The position of a swimmer below sea level is represented by –5 meters. The diver descends an additional 3 meters below sea level. Which expression describes the new position of the diver? Negative 5 + (negative 3) Negative 5 + 3 5 + (negative 3) 5 + 3 Mark

A price floor is a law that limits the minimum price at which a good, service, or factor of production can be sold while a price ceiling is a regulation that limits the maximum price at which a good, service, or factor of production can be sold

Price floors are commonly implemented to support producers, while price ceilings are typically put in place to protect consumers from higher prices that might result from shortages or monopolies.

Example of Price Floor:Agricultural subsidies are a common example of price floors. Government price floors ensure that farmers receive a minimum price for their crops.

If the market price of wheat falls below the government-established price floor, the government may buy the excess supply at the guaranteed price, ensuring that farmers are able to make a profit. If there is a price floor, the minimum price is set above the equilibrium price.

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a) The first five members of the sequence is

a1 = a0 + 2
a2 = a1 + 2 = a0 + 4
a3 = a2 + 2 = a0 + 6
a4 = a3 + 2 = a0 + 8
a5 = a4 + 2 = a0 + 10

b) The explicit formula for this sequence is:
an = 2n + a0, for n ≥ 0

A recursive sequence is a sequence where each term is defined in terms of the previous term(s). In this case, we have a sequence that is defined recursively.

Let's assume that the first term of the sequence is a0 and that the recursive formula for the sequence is given by:
an+1 = an + 2, for n ≥ 0

To find the first few terms of the sequence, we can apply the recursive formula repeatedly. Starting with a0, we get:
a1 = a0 + 2
a2 = a1 + 2 = a0 + 4
a3 = a2 + 2 = a0 + 6
a4 = a3 + 2 = a0 + 8
a5 = a4 + 2 = a0 + 10

From this, we can see that the sequence is simply the sequence of even numbers, starting with a0. So, the explicit formula for this sequence is:
an = 2n + a0, for n ≥ 0

To verify this formula using mathematical induction, we need to show that it holds for the base case (n = 0) and for the induction step (n+1).

For the base case, we have:
a0 = 2(0) + a0
a0 = a0

For the induction step, we assume that the formula holds for n and show that it also holds for n+1.

Assume that:
an = 2n + a0

Then, we have:
an+1 = an + 2    (by the recursive formula)
an+1 = 2n + a0 + 2   (substituting in the formula for an)
an+1 = 2(n+1) + a0   (simplifying)

Therefore, the formula holds for all n ≥ 0.

In conclusion, we have found the first 5 members of the sequence by applying the recursive formula, and we have found the explicit formula for the sequence by identifying a pattern in the first few terms. We have also used mathematical induction to verify the correctness of the formula.

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Answer:

k = -2

Step-by-step explanation:

\(f(x) = \frac{5}{2} x + 1 \\ g(x) = \frac{5}{2}x - 1 \\ \\ g(x) = f(x) + k \\ \frac{5}{2} x - 1 = ( \frac{5}{2} x + 1) + k \\ - 1 = 1 + k \\ k = - 1 - 1 \\ k = - 2\)

Lerchs-Grossman algorithm is a pit optimization software that helps in the determination of the most profitable final pit outline. The section of a copper porphyry ore body given has a cut-off grade of 0.45% Cu. Each block has dimensions of 16m x 16m x 16m (HxLxW).

The cost of mining a block of waste is $50, and the value of a block of ore is approximated to be $100 x (grade expressed in %). Firstly, we have to calculate the net present value (NPV) for all the blocks that are above the cut-off grade. NPV is calculated using the formula given below:

NPV = ((grade*100)*100)-50

Here, the cost of mining a block of waste is $50 and the value of a block of ore is approximated to be $100 x (grade expressed in %).

1. Firstly, the net present value (NPV) of each block above the cutoff grade is calculated.2. The blocks are then sorted in descending order of their NPVs.

3. Next, the algorithm calculates the limits of the pit at a sequence of levels, starting with the block of highest NPV.

4. It is assumed that the pit will extend downwards through the blocks from the highest NPV downwards.

5. If the pit reaches the edge of the ore body before reaching a certain level, it is truncated and the lower level is tried.

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The x-component of a vector of magnitude 6.20 pointing south is 0.

Since the vector is pointing south, it means it is in the negative y-direction. However, we are asked to find the x-component of the vector. Since the vector is purely in the y-direction (south), it does not have any x-component. Therefore, the x-component of the vector is 0.

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Answer:

Non-proportional.

Step-by-step explanation:

Membership fee of Rub-a-Dub Carwash = $100

Cost of every car wash in his visit = $12

Total payment Devon has to make in x car washes = $(12x + 100)

Graph of the relation between "total payment" and "number of visits", doesn't pass through origin. (having y-intercept = 100)

While for proportional relationship graph should pass through origin.

Therefore, this relationship is non-proportional.

Answer:

1) Y

2) Y

3) N

4) N

5) N

steps

1) How many bananas did Joe eat yesterday?

The word "many" tells you that its talking about variability.

2) What is the population of Austin, Texas?

The phrase "What is the population..." tells you that its talking about variability.

3) What kind of sandwiches does your class like?

Doesn't talk about variability.

4) What is the name of your teacher?

Doesn't talk about variability.

5) How much do televisions cost?

Doesn't talk about variability.

(YYNNN)

Answer:

p

=

2

(

4

x

+

3

)

+

2

(

2

x

−

6

)

or simplified  

p

=

12

x

−

9

Explanation:

By definition the perimeter of an object is the length of all its sides.

Also by definition, for a rectangle the 2 sides of the width are equal and the 2 sides of the length are equal.

Therefore the equation for the perimeter of a rectangle can be written as:

p

=

2

⋅

l

+

2

⋅

w

where  

p

is the perimeter,  

l

is the length and  

w

is the width.

Substituting what was given about the length and width gives the equation:

p

=

2

(

4

x

+

3

)

+

2

(

2

x

−

6

)

Simplifying this equation gives:

p

=

8

x

+

3

+

4

x

−

12

p

=

8

x

+

4

x

+

3

−

12

p

=

12

x

−

9

Step-by-step explanation:

Answer:

1000000

Step-by-step explanation:

Answer:

111

Step-by-step explanation:

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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The processes used to determine if a function is a state or path function include integration/differentiation and examining the differential form of the function. Integrating a function with respect to a variable yields a state function, while differentiating a function with respect to a variable yields a path function.

If the differential form of a function involves only state variables, it is a state function. If it involves both state and path variables, it is a path function.

To determine whether a function is a state or path function, we can examine the properties of the function and the variables involved. A state function depends only on the current state of the system and is independent of the path taken to reach that state. In contrast, a path function depends on the path taken to reach a particular state.

One common process used to determine the nature of a function is integration or differentiation. Integrating a function with respect to a variable yields a state function, whereas differentiating a function with respect to a variable yields a path function. For example, integrating the pressure (P) with respect to volume (V) yields a state function called the internal energy (U). On the other hand, differentiating the work (W) with respect to volume (V) yields a path function known as pressure (P).

Another process used is the examination of the differential form of the function. If the differential form of a function involves only state variables, then the function is a state function. For instance, the differential form of the enthalpy (H) involves only state variables (dH = dU + PdV), making it a state function. However, if the differential form involves both state and path variables, the function is a path function. An example is the differential form of heat (Q), which involves both state and path variables (dQ = dU + PdV), indicating that it is a path function.

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a. The measures of center, which is the mean are:

Mountain view school: 22.13

Seaside school: 19.53

b. The measures of variability which is the range, are:

Range for Mountain view school = 20

Range for Seaside view = 31

c. Seaside school has a typical smaller class size of 19.53, therefore, we would choose Seaside school.

Measures of centers and measures of variability are statistical concepts used to describe the distribution of a set of data.

Measures of centers are also known as measures of central tendency and are used to identify the central or typical value in a dataset. The three common measures of central tendency are the mean, median, and mode.

Measures of variability, also known as measures of spread or dispersion, are used to describe how much the values in a dataset vary from the central value. The three common measures of variability are range, variance, and standard deviation.

Part A: The measures of center we will use is the mean.

State out each of the data points and find the mean for each data set.

Data set for Mountain view school is: 10, 12, 18, 19, 20, 21, 23, 24, 24, 25, 25, 26, 27, 28, 30

Mean = sum of all data values / number of data values = 332/15 ≈ 22.13

Data set for Seaside school is: 5, 8, 10, 11, 12, 15, 16, 18, 25, 25, 27, 27, 28, 30, 36

Mean = sum of all data values / number of data values = 293/15 ≈ 19.53

Part B: The measures of variability we will use is the range

Range = highest value - lowest value

Range for Mountain view school = 30 - 10 = 20

Range for Seaside view = 36 - 5 = 31

Part C: The school with a typical mean smaller class size is the best to choose, which is: Seaside school.

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When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.

Firstly, ∠1 and ∠7 are alternate exterior angles as shown in the image, now to prove if these two angles will be congruent we can use the below proof.

First Method:

∠1  + ∠2 = 180° {Supplementary angles because both lies on the line q}

∠2 = (180° - ∠1)

Similarly, ∠2 = ∠6 = (180° - ∠1), corresponding angles are equal,

∠6 + ∠7 = 180° {Supplementary angles because both lies on the line r}

∠7 = 180° - ∠6

∠7 = 180° - (180° - ∠1)

∠7 = 180° - 180° + ∠1

∠7 = ∠1

OR

Second Method:

∠1 = ∠3 {Vertical angles formed by intersecting lines q and r}

∠3 = ∠5 {Alternate Interior angles}

∠5 = ∠7 {Vertical angles formed by intersecting lines s and r}

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For all n that is higher than or equal to 4, this statement is true.

By taking the cubes of both sides of the inequality, we can demonstrate this.

log2(n3) = \(3\sqrt{n}\)

n^(3/2) <= 3 * log2(n) (n)

Since log2(n) > 2 for n >= 4, we can write:

3 * 2 * (log2(n)) = 3 * n where n(3/2) = 3 * log2(n)

This suggests that:

\(\sqrt{n} =( \frac{3}{n{log 2}} + n) (n)\)

We come to the conclusion that the square root of n will eventually be less than or equal to log2(n3) for all n higher than or equal to 4 since the right-hand side of this inequality approaches zero as n goes to infinity. The assertion is accurate as a result.

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The compound amount for a deposit of $500 at an interest rate of 6% compounded quarterly for 3 years is approximately $595.01.

To calculate the compound amount, we can use the formula:

\(A = P(1 + r/n)^{nt}\)

Where:

A = Compound amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount (P) is $500, the annual interest rate (r) is 6% (or 0.06 in decimal form), the compounding periods per year (n) is 4 (quarterly), and the number of years (t) is 3.

Substituting these values into the formula:

\(A = 500(1 + 0.06/4)^{4*3}\\\\A = 500(1 + 0.015)^{12}\\A = 500(1.015)^{12}\\A = 500(1.195618355)\)

A =  $ 595.01

Therefore, the compound amount for a deposit of $500 at an interest rate of 6% compounded quarterly for 3 years is approximately $595.01, rounded to the nearest cent.

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After considering the given data and given set of options we conclude that sequence projects a divergence therefore the correct option is diverges.  

To estimate and find whether the sequence \(an = 3 + 5n^2 / 1+n\) converges or diverges, we can apply the following steps:
We can apply divison of both the numerator and denominator of the sequence by \(n^2\) to get an equivalent expression: \(an = (5/n) + 3n / (1/n + 1).\)
As n comes towards infinity, the term 5/n approaches zero and the term 3n approaches infinity.
Hence, the sequence diverges to infinity.
Finally, the sequence \(an = 3 + 5n^2 / 1+n\)diverges.
Then after carefully evaluating we can projects that,l the sequence diverges which can be seen in the given figure.
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1.2(3x+5)=3.6x+6

We move all terms to the left:

1.2(3x+5)-(3.6x+6)=0

We multiply parentheses

3.6x-(3.6x+6)+6=0

We get rid of parentheses

3.6x-3.6x-6+6=0

We add all the numbers together, and all the variables

=0

x=0/1

Hence, x = 0

Given all the weights and the total capacity of the elevator, we have the following expression:

where 'x' denotes the weight of the third case.

Solving for x, we get the following:

therefore, the third case must weigh 60.3 kg or less.

Answer:

47

Step-by-step explanation:

282 words in 6 minutes

? in 1 minutes

282÷6=47....

47×6=282

Answer:

157,9 pounds

Step-by-step explanation:

we know that he earn 12,50 per hour and that more  than 7 hour of work he earn x 1,4 than the normal.

1-  12,5 x 1,4= 17,5

2- 17,5 x 9 = 157,5

hope i helped u!!

Answer:

Slope = undefined

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1)

(6, 1)

(6, -6)

1 - (-6)/6 - 6= 7/0

Slope = undefined

For reference:

0/x = 0

x/0 = undefined

Hope this helps!

We are given that Mike has $36, if he spends 1/3 of this amount, the amount spent is the product of 36 and 1/3, that is:

Therefore, he spends $12 on the movie.

Now we are told that he spends 2/9 of the money, therefore, he spent:

In total, he spent $8 on the sandwich.

The money he has left is:

Therefore, he can't buy an $18 dollars book.

Answer: 8w is greater than or equal to 40 and the final answer is 8w is greater than or equal to 5

Step-by-step explanation:

The first step was to write an inequality. You take the number of weeks, w, and multiple it by 8 which is the number of toy cars he buys each weak to get to 40 or more. So the inequality is 8w is greater than or equal to 40. Now you divide both sides of the inequality by 8 which gives us the answer w is greater than or equal to 5.

The least amount of weeks it will take Trenton to have at least 40 cars in his collection is 5.

The compound interest is given by the equation CI = Amount - Principal , where A = P ( 1 + r/n )ⁿᵇ

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the principal amount be represented as P

Let the time period be represented as t = b

Let the number of periods the interest is applied be n

And , the rate of interest be r

Substituting the values in the equation , we get

The amount after b years is calculated by the formula

A = P ( 1 + r/n )ⁿᵇ

On simplifying the equation , we get the amount after b years

And , the compound interest is given by

CI = A - P , where A is the amount and P is the principal

Hence , the compound interest is solved

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Answer:

16.22%

Explanation:

The percent of increase can be calculated as:

Where vf is the final value and vi is the initial value. So, replacing vf by 10.75 and vi by 9.25, we get:

Therefore, the percent of the increase is 16.22%

Answer:

y = -(1/6)x - 6

Step-by-step explanation:

slope intercept form is

y = mx + b

m is the slope

b is the y-intercept

---------------------------

x + 6y = -24

Subtract x from both sides

6y = -x  - 24

Divide both sides by 6

y = -(1/6)x - 4

slope = -1/6

-----------------------------

Parallel lines have the same slope

therefor the parallel line is

y = -(1/6)x - 6

Answer:

I'd love to help but it seems you have not added an attachment or maybe the rest of the question..

Step-by-step explanation:

Answer:

Here is question number one's perimeter and area.

The points you are giving are really low so I will just do one