A 6-sided die is rolled 2 times. What is the probability of getting 1 both times? (Give your answer as a fraction in simplest form.

By using the slope​ formula, the slope of the line through the points (0, 0) and (4, 12) is equal to 3.

You can use mental math to find the slope of the line by simply dividing 12 by 3 because the line passes through the origin (0, 0).

In Mathematics and Geometry, the slope of any straight line can be calculated by using this this mathematical equation (expression);

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points located on the line:

Substituting the given points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (12 - 0)/(4 - 0)

Slope (m) = 12/4

Slope (m) = 3.

In conclusion, an equation which represents this line is y = 3x.

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The increase in the price of tacos shifts the demand curve to the left, causing a decrease in the equilibrium price and quantity of hamburgers.

The accompanying supply and demand diagram is depicting the market for hamburgers in your hometown. The event that is given is that the price of tacos increases. This will cause the demand curve to shift to the left, as consumers shift from hamburgers to tacos. As the demand curve shifts to the left, the equilibrium price will decrease and the equilibrium quantity will decrease. This is because the decrease in demand will cause the quantity demanded to fall and the decrease in demand will cause the price to fall. This shift in the supply and demand curves will cause the equilibrium point to move to the left and downward. The new equilibrium price will be lower than the original equilibrium price and the quantity will also be lower.

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a. The profit function P(x) is 10x - 5000.

b. The break even point is at 500 units.

c. If 350 units were sold, the loss was Rs. 1500.

d. The graph of the functions are attached below.

The solutions are obtained using the profit function.

What is profit function?

A profit function is a mathematical relationship that represents the difference produced when the cost function is subtracted from the revenue function. The graph of a profit function shows the optimal combination of revenues and expenses to produce the maximum profit.

a. We are given cost of raw material as Rs. 15 and the fixed cost is Rs. 5000. The product is sold for Rs.25 per unit.

This means that R(x) = 25x

We know that TC= FC + VC(x)

So, TC = 5000 + 15x

Therefore, the profit function will be

⇒Profit = R(x) - TC

⇒Profit = 25x - 5000 - 15x

⇒Profit = 10x - 5000

b. For break even, the profit should be 0.

Therefore,

⇒10x - 5000 = 0

⇒10x = 5000

⇒x = 500

So, the break even will be at 500 units.

c. We are given x=350

Putting this value in profit function, we get

⇒Profit = 10(350) - 5000

⇒Profit = 3500 - 5000

⇒Profit = -1500

So, there is loss of Rs. 1500.

d. The red line represents the cost function and the blue line represents the revenue function.

The break even point is the point where the two lines are meeting.

The area below the break even is the loss area and above it is the profit area.

Hence, the solutions are obtained.

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(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -90 m/s.

(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -62 m/s.

(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -34 m/s.

(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7h^2 + 70h m/s.

(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -7(25-1) + 70(4) = -7*24 + 280 = -168 + 280 = -88 m/s.

(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -7(16-1) + 70(3) = -7*15 + 210 = -105 + 210 = -95 m/s.

(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -7(9-1) + 70(2) = -7*8 + 140 = -56 + 140 = -16 m/s.

(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7(1+h)^2 + 70h = -7(1+h)^2 + 70h m/s. The average velocity of an object over a given period of time is calculated by taking the difference between the final and initial positions, and dividing it by the amount of time elapsed. In this exercise, we are given the position of an object along a line as a function of time, s(t) = -7t^2 + 70t. To solve each part, we can plug in the given time intervals into the function, and calculate the difference between the initial and final positions. We then divide this difference by the amount of time elapsed to find the average velocity. For example, in part (a), the average velocity is calculated as -7(5^2-1^2) + 70(5-1) = -90 m/s. In part (b), the average velocity is calculated as -7(4^2-1^2) + 70(4-1) = -62 m/s. In part (c), the average velocity is calculated as -7(3^2-1^2) + 70(3-1) = -34 m/s. Finally, in part (d), the average velocity is calculated as -7(1+h)^2 + 70h m/s

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The scale factor of the two triangles is 1/4 or 4

You should understand that scale factor is the ratio of any two corresponding lengths.

Looking at the triangles, the larger triangle has sides

The smaller triangle has sides

Scale factor = (Larger length)/ (Smaller length) or (Smaller length/(Larger length)

This is an indication that the triangles have scale factors of:

Scale factor = 12/3 = 4 or

Scale factor = 3/12 = 1/4

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Answer: 1/24

Step-by-step explanation:

1st even = 3/6 (2,4,6)

2nd Prime = 3/6 (2,3,5)

3rd multiple of 5 = 1/6 (5)

3/6 x 3/6 x 1/6 = 9/216

9/216 = 1/24

Let's call the two numbers x and y. We know from the problem statement that:

x + y = 1476890

y - x = 1500

To find the greater number, we can use the second equation to solve for one of the variables, and then substitute it into the first equation.

y = x + 1500

Now we can substitute this expression for y into the first equation:

x + (x + 1500) = 1476890

2x + 1500 = 1476890

2x = 1476890 - 1500

2x = 1475390

x = 1475390/2

x = 737695

So the greater number is y = x + 1500 = 737695 + 1500 = 739195

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Answer:

Prabin types 765/9 i.e, 85 words in one minute. Therefore in 30 minutes prabin will type 30 x 85 i.e., 2550 words. Again, he types 1 word in 9/765 minutes. Therefore , he will type 12750 words in 12750 x (9/765) minutes, i.e, 150 minutes.

Prabin would type 2,550 words in half an hour at the same speed. It would take him 150 minutes to type 12,750 words at the same speed.

To find out how many words Prabin would type in half an hour, we need to determine how many minutes are in half an hour. Since there are 60 minutes in an hour, half an hour would be 30 minutes. Now, we can set up a proportion to find the number of words Prabin would type in half an hour:

765 words / 9 minutes = x words / 30 minutes

Cross-multiplying, we get:

9 * x = 765 * 30

Simplifying, we find:

x = (765 * 30) / 9

x = 2,550 words

To find out how long it would take Prabin to type 12,750 words at the same speed, we can set up another proportion using the given information:

765 words / 9 minutes = 12,750 words / t minutes

Cross-multiplying, we get:

9 * (12,750) = 765 * t

Simplifying, we find:

t = (9 * 12,750) / 765

t = 150 minutes

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The number of dimes and nickels are equal to 11 and 19 respectively.

In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Since you have a total number of 30 coins, an equation which models this situation is given by;

d + n = 30     ....equation 1.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Additionally, the coins are worth 2.05 dollars;

0.1d + 0.05n = 2.05     ....equation 2.

Solving both equations simultaneously, we have:

0.1(30 - n) + 0.05n = 2.05

3 - 0.1n + 0.05n = 2.05

3 - 0.05n = 2.05

0.05n = 0.95

n = 0.95/0.05

n = 19 nickels.

For the number of dimes;

d = 30 - n

d = 30 - 19

d = 11 dimes.

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Complete Question:

You have 30 coins worth $2.05 in nickels and dimes. What's in your wallet? Create and solve system of equations to find how many dimes and how many nickels you have.

The average annual cumulative rainfall is 1  inch per month. During month of August average rain fall is greatest because slope in this month is maximum.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

The graph does not represent cumulative rainfall as a function of day.

Because they have average all values for month Total cumulative rainfall is 12 inches.

Total period is 12 month

So, average annual cumulative rainfall is

12/12 =1 inch per month

Average rainfall in the month of December= (average cumulative rainfall in December - average cumulative rainfall in November)

= 12-11

= 1 inch

Therefore, during month of August average rain fall is greatest because slope in this month is maximum.

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The standard deviation of Y is $432.00 and this can be determined by using the formula of standard deviation and the given data.

Given :

A company sells concrete in batches of 5 cubic yards.

The probability distribution of X, the number of cubic yards sold in a single order for concrete from this company, is shown in the table below.

The expected value of the probability distribution of X is 19.25 and the standard deviation is 5.76.

There is a fixed cost to deliver the concrete. The profit Y, in dollars, for a particular order can be described by  (Y = 75X - 100).

The formula to obtain the standard deviation is given below:

SD(Y) = SD(75X - 100)

Simplify the above expression by substituting the value of SD(X) and SD(100) in the above expression.

SD(Y) = 75SD(X) - SD(100)

SD(Y) = 75 SD(X) - 0

SD(Y) = 75×5.76

SD(Y) = $432

Therefore, the correct option is B.

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Answer:

Circumference = 113.097 units

Step-by-step explanation:

C = 2[tex]\pi r[/tex]

C = 2(3.14)(36/2)

C = 113.097 units

Answer:

all of them are 17

Step-by-step explanation:

7+9=16

16+1+0=17

9+7=16

16+1+0=17

1+0+9=10

10+7=17

7+1=8

8+9+0=17

hope this helped!

Answer:

y=-5x+b

Steps:

1. Put slope into y=mx+b formula

2. Plug in point: -8=-5(2)+b

3. Solve for b: 2=b

By calculating, The value of given expression 8 · (2 + 3 )²- 4² is 184

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the use of letters or alphabets with out specifying their actual values. The fundamentals of algebra taught us a way to explicit an unknown price using letters along with x, y, z, etc. those letters are known as right here as variables.

An algebraic expression can be a combination of both variables and constants. Any cost this is positioned before and extended by using a variable is a coefficient.

Given expression ,

= 8 · (2 + 3 )²- 4²

= 8. (5)^2 - 4^2

=8.25 - 16

= 200 - 16

= 184

so, the value of expression is 184.

Therefore, The value go given expression 8 · (2 + 3 )²- 4² is 184

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An equation of the line that is parallel to this line and passes through the point (4, 2) is y = 0.5x.

An equation of the line that is perpendicular to this line and passes through the point (4, 2) is y = -2x + 10.

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -1 = -1

Note: m represents the slope.

From the linear equation 3x - 6y = -8, we have:

y = 3x/6 + 8

y = 0.5x + 8

At point (4, 2), an equation of the line that is parallel to this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y - 2 = 0.5(x - 4)

y = 0.5x - 2 + 2

y = 0.5x

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

0.5 × m₂ = -1

m₂ = -2

At point (4, 2), an equation of the line that is perpendicular to this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -2(x - 4)

y = -2x + 8 + 2

y = -2x + 10

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The amount that you when a fair dice is tossed (showing is either 4 or 5, you win $1, if the number of spots showing is 6, you win $4, and if the number of spots showing is 1, 2, or 3, you win nothing) is $1.00

Given,

          when you get either 4 or 5, the reward = $1

           when you get either 6, the reward = $4

              when you get 1, 2, or 3, the reward = $0

We know that,

                     Probability of getting 6 = 1/6

                     Probability of getting 4 = 1/6

                      Probability of getting 5 = 1/6

                      Probability of getting 1 = 1/6

                      Probability of getting 2 = 1/6

                       Probability of getting 3  = 1/6

        Therefore,

                     [tex]X = \frac{1}{6}* 4 + \frac{1}{6}* 1 +\frac{1}{6}* 1+ \frac{1}{6}* 0+ \frac{1}{6}* 0 + \frac{1}{6}*0[/tex]

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

                          [tex]= \frac{6}{6}[/tex]

                          [tex]= 1[/tex]

  Hence, the Value of X = $1.

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Integration is basically used to find the areas of the two-dimensional region and computing volumes of three-dimensional objects.

What is integration?

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

Differentiation is the opposite of integration.

In other words, reversing the differentiation process merely results in integration. The example below demonstrates it:

dy/dx = 2x since y = x2 Consequently,

(dy/dx) dx = 2x dx = x2.

Together, and dx represent the integration of the function with respect to x.

The anti-differentiation is another name for integration. In this procedure, we are given a function's derivative and asked to determine the function (i.e., primitive). We are aware that cos x is the differentiation of sin x.

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In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

dne

Since 9x2 y2 9z2 is a 3-dimensional equation, it cannot be sketched on a 2-dimensional plane. Therefore, the answer is dne.

The equation 9x2 y2 9z2 is a 3-dimensional equation and cannot be represented on a 2-dimensional plane. Therefore, it is not possible to sketch the surface using this equation. As a result, the answer is dne. The equation contains three variables, x, y and z, and cannot be represented on a graph without the use of three axes. In order to accurately represent the surface, we would need to be able to plot the equation in 3-dimensions using 3-dimensional coordinates. Since this is not possible, the answer is dne.

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We can start by using the concept of percentage concentration, which states that the percentage of alcohol in a solution is equal to the number of milliliters of alcohol in the solution divided by the number of milliliters of the solution, multiplied by 100.

Let's call the number of milliliters of Solution B that Linda uses x.

We know that:

Solution A is 50% alcohol, so it contains 50/100 = 0.5 = 1/2 of alcohol.

Solution B is 10% alcohol, so it contains 10/100 = 0.1 = 1/10 of alcohol.

The resulting mixture is a 20% alcohol solution.

Linda uses 400 milliliters of Solution A.

We can set up an equation using the percentage concentration concept and the information provided:

(400 * 1/2) + (x * 1/10) = (x + 400) * (20/100)

Solving for x:

200 + x/10 = (x + 400) * 0.2

x/10 = (x + 400) * 0.2 - 200

x/10 = x * 0.2 + 80

9x/10 = x * 0.2 + 80

9x = x*2 + 800

x = 800/8 = 100

So, Linda uses 100 milliliters of Solution B to make the resulting mixture a 20% alcohol solution.

Electric potential energy is the energy that is needed to move a charge against an electric field.

Completed question :

A point charge q1 , is held stationary at the origin. A second charge q2 is placed at a point a, and the electric potential energy of the pair of charges is -6.4 x [tex]10^{-8}[/tex] J. When the second charge is moved to point b, the electric force on the charge does 4.2 x [tex]10^{-8}[/tex] J of work. What is the electric potential energy of the pair of charges when the second charge is at point b?

Given data :

PE1 = -6.4 x [tex]10^{-8}[/tex] J

Work done = 4.2 x [tex]10^{-8}[/tex] J

PE1 = PE2 + Work done

PE2  = PE1 - Work done =

= -6.4 x [tex]10^{-8}[/tex] J - 4.2 x [tex]10^{-8}[/tex] J = -10.6 x [tex]10^{-8}[/tex] J

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Answer:

First choice: 5x²+21x-20

Step-by-step explanation:

This is easy to answer if you realize that there is only one way an x² term can appear in the result and that is by the multiplication of 5x and x which results in 5x².

The only choice which has 5x² as a term is the first:  5x²+21x-20

However, it is important to know the FOIL method to multiply two terms together

FOIL stands for First Outer Inner Last and is a technique for multiplying two terms of the form (a+b) and (c+d)

In (a + b) (c + d),

First terms are a and c so their product is ac

Outer terms are a and d so their product is ad

Inner terms are b and c with product bc

Last terms are b and d with product bd

The result is the sum of all these terms

Let's take (5x - 4)(x + 5)
F: 5x·x = 5x²

O: 5x · 5 = 25x

I: -4 ·x = -4x

L: -4·5 = -20

Adding up these individual terms we get

5x² +25x - 4x - 20 = 5x²+21x-20

So first choice is the correct answer

The domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

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.

So, the parameters are as follows, taken from the query:

Downloaded Amount = $2.50

Added amount to each player = $1.50

Use x to indicate how many players there are.

The following representations are what we have.

Total amount = Amount to download + Amount to add each player * Number of players

Now, we obtain:

y = 2.50 + 1.50 * x

y = 2.50 + 1.5x

The number of players serves as the input to the aforementioned linear function.

The domain is discrete as a result.

The amount, though, can have decimal points

The range is continuous as a result.

Therefore, the domain is discrete and the range is continuous, which can be an accurate statement regarding the two terms.

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The equation of the line perpendicular to -2y = 5x + 8  and passes through (10, -1) is y = 2 / 5 x - 5.

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation is perpendicular to  -2y = 5x + 8  and passes through (10, -1).

Perpendicular lines have slopes that are negative reciprocals of one another.

Therefore,

-2y = 5x + 8

y = - 5 / 2 x - 4

Therefore,

slope = 2 / 5

Let's find the y-intercept using (10, -1)

-1 = 2 / 5(10) + b

-1 = 20 / 5 + b

b = -1 - 4

b = -5

Therefore, the equation of the line is y = 2 / 5 x - 5

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The answer to the question is d) c and l; f and h.

The concept of opposite numbers on the number line can be expressed mathematically by the equation -x = y, where x is the original number and y is the opposite number. This equation can be used to calculate the opposite of any number. For example, if the number 5 is located at point a on the number line, the opposite of 5 is located at point k and can be calculated by substituting 5 for x in the equation and solving for y. -5 = y, therefore y = -5. The opposite of 5 is therefore -5. To calculate the opposite of any of the other numbers marked on the number line, the same equation can be used. The answer to the question is d) c and l; f and h.

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Answer: the correct value of x in this will be 6.

Step-by-step explanation: According to the equation given ,

f(x) = 64

so , f(x) = 11x - 2 now putting the value of f(x) in this equation

therefore , 64 = 11x - 2

now solving the equation , 11x= 64+2

11x = 66

x = 66/11

x = 6

thus, the value of x obtained from the equation is 6

When the number of people is 16, the water lasts for 6 days, which is found using unitary method.

What is the unitary method?

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value.

a) Let the amount of water present = L

Initially, this amount was considered for 12 people for 8 days.

For 12 people,

8 days = L

1 day = L/8

So the water required for one person for one day = (L/8) / 12 = L/96

But now 4 more people joined the trek,

So for 16 people, water used in one day = (L/96)*16 = L/6

Now the water will last for 6 days since,

                   (L/6 * 6) = L

b) The assumption that is made while solving the question is that the water required by each person is considered the same(L/96) even if the number of persons increases.

Therefore the water lasts for 6 days when the whole group consists of 16 people.

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-12a is  a cubic function in exercises when Relative minimum (4,2).

What in mathematics is a relative maximum?

A point (x,y) on the graph of the function whose y-coordinate is larger than all other y-coordinates on the graph at locations "near to" is known as a relative maximum point (x,y). ( x , y ) .

  f'(x) = 3ax² + 2bx + c

(3,3) and (5,1 ) are print of  relative maximum

   so,    f'(3) = f'(5) = 0

  3a(3)² + 2b(3) + c = 0

or   27a + 6b + c = 0

and   3a(5)² + 2b(5) + c = 0

       75a + 10b + c = 0   ...................... 2

the  Inflection point occurs at point where f''(x) = 0

     d/dx ( 3ax² + 2bx + c ) ∫x = 4 = 0

       because (4,2) is point of  Inflection .

           6a(4) + 2b = 0

          24a + 2b = 0

          b = -12a

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Answer:

136/5

Step-by-step explanation:

18 9/10 + 8 3/10

change to improper fraction

=189/10 + 83/10

Adding, you have:

=272/10

2 can further divide both numbers

= 136/5

Answer:

That is correct.

Step-by-step explanation:

The greater the absolute value of a negative number, the lesser (farther left from zero) it is. The greater the absolute value of a positive number, the greater (farther right from zero) it is.

Thus,

-6 < -2 < 0 < 4 < 8

and

-5.5 < -5.2 < -5 < -2.5 < 5.5

Notice also how it is easier to compare numbers when they are converted to the same form—in this case decimal form.