Find the probability that a randomly
selected point within the circle falls
in the white area.
r = 4 cm
[? ]%
Round to the nearest tenth of a percent.
Ento

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Answer:

\(\frac{560}{3}\) or 187

Step-by-step explanation:

First convert \(4\frac{2}{3}\) to a improper fraction

It would be \(\frac{14}{3}\)

Now multiply

\(\frac{14}{3}*\frac{40}{1} = \frac{560}{3}\)

The rounded off answers for the area of the rectangles are as follows: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

Rounding of a number is a mathematical process of approximating a given number to a specified level of accuracy or precision. Rounding is done to make numbers easier to work with or to communicate, especially when the number has many decimal places or digits.

The process of rounding involves changing a number to a nearby value that is easier to use or communicate, while still retaining its approximate value. The number is rounded to a certain number of decimal places or significant digits, depending on the required level of accuracy.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To check the answer, we can estimate 4751 as 4800, and then multiply 5 by 4800 to get the approximate product of 24,000.

2. 7 x 6000 = 42,000.

To check the answer, we can simply multiply 7 by 6000 to get the product of 42,000.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

To check the answer, we can estimate 5214 as 5200, and then multiply 6 by 5200 to get the approximate product of 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To check the answer, we can estimate 3867 as 3900, and then multiply 8 by 3900 to get the approximate product of 31,200.

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The following are the scaled off results for the rectangles' area:: 1) 24,000, 2) 42,000, 3) 31,200, 4) 31,200.

The mathematical process of approximating a given number to a predetermined degree of accuracy or precision is known as rounding. In particular when a number has numerous decimal points or digits, rounding is done to make numbers simpler to work with or communicate.

In order to make a number simpler to use or communicate, a number is rounded to a more manageable value while retaining its general meaning.

Depending on the necessary level of accuracy, the number is rounded to a particular number of significant digits or decimal places.

1. 5 x 4751 ≈ 5 x 4800 = 24,000.

To verify the result, we can convert 4751 to 4800, then increase 5 by 4800 to obtain a result that is roughly 20,000.

2. 7 x 6000 = 42,000.

We can quickly multiply 7 by 6000 to obtain the result of 42,000 to verify the solution.

3. 6 x 5214 ≈ 6 x 5200 = 31,200.

By converting 5214 to 5200 and multiplying that number by 6, we can approximate the solution to be 31,200.

4. 8 x 3867 ≈ 8 x 3900 = 31,200.

To verify the solution, we can convert 3867 to 3900 and multiply 8 by 3900 to obtain a result that is roughly 31,200.

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Answer:

x = -2

Step-by-step explanation:

First, add 6 to both sides.

-6 - x = -4

+ 6        +6

    -x =  -4 + 6

    -x = 2

Then, multiply both sides by -1.

(-1)(-x) = (2)(-1)

x = -2

Answer:

\( \sf \: x = - 2\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ -6 - x = -4

Then the value of x will be,

→ -6 - x = -4

→ -x = -4 + 6

→ -x = 2

→ [ x = -2 ]

Hence, the value of x is -2.

a. The unit rate is 9 d per t

b. Find the graph in the attachment

To graph the line, we need to find its gradient or unit rate

Since t has an increase of 0.20 units in t corresponds to an increase of 1.8 units in d.

The gradient or unit rate of change is m = change in d/change in t

= Δd/Δt

Since

So, substituting the values of the variables into the equation, we have

m = Δd/Δt

= + 1.8 units/+ 0.2 units

= 9 d per t

So, the unit rate is 9 d per t

To graph the function, we need to know the equation of the graph.

So, the equation of a graph in gradient form is

m = (y - y')/(x - x') where (x', y') = (0, 0) since the graphs both start at the origin

Since m = 9, we have

m = (y - y')/(x - x')

9 = (y - 0)/(x - 0)

9 = y/x

y = 9x

So, the equation of the line is y = 9x

Find the graph in the attachment.

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Answer:

Adult tickets = 66 × \(\frac{1}{3}\)

                     = 22

Student tickets = 66 - 22

                         = 44

Answer:

250= 1.50x + 20

Step-by-step explanation:

here 250 is the goal. 1.50 is how much she makes for a cup and x is the number of times to get x much. with how much her parents gave is 20. so we add the money her parents give and 1.50 times x to know the money shegets from all the lemonade selling.  graphing the equation but I cant do it on here

God Bless :>

Answer:

a. y = c1.50 + 20

b. She would have to sell 167 cups to earn $250.50

c. im not sure on that sorryyyy

Answer:

b/4 +b + b-8 =73

2b + b/4 = 81

9b/4 = 81

9b =81 * 4

b = 9* 4

b = 36

The sides of the triangles are 9 inch, 28 inch and 36 inch respectively

Step-by-step explanation:

Answer:

0.43478

Step-by-step explanation:

From the information given:

\(The \ required \ probability = P(1st ball = red) \times P(2nd ball = red) + P(1st ball = red) \times P(2nd ball = white) + P(2nd ball = red) \times P(1st ball = white) + P(1st ball = white) \times P(2nd ball = white)\)

\(= \dfrac{6}{6+8+10}\times \dfrac{5}{5+8+10} + \dfrac{6}{6+8+10} \times \dfrac{10}{5+8+10} + \dfrac{10}{6+8+10} \times \dfrac{6}{5+8+10} \times \dfrac{10}{6+8+10} \times \dfrac{9}{5+8+9}\)

\(=(\dfrac{6}{24}\times \dfrac{5}{23})+ (\dfrac{6}{24}\times \dfrac{10}{23}) +( \dfrac{10}{24}\times \dfrac{6}{23} ) + (\dfrac{10}{24}\times \dfrac{9}{23})\)

= 0.05434782609 + 0.1086956522  + 0.1086956522  + 0.1630434783

= 0.4347826088

≅ 0.43478

Answer: 16

Step-by-step explanation:

there are 3 feet in one yard so divided 48 by 3 and you get 16

Answer:

16

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the Intermediate Phase of mathematics education, one topic that demonstrates a hierarchical and logical progression in patterns, functions, and algebra is the concept of "Linear Equations."

The topic of Linear Equations in the Intermediate Phase builds upon the foundation laid in earlier grades and serves as a stepping stone towards more advanced algebraic concepts. Here is an overview of the topic sequence and content area spread for Linear Equations:

Introduction to Variables and Expressions:

Students are introduced to the concept of variables and expressions, learning to represent unknown quantities using letters or symbols. They understand the difference between constants and variables and learn to evaluate expressions.

Solving One-Step Equations:

Students learn how to solve simple one-step equations involving addition, subtraction, multiplication, and division. They develop the skills to isolate the variable and find its value.

Solving Two-Step Equations:

Building upon the previous knowledge, students progress to solving two-step equations. They learn to perform multiple operations to isolate the variable and find its value.

Writing and Graphing Linear Equations:

Students explore the relationship between variables and learn to write linear equations in slope-intercept form (y = mx + b). They understand the meaning of slope and y-intercept and how they relate to the graph of a line.

Systems of Linear Equations:

Students are introduced to the concept of systems of linear equations, where multiple equations are solved simultaneously. They learn various methods such as substitution, elimination, and graphing to find the solution to the system.

Word Problems and Applications:

Students apply their understanding of linear equations to solve real-life word problems and situations. They learn to translate verbal descriptions into algebraic equations and solve them to find the unknown quantities.

The content area spread for Linear Equations includes concepts such as variables, expressions, equations, operations, graphing, slope, y-intercept, systems, and real-world applications. The progression from simple one-step equations to more complex systems of equations reflects a logical sequence that builds upon prior knowledge and skills.

By following this hierarchical progression, students develop a solid foundation in algebraic thinking and problem-solving skills. They learn to apply mathematical concepts and procedures in a systematic and logical manner, paving the way for further exploration of patterns, functions, and advanced algebraic topics in later phases of mathematics education.

The complement of set Q will be Q' = {2, 8}.

what exactly is a set?

In mathematics, a set is a well-defined collection of distinct objects, called elements or members, that can be anything. These objects can be numbers, letters, people, animals, or any other things that can be described in a clear and unambiguous way. Sets are usually denoted by listing their elements within curly braces, for example:

A = {1, 2, 3, 4, 5} is a set of the first five positive integers.

Now,

The complement of a set Q, denoted Q', is the set of all elements in the universal set that are not in Q. In this case, the universal set is V = {2, 4, 6, 8}.

To find the complement of Q = {4, 6}, we need to find all the elements in V that are not in Q. These elements are 2 and 8.

Therefore,

              Q' = {2, 8}.

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Answer:

It is a parallelogram because it has either two or more sets of parallel lines

The domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

Domain is the set of {x} - values for which a function {y - values} exists. It is one of the important parameter while defining the characteristics of a function.

Given is the function as -

f(x) = (x - 3)²

{ 1 } -

The domain of the function f(x) = (x - 3)².

The function has no undefined points. So, we can write the domain as -

Domain → (- ∞ , + ∞)

{ 2 } -

The inverse of the function f(x) = (x - 3)².

We have -

f(x) = (x - 3)²

y = (x - 3)²

x = (y - 3)²

y - 3 = √x

y = 3 + √x

Therefore, the domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

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(a) The 99% confidence interval for the population standard deviation at Bank A is 1.33 to 2.16.

(b) The 99% confidence interval for the population standard deviation at Bank B is 1.41 to 2.29.

To find the confidence interval for the population standard deviation, we can use the chi-square distribution. The formula for the chi-square distribution is:

(X²) / (n-1) = s²

where X² is the chi-square value, n is the sample size, and s is the sample standard deviation.

For Bank A:

n = 20

s = 1.252

Using the chi-square distribution table with a degree of freedom of n-1 = 19 and a 99% confidence level, we find the critical values to be 8.907 and 32.852. Substituting these values into the formula above, we get:

(19 x 1.252²) / 32.852 < o² < (19 x 1.252²) / 8.907

1.78 < o² < 4.67

1.33 < o < 2.16

Therefore, the 99% confidence interval for the population standard deviation at Bank A is 1.33 to 2.16.

For Bank B:

n = 20

s = 1.397

Using the chi-square distribution table with a degree of freedom of n-1 = 19 and a 99% confidence level, we find the critical values to be 8.907 and 32.852. Substituting these values into the formula above, we get:

(19 x 1.397²) / 32.852 < o² < (19 x 1.397²) / 8.907

2.00 < o² < 5.24

1.41 < o < 2.29

Therefore, the 99% confidence interval for the population standard deviation at Bank B is 1.41 to 2.29.

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Answer:

A

Step-by-step explanation:

A is the most simplifiest form between the numbers.

Answer:

Because all elements in set B can be found in set A

Answer:

8

Step-by-step explanation:

n = 6

mean = 12

Therefore, sum of numbers = 12 x 6 = 72

Using ratio : 1 + 1 + 1 + 1 + 2 + 3 = 9

Therefore 72 ÷ 9  = 8

Therefore, mulitply each number in ratio by 8 to find the numbers.

The numbers are: 8, 8, 8, 8, 16, 24

So the median is 8

Answer:

\( \frac{3}{4} \)

Step-by-step explanation:

\( \frac{4}{8} \div \frac{4}{6} \)

\( \frac{4}{8} \times \frac{6}{4} \)

\( \frac{1}{4} \times 3\)

\( = \frac{3}{4} \)

Hi fellow Army^^

Answer:

y = 42

Step-by-step explanation:

180-90-48=42

The function with the steepest slope is \(y = 7x - 3\).

The correct answer is C.

The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.

Let's compare the coefficients of x in each of the given functions:

\(y = -8x + 5\)

Slope: -8

\(y - 9 = -2(x + 1)\)

Simplifying, we get \(y - 9 = -2x - 2\)

Rearranging, we have \(y = -2x + 7\)

Slope: -2

\(y = 7x - 3\)

Slope: 7

\(y + 2 = 6(x + 10)\)

Simplifying, we get \(y + 2 = 6x + 60\)

Rearranging, we have \(y = 6x + 58\)

Slope: 6

Therefore, the steepest slope is the \(y = 7x - 3\).

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Answer:

18/28, or percentage wise, approximately 64.2%

Step-by-step explanation:

Take the seniors and divide it by the total # of students, and you got your probability!

\(g(x)=a\cdot b^x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{(\stackrel{x}{0}~~,~~\stackrel{g(x)}{12})}\implies 12=a\cdot b^0\implies 12=a\cdot 1\implies 12=a~\hfill \underline{g(x)=12b^x} \\\\\\ \stackrel{\textit{we also know that}}{(\stackrel{x}{1}~~,~~\stackrel{g(x)}{9})}\implies 9=12b^1\implies \cfrac{9}{12}=b\implies \cfrac{3}{4}=b~\hfill \underline{g(x)=12\left( \frac{3}{4} \right)^x}\)

Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.

To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.

The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.

To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).

Payback Period = Cost of Education / Annual Increase in Earning Potential

Payback Period = $36,000 / $18,262

The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.

If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.

In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.

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Answer:

700 × 10

Step-by-step explanation:

Step 1:

700 × 10

Answer:

7,000

Hope This Helps :)

The sides of a triangle can be determined if the trigonometric ratios and angles are given. The missing sides of the given triangle are 6 and 8 respectively.

The trigonometric ratios are defined for a right angled triangle.

The example of these ratios are sin, cos, tan, cosec, sec and cot.

The trigonometric ratios are useful in determining the heights and distances of the large objects.

The diagram for the given triangle is given below,

Since, sin(x) = (The side opposite to angle x) / Hypotenuse

Apply the above trigonometric ratio in triangle 1 to get,

Sin(21°) = x / 16

=> x = 16 × Sin(21°)

=> x = 16 × 0.36

=> x = 5.76

Which is approximately 6 when taken as nearest to tenth.

Similarly for triangle 2, it can be written as,

Sin(40°) = x / 12

=> x = 12 × Sin(40°)

=> x = 12 × 0.64

=> x = 7.68

Which is approximately 8 when taken as nearest to tenth.

Hence, the missing sides for the given triangles are 6 and 8 approximately.

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Answer:

the poet's mood is that of disappointment, following the poor governance of the country, that is rich in human and natural resources. Tone: the poem has the tone of ” calls for hybrid of habits ” as advocated by the forest sage