Practice Problems
1)
Chase is comparing music subscription prices. A 12-month subscription with All Ears costs
$91.80 and a 3-month subscription with Press Play costs $19.35. Which service costs less per
month?

To express the function [tex]\(G\)[/tex] in the form [tex]\(f \circ g\)[/tex] , where [tex]\(y = f(g(x))\)[/tex] , we need to find suitable non-identity functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x)\)[/tex].

Let's choose [tex]\(g(x) = \frac{1}{x}\)[/tex]  and [tex]\(f(x) = x + 8\)[/tex].

Now, we can express [tex]\(G\)[/tex] as  [tex]\(G(x) = f(g(x))\)[/tex] , which becomes:

[tex]\[G(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \frac{1}{x} + 8\][/tex]

Therefore, the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x) = \frac{1}{x} + 8\) are \(f(x) = x + 8\)[/tex] and [tex]\(g(x) = \frac{1}{x}\)[/tex].

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The following functions 1. f(x) = x+ex 3 2. f(x) = X - C03 X € = 0.0001 2 3. f(x) = x - x + sinx-1 2  By using Newton-Raphson method √29 is 4.5826.

Solve f(x) = x + e^x = 0:

Unfortunately, this equation cannot be solved analytically. We can use numerical methods such as the Newton-Raphson method to find an approximate solution. However, in this case, we will move on to the next function.

Solve f(x) = x^3 - 0.0001 = 0:

To solve this equation, we can rearrange it as follows:

x^3 = 0.0001

Taking the cube root of both sides, we get:

x = ∛0.0001

Using a calculator, we find that ∛0.0001 ≈ 0.04641588834.

Therefore, the solution to the equation f(x) = x^3 - 0.0001 = 0 is approximately x ≈ 0.0464.

Solve f(x) = x - x^2 + sin(x) - 1 = 0:

This equation also cannot be solved analytically. We can use numerical methods such as the Newton-Raphson method or graphing methods to find an approximate solution. Let's use the Newton-Raphson method.

Applying the Newton-Raphson method, we start with an initial guess, let's say x0 = 1:

Iteratively, we update x using the formula:

x_n+1 = x_n - f(x_n) / f'(x_n)

The derivative of f(x) is:

f'(x) = 1 - 2x + cos(x)

Using the initial guess:

x1 = x0 - f(x0) / f'(x0)

= 1 - (1 - 1^2 + sin(1) - 1) / (1 - 2(1) + cos(1))

≈ 1.2227

We repeat the process with x1 as the new guess:

x2 = x1 - f(x1) / f'(x1)

≈ 1.2196

Continuing this iterative process, we find:

x3 ≈ 1.2196

x4 ≈ 1.2196

The solution to the equation f(x) = x - x^2 + sin(x) - 1 = 0 is approximately x ≈ 1.2196.

Now, let's move on to finding √29 using the Newton-Raphson method.

To find √29 using the Newton-Raphson method, we need to solve the equation f(x) = x^2 - 29 = 0.

Using the Newton-Raphson method, we start with an initial guess, let's say x0 = 5:

Iteratively, we update x using the formula:

x_n+1 = x_n - f(x_n) / f'(x_n)

The derivative of f(x) is:

f'(x) = 2x

Using the initial guess:

x1 = x0 - f(x0) / f'(x0)

= 5 - (5^2 - 29) / (2 * 5)

= 5 - (25 - 29) / 10

= 5 - 4 / 10

= 5 - 0.4

= 4.6

We repeat the process with x1 as the new guess:

x2 = x1 - f(x1) / f'(x1)

= 4.6 - (4.6^2 - 29) / (2 * 4.6)

≈ 4.5826

Continuing this iterative process, we find:

x3 ≈ 4.5826

x4 ≈ 4.5826

The solution to the equation f(x) = x^2 - 29 = 0, which gives √29, is approximately x ≈ 4.5826.

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Answer:

15

Step-by-step explanation:

Prime Numbers Check

15: 5 * 3

30: 2 * 3 * 5

75: 3 * 5 * 5

Both 3 and 5 are prime numbers present in all 3 greater numbers, then you multiply them

3*5 = 15

GCF is 15

Answer:

x=2.2

y=-3.4

Step-by-step explanation:

subtract the second from the first

-5x=-11

x=2=2

substituting by x in the first equation

so y=-3.4

Answer: 7pi

Step-by-step explanation: If it completes the circumference distance (14pi) of the circle in 20 seconds, in 10 seconds it will complete half of that. or 7pi. Hope this helped!

:.the distance travelled after 10sec. =7πm

Answer:

in 20 sec distance travelled =2πr=2π×7=14πm

in 10 sec distance travelled=14πm×10/20=7πm

A triangle with a 90° angle is called a right triangle.

Option B is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Acute triangle:

The angle is less than 90 degrees.

Right triangle:

The angle is 90 degrees.

Equilateral triangle:

All sides of the triangle are equal.

Isosceles triangle:

Two sides of the triangle are equal.

Thus,

A triangle with a 90° angle is called a right triangle.

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Answer:

Yes, the fraction are equivalent

Step-by-step explanation:

Fraction shaded by candy = 2/4

Fraction shaded by Hershel = 1/2

If candy's fraction of 2/4 is reduced to it's lowest term ;

2 /4 = 1 /2 ; we also obtain the same fraction obtained by Hershel.

Hence, 2/4 is equivalent to 1/2

Answer:

y = 5, y = 7

Step-by-step explanation:

The position function becomes s(t) = 2t³ + 2t² + 9t + 8. Finally, we substitute t = 15 into the position function to obtain the particle's position at time t = 15:s(15) = 2(15)³ + 2(15)² + 9(15) + 8 = 3378. The particle's position at time t = 15 is 3378 units.

Given, the acceleration of the particle is a(t) = 12t + 4 and the particle's position and velocity at t = 0 are s(0) = 8 and v(0) = 9 respectively. To find the particle's position at time t = 15, we need to integrate the acceleration function and use the initial conditions to determine the constants of integration as follows: Integrating the acceleration function yields the velocity function:v(t) = ∫a(t) dt = ∫(12t + 4) dt = 6t² + 4t + C where C is the constant of integration. Using the initial condition that v(0) = 9, we have:9 = 6(0)² + 4(0) + C => C = 9.

Therefore, the velocity function becomes: v(t) = 6t² + 4t + 9 Now, we integrate the velocity function to obtain the position function as follows: s(t) = ∫v(t) dt = ∫(6t² + 4t + 9) dt = 2t³ + 2t² + 9t + D where D is the constant of integration. Using the initial condition that s(0) = 8, we have:8 = 2(0)³ + 2(0)² + 9(0) + D => D = 8Therefore, the position function becomes: s(t) = 2t³ + 2t² + 9t + 8Finally, we substitute t = 15 into the position function to obtain the particle's position at time t = 15:s(15) = 2(15)³ + 2(15)² + 9(15) + 8 = 3378. Therefore, the particle's position at time t = 15 is 3378 units.

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The mean absolute deviation in the given situation, where the average number of text messages students send is within 100 messages of the mean of 500 messages per day, can be calculated.

Mean absolute deviation (MAD) measures the average distance between each data point and the mean of the data set.

In this case, the average number of text messages sent by students is 500 messages per day.

Since the average is within 100 messages of the mean, we can assume a range of 400 to 600 messages.

To calculate the MAD, we need to determine the deviation of each data point from the mean. In this case, the deviations can range from -100 to 100 messages.

Since the data points are evenly distributed around the mean, the sum of these deviations will be zero.

However, to calculate the absolute deviation, we take the absolute values of the deviations.

Considering the range of -100 to 100 messages, the absolute deviations for each data point would be 100, 99, 98, ..., 2, 1, 0, 1, 2, ..., 98, 99, 100.

The average absolute deviation would be the sum of these absolute deviations divided by the total number of data points, which is 201 (from -100 to 100 inclusive).

Therefore, the mean absolute deviation in this situation is the average of these absolute deviations, which can be calculated as (100 + 99 + 98 + ... + 2 + 1 + 0 + 1 + 2 + ... + 98 + 99 + 100) / 201.

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Using the Trapezoidal Rule with n = 12, the approximation is T12 = -15.6667. Using the Midpoint Rule with n = 12, the approximation is M12 = -92. Using Simpson's Rule with n = 12, the approximation is S12 = -155.7778. So T12 =-15.6667, M12 =-92, S12 = -155.7778.

To approximate the integral using numerical methods, we'll use the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with n = 12.

Using the Trapezoidal Rule, the approximation is given by:

T12 = h/2 * [f(a) + 2(f(x1) + f(x2) + ... + f(x11)) + f(b)]

where h = (b - a)/n and xi represents the equally spaced points between a and b.

Using the Midpoint Rule, the approximation is given by:

M12 = h * [f(x1/2) + f(x3/2) + ... + f(x23/2)]

where xi/2 represents the midpoints between xi-1 and xi.

Using Simpson's Rule, the approximation is given by:

S12 = h/3 * [f(a) + 4(f(x1) + f(x3) + ... + f(x11)) + 2(f(x2) + f(x4) + ... + f(x10)) + f(b)]

Now, let's calculate the approximations:

For T12:

h = (2 - 4)/12 = -1/3

T12 = (-1/3)/2 * [4 + 2(4 + 2 + ... + 4) + 2]

T12 = -1/6 * [4 + 2(4*11) + 2]

T12 = -1/6 * [4 + 88 + 2]

T12 = -1/6 * 94

T12 = -15.6667

For M12:

h = (2 - 4)/12 = -1/3

M12 = (-1/3) * [4 + 4*3 + 4*5 + ... + 4*23]

M12 = -1/3 * [4 + 12 + 20 + ... + 44]

M12 = -1/3 * [4 + 12 + 20 + ... + 44]

M12 = -1/3 * 276

M12 = -92

For S12:

h = (2 - 4)/12 = -1/3

S12 = (-1/3)/3 * [4 + 4*4 + 2(4 + 4*3 + 4*5 + ... + 4*11) + 2(4 + 4*2 + 4*4 + ... + 4*10) + 2]

S12 = (-1/9) * [4 + 16 + 2(4 + 12 + 20 + ... + 44) + 2(4 + 8 + 16 + ... + 40) + 2]

S12 = (-1/9) * [4 + 16 + 2(276) + 2(220) + 2]

S12 = (-1/9) * 1402

S12 = -155.7778

Therefore, the approximations are:

T12 = -15.6667

M12 = -92

S12 = -155.7778

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Answer: quadratic model, 0.866

Step-by-step explanation:

Answer:

it represents a variable

Step-by-step explanation:

The number 8 is the coefficient of the variable k.

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

Given that the expression is 8k + 5. In the given expression the number 8 is the coefficient of the given expression.

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one hundred and twenty approximately

Answer:

b: 118

c: 62

Step-by-step explanation:

Angle B is a vertical angle from the given angle, so they are congruent.

Angle C is supplementary (2 angles that add up to 180 degrees) from the given angle, so we can subtract 118 from 180 to give us 62, which is angle c.

Hope this helps! :)

Answer: b=118 c=62

Step-by-step explanation: All angles add up to 360 degrees. We know one angle equals 118. We can also tell that angle b is identical to angle 118 because they are complementary angles. Now we add 118+118 which equals 236. Subtract 360 from 236. That gives us 124. Divide 124 by two since their are two angles. That gives us 62. c=62 and b=118

Answer:

YUH

Step-by-step explanation:

Answer:

you'll see...

Step-by-step explanation:

Given that the transformed graph is of function f(x) = (x + 2)^4 + 6 and the parent function g(x) = x^4

The transformed graph function g(x) was shifted two (2) units to the left and was translated six (6) units upward.

When the function is shifted to the right, the factor of x will be negative and when it's shifted to the left, the factor of x will be positive.

Therefore, function g(x) = x^4 is shifted 2 units to the left and translated 6 units upward to form f(x) = ( x + 2 )^4 + 6.

Answer:

p < 2

Step-by-step explanation:

hope this is right and have a good day

Answer:

Step-by-step explanation:

The nth term of an arithmetic sequence:  aₙ = a₁ + d(n - 1)

{d = common difference}

a₁ = 5

a₄ = 5 + d(4 - 1)

-4 = 5 + 3d

-4 - 5 = 3d

3d = -9

 d = -3

Therefore;

                  aₙ = 5 + (-3)(n - 1)

                   aₙ = -3n + 8

Check:  a₁₀ = 5 + (-3)(10 - 1) = 5 - 27 = - 22

The nth term of the sequence is Tn = 8 - 3n

The given parameters are:

a = 5, first term

T4 = -4 --- the 4th term

T10 = -22 --- the 10th term

The nth term of an arithmetic sequence is:

Tn = a + (n - 1) * d

So, we  have:

T4 = a + (4 - 1) * d

Substitute known values

-4 = 5 +(4 -1) * d

This gives

-4 = 5 + 3d

Subtract 5 from both sides

3d = -9

Divide by 3

d = -3

Recall that:

Tn = a + (n - 1) * d

So, we have:

Tn = 5 + (n - 1) * -3

Expand

Tn = 5 + 3 - 3n

Solve

Tn = 8 - 3n

Hence, the nth term of the sequence is Tn = 8 - 3n

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Im pretty sure the answer is A but if not then it is C

This is bcuz B doesn’t make sense because the graph doesn’t say anything close to 100 rides and D doesn’t make sense either.

Hope this helped.

Answer:

x= 8

Step-by-step explanation:

17x + 3 = 139

17x = 136

x = 8

Answer:

y+x = -4

Step-by-step explanation:

-4 indicates where the line intercept the y axis

if we put y=0 we can find where line intercepts the x axis.

it results x = -4

the two values are negative

At time t = 0, the capacitor in the circuit is charged to its maximum charge, qmax, and the circuit has zero current.

At t = 0, the capacitor in the circuit is fully charged, which means it has accumulated its maximum charge, qmax. The capacitor acts as a temporary energy storage device in the circuit. When the capacitor is fully charged, it contains potential energy. The charge on the capacitor creates an electric field, which opposes the flow of current through the circuit.

Since the capacitor is fully charged at t = 0, it resists any change in the current. Therefore, the circuit has zero current flowing through it. As time progresses, the capacitor will start to discharge, releasing the stored energy and allowing the current to flow. The discharge process is governed by the relationship between the voltage across the capacitor, the capacitance of the capacitor, and the resistance in the circuit.

Finally, at t = 0, the capacitor in the circuit is charged to its maximum capacity, qmax, and the circuit has zero current flowing through it.

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The type I error occurs when the null hypothesis is rejected, but in reality, the null hypothesis is true. In this case, the null hypothesis is "Carmin believes that her chemistry exam will only cover material from chapters four and five." The correct statement that corresponds to the type I error is option C: "Carmin believes that her chemistry exam will only cover material from chapters four and five when, in fact, it will not cover material only from chapters four and five."

A type I error is a false positive result, where the null hypothesis is incorrectly rejected even though it is true. In this scenario, if carmin believes that her chemistry exam will only cover material from chapters four and five, but in reality, the exam includes additional material beyond chapters four and five, it would be a type I error. Option C describes this situation, where Carmin believes the exam will cover only chapters four and five, but it actually includes material from other chapters.
Options A, B, and D do not correspond to a type I error because they either describe the correct belief or a different scenario where the null hypothesis is true.Therefore, option C represents the type I error in this context.

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Answer:

the number of users in the last year is 2,100

Step-by-step explanation:

The computation of the number of users in the last year is shown below:

Given that

The users are 2604 that are increased to 24% as compared with the last year

So, the users in the last year is

= 2604 ×100 ÷ 124

= 2,100

Hence, the number of users in the last year is 2,100

Answer:

688

Step-by-step explanation:

ithink

Answer: It is a polynomial, and the degree is 4.

Step-by-step explanation:  The degree is basically the biggest number exponent

Step-by-step explanation:

x xndndjjdjdjdowiekeie

Answer:

-5/4

Step-by-step explanation:

Answer:18

Step-by-step explanation:3^3 times 2