Find the probability that a randomly
selected point within the circle falls in the
red-shaded triangle.
12
12
P = [?]
Enter as a decimal rounded to the nearest hundredth.

Having the information that segment AC ≅ segment EF, angle B ≅ angle E, and segment BC ≅ segment FE is sufficient to prove that triangles ΔABC and ΔDEF are congruent by the Side-Angle-Side (SAS) criterion.

To prove that triangles ΔABC and ΔDEF are congruent using the Side-Angle-Side (SAS) criterion, we need the following additional information:

The length of segment AC is equal to the length of segment EF: This establishes that one pair of corresponding sides is congruent.

The measure of angle B is equal to the measure of angle E: This provides the congruent angle between the corresponding sides.

The length of segment BC is equal to the length of segment FE: This establishes that the other pair of corresponding sides are congruent.

By having this information, we can apply the SAS congruence criterion. The SAS criterion states that if two triangles have a pair of corresponding sides that are congruent, and the included angles are congruent, then the triangles are congruent.

In this case, having segments AC ≅ EF, angle B ≅ angle E, and segment BC ≅ FE would be sufficient to prove that ΔABC ≅ ΔDEF by SAS.

To learn more about Side-Angle-Side

https://brainly.com/question/30459968

#SPJ8

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

Know more about coordinates here:

https://brainly.com/question/29765572

#SPJ8

Answer:

(-2, 2)

Step-by-step explanation:

We will start by just plugging in the numbers to see if they work.

(-3, 5)

5<-(-3)+1

5<4

This is not possible, so the answer is not (-3, 5).

(-2, 2)

2<-(-2)+1

2<3

2>-2

The point (-2, 2) works for both equations, so that is the answer.

The best measure of center of the data is (a) mean; because the data are close together

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

The dataset of 10 values

Where we can see that there are no outliers present in the dataset

By definition, outliers are extreme values.

Since there are no outliers, it means that the mean is the best measure of center

This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean

From the list of options, we have the mean value to be 42.536

Hence, the true statement is (a)

Read more about mean and median at:

https://brainly.com/question/14532771

#SPJ1

Answer:

[tex]m = \frac{35 - 15}{4 - 0} = \frac{20}{4} = 5[/tex]

[tex]y = 5x + 15[/tex]

Answer:

y > Two-thirds x + 1     /c

Answer:

Here's an example:

convert 2.5 into a mixed number.

Make the denominator less than the original.

The easy way for this is to do 25/10

when you put it through a calculator it ends up being 2.5

(essentially the mixed number and the decimal are the SAME numbers.)

Hope this clarified. :)

To convert a decimal to a mixed number, follow these steps:

Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.

Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.

Step 3: Express the decimal part as a fraction by using the place value of the last digit.

Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Step 5: Combine the whole number part, the fraction, and simplify if necessary.

Here's an example:

Let's say we have the decimal 2.75.

Step 1: The whole number part is 2.

Step 2: The decimal part is 0.75.

Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.

Step 4: The fraction 3/4 is already in its simplest form.

Step 5: Combining the whole number part and the fraction, we have 2 3/4.

So, the decimal 2.75 can be written as the mixed number 2 3/4.

Remember to always simplify the fraction part if possible.

The formula to find the value of a combination is

[tex]C(n, r) = n! / (r!(n-r)!),[/tex]

where n represents the total number of items and r represents the number of items being chosen at a time. 10C0 is 1

In the  combination,

n = 10 and r = 0,

so the formula becomes:

C(10,0) = 10! / (0! (10-0)!) = 10! / (1 x 10!) = 1 / 1 = 1

This means that out of the 10 items, when choosing 0 at a time, there is only 1 way to do so. In other words, choosing 0 items from a set of 10 items will always result in a single set. This is because the empty set (which has 0 items) is the only possible set when no items are chosen from a set of items. Therefore, the value of the combination 10C0 is 1.

For more question combination,

https://brainly.com/question/1301954

Answer:

Step-by-step explanation:

Certainly! I'm here to assist you.

The given function is f(x) = -2(x - 3).

To simplify this expression, we can distribute the -2 to the terms inside the parentheses:

f(x) = -2 * x - (-2) * 3

Simplifying further:

f(x) = -2x + 6

Therefore, the simplified form of the function f(x) = -2(x - 3) is f(x) = -2x + 6.

Answer:

Step-by-step explanation:

[tex]\angle x=\angle y=\angle z=90\deg\ \text{(angle in a semi-circle is a right angle)}[/tex]

All 3 angles are examples of the theorem which states that any angle coming off the diameter of a circle going to the edge of the circle will form a right angle.

Answer:

The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.

Given a = -2 and b = 8, we can calculate t = -b/(2a):

t = -8/(2*-2) = 2

We can then substitute this value back into the height equation to find the maximum height:

h(2) = -2(2)^2 + 8*2 + 300

h(2) = -8 + 16 + 300

h(2) = 308

So, the greatest height the fireworks reach is 308 feet.

Answer:

781250

Step-by-step explanation:

The sequence is has common ratio of 5 so the equation is 10*5^x-2 or 2*5^x so 2*5^8=781250

Answer:

ar⁷= 781,250

Step-by-step explanation:

a =10

ar =50

ar² = 250

8th term = ar⁷=?

r = ar/a

= 50/10

r =5

ar⁷ = 10 × 5 ⁷

=10 × 78125

= 781,250

Answer:

Blank A:  (17, 0)

Blank B:  (-2, 19)

Step-by-step explanation:

Blank A:

Step 1:  Find the slope of AB:

Before we can find the equation of CD, we'll first need to find the slope of AB

We can do this using the slope formula, which is given by:

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

Thus, we can plug in (-10, -3) for (x1, y1) and (7, 14) for (x2, y2) in the slope formula to find m, the slope of AB:

m = (14 - (-3)) / (7 - (-10))

m = (14 + 3) / (7 + 10)

m = 17 / 17

m = 1

Thus, the slope of AB is 1.

Step 2:  Find the slope of CD:

The slope of perpendicular lines are negative reciprocals of each other as shown by the following formula:

m2 = -1 / m1, where

Thus, we can plug in 1 for m1 in the perpendicular slope formula to find m2, the slope of CD:

m2 = -1 / 1

m2 = -1

Thus, the slope of CD is -1.

Step 3:  Find the y-intercept of CD:

One of the equations we can use when looking for intercepts is the slope-intercept form of a line, whose general equation is given by:

y = mx + b, where

Thus, we can plug in (5, 12) for (x, y) and -1 for m to find b, the y-intercept of the line, allowing us to have the full equation in slope-intercept of CD:

12 = -1(5) + b

12 = -5 + b

17 = b

Thus, the equation of CD is y = -x + 17

For any x-intercept, the y-coordinate will always be 0 since the line is intersecting the x-axis.

Thus, we can find the x-coordinate of the x-intercept by plugging in 0 for y in y = -x + 17 and solving for x:

0 = -x + 17

-17 = -x

17 = x

Thus, the x-coordinate of the x-intercept of CD is 17.

Thus, the coordinates of the x-intercept of CD are (17, 0)

Blank B:

We can see that (-2, 19) lies on CD when we plug in (-2, 19) for (x, y) in y = -x + 17, as we get 19 on both sides of the equation when simplifying:

19 = -(-2) + 17

19 = 2 + 17

19 = 19

Thus, (-2, 19) lies on CD.

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

learn more on set here: https://brainly.com/question/29484130

#SPJ1

The area of the segment is 9( π-2) units²

The area of a figure is the number of unit squares that cover the surface of a closed figure.

A segment is the area occupied by a chord and an arc. A segment can be a major segment or minor segment.

Area of segment = area of sector - area of triangle

area of sector = 90/360 × πr²

= 1/4 × π × 36

= 9π

area of triangle = 1/2bh

= 1/2 × 6²

= 18

area of segment = 9π -18

= 9( π -2) units²

therefore the area of the segment is 9(π-2) units²

learn more about area of segment from

https://brainly.com/question/22599425

#SPJ1

First, we need to convert the length of the ribbon to centimeters to match the length of the ribbon pieces we plan to cut:

4m 20cm = (4 x 100)cm + 20cm = 420cm

Next, we can divide the total length of the ribbon by the length of each piece to find how many pieces we can cut:

420cm ÷ 70cm = 6

Therefore, we can cut 6 smaller ribbons, each 70cm long, from the 4m 20cm length of ribbon we have.

The two roots of the quadratic function f(b) = b² - 75 are:

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. Since the highest degree term in a quadratic function is of the second degree, therefore it is also called the polynomial of degree 2. A quadratic function has a minimum of one term which is of the second degree.

We have

Remember that the root of a function is the value of x when the value of the function is equal to zero.

In this problem

The roots are the values of b when the function f(b) is equal to zero.

So,

For f(b)=0

[tex]b^2-75=0[/tex]

[tex]b^2=75[/tex]

Square root both sides

[tex]b=(+/-)\sqrt{75}[/tex]

Simplify

[tex]b=(+/-)5\sqrt{3}[/tex]

[tex]b=5\sqrt{3}[/tex] and [tex]b=-5\sqrt{3}[/tex]

Therefore

[tex]\rightarrow\bold{b = 5\sqrt{3}}[/tex]

[tex]\rightarrow\bold{b=-5\sqrt{3}}[/tex]

Learn more about the quadratic function at:

https://brainly.com/question/30929439

The Total Surface Area of the given prism is: 1,230.4 m²

The volume of the prism is calculated as:

Volume = Base Area * Height

The total surface area is the sum of the surface area of all individual surfaces and as such we have:

Total Surface Area = (21 * 16) + (21 * 16) + (21 * 16) + 2(0.5 * 16 * 13.9)

Total Surface Area = 336 + 336 + 336 + 222.4

Total Surface Area = 1,230.4 m²

That is the final total surface area of the given rectangular based prism

Read more about surface area  at: https://brainly.com/question/30794567

#SPJ1

Based on the provided data sets, it can be observed that both Data Set K and Data Set L have identical values. Therefore, their centers and spreads are also identical.

The center of a data set can be measured using various statistical measures such as the mean, median, or mode. Since the data sets have the same values, all these measures will yield the same result for both sets.

In this case, the center of Data Set K is equal to the center of Data Set L.

Similarly, the spread of a data set refers to the measure of variability or dispersion within the data. Common measures of spread include the range, variance, and standard deviation.

However, since the data sets are exactly the same, all these measures will yield identical results for both sets. Thus, the spread of Data Set K is the same as the spread of Data Set L.

In summary, both the center and the spread of Data Set K are the same as those of Data Set L. Therefore, there is no difference between the two data sets in terms of their central tendency or variability.

For more such questions sets,click on

https://brainly.com/question/13458417

#SPJ8

The difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.

To calculate the difference in size between two people, one measuring in inches and the other measuring in centimeters, we must first convert all measurements to a common unit.

Guy measures 3 inches + 1/4 inch. We can convert 1/4 inch to a decimal fraction by dividing 1 by 4, which gives us 0.25 inches. So your measurement in inches would be 3 + 0.25 = 3.25 inches.

The other guy measures 9.045 cm. To convert centimeters to inches, we use the following relationship: 1 cm = 0.3937 inches. Multiplying the measurement in centimeters by 0.3937, we get the measurement in inches: 9.045 cm * 0.3937 = 3.5608 inches (approximately).

Now we can calculate the size difference between them. We subtract the measurement of the second chavo (3.5608 inches) from the measurement of the first chavo (3.25 inches):

3.25 inches - 3.5608 inches = -0.3108 inches.

The resulting difference is -0.3108 inches. This means that the second chavo is smaller in size than the first. Since the difference is negative, it indicates that the first chavo is bigger than the second.

In summary, the difference in size between the two guys is approximately -0.3108 inches, which implies that the first guy is bigger than the second guy.

for more such question on inches visit

https://brainly.com/question/21386205

#SPJ8

The person is approximately 7.73 miles from home.

To solve this problem, we can use the Pythagorean theorem and trigonometry. Let us assume that the person starts from the origin (0, 0) and walks 5 miles west, which takes her to the point (-5, 0) on the x-axis.

If we assume that the starting point is (0, 0) and we assign a coordinate system, then the point reached after walking 5 miles west can be represented as (-5, 0). Similarly, the point reached after walking 6 miles southwest can be represented as (-3, -6).Then, she walks 6 miles southwest, which forms a 45-degree angle with the x-axis. We can represent this vector as (6 cos 45°, -6 sin 45°) = (3√2, -3√2).

To find the total distance from home, we need to add the magnitude of these two vectors using the Pythagorean theorem:

d =[tex]\sqrt((-5)^2 + (-3\sqrt2)^2)[/tex]≈ 7.73 miles

For such more questions on miles

https://brainly.com/question/29806974

#SPJ8

Answer:

You multiply each coordinate by 4

Step-by-step explanation:

Rule: (x, y) to (4x, 4y)

A: (-6,5) to A' (-24, 20)

B: (-4, 2) to B' (-16, 8)

C: (-6, 2) to C' (-24, 8)

In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything: numbers, letters, people, or even other sets.

he concept of sets is fundamental in various branches of mathematics, including set theory, algebra, and statistics.There are different kinds of sets based on their properties:

Finite set: A set with a specific number of elements, which can be counted.Infinite set: A set with an endless number of elements.Empty set: A set with no elements. It is denoted by the symbol Ø or {}.

Singleton set: A set with only one element.Subset: A set whose elements are all contained within another set.Universal set: A set that includes all the possible elements of interest in a particular context.Operations on sets involve various ways of combining or manipulating sets:

Union: The union of two sets A and B is the set that contains all the elements from both sets. It is denoted by A ∪ B.Intersection: The intersection of two sets A and B is the set of elements that are common to both sets. It is denoted by A ∩ B.

Complement: The complement of a set A, denoted by A', is the set of all elements that are not in A but are in the universal set.Difference: The difference between two sets A and B is the set of elements that are in A but not in B. It is denoted by A - B.

Cartesian Product: The Cartesian product of two sets A and B is the set of all possible ordered pairs, where the first element is from set A and the second element is from set B. It is denoted by A × B.

For teaching the concept of the union of sets, you can use the following activity:

Activity: Venn Diagrams

Draw two overlapping circles on the board or use physical cut-out circles.Label one circle as Set A and the other as Set B.

Ask the students to suggest elements for each set and write them inside the circles.Discuss the elements that are common to both sets and write them in the overlapping region.Explain that the union of sets A and B represents all the elements in both sets.

Combine the elements from sets A and B, including the elements in the overlapping region, and write them in a new circle labeled as A ∪ B.Emphasize that the union includes all the distinct elements from both sets without repetition.

For more such questions on  distinct objects visit:

https://brainly.com/question/517994

#SPJ8

The value of the rational expression when x is equal to 4 is 2. The correct answer is option C: 2.

To find the value of the rational expression (x - 12)/(x - 8) when x is equal to 4, we substitute x = 4 into the expression:

[(4) - 12]/[(4) - 8]

Simplifying the numerator and denominator:

(4 - 12)/(-4)

Further simplifying the numerator:

(-8)/(-4)

Now, we can divide -8 by -4:

(-8)/(-4) = 2

So, when x is equal to 4, the value of the rational expression is 2.

Therefore, C is the right response.

for such more question on rational expression

https://brainly.com/question/29061047

#SPJ8

The loan principal is $12,483.33, and the loan's maturity value is $15,479.33.

To calculate the loan principal, we can use the formula for simple interest:

Interest = Principal x Rate x Time

Given that Rebecca earned $2,996 as interest, the rate is 2.00% per month (or 0.02), and the time is 12 months, we can plug in these values into the formula and solve for the principal:

$2,996 = Principal x 0.02 x 12

$2,996 = Principal x 0.24

Dividing both sides of the equation by 0.24, we get:

Principal = $2,996 / 0.24

Principal = $12,483.33

So, the loan principal is $12,483.33.

To calculate the loan's maturity value, we need to add the principal and the interest earned. Since the interest earned is $2,996 and the principal is $12,483.33, the maturity value can be calculated as:

Maturity Value = Principal + Interest

Maturity Value = $12,483.33 + $2,996

Maturity Value = $15,479.33

Therefore, the loan's maturity value is $15,479.33.

For more such questions on maturity value visit:

https://brainly.com/question/30672020

#SPJ8

A function can't have more than one value for an argument. Therefore, it's either (1,1) or (1,3), but since there's not (1,3) among the possible answers, it must be (1,1).

Answer:

Part A:

The correct expression for how many pencils Ms. Florinda has left after giving them out to her students is:

A. 100 - 2 × (22 - 19)

Part B:

To determine whether Ms. Florinda has enough pencils to give each of her students 2, we can calculate the total number of pencils needed. The total number of students is the sum of the students in both classes, which is 22 + 19 = 41.

If each student needs 2 pencils, then the total number of pencils needed is 2 × 41 = 82.

Comparing this with the initial number of pencils Ms. Florinda bought (100), we can see that she has more than enough pencils to give each of her students 2.

Yes, she has enough pencils to give each of her students 2.

She has 18 more than she needs.

Answer:

Step-by-step explanation:

To simplify the expression (5x - 2) / (x - 2) - (4x), we can follow these steps:

First, let's simplify the numerator:

5x - 2

Now, let's distribute the negative sign to the term (4x):

-4x

Next, let's combine the terms in the numerator:

(5x - 2) - 4x = 5x - 2 - 4x = x - 2

Now, let's rewrite the expression:

(x - 2) / (x - 2) - 4x

Since we have (x - 2) as both the numerator and denominator, we can simplify further by canceling out the common factor:

1 - 4x

Therefore, the simplified form of the expression (5x - 2) / (x - 2) - (4x) is 1 - 4x.

The given expression, 10f - 5f + 8 + 6g + 4, simplifies to 5f + 12 + 6g when like terms are combined.

To simplify the expression 10f - 5f + 8 + 6g + 4, we can combine like terms by adding or subtracting coefficients that have the same variables:

10f - 5f + 8 + 6g + 4

Combining the terms with 'f', we have:

(10f - 5f) + 8 + 6g + 4

This simplifies to:

5f + 8 + 6g + 4

Next, we can combine the constant terms:

8 + 4 = 12

Thus, the simplified expression is:

5f + 12 + 6g

This expression is equivalent to 10f - 5f + 8 + 6g + 4.

In summary, the expression 10f - 5f + 8 + 6g + 4 simplifies to 5f + 12 + 6g after combining like terms.

For more question on expression visit:

https://brainly.com/question/1859113

#SPJ8

The solution to the system of equations using the inverse matrix method is x = -1, y = 2, z = 3.

To solve the system of equations using the inverse matrix method, we need to represent the system in matrix form.

The given system of equations can be written as:

| 5 -4 1 | | x | = | 12 |

| 1 7 -1 | [tex]\times[/tex]| y | = | -9 |

| 2 3 3 | | z | | 8 |

Let's denote the coefficient matrix on the left side as A, the variable matrix as X, and the constant matrix as B.

Then the equation can be written as AX = B.

Now, to solve for X, we need to find the inverse of matrix A.

If A is invertible, we can calculate X as [tex]X = A^{(-1)} \times B.[/tex]

To find the inverse of matrix A, we can use the formula:

[tex]A^{(-1)} = (1 / det(A)) \times adj(A)[/tex]

Where det(A) is the determinant of A and adj(A) is the adjugate of A.

Calculating the determinant of A:

[tex]det(A) = 5 \times (7 \times 3 - (-1) \times 3) - (-4) \times (1 \times 3 - (-1) \times 2) + 1 \times (1 \times (-1) - 7\times 2)[/tex]

= 15 + 10 + (-13)

= 12.

Next, we need to find the adjugate of A, which is obtained by taking the transpose of the cofactor matrix of A.

Cofactor matrix of A:

| (73-(-1)3) -(13-(-1)2) (1(-1)-72) |

| (-(53-(-1)2) (53-12) (5[tex]\times[/tex] (-1)-(-1)2) |

| ((5(-1)-72) (-(5(-1)-12) (57-(-1)[tex]\times[/tex](-1)) |

Transpose of the cofactor matrix:

| 20 -7 -19 |

| 13 13 -3 |

| -19 13 36 |

Finally, we can calculate the inverse of A:

A^(-1) = (1 / det(A)) [tex]\times[/tex] adj(A)

= (1 / 12) [tex]\times[/tex] | 20 -7 -19 |

| 13 13 -3 |

| -19 13 36 |

Multiplying[tex]A^{(-1)[/tex] with B, we can solve for X:

[tex]X = A^{(-1)}\times B[/tex]

= | 20 -7 -19 | | 12 |

| 13 13 -3 | [tex]\times[/tex] | -9 |

| -19 13 36 | | 8 |

Performing the matrix multiplication, we can find the values of x, y, and z.

For similar question on inverse matrix method.

https://brainly.com/question/18604519  

#SPJ8