The Taylor series about x=0 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=0 is given by
f(n)(0)=(−1)n+1(n+1)!5n(n−1)2 for n≥2
The graph of f has a horizontal tangent line at , x=0 and f(0)=6
A) Write the third-degree Taylor polynomial for f about x=0.
B) Find the radius of convergence of the Taylor series for f about x=0. Show the work that leads to your answer.
C) Determine whether f has a relative maximum, a relative minimum, or neither at x=0. Justify your answer.

Answer:

Gabriella's average original speed was 56  \(\frac{mi}{h}\)

Step-by-step explanation:

Let's use the equation that defines the average speed "v" of Gabriella during the time (t) that her trip took:

\(v = \frac{distance}{time} \\v=\frac{400}{t}\)

Next let's write a similar average speed equation for the case in which she drove at (v - 7 mi/h) during the same time "t" and covered 350 miles:

\((v-7)=\frac{350}{t}\)

Notice that the time "t" in the denominator appears equally in both equations we wrote, so let's isolate them on the right:

\(\frac{v}{400} =\frac{1}{t} \\and\\\frac{(v-7)}{350} =\frac{1}{t}\)

now equal both expression since they both share the same value on the right, and solve for the unknown "v":

\(\frac{v}{400} =\frac{(v-7)}{350} \\350\,v=400\,(v-7)=\\350\,v=400\,v-2800\\2800=50\,v\\v=\frac{2800}{50} \,\,\frac{mi}{h}\\v=56\,\,\frac{mi}{h}\)

Answer:

⅖ m = 40 cm

Step-by-step explanation:

1 meter = 100 cm

1 : 100 = 2/5 : y

1 × y = 100 × 2/5

y = 40

The different ways that the students can elect a president and a vice president will be 13110.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

Given data;

Total no of students =  115

The total number of ways to elect a president = 115

If one person is elected as the president the total number of ways to elect a president  = 114

The different ways that the students can elect a president and a vice president are found as;

⇒ 115 ways × 114 ways

⇒ 13110 ways

Hence the different ways that the students can elect a president and a vice president will be 13110.

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Answer:

0.84 kg

Step-by-step explanation:

Given that :

Weight per liter = 1.12kg per liter

That is 1 Litre weighs 1.12 kilogram

The weight of saline solution of 0.75 Litre will be :

1 Litre = 1.12 kg

0.75 Litre = x

Cross multiply :

1 * x = 1.12 * 0.75

x = 0.84 kg

Hence, 0.75 Litre weighs 0.84 kg

Each x-value is paired with its corresponding y-value, which is calculated by multiplying the x-value by 8 and adding 2. For example, when x = 1, y= 8(1) + 2 = 10.

Compound interest is a method of calculating interest where the interest earned on an investment is added to the principal amount, and the interest on the new total is calculated for the next period. This process continues over time, resulting in the gradual growth of the investment.

Given by the question.

There is only one table that can represent the function y = 8x + 2, which is as follows:

x      y

0     2

1    10

2    18

3    26

4    34

5    42

6    50

7    58

8    66

9    74

10    82

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Answer:

A. \(\frac{1}{5}\)

Step-by-step explanation:

⭐ What is the multiplicative rate?

To find the multiplicative rate of this exponential function, we need to make an equation to see what each y-value gets multiplied by to get the next y-value.

I am picking the y-values 2 and 2/5, but you can choose any two consecutive y-values.

Equation (let x= the multiplicative rate of change):

\(2x = \frac{2}{5}\)

Solve for x:

\(\frac{2x}{2} = \frac{2}{5}(2)\)

\(x = \frac{2}{10}\)

Simplify:

\(x = \frac{1}{5}\)

∴ The multiplicative rate of change of the function is 1/5.

To find the center of mass of a cone of uniform density with radius R at the base, height h, and mass M, we need to use the formula:

x_cm = (1/M)∫∫∫xρdV
y_cm = (1/M)∫∫∫yρdV
z_cm = (1/M)∫∫∫zρdV

where x_cm, y_cm, and z_cm are the coordinates of the center of mass, ρ is the density, and V is the volume of the cone.

We can simplify the integral by using cylindrical coordinates, where the density is constant and equal to M/V, and the limits of integration are:

0 ≤ r ≤ R
0 ≤ θ ≤ 2π
0 ≤ z ≤ h(r/R)

Thus, the center of mass of the cone is:

x_cm = 0
y_cm = 0
z_cm = (3h/4)(r/R)^2

Therefore, the center of mass of the cone is located at (0, 0, (3h/4)(r/R)^2) with respect to the origin at the center of the base of the cone and +z going through the cone vertex.

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Answer:

-5

Step-by-step explanation:

12-7=5

7-12=-5

If this helps please mark as brainliest

Arithmetic

7-12

Meaning, 12 less than 7.

7-12=-5

We can conclude that only some of the ratios in Table A are greater than the ratios in Table B. (option-c)

To compare the ratios of squares to circles in the tables, we must divide the value in the Squares column by the value in the Circles column for each row in the table.

For Table A, the ratios of squares to circles are:

5/3 = 1.67

10/6 = 1.67

For Table B, the ratios of squares to circles are:

10/3 = 3.33

20/9 = 2.22

Comparing the ratios in Table A to the ratios in Table B, we see that the first two ratios are equal (1.67) and the last two ratios are different (3.33 in Table B is greater than 1.67 in Table A, and 2.22 in Table B is less than 1.67 in Table A).

Specifically, the ratio in the second row of Table B is greater than both ratios in Table A, but the ratios in the first row of each table are equal.(option-c)

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\(answer \frac{4}{5} \)

\(process \: \frac{1}{5} \div \frac{1}{4} \)

\( \frac{1}{5} \times \frac{4}{1} \)

\( \frac{1 \times 4}{5 \times 1} \)

To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))

First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.

Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.

Next, we calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380

Finally, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62

Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38

Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.

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Step-by-step explanation:

Equation to find the sum of the first n terms :

\(S_{n}\) = \(\frac{n}{2}\) x (2\(a_{1}\) + (n - 1)d)

- where n is the first n terms

- where \(a_{1}\) is the first term in the sequence

- where d is the difference (To find the difference: \(a_{1}\) - \(a_{2}\))

How to find n for the given sum :

1. Using the previous equation, plug in all the numbers that you know

2. PEMDAS then combine all like terms

3. Distribute what's on the outside to the inside of the parenthesis

4. Move  \(S_{n}\) to the other side to make a quadratic equation

5. Solve the quadratic, then use the positive number and round that number (term of numbers that isn't whole isn't possible ig??)

Question 1:

Sum of first 10 terms : \(S_{10}\) = \(\frac{10}{2}\) ( 2 x 2 + (10 - 1)6)

 \(S_{10}\) = \(\frac{10}{2}\) (4 + (9)6) = (4 + 54) = 58

 \(S_{10}\) = \(\frac{10}{2}\) x 58

Answer : 290

Find n for the given sum : 1704 =  \(\frac{n}{2}\) x (2 x 2 + (n - 1)6)

distribute 6 into (n-1)

1704 =  \(\frac{n}{2}\) x ( 4 + 6n - 6)

combine like terms

1704 =  \(\frac{n}{2}\) x ( -2 + 6n )

Distribute  \(\frac{n}{2}\) to ( -2 + 6n )

1704 = \(\frac{-2n}{2}\) - \(\frac{6n^{2} }{2}\)

Simplify fractions and move 1704 to the other side

-3\(n^{2}\) - n + 1704 = 0

Use a quadratic calculator to find the answer and use the answer with the whole number

Answer : -24

Question 2:

(i'm just gonna show you the answers for the rest of them-)

Sum of the first 14 terms: 490

Find n for the given sum: 33.65 (I'm gonna round it to 34)

Question 3:

Sum of the first 21 terms: 483

Find n for the given sum: 11.48 (rounded: 11)

Question 4:

Sum of the first 32 terms: -1328

Find n for the given sum: -9.34 (rounded -9)

really hope this helps in any way :D

Answer:

the hypothesis in this statement would be "if jake warned a c+"

Step-by-step explanation:

the word IF- on condition or supposition in the event that _____.

Answer:

D) 20

Step-by-step explanation:

Hope It Helps!!!

Answer:

Step-by-step explanation:B

The angle ∠DEF is equal to 90 degrees. Then the triangle ΔDEF will be a right-angle triangle.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function. The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The angle ∠DEG = 51° and angle ∠GEF = 39°.

Then prove that the triangle ΔDEF will be a right-angle triangle. Then we have

We know that if one angle of the triangle is 90 degrees then the triangle will be named a right-angle triangle.

The sum of the angle ∠DEG and ∠GEF will be

∠DEF = ∠DEG + ∠GEF

∠DEF = 51° + 39°

∠DEF = 90°

Then the triangle ΔDEF will be a right-angle triangle.

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The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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Answer: 72

Step-by-step explanation:

Cos 18 degrees = 0.951...

Sin -1 (0.951) = 72

So the answer is 72 degrees.

h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

Answer:

Absolute Value

Step-by-step explanation:

– The distance a number is from the zero on a number line. (Absolute value is always positive). Acute Angle - An angle with a measure > than 0° and < 90˚. Acute Triangle– A triangle that has all three angles that are acute.

The required missing values are $2.5 when the cup of milk is 1, $8.75 when the cup of milk is 3.5, and $6.25 when the cup of milk is 2.5.

The table is given in the question as :

Tea (cups) $3.75

Milk (cups) $1.5  $1   $3.5   $2.5

Let the missing value cup of tea would be x when the cup of milk is 1,

The missing value cup of tea would be y when the cup of milk is 3.5,

And the missing value cup of tea would be z when the cup of milk is 2.5,

According to the given question, we can write the ratio as:

$3.75 Tea (cups) : $1.5 Milk (cups) = x Tea (cups) : $1 Milk (cups)

⇒ 3.75 / 1.5 = x / 1

⇒ x = 3.75 / 1.5

⇒ x = $2.5

$3.75 Tea (cups) : $1.5 Milk (cups) = y Tea (cups) : $3.5 Milk (cups)

⇒ 3.75 / 1.5 = y / 3.5

⇒ y = (3.75 / 1.5) × 3.5  

⇒ y = 2.5 × 3.5  

Apply the multiplication operation,

⇒ y = $8.75

$3.75 Tea (cups) : $1.5 Milk (cups) = z Tea (cups) : $2.5 Milk (cups)

⇒ 3.75 / 1.5 = y / 2.5

⇒ z = (3.75 / 1.5) × 2.5  

⇒ z = 2.5 × 2.5  

Apply the multiplication operation,

⇒ z = $6.25

Thus, the required missing values are $2.5 when the cup of milk is 1, $8.75 when the cup of milk is 3.5, and $6.25 when the cup of milk is 2.5.

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Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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The probability of winning $1000 a day for life is approximately 5.245 x 10^-11 and the probability of winning $1000 a week for life is approximately 1.07 x 10^-8. The probability of winning the jackpot ($1000 a day for life) is 1/(60^5 * 4), while the probability of winning $1000 a week for life is 1/(60^5).

In the Florida Lottery Cash4Life game, a player must select five numbers from 1 to 60 and then one Cash Ball number from 1 to 4. The jackpot prize is $1000 a day for life if all five numbers and the Cash Ball match the winning numbers drawn on Monday nights. If just all five numbers match the winning numbers, the player will win $1000 a week for life.
To determine the probability of winning $1000 a day for life, we can use the formula for the probability of independent events: P(A and B) = P(A) x P(B)

(a) To win the jackpot of $1000 a day for life, the player needs to match all five numbers and the Cash Ball. There are 60 options for each of the five numbers and 4 options for the Cash Ball. The total number of possible outcomes is 60^5 (60 choices for each of the five numbers) times 4 (for the Cash Ball). So the probability of winning the jackpot is 1/(60^5 * 4). (b) To win $1000 a week for life, the player needs to match only the five numbers, without considering the Cash Ball. The total number of possible outcomes for this scenario is 60^5. Therefore, the probability of winning $1000 a week for life is 1/(60^5).

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Answer:

\( \huge \orange{y = - \frac{1}{9} x} \\ \)

Step-by-step explanation:

To find an equation of a line when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

From the question we have

\(y + 1 = - \frac{1}{9} (x - 9) \\ y + 1 = - \frac{1}{9} x + 1 \\ y = - \frac{1}{9} x + 1 - 1\)

We have the final answer as

\(y = - \frac{1}{9} x \\ \)

Hope this helps you

f(x) = √x g(x) = 1/(x - 4)

Domain of (f o g)(x) ==> 4 < x < +inf ==> x > 4

Doamain of (g o f)(x) ==> x >= 0, x different of 16

Answer:

51

Step-by-step explanation:

I did this by multiplying 42.50 by 0.06 and divide that answer with 0.05.

Answer:

-45 + 12 is equal to -33

and Choice A is also equal to -33.

Step-by-step explanation:

The probability of the horse winning the race is 4/11 or approximately 0.36 or 36%.

The odds in favor of a horse winning a race is expressed as a ratio of the number of favorable outcomes to the number of unfavorable outcomes. In this case, the odds in favor of the horse winning the race is 4:7.

This means that for every 4 favorable outcomes, there are 7 unfavorable outcomes.

To determine the probability of the horse winning the race, we can use the formula:

Probability = favorable outcomes / total outcomes

In this case, the total number of outcomes is the sum of the favorable and unfavorable outcomes, which is 4 + 7 = 11.

Therefore, the probability of the horse winning the race is:

Probability = 4 / 11

This means that the horse has a probability of approximately 0.36 or 36% of winning the race.

In summary, the odds in favor of a horse winning a race of 4:7 means that there are 4 favorable outcomes for every 7 unfavorable outcomes.

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hello

any quadrilateral that has four right angle triangles with congurent diagonal is a rectangle

the answer to this question is option B

The problem involves maximizing profit in a factory that produces products X and Y. Constraints include labor time, material availability, testing equipment usage, and minimum production requirements.

(a) To maximize profit, we need to define the objective function. Let x be the number of units of product X and y be the number of units of product Y produced. The objective function can be expressed as Z = 6x + 4.5y, representing the total profit.

The constraints can be formulated as follows:

1. Labor time constraint: 30x + 15y ≤ 60 hours (converted to minutes)

2. Material constraint: 2.5x + 2y ≤ 500 kilograms

3. Testing equipment constraint: Testing time for X ≥ 8 hours (converted to minutes)

4. Minimum production requirement: x ≥ 40 units of product X, y ≥ 80 units of product Y

5. Non-negativity constraint: x ≥ 0, y ≥ 0

(b) By graphing the system of inequalities on graph paper, the feasible region can be shaded. The feasible region represents the intersection of all the constraints.

(c) To find the weekly production that maximizes profit, we need to optimize the objective function within the feasible region. This can be done using linear programming techniques.

By solving the problem, we can determine the values of x and y that maximize the objective function Z. The expected maximum profit will be the value of Z at the optimal solution.

Note: The specific calculations and graphical representation will require numerical values and graphing tools to provide an accurate solution.

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