(Algebra 2) Using composition of functions, determine if the two functions are inverses of each other.

Answer:

Step-by-step explanation:

216 = S³

S = ∛216

S = 6 ft

The interest when the classmate is calculating the amount in a savings account after 10 years is $2600.

From the information, the classmate is calculating the amount in a savings account after 10 years and the deposit is $13,000 and the annual simple interest rate is 2%.

It should be noted that interest is calculated as:

= (Principal × Rate × Time) / 100

= ($13000 × 2 × 10) / 100

= $2600

The simple interest is $2600.

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The integration is (1/4)x sin 4x + (1/16)cos 4x + C.

To evaluate the integral ∫ x cos 4x dx using integration by parts, we need to use the formula ∫u dv = uv - ∫v du. We are given that u = x and dv = cos 4x dx. Now, we need to find v and du.

To find v, we need to integrate dv. So, v = ∫cos 4x dx = (1/4)sin 4x + C.

To find du, we need to differentiate u. So, du = dx.

Now, we can plug in the values of u, v, du, and dv into the formula and simplify:

∫ x cos 4x dx = x(1/4)sin 4x - ∫(1/4)sin 4x dx

= (1/4)x sin 4x - (1/4)∫sin 4x dx

= (1/4)x sin 4x - (1/4)(-1/4)cos 4x + C

= (1/4)x sin 4x + (1/16)cos 4x + C

So, the final answer is (1/4)x sin 4x + (1/16)cos 4x + C.

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The Laplace transform of the given function f(t) = {0, 0 < t < 1, t², t ≥ 1} is 2s⁻³.

Given the function f(t) = {0, 0 < t < 1, t², t ≥ 1}, we need to find its Laplace transform. The Laplace transform of a function f(t) is denoted by F(s) and is defined as follows:

F(s) = L{f(t)} = ∫[0,∞) f(t)e⁻ᵃˣdt,

where s is a complex variable.

To find the Laplace transform of the given function, we need to split the function into two parts: one for 0 < t < 1 and another for t ≥ 1. For 0 < t < 1, f(t) = 0, so the integral becomes:

L{0} = ∫ 0e⁻ᵃˣdt = 0.

For t ≥ 1, f(t) = t², so the integral becomes:

L{t²} = ∫ t²e⁻ᵃˣdt.

To evaluate this integral, we can use integration by parts. Let u = t² and dv = e⁻ᵃˣdt, then du/dt = 2t and v = (-1/s) e⁻ᵃˣ. Using the integration by parts formula, we get:

L{t²} = ∫ t²e⁻ᵃˣdt = (-t²/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s)∫[0,∞) te⁻ᵃˣdt.

The first term in the above equation evaluates to zero because e⁻ᵃˣapproaches zero as t approaches infinity. Using integration by parts again for the second term, we get:

L{t²} = (-t²/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s)(-t/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s²)∫[0,∞) e⁻ᵃˣdt.

The first two terms in the above equation evaluate to zero for the same reason as before. The integral in the last term evaluates to (1/s²), so we get:

L{t²} = 2/s³.

Therefore, the Laplace transform of the given function f(t) is:

L{f(t)} = L{0} + L{t²} = 0 + 2/s³ = 2s⁻³.

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Answer:

5/11

Step-by-step explanation:

1 5/6= 11/6

5/6 ÷ 11/6

5/6×6/11

30/66 = 5/11

The major influences on food habits are culture, family, personal taste and preferences, religion, and geography.

Additionally, socio-economic status, education, and media also play a significant role in shaping food habits. For example, exposure to different types of cuisines through media can broaden one's palate and lead to new food choices. Health considerations, such as allergies, diet restrictions, and weight management goals, can also influence what a person chooses to eat. Moreover, availability and cost of food items can affect the types of food people have access to and ultimately consume. Finally, social and peer pressure can also influence food choices, especially for younger people. Overall, there are many different factors that can influence a person's food habits and choices.

It's worth noting that food habits can also change over time as people's circumstances and priorities evolve. For instance, people may switch to healthier eating habits as they age or develop medical conditions that require dietary changes. Additionally, changes in personal circumstances, such as getting married or having children, can also impact food habits.

Moreover, advances in food technology and transportation have made a wider variety of food items available, regardless of geographic location. This has led to an increased exposure to new and exotic cuisines, further broadening people's palates and food habits.

In conclusion, food habits are shaped by a complex interplay of various factors, including cultural, social, economic, personal, and technological factors. These habits can change over time as people's circumstances and priorities change, leading to an ever-evolving landscape of food choices and preferences.

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The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%

Z- Score gives an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , mean = 80beats/minute

standard deviation = 10 beats/minute

x = 86 beats/minute

Applying z score formula :

z-score = (x-mean)/standard deviation

P(x>86) = P(z > 86-80/10)

=P(z>6/10)

=P(z>0.6) = 1 - P(z<0.6)

= 1 -0.7257

= 0.2742

Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742

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The numeric value of the function g(x) at x = -12 is given as follows:

g(-12) = -10.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the defined function or in the defined expression by the value at which we want to find the numeric value.

On the graph of a function, to find the numeric value for a value of x, we have to trace a vertical line at the value of x and verify where the vertical line crosses the function.

On the given graph, a vertical line at x = -12 would cross the function at y = -10, hence the numeric value is given as follows:

g(-12) = -10.

The graph of the function is presented at the end of the answer.

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It is unlikely that the projected rebounds in 15 shots will actually happen.

Total shots fired equals 10.

To find that there were 15 shots total.

Consider S to be the likelihood that your team will rebound and miss a shot.

P(S) = Number of rebounds / Total Number of outcomes

P(S) = 7/15

P(S) = 0.46

Consequently, it is unlikely that the projected rebounds in 15 shots will actually happen.

Thus, it is unlikely that the projected rebounds in 15 shots will actually happen.

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The complete question is-

During a basketball game, you record the number of rebounds from missed shots for each team.  How many rebounds should your team expect to have in 15 missed shots?

Picture for question is attached.

Answer:

No solution

Step-by-step explanation:

The lines are parallel because they have the same slope.

Elimination method also just gives you 3 = 7 which is not true, therefore no solutions.

Answer:

x = 9

Step-by-step explanation:

Unfortunately you didn’t provide the figure however we can use the picture below to work on:

from a property of the parallelogram (opposit angles) we know that angle 2 and 4 are equal in measure

then

5x - 28 = 3x - 10

then

5x - 3x = 28 - 10

then

2x = 18

then

x = 18/2

  = 9

Answer:

the answer is 76 degrees

Step-by-step explanation:

180-104=76

Answer:

M2=76°

Step-by-step explanation:

M1+M2=180° ......... Supplementary angles

104°+M2=180°

M2=180°-104°

M2=76°

By using the table of values, we have the following:

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).

In this exercise, you're required to determine the value of each function based on the value of x shown in the table above. Therefore, you would identify the input variable (x-value) that corresponds to the value of the output variable (y-value or f(x)) in the given table and vice-versa.

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The equation of the parabola that has a vertex of (0, 1) and a vertical stretch factor of 2 and reflected over the x-axis is g(x) = - 2 · x² - 2.

By the standard equation of the parabola with a vertex constant of 1 and a vertex of (x, y) = (0, 1) is described by the following formula:

y - 1 = x²                                      (1)

Besides, we need to apply two transformation rules:

Vertical stretch

g(x) = k · f(x), where k > 1          (2)

Reflection over the x-axis

g(x) = - f(x)                                 (3)

If we know that k = 2, then the image of the original parabola is:

f(x) = x² + 1

By vertical stretch and reflection over the x-axis:

g(x) = - 2 · (x² + 1)

g(x) = - 2 · x² - 2

The equation of the parabola that has a vertex of (0, 1) and a vertical stretch factor of 2 and reflected over the x-axis is g(x) = - 2 · x² - 2.

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Truckco manufactures two types of trucks: Type 1 and Type 2. Each type of truck must go through the painting shop and assembly shop.

If the painting shop were completely devoted to painting Type 1 trucks, then 804 per day could be painted; if the painting shop were completely devoted to painting Type 2 trucks then 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, then 1,500 per day could be assembled: if the assembly shop were completely devoted to assembling truck 2 engines, then 1,200 per day could be assembled.

Each Type 1 truck contributes $300 to profit: each Type 2 truck contributes $500.Truckco's objective is to maximize its profit. Let x1 be the number of Type 1 trucks and x2 be the number of Type 2 trucks .The constraints are as follows: Painting shop constraint: 804x1 + 700x2 ≤ P hours Assembly shop constraint: 1500x1 + 1200x2 ≤ A hour sNon-negativity constraints: x1, x2 ≥ 0Truckco's profit can be expressed as: Z = 300x1 + 500x2.

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To find the volume of the inscribed cube, we need to determine the edge length of the cube first. Let's denote the edge length of the inscribed cube as "x".

In a cube inscribed in a sphere, the diameter of the sphere is equal to the diagonal of the cube. Therefore, the diameter of the sphere is equal to the space diagonal of the large cube, which is given as 9 inches.

The space diagonal of a cube with edge length "a" can be found using the Pythagorean theorem:

Diagonal² = a² + a² + a²

Diagonal² = 3a²

Since the diameter of the sphere is 9 inches, we can write:

3a² = 9²

3a² = 81

a² = 81 / 3

a² = 27

a = √27

a = 3√3

Now we know the edge length of the large cube, which is 3√3 inches. The volume of a cube is given by V = a³, where "a" is the edge length.

Volume of the inscribed cube:

V = (3√3)³

V = 3³ * (√3)³

V = 27 * 3

V = 81 cubic inches

Therefore, the volume of the inscribed cube is 81 cubic inches.

The volume of the cube inscribed in the sphere, given the sphere is inscribed in a cube with an edge length of 9 inches, is 81 cubic inches.

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Answer:

Δ BEC ≅ Δ AED

Step-by-step explanation:

Consider triangles BCA and ADB. Each of them share a common side, AB. Respectively each we should be able to tell that AD is congruent to BC, and DB is congruent to CA, so by SSS the triangles should be congruent.

_________

So another possibility is triangles BEC, and AED. As you can see, by the Vertical Angles Theorem m∠BEC = m∠ADE, resulting in the congruency of an angle, rather a side. As mentioned before AD is congruent to BC, and perhaps another side is congruent to another in the same triangle. It should be then, by SSA that the triangles are congruent - but that is not an option. SSA does is one of the exceptions, a rule that is not permitted to make the triangles congruent. Therefore, it is highly unlikely that triangles BEC and AED are congruent, but that is what our solution, comparative to the rest.

Δ BEC ≅ Δ AED .... this is our solution

Answer: X 0 1 2 3 4 5 6 7 8 P(X=k) 0.05 0.07 0.13 0.12 0.20 0.25 0.07 0.03 0.08  the probability that more than 5 patients arrive at the hospital

What is the probability that more than 5 patients arrive at the hospital with flu-like symptoms between 12:00pm and 12:20pm?

Step-by-step explanation:

Group of answer choices

A. 0.43

B. 0.18

C. 0.82

D. 1

Part two of the question:

using the same information as stated before,

Match the probability statements with the correct probabilities.

(choose one answer)

The probability that X is less than or equal to 5.

A. 0.82 B. 0 C. 0.05 D. 0.48 E. 0.64 F. 1 G. 0.08 H. 0.52

The probability that X is greater than 7.

A. 0.82 B. 0 C. 0.05 D. 0.48 E. 0.64 F. 1 G. 0.08 H. 0.52

The probability that X is between 3 (noninclusive) and 7 (noninclusive).

A. 0.82 B. 0 C. 0.05 D. 0.48 E. 0.64 F. 1 G. 0.08 H. 0.52

The probability that no patients arrive in that interval.

A. 0.82 B. 0 C. 0.05 D. 0.48 E. 0.64 F. 1 G. 0.08 H. 0.52

Answer:

D.

is the correct answer

Answer:

a) (-4, 5)

b) (4, -5)

Step-by-step explanation:

Just reverse the signs or use desmos as a better example.

Answer:(4,-5) and (-4,5)

Step-by-step explanation: anything reflected from the x or y axis is the postive version which is  -4 has an absolute value of 4

Answer:

yes

Step-by-step explanation:

Answer:

x = 35° , y = 85°

Step-by-step explanation:

(2x+25) = (3x-10) // Reason: Vertical Angles are Congruent (have equal values)

Now we solve this...

2x+25 = 3x-10

25+10 = 3x-2x // Bring alike terms to one side

35 = 3x-2x

35 = x, so x = 35 °

-----

Now, to find y...

-----

We know that x is 35°, and we know that the two top angles in the picture are supplementary (meaning that they add up to 180°)

(2x+25) = 70 + 25 = 95

So 180° - 95° = y

y = 85°

Answer:

Exam??

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Function A) Rate of change is 6 because it represents 'm' from mx (6x).

Function B) Rate of change is 5 because there is an increase of 5 as it moves to the right.

Answer:

175 degrees

Step-by-step explanation:

So we see that this is a supplementary angle, which means it is equal to 180/ So set the equations up and solve for x:

\(180=29+(x-5)\\180=24+x\\156=x\\\)

Then, plug 156 back into the equation:

\(180-5\\175\)

Therefore, your answer is 175 degrees

Answer:

what exacly are you trying to figure out

Step-by-step explanation:

Answer:

I believe it is A

Step-by-step explanation:

When you subtract z1 from z2, you get 2-4i, which on the graph is point A.

Point A represents 2-4i in the graph given. Therefore, option (1) is the correct answer.

Given that, \(z_{1}=5-2i\) and \(z_{2}=3+2i\).

We need to find the value of \(z_{1}-z_{2}\).

A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.

Now, \(z_{1}-z_{2}\)=5-2i-(3+2i)

=5-2i-3-2i

=2-4i

Here, 4i is the imaginary and 2 real numbers.

Point A represents 2-4i in the graph given. Therefore, option (1) is the correct answer.

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Answer:

That is the shiniest fish tank I've ever seen!

Answer:

In order to find the surface area, you will need to add up the areas of each face of the prism. ... In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism. Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

Step-by-step explanation:

The function is given to be:

The object hits the ground when the function is equal to zero:

Solving the equation by factorization, we have:

Since the time cannot be negative, then the time will be 3 seconds.

Therefore, it will take 3 seconds for the object to hit the ground.

Answer:

A and E

Step-by-step explanation:

Given

20x² - 26x + 8 = 0 ( divide through by 2 )

10x² - 13x + 4 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 10 × 4 = 40 and sum = - 13

The factors are - 5 and - 8

Use these factors to split the x- term

10x² - 5x - 8x + 4 = 0 ( factor the first/second and third/fourth terms )

5x(2x - 1) - 4(2x - 1) = 0 ← factor out (2x - 1) from each term

(2x - 1)(5x - 4) = 0

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = \(\frac{1}{2}\) → E

5x - 4 = 0 ⇒ 5x = 4 ⇒ x = \(\frac{4}{5}\) → A