a spinner with 10 equally sized slices 4 yellow, 4 red, 2 blue. probability that the dial stops on yellow?

Answer:

x = 6

Step-by-step explanation:

the diagonal AC divides the rectangle into 2 right triangles.

Consider the right triangle ABC with legs AB , BC and hypotenuse AC

using Pythagoras' identity in right triangle ABC

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AB² + BC² = AC² ( substitute values )

x² + (x + 2)² = (x + 4)² ← expand factors using FOIL

x² + x² + 4x + 4 = x² + 8x + 16

2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

however , x > 0 , then x = 6

To find the volume of the given cylinder, we need to use the formula of volume of a cylinder which is given by V = πr²h, where V is the volume of the cylinder, r is the radius of the cylinder and h is the height of the cylinder. So, the volume is 1078.1 cubic units.

Given, Length = 14 units, Height = 11 units. Now, we know that the formula for the volume of a cylinder is given as; V = πr²h.

Here, the radius of the cylinder is half the length of the cylinder, which is; Radius = Length/2

Radius = 14/2

Radius = 7 units

Substituting the value of the radius and height, we have; V = π(7)²(11)

V = 1078.1 cubic units. Therefore, the volume of the cylinder is 1078.1 cubic units. Rounded off to one decimal place, the volume is 1078.1 cubic units.

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The net cash flow from operating activities would be $100,800.

Change in accounts receivable:

= $20,900 - $20,000

= $900

Change in inventory:

= $61,800 - $62,500

= -$700

Change in accounts payable:

= $19,700 - $18,600

= $1,100

Change in dividends payable:

= $24,000 - $22,000

= $2,000

Change in operating assets and liabilities:

= Change in accounts receivable + Change in inventory - Change in accounts payable - Change in dividends payable

= $900 + (-$700) + $1,100 + $2,000

= $2,300

Net cash flow from operating activities:

= Net income + Change in operating assets and liabilities

= $98,500 + $2,300

= $100,800.

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Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       [tex]0=\frac{1}{3} x-1[/tex]

       [tex]1=\frac{1}{3} x[/tex]

       [tex]x=3[/tex]

So x-intercept is the point (3,0).

Answer:

[tex]y = |x - 2| + 3[/tex]

The correct answer is C.

The system B is gotten from system A by operation (d)

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

x + y = 8

4x - 6y = 2

Also, we have the solution to be (5, 3)

Recall that

x + y = 8

4x - 6y = 2

Multiply the first equation by 6

So, we have

6x + 6y = 48

4x - 6y = 2

Add the equations

10x = 50

This means that the system B from system A is (d)

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Answer:

A requested task is subject to be reported when it has been completed according to the instructions provided.

To demonstrate this with chain of thought reasoning:

1. The task requested will have details outlining what needs to be done.

2. To fulfill the request of the task, the instructions outlined must be followed.

3. Once all instructions are met, the task is complete.

4. Completion of the task means it is subject to be reported.

Step-by-step explanation:

Step-by-step explanation:

a. 4/64= 1/16 for red marble

b. 40/64= 5/8 black marbles

c. 20/64= 5/16 blue marble

d. highest: black marble

e. lowest: red marble

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

The given statement proposition is a that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.

The given statement is a logical proposition involving the concept of induction. Let's break it down and analyze its components.

"If x is inductive..."

This implies that x is a concept or object that possesses the property of being inductive. In mathematics, the term "inductive" typically refers to the property of being a natural number or belonging to the set of natural numbers.

"...then so is (x ∈ X : x = Ф or x = y ∪ {y} for some y)"

Here, we have a set X that consists of elements satisfying a certain condition. The condition states that an element x in X can either be equal to the empty set (Ф) or the union of a set y with itself ({y}). This construction represents a recursive definition, where each element in X is defined in terms of a base case (Ф) and a recursive step ({y}).

"...hence each n ≠ 0 is m + 1 for some m."

This conclusion states that for every natural number n that is not equal to 0, there exists another natural number m such that n can be expressed as m + 1. In other words, any non-zero natural number is the successor of some other natural number.

Overall, the given statement is a proposition that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.

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It should be a positive graph .

Answer:

Below, rises, more, 2, 5

Step-by-step explanation:

Its an positive exponential growth function which means it increases sharply to the right it also is above the x-axis.

The graph is 2 times the graph of 5^x so its steeper or rises more

Plug in 0 to get 1*2=2

Plug in 1 to get 5*1=5

Answer:

A

Step-by-step explanation:

For a table of values to be a function, all inputs must have one unique output. The only table that doesn't violate this is table A.

Notice that while two different inputs (-4 and 1) have the same output of 7, it is still a function because both outputs of 7 are associated with two different inputs.

These are two instances where the product of two numbers yields a negative result.

To demonstrate two products that both result in negative values, we can choose two numbers with opposite signs and multiply them together. Here are two examples:

Example 1:

Let's consider the numbers -3 and 4. When we multiply these numbers, we get:

(-3) * (4) = -12

The product -12 is a negative value.

Example 2:

Let's consider the numbers 5 and -2. When we multiply these numbers, we get:

(5) * (-2) = -10

Once again, the product -10 is a negative value.

In both examples, we have chosen two numbers with opposite signs, and the multiplication of these numbers results in a negative value. Therefore, these are two instances where the product of two numbers yields a negative result.

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The correct statements are

The dependent variable is t.

When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."

When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."

The independent variable is t. Option A,D,E,F.

Let's analyze each statement to understand why it is true:

A) The dependent variable is t: In the given function, f(t), the value of f depends on the value of t. Therefore, t is the independent variable, and f is the dependent variable.

D) When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced": Here, the value of t is 2, representing the year 2002, and the value of f(t) is 1,323, representing the amount of garbage produced in tons.

E) When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced": Similar to statement D, the value of t is 4, representing the year 2004, and the value of f(t) is 1,458.6, representing the amount of garbage produced in tons.

F) The independent variable is t: As mentioned in statement A, t is the independent variable in the given function. It is the variable that we can change or manipulate, and the value of f depends on the value of t.

Statements B, C, and G are incorrect:

B) When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155": This statement is incorrect because in the given function, t represents the time in years after 2000, not the amount of garbage produced.

C) The dependent variable is f(t): This statement is incorrect because, as mentioned earlier, t is the independent variable, and f is the dependent variable.

G) The independent variable f(t): This statement is incorrect because f(t) represents the amount of garbage produced, which is the dependent variable in the given function.

So Option A,D.E.F. Are correct.

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Note the complete question is

Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.

Which statements are true for the given function?

A.) The dependent variable is t.

B.) When f(12) = 2,155, 12 represents "12 tons of garbage produced," and 2,155 represents "the year 2155."

C.) The dependent variable is f(t).

D.) When f(2) = 1,323, 2 represents "the year 2002," and 1,323 represents "1,323 tons of garbage produced."

E.) When f(4) = 1,458.6, 4 represents "the year 2004," and 1,458.6 represents "1,458.6 tons of garbage produced."

F.) The independent variable is t.

G.) The independent variable  f(t)

Answer:

The correct answer is a.

Step-by-step explanation:

The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.

Answer:

24310

Step-by-step explanation:

17 choose 8= 17 choose 9

17 choose 8= 17*16*15*14*13*12*11*10/8!= 24310

Answer:

718000

Step-by-step explanation:

718000 is already in standard form

The corresponding sides and angles of the similar and congruent triangles indicates that we get the following approximate and exact values;

Page 1;

5. [tex]\overleftrightarrow{AC}[/tex] = 4.3. 6. [tex]\overline{BP}[/tex] ≈ 7.5 7. [tex]\overline{YV}[/tex] ≈ 8

Page 2

5. [tex]\overline{DF}[/tex] = [tex]11\frac{1}{4}[/tex], 6. [tex]\overline{ED}[/tex] = 5, 7. [tex]\overline{BC}[/tex] = 22, 8. [tex]\overline{EF}[/tex] = 8

Page 3;

8. m∠ABC = 30°, 9. m∠XYP = 44°, 10. [tex]\overline{AC}[/tex] = 14

Congruent triangles are triangles that have all three corresponding sides of the same length and all three angles of the same measure.

First Page

5. The distance from the vertex B to the line segment [tex]\overleftrightarrow{AC}[/tex] in the triangle ΔABC is the altitude of the triangle, which is 4.3

6. The distance from the vertex B to [tex]\overleftrightarrow{AC}[/tex] = [tex]\overline{BP}[/tex]

Pythagorean theorem indicates that the length of the segment [tex]\overline{BP}[/tex] can be found as follows;

[tex]\overline{BP}[/tex] = √(13.5² - 11.2²) ≈ 7.5

7. The distance from Y to  [tex]\overleftrightarrow{XZ}[/tex] is the altitude of the triangle ΔXYZ, which indicates;

The distance from Y to  [tex]\overleftrightarrow{XZ}[/tex] = [tex]\overline{YV}[/tex]

The Pythagorean theorem indicates that we get;

[tex]\overline{YV}[/tex] = √(13.34² - 10.67²) ≈ 8

Second page;

5. The scale factor from ΔABC to ΔDEF = 3/4

Therefore, the length of [tex]\overline{DF}[/tex] = (3/4) × 15 = 45/4 = [tex]11\frac{1}{4}[/tex]

6. The scale factor of (1/3) indicates that we get;

[tex]\overline{ED}[/tex] = (1/2) × 10 = 5

7. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 18/9 = 10/5 = 2

The corresponding side to [tex]\overline{BC}[/tex] is [tex]\overline{EF}[/tex]

[tex]\overline{EF}[/tex] = 11, therefore, the length of [tex]\overline{BC}[/tex] = 2 × 11 = 22

8. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 4/6 = 10/15 = 2/3

The corresponding side to [tex]\overline{EF}[/tex] is [tex]\overline{BC}[/tex]

[tex]\overline{BC}[/tex] = 12, therefore [tex]\overline{EF}[/tex] = (2/3) × 12 = 8

Third page;

8. The triangles ΔABV and ΔCVB are congruent triangles by the Leg Hypotenuse congruence theorem.

The angles ∠ABV and ∠CBV are corresponding triangles, therefore;

∠ABV ≅ ∠CBV

m∠CVB = m∠ABV = 15° (Definition of congruent triangles and symmetric and substitution property)

∠ABC = ∠ABV + ∠CBV

Therefore; m∠ABC = 15° + 15° = 30°

9. The angles ∠YXP and ∠YZP are right triangles, therefore;

m∠YXP = m∠YZP = 90°

The right triangles  ΔYXP and ΔYZP are congruent by the LH congruence theorem

∠XYP ≅ ∠ZYP (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)

m∠XYP = m∠ZYP (Definition of congruent triangles)

m∠XYZ = m∠XYP + m∠ZYP (Angle addition property)

m∠XYZ = 2 × m∠XYP

2 × m∠XYP = m∠XYZ = 88°

m∠XYP = 88°/2 = 44°

10. The angles ∠ACP and ∠ABP are right angles, according to the indicated markings, therefore;

∠ACP ≅ ∠ABP (All right angles are congruent)

ΔACP ≅ ΔABP by SAA congruence theorem

[tex]\overline{AC}[/tex] ≅ [tex]\overline{AB}[/tex] (CPCTC)

[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] (Definition of congruent segments)

[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] = 14

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We have created three different linear systems using the equation 20x + 12y = 24.

System 1 has infinitely many solutions, System 2 has no solution, and System 3 has a unique solution.

Let's create three different linear systems using the equation 20x + 12y = 24 and ensure that each system has a different number of solutions.

System 1:

Equation 1: 20x + 12y = 24 (given)

Equation 2: 40x + 24y = 48

Explanation: In this system, we multiplied both sides of the given equation by 2 to create Equation 2.

By doing so, we have essentially created two equations that are multiples of each other.

Since the equations are equivalent, they represent the same line, and the system has infinitely many solutions.

Any values of x and y that satisfy the first equation will automatically satisfy the second equation as well.

System 2:

Equation 1: 20x + 12y = 24 (given)

Equation 2: 20x + 12y = 48

Explanation: In this system, we changed the constant term in Equation 2 to 48.

By doing so, we have created two parallel lines with the same slope. Since the lines are parallel, they will never intersect, and the system has no solution.

There are no values of x and y that satisfy both equations simultaneously.

System 3:

Equation 1: 20x + 12y = 24 (given)

Equation 2: 40x + 24y = 48

Explanation: In this system, we multiplied both sides of Equation 2 by 2 to create Equation 2.

By doing so, we have created two equations that have the same slope but different y-intercepts.

Since the lines are not parallel and have different y-intercepts, they will intersect at a single point, and the system has a unique solution.

There will be one specific pair of values for x and y that satisfy both equations simultaneously.

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Answer:

9

Step-by-step explanation:

Answer:540 degrees

The sum of the measures of the angles of a five-sided polygon (pentagon) is 540 degrees123. This can be calculated using the angle sum formula, S = (n − 2) × 180°, where n is the number of sides in the polygon12. Since a pentagon has five sides, the sum of the interior angles is (5 − 2) × 180° = 540°123.

Step-by-step explanation:

Answer:

540°

Step-by-step explanation:

Since a pentagon has n=5 sides, then we have:

[tex]180(n-2)=180(5-2)=180(3)=540^\circ[/tex]

The calculated value o x in the circle is 7

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

The circle

The value of x can be calculated using teh equation of the intersection of chords

So, we have

122 = 1/2(6x + 8 + 194)

Evaluate

244 = 6x + 202

So, we have

6x = 42

Divide by 6

x = 7

Hence, the solution for x is 7

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The expression you provided appears to be an integral with multiple terms involving logarithmic and trigonometric functions. To solve it, we need to break it down and evaluate each term separately.

Let's examine each term in the given expression:The integral of 1 with respect to x is simply x.The integral of 1/x is ln|x|.

The integral of tan(x) can be evaluated using a substitution or integration by parts technique, depending on the specific limits of integration or any additional context provided.

Without specific limits or further instructions, it's challenging to provide a precise solution or simplify the expression further. However, if you provide more information or clarify the problem statement, I can help you with a more detailed solution.

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The statement that is correct about the dot plots is that:

A) The distribution for Class M is approximately symmetric

A symmetric distribution in dot plots is defined as a distribution with a vertical line of symmetry in the center of the graphical representation, so that the mean is equal to the median.

A symmetric distribution is one that occurs when the values ​​of a variable occur at regular frequencies, and often the mean, median, and mode all occur at the same point. If we draw a line through the middle of the chart, we can see that the two planes mirror each other.  

Now, from the given two dot plots of class M and Class N, it is very clear that class M is very close to being symmetric about the data value 3.

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Answer:

The correct answer is "Two times r equals the diameter of the circle. When you multiply that by pi, you get the distance around the circle, or the circumference." This is because the circumference of a circle is equal to the distance around it, which is the same as the length of its perimeter. The diameter of a circle is the straight line that passes through the center of the circle and touches both sides. Therefore, if you multiply the diameter by pi, which is the ratio of the circumference to the diameter of a circle, you get the circumference. Alternatively, you can also use the formula C = 2πr, where C is the circumference and r is the radius of the circle. Since the radius is half the diameter, the formula can also be stated as C = πd, where d is the diameter of the circle.

Step-by-step explanation:

Answer:

A= 220.5ft

B= $2425.5

Step-by-step explanation:

A= 220.5ft

B= $2425.5