suppose that a function f (x) is approximated near a = 0 by the 3rd degree taylor polynomial t3(x) = 4 −3x x2 5 4x3. give the values of f (0), f ′(0), f ′′(0), and f ′′′(0)

Which statement.........

Answer:

18.10

Step-by-step explanation:

6x2.40= $14.40 + $3.70= 18.10

Answer:

18.1 dollars

Step-by-step explanation:

2.40x6+3.70

The volume of the gas under a pressure of would be 0.06 cubic meters, or 60 liters, rounded to the nearest hundredth.

Volume is a measure of the amount of three-dimensional space an object occupies. It is measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in many areas of science, including physics, chemistry and geology. It can also be used to describe the capacity of a container, such as a bottle, or the amount of liquid it can hold. Knowing the volume of a substance or object is important in many everyday situations, from measuring food portions to calculating the amount of paint needed to cover a wall.

The volume of a gas is directly proportional to its pressure and temperature. The ideal gas law states that the product of the pressure and the volume of a gas is equal to the product of the mass of the gas, the temperature, and the universal gas constant.

Therefore, using the ideal gas law, the volume of the gas under a pressure of can be calculated using the following equation:
V = (P × M × R × T) / P

where P = pressure, M = mass of the gas, R = universal gas constant, and T = temperature.

Assuming a temperature of , the volume of the gas under a pressure would be 0.06 cubic meters, or 60 liters, rounded to the nearest hundredth.

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Answer:

Rational Number

Step-by-step explanation:

A rational number : A number that can be in the form of  

q /p  , where p and q are integers and q is not equal to zero.

Answer:

A rational number : A number that can be in the form of p/q, where p and q are integers and q is not equal to zero

Step-by-step explanation:

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In the original game, there are infinitely many Nash equilibria, as any pair of numbers chosen by the players where neither player can increase their payoff by unilaterally changing their choice is a Nash equilibrium.

However, the most commonly studied Nash equilibrium in this game is for both players to choose 0.
In the modified game, where one person choosing a number less than or equal to 10 and the other choosing a number greater than 10 results in both players receiving 0, there are two Nash equilibria: one where both players choose 0 and another where both players choose numbers greater than 10.
Explanation:
(a) In the original game, let's consider the case where both players choose the same number, let's say x. In this case, both players receive x dollars, and neither player can increase their payoff by changing their choice. Therefore, any pair of numbers where both players choose the same number is a Nash equilibrium.

(b) In the modified game, if one player chooses a number less than or equal to 10 and the other chooses a number greater than 10, both players receive 0. In this case, neither player can increase their payoff by unilaterally changing their choice, as both players will still receive 0. Therefore, the Nash equilibria in this game are pairs of numbers where both players choose 0 or pairs of numbers where both players choose numbers greater than 10.
Overall, the original game has infinitely many Nash equilibria, while the modified game has two Nash equilibria: one where both players choose 0 and another where both players choose numbers greater than 10.

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Vertical Angles are the angles opposite each other when two lines cross.

In our question, we have to opposite angles. For this reason the answer is letter B.

The area of the rectangle is 150 square feet, and the area of the semicircle is approximately 39.27 square feet. Thus, the total area of the key on the basketball court is approximately 189.27 square feet.

To calculate the area of the key on a basketball court, we need to find the area of the rectangle and the area of the semicircle separately and then sum them up.

Area of the Rectangle:

The length of the rectangle is 15 feet and the width is 10 feet.

Area of the rectangle = Length * Width = 15 feet * 10 feet = 150 square feet.

Area of the Semicircle:

The radius of the semicircle is half the width of the rectangle, which is 10 feet / 2 = 5 feet.

The formula for the area of a circle is A = π * \(r^2\), where π is approximately 3.14159 and r is the radius.

Area of the semicircle = (π *\((5 feet)^2\)) / 2 = (3.14159 * 25 square feet) / 2 ≈ 39.27 square feet.

Total Area of the Key:

To find the total area of the key, we add the area of the rectangle and the area of the semicircle:

Total area of the key = Area of the rectangle + Area of the semicircle

Total area of the key = 150 square feet + 39.27 square feet ≈ 189.27 square feet.

Therefore, the area of the key on the basketball court is approximately 189.27 square feet.

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The area of the key on the basketball court is approximately 189.25 square feet.

To find the area of the key on a basketball court, we need to calculate the combined area of the rectangle and semicircle.

The rectangle's area is calculated by multiplying its length by its width:

Rectangle Area = Length × Width = 15 feet × 10 feet = 150 square feet

The semicircle's area is half the area of a full circle with a radius equal to the width of the key. Since the width of the key is 10 feet, the radius is 5 feet.

Semicircle Area = (1/2) × π × \(Radius^2\) = (1/2) × 3.14 ×\((5 feet)^2\) ≈ 39.25 square feet

Therefore, the area of the key is the sum of the rectangle's area and the semicircle's area:

Key Area = Rectangle Area + Semicircle Area = 150 square feet + 39.25 square feet ≈ 189.25 square feet

So, the area of the key on the basketball court is approximately 189.25 square feet.

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The key of a basketball court is made up of a rectangle and on semicircle. the length of the rectangle is 15 feet and the width is 10 feet. find the area of the key on the basketball court.

The minimum lens aperture (diameter) required to resolve points separated by 7 cm with 550 nm light, given a satellite orbiting at a height of 140 km, is approximately 0.062 meters or 6.2 cm.

To determine the minimum lens aperture (diameter) required to resolve points separated by 7 cm with 550 nm light, we can use the Rayleigh criterion. The Rayleigh criterion states that two points can be resolved if the central maximum of one point falls on the first minimum of the other point's diffraction pattern. The formula for the minimum resolvable angle is given by:

θ = 1.22 × (λ / D)

where:

θ is the minimum resolvable angle,

λ is the wavelength of light,

D is the diameter of the lens aperture.

In this case, we have the following values:

Separation between points (d) = 7 cm = 0.07 m

Wavelength (λ) = 550 nm = 550 × 10⁻⁹ m

To find the minimum lens aperture (D), we need to rearrange the formula as follows:

D = (1.22 × λ) / θ

Now, we need to find the minimum resolvable angle (θ). The angular resolution can be determined by the formula:

θ = d / r

where d is the separation between points and r is the distance to the satellite, which is the sum of the Earth's radius and the satellite's height.

The Earth's radius is approximately 6,371 km, so the distance to the satellite is:

r = Earth's radius + satellite's height

r = (6,371 km + 140 km) = 6511 km = 6,511,000 m

Now we can calculate the minimum resolvable angle:

θ = d / r

θ = 0.07 m / 6,511,000 m

θ ≈ 1.074 x 10⁻⁸ radians

Now we can substitute this value along with the wavelength into the formula for D

D = (1.22 × λ) / θ

D = (1.22 × 550 × 10⁻⁹ m) / (1.074 x 10⁻⁸ radians)

D ≈ 0.062 m

Therefore, the minimum lens aperture (diameter) required to resolve points separated by 7 cm with 550 nm light, given a satellite orbiting at a height of 140 km, is approximately 0.062 meters or 6.2 cm.

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Answer:

\(.75g/cm^3\)

Step-by-step explanation:

density = mass / volume

We already know the mass - 180g

Find the volume

\(10cm * 6cm * 4cm = 240 cm^{3}\)

Plug in the volume and mass in the density formula

\(density = 180g / 240cm^{3}\)

Simplify

\(Density = .75g/cm^{3}\)

Answer:

3

Step-by-step explanation:

Because values of x doesn't repeated as other options so i concluded that.

The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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For two populations for which μ₁ = 31,σ₁ = 2, μ₂ = 27, and σ₂ = 4. The shape of the distribution is approximately normal. So, the correct choice for answer is option (b). The mean of normal distribution is equals to 4.

In statistics, the collected data distribution shape sometimes normal and sometimes non-normal. In testing of hypothesis, to use the test statistics we have to check whether data is normally or not. Here we have, two populations. In first population : mean μ₁ = 31,

standard deviations,σ₁ = 2,

sample size, n₁ = 49

In case of second sample, mean, μ₂ = 27,

standard deviations, σ₂ = 4.

Sample size, n₂ = 59

Since, population standard deviation are known and sample sizes are greater than 30, therefore the shape of the sampling distribution of the difference of sample means is approximately normal. The shape of the distribution is approximately normal. Mean of the sampling distribution of \( \bar x_1 - \bar x_2\) are

\(\mu_{ \bar x_1 - \bar x_2} = \mu_1 - \mu_2 \)

= 31 - 27 = 4

Hence, Mean of the distribution is 4.

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Complete question:

Consider two populations for which μ₁ = 31,σ₁ = 2, μ₂ = 27, and σ₂ = 4. Suppose that two independent random samples of sizes n₁ = 49 and n₂ = 59 are selected. Describe the approximate sampling distribution of x₁ bar - x₂ bar (center, spread, and shape). What is the shape of the distribution?

a) The distribution would be non-normal.

b) The distribution is approximately normal.

c) The shape cannot be determined.

What is the mean of the distribution?

Without changing the value, Marcus can add 3 positive counters and 3 negative counters. Option d is correct.

To determine the difference -8 - 3 (+3), Marcus wants to use a model with counters. He starts with 8 negative counters, and in order to add 3 positive counters without changing the value, he can add 3 positive counters and 3 negative counters.

By adding 3 positive counters, he is increasing the value by 3. However, since he wants to maintain the same value, he also needs to add 3 negative counters. This ensures that the net change in value remains zero.

So, by adding 3 positive counters and 3 negative counters to the model, Marcus can represent the difference -8 - 3 (+3) without changing the overall value. Therefore, d is correct.

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The price of each shirt is $7.5.

The price of each pant is $18.5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

Cost of shirts = x

Cost of pants = y

Lisa buys her children four shirts and three pairs of pants for $85.50.

She returns the next day and buys three shirts and five pairs of pants for $115.00.

This means,

We can make two equations.

4x + 3y = 85.50

3x + 5y = 115

Now,

4x + 3y = 85.50

4x = 85.50 - 3y

x = (85.50 - 3y)/4

Substituting in 3x + 5y = 115.

3 (85.50 - 3y)/4 + 5y = 115

256.5 - 9y + 20y = 460

11y = 460 - 256.6

11y = 203.4

y = 18.5

And,

x = (85.50 - 3y)/4

x = (85.50 - 55.5)/4

x = 30/4

x = 7.5

Thus,

The cost of the shirt is $7.5.

The cost of the pant is $18.5.

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The best illustration of a probability distribution as it relates to next year's economy is "40 percent chance of recession, 60 percent chance of a normal economy". Option B is correct.

This choice accurately represents a probability distribution by assigning probabilities to different outcomes (recession and a normal economy) based on their likelihoods. The 40 percent chance of a recession and 60 percent chance of a normal economy provide a clear indication of the potential outcomes and their corresponding probabilities.

This distribution allows for a more realistic assessment of the future state of the economy, acknowledging the possibility of both positive and negative scenarios. By presenting these probabilities, decision-makers can better understand the potential risks and make informed choices based on the likelihood of different economic outcomes.

This probability distribution offers a balanced perspective, highlighting the uncertainty and potential variations that may occur in the next year's economy.

Option B holds true.

This question should be provided as:

Which one of these best illustrates a probability distribution at it relates to next year's economy? Multiple choice question:

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Proceeding with the assumption I made in my comment: in the ones place we have

4 + 5 ≡ 3 (mod b)

9 ≡ 3 (mod b)

6 ≡ 0 (mod b)

or equivalently, 0 + bk = 6 or bk = 6 for some integer k. Then b must divide 6, so b is one of {1, 2, 3, 6}. But in base n, any given number can only be composed of the digits {0, 1, 2, ..., n - 1}, so it must that b = 6.

Just to confirm:

4₆ + 5₆ + (9)₆ = (6 + 3)₆ = 13₆

2₆ + 3₆ + 1₆ = (6)₆ = (6 + 0)₆ = 10₆

3₆ + 1₆ + 1₆ = 5₆

and so

324₆ + 135₆ = 503₆

as required.

Answer:

f(x)=24.50x+55

Total cost for 7 hours: $226.5

Step-by-step explanation:

We consider that x is the amount of hours.

24.5*7+55=226.5

171.5+55=226.5

Answer:

6

Step-by-step explanation:

you need x^3 = 6x^2

Answer:

9

Step-by-step explanation:

We have to solve in order to find out if Sam is correct

Remember PEDMAS:

For Multiplication, division and addition, subtraction, do what appears first left to right

Parenthesis

Exponent

Division

Multiplication

Addition

Subtraction

16 - 18 + (2+1)+2^3

Parenthesis first: 2+1 = 3

16 - 18 + 3 + 2^3

Exponent next: 2^3 = 8

Subtraction (it's on the left) : 16-18 = -2

Addition: -2 + 3 = 1

Addition : 1 + 8 = 9

Sam is not correct, the answer is 9, not 16.

Hope this helps :)

Have a great day!

Answer:

18

Step-by-step explanation:

\(16-18:(2+1)+2^3\)

We must use the BEDMAS rules (Brackets, Exponents, Division, Multiplication, Addition, Subtraction)

We must first calculate what's in the brackets:

\(2 + 1 = 3\)

So the new expression is:

\(16-18:3+2^3\)

Next, we calculate the exponent:

\(2^3 = 8\)

So our expression is now:

\(16-18:3+8\)

Next we divide:

\(18:3 = \frac{18}{3} = 6\)

Our expression is now:

\(16 - 6 + 8\)

Then we subtract:

\(16 - 6 = 10\)

The new expression:

\(10 + 8\)

And finally we add:

\(10 + 8 = 18\)

The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Answer:

18.9

Step-by-step explanation:

perimeter of a trapezoid is base + base + side + side (p = a + b + c + d)

adding up each of the sides gives you 18.9

We can see that the graph that shows the image of ΔABC after a rotation about the origin is: 1st Graph.

In mathematics, rotation is a transformation that moves points or objects around a fixed point called the center of rotation. The center of rotation is a point that remains fixed while all other points move around it by a specified angle and direction.

A rotation can be clockwise or counterclockwise, depending on the direction in which the points are moved.

We can see here that the above is correct because A(1,6), B (7,2), C(1,2)

Therefore, after a rotation about the origin:

Rotate 90° clockwise: A'( 6,-1), B' (2, -7), C'(2,-1)

Also, rotate 90° counterclockwise: A" (-6, 1), B" (-2,7), C" (-2, 1)

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Answer:

Step-by-step explanation:15(x+2) =25

15x+30=25

15x=5

3x=1

x=1/3

The Red Savina Habanero is hotter than the Thai Pepper with a number of 6. 1 times

A ratio can be defined as the comparison of two or more numbers on the basis of  their sizes in relation to each other.

It also indicates how many times one number contains another.

Given that;

To determine the ratio, we have to divide Red Savina Habanero hotness rating by Thai Pepper  hotness rating

=  4.6 x 10^5 /  7.5 x 10^4

= 6. 1 times

Thus, the Red Savina Habanero is hotter than the Thai Pepper with a number of 6. 1 times

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Step-by-step explanation:

a+b=41

let larger number be a and smaller be b

a=21+b

placing value of a in a+b=41

21+b+b=41

2b=41-21

b=20÷2

b=10

so a=21+10

=31

the numbers are 21 and 10.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, The sum of two numbers is 41.

let "x" be the smallest number.

Since The larger number is 21 more than the smaller number.

thus,

the larger number = 21 + smaller number

The larger number = 21 + x

Thus, sum = 41

x + 21 + x = 41

2x = 20

x = 10

So,

the Largest number = 21 + 10

Therefore, The largest number and the smallest number are 21 and 10 respectively.

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Therefore, the nth term of the arithmetic sequence is given by the formula an = 11n - 14.

Given a5 = 41 and a10 = 96, we need to find out the nth term of the arithmetic sequence.The nth term of an arithmetic sequence is given by the formula:

an = a1 + (n - 1)d

where an is the nth term of the sequence, a1 is the first term, n is the term number, and d is the common difference. To find the common difference, we use the formula: d = (an - a1) / (n - 1)We can find the value of d using a5 and a10.Using the formula,

d = (a10 - a5) / (10 - 5) = 55 / 5 = 11

We now have the value of d, which is 11. We can use this value to find a1.The formula for finding a1 is a1 = an - (n - 1)dUsing a5 and d, we get:

a1 = a5 - (5 - 1)d = 41 - 4(11) = -3

Using a1 and d, we can find the nth term of the sequence.Using the formula,

an = a1 + (n - 1)d, we get:an = -3 + (n - 1)11

Simplifying, we get:an = 11n - 14

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Using the laws of decimal,

a. The decimal equivalent of the given numbers are as follows:

π = 3.14

√6 = 2.44

2√6 = 4.89

√7 = 2.64

b. Ordering these from least to greatest:

2.44, 2.64, 3.14, 4.89

Decimals are a set of numbers on a number line that appear between integers. They only serve as another way to represent fractions mathematically. Decimals give us a more precise way to express measurable quantities like length, weight, distance, money, etc.

Decimal fractions are shown to the right of the decimal point, while integers, commonly known as whole numbers, are shown to the left of the decimal point. If we continue straight from the first place, the next place, which is (1/10)th or tenth place value, is (1/10) times smaller.

As per the question,

a. The decimal equivalent of the given numbers are as follows:

π = 3.14

√6 = 2.44

2√6 = 4.89

√7 = 2.64

b. Ordering these from least to greatest:

2.44, 2.64, 3.14, 4.89

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