How do you find the area of the shaded region? Many geometry students struggle to solve shaded areas. The best way to find a shaded region's area is to familiarize yourself with the area decomposition method. The area decomposition method separates the basic shapes found in a given complex figure for fast and organized analysis. Two cases are present in obtaining the areas of the shaded regions – figures with holes and composite figures.

Answer:

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

Answer:

To solve for the time when the football hits the ground, we need to set h = 0 and solve for t. We can do this using the quadratic equation: 0 = -3.9t² + 15.6t. Solving for t results in t = 0 or t = 4. Therefore, the football hits the ground at t = 0 seconds or 4 seconds after it is kicked. The units of measurement for time are seconds.

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 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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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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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:

$ 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 probabilities are p(0)=0.027 p(5)=0.4 p(1)= 0.243 and p(2)= 0.9

and P(x) = nCx p^x (1 - p)^(n - x) = n! / (x!(n - x)!) * p^x * q^(n - x)

For n = 5, x = 1, p = 0.2:

P(1) = 5! / (1! (5 - 1)!) * 0.2^1 * (1 - 0.2)^(5 - 1) = 5 * 0.2 * 0.4096 = 0.4096

For n = 4, x = 2, q = 0.4:

P(2) = 4! / (2! (4 - 2)!) * (1 - 0.4)^2 * 0.4^(4 - 2) = 6 * 0.36 * 0.16 = 0.3456

For n = 3, x = 0, p = 0.7:

P(0) = 3! / (0! (3 - 0)!) * 0.7^0 * (1 - 0.7)^(3 - 0) = 1 * 1 * 0.027 = 0.027

For n = 5, x = 3, p = 0.1

P(3) = 5! / (3! (5 - 3)!) * 0.1^3 * (1 - 0.1)^(5 - 3) = 10 * 0.001 * 0.81 = 0.0081

For n = 4, x = 2, q = 0.6

P(2) = 4! / (2! (4 - 2)!) * (1 - 0.6)^2 * 0.6^(4 - 2) = 6 * 0.16 * 0.36 = 0.3456

For n = 3, x = 1, q = 0.9

P(1) = 3! / (1! (3 - 1)!) * (1 - 0.9)^1 * 0.9^(3 - 1) = 3 * 0.1 * 0.81 = 0.243

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The probability of an event in a binomial distribution is calculated using the formula Pr(X=x)=C(n,x)p^x(1-p)^(n-x)

(a) Pr(X=0)=C(3,0)p^0(1-p)^3=C(3,0)(0.7)^0(0.3)^3=0.027

(b) Pr(X=5)=C(5,5)p^5(1-p)^0=C(5,5)(0.4)^5(0.6)^0=0.01024

(c) Pr(X=1)=C(4,1)p^1(1-p)^3=C(4,1)(0.6)^1(0.4)^3=0.2304

(d) Pr(X=2)=C(5,2)p^2(1-p)^3=C(5,2)(0.4)^2(0.6)^3=0.3456

The probability of an event in a binomial distribution is calculated using the formula Pr(X=x)=C(n,x)p^x(1-p)^(n-x), where n is the number of trials, p is the probability of success, x is the number of successes, and C(n,x) is the number of combinations of n things taken x at a time. To calculate each of the probabilities given above, we first calculate the combinations C(n,x), followed by the probabilities for success and failure, and then multiply these values together to get the probability of the event. For example, in part (a), we calculate C(3,0)=1, p^0=1, and (1-p)^3=0.027, and the probability of the event Pr(X=0)=1*1*0.027=0.027.

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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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A compound inequality to find the range of values for the width include the following:

x ≥ 8.

x ≤ 44.

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + x)

Where:

Note: The length of the dog run is 22 feet.

Since the perimeter of the dog run must be at least 52 feet, an inequality that models the situation is given by:

2(22) + x ≥ 52.

44 + x ≥ 52.

x ≥ 52 - 44

x ≥ 8.

Since the perimeter of the dog run must be no more than 88 feet, an inequality that models the situation is given by:

2(22) + x ≤ 88.

44 + x ≤ 88

x ≤ 88 - 44

x ≤ 44.

Therefore, a compound inequality to find the range of values for the width is 8 ≤ x ≤ 44.

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Answer:

$300

Step-by-step explanation:

We know

4 headphones = $48

1 headphones = $12

25 headphones = $12 x 25 = $300

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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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 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 expected value for a random variable is defined as the sum of the product of the values and probabilities of the variable.

In this case, the expected value for C is calculated by multiplying each possible value by its probability and adding the products. This is represented mathematically as:

Exp(C) = 0 x 0.60 + 1500 x 0.05 + 5000 x 0.13 + 15000 x 0.22 = 4025

The expected value of C can be interpreted as the average cost that the insurance company can expect to pay out for a randomly selected car of this model. This means that if the company insures a large number of these cars, they can expect the cost per car to average approximately $4025. The expected value does not represent the maximum cost for insuring this car model, or the cost for insuring a set number of cars. Instead, it provides an estimate of what the average cost per car will be.

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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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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).
[ Graphs are given below ].

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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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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 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 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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An equation that is perpendicular to line y = 1/2x - 8 and passes through (7, -6) in point-slope form is y + 6 = -2(x - 7).

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided, an equation of the first line is given by;

y = 1/2x - 8

Therefore, slope (m) = 1/2

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

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

Note: m represents the slope.

At point (7, -6), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-6) = -2(x - 7)

y + 6 = -2(x - 7)

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Complete Question:

Write an equation perpendicular to line y = 1/2x - 8 and passes through (7, -6) in point-slope form.

Answer:

Step-by-step explanation:

adadadadadadadadadadadada

Answer:

18 cowry shells

Step-by-step explanation:

1 dozen which is 1(12) eggs = 3 shells

6 dozens will be 6(12) eggs = ?

Cross Multiply

(72 eggs × 3 shells) ÷ 12

= 216 ÷ 12

= 18

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 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 mean is 45 and the variance is 18

The probability values are 0.951 and 0.937

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

n = 75

p = 0.6

The notation μ is the mean and it is calculated as

μ = n*p

So, we have

= 0.6*0.75

Evaluate

= 45.

The notation σ² is the variance and it is calculated as

σ² = n*p*(1-p)

So, we have

= 75*0.6*(1-0.6)

Evaluate

= 18.

Without continuity correction

The probability P(x>=52) without continuity correction is represented as

normalcdf(52, μ, σ)

So, we have

normalcdf(52, 45, √18)

Using a calculator, we get:

P(x>=52) = 0.951

With continuity correction.

The probability P(x>=52) with continuity correction is represented as

normalcdf(51.5, μ, σ)

So, we have

normalcdf(51.5, 45, √18)

Using a calculator, we get:

P(x>=52) = 0.937

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Complete question

Let X be a binomial random variable with n = 75 and p = 0.6

a) What is μ?

b) What is σ2?

c) What is the probability of P(x≥52), without continuity correction and with continuity correction.

Answer:

25%

Step-by-step explanation:

Discount is 175 - 131.25 = 43.75

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

Answer:

Answer is Negative

Step-by-step explanation:

picture at the bottom provides proof.