There are 4 apples, 3 peaches and 2 plums in a grocery bag. If the the checkout person picks 2 plumbs and 1 peach out of the bag, what is the probability that the next piece of fruit out of the bag will be an apple? (Give your answer as a fraction in simplest form.)

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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[tex]4-6x+2-2x^{2} -4x+6x^{2}[/tex]

Which of these correctly rearranges the terms in this polynomial so like terms are next to each other?

The first step is to identify the same variable.

The equation consists of variables [tex]x, x^{2}[/tex] and constant.

Terms of variable [tex]x^{2}[/tex] are [tex]-2x^{2}[/tex] and [tex]6x^{2}[/tex]

Terms of variable [tex]x[/tex] are [tex]-6x[/tex] and [tex]-4x[/tex]

Terms of constant are [tex]4[/tex] and [tex]2[/tex]

The next step is rearranges the terms in this polynomial so like terms are next to each other

[tex]-2x^{2} +6x^{2} -6x-4x+4+2[/tex] (B)

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When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

A quadrilateral is a specific type of polygon known as a parallelogram if it contains two parallel opposed sides. A parallelogram has the following qualities:

Each coordinate of the Parallelogram :

P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)

Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37

Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37

Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17

Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17

Here, PA = RT and PT = AR ,

so when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.

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When opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram. (PA = RT and PT = AR)

What is meant by quadrilateral?

Each coordinate of the Parallelogram :

P (-3, 0) , A(3, -1) , R ( 2, -5) and T(-4, -4)

Length of PA = √((3 + 3)² + (-1 - 0)²) = √(36 + 1) = √37

Lenght of TR = √((-4 - 2)² + (-4 + 5)²) = √(36 + 1) = √37

Length of PT = √((-3 + 4)² + (0 + 4)²) = √(16 + 1) = √17

Length of AR = √((3-2)² + (-1 + 5)²) = √(16 + 1) = √17

Here, PA = RT and PT = AR ,

So when opposite sides of a quadrilateral is equal then the quadrilateral is Parallelogram.

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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: $0.075

Step-by-step explanation:

$14.95 is roughly $15

and 0.5% is 1/2 of 1/100

1/100 of 15 is 0.15 and 1/2 of that is 0.075

0.7125

Step-by-step explanation:

soln

14.25*5%

=0.7125

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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Answer:

60.26°

i have to write more so yea but do you have the answer to 83d and 91c from that chapter

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 solution to the differential equation is given by R = ±1/√(C-a*x), where C is a constant of integration.

To solve this differential equation, we first separate the variables and integrate the equation:

dR/dx = a(R^2+16)

∫ dR/dx  = ∫a(R^2+16)dx

R = ±1/√(C-a*x) + K

where K is an arbitrary constant.

To find the constant of integration, we use the initial condition. We plug in the initial values for x and R to find the constant of integration. For example, if x = 0 and R = 2, then we get

2 = ±1/√(C-0) + K

2 = ±1/√C + K

K = 2±1/√C

Therefore, the solution to the differential equation is given by R = ±1/√(C-a*x) where C is the constant of integration.

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Hose 1 takes 7 days.

Hose 2 takes 4 days.

That means in a single day, Hose 1 fills 1/7 of the pool and Hose 2 fills 1/4 of the pool.  So in one day, the two hoses will fill 1/7 + 1/4 of the pool.

If t is the number of days it takes to fill the pool with both hoses being used, then

   [tex]t\cdot \left(\dfrac{1}{7} + \dfrac{1}{4}\right) =1[/tex]

will tell us how many days it will take to fill 1 pool

Solving this:

    [tex]\begin{aligned} t\cdot \left(\dfrac{1}{7}\cdot\dfrac{4}{4} + \dfrac{1}{4}\cdot \dfrac{7}{7}\right) &=1 \\[0.5em]t\cdot \left(\dfrac{4}{28} + \dfrac{7}{28}\right) &=1 \\[0.5em]t\cdot \left(\dfrac{11}{28} \right) &=1 \\[0.5em]t &=\dfrac{28}{11} \\[0.5em]\end{aligned}[/tex]

It'll take 28/11 days, or 2 and 6/11 days, or about 2.54 days.

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.

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

Answer:

d. 9x^2 + 25x + 14

Step-by-step explanation:

Formula of area of a rectangle is L * W;

L being length

W being width

x + 2 is our W

9x + 7 is our L, thus;

(x+2)(9x+7)

[9x^2 + 25x + 14]

There were approximately 5,184 graduates in 2008.

The cubic model is a useful tool for estimating the number of graduates in a given year, as it takes into account the trend of the data points. This allows us to make an educated guess about the number of graduates in a given year, despite not having data points for that year.The cubic model for the number of graduates from an online university since 2002 can be expressed as y = -7.8x^3 + 74.4x^2 + 437x - 9,150. Here, x is the number of years since 2002, and y is the number of graduates in that year. To estimate the number of graduates in 2008, we can plug in x = 6 into the equation, giving us y = 5,184. That is, there were approximately 5,184 graduates in 2008.

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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

The value of the fraction 24(1/2 + 2/7) divided by 1 4/8 will be 16 3 / 7.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The value of the fraction 24(1/2 + 2/7) divided by 1 4/8 will be:

= 24(1/2 + 2/7) ÷ 1 4/8:

= 24 9/14 ÷ 1 1/2

= 345 / 14 × 2/3

= 690 / 42

= 16 3 / 7

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Complete question

24(1/2 + 2/7) divided by 1 4/8 will be:

The equation of the line is given as y = ( -2/5 )x + 162 , where the slope of the line is m = ( -2/5 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be represented as P ( -275 , 52 )

Let the first point be represented as P ( -280 , 54 )

Now , the slope of the line is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 54 - 52 ) / ( -280 - ( -275 ) )

On simplifying the equation , we get

Slope m = 2 / ( -5 )

Slope m = -2/5

Now , the equation of line is  y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 52 = ( -2/5 ) ( x - ( -275 ) )

y - 52 = ( -2/5 )x + 110

Adding 52 on both sides of the equation , we get

y = ( -2/5 )x + 162

Hence , the equation of line is y = ( -2/5 )x + 162

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A stationary point of a function f(x) is a point where the derivative of f(x) is equal to 0. These points are called “stationary” because at these points the function is neither increasing nor decreasing.

Once we have identified the dy dx = 0 solutions, we may utilise the first derivative to ascertain the characteristics of the stationary points. Think about the equation y = x2 + 1.

By differentiating and setting the derivative to zero, we may determine that there is a stationary point at x = 0 since dy dx = 2x = 0. Recall that placing f by x and f by y equal to zero will reveal the location of a function f's stationary point.

In this situation, partial differentiation with regard to x while treating y as a constant results in three x squared plus six x. Any stationary point's nature can be ascertained by introducing its x coordinate into the second derivative of the function, f. (x). 

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Answer:

120/20=6 pearl collected 6

Step-by-step explanation:

If Tate collected 20 times as many rare coins as Pearl, we can set up a proportion to find out how many coins Pearl collected. Let x be the number of rare coins Pearl collected. Then we have:

x / 120 = 1 / 20

To solve for x, we can cross-multiply:

20x = 120

Dividing both sides by 20, we get:

x = 6

Therefore, Pearl collected 6 rare coins.

There are four types of social norms that can help inform people about behavior that is considered acceptable: folkways, mores, taboos, and law.

Social values are the focus of sociology. Cultural norms known as social values describe the overall well-being thought desirable for a structured social existence. These presumptions concern what is morally correct and significant for society. They provide social structures and behavior its ultimate meaning and legitimacy. They are ideals or abstract feelings. "Equality of opportunity" is a prime illustration of social value. It is frequently regarded as a desirable end in and of itself.

When several people interact, a set of norms emerges that governs their interactions and behaviors. Social norms are these standards of group behavior.

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The approximation of the area under the curve f(x) = [tex]2x^2 + 6[/tex] from x = 2 to x = 4 using left rectangles and a step size of Δx = 0.5 is 60.5 square units to one decimal place.

To approximate the area under the curve f(x) = [tex]2x^2 + 6[/tex] between x = 2 and x = 4 using left rectangles and a step size of Δx = 0.5, we have to divide the interval [2, 4] into a number of sub-intervals of width 0.5 and evaluate the function at the left endpoint of each sub-interval.

First find the number of steps: (4-2)/0.5 = 4

The x-coordinates for the left endpoints of each sub-interval are: 2, 2.5, 3, 3.5, 4

We evaluate the function f(x) = [tex]2x^2 + 6[/tex] at each of these left endpoints and multiply the result by the width of the sub-interval (0.5) to find the area of each rectangle.

For [tex]x = 2[/tex], [tex]f(x) = 2(2)^2 + 6 = 14[/tex]

Area = 0.5 * 14 = 7

For [tex]x = 2.5, f(x) = 2(2.5)^2 + 6 = 19.5[/tex]

Area = 0.5 * 19.5 = 9.75

For [tex]x = 3, f(x) = 2(3)^2 + 6 = 24[/tex]

Area = 0.5 * 24 = 12

For [tex]x = 3.5, f(x) = 2(3.5)^2 + 6 = 29.5[/tex]

Area = 0.5 * 29.5 = 14.75

For [tex]x = 4, f(x) = 2(4)^2 + 6 = 34[/tex]

Area = 0.5 * 34 = 17

The sum of the areas of these rectangles is 7 + 9.75 + 12 + 14.75 + 17 = 60.5

Therefore, the approximation of the area under the curve f(x) = [tex]2x^2 + 6[/tex] from x = 2 to x = 4 using left rectangles and a step size of Δx = 0.5 is 60.5 square units to one decimal place.

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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.

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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The units of distance and speed should match, So kilometers per hour (kph) and miles per hour (mph) are the correct units.

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Answer:

The answer would be 52.8 because if the number behind the decimal you want to round is 5 or greater you round one number up. (Sorry if this is a confusing explanation)

the probability of  all calculators having no defects is 16.8%. the probability of at least one defect is 83.2%.

A sample of 4 different calculators is randomly selected from a group of 16 defective and 30 non defective calculators,

So, we have to find the probability that at least one of 4 calculators in the sample is defective.

total number of calculators= 46.

the probability of one calculator being non defective is 30/46.

when a second is chosen the probability of having non defective is 29/45.

the probability of no defective in the third is 28/44

and the fourth is 27/43.

the probability of non-defective in any one of the

calculators is found by multiplying the individual probability.

[tex](\frac{30}{46})(\frac{29}{45} ) (\frac{28}{44} )(\frac{27}{43} ) =0.168.[/tex]

the probability of of all calculators having no defects is 16.8%. the probability of at least one defect is 83.2%.

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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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Answer:

If 55% of people brought their own skates, 45% did not.

Since 100 - 55 = 45.

45% of 200 = 90

The answer is: 90 people didn't bring their skates.

The area of the triangle is 24 square meters.

The area of the triangle can be calculated using the formula A = 1/2bh, where b is the base and h is the height of the triangle. In this case, the base is 8 meters and the height is 6 meters. Therefore, the area of the triangle is A = 1/2bh = 1/2(8)(6) = 24 square meters. Therefore, the answer is D. 24 square meters.

To calculate the area of the triangle, first the base and the height of the triangle must be known. The base is the length of the bottom line of the triangle, and the height is the length of the line from the peak of the triangle to the base. Once the base and height of the triangle are known, the area formula A = 1/2bh can be used.

The formula can be broken down into several steps. First, the base and the height are multiplied together. In this case, it would be 8 x 6. This gives a result of 48. Then, the result is divided by 2, which gives a result of 24. Therefore, the area of the triangle is 24 square meters. When using the area formula, it is important to remember that the result must be divided by 2 in order to get the correct answer.

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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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