Use the triangle to evaluate each function. sin(a) = tan(a) = sec(a) =

The value of the expression is (a) (f∘g)(4) = 14√2

(b) (g∘f)(2) = 14√2

(c) (f∘f)(1) = 7√7

(d) (g∘g)(0) = 0

To find the given expressions, we'll substitute the appropriate values into the composed functions.

(a) To find \((f \circ g)(4)\), we first evaluate \(g(4)\) and then substitute the result into \(f(x)\).

  \[g(4) = 2(4) = 8\]

  \((f \circ g)(4) = f(8) = 7\sqrt{8} = 7\sqrt{4 \cdot 2} = 7 \cdot 2 \sqrt{2} = 14\sqrt{2}\)

(b) To find \((g \circ f)(2)\), we first evaluate \(f(2)\) and then substitute the result into \(g(x)\).

  \[f(2) = 7\sqrt{2}\]

  \((g \circ f)(2) = g(7\sqrt{2}) = 2(7\sqrt{2}) = 14\sqrt{2}\)

(c) To find \((f \circ f)(1)\), we substitute \(f(1)\) into \(f(x)\) twice.

  \[f(1) = 7\sqrt{1} = 7 \cdot 1 = 7\]

  \((f \circ f)(1) = f(7) = 7\sqrt{7}\)

(d) To find \((g \circ g)(0)\), we substitute \(g(0)\) into \(g(x)\) twice.

  \[g(0) = 2(0) = 0\]

  \((g \circ g)(0) = g(0) = 0\)

Therefore, the values of the given expressions are:

(a) \((f \circ g)(4) = 14\sqrt{2}\)

(b) \((g \circ f)(2) = 14\sqrt{2}\)

(c) \((f \circ f)(1) = 7\sqrt{7}\)

(d) \((g \circ g)(0) = 0\)

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The conjugate of a complex number with a real part of -5 and an imaginary part of 4i is represented by :

C) -5 - 4i.

The conjugate of a complex number with a real part of -5 and an imaginary part of 4i can be found by changing the sign of the imaginary part. In this case, the imaginary part is 4i, so the conjugate will have a negative sign for the imaginary part.

The conjugate of the complex number is given by -5 - 4i. This means that if we have a complex number of the form -5 + 4i, its conjugate will be -5 - 4i. The conjugate of a complex number is important in various mathematical operations, such as complex number multiplication and division, as it helps simplify the expressions and eliminate the imaginary parts when needed.

Among the given options, option C) -5 - 4i represents the conjugate of the complex number with a real part of -5 and an imaginary part of 4i.

The correct question should be :

Which of the following expressions represents the conjugate of a complex number with a real part of -5 and an imaginary part of 4i?

A) 5

B) 4i

C) -5 - 4i

D) -5 + 4i

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Answer:

C

Step-by-step explanation:

The two solutions are (-1,-2) and (3,6)

The calculated BMI for the given weight and height is approximately 28.478.

To calculate and output the BMI based on the user's weight and height inputs, you can use the following code in Python:

weight_pounds = float(input("Enter weight in pounds: "))

height_inches = float(input("Enter height in inches: "))

bmi = (weight_pounds * 703) / (height_inches ** 2)

print("BMI is", bmi)

When executed, the code prompts the user to enter their weight in pounds and height in inches. It then calculates the BMI using the provided equation and stores the result in the variable 'bmi'. Finally, it outputs the calculated BMI using the 'print' function.

Based on the example input provided (weight: 210 pounds, height: 72 inches), the output would be:

BMI is 28.478

This indicates that the calculated BMI for the given weight and height is approximately 28.478.

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Answer:

degree 3

Step-by-step explanation:

To get the degree, we open up the bracket

We have this as;

f(x) = x(x-2x^2)

f(x) = x^2 - 2x^3

3 is the highest power of x and thus, it is our degree

Answer:

  a) tangent

  b) radius

  c) diameter

  d) chord

Step-by-step explanation:

You want the vocabulary words associated with various segments in and around a circle.

A tangent is a line or segment that is external to the circle and intersects it at one point. A tangent is always perpendicular to a radius. (Segment a is a tangent.)

A radius of a circle is a line segment between the center and a point on the circle. (Segment b is a radius.)

A chord is a line segment internal to the circle that joins two points on the circle. (Segment d is a chord.)

A diameter of a circle is a chord that contains the center of the circle. (Segment c is a diameter, and also a chord. The more specific descriptor is "diameter.")

Option (d) An explicit formula representing the sequence is f(x) = 4(3/2)^x and option (e) The sequence shows exponential growth, are correct for the given geometric sequence.

A geometric sequence is a sequence of numbers where the ratio between any two neighboring terms is a constant. This constant ratio is called the common ratio. If the first term of the geometric sequence is a and the common ratio is r, then the n-th term (the last term) is given by a * r^(n-1). The first term is denoted by a, while the common ratio is denoted by r. Here, we are given that the recursive formula representing the sequence is f(x + 1) = 3/2(f(x )) when f(1) = 4.

By using the formula and considering f(1) = 4, we can find the first few terms in the sequence. So, the first few terms are 4, 6, 9, 27/2, …Now, let’s check each statement one by one.(a) The domain is the set of natural numbers. False.

The domain is {1, 2, 3, …} because the first term of the sequence is given and we need to use the recursive formula to find all the other terms.(b) The range is the set of natural numbers. False.

The range is not just the set of natural numbers as the sequence has decimals and fractions in it.(c) The recursive formula representing the sequence is f(x + 1) = 3/2(f(x )) when f(1) = 4.True.

This is given in the question.(d) An explicit formula representing the sequence is f(x) = 4(3/2)^x. True.

We can find the common ratio by dividing any term by its preceding term, and we get 3/2. Since the first term is 4, we can write the nth term as 4(3/2)^(n-1).(e) The sequence shows exponential growth. True.

The sequence is increasing and the ratio between any two consecutive terms is constant, which means it’s an exponential sequence.

Therefore, the answers are options (d) An explicit formula representing the sequence is f(x) = 4(3/2)^x and (e) The sequence shows exponential growth..

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Answer:

\(\huge\boxed{x=2\sqrt{286}}\)

Step-by-step explanation:

Use the Pythagorean theorem:

\(leg^2+leg^2=hypotenuse^2\)

We have:

\(leg=x\\leg=15\\hypotenuse=37\)

Substitute and solve for x:

\(x^2+15^2=37^2\\\\x^2+225=1269\qquad|\text{subtract 225 from both sides}\\\\x^2+225-225=1269-225\\\\x^2=1144\to x=\sqrt{1144}\\\\x=\sqrt{4\cdot286}\\\\x=\sqrt4\cdot\sqrt{286}\\\\x=2\sqrt{286}\)

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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Answer:

92kg is about 202.8 lbs

Step-by-step explanation:

The value of 92 in kg to lbs is 202.8 lbs

What is Kilo gram ?

Kilo gram can be defined as follows , one kilo gram is equals to thousand grams or one gram is equal to reciprocal of thousand.

Given ,

to find 92 in kg to lbs

So, we know that,

1 kg = 2.204

So, here for 92 kg

we need to multiply with 2.204

we get,

92 kg = 92 * 2.204

= 202.8

So, 92 kg = 202.8 lbs.

Therefore, the value of 92 in kg to lbs is 202.8 lbs

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The Fundamental Pythagorean Identity in trigonomety sin²(x)+cos²(x)=1

Using  the Pythagorean Identity: \(\frac{1-2cos^2x}{sinxcosx}=tanx-cotx\) ,

Hence prove.

Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,

We know that the Pythagorean theorem,

sin²(x)+cos²(x)=1

We have

1-2cos²x = sin²(x)+cos²(x) -2cos²x

1-2cos²x = sin²(x)-cos²(x)

\(\frac{1-2cos^2x}{sinxcosx}=tanx-cotx\)

To prove this take the right-hand sides

\(\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\= tanx-cotx\)

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Answer:

A rational number is a nonterminating, nonrepeating number. this is false

3n/7-2=4n-6

clear fraction .le, multiply by 7

3n-14= 28n -42

25n =28

n=28/25

n/7 =4/25

12/25-50/25= 112/25-150/25 = > 38=38.

The expression 3(r/t) "the quotient of three times a number, and 7 option (C) 3(r/t) is correct after applying the arithmetic operation.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.

It is given that:

The expression is:

The quotient of three times a number and 7

Let the two numbers be r and t:

On division:

= r/t

= 3(r/t)

Thus, the expression 3(r/t) "the quotient of three times a number, and 7 option (C) 3(r/t) is correct after applying the arithmetic operation.

The missing options are:

3 + rt

r/3t

3(r/t)

3 ÷ (r/t)

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Answer:

the awnser is:30° yup it is

Answer:

30°

Step-by-step explanation:

We Know

(4x - 2) + (20x - 10) = 180°

4x - 2 + 20x - 10 = 180

24x - 12 = 180

24x = 192

x = 8

Find m∠EBD

∠ABC is a vertical angle to ∠EBD, meaning they will equal it.

4(8) - 2

32 - 2

30°

So, m∠EBD is 30°

By combining the square roots and simplify the exponents we get the expression 1296√2a⁴b¹²c¹⁰

To simplify the expression, we can combine the square roots and simplify the exponents.

√27a³b²c⁴ x √128a⁷b⁹c⁴ x √729a¹b¹²c²

First, let's simplify the numbers inside the square roots:

√(27) = √(3² × 3) = 3√3

√(128) = √(2⁷ × 2) = 2⁴√2 = 16√2

√(729) = √(9³ × 3²) = 9√3

3√3 ×16√2 × 9√3 × a⁴ × b¹² × c¹⁰

Finally, we can simplify the expression:

3 × 16 × 9 × √(3) ×√(2) × √(3) × a⁴ × b¹² × c¹⁰

= 432 × √(3² × 2) × a⁴ × b¹² × c¹⁰

= 432×3 × √(2) × a⁴ × b¹²× c¹⁰

= 1296√2×a⁴ × b¹² × c¹⁰

Therefore, the simplified expression is 1296√2a⁴b¹²c¹⁰

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To have a valid 98% confidence interval based on a sample of size n, it is necessary to assume that the population has an approximately normal distribution (option A).

The margin of error in a confidence interval is influenced by the sample size and the confidence level. The margin of error is inversely proportional to the square root of the sample size. This means that increasing the sample size (option A) will result in a smaller margin of error, as the square root of a larger number is larger than that of a smaller number.

On the other hand, the margin of error is directly proportional to the critical value, which is determined by the confidence level. The higher the confidence level, the larger the critical value and consequently, the larger the margin of error. Thus, decreasing the confidence level (option D) will result in a larger margin of error.

Therefore, the options that will result in a larger margin of error are B and D: decreasing the sample size while keeping the same confidence level, and decreasing the confidence level while keeping the same sample size.

It's important to note that the validity of a confidence interval relies on certain assumptions. In this case, to have a valid 98% confidence interval based on a sample of size n, it is necessary to assume that the population has an approximately normal distribution (option A). This assumption is required for the central limit theorem to hold, which allows the sampling distribution of the sample mean to approximate a normal distribution. Options B, C, and D do not accurately describe the assumptions necessary for the validity of the confidence interval.

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Answer:

Step-by-step explanation:

Each term in the sequence is 4 less than the previous term.  That indicates an arithmetic sequence, which has the form a(n) = a(1) + d(n -1), where d is the common difference.  Here the common difference is -4, and so the appropriate sequence is

a(n) = 14 - 4(n - 1)

Answer:

Option A

Step-by-step explanation:

to be perpendicular, the product of two slopes should be -1

the slope of the first equation is 1/5, so the slope should be -5

(1/5) (-5)= -1

y= -5x +b

Substitute (1,1) to solve for b,

b= 6

Thus, the equation is y= -5x +6

Answer:

we know the smaller cone's height is 1/4 of 12, namely 3

Step-by-step explanation:

Because we know the radius and height of both cones, we can calculate the area of the larger one by subtracting the area of the smaller one; the Frustum's area remains.

There are two possible outcomes for flipping a coin: heads or tails. Then, there is a probability of 1/2 of flipping tails.

There are six possible outcomes for rolling a dice: 1, 2, 3, 4, 5 or 6. Then, there is a probability of 5/6 of rolling a number greater than 1.

The probability of flipping tails and rolling a number greater than 1 is the product of the probabilities of these two events happening independently:

Therefore, the answer is:

The value of P(1.41 < Z < 2.85)  is 0.0771.

Hence, the correct answer is d.

A normally distributed random variable with mean μ= 0 and standard deviation σ= 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Because the Standard Normal Distribution is a probability distribution, the area under the curve between two points indicates the likelihood that variables will take on a range of values.

The whole area under the curve is one, or one hundred percent.

The mean and variance of a normal distribution are governed by two factors.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

The probability that a standard normal random variable Z is between 1.41 and 2.85 can be found using a standard normal table with a standard normal cumulative distribution function.

The answer is approximate:

P(1.41 < Z < 2.85)

= P(Z < 2.85) - P(Z < 1.41)

= 0.9927 - 0.9185

= 0.0742

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Answer:

the answer is = a) 480 cm³

The Maclaurin series for f(x) converges absolutely for x within the interval (-2/3, 2/3).

To find the Maclaurin series for the function f(x) = (3cos(x))ln(1+x), we can use the standard formulas for the Maclaurin series expansion of elementary functions.

First, let's find the derivatives of f(x) up to the third order:

f(x) = (3cos(x))ln(1+x)

f'(x) = -3sin(x)ln(1+x) + (3cos(x))/(1+x)

f''(x) = -3cos(x)ln(1+x) - (6sin(x))/(1+x) + (3sin(x))/(1+x)² - (3cos(x))/(1+x)²

f'''(x) = 3sin(x)ln(1+x) - (9cos(x))/(1+x) + (18sin(x))/(1+x)² - (12sin(x))/(1+x)³ + (12cos(x))/(1+x)² - (3cos(x))/(1+x)³

Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series:

f(0) = (3cos(0))ln(1+0) = 0

f'(0) = -3sin(0)ln(1+0) + (3cos(0))/(1+0) = 3

f''(0) = -3cos(0)ln(1+0) - (6sin(0))/(1+0) + (3sin(0))/(1+0)² - (3cos(0))/(1+0)² = -3

f'''(0) = 3sin(0)ln(1+0) - (9cos(0))/(1+0) + (18sin(0))/(1+0)² - (12sin(0))/(1+0)³ + (12cos(0))/(1+0)² - (3cos(0))/(1+0)³ = -9

Now we can write the first three nonzero terms of the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x² + (f'''(0)/3!)x³ + ...

f(x) = 0 + 3x - (3/2)x² - (9/6)x³ + ...

Simplifying, we have:

f(x) = 3x - (3/2)x² - (3/2)x³ + ...

To determine the values of x for which the series converges absolutely, we need to find the interval of convergence. In this case, we can use the ratio test:

Let aₙ be the nth term of the series.

|r| = lim(n->infinity) |a_(n+1)/aₙ|

= lim(n->infinity) |(3/2)(xⁿ+1)/(xⁿ)|

= lim(n->infinity) |(3/2)x|

For the series to converge absolutely, we need |r| < 1:

|(3/2)x| < 1

|x| < 2/3

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Answer:

  11/15

Step-by-step explanation:

You want to know how much of a book Ronald will read in 2 1/5 hours at the rate of 1/3 book in 1 hour.

To find the quantity, multiply the rate by the time.

  q = r·t

  q = (1/3 bk/h)·(2 1/5 h) = (1/3)(11/5) bk = 11/15 bk

Ronald will read 11/15 of a book in 2 1/5 hours.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

Hanging out with my family. :D

Step-by-step explanation:

Hanging with friends and family

Option 1, {x | x = –4, –1, 3, 5, 6} is the domain of the given function.

For any function, domain is the set of all input values that are accepted by the given function. For example, if there is a function, say f(x) = x + 2, then all the values of x will make up the domain of f(x).

Here, we are given a function {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}

In this case, all the input values = all the x values

and all the output values = all the y values

Thus, the domain of the given function will be a set containing the following x values-

3, 6, -1, 5, -4

Arranging these values in the ascending order we get,

-4, -1, 3, 5, 6

Therefore, the domain of the function can be represented as {x | x = –4, –1, 3, 5, 6}.

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In geometry, congruent figures are defined as figures that have the same shape and size. Two figures are said to be congruent if one of them can be moved and rotated in such a way that it coincides exactly with the other figure. Therefore, any process that changes the shape or size of the figure will create a figure that is not congruent to the original figure shown.

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