ALGEBRA In Exercises \( 12-17 \), find the values of \( x \) and \( y \). 13

Answer:

0 < x ≤ 11

Step-by-step explanation:

perimeter = (x - 6) + (x - 6) + x + x

⇒ perimeter = 4x - 12

If the perimeter is "at most 32" then

4x - 12 ≤ 32

⇒ 4x ≤ 44

⇒ x ≤ 11

Therefore,  0 < x ≤ 11

Answer:

The adult tickets cost £17.00 and child tickets cost £9.00

Step-by-step explanation:

2a + 3c = 61

2a = 61 - 3c

a = 30.5 - 1.5c

3(30.5 - 1.5c) + 5c = 96

91.5 - 4.5c + 5c = 96

91.5 + 0.5c = 96

0.5c = 4.5

c = 9

a = 30.5 - 1.5c

a = 17

The adult tickets cost £17.00 and child tickets cost £9.00

Thus, the average value of the function f(z) = 3z² − 2z on the interval [−3, 4] is 128/42.

To find the average value of the function f(z) = 3z² − 2z on the interval [−3, 4], we need to use the formula for the average value of a function over an interval. The formula is given as:

Average value = 1/(b-a) * ∫f(z) dz from a to b

where a and b are the lower and upper limits of the interval.

In our case, a = -3 and b = 4, so we have:

Average value = 1/(4-(-3)) * ∫3z² − 2z dz from -3 to 4

Simplifying the integral, we get:

Average value = 1/7 * [(3z³/3) - (2z²/2)] from -3 to 4

Average value = 1/7 * [(64/3) - (18/2) - (-27/3) + (6/2)]

Average value = 1/7 * [(64/3) - 9/2 + 9/3]

Average value = 1/7 * [(64/3) - 9/2 + 27/6]

Average value = 1/7 * [(128/6) - 27/6 + 27/6]

Average value = 1/7 * 128/6

Average value = 128/42

Therefore, the average value of the function f(z) = 3z² − 2z on the interval [−3, 4] is 128/42. This means that if we were to take all the values of the function on this interval and find their average, it would be equal to 128/42.

Know more about the average value

https://brainly.com/question/30460573

#SPJ11

Answer:

6

Step-by-step explanation:

Answer:

Point (0,6)

Step-by-step explanation:

Point (0,6) is the highest point plotted on the graph.

So the probability that the waiting time until the next call is more than three minutes is approximately 0.223.

The Poisson distribution is a probability distribution that describes the number of events occurring in a fixed interval of time or space, given that these events occur independently and at a constant rate.

In this case, we are dealing with the number of calls received at a call center, and we are told that the average time between calls is 2 minutes.

If the number of calls follows a Poisson distribution, we can use the Poisson probability formula to calculate the probability of getting a certain number of calls in a given time period.

However, in this case, we are interested in the waiting time until the next call, which is not directly related to the number of calls. To solve this problem, we can use the fact that the time between two consecutive calls follows an exponential distribution,

which is a continuous probability distribution that describes the time between two events occurring independently and at a constant rate.

The probability density function of the exponential distribution is given by f(x) = λe^(-λx), where λ is the rate parameter (i.e., the reciprocal of the average time between events) and x is the waiting time.

In this case, λ = 1/2 (since the average time between calls is 2 minutes), and we are interested in the probability that the waiting time until the next call is more than three minutes. This can be expressed mathematically as P(X > 3), where X is the waiting time.

To calculate this probability, we can use the cumulative distribution function (CDF) of the exponential distribution, which gives the probability that X is less than or equal to a certain value.

The CDF of the exponential distribution is given by F(x) = 1 - e^(-λx). Therefore, P(X > 3) = 1 - P(X ≤ 3) = 1 - F(3) = 1 - (1 - e^(-1.5)) = e^(-1.5) ≈ 0.223, So the probability that the waiting time until the next call is more than three minutes is approximately 0.223.

This means that there is about a 22.3% chance that the call center will not receive a call for more than three minutes, given that the calls arrive independently and at a constant rate.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

Step 1:

Re-state the given function.

Step 2:

We shall state the mathematical implication of the sine function at both minimum and maximum points.

At minimum point:

Step 3: We shall substitute the values in step 2 above in the given function.

We are only interested in the value at maximum point, so

Thus, the correct answer is 13 feet ( option D)

If we contrast the different parts, x1 = 3 2 = y1 and x2 = 4 4 = y2 are the results.

To show that preferences represented by min{x₁, x₂} satisfy monotonicity but not strong monotonicity, we need to demonstrate two things:

Preferences satisfy monotonicity: If xᵢ ≥ yᵢ for all i, then x ≽ y, and if xᵢ > yᵢ for all i, then x ≻ y.

Preferences do not satisfy strong monotonicity: There exist x and y such that xᵢ ≥ yᵢ for all i, but x ≠ y, and x ≰ y.

Let's address each of these points:

Monotonicity:

Suppose x and y are two bundles such that xᵢ ≥ yᵢ for all i. We need to show that x ≽ y and x ≻ y.

First, note that min{x₁, x₂} represents the minimum value between x₁ and x₂, and the same applies to y₁ and y₂.

Since x₁ ≥ y₁ and x₂ ≥ y₂, we can conclude that min{x₁, x₂} ≥ min{y₁, y₂}.

Therefore, x ≽ y, indicating that if all components of x are greater than or equal to the corresponding components of y, then x is weakly preferred to y.

However, if x₁ > y₁ and x₂ > y₂, then min{x₁, x₂} > min{y₁, y₂}. Hence, x ≻ y, indicating that if all components of x are strictly greater than the corresponding components of y, then x is strictly preferred to y.

Thus, preferences represented by min{x₁, x₂} satisfy monotonicity.

Strong Monotonicity:

To show that preferences represented by min{x₁, x₂} do not satisfy strong monotonicity, we need to provide an example of x and y such that xᵢ ≥ yᵢ for all i, but x ≠ y, and x ≰ y.

Consider the following bundles:

x = (3, 4)

y = (2, 4)

In this case, x₁ > y₁ and x₂ = y₂, so x ≻ y.

However,Thus, xᵢ ≥ yᵢ for all i, but x ≠ y, and x ≰ y.If we compare the individual components, x₁ = 3 ≥ 2 = y₁ and x₂ = 4 ≥ 4 = y₂.

Therefore, preferences represented by min{x₁, x₂} satisfy monotonicity but not strong monotonicity.

learn more about contrast from given link

https://brainly.com/question/2477099

#SPJ11

After solving the expression we get 3x² ₊ 6x ₊ 2 .

Given f(x) = 3x₊5

g(x) = 4x² ₋ 2

h(x) = x² ₋ 3x ₊ 1

f(x)  ₊  g(x) ₋ h(x)

substitute the values.

3x ₊ 5 ₊ 4x² ₋ 2 ₋ (x² ₋ 3x ₊ 1)

4x² ₊ 3x ₊ 3 ₋ x² ₊ 3x ₋ 1

3x² ₊ 6x ₊ 2

hence we get 3x² ₊ 6x ₊ 2 .

Learn more about Functions here:

brainly.com/question/15602982

#SPJ9

The derivative of the function f(t) = (7t + 4)/(5t − 1) at the point (3, 25/14) is -3/14.At the point (3, 25/14), the function f(t) = (7t + 4)/(5t − 1) has a derivative of -3/14, indicating a negative slope.

To evaluate the derivative of the function f(t) = (7t + 4) / (5t - 1) at the point (3, 25/14), we'll first find the derivative of f(t) and then substitute t = 3 into the derivative.

To find the derivative, we can use the quotient rule. Let's denote f'(t) as the derivative of f(t):

f(t) = (7t + 4) / (5t - 1)

f'(t) = [(5t - 1)(7) - (7t + 4)(5)] / (5t - 1)^2

Simplifying the numerator:

f'(t) = (35t - 7 - 35t - 20) / (5t - 1)^2

f'(t) = (-27) / (5t - 1)^2

Now, substitute t = 3 into the derivative:

f'(3) = (-27) / (5(3) - 1)^2

      = (-27) / (15 - 1)^2

      = (-27) / (14)^2

      = (-27) / 196

So, the derivative of f(t) at the point (3, 25/14) is -27/196.The derivative represents the slope of the tangent line to the curve of the function at a specific point.

In this case, the slope of the function f(t) = (7t + 4) / (5t - 1) at t = 3 is -27/196, indicating a negative slope. This suggests that the function is decreasing at that point.

To learn more about derivative, click here:

brainly.com/question/25324584

#SPJ11

In a binomial experiment with probability of success and trials is conducted, the probability of one trial is independent of another.

How to find the number of success in a binomial distribution?

The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial expression, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.

One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials. In other words, the probability of one trial do not influence those of the others.

Therefore, in a binomial experiment with probability of success and trials is conducted, the probability of onetrial is independent of another.

To learn more about binomial distribution refer to:

brainly.com/question/9325204

#SPJ4

Answer: x= 19/21.

Step-by-step explanation:

We can expand the expression to:

28x - 8x^2 - 35 + 10x -4x + 8x^2 - 4 + 8x = -1

We can then cancel the - 8x^2 and the + 8x^2 and simplify further by adding like terms:

38x - 35 + 4x -4 = -1 --> 42x - 39 = -1

We can then add 39 on both sides:

42x = 38

We can then divide both sides by the GCF (greatest common factor), 2:

21x = 19

We divide both sides by 21:

x = 19/21

Answer:

$90

Step-by-step explanation:

7200/80=90

Answer:

$111

Step-by-step explanation: 80 divided by 72 is 111.

Answer:

(26) (5) ( A ) Would be you answer. Have a Great day.

Step-by-step explanation:

Answer:

Your answer is A.

Step-by-step explanation:  

I got it right!

Answer:

C) x + 9 = x + 9

Step-by-step explanation:

An equation has infinite solutions if can simplify to the format: a = a, where a is any number.

This is because it means that any value you plug into x will give you the same true equation and answer.

C meets these requirements as it is already in format a=a, but if we further simplify it, we can see how it works:

Subtract x from both sides: 9=9

Subtract 9 from both sides: x=x

Subtract (x+9) from both sides: 0=0

We can see that C has infinite solutions because any value you put in for x, it will cancel itself out when you solve it, therefore it has infinite solutions.

E.g. x=5

(5) + 9 = (5) + 9

14 = 14

E.g. x=-25

(-25) + 9 = (-25) = 9

-16 = -16

We can also answer this question by solving all the other equations:

A) 2x + 5 - 2x = 2x - 2x + 8

5 = 8

This is not true so this equation has NO solutions.

B) 5x - 2x - 1 = 2x - 2x + 4

3x - 1 + 1 = 4 + 1

3x = 5

x = 5/3 (One solution)

D) I think you've missed a sign here, but it is solvable either way to get to one solution.

Hope this helped!

Answer: x³-21x+20=0

Step-by-step explanation:

To find which polynomial has 1, 4, -5 as the roots, all we have to do is equal each root to 0 and multiply all factors together.

1 is (x-1)=0

4 is (x-4)=0

-5 is (x+5)=0

Now, we just multiply them together.

(x-1)(x-4)(x+5)=0                       [FOIL]

(x²-4x-x+4)(x+5)=0                    [combine like terms]

(x²-5x+4)(x+5)=0                      [FOIL]

x³+5x²-5x²-25x+4x+20=0       [combine like terms]

x³-21x+20=0

Now we know x³-21x+20=0 is the polynomial with those roots.

Answer:

578.5

Step-by-step explanation:

Answer:

2 is the right answer

I say your answer

Angle L can be calculated as follows:

angle L = angle - 180 LMO stands for angle. MNO \sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

1. We know that sides AB and CD of trapezoid ABCD are parallel. We can use the tangent function to find the length of side AD because angle B is a right angle and angle ABD is 45 degrees:

AD/AB = tan(45)

AD=AB * tan(45) AD=AB

As a result, AD = 10.

2. We know that the sides PQ and RS of the trapezoid PQRS are parallel. We can use the sine function to find the length of side PS because angle Q is a right angle and angle PSQ is 60 degrees:

PS/QS sin(60) =

PS = sin * QS (60)

5 * sqrt = PS (3)

As a result, PS = 5*sqrt (3).

3. We know that the sides UV and WX of a trapezoid UVWX are parallel. We can use the cosine function to find the length of side WU because angle V is a right angle and angle WVU is 30 degrees:

WU/UV cos(30) =

UV * cos WU (30)

5 * sqrt(3) / 2 = WU

As a result, WU = (5/2)*sqrt (3).

4. We know that the sides LM and NO of the trapezoid LMNO are parallel. We can use the sine function to find the length of side MO because angle L is a right angle and angle MNO is 30 degrees:

MO/NO sin(30) =

MO = 4 / 2 MO = NO * sin(30)

As a result, MO = 2.

Because angles MNO and LMO add up to 180 degrees, we can calculate angle LMO as follows:

LMO angle = 180 - angle LMO MNO angle = 150 degrees

Finally, because angle N is a right angle, we can calculate angle L as follows:

angle L = angle - 180 LMO stands for angle. MNO\sangle L = 180 - 150 - 30 degree angle L = 0

As a result, angle L is 0 degrees.

To know more about Length visit:

https://brainly.com/question/30100801

#SPJ1

Answer:

Expressions: Student 1 and 4

Equations: Student 2 and 3

Step-by-step explanation:

Equations have an = sign. Expressions do not.

By definition of inverse function,

\(F\left(F^{-1}(x)\right) = x\)

so that

\(5F^{-1}(x) - 6 = x\)

\(5F^{-1}(x) = x + 6\)

\(F^{-1}(x) = \dfrac{x + 6}5\)

Similarly,

\(G\left(G^{-1}(x)\right) = G^{-1}(x) - 4 = x \implies G^{-1}(x) = x+4\)

Then the inverse of the composition \(F\circ G\) is such that

\(\left(F \circ G\right) \left((F \circ G)^{-1}(x)\right) = x\)

By definition of composition,

\((F\circ G)(x) = F(G(x))\)

Applying \((F\circ G)^{-1}\) to this recovers x, and this involves first inverting F, then G:

\((F\circ G)^{-1}(x) = G^{-1}\left(F^{-1}(x)\right)\)

So, we find

\((F\circ G)^{-1}(x) = G^{-1}\left(F^{-1}(x)\right) = G^{-1}\left(\dfrac{x+6}5\right) = \dfrac{x+6}5 + 4 = \boxed{\dfrac{x+26}5}\)

The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

Learn more about Rhombus at;

brainly.com/question/20627264

#SPJ1

complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

Is the relation a function:

To determine if the relation is a function, we need to check if there is exactly one output for each input.

Looking at the given set of points, we see that there are two points with an x-coordinate of -1: (-1, 3) and (-1, -2).

This means that there are two outputs for the same input, so the relation is not a function.

Therefore, the correct answer is: "No, because for each input there is not exactly one output."

Learn more about graphs at

https://brainly.com/question/19040584

#SPJ1

Answer:

C≈25.13ft

Step-by-step explanation:

C=2πr=2·π·4≈25.13274ft

The correct choice is the sequence is not monotonic. The sequence is bounded. The sequence converges, and the limit is -2 (option c).

The given sequence (-2) does not vary with the index n, as it is a constant sequence. Therefore, the sequence is both monotonic and bounded.

Since the sequence is bounded and monotonic (in this case, it is non-decreasing), we can conclude that the sequence converges.

The limit of a constant sequence is equal to the constant value itself. In this case, the limit of the sequence (-2) is -2.

Therefore, the correct choice is:

OC. The sequence is not monotonic. The sequence is bounded. The sequence converges, and the limit is -2.

To know more about sequence:

https://brainly.com/question/30262438

#SPJ4

The limit of the sequence is -2.

Given sequence is ((-2)}

To find the limit of the given sequence, we have to use the following formula:

Lim n→∞ anwhere a_n is the nth term of the sequence.

So, here a_n = -2 for all n.

Now,Lim n→∞ a_n= Lim n→∞ (-2)= -2

Therefore, the limit of the given sequence is -2.

Also, the sequence is not monotonic. But the sequence is bounded.

So, the correct choice is:

The sequence is not monotonic.

The sequence is bounded.

The sequence converges, and the limit is -2.

learn more about sequence on:

https://brainly.com/question/28036578

#SPJ11

Question: What is the Question?