Express the following probability as a simplified fraction and as a decimal.
If one person is selected from the population described in the​ table, find the probability that the person

The equation of the circle is determined as (x + 3)²  + (y - 9)² = 25.

The equation of the circle is calculated as follows;

For the equation;

y = 3/4x+5

Slope = 3/4,  the slope of the line perpendicular to the line = -4/3.

it is pass through the (0, 5).

The equation of the line: y - 5 = -4x/3

For the equation;

3x + 4y = 38

4y = -3x + 38

y = -3x/4 + 38

slope = -3/4, the slope of the line perpendicular to the line = 4/3

it is pass through the (6, 5)

The equation of the line: y - 5 = 4/3(x - 6)

Solve the two equations together to find the point of intersection;

(-4/3)x + 5 = (4/3)(x - 6) + 5

-4x/3 = 4x/3 - 8

8x/3 = -8

8x = -24

x = -3

y - 5 = -4x/3

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

y - 5 = 4

y = 9

The center of the circle = (-3, 9)

The radius of the circle is calculated as;

r = √ (-3 -0)² + (9 - 5)²

r = √(9 + 16)

r = 5

The equation of the circle becomes;

(x - a )² + (y - b)² = r²

(x + 3)²  + (y - 9)² = 5²

(x + 3)²  + (y - 9)² = 25

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Mr. Moketsi could help students in their learning of properties of 2D shapes through hands-on activities and discovery, as suggested by the constructivist perspective.

Mr. Moketsi initiates the class by inquiring about their comprehension of 2D shapes and their properties, provoking conversation amongst students as they share their thoughts with their peers and their teacher.

He subsequently introduces an assortment of manipulatives, such as pattern blocks, geoboards, and tangrams to encourage experimentation and inquiry into these geometric figures, while posing thought-provoking questions throughout the lesson to help learners make connections between different shapes with a focus on discovering their unique attributes.

Mr. Moketsi encourages reflection, questioning how this newfound knowledge may be applied in reality, stimulating critical thinking abilities during classroom interaction with surfaces representing planes containing lengths and widths.

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Answer:

x=7

(x)(x+1)=(4)(4+10)

Step-by-step explanation:

Expanding the right-hand side of the equation, we get:

(x)(x+1) = (4)(14)

Simplifying, we get:

x^2 + x = 56

Moving all terms to the left-hand side, we get:

x^2 + x - 56 = 0

Now we can factor this quadratic equation:

(x + 8)(x - 7) = 0

So the solutions are x = -8 or x = 7.

Answer: X=7

Step-by-step explanation:

To Solve this problem we have to remember a formula regarding secants in circles it states (A+B)*B=(C+D)*D, I have attached said Theorem. This is Exactly what your problem is asking.

So First

B = 4

A = 10

D = x

C = 1

(A+B)*B=(C+D)*D

(10+4)*4=(1+x)*x

14*4=x²+x

-x²-x+56=0

Using Quadratic Formula

X = 7, X = -8

Since you cant have - side length X= -8 is Extraneous

Thus Final solution is X = 7

On performing the given row-operation on the given augmented-matrix:

(a) multiplying row1 by -2 and adding to row2, we have [tex]\left[\begin{array}{ccc}5&-2&6\\-10&10&-15\end{array}\right][/tex],

(b) interchanging row1 and row2, we have [tex]\left[\begin{array}{ccc}0&6&-3\\5&-2&6\end{array}\right][/tex],

(c) Multiplying row1 by 2, the matrix becomes [tex]\left[\begin{array}{ccc}10&-4&12\\0&6&-3\end{array}\right][/tex].

The augmented matrix on which we have to perform the row operation is

⇒ [tex]\left[\begin{array}{ccc}5&-2&6\\0&6&-3\end{array}\right][/tex],

Part(a) : We have to multiply row1 by -2 and and add to row2,

The row-operation is performed as : [tex]\left[\begin{array}{ccc}5&-2&6\\(5\times-2)+0&(-2\times-2)+6&(6\times-2)-3\end{array}\right][/tex];

Simplifying further ,

We get,

[tex]\left[\begin{array}{ccc}5&-2&6\\-10&10&-15\end{array}\right][/tex].

Part(b) : We have to interchange the "row1" and "row2",

On interchanging,

We get,

[tex]\left[\begin{array}{ccc}0&6&-3\\5&-2&6\end{array}\right][/tex].

Part(c) : We have to multiply the elements of "row1" by 2,

So, On multiplying the "row1" by 2,

We get,

⇒ [tex]\left[\begin{array}{ccc}5\times 2&-2\times 2&6\times 2\\0&6&-3\end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{ccc}10&-4&12\\0&6&-3\end{array}\right][/tex].

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Answer:

  (a)  (-5,20) and (4,11)

Step-by-step explanation:

You want the solutions to the system of equations ...

Using the second equation to substitute for y in the firs equation, we have ...

  x +x² -5 = 15

  x² +x -20 = 0 . . . . . subtract 15, put in standard form

  (x +5)(x -4) = 0 . . . . . factor

A product is zero only when one or more factors is zero. The values of x that make the factors zero are ...

  x = -5  and  x = 4

The corresponding values of y are ...

  y = 15 -x

  y = 15 -{-5, 4} = {20, 11}

The solutions are (x, y) = (-5, 20) and (4, 11).

The value of P(x=1) from the given discrete data is 0.5.

From the given data

Let P(x=2)=x

p+p+x=1

x=1-2p

E(x²)=∑PiXi²=P(0)²+p(1)²+(1-2p)(2)²

= 0+p+(1-2p)4

= 4-7p

E(x)=∑PiXi=P(0)+P(1)(1-2p)(2)

= 0+p+2-4p

= 2-3p

Given that, E(x²)=E(x)

4-7p=2-3p

4p=2

p=0.5

Therefore, the value of P(x=1) from the given discrete data is 0.5.

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An equivalent fraction to 1 whole and 7/8 is 15/8.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. It is, in other words, a "top-heavy" fraction since the fraction represents a value greater than one full unit.

1 whole and 7/8 can be written as a mixed number, which is a combination of a whole number and a fraction:

1 whole and 7/8 = 1 + 7/8

To find an equivalent fraction, we can convert the mixed number to an improper fraction by multiplying the whole number by the denominator of the fraction, and then adding the numerator. The result is the numerator of the improper fraction, and the denominator stays the same:

1 + 7/8 = (1 × 8 + 7)/8 = 15/8

Therefore, an equivalent fraction to 1 whole and 7/8 is 15/8.

For instance, the improper fraction 7/4 results from the numerator's (7), which is greater than the denominator (4).

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The equation in standard form of the eclipse is expressed as:

D. x²/9 + y²/8 = 1.

The standard form equation for an ellipse with center at the origin, a vertex at (a, 0), and a focus at (c, 0) is:

x²/a² + y²/b² = 1, where c² = a² - b².

In this case, the center is at the origin, a vertex is at (3, 0), and a focus is at (1, 0).

Since the center is at the origin, we know that a vertex is located a distance of a units to the right and left of the center, so a = 3.

Since the focus is located a distance of c units to the right and left of the center, we know that c = 1.

Using c² = a² - b², we can solve for b²:

1² = 3² - b²

b² = 8

So the equation in standard form is:

x²/9 + y²/8 = 1.

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The surface area of the triangular prism is given as follows:

S = 549.15 m².

The surface area of a prism is given by the sum of the areas of all the parts that compose the prism.

The prism for this problem is composed as follows:

Hence the surface area is obtained as follows:

S = 15 x 13 + 15 x 15.81 + 2 x 0.5 x 9 x 13

S = 549.15 m².

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The triangular prism's surface area is given as follows:

S = 549.15 m².

The total area of all the prism's component components determines the prism's surface area.

The following is the structure of the prism for this issue:

rectangle with 15 and 13 meter sides.

rectangle with measurements of 15 and 15.81 meters.

two right triangles with 9 and 13 meter sides. So, the following is how the surface area is determined:

S is equal to 15 x 13 plus 15 x 15.81 and 2 x 0.5 x 9 x 13

S = 549.15 m².

The option that is not a run-on sentence is this: According to data collected throughout film history, the average length for a feature film is between 80 and 100 minutes, although some far exceed the standard running time.

A run-on sentence is a sentence that continues without using appropriate punctuation to join independent clauses. In the sentence above, the comma is used in the right place to join the independent clause, so we may not refer to this as a run-on sentence.

The other three options continue on end without appropriate punctuation to break off the independent clauses.

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The matrix row operation on the matrix A gives us: 0x + 10y - 25z = 4

There are 3 primary basic operations that are utilized on the rows of a matrix when we utilize the matrix to solve a particular system of linear equations . The aim is usually to get the left region of the matrix to resemble the identity matrix .

The three primary operations are:

Switching Rows

Multiplying a Row by a Number

Adding Rows

Now, from the given matrix, the equations are:

x - y + 5z = -1

x - y - 4z = 5

5x + y + 0z = -1

We are told to add -5 times row 1 to row 3 and this gives:

-5x + 5x + 5y + 5y - 25z + 0z = 5 - 1

0x + 10y - 25z = 4

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Answer:(a) The rate of decay is 14.4% per day, which can be written as a decimal by dividing by 100: r = 0.144.

(b) The formula for continuous decay is given by:

A = A₀ * e^(-rt)

where A is the remaining amount of the substance after time t, A₀ is the initial amount, r is the rate of decay, and e is the mathematical constant approximately equal to 2.71828.

Plugging in the given values, we get:

A = 140 * e^(-0.144*15)

A = 140 * e^(-2.16)

A ≈ 47.23

Therefore, after 15 days, approximately 47.23 mg of the radioactive substance will be left, rounded to two decimal places.

Step-by-step explanation:

Answer:

$74.66

Step-by-step explanation:

Plot the points on the graphing calculator (x = length of HDMI cord, y = cost). Then generate a linear regression model:

y = 3.68x + 1.06 (approximately)

x = 20, so y = 74.66

$74.66 is the correct answer.

The volume of the clay used to make the vase is 36 in³

To determine the volume of clay that was used for the vase, we need to consider that;

The formula for the volume of a rectangular prism is expressed as;

Volume = lwh

Such that;

For the bigger prism, we have;

Volume = 3 × 3 × 5

Multiply the values

Volume = 45 in³

For the hole, we have;

Volume = 4 × 3/2 × 3/2

Multiply the values

Volume = 9 in³

Then, the volume of clay used for the vase = 45 - 9 = 36 in³

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Answer:

Experiencing anxiety on the day of the examination is a common problem for many students, especially those in grade 12 who may feel a lot of pressure to perform well. However, there are several strategies that they can use to minimize the impact of anxiety and enhance their performance in the examination. Some of these strategies include:

1. Get enough sleep: Getting enough sleep is essential for students to perform well on the day of the examination. Students should aim to get at least 7-8 hours of sleep before the exam day. A well-rested brain will be able to function better, and students will be less likely to feel anxious or stressed.

2. Eat a balanced breakfast: Eating a balanced breakfast on the day of the examination can help students feel more alert and focused. A healthy breakfast can also provide the necessary energy needed to get through the examination.

3. Plan your day: Plan your day well ahead of the examination. This will help you feel more in control and reduce feelings of anxiety. Set aside time to review notes, relax and mentally prepare for the exam.

4. Practice relaxation techniques: Practice relaxation techniques such as deep breathing or progressive muscle relaxation to help calm your nerves. These techniques can help students reduce stress levels and anxiety, which in turn can enhance their performance.

5. Avoid last-minute cramming: Cramming at the last minute can increase feelings of anxiety and negatively impact performance. Instead, spend time reviewing notes and practicing past papers in the days leading up to the examination.

6. Stay positive: It is essential to stay positive and avoid negative thoughts or self-doubt. Remind yourself of your hard work and preparation for the exam. Believe in your abilities, and focus on what you can do rather than what you cannot.

By implementing these strategies, grade 12 students can minimize the impact of anxiety on the day of the examination, and enhance their overall performance. Remember that exam performance is not just about what you know, but also about how you manage your anxiety and stress levels.

The height of the traffic barrel is 42.97 inches.

The surface area of a cylinder is derived with A = 2πr² + 2πrh. A = surface area, r = radius and h = height.

Since diameter is given as 18 inches, we can get radius by dividing the diameter by 2:

r = 18 / 2

r = 9 inches.

Substituting these values, we get:

2,939.04 = 2π(9²) + 2π(9)h

2,939.04 = 162π + 18πh

2,939.04 - 162π = 18πh

h = (2,939.04 - 162π) / (18π)

h = 42.9736382161

h = 42.97 inches

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The probability of landing on red is given by the number of red sections divided by the total number of sections. In this case, there are 2 red sections out of a total of 6 sections. Therefore, the probability of landing on red is:

P(red) = 2/6 = 1/3

So the probability of landing on red is 1/3.

The logarithm expression In(9/x) can be expanded as In(9) - In(x)

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

In(9/x)

Using the logarithmic identity log a/b = log a - log b, we can expand ln(9/x) as follows:

ln(9/x) = ln(9) - ln(x)

Therefore, ln(9/x) can be expressed as the difference of two natural logarithms: ln(9) and ln(x).

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Answer:

Step-by-step explanation:

When x_1 =7 then you can figure out by given condition say X_n+1= 2X_n-3

then X_2= 11 by substituting the value of X_1 as 7 similarly you can find out the value of X_3 by substituting X_2 as 11 so X_3 =19.

Similarly you can find out b)

Answer:

3

Step-by-step explanation:

The inverse function returns the original value for which a function gave the output.

This means if there is a function f(x) and at x = a, f(a) = k then f⁻¹(k) = a

This may be difficult to grasp with variables but essentially returning to the specific question
if f(3) = 17

then

f⁻¹(17) = 3

And that is the answer

Answer:

[tex]\dfrac{\boxed{2}}{\boxed{3}} \times \dfrac{\boxed{1}}{\boxed{2}} = \dfrac{\boxed{1}}{\boxed{3}}[/tex]

Step-by-step explanation:

The square is 1 unit long and 1 unit wide
There are 3 smaller rectangles in the horizontal direction

Length of each rectangle is therefore 1/3 unit

There are 6 rectangles along the vertical direction

The height of each rectangle is therefore 1/6 unit

The shaded area is 2 rectangles wide and 3 rectangles in height

Width of shaded area = 2 x 1/3 = 2/3

Height of shaded region = 3 x 1/6 = 1/2

Area of shaded rectangle is

[tex]\dfrac{\boxed{2}}{\boxed{3}} \times \dfrac{\boxed{1}}{\boxed{2}} = \dfrac{\boxed{1}}{\boxed{3}}[/tex]

Answer:

f(x) = x²-8x+15

g(x) = x -3

h(x) = f(x) ÷ g(x)

= x²-8x+15 ÷ x-3

x-3√x²- 8x +15 | x-5

x² - 3x

-5x + 15

- 5x + 15

-----------

h(x) = x-5

Answer:

Let's use "K" to represent Kevin's current age, and "M" to represent his mother's current age.

According to the problem, if you triple Kevin's age, the result is 1 less than his mother's age:

3K = M - 1

We can simplify this equation by adding 1 to both sides:

3K + 1 = M

This equation tells us that if we add 1 to three times Kevin's age, we get his mother's age. We can use this equation to solve for Kevin's age if we know his mother's age, or we can use it to solve for his mother's age if we know Kevin's age.

Answer:

<2  = 30°

Step-by-step explanation:

Let angle 1 = x

Let angle 2 = y

x + y = 95

x = 35 + y  Substitute 35 + y for x in x + y = 95

x + y = 95

35 + y + y = 95  Subtract 35 from both sides

y + y = 60    Combine like terms

2y = 60  Divide both sides by 2

y = 30

Helping in the name of Jesus.

The solution of the equation is x = -1.

Given is an equation we need to solve it,

3x/4 + 3 - 2x = -1/4 + x/2 +5

Multiplying the equation by 4 both the sides,

3x + 12 - 8x = -1 + 2x + 20

Combining the like terms,

3x - 8x - 2x = 20 - 1 - 12

3x - 10x = 7

-7x = 7

x = -1

Hence the solution of the equation is x = -1.

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Answer:

Step-by-step explanation:

Answer: I did not do the math, I just tell people how to do it

Hope I helped.

Step-by-step explanation:

Multiply the number of triangles you created by 180.

The equation of p(x) in vertex form is p(x) = 3(x + 1)² - 3.

Option C is the correct answer.

Since, Polynomial is an equation written as the sum of terms of the form kxⁿ.

where k and n are positive integers.

We have,

From the table,

From p(x) = 24 to p(x) = -3 the value of p(x) is decreasing and from p(x) = -3 to p(x) = 24 it is increasing.

So,

The vertex is (- 1, -3).

The vertex form of p(x).

p(x) = a ( x - h)² + k

Where (h, k) is the vertex.

Now,

(-1, -3) = (h, k)

Make (- 2, 0) = (x, p(x))

0 = a (- 2 + 1)² + (-3)

0 = a x 1 - 3

a = 3

Thus, The vertex equation of p(x).

p(x) = 3(x + 1)² - 3

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According to the information, Hannah donated b/50 books in total.

First, we need to find the average number of books donated by each student. We can do this by dividing the total number of books donated by the number of students:

Hannah donated 3 times this amount, so we can multiply the average by 3 to find how many books she donated:

Simplifying this expression, we get:

Therefore, Hannah donated b/50 books in total.

Note: This question is in Spanish. Here is the question in English:

Hannah's school organized a book donation. There are 150 students in her school who donated a total of b books. Hannah donated 3 times the average number of books donated by each student. How many books did Hannah donate?

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