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10. A fair die is rolled repeatedly until a 6 appears. What is the probability that the experiment stops at the fourth roll? (0.5) 11. If A basketball player could make a free throw with probability 0

Main Answer:The area of the first five squares in the sequence are: 1,4,9,16,25.This is a quadratic progression and the general term of the sequence is \(n^{2}\) ,where n is the term number.

The sum of the areas of the infinite squares generated by this sequence is infinte.

Supporting Question and Answer:

What is the formula for the sum of an infinite series of quadratic terms?

The formula for the sum of an infinite series of quadratic terms is ∑\(n^{2}\) =\(\frac{n(n+1)(2n+1)}{6}\) ,where ∑\(n^{2}\) represents the sum of the terms in the sequence,from n=1 to infinity.

Body of the Solution: The first five squares in the sequence are: \(1^{2} ,2^{2}, 3^{2}, 4^{2} ,5^{2}\)

And their corresponding areas are:

1,4,9,16,25

We can observe that this is a quadratic progression, since the difference between consecutive terms in the sequence increases by a constant amount of 2, indicating a quadratic relationship between the terms.

The general term of the sequence is \(n^{2}\) ,where n is the term number.

To calculate the sum of the areas of the infinte squares generated , we can use the formula for the sum of an infinite series of quadratic terms:

∑\(n^{2}\) =\(\frac{n(n+1)(2n+1)}{6}\) ,where ∑\(n^{2}\) represents the sum of the terms in the sequence,from n=1 to infinity.

Substituting n=∞ in the formula ,we get:

∑\(n^{2}\)= \(\lim_{n \to \infty} \frac{n(n+1)(2n+1)}{6}\)

Evaluting the limit,we get

∑\(n^{2}\)=∞

That is, the sum of the areas of the infinite squares generated by this sequence is infinte.

Final Answer: The area of the first five squares in the sequence are: 1,4,9,16,25.

This is a quadratic progression.

The general term of the sequence is \(n^{2}\) ,where n is the term number.

The sum of the areas of the infinite squares generated by this sequence is infinte.

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Answer:

∠ 4 = 140°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ 4 is an exterior angle of the triangle, then

∠ 4 = ∠ 1 + ∠ 2 ( substitute values )

11x + 8 = 6x + 7 + 4x + 13

11x + 8 = 10x + 20 ( subtract 10x from both sides )

x + 8 = 20 ( subtract 8 from both sides )

x = 12

Then

∠ 4 = 11x + 8 = 11(12) + 8 = 132 + 8 = 140°

The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Each portion was greater than 13 pound. The correct option is D.

We can solve this problem by setting up an inequality based on the information given.

Let x be the size of each portion of flour that William used. Then, he used 3 portions, so the total amount of flour he used is 3x.

According to the problem, he had less than 7 pounds of flour left after using the portions. So, we can write:

\(8 - 3x < 7\)

Simplifying this inequality, we get:

\(3x > 1\)

Dividing both sides by 3, we get:

\(x > 1/3\)

Therefore, each portion was greater than 1/3 of a pound, which is equivalent to 5.33 ounces.

Among the answer choices, the statement that BEST describes the size of the portions is option D: Each portion was greater than 13 pounds. This is because option D is the only one that is always true given that each portion is greater than 1/3 of a pound. Option B is too small, option A is too small and, in any case, less than 13 pounds, and option C is too large since 3 portions greater than 213 pounds would exceed the initial amount of flour William had.

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According to the question to maximize the area of the pen, the dimensions should be a length of 450 feet and a width of 225 feet.

To maximize the area of the rectangular pen, we need to find the dimensions that use up the entire 900 feet of fencing.

Let's assume the length of the pen is L and the width is W. Since there are three sides that need fencing, we have \(2W + L = 900.\)

To maximize the area, we need to express the area A in terms of a single variable. The area of a rectangle is given by \(A = L * W.\)

From the equation \(2W + L = 900\), we can solve for L to get \(L = 900 - 2W.\)

Substituting this value of L in the equation for the area, we have \(A = (900 - 2W) * W.\)

Expanding and simplifying, we get \(A = 900W - 2W^2.\)

To find the dimensions that maximize the area, we need to find the vertex of the quadratic function \(A = -2W^2 + 900W\). The vertex can be found using the formula \(W = -b / (2a)\), where \(a = -2\) and \(b = 900.\)

\(W = -900 / (2 * -2) = 225.\)

Substituting this value of W back into the equation for L, we have \(L = 900 - 2(225) = 450.\)

Therefore, to maximize the area of the pen, the dimensions should be a length of 450 feet and a width of 225 feet.

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An expression for the amount of money that Alicia earns in a day is 40y-3g.

Given that, Alicia runs a small business mowing yards in the summer. For every yard she mows, she earns $40. However, she spends part of this money on gasoline for her lawnmower. Each gallon of gasoline costs $3.

We need to find an expression for the given situation.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Now, expression =40y-3g

Therefore, an expression for the amount of money that Alicia earns in a day is 40y-3g.

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Answer: $40y − $3g

Step-by-step explanation:

Answer:

Step-by-step explanation:

= 3x + 15 = 8x +25

= 3x - 8x = 25 - 15

= 5x = 10

= x = 10 : 5

= x = 2

The length of the required line segment JM is 9 units.

Use the concept of a line defined as:

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

In the given figure,

Segment JM = 3x + 15

Segment  MK = 8x + 25

And JM = MK

Since both segments are of equal length,

Therefore,

8x + 25 =3x + 15

Subtract 3x on both sides,

5x + 25 = 15

Subtracting 25 on both sides,

5x =  -10

Divide by 5 on both sides,

x = -2

Now the length of JM = |3x + 15| as length is a positive quantity.

Put the value of x

JM = |3(-2) + 15|

JM = 9

Hence,

The length of the line segment JM is 9 units.

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The complete question is:

Find the length of JM.

Answer:

Step-by-step explanation:

The ratio would be 36:4. The bigger number is on either side but when it concludes "for" means it's a ratio.

Answer:

y = 2x + 3

Step-by-step explanation:

the same slope would be 2x still

the 3rd and 4th choice are the only ones that have the correct slope

and 1 unit lower than 4 is 3

Answer:

y = 2x + 3

Step-by-step explanation:

the same slope would be 2x still

the 3rd and 4th choice are the only ones that have the correct slope

and 1 unit lower than 4 is 3

The secant of circle D is the 'line GH'. Where the line segment EF is the diameter of the circle, line segment DC is the radius, and the ray AB is the tangent of the given circle.

The line that passes through the circle and touches the circle at two points is said to be a secant line of the circle.

The given circle D has a center at D.

The radius of the circle is given by the line segment CD

The diameter (or) the longest chord of the circle is given by the line segment EF

The ray AB passes touches the circle at point B, which is called the tangent of the circle.

Where the line GH passes through the circle and touches at two points. So, this line GH is said to be the secant of the circle.

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Disclaimer: The given question is incomplete(needs a diagram). Here is the required diagram attached.

Question: In circle D, which is a secant?

a) EF

b) DC

c) Line segment AB

d) Line GH

Answer:

ray ab

Step-by-step explanation:

ANSWER

P(3) = 0

Step-by-step explanation:

Factor Theorem is a consequence of Remainder Theorem.

Remainder Theorem states that if polynomial f(x) is divided by a binomial (x - a) then the remainder is f(a).

Factor Theorem states that if f(a) = 0, then the binomial (x - a) is a factor of f(x).

We have the polynomial

P(x) = x^5-3x^4+5x^3-15x^2-6x+18P(x)=x

5

−3x

4

+5x

3

−15x

2

−6x+18

To prove that x-3 is a factor of P, we calculate P(3):

P(3) = 3^5-3*3^4+5*3^3-15*3^2-6*3+18P(3)=3

5

−3∗3

4

+5∗3

3

−15∗3

2

−6∗3+18

P(3) = 243-243+135-135-18+18P(3)=243−243+135−135−18+18

P(3) = 0P(3)=0

Thus, x-3 is a factor of P(x)

Answer:

0, 5%, 1/5, 5

5% is equal to 5÷100=0,05

1/5 is equal to 1÷5=0,2

Answer:

x = 2.285 hours

y = 2.1425  feet

Step-by-step explanation:

Let us say that y represents the depth of the pool in feets and x represents the time in hours

The two set of equations are

y = 1/2x + 1

y= -1.25x + 5

Solving the above two equations we get

Subtracting eq (1) from eq (2), we get -

y-y = -1.25 x -0.5 x + 4

0 -1.75 x + 4

x = 4/1.75

x = 2.285 hours

y = 0.5 * 2.285 + 1

y = 2.1425  feet

ANSWER:

10

STEP-BY-STEP EXPLANATION:

We can calculate the value of x, knowing that the subtraction between the plane angle (180°) and 7x -10 is equal to 120°, therefore, we have the following equation:

The value of x is 10

B (second option)

characters characters characters

The equation for finding the length between two points is:

where point 1 has coordinates (x1, y1) and point 2 has coordinates (x2, y2).

We assign A to be point 1 and B be point 2

Therefore,

Answer:

$14.25

Step-by-step explanation:

5% = 0.05

15 times 0.05 = $0.75

15 - 0.75 = $14.25

So, the sale price is $14.25

Answer:

$14.25

Step-by-step explanation:

5% = 0.05

15 times 0.05 = $0.75

15 - 0.75 = $14.25

So, the sale price is $14.25

Answer:

x = 8√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use PT to solve for the missing length.

Step 2: Identify Variables

Leg a = 8

Leg b = 8

Hypotenuse c = x

Step 3: Solve for x

The method of reduction of order is a technique used to find a second solution to a homogeneous linear differential equation when one solution is already known.

However, it cannot be directly used for nonhomogeneous linear differential equations. In nonhomogeneous equations, the method of undetermined coefficients or variation of parameters is typically used to find a particular solution.

Therefore, the statement "the method of reduction of order can also be used for the nonhomogeneous equation" is false. It is important to understand the different techniques for solving differential equations, and to choose the appropriate method based on the type of equation and boundary conditions given.

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Answer:

x=1

Step-by-step explanation:

it is

Answer:

$41

Step-by-step explanation:

(20x205)/100=20% of 205=

41

(B) 4 hr is the correct answer.

★ Speed of body is defined as the ratio of distance travelled to the time taken\(.\)

Given that,

distance = 56 miles

speed = 14 miles per hour

By substituting the values, we get

⭆ time = distance/speed

⭆ time = 56/14

⭆ time = 4 hr

Answer:

B

Step-by-step explanation:

Answer:

6 +x

Step-by-step explanation:

Let the number = x

Sum of 14 and a number = 14 +x

8 fewer than (14 + x )= 14 + x - 8 = 6 +x

Answer: 14 + x - 8 (can also be 6 + x)

Step-by-step explanation:

8 fewer means we're subtracting 8, which is -8

Sum of 14 and a number would be 14 + x

All of this combined would be 14 + x - 8 but if you want to simplify it, you can subtract 8 from 14 and get 6. This would be 6 + x.

In Question 10, to determine the year when Ryan's salary was highest in real terms, we need to adjust his earnings for inflation using the Consumer Price Index (CPI). Given the CPI values for 1970, 1980, and 1990, we can calculate the real value of Ryan's salary for each year and compare them.

In Question 11, we are asked to identify which item will be included in GDP. GDP measures the value of goods and services produced within a country's borders during a specific time period. We need to determine if the given options represent items that contribute to GDP.

In Question 13, we are discussing the problems with CPI calculations. CPI is used to measure inflation and changes in the cost of living. We need to identify the specific issues associated with CPI calculations.

Question 10: To determine the highest real salary, we need to adjust Ryan's earnings for inflation. We can do this by dividing his earnings in each year by the respective CPI value and then comparing the real values. By performing the calculations, we find that Ryan's salary was highest in 1970 when adjusted for inflation.

Question 11: In this question, option a (vegetables produced in the backyard for self-consumption) is not included in GDP as it represents non-market production for personal use. Option b (jewelry set bought from an antique store) is included in GDP as it involves a market transaction. Option c (rental value of owner-occupied houses) is not included in GDP as it is imputed and not a market transaction. Option d (purchase of a pre-owned car) is included in GDP as it involves a market transaction.

Question 13: The problem with CPI calculations includes both the substitution bias and unmeasured quality change. The substitution bias arises because CPI assumes constant consumption patterns and does not account for consumers' ability to substitute cheaper goods for more expensive ones. Unmeasured quality change refers to the difficulty of accurately capturing changes in the quality of goods and services over time in the CPI calculation. Therefore, the correct answer is that both the substitution bias and unmeasured quality change are problems with CPI calculations.

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Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Width  =x-2

Length=x  

Perimeter  =48

Perimeter =x*(x-2)

Substitute: 48=x*(x-2)

Simplify: 48=x^2-2x

x=48/2=24

Answer:

8.5 mph

Step-by-step explanation:

First find how far Hobbit traveled in 4 hrs (8AM - Noon)

3 mph x 4 hr = 12 miles

Now find Gandalf's speed:

Galdalf traveled the same 12 miles that Hobbit did PLUS 5 more miles in 2 hours (10AM -Noon) for a total of 17 miles

Speed = 17 mi / 2 hr = 8.5 mph

a) To find dy/dx, we need to use implicit differentiation. Taking the derivative of both sides with respect to x, we get:

dy/dx + 2 = 10x - (27x + V3x + 1)/(2V3x + 2)

Now we can solve for dy/dx:

dy/dx = (10x - (27x + V3x + 1)/(2V3x + 2)) - 2

Simplifying, we get:

dy/dx = (5x(4xV3 - 13) - 2)/(xV3 + 1)

b) To find dy/dx, we can use the power rule and the chain rule:

dy/dx = (-6x + 2)/(14-3x2+2x)^2

c) To find dy/dx, we need to use the chain rule and the power rule:

dy/dx = 8(2x - sin²(3x))(2cos(3x)3x)

d) To find dy/dx, we can simply take the derivative:

dy/dx = 3

e) To find dy/dx, we need to use the chain rule and the product rule:

dy/dx = 2sec²(2x) + 2/(w2x + 7)

f) To find dy/dx, we need to use the product rule and the chain rule:

dy/dx = 2xsec²(x) + 2tan(x)

g) To find dy/dx, we need to use the chain rule and the logarithmic differentiation:

dy/dx = (1/xln2)(-csc(x) - cot(x)ln2)

h)  There is no question provided for part h.

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Straight-line graphs are commonly referred to as "linear graphs" or "linear equations."

We have,

A straight line graph, often referred to as a linear graph or linear equation, represents a relationship between two variables that can be expressed by a linear equation in the form y = mx + b.

In this equation, 'x' and 'y' are the variables, 'm' is the slope of the line, and 'b' is the y-intercept (the point where the line crosses the y-axis).

The slope 'm' determines the steepness or incline of the line.

A positive slope indicates the line rises as 'x' increases, while a negative slope indicates the line descends as 'x' increases.

The y-intercept 'b' represents the value of 'y' when 'x' is zero, determining where the line crosses the y-axis.

Thus,

Straight line graphs are commonly referred to as "linear graphs" or "linear equations.

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