In angleABC, AB = 4.12, BC = 4, AC = 5. What is m 2 C?
A.25
B. 37.5
C. 43.93
D. 53.08

Answer: illustrates similarity of figures

Step-by-step explanation: more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.

The number of children are there in the given scenario are 400.

Given that, the ratio of children to adults on a school trip is initially 10:1.

Here, the given ratio can be written as 10x:1x

5 more children and 5 more adults join the trip so that the ratio is now 9:1

10x+5:1x+5

The new ratio is (10x+5)/(x+5) = 9/1

10x+5=9(x+5)

10x+5=9x+45

10x-9x=45-5

x=40

So, the number of children =10x=400

Therefore, the number of children are there in the given scenario are 400.

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The measure of the angles m∠1 and m∠2 for the polygon are 72° and 54° respectively.

To calculate the sum of interior angles of a polygon, you can use the following formula:

Sum of interior angles = (n-2) x 180 degrees

Where "n" represents the number of sides (or vertices) of the polygon.

Given the 5 sided polygon;

(5 - 2) × 180 = 540

one interior angle = 540/5 = 108°

m∠2 = 108°/2

m∠2 = 54°

m∠1 = 180 - [2(54°)]

m∠1 = 180 - 108

m∠1 = 72°

Therefore, the measure of the angles m∠1 and m∠2 are 72° for the polygon and 54° respectively.

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There are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.

For each play date, you have 3 options for the show time.

Since the events are independent and all options are equally likely, you can multiply the number of options together to find the total number of possible outcomes.

Number of possible outcomes

= Number of play dates × Number of show times

= 4 × 3

= 12

Therefore, there are 12 possible outcomes when considering all combinations of 4 play dates and 3 show times.

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A firm should record an impairment in the value of property, plant, or equipment by reducing the carrying amount of the asset and recognizing the impairment loss as an expense in the financial statements.

When the value of property, plant, or equipment is impaired, meaning its recoverable amount is lower than its carrying amount, a firm should recognize this impairment in its financial statements. The impairment is recorded by reducing the carrying amount of the asset to its recoverable amount, which is the higher of its fair value less costs to sell or its value in use. The difference between the carrying amount and the recoverable amount is recognized as an impairment loss and recorded as an expense in the income statement. This adjustment reflects the decrease in the value of the asset and allows the firm to accurately report its financial position and performance.

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For vector arithmetic, vector addition (adding two vectors) and scalar multiplication (multiplying a vector by a scalar) is "component-wise". So when adding two vectors you add each component in the first vector to the corresponding one in the second to get the resulting vector. In scalar multiplication you multiply each vector component by the scalar and that gives the resulting vector.

So if u = <3,-2> and v = <-1,4>,

3u = <3*3,-2*3> = <9,-6>

2v = <-1*2,4*2> = <-2,8>

3u + 2v = <9,-6> + <-2,8> = <9+(-2),-6+8> = <7,2>

Answer:

”an event can have a probability of 0”

Step-by-step explanation:

A probability can not be 0 it has to be more then 0

Answer:

A. 72

Step-by-step explanation:

63/x = 87.5/100

x = 6300 divided by 87.5

x = 72

The solution to the equation -7x - 3 = -31 is x = 4.

To solve the equation -7x - 3 = -31, we will isolate the variable x.

Step 1: Begin by moving the constant term to the other side of the equation.

-7x - 3 + 3 = -31 + 3

Simplifying, we get:

-7x = -28

Divide both sides of the equation by -7 to solve for x.

(-7x) / -7 = (-28) / -7

Simplifying, we have:

x = 4

Therefore, the solution to the equation -7x - 3 = -31 is x = 4.

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Answer:option c is the answer

Step-by-step explanation:

We can see here that the expression that is equal to the rational expression when x doesn’t equal 1 or -1 is 5/(x+1).

A fraction with a polynomial in the numerator and denominator is referred to as a rational expression. No numerator can be 0. A polynomial is an expression that only supports the operations of addition, subtraction, multiplication, and non-negative integer exponents. It can also contain constants, variables, and exponents.

The given expression is: 5(x-1)/(x+1)(x-1) where x doesn’t equal 1 or -1.

Thus, if we cancel out numerator and denominator, we will have: 5/(x+1).

Thus, 5/(x+1) is the correct answer.

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The complete question is:

Which of the following is equal to the rational expression when x doesn’t equal 1 or -1? 5(x-1)/(x+1)(x-1).

Let's say the total work to be done is represented by 1.

On the first day, three-fifths of the work is completed. Therefore, the remaining work to be done is 1 - 3/5 = 2/5.

On the second day, three-quarters of the remainder is completed. The remainder after the first day's work is 2/5. So, the work completed on the second day is 3/4 x 2/5 = 3/10. The remaining work to be done is 2/5 - 3/10 = 1/5.

On the third day, seven-eighths of what remained is done. The remaining work to be done after the second day's work is 1/5. So, the work completed on the third day is 7/8 x 1/5 = 7/40.

Therefore, the fraction of work still remaining to be done is 1/5 - 7/40 = 8/40 - 7/40 = 1/40.

Correct inequality that shows number of questions, q, will be on the quiz is,

⇒ q ≤ 15

Since, A relation by which we can compare two or more mathematical expression is called an inequality.

Here, We have to given that;

Mr. Pham assigns a quiz that will have at most 15 questions.

Since, Symbol of at most is, ( ≤ )

Hence, Correct inequality that shows number of questions, q, will be on the quiz is,

⇒ q ≤ 15

Thus, Correct inequality that shows number of questions, q, will be on the quiz is,

⇒ q ≤ 15

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The model that represents the sum of 5/3 and 2/3 is 7/3.

to find the sum of 5/3 and 2/3, we need to add the numerators (top numbers) together and keep the same denominator (bottom number). so, we have:

5/3 + 2/3 = (5+2)/3 = 7/3 to represent this visually, you could imagine a number line with 0 on the left and increasing values to the right. each whole number is divided into three equal parts. the model for 5/3 would be a point 5/3 of the way from 1 to 2, and the model for 2/3 would be a point 2/3 of the way from 0 to 1. to find the model for 7/3, we would locate the point 7/3 of the way from 2 to 3 on the number line.

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The approximate surface area of the balloon is 199 cm².

The approximate volume of the balloon is 262 cm³

Here, we have,

the surface area and the volume of the balloon:

Radius of the balloon = circumference / 6.2832

25 / 6.2832 = 3.98cm

we know that,

Surface area = 4πr²

4 x 22/7 x 3.97² = 199 cm²

we have,

Volume =  4/3πr³

4/3 x 22/7 x 3.97³ = 262.20 cm³

Hence, The approximate surface area of the balloon is 199 cm².

The approximate volume of the balloon is 262 cm³

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complete question:

A spherical balloon has a circumference of 25 cm.

a.) What is the approximate surface area of the balloon to the nearest square centimeter?

b.) What is the approximate volume of the balloon to the nearest cubic centimeter?

The probability that the kicker makes his first two kicks is 63.21%. This means that out of 100 attempts, the kicker is likely to make both kicks 63 times.

To solve this problem, we need to use conditional probability. We know that the kicker usually makes 71% of his first field goal attempts. So, the probability that he makes his first kick is 0.71. If he makes his first attempt, his success rate rises to 89%. So, the probability that he makes his second kick given that he made his first kick is 0.89.
Now, to find the probability that he makes his first two kicks, we need to multiply the probability of him making his first kick by the probability of him making his second kick given that he made his first kick. This can be represented as:
P(2 successful kicks) = P(1st kick is successful) x P(2nd kick is successful | 1st kick is successful)
P(2 successful kicks) = 0.71 x 0.89
P(2 successful kicks) = 0.6321 or 63.21%
Therefore, the probability that the kicker makes his first two kicks is 63.21%. This means that out of 100 attempts, the kicker is likely to make both kicks 63 times.

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The rate of change of a periodic function is itself a periodic function. In the case of a sinusoidal wave, the derivative is also a sinusoidal wave with the same period, but shifted by a phase angle of [tex]π/2.[/tex]

The rate of change of a periodic function at a specific point is equal to the instantaneous slope of the tangent line to the graph of the function at that point.

To calculate the rate of change of a periodic function, you need to take the derivative of the function with respect to the independent variable (usually time). If the function is a sinusoidal wave, you can use trigonometric identities to find the derivative.

For example, let's say we have a function f(t) = sin(t), which represents a sinusoidal wave. To find the rate of change of the function at a particular point t = a, we need to take the derivative of the function with respect to t:

f'(t) = cos(t)

Then we can evaluate this derivative at t = a to find the rate of change at that point:

f'(a) = cos(a)

This tells us the instantaneous rate of change of the function at the point t = a.

Note that the rate of change of a periodic function is itself a periodic function. In the case of a sinusoidal wave, the derivative is also a sinusoidal wave with the same period, but shifted by a phase angle of [tex]π/2.[/tex]

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Answer:

Measure the distance between those 2 points, A and B. Then when you get your answer, round it to the second number after your decimal. (The hundredth place) It is explained more below:

Step-by-step explanation:

After measuring, you should get a decimal number. With that number, you need to round to the nearest hundredth.

-Meaning you need to check the 2nd number right after the decimal. The second number right after the decimal will be 2 in this example.

I hope this helped. <3

We cannot find the value of y'' at the point where x = 0 using this method.

To find y'' at the point where x = 0, we need to differentiate the given equation twice with respect to x.

First, we take the derivative of both sides with respect to x:

y + xy' + 4ey' = 0

Next, we take the derivative of this equation with respect to x:

y' + xy'' + y' + 4ey'' = 0

Simplifying this expression, we get:

2y' + xy'' + 4ey'' = 0

We are given that xy + 4ey = 4e. Differentiating this equation with respect to x, we get:

y + xy' + 4ey' = 0

Substituting y' = -(y + 4ey')/x from this equation into the previous equation, we get:

2y' - (y + 4ey') + 4ey'' = 0

Simplifying this expression, we get:

y'' = (y + 4ey' - 2y')/(4e)

When x = 0, we have y = 4e/4e = 1 and y' = -(1 + 4e*y')/0, which is undefined.

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Use an Explicit formula to calculate how much it will cost Jiya to rent the truck for 7 hours .The correct answer is option (d) a7=55+(7-1)10

The rental company charges $55 for the first hour and then $10 per hour after that, we can use an explicit formula to calculate how much it will cost Jiya to rent the truck for 7 hours.

The explicit formula for the total cost of renting the truck for a given number of hours can be written as:

a(n) = c + (n-1)d

where a(n) is the total cost of renting the truck for n hours, c is the cost of the first hour, and d is the additional cost per hour.

Using this formula, we can find the cost of renting the truck for 7 hours:

a(7) = 55 + (7-1)*10

Simplifying the expression in the parentheses, we get:

a(7) = 55 + 6*10

Multiplying 6 by 10, we get:

a(7) = 55 + 60

Adding 55 and 60, we get:

a(7) = 115

Therefore, the explicit formula that describes how much it will cost Jiya to rent the truck for 7 hours is:

a7=55+(7-1)10

Simplifying the expression, we get:

a7 = 55 + 6*10

a7 = 55 + 60

a7 = 115

Therefore, the correct answer is option (d) a7=55+(7-1)10.

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Answer:

y - 4 = 1/3(x + 5)

Step-by-step explanation:

The general equation for the point-slope form of a line is given by:

y - y1 = m(x - x1), where

Step 1:  To find the equation of the line through (-5, 4) and (1, 6), we first need to find the slope of the line using the slope formula, which is:

m = (y2 - y1) / (x2 - x1), where

We can allow (-5, 4) to be our (x1, y1) point and (1, 6) to be our (x2, y2) point:

m = (6 - 4) / (1 - (-5))

m = 2 / (1 + 5)

m = 2/6

m = 1/3

Now we can use the point-slope form of the equation with either of the two points.  

y - 4 = 1/3(x - (-5))

y - 4 = 1/3(x + 5)

Thus, the point-slope equation of the line through (-5, 4) and (1, 6) is:

y - 4 = 1/3(x + 5)

The correct sequence of transformations that could have been used to transform Trapezoid ABCD to produce trapezoid A''B''C''D'' is that trapezoid ABCD was reflected across the y-axis and then across the x-axis.

To transform trapezoid ABCD into trapezoid A''B''C''D'', we need to apply a sequence of transformations that will result in the same size and shape of the two trapezoids, which means that they are congruent.

One possible sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A''B''C''D'' is:

Trapezoid ABCD was reflected across the y-axis and then across the x-axis.

This sequence of transformations would result in the same size and shape of the two trapezoids, which means that they are congruent. Let's see why this is true.

When we reflect trapezoid ABCD across the y-axis, each point on the trapezoid is reflected across the y-axis, which means that its x-coordinate is multiplied by -1 while its y-coordinate remains the same. This results in a mirror image of the trapezoid on the opposite side of the y-axis.

Next, when we reflect the trapezoid across the x-axis, each point is reflected across the x-axis, which means that its y-coordinate is multiplied by -1 while its x-coordinate remains the same. This results in a mirror image of the trapezoid on the opposite side of the x-axis.

The resulting trapezoid is now in the same position and orientation as trapezoid A''B''C''D'', but it may not be in the same location. However, since the trapezoid is congruent, we can translate it to match the position of trapezoid A''B''C''D''.

Therefore, the correct sequence of transformations that could have been used to transform trapezoid ABCD to produce trapezoid A''B''C''D'' is that trapezoid ABCD was reflected across the y-axis and then across the x-axis.

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The central angle formed by the Self Help slice is 86.4°.

A circle is formed when you draw a point and connect it from end to end forming a complete revolution.

We have to find the central angle formed by the Self Help slice

One revolution equals 360°.

Therefore, each piece of pie for each type of book is a fraction of one revolution.

The fraction can be determined by dividing the number for a specific type of book to the total number of books.

Specifically, the fraction for the Self Help slice would be 90/375 which is equal to 0.24 or 24%.

Then, 24% of 360 is 86.4.

Therefore, the central angle formed by the Self Help slice is 86.4°.

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There are 375 books sold at Sid's Bookstore. The table below summarizes these books by genre. This info is presented in circle graph. Find the central angle measure for Self Help slice in graph. Mystery 99, romance 81, self help 90, cooking 57, biography 48.

1/4 - 1/2 = -1/4. Don't forget to include the negative sign in your answer, which indicates that the result is less than 0.  it's important to find a common denominator so that you can add or subtract them easily.

To subtract unit fractions like 1/4 and 1/2, you need to find a common denominator. A common denominator is a number that both denominators can divide into evenly. In this case, the smallest common denominator is 4, since 4 can be divided evenly by both 4 and 2.

To get both fractions to have a denominator of 4, you need to multiply 1/4 by 1 and 1/2 by 2/2, which equals 2/4.

Now that both fractions have the same denominator, you can subtract the numerators:

1/4 - 2/4 = -1/4


Overall, when working with unit fractions,

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The area covered by the lawn sprinkler is approximately 461.63 square feet.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that; the diameter of the circle is 24.25 feet.

The radius of the circle is half of the diameter, so:

Radius r = diameter/2

Radius r = 24.25 / 2

Radius r = 12.125 feet

Next, plug the values into the above formula and solve for area.

Area = πr²

Area = 3.14 × ( 12.125 ft )²

Area = 3.14 × ( 12.125 ft )²

Area = 461.63 ft²

Therefore, the area is 461.63 ft².

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The length of the missing side (the hypotenuse) is 10 ft.

We have,

We can use the Pythagorean theorem to find the length of the missing side of the right triangle.

So,

a² + b² = c²

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

In this case,

The opposite side (which is the leg) has a length of 8 ft, and the adjacent side (which is the other leg) has a length of 6 ft.

Let x be the length of the missing side. Then we have:

a = 8 ft

b = 6 ft

c = x

Plugging these values into the Pythagorean theorem, we get:

8² + 6² = x²

64 + 36 = x²

100 = x²

Taking the square root of both sides, we get:

x = √100 = 10 ft

Therefore,

The length of the missing side (the hypotenuse) is 10 ft.

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The trigonometric identity 1 + cot⁴θ = cosec⁴θ - 2cot²θ

Trigonometric identities are mathematical equations that contain trigonometric ratios in which one side is equal to the other.

Given the trigonometric identity

1 + cot⁴θ = cosec⁴θ - 2cot²θ, we need to show that the Left hand side L.H.S equals the Right Hand side R.H.S. we proceed as follows.

So, L.H.S = 1 + cot⁴θ

Now using the trigonometric identity

1 + cot²θ = cosec²θ

Making cot²θ subject of the formula, we have that

cot²θ = cosec²θ - 1

So, substituting this into the equation, we have that

1 + cot⁴θ =  1 + (cot²θ)²

= 1 + (cosec²θ - 1)²

Expanding the bracket, we have that

= 1 + cosec⁴θ - 2cosec²θ + 1

=  cosec⁴θ - 2cosec²θ + 1 + 1

=  cosec⁴θ - 2cosec²θ + 2

=  cosec⁴θ + 2 - 2cosec²θ

= cosec⁴θ + 2(1 - cosec²θ)

= cosec⁴θ + 2cot²θ

= R.H.S

Since L.H.S = R.H.S

1 + cot⁴θ = cosec⁴θ - 2cot²θ

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The sector area is 6π square meters.

We can use the formula for the area of a sector of a circle, which is:

A = (θ/2π) × πr²

where θ is the representation of the central angle in radians, and r is the representation of the radius of the circle.

In this case, we are given that 2π/3 is the central angle and r = 6 m. We can simplify 2π/3 as 120 degrees or π/3 radians.

When we enter these values into the formula, we get:

A = (π/3 × 1/2π) × (36)

= (1/6) × 36π

= 6π

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