1 The functions f, g and h are defined as follows: 7X g(x) = (x+3) h(x)= + f(x) = 4x - 6 ( — 2 (a) a Find (0) (ii) the value of g(3) f(3-2b) [5 marks] Determine the inverse of the function h. [4 mar

Each pendant costs approximately $3.40.

Let's assume the cost of each pendant is represented by "x" dollars.

The total cost of the beads for all 6 necklaces is $2.50 per necklace, so the total cost of the beads is 6 * $2.50 = $15.

The total cost of the beads and pendants for all 6 necklaces is $35.40.

Therefore, we can set up the equation:

Cost of beads + Cost of pendants = Total cost

$15 + 6x = $35.40

To find the cost of each pendant, we can solve for "x" in the equation.

Subtracting $15 from both sides of the equation:

6x = $35.40 - $15

6x = $20.40

Dividing both sides by 6:

x = $20.40 / 6

x ≈ $3.40

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The solution of the inequality expression given as 12 + 4y < 32 is y < 5

An inequality expression is an expression where both sides of the expression have unequal values and they make use of any of the symbols <, >, <=, >= and !=

The inequality expression is given as

12 + 4y < 32

Subtract 12 from both sides of the inequality

So, we have the following expression

12 - 12 + 4y < 32 - 12

Evaluate the like terms in the above inequality

So, we have the following expression

4y < 20

Divide both sides of the inequality by 4

So, we have the following expression

4y/4 < 20/4

Evaluate the quotient

y < 5

Hence, the solution is y < 5

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Answer:

The answer is D: Max hasn't planted any but he says he can plant 20 flowers per hour. Reagan has planted 9 plants per hour in her mother's flower garden. Max says he will  finish planting the other 25.

Step-by-step explanation:

Answer:

If the second person's pay is 891, then the 5th should be 1002.

Answer:

-1

Step-by-step explanation:

Answer:

No, No, Yes, No, Yes, Yes

Step-by-step explanation:

A graph is a function if it passes the vertical line test (in other words, every vertical line that can be drawn intersects the graph at no more than one point).

This is because for a function, each input must map onto no more than one output.

Answer: Alternative optimal

Step-by-step explanation:

Alternative optimal solution means that

there are several optimal solutions that can be used to get identical objective function value.

Therefore, a scenario whereby the optimal objective function contour line coincides with one of the binding constraint lines on the boundary of the feasible region will lead to alternative optimal solution.

(a) Consider a regular graph, such as a regular 4-regular graph or a 4-cube. (b) It is not possible to have a graph with the given conditions.(c) It is not possible to have a graph with the given conditions. (d) Such a graph is possible.

(a) To have a graph with 16 vertices where every vertex has degree 4, we would need a total degree of 4 * 16 = 64. However, the total degree must be even since each edge contributes 2 to the total degree. But 64 is an even number, which means such a graph is possible. One way to construct such a graph is to consider a regular graph, such as a regular 4-regular graph or a 4-cube.

(b) In a graph with 15 vertices, if 8 vertices have degree 6, then the total degree would be 8 * 6 = 48. Similarly, if 7 vertices have degree 5, the total degree would be 7 * 5 = 35. However, the total degree must be even, and 48 and 35 are both odd numbers. Therefore, it is not possible to have a graph with the given conditions.

(c) If we have a graph on 14 vertices where every vertex has degree 3 and the shortest cycle has length 6, it implies that there are cycles of length 6 but no cycles of length less than 6. This contradicts the fact that if there is a cycle of length 6, there will also be cycles of length less than 6 (such as 3, 4, and 5). Therefore, it is not possible to have a graph with the given conditions.

(d) To have a graph on 11 vertices where every vertex has a degree of at least 6 and there are no cycles of length 3, we can consider a complete bipartite graph K(6, 5). This graph has 6 vertices of degree 6 and 5 vertices of degree 5. It satisfies the given conditions because every vertex has a degree of at least 6, and there are no cycles of length 3 since it is bipartite. Thus, such a graph is possible.

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Answer: Each person can get 12 cookies, or 12.2

Step-by-step explanation:

All you have to do is divide 61 by 5, your answer would 12 remainder 1, you would then divide 1 by 5 to get 0.2 . Add 12 and .2 to get your answer. The quotient would be 12 and the remainder 1.

The steps correcting the error;

Step 1: Convert the mixed fraction to improper fractions

Step 2: Find the lowest common  factor

27/8

A fraction can be defined as the part of a whole number, variable or element.

The different types of fractions are;

From the information given, we have that;

10 1/4 - 6 7/8

First, convert the mixed fractions to improper fractions, we have that;

Multiply the numerator of the fraction by the whole number then add the numerator

41/4 - 55/8

Find the LCM

82 - 55 /8

subtract the value

27/8

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Answer:

photo isn't clear, first of all u have to click clear picture

Answer: 94.3 meters

Step-by-step explanation:

1. The inference rule illustrated by the argument is the transitive property.

2. Based on the given information, the conclusion that can be reached is: If the weather turns bad, then the flight will be canceled.

1. The inference rule illustrated by the argument is the transitive property. It states that if a condition is true for one element, and that element implies another element, then the condition is also true for the second element.

In this case, the argument is using the transitive property to conclude that if Paul is a good swimmer (first element), and being a good swimmer implies being a good runner (second element), then Paul is also a good biker (third element).

2. Based on the given information, the conclusion that can be reached is: If the weather turns bad, then the flight will be canceled. This conclusion is derived from the statement "either the weather will turn bad or we will leave on time" and the fact that the flight will be canceled if the weather turns bad.

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Answer:

77 is 35% of:  220

Step-by-step explanation:

Answer:

b = y - mx

Step-by-step explanation:

So we are trying to solve for b in the equation y = mx + b. To do this, we will have to somehow get the b by itself on one side and all of the non-b parts of the equation on the other side.

y = mx + b

Subtract mx from both sides.

y - mx = b

b = y - mx

So we have not solved for b. We have found that b = y - mx.

I hope you find my answer and explanation helpful. Happy studying. :)

f(x) = 4. 8x² function can be used to compute the approximate area, in square inches, of a stop sign if it has a side length of x inches.

A function, which produces single output from either a single input, is an illustration of a rule. Alex Federspiel was contacted to collect the image. An illustration of this is the equation y=x2. For each input of x, there is simply one output of y. Considering that x is actually the input value, we would claim that y is just a rational number.

area = (# of sides * side length^2) / [4 * tan (180/n)]

area = (8 * x^2) / 4 * tan (22.5)

area = 8 x^2 / (4 * 0.41421)

area = 8 x^2 / 1.65684

area = 4.8 x^2

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The graph that accurately shows the velocity of the park or at any time is as shown in the attached image.

Velocity is defined as the rate of change of position of object with respect to time. Velocity is also defined as the speed of an object moving in a definite direction.

Velocity is a vector quantity and so it has both magnitude and direction. Its' SI unit is in meters per second.

The velocity of a particle is modeled by the function;

v(t) = ¹/₁₀(3t - 8)³ + 2

The given velocity function is cubic function and as such the attached graph shows the velocity of the particle at any time.

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The value of function, f(t) for L⁻¹ ( e−s /(s²+ 1)) is equals to sin( t - π ) u(t-π) .

The Laplace transform is the essential term of the given derivative function. Moreover, it comes with a real variable (t) for converting into complex function with variable (s). For ‘t’ ≥ 0, let ‘f(t)’ be given, the Laplace transform of ‘f(t)’, denoted by 'L{f(t)}' or ‘F(s)’ is definable with the equation:

\( L(f(t)) = F(s) = ₀∫^{ \infty } e⁻ˢᵗ f(t)dt\)

we have L⁻¹ ( e−s /(s²+ 1))

Now, L⁻¹ (1 /(s²+ 1)) = sin(t)

so, L⁻¹ ( e−s /(s²+ 1)) = sin( t - π ) u(t-π)

where u(t-π) is unit of step function.

so, required function f(t) is sin( t - π ) u(t-π).

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Complete question:

Find f(t) ℒ−1 (e−s /(s²+ 1))

f(t)=? + (?) (t - ?)

3x + 2y ≥ 120

you are asking me to confirm whether the below statement is true

10 * 3 + 45 *2 ≥ 120 ?

30 + 90 = 120

120 ≥ 120

its not greater but its equal which means it is a possible solution

Step-by-step explanation:

\(8 \times (10 + 7) = \bigg( \boxed{8 \times 10} \bigg)+ \bigg( \boxed{8 \times 7} \bigg)\)

y = 3/5x -1

3/5 is rise/run (slope) and -1 is the y-intercept

The 95% confidence interval for the mean weight of all the units is proved that is, (47.99, 54.01) ounces.

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

Confidence Interval = Sample Mean ± Margin of Error

First, we calculate the sample mean. Summing up all the weights and dividing by the sample size (8), we get:

Sample Mean = (50 + 48 + 55 + 52 + 53 + 46 + 54 + 50) / 8 = 49.75

Next, we need to calculate the margin of error. Since the population standard deviation is unknown, we can use the t-distribution. With a sample size of 8, the degrees of freedom (df) is 7. Consulting the t-distribution table at a 95% confidence level and df = 7, we find the critical value to be approximately 2.365.

Standard Error = Sample Standard Deviation / \(\sqrt{sample size}\)

Sample Standard Deviation = \(\sqrt{\frac{sum of squared deviations}{sample size-1} }\)

Calculating the standard error and sample standard deviation, we get:

Standard Error = \(\frac{\sqrt{(50.9375-49.75)^{2} +(48.9375-49.75)^{2} +...+(54.9375-49.75)^{2} }}{\sqrt{8-1} }\) ≈ 2.111

Sample Standard Deviation = \(\frac{\sqrt{(50.9375-49.75)^{2} +(48.9375-49.75)^{2} +...+(54.9375-49.75)^{2} }}{\sqrt{8-1} }\) ≈ 2.166

Finally, we can calculate the margin of error:

Margin of Error = t-value × Standard Error ≈ 2.365 × 2.111 ≈ 4.99

Plugging the values into the confidence interval formula, we get:

Confidence Interval = 49.75 ± 4.99 = (47.99, 54.01)

Therefore, we can be 95% confident that the mean weight of all the units falls within the interval (47.99, 54.01) ounces.

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The solution to the differential equation dy/dt + 2y = 0 where y(0) = 3 is y = 3e^(-2t).

The solution to the differential equation dy/dt + 2y = 0 can be found by separating the variables and integrating both sides.

First, separate the variables:
dy/dt = -2y

Next, integrate both sides:
∫dy/y = ∫-2dt

This gives us:
ln(y) = -2t + C

Now, solve for y:
y = e^(-2t+C)

Since we know that y(0) = 3, we can plug in 0 for t and 3 for y to solve for C:
3 = e^(C)
C = ln(3)

So the solution is:
y = e^(-2t+ln(3))

Simplifying further gives us:
y = 3e^(-2t)

Therefore, the solution to the differential equation dy/dt + 2y = 0 where y(0) = 3 is y = 3e^(-2t).

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x=hours

7.5=2.5x

3=x

x=3

3 hours until the power was restored

Answer:

Step-by-step explanation:

y - 6 ≥ -22

OR

y ≥ 16

Hope that helps!

In the given expression :

rate of change = 1

Initial condition = - 21

Answer:

Step-by-step explanation:

Given relationship:

It could be shown as:

The rate of change is 1 and the initial condition is -21.

Correct choice is B

The correct answer choice for the MPC (marginal propensity to consume) when the multiplier is 6 is not provided among the options A. 0.16, B. 0.83, C. 0.71, or D. 0.86.

The MPC is calculated as the ratio of the change in consumption to the change in income. When the multiplier is given, we can derive the MPC using the formula MPC = 1 / (1 + MPC). In this case, the multiplier is stated to be 6.

To find the corresponding MPC, we can solve the equation 1 / (1 + MPC) = 6 for MPC.

Rearranging the equation, we have 1 + MPC = 1 / 6. Subtracting 1 from both sides, we get MPC = 1 / 6 - 1 = -5 / 6.

The result MPC = -5 / 6 implies a negative MPC, which does not align with any of the given answer choices.

Additionally, all the answer choices provided (0.16, 0.83, 0.71, and 0.86) are positive values, further confirming that none of them represents the correct MPC when the multiplier is 6.

Therefore, the correct answer choice for the MPC when the multiplier is 6 is not listed among the options A. 0.16, B. 0.83, C. 0.71, or D. 0.86.

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The probability of selecting a pediatrician or a cardiologist at a medical convention can be found by adding the probabilities of selecting each. The probability is 12/19 or approximately 0.63.

The total number of participants at the medical convention is 7 + 5 + 3 + 4 = 19.

The probability of selecting a pediatrician is 7/19, since there are 7 pediatricians out of 19 participants.

The probability of selecting a cardiologist is 5/19, since there are 5 cardiologists out of 19 participants.

Since we are looking for the probability of selecting a pediatrician or a cardiologist, we can add these probabilities together:

P(pediatrician or cardiologist) = P(pediatrician) + P(cardiologist)

P(pediatrician or cardiologist) = 7/19 + 5/19

P(pediatrician or cardiologist) = 12/19

Therefore, the probability of selecting a pediatrician or a cardiologist is 12/19, or approximately 0.63 (rounded to two decimal places).

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