The amount P of pollution varies directly with the population N of people. City A has a population of 468,000 and produces 260,000 tons of pollutants. Find how many tons of pollution we should expect City B to produce, if we know that its population is 350,000.​

The solution is given below.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The perimeter of a rectangle is 40 cm. The length is 14 cm.

Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.

Fran says she can find the width using the equation 2x + 28 = 40.

now, we get,

1. Divide both sides by 2

 2(x+14) = 40

 x+14 = 20

2. Isolate the x term by subtracting 14 from both sides

3. x = 6. The width of the triangle is 6 cm.

4. Isolate the x term by subtracting 28 from both sides

 2x + 28 = 40

 2x = 12

5. Divide both sides by 2

6. x = 6

7. The two equations have the same solution, because by the distributive rule, 2(x+14) = 2x+28.

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The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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Answer:

4

Step-by-step explanation:

26x+6 - 12x +2 = 14x +4

60-4 = 56

56/14=4

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer: 1 mile

Step-by-step explanation:

Well it's 1 because half of 2 is 1, so Zachary ran 1 lap around the lake.

Answer:

The answer is A because sixteen divide by two equals eight also two is common

Three minutes equal 180 beats on the double number line. three minutes of 270 beats 2:180=90 , 3:270=90

In music, a beat is a pulse that occurs repeatedly. Simple meters are those in which the beat first breaks into two, and subsequently into four. There are two beat groups in double meters, three beat groups in triple meters, and four beat groups in quadruple meters.

For double, triple, and quadruple meters, there are several conducting patterns. One group of beats equals one measure (duple, triple, or quadruple). Bar lines divide the measures. Simple meters' time signatures specify two things: the beat unit, or note value that represents the beat, and the number of beats in each measure (the top number). Notes are graphically grouped by beat and connected by a beam.

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1. The preparation of the journal entries for Wildhorse Company is as follows:

Date              Account Titles and Explanation     Debit      Credit

July 1, 2022: Cash                                              $98,000

                     Notes Payable                                              $98,000

Nov. 1, 2022: Cash                                          $101,000

                      Notes Payable                                           $101,000

2. The preparation of the adjusting entries for Wildhorse Company is as follows:

Date                 Account Titles and Explanation     Debit      Credit

Dec. 31, 2022: Interest Expenses                         $3,920

                        Interest Payable                                           $3,920

Dec. 31, 2022: Interest Expense                             $1,010

                        Interest Payable                                           $1,010

3. The preparation of the journal entries for Wildhorse Company is as follows:

Date              Account Titles and Explanation     Debit      Credit

Feb. 1, 2023: Interest Expense                           $505

                      Interest Payable                          $1,010

                     Notes Payable                         $101,000

                     Cash                                                           $102,515

Apr. 1, 2023: Interest Expense                         $1,960

                     Interest Payable                         $3,920

                     Notes Payable                         $98,000

                     Cash                                                        $103,880

Adjusting journal entries are made at the end of the financial period to agree with the accounting records according to the accrual concept of generally accepted accounting principles.

Other journal entries are made to recognize the business transactions in the accounting records as they occur.

July 1, 2022: Cash $98,000 Notes Payable $98,000 (9-month, 8% note)

Nov. 1, 2022: Cash $101,000 Notes Payable $101,000 (3-month, 6%)

Dec. 31, 2022: Interest Expenses $3,920 Interest Payable $3,920

Dec. 31, 2022: Interest Expense $1,010 Interest Payable $1,010.

Feb. 1, 2023: Interest Expense $505 Interest Payable $1,010 Notes Payable $101,000 Cash $102,515

Apr. 1, 2023:Interest Expense $1,960  Interest Payable $3,920 Notes Payable $98,000 Cash $103,880

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A. The y-intercept is at the point (0, 0).

B.  The zeros are x = 0 or x = ±√5

C.

A) The y-intercept of this graph is the point where x = 0.

When  x = 0, the value of y

= 0^4 - 5*0^2

= 0.

Therefore, the y-intercept is at the point (0, 0).

B) The x-intercepts/roots of the function are the values of x that make y = 0.

To find these values, we need to set y = 0 and solve for x:

x⁴ - 5x² = 0

x⁴ = 5x²

x² = x⁴/5

x = ±√(x⁴/5)

We can simplify this expression by factoring x² out of both sides:

x²(x² - 5) = 0

x² = 0 or x² - 5 = 0

x = 0 or x = ±√5

hence the x-intercepts are at x = 0 and x = ±√5.

C) The end behavior of this function refers to how the graph of the function approaches the x-axis as x approaches positive infinity and negative infinity.

x → ∞ f(x) → ∞

x → -∞ f(x) → -∞

D) The graph is attached

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Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.

We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.

We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.

Answer:

Theres more than one answer so b and a

Step-by-step explanation:

The car salesperson made $62,000 in sales for the month

Let us say the amount of sales the car salesperson made in a month is x. Then, the total income can be represented as:

$1,400 + 0.05x = $4,500

The equation represents the total income of the car salesperson as the base salary of $1,400 per month plus a commission of 5% on sales. To find the amount of sales made, we have to solve x.

Subtracting $1,400 from both sides:

0.05x = $4,500 - $1,400 = $3,100

Dividing both sides by 0.05:

x = $3,100 / 0.05 = $62,000

So the car salesperson made $62,000 in sales for the month.

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In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

The  given standard error of the mean for a sample of 100 is 30. So to cut the standard error of the mean to 15, we have to proceed by increasing the sample size to 400.

The  formula for evaluating the standard error of mean
SEM = SD / √(n)
here, SEM = standard error of the mean,
SD = standard deviation
n = sample size
Staging the values
15 = SD / √(100)
15 x √(100) = SD
SD = 150
Now evaluating for the value of n
15 = 150 / √(n)
15 x √(n) = 150
√(n) = 10
n = 100
Now looking at the formula, we need to decrease SEM by half,

So we proceed by increasing the  sample size by a factor of 4.

In the event of shortening the standard error of mean to 15 we have to increase the size to 400. Therefore, the correct answer is Option B.

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Answer:

Step-by-step explanation:

Answer:

Sure! Let’s solve this equation step by step.

(7000).03 + (x).05=830

First, we can simplify the left side of the equation:

210 + 0.05x = 830

Next, we can subtract 210 from both sides:

0.05x = 620

Finally, we can divide both sides by 0.05 to solve for x:

x = 12400

So the solution to the equation (7000).03 + (x).05=830 is x = 12400.

Answer:y=50

Slope is zero

Step-by-step explanation:

50-50/25--25=0/50=0

Answer: y=50

Step-by-step explanation:

did it on edge 2020

Answer: i) 12.5%       ii) 87.5%        iii) 23.4%

Step-by-step explanation:

There are two die, each with 8 sides so the total number of outcomes is 8²

i) Product is a prime number --> 2, 3, 5, 7

Since it is a prime we only have the option of one die being a 1 and the other being the prime number.

So possible successful outcomes is: (1, 2), (1, 3), (1, 5), (1, 7), (7, 1), (5, 1), (3, 1), and (2, 1) = 8 options.

\(\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{8}{8^2}=\dfrac{1}{8}=\large\boxed{12.5\%}\)

ii) Not a perfect square.  Let's find the probability that it IS a perfect square and subtract that value from the total (64).

Product IS a perfect square --> 1, 4, 9, 16, 25, 36, 49, 64

Possible successful outcomes of a perfect square: (1, 1) (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8) = 8 options.

Product is NOT a perfect square = 64 - 8 = 56 options

\(\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{56}{8^2}=\dfrac{7}{8}=\large\boxed{87.5\%}\)

iii) Product is a multiple of 5 --> 5, 10, 15, 20, ,25, 30, 35, 40,

Possible successful outcomes of a multiple of 5: (1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (7,5), (8, 5), (5, 8), (5, 7), (5, 6), (5, 4), (5, 3), (5, 2), (5, 1) = 15 options

\(\dfrac{successful\ outcomes}{total\ possible\ outcomes}=\dfrac{15}{8^2}=\dfrac{15}{64}=\large\boxed{23.4\%}\)

You are limited to 3 questions on Brainly so hopefully you can follow what I did to answer the last two questions (less than or equal to 21) and (divisible by 4 or 6). If not, please post this question again and state "Need iv and v only".

Answer:

The correct option is;

E) The average wait time to make payment and the number of cashiers working in a store

Step-by-step explanation:

An inversely proportional relationship is a relationship between two variables one where the increase in the magnitude one variable leads to the reduction in the magnitude of a second variable written mathematically as follows;

y ∝ 1/x

Therefore, given that as the number of cashiers at a store increases, the number of customers attended to per unit time by all the cashiers together increases, and the number of wait time observed by a customer to pay for the goods bought decreases.

Answer:

B.) The total number of stores visited and the average time spent in each store

E.) The average wait time to make a purchase and the number of cashiers working in a store

Step-by-step explanation:

It is correct I just took the test :)

Yes, this series is {[( P ∧ q → R → P → q → R )]} tautology because a tautology is a formula or statement that is true in all possible interpretations. For example, "x = y or x ≠ y".

A tautology  is a formula or statement that is true in all possible interpretations. For example, "x = y or x ≠ y". Similarly, "Either the ball is green or the ball is not green" is always true regardless of the color of the ball.

Such a formula can be true or false based on the value assigned to its set variable. The turnstile double notation S is used to indicate that S is a tautology. Tautology is sometimes symbolized by "Vpq", and contradiction by "Opq". The tee (Τ)  symbol  is sometimes used to denote an arbitrary tautology, with the dual symbol representing an arbitrary contradiction; in any symbolism, a tautology may be substituted for the truth value "true", as symbolized, for instance, by "1".

Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. A key property of tautologies in propositional logic is that an effective method exists for testing whether a given formula is always satisfied (equiv., whether its negation is unratifiable).

The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of propositional logic. Indeed, in propositional logic, there is no distinction between a tautology and a logically valid formula. In the context of predicate logic, many authors define a tautology to be a sentence that can be obtained by taking a tautology of propositional logic, and uniformly replacing each propositional variable by a first-order formula (one formula per propositional variable). The set of such formulas is a proper subset of the set of logically valid sentences of predicate logic.

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Answer:

y-intercept= 12.99      slope= 15.00x+12.99

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Use Pythagoras theorem to solve

4/8 = .5

28 x .5 = 14

He will hit about 14 balls in the next 28 games

The average length by which finger nails will grow in 12 months will be 60mm, considering that they grow by an average of 5mm every month.

As per the question statement, there is no information provided about the average monthly growth of fingernails, and we required to calculate the average length by which finger nails will grow in 12 months.
To solve this question, we assumed that, the fingernails grow by an average of 5mm every month.

Now, using the unitary method, we can form a series of Mathematical statements to solve this question, which goes as follows:

If the average monthly growth of fingernails is 5mm,

It means that, fingernails grow in 1 month, by an average of 5mm.

Therefore, they will grow in 12 months, by an average of (5 * 12) = 60mm.

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If there is at-least one-song liked by those two girls but disliked by the third, then the "different-ways" this is possible is 132 ways.

There are ⁴C₃ ways to choose the "3-songs" which are liked by "3-pairs" of girls.

There are 3! ways to find the three songs are liked by which pair of girls.

In total, there are ⁴C₃×3! possibilities for the first "3-songs".

There are "3-cases" for fourth song, let that song be "D".

Case 1: Song "D" is disliked by all three girls means there is only one possibility.

Case 2: Song "D" is liked by exactly one girl means there are three possibility.

Case 3: Song "D" is liked by exactly two girls means there are three pairs of girls to choose from.

However, there is an overlap when "other-song" is liked by "same-pair" of girl is counted as "fourth-song" at some point, in which "case-D" will be counted as one of first "three-songs" liked by same girls.

Counting the overlaps, there are "three-ways" to choose pair with overlaps and 4×3=12 ways to choose what the other "two-pairs" like independently.

In total, there are 3×12=36 over-lapped possibilities,

Therefore, there are ⁴C₃ × 3! ×(3+1+3)-36 = 132 ways for the songs to be likely by the girls.

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The present value (PV) is $3000.45 when it is rounded to two decimal places.

We can use the following formula for the present value of an annuity:

PV = PMT * [(1 - (1 + i)^(-n)) / i]

Here, n = 20, i = 0.027, and PMT = $207. Now, plug in the values:

PV = 207 * [(1 - (1 + 0.027)^(-20)) / 0.027]

First, calculate the values inside the parentheses:

(1 + 0.027)^(-20) = 0.60829 (rounded to 5 decimal places)

Next, subtract this value from 1:

1 - 0.60829 = 0.39171 (rounded to 5 decimal places)

Now, divide the result by the interest rate:

0.39171 / 0.027 = 14.50704 (rounded to 5 decimal places)

Finally, multiply this value by the payment amount:

207 * 14.50704 = 3000.45

So, the present value (PV) is $3000.45 when rounded to two decimal places.

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Answer:

i) Total Profit =  ₹ 33,000

ii) Number of White Cement bags company has to sell = 3000

Step-by-step explanation:

Let

Total number of white cement bags = x

Total number of grey cement bags = y

Profit for White Cement =   ₹ 9 / bag

Profit for x number of white cement bags = 9x

As "LOSS" can also be written as "- PROFIT"

Profit for Grey Cement =  -₹ 5 / bag

Profit for y number of Grey cement bags =  -5y

Total Profit = 9x - 5y

(If value of Total Profit is negative, it is a Loss)

x = 7000

y = 6000

Total Profit = 9x - 5y

Total Profit = 9(7000) - 5(6000)

Total Profit =  ₹ 33,000

y = 5400

Total Profit = 0

Total Profit = 9x - 5y

0 = 9x - 5(5400)

9x = 5(5400)

x = 5(54000/9

x = 3000 bags