12. (A.10.B) A sidewalk was built around a rectangular garden. Find the area of the sidewalk in terms of x
x
3x
2x-1
X+2

Answer: 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

The 30-60-90 triangle rule states that the hypotenuse is twice the length of the shortest leg (which would be 5) and the longer leg is [tex]\sqrt{3}[/tex] times the length of the shorter leg.

Since we are trying to find x we would use the rule for the longer leg

so 5 * [tex]\sqrt{3}[/tex] would just be 5[tex]\sqrt{3}[/tex]

The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.

The 30°-60°-90° Triangle Theorem states that in such a triangle, the side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is the product of the length of the hypotenuse and the square root of 3 divided by 2.

here, we have,

Using this theorem, we can write:

y = hypotenuse

Opposite of 30° angle = 5 = hypotenuse/2

Opposite of 60° angle = x = hypotenuse × (√(3)/2)

Solving for the hypotenuse in terms of y from the first equation, we get:

hypotenuse = 5×2 = 10

Substituting this value into the third equation, we get:

x = 10 × (√(3)/2) = 5 × √(3)

Hence, The value of the x is 5√3 after we successfully do the application of the 30°-60°-90° Triangle theorem.

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If there are 450 grams of element and half life is 8 minutes, then it will take 28.83 minutes the element to decay to 37 grams

Half life of radio active element = 8 minutes

Initial quantity of radio active element = 450 gram

Final quantity of radio active element = 37 grams

y = a(0.5)^(t/h)

Substitute the values in the equation

37 = 450 (0.5)^(t/8)

Move 37 to left hand side of the equation

37 / 450 = 0.5^(t/8)

Convert the terms to logarithm

t/8 = [tex]log_{0.5}\frac{37}{450}[/tex]

t/8 = 3.60

t = 8 × 3.60

Multiply the numbers

t = 28.83 minutes
Therefore, the it will take 28.83 minutes to decay to 37 grams

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Answer:

You are correct it is 12.

Step-by-step explanation:

Answer: Square root of 288, or estimated 16.97

Step-by-step explanation:

Conveniently, the points form a diagonal line as you show, so we can use the Pythagorean Theorem to find the distance.

The x-component of this is the distance between -6 and 6, which is 12, and the y-component is again the distance between -6 and 6, which is also 12.

Therefore, the distance is the square root of 12^2 + 12^2, or the squareroot of 288.

a) The x-range of a unit square is from o to 1 and y-range is also from 0 to 1

Sample space = {(x, y)} , 0≤x≤1,  0≤y≤1.

So, sample space associated with this random experiment is

{(x, y)} , 0≤x≤1,  0≤y≤1.

b) From the given data,

Sample space for A : {1, 3, 5, 7, 9, 11,...}

Sample space for B: {5, 10, 15, 20, 25,...}

Therefore, the sample space for A∩B will be the set of all odd natural numbers divisible by 5 which is

{5, 15, 25, 35,....}

c) First letter is the capital letter = 26 Possibilities

then four digits = 9*10*10*10

two lower case letters = 26*26

Total possible ways = 26*9*10*10*10*26*26

= 15,81,84,000 ways.

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Complete question:

Suppose a point is to be selected at random from the unit square. Write the sample space associated with this random experiment. 2. Let S = {0, 1, 2, 3, 4, ...), A = the set of odd natural numbers, and B = the set of natural numbers divisible by 5. What is the set An B? 3. A computer password consists of two lowercase letters followed by a capital letter and four digits. Find the total number of possible passwords.

The value of the expression  5c−3d+11 is 22 when c is 7 and d is 8.

An expression is combination of variables, numbers and operators.

The given expression is 5c−3d+11

Five c minus three times of d plus eleven.

c and d are the variables in the expression

Given that value of c is seven and value of d is eight

c=7 and d=8

Now we have to find the value of the expression when c is 7 and d is 8

Plug in the value of c and d in expression.

5(7)-3(8)+11

Five times seven is 35 and three times of eight is 24, we get

35-24+11

22

Hence, the value of the expression  5c−3d+11 is 22 when c is 7 and d is 8.

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Complete question is given below,

5c−3d+115, find the value of expression when c=7 and d=8

Answer:its hard to say

The above-shown note is labeled B based on the information provided.

A point is considered to really be equidistant from both of two other points when they are equally distanced from one another. The distance between any two given points may be calculated using the distance formula utilizing the coordinates of the two points.

Example: Given that points A and B have the coordinates (1, -2) and (5, 6), respectively, determine the midpoint of line segment AB. Find the midpoint's distance between points A and B to confirm it. The midpoint is confirmed to be equally far from points A and B because both of those places are from it.

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The shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.

The mean of the sampling distribution of the sample mean height for samples of size 10 will also be 40 inches.

The standard deviation of the sampling distribution of the sample mean height can be calculated as:

σ/sqrt(n) = 5.2/sqrt(10) = 1.645

So, the shape of the sampling distribution will be approximately normal, with a center at 40 inches and a standard deviation of 1.645 inches.

The variability of the sampling distribution is smaller than the variability of the population distribution, because the standard error is smaller than the population standard deviation. This means that the sample means are more likely to be closer to the population mean than the individual heights in the population.

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The exponent of g, r, is -65536.

The exponent of y, s, is 1.

The leading coefficient, k, is 4.

Note: The expression 4^65536g³y² √√/65536g³y² is not equal to kg³y³, but instead represents the value of 4 raised to the power of 65536 times g raised to the power of -65536, divided by the square root of 65536 times g raised to the power of -65536 times y squared. The square root symbol is used twice, which is equivalent to taking the square root of the square root, or the fourth root.

The graph of the inequality is added as an attachment

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

yz|x+2

Express properly

So, we have the following representation

y < x + 2

The above expression is an inequality that implies that

The value of y does not exceed 2 added to x

Next, we plot the graph

See attachment for the graph of the inequality

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If both bound trains leave together at 8, they will also start together at 11:45 the next time.

The LCM of two numbers is the smallest possible number that is divisible by both of those two numbers. The prime factorization and the division methods are generally used to find the LCM.

An eastbound train leaves the station every 25 minutes whereas a westbound train leaves the station every 45 minutes.

These two types of trains will leave the station together if the time is divisible by both 25 and 45, that is, the LCM of them.

Find the LCM of 25 and 45 using the prime factorization method.

25=5×5

45=3×3×5

LCM(25,45)=3×3×5×5

=225

As 1 hour equals 60 minutes, it follows that 225 minutes equals 3 hours and 45 minutes.

If 3 hours 45 minutes is added to 8 hours, it will be 11 hours 45 minutes.

Therefore, the two trains leave the station together at 11 hours 45 minutes.

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The second statement in your question is the correct response.

What is the sampling distribution?

A sampling distribution is the probability distribution of a statistic (such as the sample mean or sample proportion) based on all possible random samples of a fixed size from a population.

The following statement must be true for an estimator of a population parameter to be unbiased:

The expected value of the estimator is equal to the population parameter.

Hence, the second statement in your question is the correct response.

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Check the picture below.

The degree of the polynomial function represented by the graph is 4 and its leading coefficient is negative

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

The graph

The degree of the polynomial function is the number of times the curve tends to touch or intersect with the graph

In this case, we have

Degree = 4

For the leading coefficient, we have

leading coefficient = negative

This is because the graph opens down

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Answer:

Step-by-step explanation:

135°

Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero.

Approximate year when the Europe began circulating the printed newsletters is given by option c. 1600.

Therefore, the year when first printed newsletter began circulating in the Europe is equal to option c. 1600.

The above question is incomplete , the complete question is :

In approximately what year did printed newsletters begin circulating in Europe?

a]  1200     b]  1450      c] 1600         d ] 1850

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Online math courses can also offer some benefits, such as the flexibility to work at your own pace and the ability to review lectures and assignments as needed. Overall, taking an online math course requires self-discipline, motivation, and a willingness to seek help when needed.

Online classes are virtual classrooms that offer students the opportunity to learn from anywhere, at any time, with a reliable internet connection. The primary focus of online classes is to provide students with the same level of academic instruction as they would receive in a traditional classroom setting. Many educational institutions and organizations offer online classes, including colleges, universities, and K-12 schools.

One of the significant advantages of online classes is that they offer flexibility, which means students can manage their coursework according to their schedule. Students can also access course material, lectures, and assignments from anywhere, which eliminates the need to attend a physical classroom. Online classes also offer students the ability to work at their own pace and review course material as often as they need to.

Online classes provide students with access to a wide range of educational resources, including video lectures, interactive quizzes, discussion forums, and other learning tools. Many online classes also provide students with personalized support, including one-on-one virtual sessions with instructors or teaching assistants.

Taking an online math course can be different from taking other subjects online. Typically, online math courses involve watching pre-recorded video lectures, completing online assignments, and participating in online discussions or forums. Online math courses may also use virtual tools, such as interactive graphs or calculators, to enhance the learning experience.

Compared to other online courses, learning math online may require more self-discipline and motivation, as it can be challenging to stay engaged with the material without the structure of a traditional classroom. Additionally, math is a subject that often builds on previous concepts, so it is essential to stay on top of the material and seek help if needed.

However, online math courses can also offer some benefits, such as the flexibility to work at your own pace and the ability to review lectures and assignments as needed. Overall, taking an online math course requires self-discipline, motivation, and a willingness to seek help when needed.

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The equation representing the scenario is 1.5x + 8 = 20 and the possible number of rides is 8.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, The cost of entering the fair is $8 and the cost of each ride is $1.50.

Let, The number of rides be 'x'.

Therefore, The equation can be formed as, 1.5x + 8 = 20.

Now, To obtain the number of rides,

1.5x + 8 = 20.

1.5x = 12.

x = 12/1.5.

x = 8.

So, 8 rides are possible.

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The graph which is most likely to represent the residuals from the best fit line is Option C.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that from the graphs of residuals is  the same set of data using different lines to fit the data.

The best fit line is the line that minimizes the sum of the squared residuals.

In other words, it is the line that has the smallest sum of the squared differences between the actual data points and the predicted values from the line.

The residuals represent the differences between the actual data points and the predicted values, and any systematic pattern in the residuals would suggest that the line is not a good fit for the data.

Hence, Option C is correct, the graph which is most likely to represent the residuals from the best fit line.

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The value of x to the nearest tenth are as follows;

x = 47.0 units.

x = 25.1 units.

x = 23.8 units.

x = 29.7 units.

x = 21.1°.

x = 39.6°.

x = 58.0°.

x = 72.9°.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

Opposite side = x.

Adjacent side = 25.

Therefore, we would determine the value of x by using Tan trigonometric function:

Tanθ = Opposite side/Adjacent side

Tan45 = 25/x

x = 25Tan62

x = 47.0 units.

For right-angled triangle 3, we have:

Sin26 = 11/x

x = 11/0.4384

x = 25.1 units.

For right-angled triangle 4, we have:

Sin48 = x/32

x = 32sin48

x = 23.8 units.

For right-angled triangle 5, we have:

Cos12 = 29/x

x = 29/0.9782

x = 29.7 units.

For right-angled triangle 6, we have:

Cosθ = 14/15

θ = cos⁻¹(0.9333)

θ = 21.1°.

For right-angled triangle 7, we have:

Tanθ = 19/23

θ = tan⁻¹(0.8261)

θ = 39.6°.

For right-angled triangle 8, we have:

Cosθ = 9/17

θ = cos⁻¹(0.5294)

θ = 58.0°.

For right-angled triangle 9, we have:

Sinθ = 43/45

θ = sin⁻¹(0.9556)

θ = 72.9°.

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The function f(x) = 3x³ + 5 is neither even nor odd. To determine whether a function is even or odd, you need to check how the function behaves when x is replaced with -x.

To determine whether the given function is even, odd, or neither, we need to check the following conditions:

Even function: If f(-x) = f(x) for all x in the domain of f, then the function is even.

Odd function: If f(-x) = -f(x) for all x in the domain of f, then the function is odd.

Let's check these conditions for the given function:

f(x) = 3x³ + 5

f(-x) = 3(-x)³ + 5 = -3x³ + 5

f(x) = 3x³ + 5

Since f(-x) is not equal to f(x), the function is not even.

f(-x) = 3(-x)^3 + 5 = -3x^3 + 5

-f(x) = -(3x^3 + 5) = -3x^3 - 5

Since f(-x) is not equal to -f(x), the function is not odd.

Therefore, the given function is neither even nor odd.

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Lindsey made 35 free throws, 143 two-point field goals, and 107 three-point field goals during the 2006 regular season.

Two or more expressions with an Equal sign is called as Equation.

Let's denote the number of two-point field goals Lindsey made by x, and the number of three-point field goals she made by y.

x + y + (x+y-71)/2 + (x+y-71)/2 - 21 = 862 (total points equation)

x = 2y - 71 (two-point field goals equation)

Simplifying the first equation and substituting the second equation, we get:

3x + 3y = 1964

Substituting x = 2y - 71 into this equation, we get:

3(2y-71) + 3y = 1964

Solving for y, we get:

y = 107

Substituting this value into the equation x = 2y - 71, we get:

x = 143

Now, (x + y - 71)/2 - 21 = (143 + 107 - 71)/2 - 21 = 35

Therefore, Lindsey made 35 free throws, 143 two-point field goals, and 107 three-point field goals during the 2006 regular season.

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Answer:

After substituting -4 for "a" and 16 for "b", the equation can be simplified and solved.

-The equation 2 (2x - 11) + 6 = -4x + 16

Expanding the equation on the left-hand side, we get:

4x - 22 + 6 = -4x + 16

Simplifying, we get:

10 = -10x + 32

Subtracting 32 from both sides, we get:

-22 = -10x

Dividing both sides by -10, we get:

x = 2.2

This means that there is exactly one solution, which is x = 2.2. So, statement 3 is true.

-The equation 4x - 8 (x - 2) = -4x + 16

Expanding the equation on the left-hand side, we get:

4x - 8x + 16 = -4x + 16

Combining like terms, we get:

-4x + 16 = -4x + 16

This equation is true for all values of x, so there are infinitely many solutions. So, statement 2 is true.

-The equation 10 + x + 2 - 6x = -4x + 16

Expanding the equation on the left-hand side, we get:

10 + x + 2 - 6x = -4x + 16

Combining like terms, we get:

-5x + 12 = -4x + 16

Adding 4x to both sides, we get:

-x + 12 = 16

Adding x to both sides, we get:

12 = 16

This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.

-The equation 9x +3 - 13x + 6 = -4x + 16

Expanding the equation on the left-hand side, we get:

9x + 3 - 13x + 6 = -4x + 16

Combining like terms, we get:

-4x + 9 = -4x + 16

Adding 4x to both sides, we get:

9 = 12

This equation is not true for any values of x, so there are no solutions. So, statement 1 is true.

Therefore, the true statements are:

-The equation 2 (2x - 11) + 6 = ax + b has no solution.

-The equation 4x - 8 (x - 2) = ax + b has infinitely many solutions.

-The equation -5 (4x-6) 14 = ax + b has exactly one solution.

The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

A quadratic function,

3x² - 9x + 2.

The standard form of the quadratic function is

ax² + bx + c.

The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.

Therefore, 3x² - 9x + 2.

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Answer:

the answer is : m= -1/3

Step-by-step explanation:

you need the steps?