If the circumference of a circle is 13 pi, what is the diameter of the circle.

The point needed for the relation is \(P(x,y) = (3, 4)\) if P and P' are symmetric about the x-axis.

The point needed for the relation is \(P(x,y) = (-3, -4)\) if P and P' are symmetric about the y-axis.

In this exercise we are supposed to determine the coordinates of a point P under an assumption of rigid transformation. Now, we must use the following symmetry transformations:

Reflection about the x-axis

\(S'(x,y) = S(x,y) - 2\cdot (0, s_{y})\) (1)

Reflection about the y-axis

\(S'(x,y) = S(x,y) - 2\cdot (s_{x}, 0)\) (2)

Where:

If we know that \(P'(x,y) = (3, -4)\), the coordinates for each reflection are, respectively:

Reflection about the x-axis

\(P(x,y) = (3,-4) - 2\cdot (0, -4)\)

\(P(x,y) = (3, 4)\)

\(P(x,y) = (3, 4)\) if P and P' are symmetric about the x-axis.

Reflection about the y-axis

\(P(x,y) = (3, -4) - 2\cdot (3, 0)\)

\(P(x,y) = (-3, -4)\)

\(P(x,y) = (-3, -4)\) if P and P' are symmetric about the y-axis.

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Based on the given information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own graphing TI calculators so it can be estimated that the proportion of students who do not own a TI graphing calculator is 50%.

To estimate the proportion of students who do not own a TI graphing calculator, we can use the information provided that out of the 4 students who owned a TI calculator, 2 had graphing calculators. Since we know that all graphing calculators are TI calculators, we can assume that the 2 students with graphing calculators are included in the total count of students who own TI calculators. Therefore, the remaining 2 students who own TI calculators must have non-graphing calculators.

Based on this information, we can estimate that out of the total population of students, 2 out of 4 students (or 50%) own non-graphing TI calculators. Therefore, we can estimate that the proportion of students who do not own a TI graphing calculator is 50%.

It's important to note that this is an estimation based on the limited information provided. To obtain a more accurate estimate, a larger sample size or more comprehensive data would be needed. Additionally, this estimation assumes that the sample of 4 students is representative of the entire student population in terms of calculator ownership. If there are any biases or limitations in the sampling method or if the sample is not representative, the estimate may not accurately reflect the true proportion of students who do not own a TI graphing calculator.

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Ms. Davis drove approximately 176.54 kilometers in June.

Let's assume that Ms. Davis drove x kilometers in July. According to the given information, she drove 72.6 kilometers less in June than in July. Therefore, her distance in June can be expressed as (x - 72.6) kilometers.

The total distance she drove in June and July is 425.68 kilometers. So, we can set up the equation:

(x - 72.6) + x = 425.68

Simplifying the equation:

2x - 72.6 = 425.68

Adding 72.6 to both sides:

2x = 498.28

Dividing both sides by 2:

x = 249.14

Therefore, Ms. Davis drove approximately 249.14 kilometers in July. Since she drove 72.6 kilometers less in June, her distance in June can be calculated as:

249.14 - 72.6 = 176.54 kilometers

Therefore, Ms. Davis drove approximately 176.54 kilometers in June.

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Answer:

396

Step-by-step explanation:

5280/40 =132

132x3 =396

The rank of a matrix is the number of linearly independent columns or rows in the matrix.

If the columns of an n × n matrix A are linearly independent as vectors in ℝn, then the rank of A is n. This is because linearly independent vectors are not multiples of each other, and therefore do not reduce to a smaller set of linearly independent vectors when the matrix is put in reduced row echelon form. As a result, the rank of the matrix is equal to the number of columns, which is n. Therefore, the rank of A is n.

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Answer:

0.3232323232... is an irrational number

Step-by-step explanation:

An irrational number is any number that cannot be written as a fraction of whole numbers.

Answer:

3rd graph

Step-by-step explanation:

Since the inequality has a greater than symbol (>) and not a greater than or equal to symbol (\(\geq\)), the graph will have a dotted line, meaning only the third and fourth graphs could be the one.

Since 2x+3y is GREATER THAN 6 and not LESS THAN 6, we know that the shaded part of the graph will be above (or more) than the line. Therefore, the third graph is the graph that represents the inequality.

The attached picture proves it :)

Hope this helps!

Answer:

62%

Step-by-step explanation:

10 000 ÷ 100 = 100

620 ÷ 100

= 62%

The appropriate domain restriction for this work problem would be:

x ≤ 8

The appropriate domain restriction for this problem would be based on the maximum number of hours

Josephine can work per day, which is 8 hours. Since she cannot work more than 8 hours, the domain restriction would be that the number of hours worked (x) should be less than or equal to 8.

This ensures that the number of hours worked is within the permissible limit imposed by child labor laws.

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The investor can obtain an annual annuity payment of approximately $48,651 for his retirement years.

To calculate the annual annuity payment, we can use the present value of an ordinary annuity formula. The formula is:

PV = C × [(1 - (1 + r)^-n) / r]

Where:

PV is the present value of the annuity,

C is the annual payment,

r is the interest rate,

n is the number of periods.

In this case, the investor has a retirement period of 25 years, and the interest rate is 7.5%.

The present value of the annuity is the amount the investor can invest today plus the present value of the annual payments he can make for 30 years.

Using the formula, we can solve for C, the annual payment, which comes out to approximately $48,651.

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The dividing by 0.5 is not the same as dividing by 2 , because 0.5 and 2 are different numbers  .

Let us understand the Division with the help of example ;

let the number be 10 ;

first we divide the number 10 by 0.5 ;

this can be written mathematically as ⇒ \(\frac{10}{0.5}\)  ;

⇒ \(\frac{10}{\frac{1}{2} }\) = \(10\times2\) = 20 ;

So , on dividing 10 by 0.5 , we get the answer as 20 .

Second , the number 10 is divided by 2 ;

this can be written mathematically as ⇒ \(\frac{10}{2}\) ;

⇒ \(\frac{10}{2 }\)  = 5  ;

So , on dividing 10 by 2 , we get the answer as 5  .

Therefore , dividing by 0.5 is not same as dividing by 2 .

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T is a point in the line segment SU

ST + TU = SU

ST = 6

TU = 5

HOPE THIS WILL HELP....

The triangles ∆ABC and ∆ADC are similar triangles, and:

m∠BAC = m∠DAC = 70°

m∠ACB = 20°

CB = CD = 12

AB = DA = 7

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

Considering the angles of the right triangle ACD;

m∠DAC = 180° - (90 + 20)°

m∠DAC = 70°

The angle m∠BAC corresponds to m∠DAC so;

m∠BAC = m∠DAC = 70°

The angle m∠ACB corresponds to m∠ACD so;

m∠ACB = m∠ACD = 20°

The side AB corresponds to side DA hence;

5x - 3 = 3x + 1

5x - 3x = 1 + 3 {collect like terms}

2x = 4

x = 4/2

x = 2

AB = 5(2) - 3 = 7

AB = DA = 7

In conclusion, since the triangles ∆ABC and ∆ADC are similar triangles, then:

m∠BAC = m∠DAC = 70°

m∠ACB = 20°

CB = CD = 12

AB = DA = 7

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Answer:

8times -12

Step-by-step explanation:

hope that helps

Expression 4(2x - 3) will have an analogous expression of 12x - 12.

The link between numbers, variables, and functions using mathematical signs like addition, subtraction, multiplication, and division is referred to as expression in mathematics.

Mathematical expression is defined as the relationship between numerical variables and mathematical operations such addition, subtraction, multiplication, and division.

Given expression is 4(2x - 3 ). The equivalent expression will be solved as below,

E = 4(2x - 3 )

E = 8x - 12

Hence, 8x – 12 will be the equivalent expression.

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1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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Expressions is equivalent to f(x) is (2x²-7x+6).X-terms and constants should be combined with any other like terms on either side of the equation.

f(x)=4x²-14x+12

In the first stage, a common factor of 2 is eliminated.

2(2x²-7x+6)

Since the quadratic cannot be factored further, the short answer is:

(2x²-7x+6)

Expressions is equivalent to f(x) is (2x²-7x+6).

X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same order, with the x-term usually coming before the constants. The two formulations are equal if and only if each term in both of them is the same.Two systems of equations are equivalent if they have the same solution.

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The equivalent expression to f(x) is (2x2-7x+6). On either side of the equation, X-terms and constants should be combined with any other like terms.

Given

f(x) = 4x² - 14x + 12

In the first stage, a common factor of 2 is eliminated.

(4x² - 14x + 12) / 2

Then we get,

2(2x² - 7x + 6)

Since the quadratic cannot be factored further, the short answer is:

(2x² - 7x + 6)

Expressions is equivalent to f(x) is (2x² - 7x + 6).

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Therefore, the common difference of the arithmetic sequence is -3.

An arithmetic sequence is a sequence of numbers where each term is obtained by adding or subtracting a fixed value, called the common difference, to the previous term. In this case, the sequence is 24, 21, 18, 15, and so on.

To determine the common difference, we can observe that each term is obtained by subtracting 3 from the previous term. For example, we have:

21 = 24 - 3

18 = 21 - 3

15 = 18 - 3

This pattern continues for all the terms in the sequence. Therefore, the common difference in this arithmetic sequence is -3, which means that we subtract 3 from each term to get the next term in the sequence.

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The distance, that car will travel in 15 minute, is 28 km.

The formula used to explain the relationship between speed, distance, and time is speed distance time.

That is speed = distance/ time

So, distance = speed * time

Alternatively, you can calculate the time by dividing the distance traveled by the speed. You can figure out the third input if you know two of the inputs.

Given Speed of car = 112 km per hour

Time = 15 minutes = 15/60 hour

Time = 1/4 hour

Distance traveled by car in 15 minute = Speed of car * time

Distance = 112 * 1/4

Distance = 28 km

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She has to find if the tree is tall enough to fall into her house.

She is using a 12-inches ruler to find proportions. We can draw this as:

The triangle that can be drawn using as vertices the base of the tree, the top of the tree and the house is similar to the triangle formed by the rule and the the distance of 1 ft.

We can see that as the height of the ruler that indicates the top of the tree is smaller than the foot, we know that the height H of the tree is smaller than the distance D from the house to the tree, in the same proportion.

We can calculate the height of the tree using the following proportion:

Answer: The house is far enough, as the height of the tree is less than 50 ft (it is 37.5 ft)

Answer:

The average rate of change is 4.

Step-by-step explanation:

Average rate of change is simply a fancy way of saying "find the slope".  

So for slope, we use (y2-y1)/(x2-x1).

(3-(-13))/(2-(-2))

16/4

4

The fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

Slope of a line = change in y/change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\)

Given the following points:

(4, 9) and (0, 5)

Slope of the line would be:

Slope = (5 - 9)/(0 - 4)

Slope = (-4)/(-4)

Slope = 1

Therefore, the fraction that represnts the slope formula for the line that contains the points, (4, 9) and (0, 5) is given as: Slope = (-4)/(-4) = 1

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The probability that Linda randomly selects a peanut butter cookie, eats it, and then randomly selects an oatmeal cookie is 2/43.

1. First, we need to find the total number of cookies in the bag. The bag contains:
  - 8 chocolate chip cookies
  - 5 peanut butter cookies
  - 9 sugar cookies
  - 8 oatmeal cookies

  Total cookies = 8 + 5 + 9 + 8 = 30 cookies

2. Next, we find the probability of Linda randomly selecting a peanut butter cookie:
  Probability of peanut butter = (Number of peanut butter cookies) / (Total number of cookies)
  Probability of peanut butter = 5/30

3. After eating the peanut butter cookie, there are now 29 cookies left in the bag (and 4 peanut butter cookies remaining).

4. Now, we find the probability of Linda randomly selecting an oatmeal cookie:
  Probability of oatmeal = (Number of oatmeal cookies) / (Total number of remaining cookies)
  Probability of oatmeal = 8/29

5. To find the overall probability of both events occurring, we multiply the individual probabilities:
  Probability of both events = (Probability of peanut butter) * (Probability of oatmeal)
  Probability of both events = (5/30) * (8/29)

6. Simplify the fraction:
  Probability of both events = 40/870

7. Reduce the fraction to its lowest terms:
  Probability of both events = 2/43

So the probability that Linda randomly selects a peanut butter cookie, eats it, and then randomly selects an oatmeal cookie is 2/43.

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Given:

The above expression can be expressed as,

The total weight is 18.5 kilograms

Answer:

its b

Step-by-step explanation:

have a great day <3

The growth rate of your credit card balance is approximately 0.0142.

Therefore, the correct option is B.

Given that you got a credit card, you purchased a stereo system for $200. your credit limit is $1000.

The monthly interest rate is 1.42%.

We need to determine the growth rate of your credit card balance,

To calculate the growth rate of your credit card balance, we need to consider the monthly interest rate and the initial purchase amount.

The monthly interest rate is 1.42%, which can be expressed as a decimal by dividing it by 100: 0.0142.

The initial purchase amount is $200.

Assuming no payments are made and no additional purchases are made, the credit card balance will increase each month due to the accrued interest.

To calculate the growth rate, we can divide the accrued interest by the initial purchase amount.

Accrued interest = Monthly interest rate x Initial purchase amount

= 0.0142 x $200

= $2.84

Growth rate = Accrued interest / Initial purchase amount

= $2.84 / $200

≈ 0.0142

Therefore, the growth rate of your credit card balance is approximately 0.0142, which corresponds to option B.

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The view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

The view factor (F) from Surface A to Surface B can be calculated using the formula:

F = A / (A + B)

where A and B are the areas of Surface A and Surface B, respectively.

The area of a triangle can be calculated using Heron's formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter of the triangle and a, b, and c are the side lengths of the triangle.

For Surface A:

a = 2 cm

b = 3 cm

c = 4 cm

s = (a + b + c) / 2 = (2 + 3 + 4) / 2 = 4.5 cm

Area_A = sqrt(4.5 * (4.5 - 2) * (4.5 - 3) * (4.5 - 4))

= √(4.5 * 2.5 * 1.5 * 0.5)

=√(5.625) ≈ 2.37 cm²

For Surface B:

a = 2 cm

b = 4 cm

c = 3 cm

s = (a + b + c) / 2 = (2 + 4 + 3) / 2 = 4.5 cm

Area_B = √(4.5 * (4.5 - 2) * (4.5 - 4) * (4.5 - 3))

= √(4.5 * 2.5 * 0.5 * 1.5)

=√(5.625) ≈ 2.37 cm²

Now we can calculate the view factor (F):

F = Area_A / (Area_A + Area_B)

= 2.37 / (2.37 + 2.37)

≈ 0.5

Therefore, the view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

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