simplify (1+1/a)^2-(1-1/a)^2

The probability that the number rolled is a 3 or 4 is 1/3.

Probability is the likelihood that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. If there is a equal chance that the event would occur or not equal, the probability value would be 0.5.

P(B) = probability that the number rolled is a 3 or 4 = (number of sides that is a 3 / total number of sides) +  (number of sides that is a 4 / total number of sides)

= 1/6 + 1/6 = 2/6 = 1/3

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The solution is (-0.5, -1). The graph of the system of linear equations is attached below.

What is a linear equation?

A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.

We are given two equations:

y-2x=0

⇒ y=2x

and y=8x+3

So,

⇒2x = 8x+3

⇒-6x = 3

⇒x = -0.5

Putting this value in y=2x, we get

y= -1

Thus, the solution is (-0.5, -1).

The graph of the system of linear equations is attached below wherein the blue line represents y-2x=0 and green line represents y=8x+3.

Holly must have got confused in the x-coordinates and the y- coordinates while writing the ordered pair.

Hence, the solution is (-0.5, -1).

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The number of candy still in the bag is the dependent variable, while the independent variable, x, stands for the length of time spent eating, as the number of candies still in the bag relies on the length of time spent eating. A function relating these variables is H(x) = 60 - 5x. So H (10) = 40, meaning there are 40 candies left in the bag.

H(x) = 60 - 5x

H(10) = 60 - 5(10)

H(10) = 60 - 50

H(10) = 10

The independent variable, x, represents the number of minutes eating and the dependent variable is the number of candies left in the bag because the number of candies left depends on the number of minutes eating. This is a linear relationship, meaning that the rate at which the candies are being eaten is constant, so the decrease in the number of candies is proportional to the number of minutes eating. A function relating these variables is H(x) = 60 - 5x. This is a linear equation, with a slope of -5, which means for every minute eating, the number of candies left decreases by 5. So, when x = 10, H(10) = 60 - 5(10) = 60 - 50 = 10, meaning there are 10 candies left in the bag. This function can be used to determine the number of candies left in the bag at any point in time.

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The surface area of the smaller cubical package is given S = 150 inches²

The formula for surface area of a cube is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube.It is basically the total surface area.

Surface area S = 6a² ,

where a is the side of the cube

Given data ,

Let the surface area of the smaller cube be represented as S

Now , the surface area of the larger cube L = 384 inches²

And , side length of smaller cube = side length of larger cube - 3

Now , the equation will be

Surface area of the larger cube L = 6 ( A )² ,

where A is the side length of the larger cube

So , substituting the values in the equation , we get

6 ( A )² = 384

Divide by 6 on both sides of the equation , we get

A² = 64

Taking square roots on both sides of the equation , we get

A = 8 inches

Now , side length of smaller cube a = 8 - 3 = 5 inches

So , surface area of the smaller cube S = 6 ( a )²

Substituting the values in the equation , we get

Surface area of the smaller cube S = 6 ( 5 )²

Surface area of the smaller cube S = 6 x 25

Surface area of the smaller cube S = 150 inches²

Hence , the surface area is 150 inches²

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Answer:

Step-by-step explanation:

adadadadadadadadadadadada

The demand function is linear, so we can write it in the form of:

q = a - bp

Where a and b are constants and q is the quantity demanded and p is the price. We have two points, one at a price of $3.25 with a quantity of 2,500, and another at a price of $2.83 with a quantity of 3,900.

We can use these two points to solve for the values of a and b in the equation.

Plugging in the first point:

2500 = a - (3.25)b

Plugging in the second point:

3900 = a - (2.83)b

We can then solve this system of equation by substituting the first equation with the second one

3900 = a - (2.83)b

=2500 + 1400 = a - (3.25)b + (2.83)b

=a - (0.42)b

So the equation is:

q = 3900 - 0.42p

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△ABC∼△ACE∼△CBE is true according to the given data of triangles.

Triangles are said to be congruent if, under a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.

Given, ABC is a right triangle with altitude CE

Now,

In Triangle ABC and Triangle ACE

angle CAB = angle EAC

(common angle)

angle ACB = angle AEC (Right angle)

So,

Triangle ABC is similar to triangle ACE

Similarity,

For ΔABC and ΔCBE;

∠ABC = ∠CBE (common angle)

∠ACB = ∠CEB (right angle)

So,

ΔABC is also similar to ΔCBE

thus,

ΔABC  ≅ ΔACE ≅ ΔCBE

Therefore, Option (a) △ABC∼△ACE∼△CBE is correct.

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Complete question:

Answer:

25%

Step-by-step explanation:

Discount is 175 - 131.25 = 43.75

Rate of discount = 43.75/175 x 100 = 25%

Carol should decide on the average of the two anticipated numbers. She must thus decide to select  [tex]\frac{13}{24}[/tex].

Probability is an area of mathematics that examines the possibility that a particular event will occur. In most cases, the probability values for the specified experiment are specified between a range of numbers. The values fall in the range of 0 and 1. A negative number cannot be the probability value. Experimental probability, also known as Empirical probability, is based on actual experiments and adequate recordings of the happening of events. For Alice's number, the anticipated value is [tex]\frac{1}{2}[/tex] and the expected value of Bob's number is [tex]0.5*[\frac{1}{2} +\frac{2}{3} ][/tex]. Carol should pick the middle between these two projected figures to increase her chances of winning. She must thus choose [tex]0.5*[\frac{1}{2} + \frac{7}{12} ][/tex] = [tex]\frac{13}{24}[/tex]. Alternatively, once we recognize that the answer lies in the interval [tex](\frac{1}{2},\frac{7}{12} )[/tex], it is straight forward that she has chosen the right number.  

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The domain and the range of the relation shown to the right are given as follows:

The relation is not a function, as there are inputs that are mapped to multiple outputs.

The domain of a function is the set that contains all the input values of the function, hence on the graph it is the values of x, thus the domain is of:

x >= -5.

The range of a function is the set that contains all the output values of the function, hence on the graph it is the values of y, thus the domain is of:

All real values.

Tracing a vertical line through the graph of the function, there are values of x for which the graph would be crossed two times, meaning that the relation is not a function.

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C. The warmer the temperature, the more often crickets chirp.

The graph shows a direct correlation between temperature and the rate of chirping. As the temperature increases, the rate of chirping increases as well. Using the formula y=mx+b, where m is the slope of the line and b is the y-intercept, the slope of the line in the graph is approximately 0.5, which means that for every 1 degree Celcius increase in temperature, the rate of chirping increases by 0.5 chirps per second. This proves that the warmer the temperature, the more often the crickets chirp.

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The percentage of the whole population voted. A pie chart is best used to show the percentage of the whole that different categories represent, in this case the percentage of the whole population that voted.

A pie chart is one of the most commonly used types of data visualization because it provides an easy way to understand the proportional distribution of the data that is being presented. In a presentation about voter turnout, a pie chart would be an excellent way to illustrate what percentage of the whole population voted. Pie charts can be used to show how a whole is divided into different categories, and how much of the whole each category represents. This type of chart is especially useful for presenting data in a visually appealing way and for making comparisons between different categories. In the case of voter turnout, a pie chart would be ideal for showing the percentage of the population that voted, and for comparing the proportions of those who did and did not vote.

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The equation of the plane is 2(x-2) + 4(y+5) - c(z-c/2) = 0

From the question, we have the following parameters that can be used in our computation:

points (3,-7,c) and (1,-3,0)

The equation is then calculated as follows:

Start by calculating the midpoint M

M = ( (3+1)/2 , (-7-3)/2 , (c+0)/2 ) = (2,-5,c/2)

Then we need to find the vector parallel to the line, which is given by

v = (1-3, -3-(-7), 0-c) = (-2,4,-c)

Substitute the coordinates of the midpoint and the normal vector into the equation of a plane "ax + by + cz = d"

Where (a,b,c) is the normal vector and d is a constant.

-2(x-2) + 4(y+5) - c(z-c/2) = 0

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The simplified rational expression in this problem is given as follows:

[tex]\sqrt{x^{100}y^{16}} = x^{50}y^8[/tex]

The rational expression for this problem is defined as follows:

[tex]\sqrt{x^{100}y^{16}}[/tex]

The power of power rule states that when an exponential expression is elevated to a power, the powers are multiplied.

With powers, the expression is given as follows:

(x^100y^16)^1/2.

Hence the powers of the simplified expression are given as follows:

These two powers are the powers of the simplified expression given in the beginning of the answer.

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The area of R can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1.

The integral expression is ∫e^(2x-x^2)dx = ∫e^u du = e^u + C = e^(2x-x^2) + C. Evaluating the integral between x = 0 and x = 1 gives the area of R as e^2 - 1.

(b) The area of S can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1, minus the integral of the function y = 1 between x = 0 and x = 1. The integral expression for S is ∫e^(2x-x^2)dx - ∫1dx = ∫e^u du - x = e^u + C - x = e^(2x-x^2) + C - x. Evaluating the integral between x = 0 and x = 1 gives the area of S as e^2 - 1 - 1.

(c) The volume of the solid generated when R is rotated about the horizontal line y = 1 can be found using the integral expression ∫2πx(e^(2x-x^2) - 1)dx. This expression represents the area of the circular cross-sections of the solid multiplied by 2πx, which is the circumference of the circle. When evaluated between x = 0 and x = 1, this integral gives the volume of the solid generated when R is rotated about the horizontal line y = 1.

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The equation describes the relationship between the rate of change of x with respect to time and the rate of change of y with respect to time  is  b)  dx/dt = -2dy/dt.

We are given that ...

 x(t) +2y(t) = k

for some functions x(t) and y(t) and some constant k.

Differentiating with respect to time gives ...

 x'(t) +2y'(t) = 0

 x'(t) = -2y'(t) . . . . . subtract the y term

In the form used in the answer choices:

 dx/dt = -2dy/dt . . . . . matches choice B

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Answer:

$ 3916

Step-by-step explanation:

Amount= $5500

%decrease= 28.8% or .288

Amount decreased= 5500 x .288; $1584.

End of last year= 5500 - 1584; 3916

The area of the shaded region can be found by Area Decomposition Method.

Outer Area Minus Inner Area: Area of the shaded region = Area of the outer shape - Area of the unshaded inner shape

Area of Composite Figures: Area of the shaded region = Area of Region 1 + Area of Region 2 + ...... + Area of nth Region

The Area Decomposition Method:

Understanding the area decomposition method is the key to determining the area of a darkened zone.

For quick and efficient analysis, the area decomposition approach divides the fundamental forms present in a given complex figure.

To obtain the areas of the shaded zones, there are two scenarios.

They are of:

(1) Figures with holes and

(2) Composite figures.

Outer Area Minus Inner Area:

In figures with holes, take into account the area of the figure as a whole without the hole or hollow. By deducting the punch hole area from the whole figure, the remaining area can be found.

The area of the shaded region is equal to the Area of the outer shape minus the Area of the unshaded inner shape

Area of Composite Figures:

A composite plane figure's overall area is the same as the sum of its component areas.

The area of the shaded region is equal to the sum of the Area of Region 1, Area of Region 2, ......, Area of nth Region.

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Answer:

The probability of choosing a short straw from a bag that contains 1 short straw and 9 long straws is 1/10 (A).

The expression which represents the given word phrase as required to be written is; 10⁵ + 7.

It follows from the task content that the expression which represents the sequence of operations described be written.

First, the word phrase says; raise 10 to the 5th power, therefore, we have;

10⁵

Finally, the word phrase says to add the result to 7; Hence, the final expression is; 10⁵ + 7.

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The Inequalities that represent the above situation are => x + y ≤ 50 and 2x + 3y ≥ 100 and the possible combinations are (20, 30) and (30, 20).
[ Graphs are given below ].

To form the required inequalities, represent the unknown quantities with variables like x, y,..etc.

In the given problem, we don't know the number of items that Jenny will sell so here we represent them with variables 'x' and 'y'.

And obtain expression according to the condition of the given problem. Since we need to represent them in inequalities use signs like less than, greater than, etc.  

Here we have

Jenny would like to make at least $100 in sales.

She estimates that she will sell at most 50 pieces of jewelry.

The bracelets that she is selling cost $2 and the necklaces cost $3  

Let Jenny sold 'x' bracelets and 'y' necklaces

Number of pieces that Jenny estimated = 50

=> x + y ≤ 50 ----- (1)

Jenny would like to make at least $100 in sales.

=> 2x + 3y ≥ 100 ---- (2)      

Let Jenny sell 20 bracelets and 30 necklaces  

=> 2(20) + 3(30) ≥ 100      

=> 40 + 90 ≥ 100  

=>  130 ≥ 100  [ which is true ]

Let Jenny sell 30 bracelets and 20 necklace

=> 2(30) + 3(20) ≥ 100  

=> 60 + 60 ≥ 100    

=> 120 ≥ 100    

∴ The possible combinations are (20, 30) and (30, 20)

Therefore,

The Inequalities that represent the above situation are => x + y ≤ 50 and 2x + 3y ≥ 100 and the possible combinations are (20, 30) and (30, 20).
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Answer:

the rise would be 4 and the run would be -8.

Step-by-step explanation:

So, we would write it in a y=mx+b formula. It would be y=4x-8.

Answer:

complicated

Step-by-step explanation:

so your screen quality is os$ so ill just tell you what to do.

first look at to points on the graph the meet on the line

second, find how much the rise is (it will be a negative number.)

third, find the run (how far the x moves)

put rise over run and theres your answer

Answer: it would be (A)

The equation shows a linear relationship, but not a proportional relationship.

let me know if it helped

Answer:

it would be (A)

Step-by-step explanation:

A two proportion significance test must be performed and pass all parameters. Ans is true since all three requirements have been met (I, II and III). Option (e).

Given,

For the two proportion significance test, the following assumptions were met: The populations are independent. (Populations exist in distinct groups.) The sample size multiplied by the success probability for each population is more than or equal to ten, as is the sample size multiplied by the failure probabilities. (We look at this normality criterion; if it holds true, we say that the data is roughly normally distributed.)

Every sample is chosen randomly. (The sample must be selected at random; else, bias may occur.) A two-proportion Z-test is a statistical hypothesis test that determines whether two proportions are different from one another. Two independent samples are used in the test, and Z-statistics are calculated with the null hypothesis that the two proportions are equal.

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Answer:

Answer is Negative

Step-by-step explanation:

picture at the bottom provides proof.

Answer:

The first option (1)

Step-by-step explanation:

Because i am always right and i know how to do math :) .

Your welcome

The exponential model for the rodent's population is 25,000[tex](0.08)^{x}[/tex], where x is the number of years and 0.8 is the rate of decrease in population size per year.

An exponent is a mathematical notation that indicates how many times a number has been multiplied by itself. It is commonly shown as a superscript next to the basic number, such as [tex]4^{2}[/tex], which equals 4 x 4 = 16.

a. The exponential model for the rodent's population is Y = 25,000[tex](0.08)^{x}[/tex], where x is the number of years.

b. The "a" in the exponential model is 25,000, which is the starting population of the rodent species. The "b" is 0.8, which is the rate of decrease in population size per year.

c.

X  Y

0   25000

1   20000

2   16000

3   12800

4   10240

5   8192

d. After 10 years, the estimated population of the rodents is 2048. This is because the population decreases by a factor of 0.8 each year, so the population after 10 years is 25000[tex](0.8)^{10}[/tex] = 2048.

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Of the 18 number of seniors not enrolled in an AP class or a club, 8 are enrolled in an AP class but not a club, and 10 are not enrolled in an AP class or a club.

First, we need to calculate the total number of seniors enrolled in AP classes and clubs. We know that 32 number of  seniors are enrolled in at least one AP class and 35 are in a club. That means that there are 67 seniors total enrolled in either an AP class or a club.

Next, we need to determine the number of seniors enrolled in both an AP class and a club. We can subtract the total number of seniors enrolled in either an AP class or a club from the total number of seniors at the school (80). This will give us the number of seniors not enrolled in either an AP class or a club, which is 18.

Finally, we can calculate the number of seniors enrolled in an AP class but not a club, and the number of seniors not enrolled in an AP class or a club. We know that there are 18 seniors not enrolled in either an AP class or a club, so we can subtract the number of seniors enrolled in an AP class (32) from 18 to get the number of seniors enrolled in an AP class but not a club, which is 8. We can also subtract the number of seniors enrolled in both an AP class and a club (67) from 18 to get the number of seniors not enrolled

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The correct option regarding the expected value of her game is given as follows:

B. She looses $0.5 per roll.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

As each outcome is equally as likely, the distribution of earnings for her game is given as follows:

Hence the expected value for the game is of:

E(X) = (1 + 2 + 3 + 4) x 1/6 - 6.5 x 2/6

E(X) = -$0.5.

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