write clear
Sketch the graph of the quadratic function. f(x)=x^{2}+4 x+4 Selection Tool Line Ray Segment Circle Vertical Parabola

The volume of the jewelry box that has the shape of a cube would be = 216 in³.

The volume of an object is defined as the the number of unit cubes that can be fit into the object.

The formula of the volume of a cube ;

= a³

where a= 6 inches.

The volume= 6³

= 6×6×6

=216 in³

Therefore the volume of the jewelry box which has the shape of a cube with edges as 6 in would be = 216 in².

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Answer:

Speed=Distance÷time

speed=25km÷0.5hour=50km/h

Step-by-step explanation:

First you must convert minutes to hours (divide by60/ (÷60) ) to get 0.5

30÷60=0.5hours

Answer:

x=44

Step-by-step explanation:

The standard deviation is 7.35.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79

Determine the difference between each value and the mean and then square the result:

(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)²  + (84- 79)²  + (68 - 79)²  +( 75- 79) ²

64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√432 / 8 = 7.35

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Answer:

Slope: 3/4

Y-intercept: 2

Equation: y=3/4x+2

Step-by-step explanation:

Answer:

slope=3/4

y int =2

equation= y=3/4x+2

Answer:

A square with side length 1 unit, called 'a unit square,' is said to have 'one square unit' of area, and can be used to measure area.

A drop of water is denser than a ping-pong ball.

Usually, water is made of particles that are firmly pressed together. In differentiation, plastic (the material ping pong balls are made of) may be a lightweight fabric and the particles are not as firmly stuffed together.

The thickness of a ping pong ball is 0.0840 g/cm³, though water’s thickness is 997 kg/m³. Subsequently, ping pong balls aren’t about as thick as water and will continuously coast and surface greatly quickly.

The ping pong ball appears to oppose gravity and coast within the air.

Ping-pong balls drift within the water since they are amazingly lightweight, empty, and filled with air. Too, the water’s surface pressure makes it simple for the ping pong ball to drift.

In expansion, water is denser than ping pong balls, making them look for the most noteworthy point of water.

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The sound which we hear when the pig pong ball is bounced on the floor

is 19.48 DB

The repeating of sounds, especially in rhyme, is the form of repetition that most people connect with poetry. Alliteration, assonance, and onomatopoeia are other sound patterns in poetry that give additional meaning in addition to rhyme. Every one of these audio elements has a certain purpose in a poem.

a) \(\sum \ log(n)\)

by expanding the series for each value of n is

log (1) + log (2) + log(3) + log (4) + ......... + log ( 96)

simplify the expanded form we get

0 + 0.3010 + 0.4771+0.6020 ......................... + 1.982

=> 149.9963

b) \(\sum_{n=0}\) to infinity \(\sqrt{0.9^n}\)

formula for the sum of number in geometric progression

is  a/1-r

to find the ratio of the successive terms

plugging into the formula

r = \(\frac{a_{n+1}}{a_n}\)

r = \(\frac{\sqrt{0.9^{n+1}} }{\sqrt{0.9^n} }\)

=> r = \(\frac{\sqrt{0.9^n \times 0.9} }{\sqrt{0.9^n} .1}\)

=> r = \(\frac{\sqrt{0.9} }{1}\)

=> r = \(\sqrt{0.9}\)

=> a = \(\sqrt{0.9^0}\)

=> a = \(\sqrt{1}\)

=>  a= 1

by applying the formula having the value a =1 is

\(\frac{1}{1-\sqrt{0.9} }\)

rationalize the denominator by multiplying with \(1+\sqrt{0.9}\)

=> \(\frac{1+\sqrt{0.9} }{(1-\sqrt{0.9} ) (1+\sqrt{0.9}) }\)

=> 19.4868

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Answer:

Ummm this isn't really math what'ss the question?

Step-by-step explanation:

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer:

According to the sum of cubes formula, Janis is correct

Step-by-step explanation:

The sum of cubes formula is given as follows;

x³ + y³ = (x  + y)·(x² - x·y + y²)

The given expression is presented as follows;

27·x³ + 8

The given expression can be expressed as 27·x³ + 8 = (3·x)³ + 2³

Therefore, using the sum of cubes formula, we have;

(3·x)³ + 2³ = (3·x + 2)·((3·x)² - 3·x·2 + 2²) = (3·x + 2)·(9·x² - 6·x + 2²)

∴ 27·x³ + 8 = (3·x)³ + 2³ = (3·x + 2)·(9·x² - 6·x + 2²)

Therefore, Janis is correct, by the sum of cubes formula, we get;

27·x³ + 8 = (3·x + 2)·(9·x² - 6·x + 2²).

Janis's answer, (3x + 2)(9x² - 6x + 4), is correct.

Janis did not make an error in her factorization. Let's calculate the factorization correctly:

To factor 27x³ + 8 using the sum of cubes formula, we have:

27x³ + 8 = (3x)³ + 2³

Now, applying the sum of cubes formula, we can write it as:

(3x + 2)(9x² - 6x + 4).

Therefore, Janis's answer, (3x + 2)(9x² - 6x + 4), is correct.

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Answer:

x = 2

Step-by-step explanation:

Given a line parallel to a side of a triangle and intersecting the other 2 sides then it divides those sides proportionally, that is

\(\frac{6}{x+1}\) = \(\frac{4}{x}\) ( cross- multiply )

6x = 4(x + 1)

6x = 4x + 4 ( subtract 4x from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

The question presents a scenario where three dice, represented by the colors red (r), green (g), and blue (b), are rolled. The possible outcomes are either rolling a 1 on each die or rolling a 2 on each die. The task is to select the option that represents the probability of this event.

To calculate the probability of rolling a 1 on each die or a 2 on each die, we need to determine the probability of rolling a 1 or a 2 on a single die and then multiply these probabilities together for each die. The probability of rolling a 1 or a 2 on a single die is 1/6, as there are six equally likely outcomes on a standard six-sided die. Since we have three dice and the events are independent, we multiply the probabilities together: (1/6) × (1/6) × (1/6) = 1/216. Therefore, the option that represents the probability of this event is d) 1/216.

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Answer:

no pic

Step-by-step explanation:

The h'(3) = h'(x)|x=3 = 22. We can see from the calculation that the value of h'(3) depends on the slopes of both f(x) and g(x) at x=3, as well as their values at x=3.

To evaluate h'(3) for h(x) = f(x) * g(x), we will use the product rule. The product rule states that if h(x) = f(x) * g(x), then h'(x) = f'(x) * g(x) + f(x) * g'(x).
Given the graphs of f(x) and g(x), we need to find the values of f(3), g(3), f'(3), and g'(3).
1. Locate the point x = 3 on the graph of f(x) and determine the value of f(3).
2. Locate the point x = 3 on the graph of g(x) and determine the value of g(3).
3. Determine the slope of the tangent line at x = 3 on the graph of f(x), which represents f'(3).
4. Determine the slope of the tangent line at x = 3 on the graph of g(x), which represents g'(3).
Once you have the values of f(3), g(3), f'(3), and g'(3), plug them into the product rule formula:
h'(3) = f'(3) * g(3) + f(3) * g'(3)
After calculating, you'll get the value of h'(3). Please refer to the graphs of f(x) and g(x) to obtain the necessary values and complete the evaluation.

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Answer:

72 sides.

Step-by-step explanation:

Each exterior angle of the polygon with n sides has the measure = 5°

Formula to get the exterior angle with n sides of the polygon is,

Measure of exterior angle = \(\frac{360}{n}\)

By substituting the value of exterior angle in the formula,

5 = \(\frac{360}{n}\)

n = \(\frac{360}{5}\)

n = 72 sides

Therefore, the given polygon has 72 sides.

Answer:

$207

Step-by-step explanation:

We do 1242 / 6 = 207

It costs $207 for each family member.

Answer:

207 each

Step-by-step explanation:

Take the total cost and divide by the number of family members

1242 / 6

207 each

To find the length of the curve defined by the vector function r(t), we can use the arc length formula for a parametric curve:

L = ∫[a,b] √[(dx/dt)² + (dy/dt)² + (dz/dt)²] dt

Here, r(t) = ⟨cos(πt), 2t, sin(2πt)⟩.

Let's calculate the integrand and evaluate the integral using numerical methods:

First, we'll find the derivatives dx/dt, dy/dt, and dz/dt:

dx/dt = -πsin(πt)

dy/dt = 2

dz/dt = 2πcos(2πt)

Next, we'll square them and sum them up:

(dx/dt)² = π²sin²(πt)

(dy/dt)² = 4

(dz/dt)² = 4π²cos²(2πt)

Now, we'll find the square root of their sum:

√[(dx/dt)² + (dy/dt)² + (dz/dt)²] = √(π²sin²(πt) + 4 + 4π²cos²(2πt))

Finally, we'll integrate it over the given interval [1,12]:

L = ∫[1,12] √(π²sin²(πt) + 4 + 4π²cos²(2πt)) dt

Since integrating this expression analytically is challenging, let's use a calculator or computer to approximate the integral.

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=====================================================

Explanation:

The block on top has length, width and height of 4, 4 and 20-4 = 16.

The volume of this block is 4*4*16 = 256 cubic feet.

The volume of the block down below is 160 cubic feet because 10*4*4 = 160.

The total volume is therefore: 256+160 = 416 cubic feet

Answer:

exponential growth or exponential decay , and what ... The value of a car purchased for $20,000 decreases ... population, P, increases by 20%each year,

The cut separates the variables from their negations, each clause will have at least one true literal, satisfying the 3SAT instance.

To show that MAX-CUT is NP-complete, we need to demonstrate two things: First, that MAX-CUT is in the NP complexity class, meaning that a proposed solution can be verified in polynomial time. Second, we need to reduce a known NP-complete problem to MAX-CUT, showing that MAX-CUT is at least as hard as the known NP-complete problem.

MAX-CUT is in NP:

To verify a proposed solution for MAX-CUT, we can simply check if the cut separates the vertices into two disjoint subsets S and T, and count the number of edges that cross the cut. If the number of crossing edges is equal to or larger than k, we can accept the solution. This verification process can be done in polynomial time, making MAX-CUT a member of the NP complexity class.

Reduction from a known NP-complete problem:

We will reduce the known NP-complete problem, 3SAT, to MAX-CUT. The 3SAT problem involves determining if a given Boolean formula in conjunctive normal form (CNF) is satisfiable, where each clause contains exactly three literals.

Given an instance of 3SAT with n variables and m clauses, we construct a graph G for MAX-CUT as follows:

Create a vertex for each variable and its negation, resulting in 2n vertices.

For each clause (a ∨ b ∨ c), introduce three additional vertices and connect them in a triangle. Label one vertex as a, another as b, and the third as c.

Connect the variable vertices with the corresponding clause vertices. For example, if the variable is x and it appears in the clause (a ∨ b ∨ c), create edges between x and a, x (negation of x) and b, and x and c.

Now, we claim that there exists a cut in G of size k or more if and only if the 3SAT instance is satisfiable.

If the 3SAT instance is satisfiable, we can assign truth values to the variables such that each clause evaluates to true. We can then define the cut by placing all true variables and their negations in one subset S, and the remaining variables and their negations in the other subset T. The number of crossing edges in the cut will be at least k, as each clause triangle will have at least one edge crossing the cut.

If there exists a cut in G of size k or more, we can use it to derive a satisfying assignment for the 3SAT instance. Assign true to all variables in subset S and false to those in subset T.

Therefore, we have successfully reduced 3SAT to MAX-CUT, showing that MAX-CUT is NP-complete. This conclusion is based on the assumption that 3SAT is already a known NP-complete problem, as stated in Problem 7.26.

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Answer:

$0.18

Step-by-step explanation:

apple(s) : price

8         :    $1.44

4         :    $0.72

2         :    $0.36

1          :    $0.18

Answer:

Step-by-step explanation:

Part A: Based on the given graph, we can observe that as the temperature of the city increases, the number of people at the swimming pool generally tends to increase as well. This suggests a positive correlation between temperature and the pool's population. In other words, when it gets hotter, more people are likely to visit the swimming pool. The relationship is not strictly linear, but it shows a general trend of increasing pool population with increasing temperature.

Part B: To determine the line of best fit, we can calculate the approximate slope and y-intercept using the given data points. Let's select two points from the data, such as (2.5, 1) and (12, 12):

Slope (m) = (change in y) / (change in x)

= (12 - 1) / (12 - 2.5)

= 11 / 9.5

≈ 1.16

To find the y-intercept (b), we can choose one of the points and substitute the values into the slope-intercept form (y = mx + b). Let's use the point (2.5, 1):

1 = 1.16 * 2.5 + b

1 = 2.9 + b

b ≈ -1.9

Therefore, the approximate slope of the line of best fit is 1.16, and the approximate y-intercept is -1.9.

Answer:

Step-by-step explanation:

Uh sorry but there is no picture here

Answer:

no graph is attached

Step-by-step explanation:

Answer:

  1.  S(1) = 1; S(n) = S(n-1) +n^2

  2. see attached

  3. neither

Step-by-step explanation:

1. The first step shows 1 square, so the first part of the recursive definition is ...

  S(1) = 1

Each successive step has n^2 squares added to the number in the previous step. So, that part of the recursive definition is ...

  S(n) = S(n-1) +n^2

__

2. See the attachment for a graph.

__

3. The recursive relation for an arithmetic function is of the form ...

  S(n) = S(n-1) +k . . . . . for k = some constant

The recursive relation for a geometric function is of the form ...

  S(n) = k·S(n-1) . . . . . . for k = some constant

The above recursive relation is not in either of these forms, so it is neither geometric nor arithmetic.

Answer:

(1,2), (2,4), (5,10), (8,16)

Step-by-step explanation:

For the time, the number it land on that would be you x axis and the distance would be your y axis

Answer:

Move

17

60

to the left side of the equation by adding it to both sides.

1

5

x

−

1

4

x

+

1

3

x

+

17

60

=

0

Step-by-step explanation:

Sana makatulong

Answer:

2696/26=x or if you want exact then 103.69=x

Answer:

8% como un decimal es 0.08%

Espero que te ayude!

To determine why the function f(x) = x^4 if x ≤ -1, and f(x) = 2x if x > -1 is discontinuous at a = -1, we need to examine the behavior of the function around that point.

The function has two different definitions based on the value of x:

For x ≤ -1, f(x) = x^4

For x > -1, f(x) = 2x

Now let's consider the left-hand limit (LHL) and the right-hand limit (RHL) of the function at x = -1.

LHL of f(x) as x approaches -1: lim(x->-1-) f(x) = lim(x->-1-) x^4 = (-1)^4 = 1

RHL of f(x) as x approaches -1: lim(x->-1+) f(x) = lim(x->-1+) 2x = 2(-1) = -2

Since the LHL and RHL of the function at x = -1 are different (1 and -2, respectively), the function does not have a limit at x = -1. Therefore, the function is discontinuous at x = -1.

In summary, the function is discontinuous at x = -1 because the left-hand limit and the right-hand limit at that point are not equal.

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Thus after spraying x times the number, of termites \(f(x)=12000*(\frac{1}{4} )^{x}\)

Whole Numbers: The collection of positive integers that include the number 0. Integers are whole integers that are next to its counterparts (negative numbers). Factorization are any values that may be stated as fractions.

The meaning or numeric magnitude of a numerical sign is the main information it refers to (for example, the number "4" denotes a group of four items). Numerical names, another sort of language processing carried by numerical symbols,

Given that the home was sprayed a certain number of times.

When the home was treated x times, let f(x) represent the number of termites that were there.

We are also informed that a residence has 12,000 termites. The quantity of termites decreased to one-fourth of the previous level each time a house was treated.

Hence, after treating x times as many termites\(=f(x)=12000*(\frac{1}{4} )^{x}\)

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