You roll two six-sided dice. What is the probability that the sum is equal to 5? Write your answer as a fraction in simplest form.

Answer:

180/7

Step-by-step explanation:

Direct variation:

y varies directly as k

y = kx

y varies directly as √x

y = k√x

We need to find k. We use the given data to find k.

y = 12 when x = 49

12 = k√49

12 = 7k

k = 12/7

The equation  of direct variation is

y = (12/7)√x

x = 225

y = (12/7)√225

y = (12/7)(15)

y = 180/7

The given algebraic equation  formula i.e., [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b of -3 and -5 respectively.

As per the question statement, we are supposed to verify the algebraic equation formula

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

We are given that a = -3 and b = -5

Now substituting the values of a and b in the  algebraic equation formula

[tex](a^{2} -b^{2} )=(a+b)(a-b)\\LHS = (a^{2} -b^{2} )\\LHS= ([-3]^{2} -[-5]^{2} )\\LHS=(9-25)\\LHS = -16[/tex]

LHS = Left hand side of the equation

Now considering RHS i.e., Right hand side

[tex]RHS = (a+b)(a-b)\\RHS = ([-3]+[-5])([-3]-[-5])\\RHS= (-8)(2)\\RHS = -16[/tex]

As Left Hand Side LHS = Right Hand Side RHS

Hence the equation, [tex](a^{2} -b^{2} )=(a+b)(a-b)[/tex] is verified for the given values of a and b and is true for all real values of a and b.

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Answer:

He needs to get 100% on his next test

Explanation:

(59 + 80 + 65 + 96 + 100) / 5

Answer:

4,      -1,         5,          -2

Step-by-step explanation:

Answer:

A = 26          B = 82

Step-by-step explanation:

The angle A = 180 - ∅

So A is:

180 - (4x+10)

180 - 4x - 10

170 - 4x

The total angle of a triangle is 180, so A + B + C = 180

(170 - 4x) + (2x + 10) + 72 = 180

170 - 4x + 2x + 10 + 72 = 180

170 - 2x +82 = 180

252 - 2x = 180

252 - 180 = 2x

72 = 2x

72/2 = x

36 = x

A = (170 - 4x) = (170 - 4(36)) = 26

B = (2x + 10) = (2(36) + 10) = 82

C = 72

Answer:

630 seconds

Step-by-step explanation:

1 minute = 60 seconds

Number of minutes × Number of seconds per minute = Number of seconds in total

60 × 10 ½ = 630 seconds

Hope this helped! ^^

The polynomial representing the area of the is 49n² - 25

The formula for area of a square is expressed as;

Area = a²

Where a is the side length

From the image shown, we can see that the side length takes the value (7n - 5)

Substitute the value into the formula

Area = a²

Area = (7n - 5)²

Area = (7n - 5) ( 7n + 5); this is so because of the difference of two squares

Expand the bracket

Area = 49n² + 35n - 35n - 25

collect like terms

Area = 49n² - 25

Thus, the polynomial representing the area of the cube is 49n² - 25

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Answer:

sometimes

Step-by-step explanation:

There are several ways that dilation is used in real life. Here are several:

In graphic design. I actually do some graphic design, and I use dilation a lot. It is common to dilate photos to fit the space that you want it to fit.

In police work and crime investigation. Detectives and police dilate photos to see smaller details and evidence.

In architecture. It is normal for architects to make a prototype of their design or building. In order to make the building true to the prototype, they must dilate the scale and measurements.

In the doctor's office. Dilation is used in eye exams so that the eye doctor can view the patient's eye better. After a while it will slowly reduce in size and return back to normal.

HOW TO DO???

- First you have to find how much money does she get per hour on each day

- Then add the amounts together

SLOVE

Lisa get: 55 : 5= 11$ per hour on Friday

Lisa get: 88 : 8= 11$ per hour on Saturday

Lisa get: 33 : 3= 11$ per hour on Sunday

At the end Lisa get: 11$ x 3= 33$  per hour at her job

{ I think my English isn't very good either because I'm just intermediate so I hope you understand it.}

Answer:

D Reflect across the line y = -3

Step-by-step explanation:

The only way you can divide the trapezoid so that there are two congruent parts is when you draw a line on y=-3.

Answer:

the anser in 60

Step-by-step explanation:

Let the original number be x.

According to the question we can write as (2/3)x+20x

On rearranging x−(2/3)x=20

Now taking the L.C.M od 1 and 3 is 3

(3x−2x)/3=20

x/3=20

Again by transposing x=60

So the original number is 60

Answer:

6

Step-by-step explanation:

6 x 6 = 36

Answer:

Step-by-step explanation:

3z2 − 4z + 103z2 −4z + 10

3z2  + − 4z+ 103z2 +− 4z + 10

3z2  +− 4z+ 103z2 + − 4z + 10

( 3z2  + 103z2 ) + ( −4z+−4z ) + ( 10 )

106z2 + − 8z + 10

4 people can go to the amusement park.

Let the number of people that can go to amusement park be x.

The parking fee will be paid once only, while cost of ticket will be multiplied based on the number of people.  

Forming equation as per the given information in question -

11.25 + 35.75 × x = 154.25

Solving the equation as per the operators -

Shifting 11.25 to Right Hand Side of the equation

35.75x = 154.25 - 11.25

Performing subtraction on Right Hand Side of the equation

35.75x =  143

Shifting 35.75 to Right Hand Side of the equation

x = 143 ÷ 35.75

Performing division on Right Hand Side of the equation

x = 4

Therefore, 4 people can go to the amusement park.

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Answer:

So what's M and N?

Step-by-step explanation:

Answer:

0.2888888889

Step-by-step explanation:

d=m/v

v=15×5×3=225

d=65/225

d=0.2888888889g/cm³

Answer:

0.29 g/cm³

Explanation:

[tex]\sf density \ (g/cm^3) = \dfrac{mass \ (g)}{volume \ (cm^3)}[/tex]

Here given following:

Find density:

[tex]\sf \rightarrow density = \dfrac{65}{225}[/tex]

[tex]\sf \rightarrow density = 0.2888...[/tex]

[tex]\sf \rightarrow density = 0.29[/tex]

Since both triangles are congruent, then we can conclude that AC = BD by Angle - Side - Angle congruence theorem.

In ΔOAC and ΔODB, we have the following observations

CO = DO because it is shown that they are congruent

∠AOC = ∠BOD because vertical angles are congruent

∠ACO = ∠BDO because we are given that they are congruent

Now, the congruency theorem that we can use here is ASA which means Angle - Side - Angle. This implies that 2 corresponding angles and the included side are congruent.

If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by Angle - Side - Angle congruence theorem.

Since both triangles are congruent, then we can conclude that AC = BD by Angle - Side - Angle congruence theorem.

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[tex]\stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} \\\\\\ 6\cdot 2\frac{3}{4}\implies \cfrac{6}{1}\cdot \cfrac{11}{4}\implies \cfrac{66}{4}\implies \cfrac{33}{2}\implies {\LARGE \begin{array}{llll} 16\frac{1}{2} \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{mixed}{3\frac{1}{3}}\implies \cfrac{3\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{10}{3}} ~\hfill \stackrel{mixed}{3\frac{2}{5}}\implies \cfrac{3\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{17}{5}} \\\\\\ -3\frac{1}{3}\cdot -3\frac{2}{5}\implies -\cfrac{10}{3}\cdot -\cfrac{17}{5}\implies +\cfrac{170}{15}\implies \cfrac{34}{3}\implies {\LARGE \begin{array}{llll} 11\frac{1}{3} \end{array}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} ~\hfill \stackrel{mixed}{8\frac{2}{3}}\implies \cfrac{8\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{26}{3}} \\\\\\ -4\frac{1}{2}\cdot 8\frac{2}{3}\implies -\cfrac{9}{2}\cdot \cfrac{26}{3}\implies -\cfrac{234}{6}\implies \cfrac{-39}{1}\implies \text{\LARGE -39} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{mixed}{1\frac{5}{6}}\implies \cfrac{1\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{11}{6}} \\\\\\ 1\frac{5}{6}\cdot (-9)\implies \cfrac{11}{6}\cdot \cfrac{(-9)}{1}\implies -\cfrac{99}{6}\implies -\cfrac{33}{2}\implies \LARGE \begin{array}{llll} -16\frac{1}{2} \end{array}[/tex]

Answer:

∠1 is 101 ∠4 is 79 and ∠2 is 79

Step-by-step explanation:

This is because ∠1 is a vertical angle of ∠3 so they have the same angle

For ∠4 and ∠2 you would do 101-180 because they are supplementary do they add up to 180

Number of bags per site tested before 2012 based on study it dropped by 62% down to 80 bags per site in 2012 is 129 (approximately).

As given,

In 2012, bag per site tested dropped by 62%

Let n be the number of bags per site before 2012

As per condition,

62% of n = 80

⇒(62/100) × n = 80

⇒ n = (80 × 100)/62

      = 129.03

      ≈ 129

Therefore, number of bags per site tested before 2012 based on study it dropped by 62% down to 80 bags per site in 2012 is 129 (approximately).

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Answer:

For f (x):

f (x) = (x + 3) ^ 2 - 2

For x = -1

f (-1) = (-1 + 3) ^ 2 - 2

f (-1) = (2) ^ 2 - 2

f (-1) = 4 - 2

f (-1) = 2

For x = 3

f (3) = (3 + 3) ^ 2 - 2

f (3) = (6) ^ 2 - 2

f (3) = 36 - 2

f (3) = 34

AVR = ((34) - (2)) / ((3) - (- 1))

AVR = 8

For g (x):

linear graph with and intercept of negative 3 over 2 and x intercept of 3

y = mx + b

b = -3/2

For me we have:

0 = m (3) - 3/2

3m = 3/2

m = 1/2

The function g (x) is:

g (x) = (1/2) x - 3/2

For x = -1

g (-1) = (1/2) (- 1) - 3/2

g (-1) = -1/2 - 3/2

g (-1) = -4/2

g (-1) = -2

For x = 3

g (3) = (1/2) (3) - 3/2

g (3) = 3/2 - 3/2

g (3) = 0

AVR = ((0) - (- 2)) / ((3) - (- 1))

AVR = 1/2

For h (x):

Using the table we have:

AVR = ((62) - (14)) / ((3) - (- 1))

AVR = 12

Step-by-step explanation:

Answer:

from least to greatest:

1) g (x)

2) f (x)

3) h (x)

Step-by-step explanation:

The value of expression using PEMDAS rule is 28 .

Given : expression [ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )

To find : value of expression

Calculation : Using V-BODMAS

[ 8 ( 2 ) - [tex]( 4 )^{2}[/tex]] + 7 ( 4 )

= [ ( 8 * 2 ) - ( 4 * 4 ) ] + ( 7 * 4 )

= [ 16 - ( 4 * 4 ) ] + ( 7 * 4 )

= [ 16 - 16 ] + ( 28 )

= [ 0 ] + ( 28 )

= 28

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The median of all these numbers in dollars is 7.5.

When the no. of given data are odd we arrange those nos. in an order increasing or decreasing order and the middle no. is the median of the given odd numbers.

According to the given question the following values represent the amount of money (in dollars) 10 people have in their wallets: 10, 12, 19, 5, 6, 8, 1, 13, 4, 7 and we have to find the median.

First we observe that no. of people is even so there will be two middle nos.

Now lets arrange these nos. in an order from least to greatest which is

1, 4, 5, 6, 7, 8, 10, 12, 13, 19 in this 7 and 8 are middle numbers.

So, to find the median of all these nos. we will divide these two middle nos. by 2.

∴  ( 7 + 8 )/2

= 15/2

= 7.5.

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Answer:

1.(x-3)(x-5)

2.(y+2)(y+9)

3.(x+4)(x-5)

4.(x+1)(x+7)

5.(n-7)(n+8)

The piecewise function that describes what the instructor charges is; f(x) = 500x , 0 < x ≤ 10

400x , 10 < x < 25

350x , x ≥ 25

Let x represent the number of participants and let y represent the charge per participant.

Now, y depends on x, and as such we can say that;

f(x) = y

For, 0 < x ≤ 10, the total charges is 500x,

f(x) = 500x , 0 < x ≤ 10

For 10 < x < 25, total charge is 400x,

f(x) = 400x , 10 < x < 25

For x ≥ 25, the total charge is 350

f(x) = 350x x ≥ 25

Therefore, we can say that;

f(x) = 500x , 0 < x ≤ 10

400x , 10 < x < 25

350x , x ≥ 25

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Write the piecewise function that describes what the instructor charges.

[tex]\cfrac{2}{3}\left( \cfrac{9}{10} \right)\left( \cfrac{1}{2} \right)\implies \cfrac{2}{3}\cdot \cfrac{9}{10}\cdot \cfrac{1}{2}\implies \cfrac{9}{3}\cdot \cfrac{1}{10}\cdot \cfrac{2}{2}\implies 3\cdot \cfrac{1}{10}\cdot 1\implies \cfrac{3}{10}[/tex]

Answer:

p = 12, q = 16,

Step-by-step explanation: