Solve the system of equations using the substitution method Show all work,
y = 5x - 7
3x + 2y = 12

2.4 is the mean for the given probability distribution.

To find the missing value required to create a probability distribution, we need to add the probabilities given for x = 0, 1, and 2. The sum of these probabilities is equal to 0.03 + 0.18 + 0.15 = 0.36.

The probability of x = 3 can be found by subtracting the sum of the probabilities for x = 0, 1, and 2 from 1. Therefore,

P(x = 3) = 1 - 0.36 = 0.64

Now, we can create the complete probability distribution as follows:

x / P(x)

0 / 0.03

1 / 0.18

2 / 0.15

3 / 0.64

To find the mean for the given probability distribution, we use the formula:

μ = Σ(x * P(x))

where Σ represents the sum of the products x * P(x) for all possible values of x. We can use the table above to calculate the sum as follows:

μ = (0 * 0.03) + (1 * 0.18) + (2 * 0.15) + (3 * 0.64)

μ = 0 + 0.18 + 0.3 + 1.92

μ = 2.4

Therefore, the mean for the given probability distribution is 2.4 (rounded to the nearest hundredth).

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Regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

This problem can be modeled as a game of incomplete information. The Inspector and Owner are players in the game, and each has two possible strategies: either choose container B, or switch to container C. The payoffs for each player depend on the strategy they choose and which container contains the counterfeit goods.

To solve this game, we can use backward induction. We start by considering the final decision point: whether to switch to container C after seeing that container A does not contain the counterfeit goods. Let's consider the two cases:

If the counterfeit goods are in container B, then the Inspector knows that container C also does not have the counterfeit goods. In this case, the payoff for choosing container B is 100 (if they find the counterfeit goods) or -100 (if they do not).

If the counterfeit goods are in container C, then the Inspector knows that container B does not have the counterfeit goods. In this case, the payoff for switching to container C is 100 (if they find the counterfeit goods) or -100 (if they do not).

Since the Inspector does not know which container has the counterfeit goods, they should choose the strategy with the higher expected payoff. To calculate the expected payoffs, we need to consider the probability that the counterfeit goods are in each container. Since the owner chose one container at random, each container has a 1/3 chance of containing the counterfeit goods.

If the Inspector chooses container B, the expected payoff is:

Expected payoff (choose container B) = (1/3) * 100 + (2/3) * (-100) = -33.33

If the Inspector switches to container C, the expected payoff is:

Expected payoff (switch to container C) = (1/3) * 100 + (2/3) * (-100) = -33.33

Therefore, regardless of what the Inspector chooses, their expected payoff is the same (-33.33). This means that the Inspector does not have a better option than choosing container B, and switching to container C does not improve their chances of finding the counterfeit goods.

For the Owner, if the Inspector chooses container B, then the Owner's expected payoff is:

Expected payoff (Inspector chooses container B) = (1/3) * (-100) + (2/3) * 100 = 33.33

If the Inspector switches to container C, then the Owner's expected payoff is:

Expected payoff (Inspector switches to container C) = (1/3) * (-100) + (2/3) * 100 = 33.33

Therefore, regardless of what the Inspector chooses, the Owner's expected payoff is the same (33.33). The Owner does not have a better option than waiting for the Inspector to choose container B.

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Answer:

I'm unsure, I've seen questions like this before but not this one

2x + 17 grows no faster than 3x as x approaches infinity.

To show that 2x + 17 is O(3x), we need to find two positive constants, C and k, such that:

|2x + 17| <= C|3x| for all x > k

We can start by simplifying the left-hand side:

|2x + 17| = 2x + 17 (since x is always non-negative)

Next, we can simplify the right-hand side:

|3x| = 3x

Now, we need to find C and k that satisfy the inequality:

2x + 17 <= C*3x for all x > k

Dividing both sides by 3x, we get:

(2/3) + (17/3x) <= C for all x > k

Since (2/3) is a constant, we only need to find a value of k such that (17/3x) is less than some other constant. Let's choose k = 1, then:

(17/3x) < 6 for all x > 1

So, we can choose C = 6 and k = 1. Therefore, we have shown that:

|2x + 17| <= 6|3x| for all x > 1

This satisfies the definition of 2x + 17 being O(3x), which means that 2x + 17 grows no faster than 3x as x approaches infinity.

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Answer:

300 gallons per hour.

Step-by-step explanation:

It takes 4 of 1/4 hours to make 1 hour. Now multiply gallons per quarter hour by four.

75 x 4 = 300

Answer:

22662

Step-by-step explanation:

Since the growth is exponential, your equation will be y = a • b^x. a being the beginning amount, b the percentage it increases by, and x is the time taken.

y = 14000 • 1.035^14

  = 22661.72

Round your answer since people can only be integers and your answer is a population of 22662  

The value of x is 4

Given that the median of the list 2x, 3x, 5x, and 8x is 12, we can arrange the list in order to find the value of x:

2x, 3x, 5x, 8x

To find the median, we need to find the middle value of the list. Since the list has an odd number of values, the median is the middle value.

2x < 3x < 5x < 8x

The median is 3x = 12, so x = 12/3 = 4

Therefore, the value of x is 4.

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The rate of change in altitude of the plane during the time is 625 ft/min.

Given the Parameters:

Altitude at 2.40 pm = 30000 feets

Altitude at 2.48 pm = 25000 feets

Rate of change = change in altitude/change in time

change in time = 2.48 - 2.40 = 8 minutes

change in altitude = 30000 - 25000 = 5000 feets

Rate of change = 5000/8 = 625 feets per minute

Therefore, the rate of change in altitude of the plane is 625 ft/min.

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The  \(13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12\)  equation can be used to calculate the surface area of the triangular prism.

It is given that the triangular prism net showing in the figure with dimensions.

It is required to find which equation can be used to find the surface area of the triangular prism net.

It is defined as the area of 3-dimensional geometry surfaces area sum which is occupying the outer area of the object.

We know the area of a rectangle = length × width

Area of the top rectangle = 13×10

Area of the middle rectangle = 12×10

Area of bottom rectangle=  5×10

The formula for finding the area of a triangle:

\(\rm A=\frac{1}{2} \times bh\)

Area of right triangle = \(\rm \frac{1}{2} \times 5 \times12\)

Area of left triangle = \(\rm \frac{1}{2} \times 5 \times12\)

The surface area = Area of top+ Area of middle+ Area of bottom+ Area of    

                                a right triangle+ Area of the left triangle  

\(=13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12\)

Thus, the \(13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12\)  equation can be used to calculate the surface area of the triangular prism.

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Answer:

8,1

Step-by-step explanation:

maybe i think this will help you

The total amount Lusac have in his savings after 3 more years with 1.8% saving interest is $1055.10.

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

\(I=\dfrac{Prt}{100}\)

Here, (I) is the interest amount earned on the principal amount of (P) with the rate of (r) in the time period of (t).

Lucas spends $83.42 in additional interest and charges on monthly payments as the result of a prior bankruptcy. The amount save in a year (12 months) is,

\(P=83.42\times12\\P=1001.04\)

The interest earned on this principal amount with earning 1.8% simple interest, after 3 years is,

\(I=\dfrac{1001.04\times1.83}{100}\\I=54.06\)

The total total amount in his bank account after 3 years is,

\(A=P+I\\A=1001.04+54.06\\A=1055.10\)

Hence, the total amount Lusac have in his savings after 3 more years with 1.8% saving interest is $1055.10.

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Answer:

b.

$1,055.10

Step-by-step explanation:

right on edg 22

Therefore, it will take approximately 13.7 years for the population to double.

a. To determine the growth rate, you need to calculate the percentage increase in population. The formula for growth rate is:

Growth Rate = (New Value - Old Value) / Old Value * 100

Using the given values, we have:

Growth Rate = (1577 - 1500) / 1500 * 100
Growth Rate = 77 / 1500 * 100
Growth Rate ≈ 5.13%

b. To write a general equation for the population, you can use the formula:

p(t) = p(0) * (1 + r/100)^t

where p(t) is the population at time t, p(0) is the initial population, r is the growth rate, and t is the number of years.

c. To estimate the population in 2010, we need to find the population at time t = 2010 - 2000 = 10 years. Using the general equation from part b, and substituting the given values:

p(10) = 1500 * (1 + 5.13/100)^10
p(10) ≈ 1500 * (1.0513)^10
p(10) ≈ 1500 * 1.6436
p(10) ≈ 2465.4

Therefore, the estimated population in 2010 is approximately 2465.

d. To find out how many years it will take for the population to double, we need to solve the equation:

2 * p(0) = p(0) * (1 + r/100)^t

Simplifying the equation, we have:

2 = (1 + r/100)^t

Taking the logarithm of both sides, we get:

log(2) = t * log(1 + r/100)

Finally, solving for t, we have:

t = log(2) / log(1 + r/100)

Substituting the growth rate from part a, we have:

t = log(2) / log(1 + 5.13/100)
t ≈ log(2) / log(1.0513)
t ≈ 13.7 years

Therefore, it will take approximately 13.7 years for the population to double.

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The equation of the given line is:

Slope intercept form is: y = -x + 6

Point slope form is: (y - 6) = -1(x - 0)

Standard form is: x + y = 6

The formula for the linear equation between two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

The two coordinates are:

(0, 6) and (1, 5)

Thus:

(y - 6)/(x - 0) = (5 - 6)/(1 - 0)

This can be simplified as:

(y - 6) = -1(x - 0)

It can be further written as:

y - 6 = -x - 0

y = -x + 6

The formula for linear equation in standard form is:

Ax + By = C

Thus, we have: x + y = 6

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The area of the triangle and the square are the same = 4 square units

How to determine the area?

You should know that the area talks about the floor space occupied by each shape.

The square occupies 2 units on the base and two units on the height

The triangle occupies two grids on the base and four grids on the height

Area of square is S² and Area of a triangle is 1/2base*height

⇒Area of square is = 2² = 4 ²square units

Area of triangle = 1/2 * 2 * 4 = 4 square units.

In conclusion the area of the triangle is equal to the area of the square with 4 units square each

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Answer:

\(y = \frac{2}{3}x + 4\)

Step-by-step explanation:

y = mx + b

4 = m(0) + b

b = 4

6 = m(3) + 4

2 = 3m

m = 2/3

(a) The two vectors and the path on a quadrant I plot: Given vectors: S = 2m  i  + 10m  j ;E = 8m  i  + 4m  j .Plotting the given vectors on the Cartesian plane, we get, Graphical representation of the given vectors
(b) A point on the path is a fraction f of the way between the start and the end. Write this as a vector equation involving f.If a point on the path is a fraction f of the way between the start and end points, then the position vector of this point can be given as:
P(f) = fE + (1 - f)S
= f(8m  i  + 4m  j ) + (1 - f)(2m  i  + 10m  j )
= (8f + 2 - 6f) m i  + (4f + 10 - 6f) m j
= (6f + 2) m i  + (6 - 2f) m j
So, the required vector equation is P(f) = (6f + 2) m i  + (6 - 2f) m j .
(c) Evaluate your expression from part (b) for f=0, P(0), and f=1, P(1).

Explain whether these results confirm if your expression in part (b) is reasonable or not.
For f = 0, P(0) = (6 × 0 + 2) m i  + (6 - 2 × 0) m j  = 2 m i  + 6 m j
For f = 1, P(1) = (6 × 1 + 2) m i  + (6 - 2 × 1) m j  = 8 m i  + 4 m j
These results are reasonable since P(0) is the starting vector S and P(1) is the ending vector E, which is as expected.

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Answer:

Step-by-step explanation:

First you have to figure out the total.  

42+23= 65

So plug it in.

23/65 = 35%

Your answer is 35%.

Hope this helped!!!!!!!!!!!!!!!!!

Answer:

35.4%

Step-by-step explanation:

Total of tiles:  42+23= 65 tiles

red tiles/ total amount of tiles

23/65= 0.3538= 35.38%

rounded to the nearest tenth= 35.4%

The following statements are true:

P(6) = P(1)

P(5) = One-half

P(>10) = 0

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

If A ⊂ S; A could be {1, 3, 5, 7, 9}

A breakdown of the probabilities of each statement being true or false:

P(6) = P(1): The probability of drawing a 6 or a 1 from a set of 10 numbers is 1/10, so P(6) = P(1) = 1/10.

P(5) = One-half: The probability of drawing a 5 from a set of 10 numbers is 1/10, so P(5) = 1/10 = one-half.

P(>10) = 0: There are no numbers greater than 10 in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, so P(>10) = 0.

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}: This is the set of all possible numbers that can be drawn from a set of 10 numbers.

If A ⊂ S; A could be {1, 3, 5, 7, 9}: A is a subset of S if all the elements of A are also elements of S. In this case, A = {1, 3, 5, 7, 9} is a subset of S because all the elements of A are also elements of S.

P(1 < x < 10) = 100%: There are 9 numbers in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} that satisfy the condition 1 < x < 10, and there are 10 total numbers in the set. Therefore, the probability that a number chosen at random from the set will satisfy the condition is 9/10 = 90%, not 100%.

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Complete question:

Ten identical slips of paper each contain one number from one to ten, inclusive. The papers are put into a bag and then mixed around.

Which statements about the situation are true? Check all that apply.

P(6) = P(1)

P(5) =

P(>10) = 0

P(1 < x < 10) = 100%

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

If A ⊂ S; A could be {1, 3, 5, 7, 9}

a) The probability that the score of a person more than 125 is 0.0478

b)  The probability that the score of a person between 90 and 110 is  0.4972

Let us assume that  X be a random variable that represents a random person's IQ

here the mean (μ) = 100 and standard deviation (σ) = 15

a) To find: the Probability that the score of a person more than 125

P(X > 125)

= 1 - P(X ≤ 125)

= 0.0478

b)  the probability that the score of a person between 90 and 110

P(90 ≤ X ≤ 110)

= P(X ≤ 110) - P(X ≤ 90)

= P(\(\frac{X-100}{15}\) ≤ \(\frac{110-100}{15}\)) - P(\(\frac{X-100}{15}\) ≤ \(\frac{90-100}{15}\))

= 0.4972

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The complete question is:

A randomly chosen IQ test taker obtains a score that is approximately a normal random variable with mean 100 and standard deviation 15. What is the probability that the score of such a person is (a) more than 125; (b) between 90 and 110?

Answer:

300ft^2

Step-by-step explanation:

The probability approach that we can apply when the possible outcomes of an experiment are equally likely to occur is classical probability.

Classical probability is also known as 'priori' probability. It is mainly used when the outcomes of the sample space are equally likely to occur. In other words, it is used when the probability of each event is the same.

C) Classical probability.

Probability theory is a very important part of mathematics. It is the branch of mathematics that deals with the study of random events and the occurrence of these events. It is used to study the likelihood or chance of an event taking place. There are four different types of probability approaches that we can apply depending upon the situation. These approaches are subjective probability, conditional probability, classical probability, and relative probability.

Each probability approach has a specific situation where it can be used.

Classical probability is one of the types of probability approaches that we can apply when the possible outcomes of an experiment are equally likely to occur. Classical probability is also known as 'priori' probability. It is mainly used when the outcomes of the sample space are equally likely to occur. In other words, it is used when the probability of each event is the same. Classical probability is the simplest type of probability.

It can be defined as the ratio of the number of ways an event can occur to the total number of possible outcomes. The probability of an event happening is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is usually represented in the form of a fraction or a decimal.Classical probability is mainly used in games of chance such as dice, cards, etc. In these games, each possible outcome is equally likely to occur. Therefore, the classical probability approach is used to calculate the probability of an event happening.

Classical probability is one of the types of probability approaches that we can apply when the possible outcomes of an experiment are equally likely to occur. It is mainly used when the outcomes of the sample space are equally likely to occur. It is usually represented in the form of a fraction or a decimal.

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Answer: 0.35

Step-by-step explanation:

Answer: There would be 2224 kilograms left in the truck

Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

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Answer:

if they have the same absolute value but different signs.

Step-by-step explanation:

Answer:

if they have the same absolute value but different signs. Opposites are the same distance from 0 on a number line, and they are on opposite sides of 0. The opposite of 0 is 0

Answer:

The correct option is;

D. y = 3·x - 5

Step-by-step explanation:

From the graph of the scatter plot created with Microsoft Excel, we have that the first and the last point describe a line of best fit, (with trend line equation included) therefore, we have;

The slope = (1 - (-7))/(2 - (-0.5)) = 3.2

Taking the slope of the line of best fit as approximately equal to 3, we have;

3.2 ≈ 3

The equation of the line in point and slope form is therefore;

y - 1 = 3 × (x - 2)

y = 3·x - 6 + 1

∴ y = 3·x - 5

Answer:

D

Step-by-step explanation: