the amount of sodium (in milligrams) in one serving for a random sample of three different kinds of foods is listed here. condiments cereals desserts 270 260 100 130 220 180 230 290 250 180 290 250 80 200 300 70 320 360 200 140 300 160 at the 0.05 significance level, is there sufficient evidence to conclude that a difference in mean sodium amounts exists among condiments, cereals and desserts?

The nth Taylor polynomial for the function is P₄(x) = ln3 + 1/3 (x-3) - 1/9*2!(x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴

Given:

f(x) = ln(x)

n = 4

c = 3

To find:

nth Taylor polynomial for the function, centered at c

The Taylor series for f(x) = ln x centered at 3 is:

Now

f(3) = ln 3

f'(x) = 1/x ⇒ f'(3) = 1/3

f''(x) = -1/x² ⇒ f''(3) = -1/3² = -1/9

f'''(x) = 2/x³  ⇒ f'''(3) = 2/3³ = 2/27

f (x) = -6/x⁴ ⇒ f (3) = -6/3⁴ = -6/81 = - 2/27

So Taylor polynomial for n=4 is:

P₄(x) = ln3 + 1/3 (x-3) - 1/9*2! (x-3)² + 2/27*3! (x-3)³ - 2/27*4! (x - 3)⁴

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If the equation be 3log₂x-(log₂3-log₂ (x+4)) then we get[tex]$\log _2\left(\frac{x^2(x+4)}{3}\right)[/tex].

An exponential function has an opposite called a logarithmic function. In both exponential and log functions, the basis is the same.

An exponent and a number (the base) are inputs into a logarithmic function, which yields a result (the logarithm). The base that must be raised in order to obtain a number is represented by the number's logarithm.

The features of exponential functions can be investigated and exponential equations can be solved using logarithms. In calculus, where they are used to determine the slope of specific functions and the region enclosed by specific curves, they also become incredibly useful.

Let the given equation be 3log₂x-(log₂3-log₂ (x+4))

[tex]$$& \log _a(x)-\log _a(y)=\log _a\left(\frac{x}{y}\right) \\[/tex]

[tex]$$& {alog}(x)=\log \left(x^a\right)[/tex]

3 log₂ x - (log₂3 - log₂ (x+4))

simplifying the above equation, we get

log₂(x²) - log₂(3/x+4)

[tex]$& \left.\log _2 \left(\frac{\frac{x^2}{3}}{\frac{3}{x+4}}\right)=\log _2\left(\frac{x^2(x+4)}{3}\right)[/tex]

Therefore, by simplifying the equation 3log₂x-(log₂3-log₂ (x+4)) we get[tex]$\log _2\left(\frac{x^2(x+4)}{3}\right)[/tex].

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The linear  equation [tex]\frac{17}{3} - \frac{3}{4}x = \frac{1}{2}x + 5[/tex] has been solved

Value of x is [tex]\frac{8}{15}[/tex]

What is linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign

A one degree equation is known as linear equation.

The linear  equation is [tex]\frac{17}{3} - \frac{3}{4}x = \frac{1}{2}x + 5[/tex]

Now,

[tex]\frac{17}{3} - \frac{3}{4}x = \frac{1}{2}x + 5[/tex] [ Given]

[tex]\frac{17}{3} - \frac{3}{4}x-\frac{17}{3} = \frac{1}{2}x + 5-\frac{17}{3}[/tex] [Subtraction property of equality]

[tex]- \frac{3}{4}x = \frac{1}{2}x -\frac{2}{3}[/tex] [Simplification]

[tex]- \frac{3}{4}x - \frac{1}{2}x = \frac{1}{2}x -\frac{2}{3} - \frac{1}{2}x[/tex] [Subtraction property of equality]

[tex]-\frac{5}{4}x = -\frac{2}{3}[/tex] [Simplification]

[tex]-\frac{5}{4}x. -\frac{4}{5}= -\frac{2}{3}.-\frac{4}{5}[/tex] [Division property of equality]

[tex]x = \frac{8}{15}[/tex] [Simplification]

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The different percentages are, 42%, 21% and 63%.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The word "percent" is used to symbolize it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Now, according to the given information, the double number line shows that 42 people watched Deon's new video today.

Now, we are to find,

100% of 42 people.

This is, (100/100)*42 = 42%.

Again, 50% of 42 people is,

(50/100)*42 = 21%.

Again, 150% of 42 people is,

(150/100)*42 = 63%.

Hence, the percentages are, 42%, 21% and 63%.

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Answer:

Answers are in the explaination.

Step-by-step explanation:

100% of 42 people answer is 42

50% of 42 people answer is 21

150% of 42 people answer is 63

A) The probability that a person selected at random from the general population is senior citizen who will get the flu this season is 0.017.

B) The probability that a person selected at random from the general population is a person under age 65 who will get the flu this year is 0.207.

C) a) 0.1547 community has 91% senior citizens.

    b) 0.0207 community has 91% senior citizens.

D) a) 0.0884 community has 52% senior citizens.

    b) 0.1104 community has 52% senior citizens.

Probability is a measure of the uncertainty of various phenomena. For example, if you roll a die, the possible outcomes are defined by probabilities. This distribution can be defined using random experiments with uncertain or unpredictable outcomes.

A) (a) The probability that a person selected at random from the general population is senior citizen who will get the flu this season is

                      0.10 x 0.17 = 0.017

(b) The probability that a person selected  randomly from the general population is a person under age 65 who will get the flu this year is

             (1 - 0.10) x 0.23 = 0.9 x 0.23 = 0.207

(c) (a) 0.91 x 0.17 = 0.1547

    (b) (1 - 0.91) x 0.23 = 0.09 x 0.23 = 0.0207

Therefore, 91% senior citizens has 0.1547 flu

        and b) 0.0207 senior citizens are there.

(d) (a) 0.52 x 0.17 = 0.0884

    (b) (1 - 0.52) x 0.23 = 0.48 x 0.23 = 0.1104

Therefore, 52% senior citizens has 0.0884 probability of getting flu.

             b) 0.1104 community has flu.

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The value of the function f(x) = x when the limit x approaches to 0 is equal to 0.

As given in the function,

Given function is equal to:

f(x) = x

Value for the limit x approaches to zero

When x approaches to zero means x approaches to right hand side limit to zero or left hand side limit to zero

When limit x→0+ then the function f(x) = x is equal to 0

When limit x → 0- then the function f(x) = x is equal to 0.

[tex]\lim_{x \to 0} f(x)[/tex]

= [tex]\lim_{x \to 0} ( x )[/tex]

= 0

Therefore, the value of the function f(x) when limit x approaches to zero is equal to 0.

The complete question is:

What is the limit of f(x) = x when x approaches to 0?

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Answer: 10 burritos

Step-by-step explanation:

Let y be the total cost, and b is the number of burritos

So we have the equation is

y= 5.50b + 7

Now we put a total cost of $62 in the y spot

62 = 5.50b + 7

Subtract 7 from both sides

55 = 5.50b

Divide 5.50 from both sides

b = 10 burritos

Answer: 10 burritos

Step-by-step explanation:

This is a worded question. The first step would be to extract the essential information and represent it as an easily understandable equation:

b is the number of burritos

$5.50 is the cost for each burrito

$7 is additionally charged for a service fee

We have to find the number of burritos (b)

Therefore, we can write the equation like this:

(5.50 * b) + 7 = 62

We can then rearrange the equation to get b on one side. Remember to follow the BIDMAS rules backwards!

(5.50 * b) + 7 = 62

5.50*b = 62-7

5.50*b = 55

b = 55/5.50

b = 10

Finally, always write a worded answer because it is a worded equation. For example, you could write:

Marie bought 10 burritos

Hoped this helped!

Answer:

6

Step-by-step explanation:

The intersection of B Street and 6th Street is 600 yards east of the intersection of B Street and Ford Street, so it is 600 yards north of the intersection of B Street and Ford Street.

The total money which Nakeisha would have after 8 weeks of saving is equal to $134.

An expression that represents the amount of money Nakeisha would have saved in w weeks is T = 8w + 70.

Mathematically, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;

T = mw + b

Where:

Therefore, the required linear function that represents the total amount of money which Nakeisha would have saved in weeks (w) is given by this mathematical expression;

T = 8w + 70

After 8 weeks of saving, Nakeisha would have saved this amount of money;

T = 8(8) + 70

T = 64 + 70

T = $134.

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Answer:17

Step-by-step explanation:

answer p+ 28 > 45

p>17

Answer:

[tex](x+10)+(2x+5)+35=180[/tex]

Step-by-step explanation:

Angles in a triangle add to [tex]180^{\circ}[/tex].

Answer:

x=43

2x=86

x+8=51

Step-by-step explanation:

2x+x+(x+8)=180

2x+x+x+8=180

4x+8=180

4x=172

x=43

2x=86

x+8=51

43+86+51

The formula for raw score is simply the number of correct answers given by an individual on a test. It is calculated by subtracting the number of incorrect answers from the number of correct answers.

The formula for raw score is calculated by subtracting the number of incorrect answers given by an individual on a test from the number of correct answers given. This can be expressed as Raw Score = Number of Correct Answers - Number of Incorrect Answers.To calculate a raw score, start by counting the number of correct answers given by the individual on the test. Then, count the number of incorrect answers given. Subtract the number of incorrect answers from the number of correct answers. The result is the individual's raw score. This can be expressed as: Raw Score = Number of Correct Answers - Number of Incorrect Answers.

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Considering the given figure the area of the square is calculated to be

1 squared centimeters units

The area of the square is calculated using the formula

= length * length

The regular hexagon have a side 1 cm, angles in a regular hexagon is also 60 at the vertex

dropping a perpendicular angle bisector to divide BD at point say m, a right triangle is formed

hypotenuse BC = 1

opposite = BM

adjacent = CM

sin 30 = BM / BC

BM = sin 30 * 1

BM = 0.5 cm

side of the square BD = BM + DM = 0.5 + 0.5 = 1 cm

Area of the square

= 1 * 1

= 1 centimeter square

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The recursive formula of geometric sequence is aₙ = -2 x [tex]8^{n-1}[/tex].

A unique kind of sequence called a geometric sequence has a constant ratio between every two succeeding terms. This ratio is regarded as one of the geometric sequence's common ratios.

We have geometric sequence;

-2, -16, -128, -1024 ,......

The terms;

a₁ = -2

a₂ = -16

a₃ = -128

a₄ = -1024

The common ratio;

a₂ = -16 = -2 x 8

a₃ = -128 = -16 x 8

a₄ = -1024 = -128 x 8

So, the common ratio is 8.

Therefore, the recursive formula is aₙ = -2 x [tex]8^{n-1}[/tex].

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The slope-intercept form of the linear equation will be y = 6x - 4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The points are given below.

(-1, -10) and (3, 14)

The equation of the line that passes through the points (-1, -10) and (3, 14) will be given as,

(y + 10) = [(14 + 10) / (3 + 1)](x + 1)

y + 10 = 6(x + 1)

y + 10 = 6x + 6

y = 6x - 4

The slope-intercept form of the linear equation will be y = 6x - 4.

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Maximum area enclosed by Mona for the fencing is 640,000 square yards. And the dimensions( length and width ) of the rectangle to enclosed maximum area are 800 yard each.

As given in the question,

Perimeter of the rectangular area encloses for fencing = 3200 yards

Let 'x' and 'y' be the length and width of the rectangle.

2( x + y ) = 3200

⇒ x + y = 3200/2

⇒y = 1600 - x

Area of rectangular field 'A' = xy

⇒ A = x ( 1600 - x )

⇒ A = 1600x - x²

Differentiate both the side of the equation we get,

dA/dx = 1600 - 2x

For Maximum Area dA/dx = 0

1600 -2x =0

⇒ 2x = 1600

⇒ x= 800 yards

Now, y = 1600 - 800

          = 800 yards

Maximum area = (800) (800)

                        = 640,000 square yards

Therefore, the dimensions of the rectangular area are 800yards each and its maximum area is equal to 640,000 square yards.

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Answer:

1/2

Step-by-step explanation:

I first turned 1 1/3 into 4/3 because it's easier to work with.

[tex]\frac{4}{3} * \frac{3}{8}[/tex]

You can cancel out the threes, so all that's left is:

[tex]\frac{4}{8}[/tex]

which can then be simplified into 1/2

Answer: Shoot sorry I thought it was 11/3 x 3/8 I'm so sorry! But its 1/2

The solution to inequality [tex]3(y + \dfrac{1}{4} ) \geq \dfrac{3}{4}[/tex] would be [tex]y \geq 0[/tex].

Used the concept of inequality that states,

A relation by which we can compare two or more mathematical expressions is called an inequality.

Given the inequality,

It is bigger than or equal to three-quarters when the amount y is multiplied by 3 times.

Now it can be written in inequality form,

[tex]3(y + \dfrac{1}{4} ) \geq \dfrac{3}{4}[/tex]

Simplify the inequality for the values of y as

[tex]3(y + \dfrac{1}{4} ) \geq \dfrac{3}{4}[/tex]

Divide both sides by 3,

[tex](y + \dfrac{1}{4} ) \geq \dfrac{1}{4}[/tex]

Subtract both sides by 1/4,

[tex](y + \dfrac{1}{4} - \dfrac{1}{4} ) \geq \dfrac{1}{4} - \dfrac{1}{4}[/tex]

[tex]y \geq 0[/tex]

Therefore, the solution is [tex]y \geq 0[/tex].

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The side that is opposite the 95-degree angle should be the longest, followed by the 53-degree angle and finally the 32-degree angle, which will be the shortest. The answer is (b).

How do you tell which angle is larger: The largest angle is located across from the longest side, just like with the sides. Theorem: If and only if angle A (= angle CAB) is greater than angle B (= angle ABC), then side BC of a triangle ABC will be longer than side CA. To put it another way, larger sides are in opposition to larger angles.

If you have an angle and its opposite side, you may calculate the hypotenuse by dividing the length of the opposing side by sin(). To find the length of the side next to the angle, you can also divide the length by tan(). Less than 90 degrees is the acute angle measurement. Right angles are 90 degrees in length. Angles that are obtuse are more than 90 degrees. Hint: There are two fundamental units used to measure angles from one of the two fundamental units, radians () or degrees ().

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Correct Question:

The main difference between Theory and Hypothesis is B) Theory is an explanation that has been carefully examined and tested.

A theory is a rational way of thinking abstractly about a phenomenon or the consequences of such thinking. Contemplative and rational thought processes are often associated with processes such as observational studies and research. A theory can be scientific, it can belong to a non-scientific field, or it can belong to no field at all. For example, depending on the context, a theory's assertions may include generalized explanations of how nature works. The word has ancient Greek roots, but has taken on several related meanings in modern usage.

In mathematics, the term theory is used differently. Because, inevitably, mathematics itself does not contain an explanation of natural phenomena. However, it can help provide insight into or take inspiration from natural systems. In a general sense, mathematical theory is a branch or topic of mathematics. Individual textbooks for set theory, number theory, group theory, probability theory, game theory, control theory, perturbation theory, etc.

Equivalently, but more precisely, the term theory means a large-scale, structured theory organized in such a way that the proof of each theorem requires only the preceding theorems and axioms (not circular proofs) is a set of theorems. Ideally, the order in which the theorems are presented makes the purpose of the textbook clear in the field of mathematics, but is as easy to understand as possible. they are not written mathematical theories.

A hypothesis (hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, it must be able to be tested by scientific methods. Scientists generally form scientific hypotheses based on previous observations that cannot be fully explained by available scientific theories. Although the terms "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a tentatively accepted hypothesis proposed for further research in a process that begins with educated guessing or thinking.

Another meaning of the term hypothesis is used in formal logic to denote the antecedent of a proposition. So in the sentence "If P, then Q", P denotes a hypothesis (or premise). Q can be called a sequence. P is a (possibly counterfactual) what-if question assumption.

The adjective hypothesis, meaning "having the nature of a hypothesis" or "supposed as a direct result of a hypothesis", may refer to either of these meanings of the term "hypothesis".

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The scale 1 : 1 means that the size of the image and the pre-image will be same

The given scale = 1 : 1

The scaling is the process of changing the size of the figure using the scale factor. The scaling is also the transformation of figure.

The scale is 1 : 1, that is the ratio of the actual size of the figure and the size of the figure after transformation.

Here the scale 1 : 1 means the actual size and new size will be same. If we consider the figure the image and the preimage will be same

The image is the figure after the transformation and the pre-image is the figure before transformation

Therefore, the scale 1:1 means actual size and new size will be same

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Answer: b = -27.2

Step-by-step explanation:

6.8x + b = 3.4(2x - 8)

6.8x + b = 6.8x - 27.2

b = -27.2

The graph of g is Transformation up 7 units.

what is Transformation?

A graph transformation is a method for altering an existing graph or graphed equation to create a different version of the graph that follows. The modification of algebraic equations is a typical form of algebraic issue.

solution:

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

g(x) = f(x) + k

Also, we have the value of k to be

k = 7

From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units

This means that

g(x) = f(x) + k

So, we have

g(x) = f(x) + 7

Hence, the transformation is (a) translated up 7 units

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Answer:

option D is the right answer

Answer:

The expected value of spinning the wheel once is $61.11.

Step-by-step explanation:

To calculate the expected value, we need to multiply the value of each outcome by its probability, and then add all of these products together. In this case, we have:

Expected value = ($20 * 4/9) + ($60 * 2/9) + ($80 * 2/9) + ($120 * 1/9)

Expected value = $71.11

Therefore, the expected value of spinning the wheel once is $61.11. This is the average value we would expect to get if we spun the wheel many times.

Answer: this would be 20$

Step-by-step explanation: Hope it helps, please mark brainliest!

Answer: 420

Step-by-step explanation:

Answer:143.30

Step-by-step explanation:

Answer:

So to convert from a value in inches to one in yards, we need to divide by 36. To convert a value in yards to inches, we need to multiply by 36.

Answer:

To convert 13 inches into yards, you can use the conversion factor that 1 yard is equal to 36 inches. Since there are 36 inches in 1 yard, to convert 13 inches into yards, you would simply need to divide 13 by 36. This would give you a result of 0.36 yards.

Yes, an equation can have three roots. An equation with three roots is known as a cubic equation expression.

An equation is represented by two expressions being separated by the equals sign ("="). The phrases on either side of the equals sign are referred to as the "left-hand side" and "right-hand side," respectively. The right side of an equation is frequently considered to be zero. An equation is an expression that contains an equal sign and can be solved to find the value of a variable. An equation can have one, two, three, or even more roots, which are the values of the variable that make the equation true. A cubic equation is an equation with three roots and can be written in the form ax^3 + bx^2 + cx + d = 0.

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