The Maclaurin series for a function f is given by f(x)=x−x^3/3!+x^5/5!−x^7/7!+⋯+(−1)^n*x^2n+1/(2n+1)!+⋯ and converges to f(x) for all x. Let g be the function defined by g(x)=f(x2)

Any function of the form [tex]y = \sqrt[3]{x + a}[/tex] is a translation left a units of the graph of [tex]g(x) = \sqrt[3]{x}[/tex], which has one x-intercept.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The function in this problem has a single x-intercept, hence a translation left only moves the function laterally, meaning that it would also have only one x-intercept.

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The name of the angle formed by Ray KL and Ray HK is ∠LKH or ∠HKL.

An angle is formed by two rays that share a common endpoint, called a vertex. In this case, Ray KL and Ray HK share the endpoint, K, which is the vertex of the angle. The name of an angle is determined by the letters assigned to its three points, with the vertex letter in the middle.

In this case, the angle can be named ∠LKH or ∠HKL, depending on the order in which the points are listed. The symbol ∠ is used to represent an angle. Therefore, the correct way to refer to the angle formed by Ray KL and Ray HK is ∠LKH or ∠HKL.

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The maximum altitude the object reaches is approximately 0.459 meters, and it takes approximately 0.612 seconds for the object to hit the ground after being shot upwards from ground level.

To find the maximum altitude and the time at which the object hits the ground after being shot upwards from ground level with an initial velocity of 3 meters per second and subject only to the force of gravity,

we can use the following steps:

1. Calculate the time it takes to reach its maximum altitude:

To do this, we can use the formula vf = vi - gt, where vf is the final velocity (0 m/s at the peak), vi is the initial velocity (3 m/s), g is the acceleration due to gravity (9.81 m/s²), and t is the time. Rearranging and solving for t:

0 = 3 - 9.81t

t = 3 / 9.81 ≈ 0.306 seconds

2. Calculate the maximum altitude:

We can use the formula h = vit - 0.5gt², where h is the maximum altitude. Plugging in the values:

h = (3 m/s)(0.306 s) - 0.5(9.81 m/s²)(0.306 s)²

h = 0.459m

3. Calculate the time it takes to hit the ground:

Since the object will take the same amount of time to fall from its maximum altitude to the ground as it took to reach the maximum altitude, the total time to hit the ground is double the time it took to reach the maximum altitude:

total time = 2 × 0.306 s ≈ 0.612 seconds

So, the maximum altitude the object reaches is approximately 0.459 meters, and it takes approximately 0.612 seconds for the object to hit the ground after being shot upwards from ground level.

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The amount of more sauce needed is 5/12.

Thus we are given that the total amount of sauce required for making the pizza is 2/3 cup.

Thus we already have 1/4 cup of tomato sauce present.

Hence, for making the recipe the leftover amount of sauce will be the difference in the sauce we have got to the sauce required.

Tomato sauce required= Total tomato sauce needed - Sauce already present

Therefore,

Tomato sauce required= 2/3-1/4

Thus we have to make the denominators qual by taking their LCM as the denominator.

The LCM of the denominators comes out to be 12.

Therefore,

[tex]=\frac{8-3}{12}[/tex]

[tex]=\frac{5}{12}[/tex]

Therefore, the amount of sauce required is 5/12.

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Answer:

Yes they are mutually exclusive

Step-by-step explanation:

You cannot both be a rational number and an irrational number

Answer:

search them up it should give you the answers

Step-by-step explanation:

Hamid's soccer game starts at 10:00 am with players warming up 45 minutes earlier and ends by 1:15.

Hamid's soccer game is scheduled to start at 10:00 am, but the players must arrive at the field 45 minutes early to warm up. This means that they need to be there at 9:15 am. The duration of the game is not given, but we know that it must end by 1:15 pm.

Assuming that the game will last for 90 minutes, it would end at 11:30 am. This would give the players ample time to change, clean up, and leave the field by 12:00 pm. However, if the game were to last longer, say for 2 hours, it would end at 12:00 pm, leaving only 15 minutes for the players to get ready to leave.

Therefore, it is important for the players to play efficiently and within the time allotted so that they have enough time to change and leave before the deadline. It is also important for the players to arrive at the field on time to ensure that they have enough time to warm up and prepare for the game.

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The 99% confidence interval of the true mean weight of minivans with 4150 pounds is CI = (3950, 4350).

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.

Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.

Point estimate is the sample mean, which is 4150 pounds. It is the best "guess" one has.

selected minivans was 4,150 pounds,

(z < 0.99) = 2.58

99% CI = ±2.58

Standard Error of the mean.

It is the = [tex]\frac{standard \ deviation}{\sqrt{sample \ size} }[/tex]

SE = [tex]\frac{490}{\sqrt{40} }[/tex]

SE = 77.475

To the nearest decimal ,

z x SE = ±200

CI = (3950, 4350) units are pounds.

Therefore, the confidence interval of the true mean weight of minivans is (3950, 4350).

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Answer:

70 dogs

Step-by-step explanation:

sum the parts of the ratio , 5 + 2 = 7 parts

divide total by 7 to find the value of one part of the ratio

98 ÷ 7 = 14 ← value of 1 part of the ratio , then

5 × 14 = 70 ← number of dogs

There are 1140 different predictions possible for this game of chance.

In this scenario, customers have an opportunity to predict three numbers out of 20, which will be drawn from a bin. The order in which the numbers are selected does not matter, which means the same set of numbers in different orders will be considered as the same prediction.

To solve this problem, we can use the formula for combinations, which is

=> [tex]^nC_x = \frac{n!}{ x! \times (n-x)!}[/tex]

where n is the total number of items, and x is the number of items to be selected.

In this case, we have 20 balls, and we want to select three balls without replacement. So, the formula becomes

=> [tex]^{20}C_3 = \frac{20!} { 3! \times (20-3)!}[/tex]

Using a calculator or simplifying the equation, we get:

[tex]= > ^{20}C_3 = \frac{201918} { 321} = 1140[/tex]

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Answer: x² - 2x - 3

Step-by-step explanation:

      What is FOIL? The FOIL method is used to multiply two binomials.

F ➜ First
O ➜ Outer
I ➜ Inner
L ➜ Last

      Let us break it down into each piece by multiplying, following the pattern.

F ➜ x * x ➜ x²
O ➜ x * 1 ➜ x
I ➜ x * -3 ➜ -3x
L ➜ -3 * 1 ➜ -3

      Lastly, we add these pieces together.

x² + x - 3x - 3 = x² - 2x - 3

The total area of the first floor of the tiny house is 121 square feet

The total area of the first floor of the tiny house can be expressed as the sum of the areas of each room. The area of a rectangle is calculated by multiplying the length by the width. Therefore, we can write:

Total area = Area of kitchen + Area of bathroom

The area of the kitchen is given by the product of the length and the width of the kitchen, which is 11 feet and 7 feet, respectively. Therefore, the area of the kitchen can be written as:

Area of kitchen = 11 x 7 = 77 square feet

Similarly, the area of the bathroom is given by the product of the length and the width of the bathroom, which is 11 feet and 4 feet, respectively. Therefore, the area of the bathroom can be written as:

Area of bathroom = 11 x 4 = 44 square feet

Substituting these expressions into the equation for the total area, we get:

Total area = Area of kitchen + Area of bathroom

= 77 + 44

= 121 square feet

Therefore, the total area of the first floor of the tiny house is 121 square feet, which can also be expressed as the sum of the areas of the kitchen and bathroom.

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A planet's radius is approximately 2,812 mi. About two-thirds of the planet's surface is covered by water. An estimate for the land area on the planet is 33 million mi²

The surface area of a sphere is given by the formula:

S = 4πr²

where S is the surface area and r is the radius.

Substituting the given radius, we get:

S = 4π(2,812)²

S ≈ 99,392,252.4 mi²

Since two-thirds of the planet's surface is covered by water, we can estimate the land area as one-third of the total surface area:

Land area ≈ (1/3) x 99,392,252.4

Land area ≈ 33,130,750.8 mi²

Rounding this to the nearest million, we get an estimate of 33 million mi² for the land area on the planet.

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The density of the object is 0.0018 g/mL.

To calculate the density of the object, we need to use the formula:

Density = Mass / Volume

Given that the mass of the object is 4.70g and the volume is 2.55L, we can substitute these values into the formula:

Density = 4.70g / 2.55L

We need to convert the units of mass and volume to a consistent unit. Let's convert the volume from liters to milliliters (1L = 1000mL):

Density = 4.70g / 2550mL

Now we can simplify by dividing both the numerator and denominator by 10:

Density = 0.47g / 255mL

Finally, we can express the answer in units of g/mL:

Density = 0.0018 g/mL

Therefore, the density of the object is 0.0018 g/mL.

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Last week, the ratio of bananas sold to watermelons sold was 4 : 3.

This ratio means that for every 4 bananas sold, the number of watermelons sold was 3.

Since there were 48 bananas sold, we can find the number of watermelons sold by subtracting 12 from 48:

48 bananas - 12 = 36 watermelons

Now, we can determine the ratio of bananas sold to watermelons sold. The ratio would be:

Bananas : Watermelons = 48 : 36

To simplify this ratio, we can divide both numbers by their greatest common divisor (GCD), which in this case is 12:

48 ÷ 12 = 4
36 ÷ 12 = 3

So, the simplified ratio is:

4 : 3

This ratio means that for every 4 bananas sold, the number of watermelons sold was 3. In other words, out of every 7 fruits sold (4 bananas + 3 watermelons), 4 were bananas and 3 were watermelons. This provides an easy way to understand the proportion of each type of fruit sold at Jun's fruit stand last week.

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The volume  33.5 cubic inches

To calculate the volume of the cylinder, we need to use the formula:

V = π[tex]r^2[/tex]h

where V is the volume, π is the constant pi, r is the radius of the base (which is half the diameter), and h is the height.

First, we need to convert the diameter of the cylinder to inches:

2 3/4 inches = (2*4 + 3)/4 inches = 11/4 inches

The radius of the cylinder is half the diameter, so:

r = (11/4)/2 = 11/8 inches

Now we can plug in the values into the formula:

V = π[tex](11/8)^2[/tex](11) cubic inches

V ≈ 33.5 cubic inches (rounded to the nearest tenth)

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The derivative of f(x) = sinº (4x) is f '(x) = 4cos (4x).

To find the derivative of f(x) = sinº (4x), we can use the chain rule.

First, we need to find the derivative of the outer function, which is sinº (4x). This can be done using the derivative of the sine function:

f '(x) = cos (4x)

Next, we need to multiply this by the derivative of the inner function, which is 4.

f '(x) = cos (4x) * 4

Simplifying this expression, we get:

f '(x) = 4cos (4x)

Therefore, the derivative of f(x) = sinº (4x) is f '(x) = 4cos (4x).

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Answer:  [tex]\frac{x-4}{x-7}[/tex]

Step-by-step explanation:

[tex]\frac{x^{2}-5x+4 }{x^{2} -8x+7}[/tex]    

factor the top and bottom by finding numbers that multiply to the last term but add to middle

for top part:

-4 and -1   multiply to +4 and add to -5

for bottom part:

-7 and -1 multiply to to +7 and add to -8

Those are your factored numbers, put into factored form

[tex]\frac{(x-4)(x-1)}{(x-7)(x-1)}[/tex]    now cross off same factors from top and bottom only

[tex]\frac{x-4}{x-7}[/tex]

By using  sum , difference , product , quotient and one that involves at least two operations that have the value of -3/4.

Now, We have to find the five expressions :

Expression for sum is -

1/4 + (-1) = -3/4

Expression for difference is -

(1/4 - 1) = -3/4

Expression for product is -

(-3/2)(1/2) = -3/4

Expression for quotient is -

(1 - 4)/4 = -3/4

Expression that involves at least two operations is -

-(1/4 + 2/4) = -3/4

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To use Newton's method to approximate a root of the equation

In (4x) = arctan(x -0.1),

we will need to find the first derivative of the function f(x) = In(4x) - arctan(x-0.1). f(x) = In(4x) - arctan(x-0.1) f'(x) = 4/(4x) - 1/(1+(x-0.1)^2) Using the initial approximation x1 = 0.1,

We can find the second approximation x2: x2 = x1 - f(x1)/f'(x1) x2 = 0.1 - [In(4*0.1) - arctan(0.1-0.1)] / [4/(4*0.1) - 1/(1+(0.1-0.1)^2)] x2 = 0.1076

We can repeat this process to find the third approximation x3: x3 = x2 - f(x2)/f'(x2) x3 = 0.1076 - [In(4*0.1076) - arctan(0.1076-0.1)] / [4/(4*0.1076) - 1/(1+(0.1076-0.1)^2)] x3 = 0.1078

Now we can find the fourth approximation x4: x4 = x3 - f(x3)/f'(x3) x4 = 0.1078 - [In(4*0.1078) - arctan(0.1078-0.1)] / [4/(4*0.1078) - 1/(1+(0.1078-0.1)^2)] x4 = 0.1078

Finally, we can find the fifth approximation x5: x5 = x4 - f(x4)/f'(x4) x5 = 0.1078 - [In(4*0.1078) - arctan(0.1078-0.1)] / [4/(4*0.1078) - 1/(1+(0.1078-0.1)^2)] x5 = 0.1078

Therefore, the fourth approximation x4 is 0.1078 and the fifth approximation x5 is also 0.1078.

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Answer: B

Step-by-step explanation:

Your original matrix:

1 0

0 1

after dilation

3 0

0 3

after reflection... it only changes sign of y because its reflected across x-axis

3 0

0 -3

B

To find the derivative of f(x) = (2e^(3x) + 2e^(-2x))^4, we can use the chain rule and the power rule.

First, we need to find the derivative of the function inside the parentheses, which is:

g(x) = 2e^(3x) + 2e^(-2x)

The derivative of g(x) is:

g'(x) = 6e^(3x) - 4e^(-2x)

Now, using the chain rule and power rule, we can find the derivative of f(x):

f'(x) = 4(2e^(3x) + 2e^(-2x))^3 * (6e^(3x) - 4e^(-2x))

Simplifying this expression, we get:

f'(x) = 24(2e^(3x) + 2e^(-2x))^3 * (e^(3x) - e^(-2x))
To find the derivative of f(x) = (2e^(3x) + 2e^(-2x))^4, we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Let u = 2e^(3x) + 2e^(-2x). Then f(x) = u^4.

First, find the derivative of the outer function with respect to u:
df/du = 4u^3

Next, find the derivative of the inner function with respect to x:
du/dx = d(2e^(3x) + 2e^(-2x))/dx = 6e^(3x) - 4e^(-2x)

Now, use the chain rule to find the derivative of f with respect to x:
df/dx = df/du * du/dx = 4u^3 * (6e^(3x) - 4e^(-2x))

Substitute the expression for u back into the equation:
df/dx = 4(2e^(3x) + 2e^(-2x))^3 * (6e^(3x) - 4e^(-2x))

This is the derivative of f(x) with respect to x.

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The values on the relative frequency table indicates;

Part A; 55%

Part B; 20%

Part C; There is an association between passing the exam and completing the exam review

The relative frequency table shows the mode of a dataset, from the sample obtained from a population.

The data in the table can be expressed as follows;

[tex]{}[/tex]                                           Passed exam Did not pass exam Row totals

Completed exam review [tex]{}[/tex]            55%        10%                         65%

Did not completed exam review[tex]{}[/tex] 20%       15%                          35%

Column Total [tex]{}[/tex]                               75%        25%                         100%

Part A; The above table indicates that the percentage who passed the exam given that they completed the exam review is 55%

Part B; The percentage that passed the exam given that they did not complete exam review is 20%

Part C; The conditional percentages of passing the exam and completing the exam review are very different indicating that there is an association between passing the exam and completing exam review

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2(2.5) + 5(23) = 150

3(2.5) + 4(23) = 144.5

Both equations are satisfied, so our solution is correct.

To solve the problem, let's first assign some variables. Let x be the cost of one pine tree and y be the cost of one hydrangea bush. We can then use these variables to set up a system of equations:

2x + 5y = 150 (equation 1)

3x + 4y = 144.5 (equation 2)

We can solve this system of equations using various methods. Here, we will use the substitution method.

From equation 1, we can solve for x in terms of y:

2x = 150 - 5y

x = (150 - 5y)/2

We can then substitute this expression for x into equation 2:

3((150 - 5y)/2) + 4y = 144.5

Multiplying both sides by 2 to eliminate the fraction:

3(150 - 5y) + 8y = 289

Expanding and simplifying:

450 - 15y + 8y = 289

-7y = -161

y = 23

We can now substitute this value for y into either equation 1 or 2 to solve for x:

2x + 5(23) = 150

2x = 5

x = 2.5

Therefore, one pine tree costs $2.50 and one hydrangea bush costs $23.

To check our work, we can substitute these values into both equations:

2(2.5) + 5(23) = 150

3(2.5) + 4(23) = 144.5

Both equations are satisfied, so our solution is correct.

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The probability that more than 2 minutes pass before a sale is completed is approximately 0.895 or 89.5%.

The CDF of the exponential distribution is given by:

F(x) = 1 - e^(-λx)

where λ is the rate parameter, which is the reciprocal of the mean, λ = 1/18 in this case. The variable x is the time it takes for a sale to be completed.

To find the probability that more than 2 minutes pass before a sale is completed, we need to find the complement of the probability that a sale is completed within the first 2 minutes. That is:

P(X > 2) = 1 - P(X ≤ 2)

Substituting into the CDF formula:

P(X > 2) = 1 - F(2) = 1 - [tex](1 - e^{(-\lambda_2)} = e^{(-\lambda_2)}[/tex]

Plugging in the value of λ:

P(X > 2) = [tex]e^{(-(1/18)\times2)}[/tex] ≈ 0.895

This means that there is a high chance that it will take more than 2 minutes for a sale to be completed on the phone.

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The simplification of the given algebraic expression is: -3x - 9y

Algebraic expressions are defined as the idea of expressing numbers with the aid of letters or alphabets without really specifying their actual values.

Now, the algebraic operations are known by the acronym PEMDAS which denotes:

P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

We want to find the sum of the algebraic expressions given as (-10x - 4y) and (7x - 5y) in simplest form.

Thus, we have:

(-10x - 4y) + (7x - 5y)

= -10x - 4y + 7x - 5y

= -3x - 9y

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Complete question:

Find an expression which represents the sum of (-10x - 4y) and (7x - 5y) in simplest terms.

Answer:

Step-by-step explanation:

16 - (y^2/sqrt(49)) +12

at y = -5

16 - ( (-5)^2 / sqrt(49)) +12    

16 - ( 25 / 7) + 12

28 - (25/7)

(28*7 - 5) / 7    (LCM)

(196 - 5) / 7

(191/7)

27.2857 = Ans

The function that would best represent this is given as p(t) = 1150 (0.8769)^t

An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a constant called the base and "x" is the variable. The base is usually a positive number greater than 1, but it can also be a fraction between 0 and 1, or even a negative number.

Exponential functions are characterized by the fact that the variable "x" appears as an exponent. As a result, these functions grow or decay very rapidly as "x" increases or decreases, depending on the value of the base "a".

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the intersection point is approximately (2.215421, 3.256684). For the first question, the initial value problem is given by the differential equation f'(u) = 5(cost - sinus) with the initial condition f(3xN) = 3.

To solve this problem, we can separate the variables and integrate both sides as follows:

f'(u) = 5(cosu - sinu)
∫ f'(u) du = ∫ 5(cosu - sinu) du
f(u) = 5sinu + 5cosu + C

Using the initial condition f(3xN) = 3, we can solve for the constant C:

f(3xN) = 5sin(3xN) + 5cos(3xN) + C = 3
C = 3 - 5sin(3xN) - 5cos(3xN)

Thus, the solution to the initial value problem is given by:

f(u) = 5sinu + 5cosu + 3 - 5sin(3xN) - 5cos(3xN)

For the second question, we are asked to find the intersection points of the two curves y = 16/* and y = x + 1 using Newton's method. To applyhttps://brainly.com/question/2228446 we need to find the function f(x) that represents the difference between the two curves:

f(x) = 16/x - (x + 1)

The intersection points correspond to the roots of f(x), which can be found using Newton's method:

x_{n+1} = x_n - f(x_n)/f'(x_n)

where x_n is the nth approximation of the root. We start with an initial guess of x_0 and iterate until we reach a desired level of accuracy. For example, if we start with x_0 = 1, the iterations are as follows:

x_1 = 1 - (16/1 - (1 + 1))/(16/1^2 + 1) = 2.5
x_2 = 2.5 - (16/2.5 - (2.5 + 1))/(16/2.5^2 + 1) = 2.267857
x_3 = 2.267857 - (16/2.267857 - (2.267857 + 1))/(16/2.267857^2 + 1) = 2.219208
x_4 = 2.219208 - (16/2.219208 - (2.219208 + 1))/(16/2.219208^2 + 1) = 2.215430
x_5 = 2.215430 - (16/2.215430 - (2.215430 + 1))/(16/2.215430^2 + 1) = 2.215421

Thus, the intersection point is approximately (2.215421, 3.256684).

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