2-7x-42 = 0 by Completing The Square .

Add  42  to both side of the equation :

  x2-7x = 42

Now the clever bit: Take the coefficient of  x , which is  7 , divide by two, giving  7/2 , and finally square it giving  49/4

Add  49/4  to both sides of the equation :

 On the right hand side we have :

  42  +  49/4    or,  (42/1)+(49/4)

 The common denominator of the two fractions is  4   Adding  (168/4)+(49/4)  gives  217/4

 So adding to both sides we finally get :

  x2-7x+(49/4) = 217/4

Adding  49/4  has completed the left hand side into a perfect square :

  x2-7x+(49/4)  =

  (x-(7/2)) • (x-(7/2))  =

 (x-(7/2))2

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

  x2-7x+(49/4) = 217/4 and

  x2-7x+(49/4) = (x-(7/2))2

then, according to the law of transitivity,

  (x-(7/2))2 = 217/4

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-(7/2))2   is

  (x-(7/2))2/2 =

 (x-(7/2))1 =

  x-(7/2)

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

  x-(7/2) = √ 217/4

Add  7/2  to both sides to obtain:

  x = 7/2 + √ 217/4

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

  x2 - 7x - 42 = 0

  has two solutions:

 x = 7/2 + √ 217/4

  or

 x = 7/2 - √ 217/4

Note that  √ 217/4 can be written as

 √ 217  / √ 4   which is √ 217  / 2

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-7x-42 = 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   =    -7

                     C   =  -42

Accordingly,  B2  -  4AC   =

                    49 - (-168) =

                    217

Applying the quadratic formula :

              7 ± √ 217

  x  =    —————

                   2

 √ 217   , rounded to 4 decimal digits, is  14.7309

So now we are looking at:

          x  =  ( 7 ±  14.731 ) / 2

Two real solutions:

x =(7+√217)/2=10.865

or:

x =(7-√217)/2=-3.865

Answer:

x^2 - 7x - 42

x^2 - x (21 - 14 ) - 42

x^2 - 21x + 14x -42

7x ( x - 3) + 14 ( x- 3)

(x -3) (7x + 14)

hope this helps you

Answer:

to find volume you multiply length x width x height

Step-by-step explanation:

5 x 3.5 x 6= 105

Answer:

5 x 3.5 x 6= 105

Step-by-step explanation:

PLZZZ give me brainliest

Answer:

they are equivalent

Step-by-step explanation:

8/6

Divide the top and bottom by 2

4/3

16/12

Divide the top and bottom by 4

4/3

They are  the same so they are equivalent

Answer:

A

Step-by-step explanation:

This is because vertical angles are always congruent, they cross diagonally which makes them equal to each other.

When two perpendiculars line intersect the angles formed must be a right angle. Hence option b is correct.

The angle can be defined as the one line inclined over other line.

Here, When perpendicular lines intersect each other the angle formed between them is 90 degree. So the angles are right angles.

Thus, when two perpendiculars line intersect the angles formed must be a right angle.

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[tex]\text{You would use the distributive property to get your answer} \\\\\text{This means that you would distribute the 5 to the numbers inside the}\\\text{parenthesis}\\\\\text{When you distribute, you would multiply}\\\\\text{Distribute:}\\\\5(6-1)\\\\5(6)-5(1)\\\\30-5\\\\\text{You would see that this is equal to answer choice C, therefore making}\\\text{C your answer}\\\\\boxed{\text{C). 30 - 5}}[/tex]

Answer:

8

Step-by-step explanation:

thank u god!

Answer:

5+3 = 8!!!! :D

Step-by-step explanation:

Five plus three, is going to equal to eight total.

Answer:

d. 40

Step-by-step explanation:

2x + x +( x + 20) have to all equal 180 degrees in a triangle.

2x + x + x + 20 = 180

2x + 2x + 20 = 180

4x + 20 = 180

4x = 180 - 20

x = (180-20) / 4

x = 160 / 4

x = 40

Answer:

Step-by-step explanation:

This is the answer that was right for me, I just did this question :) Hope this helps! :D

Answer:

B. to show the general tendency of the points in a scatterplot

Step-by-step explanation:

Answer:

18-6×10=-42

Step-by-step explanation:

all i did was put it in my calculator

Answer:

C many solutions

Answer:

The complete table is shown below.

Step-by-step explanation:

The data provided is:

Number Rolled       Observed Frequency       Relative frequency

          1                                     10                                [tex]\frac{10}{60}=\frac{1}{6}[/tex]

         2                                     12                                [tex]\frac{12}{60}=\frac{1}{5}[/tex]

         3                                     10                                [tex]\frac{10}{60}=\frac{1}{6}[/tex]

         4                                     10                                [tex]\frac{10}{60}=\frac{1}{6}[/tex]

         5                                      8                                [tex]\frac{8}{60}=\frac{2}{15}[/tex]

         6                                     10                                [tex]\frac{10}{60}=\frac{1}{6}[/tex]

    TOTAL                                60                                     1

The complete table is shown above.

Answer:

A= 1/5

B.2/15

Step-by-step explanation:

trust me i got it right on edg

Answer:

because

most people like green apples

Answer:

u = -4w+9

Step-by-step explanation:

u - 5 = -4(w-1)

Distribute

u - 5 = -4w +4

Add 5 to each side

u -5+5 = -4w +4+5

u = -4w+9

Answer:

1/ 6

Step-by-step explanation:

Therefore, the required probability is 1/6.

Answer:

1/6

Step-by-step explanation:

Think of drawing 1 student at a time without replacement.

First drawing:

p(boy) = 6/10

Second drawing:

p(boy) = 5/9

Third drawing:

p(boy) = 4/8

p(3 boys) = 6/10 * 5/9 * 4/8 = 3/5 * 5/9 * 1/2 = 3/18 = 1/6

Answer: 1/6

Answer:

Number of nickels: 2,

Number of dimes: 6

Step-by-step explanation:

Say d ⇒ number of dimes, n ⇒ number of nickels; from this we can formulate two equation knowing the cost per dime ⇒ $ 0.1, and the cost per nickel ⇒ $0.05

d + n = 8,

0.1 * d + 0.05 * n = 0.7 ⇒ Let us solve through substitution

d = 8 - n into 0.1 * d + 0.05 * n = 0.7,

0.1 * ( 8 - n ) + 0.05 * n = 0.7,

0.8 - 0.1 * n + 0.05 * n = 0.7,

0.8 - 0.1n + 0.05n = 0.7,

- 0.05n = - 0.1,

Number of nickels: 2 ⇒ Now let us substitute this value into the first equation as to solve for d, dimes

d = 8 - 2,

Number of dimes: 6

Answer:

5/16 and 3/8 are two

Step-by-step explanation:

idk a third

Answer:

the answer is attached to the picture

The volume of a sphere with a radius of 9.9 ft is 4062.3 cubic foot.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of the sphere is 4/3πr³

Radius is 9.9 ft.

Volume =4/3×3.14×(9.9)³

=4/3×3.14×970.3

=12187/3

=4062.3

Hence, the volume of a sphere with a radius of 9.9 ft is 4062.3 cubic foot.

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Answer: The price of the stock yesterday was $78.59

Step-by-step explanation:

p - 6.28=72.31

   +6.28   + 6.28

p= 78.59

Answer:

78.59$

Step-by-step explanation:

p-6.28=72.31

p=72.31+6.28

p=78.59$

Answer:

A

Step-by-step explanation:

Because it's subtracting 2 hours every day, the slope is -2. Also because it's 30 hours, it's 30. Therefore: A.) y=-2x+30 is the answer.

Hopes this Helps!

Answer:

1. 1/2 * 5 * 5

2. 4

3. 7

4. 79

Step-by-step explanation:

IReady test

The volume of the paperweight will be 79.17 cubic inch

A solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms is known as prism

The steps are as follow:

∴ Area of floor = Area of triangle = ah/2

Where a=5 and h=5 from figure given

∴ Area of floor = (5*5)/2 = 12.5 sq.inch

[tex]V_{1} = \frac{1}{3}sh \\V_{1} = \frac{1}{3}*7*\frac{1}{2}*5*5\\V_{1} = 29.17[/tex]

[tex]V_{2} = sh\\V_{2} = 4*\frac{1}{2}*5*5 \\V_{2} = 50[/tex]

∴ Total volume

[tex]=50+29.17\\=79.17[/tex]

Therefore the total volume of paperweight will be 79.17 cubic inch

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Answer:

d= 5.2

[][][]-[][][]

P = √5.2 ^3

P = √5.2 × 5.2 × 5.2

P = √140.608 (plug into calculator)

P = 11.857824421

P = 11.86

The orbital period of Jupiter is 11.86 Earth years.

Answer:

Slope (m) =0

Slope (m) =  

ΔY

ΔX

= 0

θ =  

arctan( ΔY )

ΔX

= 0°

ΔX = 3 – 13 = -10

ΔY = -2 – -2 = 0

Distance (d) = √ΔX2 + ΔY2 = √100 = 10

Answer:

In total there are 30 cups and there are 2 left over

Step-by-step explanation:

The first thing is to clarify the equivalences, we have to:

1 gallon = 4 quarts

1 quart = 2 pints

1 pint = 2 cups

We will pass everything to cups,

1 gallon of orange juice = 16 cups

3 pints of pineapple juice = 6 cups

2 quarts of lemon ‐ lime soda = 8 cups

So in total they would be 16 + 6 + 8 = 30 cups

How to get 2 cups for 14 guests in total would be 28 cups, which means that if 2 cups are left and left over.

Answer:

1/2

Step-by-step explanation:

When you find the sine of an angle, it is the opposite side / hypotenuse. This means that the hypotenuse of this triangle is 2 and the side opposite to 60° is √3. This means that the side adjacent to 60° is 1 (Pythagorean Theorem). When you find the cosine of an angle, it is the adjacent side / hypotenuse, which in this case will be 1 / 2. Hope this helps!

Answer:

1/2.

Step-by-step explanation:

Sine = opposite side / hypotenuse.

The side opposite 60 degrees has length√3 and the hypotenuse = 2.

By Pythagoras the side adjacent to the angle 60 = √( 2^2 - 3)

= 1 unit.

So cos 60 = adjacent / hypotenuse = 1/2.

Answer:

a) Total distance travelled to the nearest foot = 105ft

b) First 5 terms = 12, 9, 6.75, 5.0625, 3.796875

Step-by-step explanation:

From the question above, we can see that this is a geometric series or progression

Formula for geometric progression:

Tn = arⁿ-¹

Where

a = first term

r = common ration

n = number of terms

From the question, we are told that the ball dropped from 16 feet

Hence First term(a) = 16

We are told that the ball rebounds to 3/4 of it's previous height anytime it hits the surface.

Hence, common ratio(r) = 3/4

a) We are told to find total distance to the nearest foot that the ball travelled when it strikes the ground for the 10th time

This means we are to find the sum of the first 10 terms.

Because the ball rises and falls, we would use the rises form

Where the first term = 12 and the number of times is 9 because it rises 9 times

The formula we would use to find this sum is based on if the common ratio is less than or greater than 1

Our common ratio = 3/4, hence it is less than 1.

When r< 1, sum of n terms =

Sn = a(1 - rⁿ)/ 1 - r

It is important to

Where a = 12

r = 3/4

n = 9

Sn = 12( 1 - (3/4)^9) / 1- 3/4

Sn = 104.79ft

Approximately = 105ft

b) First five terms

Using the formula

Tn = arⁿ-¹

Where

a = first term = 12

r = common ration

n = number of terms

First term, n = 1 = 12 × 3/4^(1-1)

= 12 × 3/4 ^(0)

= 12× 1

= 12

Second term, n = 2 = 12 × 3/4^(2-1)

= 12 × 3/4 ^(1)

= 36/4

= 9

Third term, n = 3 = 12 × 3/4^(3-1)

= 12 × (3/4)²

= 6.75

Fourth term, n = 4= 12 × 3/4^(4-1)

= 12 × (3/4)³

= 5.0625

Fifth term, n = 5 = 12 × 3/4^(5-1)

= 12 × (3/4)⁴

= 3.796875

Therefore, the first 5 terms = 12, 9, 6.75, 5.0625, 3.796875

The rebound of the ball from the height is an illustration of a geometric series

(a) The total vertical distance

The given parameters are:

[tex]\mathbf{a = 16}[/tex] -- the first term

[tex]\mathbf{r = \frac 34}[/tex] -- the common ratio

[tex]\mathbf{n = 10}[/tex] -- number of terms

The total vertical distance when it strikes for the 10th time is the sum of nth terms of the geometric series.

So, we have:

[tex]\mathbf{S_n = \frac{a(1 - r^n)}{1- r}}[/tex]

Substitute values for (a), (r) and n

[tex]\mathbf{S_{10} = \frac{16(1 - 3/4^{10)}}{1- 3/4}}[/tex]

Simplify

[tex]\mathbf{S_{10} = \frac{16(0.943)}{0.25}}[/tex]

[tex]\mathbf{S_{10} = 60.352}[/tex]

Hence, the total vertical distance at the 10th rebound is 60.352 feet

(b) The first five terms of this sum

The nth term of a geometric series is:

[tex]\mathbf{T_n = ar^{n-1}}[/tex]

So, we have:

[tex]\mathbf{T_1 = 16}[/tex]

[tex]\mathbf{T_2 = 16 * 3/4 = 12}[/tex]

[tex]\mathbf{T_3 = 12 * 3/4 = 9}[/tex]

[tex]\mathbf{T_4 = 9 * 3/4 = 6.75}[/tex]

[tex]\mathbf{T_5 = 6.75 * 3/4 = 5.0625}[/tex]

Hence, the first five terms of the sum are 16, 12, 9, 6.75 and 5.0625

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