Match each equation to the value(s) of x that make the equation true. Matching!
choices= (no real solution) (x=9) (x=3) (x= -7) (x-7)
A) 3(x-5) = 2(x-11)
B) 4(3x+7) -5 = 12x +8
C) 3(x+1) -2x = x+3

The breadth of the rectangle is 6 cm.

To find the breadth, we can use the formula for the perimeter of a rectangle:

Perimeter = 2 × (length + breadth)

Substituting the given values, we get:

18 cm = 2 × (3 cm + breadth)

Simplifying the right side of the equation, we get:

18 cm = 6 cm + 2 × breadth

Subtracting 6 cm from both sides of the equation, we get:

12 cm = 2 × breadth

Dividing both sides by 2, we get:

breadth = 6 cm

Therefore, the breadth of the rectangle is 6 cm.

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Answer:

Sullivan is hanging on by 2 fingers.

Step-by-step explanation:

Since Sullivan has 8 fingers, a quarter of them (1/4) would be 8*1/4=2.

The value for P(A | B) is 0.3 for P(B | A) is 0.2, P(A | A U B) is 0.625 and P(A | A ∩B) is 0.33

Total number of events = A and B

P(A) = 0.5

P(B) = 0.3

P(A ∩B) = 0.1,

The given questions will be solved by the concept of conditional probability

a.

P(A | B)

= P(A ∩ B) / P(B)

= 0.1 / 0.3 = 1/3 or 0.33.

b.

P(B | A)

= P(A ∩ B) / P(A)

= 0.1 / 0.5

= 1/5 or 0.2.

c.

P(A | A U B)

= P(A ∩ (A U B)) / P(A U B)

= P(A) / P(A U B)

= 0.5 / (0.5 + 0.3 - 0.1)

= 0.625

d.

P(A | A ∩B) = P(A ∩ B) / P(B)

= 0.1 / 0.3

= 1/3 or 0.33.

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Answer:

The circumference is:

\(C=84.8\: cm\)

Step-by-step explanation:

The pizza is a circle, so the circumference equation is given by:

\(C=2\pi R\)

Where:

Therefore, the circumference is:

\(C=2\pi*13.5\)

\(C=84.8\: cm\)

I hope it helps you!

Charles Revson's statement refers to the augmented level of the product among the three levels of the product concept.

The product concept consists of three levels: core product, actual product, and augmented product. The core product represents the fundamental benefit or service that the customer is seeking. The actual product is the tangible product itself, including its features, design, and packaging. The augmented product includes additional services or benefits that enhance the customer experience beyond the core and actual product.

Charles Revson's remark, "In the factory, we make cosmetics; in the store, we sell hope," suggests that he recognized the importance of going beyond the physical cosmetics and offering intangible benefits to customers. He understood that customers are not only buying a physical product but also seeking emotional and psychological satisfaction. By emphasizing the emotional experience and the hope that customers would feel when using Revlon cosmetics, Revson was highlighting the augmented level of the product.

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When dealing with replacement, there is always a certain degree of uncertainty as to what the next outcome will be. This is the reason theoretical probability predict on exact numbers of outcomes.

Theoretical probability is a branch of mathematics that deals with the study of the probability of events occurring based on the assumptions of certain conditions.

It involves the use of formulas and mathematical models to predict the likelihood of certain outcomes. However, it cannot predict the exact numbers of outcomes of a replacement because of the randomness involved in such events.

This is because the replacement process involves randomness, and the outcome of each trial is independent of the previous trials. Therefore, even though the theoretical probability may provide a reasonable estimate of the likelihood of certain outcomes, it cannot predict the exact numbers of outcomes with certainty.

For instance, consider a situation where you have a bag containing ten balls numbered from 1 to 10. You draw a ball, record its number, and then replace it before drawing again.

The theoretical probability of drawing any of the ten balls is 1/10, but it cannot predict the exact number of times a particular ball will be drawn. The outcome of each draw is independent of the others, and the replacement process involves randomness, making it impossible to predict the exact numbers of outcomes.

In conclusion, theoretical probability is a useful tool for predicting the likelihood of certain outcomes in various scenarios. However, when it comes to predicting the exact numbers of outcomes of a replacement, the randomness involved in the process makes it impossible to provide an exact prediction.

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To calculate the annual deposit Randy Hill needs to make, we can use the formula for the future value of an ordinary annuity:

\[ FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right) \]

Where:

FV = Future value (desired retirement amount)

P = Annual deposit

r = Interest rate per period

n = Number of periods (years in this case)

Plugging in the given values:

FV = $1,500,000

r = 0.10 (10% per year)

n = 20

\[ $1,500,000 = P \times \left(\frac{(1 + 0.10)^{20} - 1}{0.10}\right) \]

Simplifying the equation:

\[ P = \frac{$1,500,000}{\left(\frac{(1 + 0.10)^{20} - 1}{0.10}\right)} \]

Evaluating the expression:

\[ P \approx $26,189 \]

Therefore, Randy Hill needs to deposit approximately $26,189 each year to reach his goal of $1,500,000 in 20 years. Therefore, the correct answer is c) $26,189.

Looking at the graph we can see that around 25% of apartment residents pay between $700-749

And we also have around 4% that pay more than 749, then the total of residents that pay more than 700 will be

To match the answers we can round the 4% to 5%, which changes the result to

Therefore the correct result is 30%

Answer:

See below

Step-by-step explanation:

-1.8c + 5.1d   plug the numbers in that you were given.

-1.8(2.9) + 5.1(-4.2)

Multiply the first and second group of numbers

-1.8 x 2.9 = - 5.22

5.1 x -4.2 = - 21.42

Now add the two numbers together but remember they are both negative numbers.  So when you add them together, it will end up being a more negative number.

-5.22 + -21.42 = - 26.64

Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

The conditional probabilities are as follows: P(B | C) = 0.295, P(C | B) = 0.371, P(A | B) = 0.371, P(B | A) = 0.333, P(A | C) = 0.273, and P(C | A) = 0.308. These probabilities represent the likelihood of one event occurring given that another event has already occurred.

To determine the conditional probabilities, we can use the formula:

P(X|Y) = P(X ∩ Y) / P(Y)

where X and Y are events.

1. P(B | C):

P(B | C) = P(B ∩ C) / P(C)

P(B ∩ C) = P(B n C) = 0.13

P(C) = 0.44

P(B | C) = 0.13 / 0.44 = 0.295

2. P(C | B):

P(C | B) = P(C ∩ B) / P(B)

P(C ∩ B) = P(B n C) = 0.13

P(B) = 0.35

P(C | B) = 0.13 / 0.35 = 0.371

3. P(A | B):

P(A | B) = P(A ∩ B) / P(B)

P(A ∩ B) = P(A n B) = 0.13

P(B) = 0.35

P(A | B) = 0.13 / 0.35 = 0.371

4. P(B | A):

P(B | A) = P(B ∩ A) / P(A)

P(B ∩ A) = P(A n B) = 0.13

P(A) = 0.39

P(B | A) = 0.13 / 0.39 = 0.333

5. P(A | C):

P(A | C) = P(A ∩ C) / P(C)

P(A ∩ C) = P(A n C) = 0.12

P(C) = 0.44

P(A | C) = 0.12 / 0.44 = 0.273

6. P(C | A):

P(C | A) = P(C ∩ A) / P(A)

P(C ∩ A) = P(A n C) = 0.12

P(A) = 0.39

P(C | A) = 0.12 / 0.39 = 0.308

Therefore, the conditional probabilities are:

P(B | C) = 0.295

P(C | B) = 0.371

P(A | B) = 0.371

P(B | A) = 0.333

P(A | C) = 0.273

P(C | A) = 0.308

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To find the particle's speed at time t = 12 s, we need to find the magnitude of its velocity vector at that time. The velocity vector is the derivative of the position vector with respect to time.

c'(t) = (4, 16)

The magnitude of the velocity vector is calculated as:

|c'(t)| = sqrt((4)^2 + (16)^2)

       = sqrt(16 + 256)

       = sqrt(272)

       = 16.49 m/s (rounded to two decimal places).

Therefore, the particle's speed at t = 12 s is approximately 16.49 m/s.

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1. The frequency of the second harmonic is twice that of the fundamental frequency. The frequency of the second harmonic is, therefore, 120 Hz.

2. The 3rd, 9th, and 15th harmonics are triplen harmonics. Triplen harmonics are so-called because they are three times the fundamental frequency (50Hz). They are multiples of the third harmonic (150Hz) and are considered triplen harmonics.
3. A positive-rotating harmonic would be more damaging to an induction motor. Harmonics that rotate in the opposite direction to the fundamental frequency are referred to as negative-rotating harmonics. Positive-rotating harmonics are harmonics that rotate in the same direction as the fundamental frequency. Negative-sequence currents are created by negative-rotating harmonics, which cause a rotating magnetic field that rotates in the opposite direction to the fundamental frequency's magnetic field. This causes stator windings to heat up, which can cause a great deal of damage to an induction motor.
4. An ammeter should be used to determine what harmonics are present in a power system. An ammeter is used to determine the presence and quantity of current harmonics. It can also be used to compare the percentage of current distortion in the system with the maximum allowable percentage of current distortion, which is determined by the nature of the load.
5. The transformer's rating should be derated to avoid overheating. If an ammeter that indicates peak current is used instead of a true-RMS ammeter, the current reading is multiplied by 1.414 (the peak of the sine wave). The true-RMS current, on the other hand, is what creates heat in the transformer. The transformer should be derated to compensate for the current difference between the two meters. The derating factor can be found using the following equation:

true-RMS current/Peak reading x 100%. 94 A/204 A x 100%

= 46%.

The transformer should be derated by 46%.

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x-intercept -4.8

y-intercept 12

slope 2.5

plot points

x y

-2, 7

-1, 9.5

0, 12

1, 14.5

2 ,17

Answer:

Step-by-step explanation:

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Let's evaluate :

The name of the isotope of oxygen with a mass of 17 is "oxygen-17."

Isotopes are variants of an element that have the same number of protons but differ in  number of neutrons. Since the atomic mass of an atom is determined by the sum of its protons and neutrons, different isotopes of an element have different atomic masses.

In the case of oxygen, the most common and stable isotope is oxygen-16, which has 8 protons and 8 neutrons, giving it an atomic mass of 16. However, oxygen-17 is an isotopic variant of oxygen with one additional neutron, resulting in an atomic mass of 17.

By convention, the name of an isotope is written by appending the atomic mass to the name of the element. In this case, since the element is oxygen and the atomic mass is 17, the isotope is called "oxygen-17." This naming convention helps distinguish between different isotopes of an element based on their atomic masses.

The name of the isotope of oxygen with a mass of 17 is "oxygen-17."

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The horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

To determine the horizontal asymptote of a function, we need to examine the behavior of the function as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the terms involving x-2 and x-3 become insignificant compared to the higher power of (x-3) squared in the denominator.

As x approaches positive or negative infinity, the (x - 2) term in the numerator does not affect the overall behavior of the function. However, the (x - 3)^2 term in the denominator becomes dominant.

Since (x - 3)^2 will always be positive, the function is always positive or zero. Therefore, as x approaches positive or negative infinity, the function approaches zero or a positive value but never crosses the horizontal line y = 0. Hence, the horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

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The first law of thermodynamics is a fundamental principle in physics that states energy cannot be created or destroyed, only converted from one form to another. It can be expressed in terms of heat and work through the equation:

ΔU = q - w

where ΔU represents the change in internal energy of a system, q represents the heat added to the system, and w represents the work done on or by the system.

Now, let's address when the quantities q and w would be negative numbers.

1) When q is negative: This occurs when heat is removed from the system, indicating an energy loss. For example, when a substance is cooled, heat is extracted from it, resulting in a negative value for q.

2) When w is negative: This occurs when work is done on the system, decreasing its energy. For instance, when compressing a gas, work is done on it, leading to a negative value for w.

In both cases, the negative sign indicates a reduction in energy or the transfer of energy from the system to its surroundings.

In summary, the first law of thermodynamics can be expressed as ΔU = q - w, and q and w can be negative numbers when energy is lost from the system through the removal of heat or when work is done on the system.

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Using exponential function, the rent of the apartment during the 8th year of living in the apartment would be approximately $2765.5.

What is an exponential function?

The formula for an exponential function is \(f(x) = a^x\), where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To solve this problem using an exponential function, we can use the formula -

\(y = a \times (1 + r)^t\)

where -

y is the final value we want to find (in this case, the rent in the 8th year)

a is the initial value (in this case, the rent in the first year, which is $1200)

r is the growth rate per period (in this case, 11% per year, or 0.11)

t is the number of periods (in this case, 8 years)

Plugging in the values in the equation, we get -

\(y = 1200 \times (1 + 0.11)^8\)

y = 1200 × 2.30453777

y = 2765.44532

Rounding to the nearest tenth, we get -

y ≈ $2765.5

Therefore, the rent of the apartment value is obtained as $2765.5.

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Answer:

2.5(x)/10 = 50/200

Step-by-step explanation:

hope that helps :)

So 50/200=0.25

therefore, x has to be divided by 10 and be equal to that number, so 2.5/10=0.25 but let's do it with steps

1) Simplify or combine like terms (in this case we need to simplify 50/200 which is 0.25)

2) To isolate x, do the opposite operation on BOTH SIDES.

x/10 ×10 cancels out the 10

x=0.25×10

x=2.5

The 2008 AP Multiple Choice AB answers and solutions can be found on the College Board website or through other online resources.

However, it is important to remember that simply looking up the answers will not help you in the long run. It is important to understand the concepts and methods behind each question in order to be successful on the AP exam.

Here are the answers to the 2008 AP Multiple Choice AB exam:

1. B
2. D
3. C
4. B
5. A
6. D
7. D
8. C
9. B
10. D
11. C
12. B
13. D
14. A
15. D
16. B
17. C
18. D
19. A
20. D
21. B
22. C
23. D
24. B
25. C
26. D
27. A
28. B

It is important to remember that simply knowing the answers will not guarantee success on the AP exam. It is important to understand the concepts and methods behind each question in order to be successful. If you are having difficulty with a particular question or concept, it is recommended that you seek out additional resources or assistance from a teacher or tutor.

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Answer:

69

Step-by-step explanation:

The median is the middle number.  Using the box and whisker box, the median is the middle line in the box.    The line is at 69 for  Genevieve

A perfectly competitive firm will produce 10 units of output at a market price of $50 by setting its marginal cost (SRMC) equal to the market price: 2q + 30 = 50. The short-run supply function of this firm is q = 10 when p = $50.

a. If the market price is $50, this firm will produce the output level at which the marginal cost (SRMC) equals the market price. To find this output level, we set the marginal cost equal to the market price:

2q + 30 = 50

2q = 20

q = 10

So the firm will produce 10 units of output at a market price of $50.

It is not necessarily true that $50 is a long-run equilibrium price. In the long run, a perfectly competitive firm will exit the market if the market price is lower than its average total cost, and it will enter the market if the market price is higher than its average total cost. Therefore, to determine if $50 is a long-run equilibrium price, we need to know the firm's average total cost.

b. The short-run supply function of a perfectly competitive firm is the relationship between the market price and the quantity of output that the firm is willing and able to produce. It is found by combining the cost function (SRTC) and the profit-maximizing rule (producing at the level where marginal cost equals the market price).

The equation of the short-run supply function is:

q = (50 - 30)/2 = 10 units of output at a market price of $50

So the short-run supply function of this firm is:

q = 10 when p = $50

Complete Question:

A perfectly competitive firm has the following short-run cost function: SRTC = q2+30q+400

The corresponding short-run marginal cost function is given by: SRMC = 2q + 30

a. If the market price is $50, how much output will this firm produce? Is $50 a long-run equlibrium price? Explain your reasoning.

b. Find the equation of this firm's short-run supply function.

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The answer is (D), the function has at least one zero in the set of complex numbers, is correct.

What is the polynomial function?

A polynomial function is defined as a function in which the highest power of the independent variable is finite. The degree of a polynomial function is equal to the highest power of the independent variable.

In this case, the highest power of x is x^5, so the degree of the function is 5.

Therefore, the answer is (D), the function has at least one zero in the set of complex numbers, is correct.

All polynomial functions have at least one zero in the set of complex numbers by the Fundamental Theorem of Algebra. The other answers (A), (B), and (C) are incorrect.

Hence, the answer is (D), the function has at least one zero in the set of complex numbers, is correct.

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When the height of the prism doubles, the percentage increase in the volume is 100%

The volume of a prism is:

V₁ = BH

Where:

B represents the base area and H represents the height.

When the height doubles, the volume becomes

V₂ = 2BH

The percentage increase is then calculated using:

%Increase = (V₂ - V₁)/V₁

So, we have:

%Increase = (2BH - BH)/BH

Evaluate

%Increase = 1

Express as percentage

%Increase = 100%

Hence, the percentage increase is 100%

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Answer:

The length of row = 3.2 inches.

Step-by-step explanation:

The length of a chocolate = 4/5 inch

Total number of chocolate pieces placed = 4

Now we have given the length of one chocolate and it is required to find the total length of the row when four chocolates are placed end to end. So in order to find the length of the chocolate row we have to multiply the size of one chocolate by the number of chocolates.

The length of row = Length of one chocolate × number of chocolates

The length of row = 4/5 × 4

The length of row = 3.2 inches.

The piece of chocolate and the number of chocolates in a row can be represented using equations.

A row of chocolate is 3.2 inches long

Given that:

\(L = \frac 45\)  ---- Length of a piece

\(n =4\) --- number of chocolate pieces

The length of the chocolate in a row is calculated as follows:

\(Length = n \times L\)

So, we have:

\(Length = 4 \times \frac 45\)

\(Length = 4 \times 0.8\)

\(Length = 3.2\)

Hence, a row of chocolate is 3.2 inches long

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(I) The proportion of times we get a red candy will approach 0.2 as the number of trials increases. (m) The probability of winning at a 'daily number' lottery game is 1/1000 implies that if we play the game repeatedly, the proportion of times we win will approach 1/1000 as the number of plays increases. (n) Saying there is a 30% chance of rain tomorrow indicates that if we observe the occurrence of rainy days over a long period. (o) If 70% of the adult American population wants to retain the penny, then randomly selecting. (p) If we take multiple random samples of 100 people from the adult American population.

(I) The long-run relative frequency definition of probability states that if we repeatedly select M&M candies at random from a large bag, the proportion of times we get a red candy will approach 0.2 as the number of trials increases.

(m) The long-run relative frequency definition of probability states that if we play the 'daily number' lottery game repeatedly, the proportion of times we win will approach 1/1000 as the number of plays increases.

(n) The long-run relative frequency definition of probability states that if we observe the occurrence of rainy days over a long period of time, the proportion of days with rain will approach 30% as the number of days observed increases.

(o) The long-run relative frequency definition of probability states that if we randomly select individuals from the population of adult Americans repeatedly, the proportion of individuals who want to retain the penny will approach 0.70 as the number of selections increases.

(p) The long-run relative frequency definition of probability states that if we take multiple random samples of 100 people from the population of adult Americans, the proportion of samples in which the sample proportion exceeds 0.80 will approach 0.015 as the number of samples increases.

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The first statement is true. As stepwise selection starts with an empty model  and add predictors. The second statement is true. As predictors  is removed.

1. True. In the forward stepwise selection method, the predictors in the k-variable model are a subset of the predictors in the (k+1)-variable model. This is because forward stepwise selection starts with an empty model and adds predictors one by one based on their ability to improve the model's performance.

2. True. In the backward stepwise selection method, the predictors in the k-variable model are also a subset of the predictors in the (k+1)-variable model. Backward stepwise selection starts with a full model containing all predictors and removes them one by one based on their contribution to the model's performance. When a predictor is removed, the remaining predictors form a subset of the original set.

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The number Mrs. Gardner thought of is: 52.

To find the number we must take into account all the clues they give us, for example:

The number is not odd and as such we know the number is even.

The sum of their numbers is 7.

Thus:

1 + 6, could be 16 or 61

2 + 5, could be 25 or 52

3 + 4, could be 34 or 43

It is a multiple of 13.

The only possible multiple of 13 is 52.

52 ÷ 13 = 4

Is greater than 4 × 5 = 20

52 > 20

It is a multiple of 4.

52 ÷ 4 = 13

It is less than 7 × 8 + 23 = 79.

52 < 79

The number Mrs. Gardner thought of is 52.

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