There are 4 paperback and 10 hardback books on a reading list. Your teacher randomly assigns you 3 books to take home. What is the probability that you are assigned all hardback books?

Answer:

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Use the sum of the first n terms formula:

We are given:

First, let's find n using the nth term formula:

Now, we can find the sum using the formula:

The sum of the geometric series is 186.

To rewrite the function in the chain rule form, we need to find two functions f(u) and g(x) such that y = f(u) and u = g(x). The function u(x) represents the inner function, while the function f(u) represents the outer function.

Once we have found f(u) and g(x), we can use the chain rule to find the derivative of y with respect to x, which will give us Y as a function of x. The chain rule tells us that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function times the derivative of the inner function with respect to x.

Since {f(u), u} = {C}, we can take f(u) = C/u and u = g(x) = x^2. Thus, y = f(u) = C/x^2.

To find Y, we substitute x = 2t into the expression for y, which gives us:

Y = C/(2t)^2 = C/4t^2

Therefore, Y = C/4x^2.

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Answer:

\(4.2 / 0.35 =\frac{4.2}{0.35} *\frac{100}{100}= \frac{420}{35} = 420/35\)

Step-by-step explanation:

By multiplying both the numerator and the denominator of the fraction 4.2/0.35, the resulting equivalent fraction is 420/35.

9514 1404 393

Answer:

  (a), (b), (c) are non-proportional

  (d) is proportional

Step-by-step explanation:

An equation or graph with a non-zero y-intercept is non-proportional. That is true for (a), (b), (c).

The table of (d) is proportional, with a constant of proportionality of 6.5.

__

Comment on (c)

In a proportional relation, price would go up with quantity, not down. If the prices both end in 9, one cannot be double the other, as would be required for the price of a gallon to be proportional to the price of a half-gallon.

The side x = 104 unit and angle y = 74 °

A quadrilateral is referred to as a parallelogram in geometry.

The opposite sides of a parallelogram are parallel and of equal length.

Rhombus, rectangle, and square are a few instances of parallelograms.

The special properties of a parallelogram is that the two opposing sides are both equal and parallel. Also the opposite angles are equal. And the angles inside the parallelogram on the same side , their sum is 180 degrees .

Given : A parallelogram ABCD.

Now in a parallelogram opposite sides are both equal and parallel.

So in this parallelogram ;

97 = x - 7

⇒ x = 97 + 7

⇒ x = 104 .

Also opposite angles of a parallelogram are equal.

⇒ y = 74 °

Thus the required solution is x= 104 degree and y= 74 degrees

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Rosie, this is the solution to the problem, according to the information provided:

Triangles = 1.5 grams

Circles = 2 grams

Squares = x grams

Left string: 4x + 1.5 * 2 + 2 * 2

4x + 3 + 4

4x + 7

Right string: 2x + 1.5 + 3 * 2

2x + 1.5 + 6

2x + 7.5

Rosie, I think we can express this situation rather as an inequality than a equation. Thus:

4x + 7 > 2x + 7.5

Answer:

6:1

Step-by-step explanation:

6 people per van

Answer:

6:1

Step-by-step explanation:

From a random sample of 35 consumers, the probability that the ARPU will be between $62 and $66 is around 0.1579, or 15.79%.

In order to solve it,

we have to use the central limit theorem.

Since we have a sample size of 35.

The central limit theorem states that the sampling distribution of the Sample means will be approximately normal as long as the sample size is large enough.

So in this case, n = 35 is large enough.

First,

we have to standardize the values of $62 and $66 by using the formula,

⇒ z = (x - μ) / (σ / √(n))

Where,

x = the value we want to standardize (either $62 or $66)

μ = the mean of the population (given as $67.81)

σ = the standard deviation of the population (given as $18.45)

n = the sample size (given as 35)

For $62, we get,

⇒ z = ($62 - $67.81) / ($18.45 / √(35))

      = -1.77

For $66, we get,

⇒ z = ($66 - $67.81) / ($18.45 / √(35))

      = -0.70

Now we have to find the area under the standard normal distribution curve between these two z-scores using a standard normal distribution table.

The area between -1.77 and -0.70 = 0.1579.

Therefore,

The probability that the ARPU will be between $62 and $66 from a random sample of 35 customers is 0.1579 or 15.79%.

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There will be infinite number of states and paths when the state space is (x,y) as the state space (i.e., a set of possible locations for the robot) consists of all possible positions (x, y) in the plane.

The collection of every possible setup for a system is its state space. It is a common abstraction in the study of artificial intelligence and game theory because it can be used to reason about the behavior of a specific system. A state space is typically introduced into a system description without being given any thought to its precise physical meaning. However, it is well known that choosing an appropriate state space representation makes it simpler for us to comprehend or control a system's property.

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Rewriting 48 - 28 using the Distributive Property and the GCF of the numbers, you get 4(5) = 20.

To rewrite 48 - 28 using the Distributive Property and the GCF of the numbers, follow these steps:
Step:1. First, find the GCF (Greatest Common Factor) of 48 and 28.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 28 are: 1, 2, 4, 7, 14, 28
The GCF of 48 and 28 is 4.
Step:2. Now, use the Distributive Property to factor out the GCF from both numbers.
48 - 28 = 4(12) - 4(7)
Step:3. Distribute the GCF to both terms in parentheses.
48 - 28 = 4(12 - 7)
Step:4. Finally, simplify the expression inside the parentheses.
48 - 28 = 4(5)
So, rewriting 48 - 28 using the Distributive Property and the GCF of the numbers, you get 4(5) = 20.

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The expression that shows how many sweatshirts were not adult sizes is  s - 19 .

Given :

the lacrosse team sold s team booster sweatshirts, and 19 of them were adult sizes.

Expression :

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Expression = number of sold sweatshirts - number of adult sizes.

= s - 19.

This gives the number of sweatshirts that are not adult sizes

if s = 25

then not adult sizes sweatshirts = s - 19

= 25 - 19

= 6

Hence the expression is s - 19.

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The dependent variable of interest in examining whether the degree of parental involvement differs based on students' grade in school is the degree of parental involvement.

In this scenario, the independent variable is the students' grade in school (i.e., first, second, third, etc.). The dependent variable is the variable that is expected to be influenced by the independent variable. In this case, the dependent variable of interest is the degree of parental involvement.

The degree of parental involvement refers to the level or extent to which parents are engaged in their child's education and school-related activities. It can encompass various aspects, such as attending parent-teacher meetings, volunteering at school, helping with homework, and participating in school events.

By examining whether the degree of parental involvement differs based on students' grade in school, researchers or educators aim to explore any potential patterns or differences in parental involvement as children progress through different grade levels. This investigation can provide insights into how parental involvement may vary across grade levels and inform strategies to enhance parental engagement in education at specific stages of a child's schooling. Thus, the dependent variable of interest is the degree of parental involvement.

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The prices in order from greatest to least unit rate is Price A>Price C>Price B.

Given a table that showing different prices for cans of soup as shown in attached image.

Here, we will calculate the price of 1 quantity of each type of soup.

The Price of 3 quantities of soup price A=$3.87

Now, we will find the price of soup A for the 1 quantity.

The Price of 1 quantity of soup price A=$3.87/3=$1.29

The Price of 2 quantities of soup price B=$2.38

Now, we will find the price of soup B for the 1 quantity.

The Price of 1 quantity of soup price B=$2.38/2=$1.19

The Price of 7 quantities of soup price C=$8.75

Now, we will find the price of soup C for the 1 quantity.

The Price of 1 quantity of soup price C=$8.75/7=$1.25

Hence, the prices in order, from greatest to least unit rate from the given table which is shown in attached image is Price A>Price C>Price B or $1.29>$1.25>$1.19.

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a. The y coordinate of the center of the circle is -1.

b. The value of b in the equation is 44 units.

The solution has been obtained using circles.

What is a circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

a. We are given the equation as

x² + y² - 4 x + 2 y = b

On solving the equation, we get

x² - 4 x + 4 + y² + 2 y + 1 = b + 4 + 1

This can be written as

( x - 2 )² + ( y + 1 )² = b + 5   ...(1)

So, the y - coordinate of the center of the circle is - 1.

b. We know that equation of circle is

( x - a )² + ( y - c)² = r²

On comparing this with (1), we get

b + 5 = r²

b + 5 = 7²

b + 5 = 49

b = 49 - 5

b = 44

Hence, the value of b is 44 units.

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Answer:

y = 7

Step-by-step explanation:

y = -x + 5

when x = -2

y = - (-2) + 5

Double negative is positive

y = 2 + 5

y = 7

Answer:

y=7

Step-by-step explanation:

When x=-2,

y=-x+5

 =-(-2)+5

 =2+5

 =7

The formula is given by

Or

Where

Graphically, the solution to a system of two independent linear equations is represented by the point of intersection of the two lines.

The solution to a system of two independent linear equations can be graphically represented as the point of intersection between the two lines.

When two linear equations are plotted on a graph, each of them will generate a straight line, and their solution is the point that satisfies both equations simultaneously. This point is represented by the intersection of the two lines.

If the two linear equations represent parallel lines, then there is no solution since the lines do not intersect. If the two linear equations represent the same line, then there are infinitely many solutions.

However, in the case where the two linear equations are independent, meaning they have different slopes, and different y-intercepts, they will intersect at a unique point that represents their solution. In other words, the point of intersection represents the ordered pair that satisfies both equations and is the solution to the system of equations.

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Answer:

3.5

Step-by-step explanation:

Given that:

Population mean (m) = 100

Standard deviation (σ) = 21

Sample size (n) = 36

The standard error of the sampling distribution of sample mean :

Standard Error is given by:

Standard deviation / sqrt(n)

Thus,

Standard Error = 21 / sqrt(36)

Standard Error = 21 / 6

Standard Error = 3.5

Answer:

31

Step-by-step explanation:

25/0.80=31.25

(You cant have a quarter of a parking space.)

Answer:

You keep them if you test 3 and all pass.

There are 18 good ones and 6 bad (making 24)

Chance of first passing is 18/24

If it passes, there are now one less good and one less total.

Chance of second passing is 17/23

If it passes, there are now one less good and one less total.

Chance of second passing is 16/22

Total is (16 x 17 x 18) / (22 x 23 x 24) = about 0.4 (0.403162055 is you really want to know).

So probability all are ok is 0.4

Thus probability you find at least one bad one is 0.6

Hope this helps you out!

Answer:

y - 4 = 3x + 12

y= 3x + 12 + 4

y = 3x + 16

Answer:

y = 3x + 16

Step-by-step explanation:

The slope-intercept form is: y = mx + b

m is the slope which in this question is 3.

y = 3x + b

4 = 3(-4) + b

4 = -12 + b

16 = b

Answer:

200 Recyclables Items

Step-by-step explanation:

The first step is to find the common ratio using this formula

Common ratio= Numbers of recyclable items/Number of minutes it takes to sort the recyclable item

Let plug in the formula

Common ratio =150/3 = 50

This means that we have 50 Recyclables Items per minute.

Now let calculate how many recyclable items that Faye can sort in 4 minutes

This means we are going to multiply 4 minutes by the 50 recyclable items per minutes

Hence,

4 * 50 = 200 Recyclables Items

Therefore Based on the ratio shown in the double number line, this means that Faye can sort 200 recyclable item in 4 minutes

Answer: 200

Step-by-step explanation: Since 150 divided by 3 is 50 add a 50 to 150 and you get 200

Therefore, the Laplace transform of the given function is F(s) = 2 / (s^2 ₓ(s + t)^2).

Express the function f(t) = t^2, for t > 1, and f(t) = 0, for t <= 1, in terms of unit step functions and find its Laplace transform F(s).

To express the given function in terms of unit step functions, let's assume the function is defined as follows:

f(t) = t^2, for t > 1

f(t) = 0, for t <= 1

Now, we can find the Laplace transform of the function F(s):

F(s) = L{f(t)} = L{t^2} = ∫[0 to ∞] t^2 ₓ e^(-st) dt

To calculate this integral, we can use the standard Laplace transform table, which states that:

L{t^n} = n! / s^(n+1)

Using this formula, we can find the Laplace transform of f(t):

F(s) = ∫[0 to ∞] t^2 ₓ e^(-st) dt

    = [t^2 / (-s) ₓ e^(-st)] evaluated from t = 0 to t = ∞ + ∫[0 to ∞] (2t / (-s) ₓ e^(-st)) dt

    = [0 - (0^2 / (-s) ₓ e^(-s ₓ 0))] + 2/s ∫[0 to ∞] t ₓ e^(-st) dt

Simplifying further, we have:

F(s) = 0 + 2/s ∫[0 to ∞] t ₓ e^(-st) dt

    = 2/s ∫[0 to ∞] t ₓ e^(-st) dt

Now, the Laplace transform of t ₓ e^(-st) can be found using the formula:

L{t ₓ e^(-st)} = -d/ds (L{e^(-st)})

Applying this formula, we get:

F(s) = 2/s ₓ (-d/ds (L{e^(-st)}))

    = 2/s ₓ (-d/ds (1 / (s + t)))

Taking the derivative and simplifying, we have:

F(s) = 2/s ₓ (-(-1) / (s + t)^2)

    = 2 / (s^2 ₓ (s + t)^2)

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The function in terms of unit step functions is F(t) = t^2u(t), and its Laplace transform is F(s) = 2/(s^3).

The given function F(t) = t^2 can be expressed in terms of unit step functions. The unit step function u(t) represents the switch-on behavior at t = 0. Multiplying t^2 by u(t) ensures that the function is zero for t < 0 and follows the original function for t ≥ 0. Hence, F(t) = t^2u(t).

To find the Laplace transform of F(t), denoted as F(s), we can use the definition of the Laplace transform. The Laplace transform of t^n, where n is a positive integer, is given by n!/s^(n+1). Applying this formula to F(t) = t^2u(t), we have F(s) = 2!/s^(2+1) = 2/(s^3).

Unit step functions are essential tools in expressing functions with different behaviors. They are commonly used in various mathematical and engineering applications, particularly in solving differential equations and analyzing systems with time-dependent inputs or outputs. Understanding how to express functions using unit step functions allows for a clearer representation of piecewise-defined functions and simplifies the calculation of their Laplace transforms.

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Answer:

3x² + x

Step-by-step explanation:

collect the like terms first:

2x² + x² - 4x + 5x + 1 - 1

3x² + x

Answer:

the last answer. 3x to the second power + x

Step-by-step explanation:

Answer:

if we solve for y the answer is y= 2x+5

Real numbers are numbers that are continous on the number line. They include positive and negative numbers. They can be integers, natural numbers, rational or irrational numbers.

In this exercise the number 1.030030003 is a real number because it can be found on the real number line

It is also a rational number because it is a repeating decimal

The sum of - 4 and 6 can be obtained by moving 6 units to the right from

- 4.

A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.

To find the sum of - 4 and 6 first we'll locate - 4 on the number line and then move 6 units to the right as the digit 6 is a positive integer.

Now, After moving 6 units to the right from - 4 we'll reach to the digit 2 in the number line.

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According to the given equation,

a) As we have shown that if there exist two solutions x and y in R, then they must be equal.

b) As we have shown that if there exist two solutions x and y in R, then they must be equal.

Part (a) of the problem asks us to prove that the equation a + x = b has a unique solution in R, given that a and b are elements of R. To show this, we need to demonstrate that there exists a solution x in R that satisfies the equation, and that this solution is the only one.

First, we will show that a solution x exists. We can do this by solving for x in terms of a and b: x = b - a. Since R is a ring, both a and b belong to R, and therefore b - a also belongs to R. This means that the equation a + x = b has a solution in R.

Next, we will prove that this solution is unique. Suppose there exist two solutions x and y in R such that a + x = b and a + y = b. Then, we have:

x = x + 0 (since 0 is the additive identity in R)

= x + (a + y - b) (substituting a + y - b for y, which also satisfies the equation)

= (x + a) + y - b (associativity of addition in R)

= (a + x) + y - b (commutativity of addition in R)

= b + y - b (since a + x = b)

= y (cancellation property of addition in R)

Hence, the equation a + x = b has a unique solution in R.

Part (b) of the problem deals with the equation ax = b, where R is a ring with identity and a is a unit (i.e., has a multiplicative inverse). We need to prove that this equation also has a unique solution in R.

To show that a solution exists, we can simply multiply both sides of the equation by a⁻¹, the multiplicative inverse of a in R. This gives us:

a⁻¹ax = a⁻¹b

x = a⁻¹b

Since R is a ring with identity, a⁻¹ and b both belong to R, so x also belongs to R. Hence, the equation ax = b has a solution in R.

To prove that this solution is unique, suppose there exist two solutions x and y in R such that ax = b and ay = b. Then, we have:

x = 1x (since 1 is the multiplicative identity in R)

= a⁻¹ax (multiplying both sides by a⁻¹)

= a⁻¹b (since ax = b)

= a⁻¹ay (multiplying both sides by a⁻¹)

= y (since ay = b)

Hence, the equation ax = b has a unique solution in R.

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Answer:

The length is 20

Step-by-step explanation:

Assuming it is a rectangle:

Perimeter = 2 * length + 2 * width

64 =  2 * (x+6) + 2 * 12

64 = 2 * (x+6) + 24

40 = 2 * (x + 6)

20 = x + 6

x=14

The length is 20.

Answer:

length is 20 ft

Step-by-step explanation:

first we know that when we add all sides we get the perimeter so one side is 12 ft so it would be 64 ft - 24 ft and you are left with 40 ft for the rest of the perimeter which is two times x+6 because there are 2 remaining sides.

40= 2(x+6)

40= 2x + 12

-12 -12

28= 2x. divide by 2 both sides

14=x

so (14)+6=20

The context that could not be modeled by a linear function is: a town's population shrinks at a rate of 7.9% every year.

A linear function represents a relationship where the change in one variable is directly proportional to the change in another variable. In the given contexts:

However, the context of a town's population shrinking at a rate of 7.9% every year cannot be modeled by a linear function. The population change in this scenario is not constant but rather decreases by a percentage each year. The population decline would follow an exponential or logarithmic function, as the rate of decrease is proportional to the existing population size.

Out of the given contexts, the town's population shrinking at a rate of 7.9% every year cannot be accurately modeled by a linear function. Linear functions are suitable for situations with constant rates of change, while exponential or logarithmic functions are better suited for representing population changes that involve percentages or growth/decay rates.

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