Find b.
L
15 m P
b =
8 m
60 m
Write your answer as a whole number or a decimal. Do not round.
b
meters

Answer: Let x = 0.727272...

Then, 100x = 72.727272...

Subtracting x from 100x gives:

100x - x = 72.727272... - 0.727272...

99x = 72

x = 72/99

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 9. Therefore:

x = (72/9) / (99/9) = 8/11

So, a = 8 and b = 11. Therefore, the recurring decimal 0.727272... can be expressed as the fraction 8/11.

Step-by-step explanation:

There is only one solution for this equation. v = 31/4 is the only solution to this equation.

To solve for v in the equation (3)/(4v)+(7)/(v)=1, we need to get a common denominator and then solve for v.

Step 1: Get a common denominator. The common denominator for 4v and v is 4v. So, we will multiply the second fraction by 4/4 to get a common denominator:
(3)/(4v)+(7*4)/(v*4)=1

Step 2: Simplify the fractions:
(3)/(4v)+(28)/(4v)=1

Step 3: Combine the fractions:
(3+28)/(4v)=1

Step 4: Simplify the numerator:
(31)/(4v)=1

Step 5: Cross-multiply to solve for v:
31=4v

Step 6: Divide both sides by 4 to get v:
v=31/4

The solution is v=31/4.

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The given function f(x) = 5 (2.3)^x is an exponential function.

The given function is f(x) = 5 (2.3)^x.

To determine if the function is linear, quadratic, or exponential, we need to examine the form of the function.

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

A quadratic function has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

An exponential function has the form f(x) = ab^x, where a and b are constants.

The given function, f(x) = 5 (2.3)^x, is in the form of an exponential function, with a = 5 and b = 2.3. Therefore, the function is exponential.

In conclusion, the given function f(x) = 5 (2.3)^x is an exponential function.

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1. (a)  Using a z-table, we can find the probability corresponding to this z-score, which is 0.758. Therefore, the probability that a student's mark is less than 52 is 0.758. (b) To find the number of students whose marks are between 45 and 55, we need to calculate the z-scores for 45 and 55 . The z-score for 45 is (45 - 45) / 10 = 0, and the z-score for 55 is (55 - 45) / 10 = 1.  (c)  The probability corresponding to this z-score is 0.3085. Therefore, the percentage of students whose marks exceed 40 is 1 - 0.3085 = 0.6915, or 69.15%. 2. (a)  So, the probability that a student only has regular study time is 750/1000 - 550/1000 = 200/1000 = 0.2. (b) The probability that a student either has a regular study time or uses reference books is 750/1000 + 550/1000 - 550/1000 = 750/1000 = 0.75. (c) The probability that a student neither studies regularly nor uses reference books is 1 - 0.75 = 0.25.

Therefore, the probability that a student's mark is between 45 and 55 is 0.8413 - 0.3413 = 0.5. Since there are 220 students in the college, the number of students whose marks are between 45 and 55 is 0.5 * 220 = 110.

To find the probability that a student's mark is less than 52, we need to calculate the z-score for 52 using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation. So, z = (52 - 45) / 10 = 0.7.

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Answer:

x=6

My best attempt

Step-by-step explanation:

The ratio is 4:5.6 from top to bottom.

We have a ratio of x:8.4

We will make an equation.

4:5.6=x:8.4

Cross multiply:

5.6x=4x8.4

5.6x=33.6

Divide both sides by 5.6:

x=6

The function that represents exponential growth is C. Of(x) = 0.3(1.05)^(x), where x is the input variable.

Exponential growth occurs when a quantity increases at a constant percentage rate over time, which is exactly what happens in the function C. As x increases, the term (1.05)^(x) grows larger and larger, leading to a corresponding increase in the value of the function. The coefficient 0.3 scales the rate of growth so that it starts at a manageable level.

Functions A, B, and D do not represent exponential growth. Function A decreases over time as the base is less than 1, function B represents a linear growth, and function D represents linear growth as well.

The function with Exponential growth is  f(x) = 0.3 [tex](1.05)^x[/tex].

An exponential function is a nonlinear function with the formula y = [tex]a(b)^x[/tex], where a = 0 and b = 1.

The function is an exponential growth function for a > 0 and b > 1. The function is an exponential decay function when a > 0 and 0 b 1.

First function, f(x) = 134 [tex](0.75)^x[/tex]

Here the value of b < 1 then it Exponential Decay.

Now,  f(x) = 513 + 0.2x is linear function.

Now,  f(x) = 0.3 [tex](1.05)^x[/tex]

Here the value of b > 1 then it Exponential Growth.

Now,  f(x) = 15+ 1.6x is linear function.

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To get the chart that you have circled in the second picture, you need to create a table using the given formulas and then create a chart using the table. Here are the steps:

1. Create a table with the following columns: Iteration, Random, Demand, Revenue, Cost, Refund, and Profit.
2. In the first row of the table, enter the given formulas in the respective columns. For example, in the first row of the Random column, enter =RAND(), in the first row of the Demand column, enter =ROUND ( NORM.INV ( RAND(), Mean, Standard Deviation),0), and so on.
3. Copy the formulas down to the 5000th row to get the values for all 5000 iterations.
4. Select the entire table and click on the Insert tab in the Excel ribbon.
5. In the Charts group, click on the type of chart that you want to create. In this case, it looks like you want to create a scatter chart.
6. In the Chart Design tab, click on the Select Data button in the Data group.
7. In the Select Data Source dialog box, click on the Add button in the Legend Entries (Series) section.
8. In the Edit Series dialog box, enter a name for the series, select the Profit column for the Series X values, and select the Demand column for the Series Y values.
9. Click on the OK button to close the Edit Series dialog box and then click on the OK button to close the Select Data Source dialog box.
10. Your chart should now be created and should look like the one that you have circled in the second picture.

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Ans - The pilot is 1868.08 mi from her starting position, To find the distance the pilot is from her starting position, we can use the law of cosines. The law of cosines states that for any triangle with sides a, b, and c, and angle C opposite side c:

[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]

In this case, the pilot's original path is one side of the triangle (a), her new path after the course correction is another side of the triangle (b), and the distance she is from her starting position is the third side of the triangle (c). The angle between the two paths is 20 degrees (C).

First, we need to find the length of sides a and b. The pilot flew for 1.5 hrs at a speed of 685 mi/h on her original path, so:

a = 1.5 hrs * 685 mi/h = 1027.5 mi

She then flew for 2 hrs at the same speed on her new path, so:

b = 2 hrs * 685 mi/h = 1370 mi

Now we can plug these values into the law of cosines to find the distance the pilot is from her starting position (c):

[tex]c^2 = 1027.5^2 + 1370^2 - 2*1027.5*1370*cos(20)[/tex]
[tex]c^2 = 3,488,806.25[/tex]
[tex]c = sqrt(3,488,806.25)[/tex]
[tex]c = 1868.08 mi[/tex]

Therefore, the pilot is 1868.08 mi from her starting position.

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Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set.

Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order.

Mode: The mode is the number that appears most frequently in a set of numbers.

Hi there! Yes, I can certainly show and explain the methods for calculating Mean, Median, and Mode. These are all measures of central tendency, which are used to describe the center of a data set.

Mean: The mean is the average of a set of numbers. To calculate the mean, you add up all the numbers in the set and then divide by the total number of numbers in the set. For example, if you have the numbers 2, 4, 6, 8, and 10, the mean would be (2 + 4 + 6 + 8 + 10) / 5 = 6.

Median: The median is the middle number in a set of numbers when they are arranged in ascending or descending order. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. For example, if you have the numbers 2, 4, 6, 8, and 10, the median would be 6. If you have the numbers 2, 4, 6, 8, 10, and 12, the median would be (4 + 6) / 2 = 5.

Mode: The mode is the number that appears most frequently in a set of numbers. If there is more than one number that appears the same number of times, there can be more than one mode. For example, if you have the numbers 2, 4, 6, 8, 10, and 10, the mode would be 10 because it appears twice and the other numbers only appear once.

I hope this helps! Let me know if you have any other questions.

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If you are solving for z:

-8=z/14

multiply by 14 on both sides:

z = -112

If there are 578 coyotes in 2003 with initial growth of 1.52, there will be approximately 336113 coyotes in 2028.

The number of coyotes in 2028 can be found by using the formula for exponential growth:

[tex]A = P(1 + r)^t[/tex]

Where:

A = final amount
P = initial amount
r = growth rate
t = time in years

Plugging in the given values:

[tex]A = 578(1 + 1.52)^25[/tex]

Using a calculator, we get:

[tex]A = 578(1.52)^25[/tex]
[tex]A = 578(581.68)[/tex]
[tex]A = 336112.64[/tex]

Therefore, there will be approximately 336113 coyotes in 2028.

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The polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials as:

x^(2)y^(4)(2y + 3)(2y - 3)

The polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials by factoring out the common factor of x^(2)y^(4). This leaves us with:

x^(2)y^(4)(4 - 9y^(2))

Now, we can factor the polynomial inside the parentheses as a difference of squares:

x^(2)y^(4)(2y + 3)(2y - 3)

Therefore, the polynomial 4x^(2)y^(4) - 9x^(2)y^(6) can be rewritten as a product of polynomials as:

x^(2)y^(4)(2y + 3)(2y - 3)

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\(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\)

Let \(n \in \mathbb{N}\) with \(n>2\). We consider the set \( S = \{a \in \mathbb{Z}_{n} \ | \ a^{2} = [1] \in \mathbb{Z}_{n}\} \). We have to prove that \( S \neq \emptyset \).

We prove by contradiction. Suppose \( S = \emptyset \). This implies that for all \( a \in \mathbb{Z}_{n}, \ a^{2} \neq [1] \in \mathbb{Z}_{n}\). Thus, \( [1] \) is not a square in \(\mathbb{Z}_{n}\). But since \(n >2\), \([1]\) has at least two square roots in \(\mathbb{Z}_{n}\) which implies that \( S \neq \emptyset \).

Therefore, \(S \neq \emptyset\) and thus there exists \(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\).

This proves that there exists an \(a \in \mathbb{Z}_{n}\) such that \(a^{2} = [1] \in \mathbb{Z}_{n}\) and \(a \neq [1]\).

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The equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).

The area of mixed shapes is the area that is covered by any hybrid shape. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These forms or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.

A composite form is essentially a combination of fundamental shapes. A "composite" or "complex" shape is another name for it.

The area of the rectangle is given as:

A = (l)(w)

A = 10(8)

A = 80 sq. units

The area of the triangle is:

A = 1/2(b)(h)

In the figure:

b = 16 - 10 = 6 and h = 8.

A = 1/2(6)(8)

A = 24 sq. units

The total area of the figure is:

Area = area of rectangle + area of triangle

Area = 80 + 24

Area = 104 sq. units

Hence, the equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).

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Answer: 89 miles

Step-by-step explanation:

Well, if the construction crew added one mile every day for 38 days, then the formula would look like this.

L = 51 + (38)

51 + 38 = 89

L = 89 miles

Answer:

B

Step-by-step explanation:

2 is hundred = 2x100

0 is tens =0x10

4 is unit =4 x 1

All numbers after the decimal point to the right are fractions

0 is tenth = 0/10 =0

1 is hundredth =1/100

7 is thousandth 7/1000

Now you can choose the right answer

The probability of rolling a prime number every time

The probability of rolling a prime number on a single die is 3/6 or 1/2, since there are three prime numbers (2, 3, 5) out of six possible outcomes.

To find the probability of rolling a prime number ten times in a row, we need to multiply the probabilities together. This is because each roll is independent of the others, so the probability of rolling a prime number on each roll is the same.

So the probability of rolling a prime number ten times in a row is:

(1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 1/1024

Therefore, the probability of rolling a prime number every time a die is rolled ten times is 1/1024.

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a) To solve for the unknowns using Gaussian elimination, follow these steps:
1. Multiply the first equation by -1 and add it to the second equation to get x2 = 7 + x3.
2. Multiply the first equation by -3 and add it to the third equation to get x3 = 3.
3. Substitute x3 = 3 into the first equation to get x1 = 2.

b) To solve for the unknowns using Gauss-Jordan elimination, follow these steps:
1. Multiply the first equation by -1 and add it to the second equation to get x2 = 7 + x3.
2. Multiply the first equation by -3 and add it to the third equation to get x3 = 3.
3. Substitute x3 = 3 into the second equation to get x2 = 4.
4. Substitute x3 = 3 and x2 = 4 into the first equation to get x1 = 2.

c) To solve for the unknowns using LU decomposition, follow these steps:
1. Compute the LU decomposition of the coefficient matrix A.
2. Solve Ly = b using forward substitution to get y = [1, 4, 3]^T.
3. Solve Ux = y using backward substitution to get x = [2, 4, 3]^T.

d) To solve for the unknowns using matrix-inverse based solution, follow these steps:
1. Compute the inverse of the coefficient matrix A.
2. Multiply the inverse of A with b to get x = [2, 4, 3]^T.

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The chemist must use 12 ml of the 11% acid solution and 42 ml of the 20% acid solution to make a solution of quantity 54 ml of 18% concentration acid solution.

It is already given that the chemist wishes to make a solution of 54 milliliters of 18 percent concentration using two different solutions of concentration 11% and 20% each.

Now let us consider that the quantity of acid to be present in the final solution is (18/100)×54 = 9.72 ml

If we consider that x ml of 11% solution and y ml of 20% solution are added, then following relations can be obtained:

Total volume of x and y in the final solution = x + y = 54 ...(1)

Considering the concentration of acid and its volume, the following equation is formed:

0.11x + 0.2y = 9.72 ...(2)

Solving the equations (1) and (2) for the value of x and y, we get:

x = 54 - y

∴ 0.11(54 - y) + 0.2y = 9.72

⇒ 5.94 - 0.11y + 0.2y = 9.72

⇒ 0.09y = 3.78

⇒ y = 42 ml

Putting the value of y in equation (1), we get

x = 54 - y

x = 54 - 42 = 12 ml

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The total distance of 2 and 1/7 laps of the race track is given as follows:

[tex]3\frac{39}{42}[/tex]

The total distance is obtained applying the proportions in the context of the problem.

The length of one lap, as a fraction, is given as follows:

1 and 5/6 km = (6 + 5)/6 = 11/6 km.

The number of laps is given as follows:

2 and (1/7) = (14 + 1)/7 = 15/7 laps.

Hence the total distance is given as follows:

11/6 x 15/7 = 165/42.

165 divided by 42 has a quotient of 3 with a remainder of 39, hence the mixed number representing the number of laps is given as follows:

[tex]3\frac{39}{42}[/tex]

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The experimental probability of choosing a nickel based on the 13 trials is 4/13.

What is probability ?

Probability can be defined as ratio number of favourable outcomes, total number of outcomes.

Based on the experimental probabilities shown in the table, we can calculate the probability of choosing a nickel on the 13th trial using the following steps:

Calculate the total number of trials: 12 + 1 = 13

Calculate the total number of times a nickel was chosen in the 12 trials: 12 * 1/4 = 3

Add 1 to the total number of times a nickel was chosen to account for the 13th trial: 3 + 1 = 4

Calculate the experimental probability of choosing a nickel based on the 13 trials: 4/13

Therefore, the experimental probability of choosing a nickel based on the 13 trials is 4/13.

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The Height of the pool should be 1.6 m.

Every three-dimensional item requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an object inside the confines of three-dimensional space. It is also known as the object's capacity.

Given:

length of pool= 12.5 m

width of pool = 5.7 m

and, Maximum volume of pool = 114 m³

So, Volume= l w h

114 = 12.5 x 5.7 x h

114 = 71.25 h

h = 114/ 71.25

h = 1.6 m

Thus, the height can be 1.6 m.

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Using synthetic division, the value of h(-4) is - 24.

1. Set up the synthetic division grid with the divisor (-4) in the top left corner and the coefficients of the polynomial in the top row.
-4 | 2   0   -25   4

2. Bring down the first coefficient to the bottom row.
-4 | 2   0   -25   4
   |                      
     2

3. Multiply the divisor (-4) by the first number in the bottom row (2) and put the result (-8) in the second column of the top row.
-4 | 2   0   -25   4
   |     -8            
     2

4. Add the numbers in the second column (0 and -8) and put the result (-8) in the second column of the bottom row.
-4 | 2   0   -25   4
   |     -8            
     2  -8

5. Repeat steps 3 and 4 for the remaining columns.
-4 | 2   0   -25   4
   |     -8     32  -28    
     2  -8      7   -24

6. The last number in the bottom row (-24) is the remainder and the value of h(-4). The other numbers in the bottom row (2, -8, 7) are the coefficients of the quotient polynomial.

Therefore, h(-4) = 24.

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the friends receive one eighteenth each

Answer:

12

Step-by-step explanation:

g(-4)=2(-4)^2+4(-4)-8

g(-4)=8

f(8)=2(8)-4

f(8)=12

Answer:

To calculate the ending balance, we can use the following formula:

Ending Balance = Principal x (1 + Interest Rate x Time)

Given:

Principal = $7,900

Interest Rate = 1.9%

Time = 2 3/4 years

Therefore,

Ending Balance = $7,900 x (1 + 0.019 x 2.75) = $8,084.60

Answer: 8319.66994

Step-by-step explanation:

your initial x your interest all raised to your time interval.

7,900(1+.019)^2.75

Answer: 1.1 The diameter of the tin on the picture is approximately 90 mm.

1.2 The circumference of the base of the tin is approximately 565 mm (2πr = 2π(45) = 565).

Step-by-step explanation: math is stressful fr

We can write the diameter and circumferance of base as -

D = 2√(750ρ/πh)

C = 2π√(750ρ/πh)

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

Given is to find the diameter and height of the tin can.

Assume the density of coffee as {ρ}. We can write the volume of the tin can as -

Volume = mass x density

Volume = 750ρ

We can write -

πr²h = 750ρ

r = √(750ρ/πh)

D = 2r

D = 2√(750ρ/πh)

Now, we can write the circumferance as -

C = 2πr

C = 2π√(750ρ/πh)

Therefore, we can write the diameter and circumferance of base as -

D = 2√(750ρ/πh)

C = 2π√(750ρ/πh)

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Answer:

22

Step-by-step explanation:

10+11=21

.05+.05=1

1+21=22

The number of points Wyatt has left is 58.

If Wyatt loses 7 points every time he falls off a rock and he falls off 6 rocks, he will lose a total of 42 points (7 x 6 = 42). To find out how many points he has left, we can subtract 42 from his starting points of 100:

100 - 42 = 58

Therefore, Wyatt has 58 points left after falling off 6 rocks in the Rock Climber video game.

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