Marcus is responsible for maintaining the swimming pool in his community. He adds chemicals, when needed, to lower the pH of the pool.



-The maximum pH value allowed for the pool is 7. 8.


-The pool currently has a pH value of 6. 9.


-The pH value of the pool increases by 0. 05 per hour.



Write an inequality that can be used to determine x, the number of hours before Marcus will need to add chemicals to maintain the pH for the pool

\(\large{\underline {\underline {\frak {SolutioN:-}}}}\)

➝ -4 × (-2) [2 × (-6)+ 3×(2×6-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-4-4) ]

➝ -4 × (-2) [2 × (-6) + 3 × (12-8) ]

➝ -4 × (-2) [2 × (-6) + 3 × (4) ]

➝ -4 × (-2) [2 × (-6) + 12 ]

➝ -4 × (-2) [(-12) + 12 ]

➝ -4 × (-2) [0]

➝ -4 × 0

➝ 0

Answer:

-4*-2

Step-by-step explanation:

the multiple of both side is 4*2*,26+*32*--=6 44

Answer:

143

Step-by-step explanation:

Answer:

she would have to buy 6 packs of cards and 5 packs of envelopes to have even numbers.

6 packs of cards- 60 cards

5 packs of envelopes- 60 envelopes

Given dataAn element with mass 310 grams decays by 5.7% per minute. We need to find how much of the element is remaining after 9 minutes, to the nearest 10th of a gram.Solution

Let P be the amount of the element remaining after 9 minutes. Then, the amount of the element that decayed in 9 minutes is:Q = 310(1 - 0.057)^9= 310(0.943)^9≈ 174.24 gramsTherefore, the amount of the element remaining after 9 minutes is:P = 310 - Q≈ 135.76 grams.So, the amount of the element remaining after 9 minutes is approximately 135.76 grams, rounded to the nearest 10th of a gram.

Let x be the number of ounces of the 40% alloy Dr. Hamilton used.Then (80 - x) would be the number of ounces of the 60% alloy he used. Therefore, the equation is:0.4x + 0.6(80 - x) = 0.45(80)Simplify this equation to solve for x as follows:0.4x + 48 - 0.6x = 36Add like terms:-0.2x + 48 = 36Subtract 48 from both sides of the equation:-0.2x = -12Solve for x by dividing both sides of the equation by -0.2:x = 60Therefore, Dr. Hamilton used 60 ounces of the 40% alloy.

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On solving the provided question, we can say that the quadratic equation is  y = 5x² - 9x + 3 this quadratic equation can not factorized further

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is

y = 5x² - 9x + 3

this quadratic equation can not factorized further

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after 4 females leave the team, the percentage of remaining team members who are male is 60%.

Initially, the team has 34 members with 18 males and 34 - 18 = 16 females. If 4 females leave the team, the number of females becomes 16 - 4 = 12. The number of remaining team members is 34 - 4 = 30 (since 4 members left).

To calculate the percentage of remaining team members who are male, we divide the number of males (18) by the total number of remaining team members (30) and multiply by 100:

Percentage of remaining team members who are male = (18 / 30) * 100 = 60%

Therefore, after 4 females leave the team, the percentage of remaining team members who are male is 60%.

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Check the picture below.

so from the picture we can pretty much tell two solutions or zeros and another point where it passes up above, so

\(\begin{cases} x=-1\implies &x+1=0\\\\ x=7\implies &x-7=0 \end{cases}\hspace{8em} \begin{array}{llll} a(x+1)(x-7)=0\\\\ a(x+1)(x-7)=y \end{array} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} x=5\\ y=3 \end{cases}\implies a(5+1)(5-7)=3 \\\\\\ a(6)(-2)=3\implies -12a=3\implies a=\cfrac{3}{-12}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill\)

\(-\cfrac{1}{4}(x+1)(x-7)=y\implies -\cfrac{1}{4}\stackrel{F~O~I~L}{(x^2-6x-7)}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{3x}{2}+\cfrac{7}{4}=y \end{array}}~\hfill\)

Answer:

10 seconds, decreasing, standing still

Step-by-step explanation:

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Tax Liability = Tax on 10% Bracket + Tax on 12% Bracket + Tax on 22% Bracket + Tax on 24% Bracket

To determine Fred and Ginger's tax liability for 2021, we will use the tax formula and consider the various items of income and expenses provided. Let's go through each category step by step:

Calculate Adjusted Gross Income (AGI):

AGI = (Fred's Salary) + (Ginger's Salary) + (Interest Income on State of Arizona Bonds) + (Interest Income on US Treasury Bonds) + (Qualified Cash Dividends) + (Share of Hollywood Corporation S Corporation Income) + (Short-term Capital Gains) + (15% Long-term Capital Gains) + (Share of RKO Partnership Loss) + (Life Insurance Proceeds)

AGI = $110,000 + $125,000 + $3,000 + $8,000 + $6,000 + $30,000 + $5,000 + $30,000 + (-$10,000) + $150,000

AGI = $547,000

Determine Itemized Deductions:

Itemized Deductions = (Home Mortgage Interest) + (Home Equity Loan Interest) + (Vacation Home Loan Interest) + (Car Loan Interest) + (Home Property Taxes) + (Vacation Home Property Taxes) + (Car Tags) + (Arizona Sales Taxes Paid) + (Medical Insurance Premiums) + (Unreimbursed Medical Bills) + (Charitable Contributions)

Itemized Deductions = $18,000 + $6,000 + $8,400 + $3,000 + $6,000 + $1,800 + $950 + $6,500 + $12,000 + $10,000 + $12,000

Itemized Deductions = $95,650

Calculate Taxable Income:

Taxable Income = AGI - Itemized Deductions

Taxable Income = $547,000 - $95,650

Taxable Income = $451,350

Determine Tax Liability using the Tax Table or Tax Formula:

Based on the provided information, we'll assume Fred and Ginger are filing as Married Filing Jointly for 2021. Using the tax brackets and rates for that filing status, we can calculate their tax liability. Please note that the tax rates and brackets are subject to change, so it's important to refer to the most recent tax regulations.

Tax Liability = (Tax on 10% Bracket) + (Tax on 12% Bracket) + (Tax on 22% Bracket) + (Tax on 24% Bracket)

The taxable income falls into multiple brackets, so we'll calculate the tax liability for each bracket separately:

Tax on 10% Bracket: $0 - $19,900 = $0

Tax on 12% Bracket: $19,901 - $81,050 = ($81,050 - $19,900) * 0.12

Tax on 22% Bracket: $81,051 - $172,750 = ($172,750 - $81,050) * 0.22

Tax on 24% Bracket: $172,751 - $451,350 = ($451,350 - $172,750) * 0.24

Calculate the total tax liability:

Tax Liability = Tax on 10% Bracket + Tax on 12% Bracket + Tax on 22% Bracket + Tax on 24% Bracket

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Answer:

Step-by-step explanation:

slope of line y=4x+12 is 4

slope of line perpendicular to y=4x+12 is -1/4

eq. of perpendicular line or perpendicular linear function is y=-1/4x+b  where b is the y-intercept.

Hey there!

Do PEMDAS

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

15 + 2(2 * 4) - 4^2

= 15 + 2(8) - 4^2

= 15 + 16 - 4^2

= 31 - 4^2

= 31 - 4 * 4

= 31 - 16

= 15

Therefore, your answer is: 15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

The answer is 15.

Step-by-step explanation:

\({\tt{\underline{\underline{\pink{SOLUTION:}}}}}\)

To solve the above equation we will follow the BODMAS rule.

It stands for :

Solving this question by bodmas rule :

\(\begin{gathered}\qquad{\twoheadrightarrow{\tt{15 + 2(2 \times 4) - {4}^{2}}}} \\ \\ \qquad{\twoheadrightarrow{\tt{15 + 2(8) - {4}^{2}}}} \\ \\ \qquad{\twoheadrightarrow{\tt{15 + 2 \times 8 - {4}^{2}}}} \\ \\ \qquad{\twoheadrightarrow{\tt{15 + 16 - {4}^{2}}}} \\ \\ \qquad{\twoheadrightarrow{\tt{31 - {4}^{2}}}} \\ \\ \qquad{\twoheadrightarrow{\tt{31 - {4} \times 4}}} \\ \\ \qquad{\twoheadrightarrow{\tt{31 - 16}}} \\ \\ \qquad{\twoheadrightarrow{\tt{\underline{\underline{15}}}}} \end{gathered}\)

Hence, the answer is 15.

\(\rule{300}{2.5}\)

The specific name of the quadrilateral is trapezoid

The measure of the missing angle is 55 degrees

To determine the measure of the angle, we need to know the following;

The properties of a trapezoid are listed as;

From the information given, we have that;

125 + x = 180

collect the like terms, we have;

x = 180 - 125

subtract the values, we get;

x = 55 degrees

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To find the average quarterly loads for the rest of the years, you can use the formula below:

Average Quarterly Load = Total Annual Load  4 For example, let's say the total annual load for Year 1 is 800.

To find the average quarterly loads for Year 1, we would divide 800 by 4 to get an average quarterly load of 200. Then, you can use this average quarterly load to find the seasonal indices for each quarter of each year.To find the seasonal index for a given quarter and year, you would divide the actual quarterly load by the average quarterly load for that year.

For example, let's say the actual load for Quarter 1, Year 1 is 240. To find the seasonal index for this quarter and year, we would divide 240 by 200 to get a seasonal index of 1.2. You would repeat this process for each quarter and year to find the seasonal indices for all quarters and years.

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Answer:

8/40 is the correct answer

Regarding the scales to plot the points on the table, we have that:

To find the ideal scales, we have to verify which are the extrema values of each variable, that is, the minimum and maximum value of each x and y.

From the table, the minimum and maximum values of X are given as follows:

This is a small range of values, hence the horizontal scale should be of 1.

From the same table, second column, the minimum and maximum values of Y are given as follows:

This is a large range of values, hence an ideal vertical scale is of 200, as then the number of traces would be almost the same as the number of traces of x.

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Answer:

b=-9

Step-by-step explanation:

b/-1=9

times both sides by -1

b=-9

Answer:

44 - 33 = 11

11/44 X 100 = 25%

Step-by-step explanation:

find the difference between the original price and new price (change)

change/original price X 100 = percentage change

Answer:

k= 0

Step-by-step explanation:

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate

\( - 7 = \frac{k - 7}{ - 8 - ( - 9)} \)

\( - 7 = \frac{k - 7}{ - 8 + 9} \)

\( - 7 = \frac{k - 7}{1} \)

k -7= -7

+7 on both sides:

k= -7 +7

k= 0

A) Pansy Meadows Primary Care Clinic's total revenue per month is $10,000. B) The clinic's monthly profit is a loss of $15,000. C)  if the commercial insurance company changes the reimbursement rate to $65, the monthly profit would be $30,000. D) if all commercially insured patients are covered by a capitated contract, the monthly profit would be a loss of $33,000.

To calculate the clinic's total revenue, monthly profit/loss, and the impact of changes in reimbursement rates, we'll use the given information and perform the necessary calculations.

Given:

Number of office visits per month = 1000

Fixed costs = $25,000 per month

Variable costs per office visit = $10

A) Total revenue per month:

Revenue per office visit = $10 (variable cost per visit)

Total revenue per month = Revenue per office visit * Number of office visits per month

Total revenue per month = $10 * 1000

Total revenue per month = $10,000

Therefore, Pansy Meadows Primary Care Clinic's total revenue per month is $10,000.

B) Monthly profit (loss):

Profit (loss) = Total revenue per month - Fixed costs - (Variable costs per office visit * Number of office visits per month)

Profit (loss) = $10,000 - $25,000 - ($10 * 1000)

Profit (loss) = -$15,000

Therefore, the clinic's monthly profit is a loss of $15,000.

C) Impact of changing the commercial insurance reimbursement rate to $65:

To determine the impact on profitability, we need to recalculate the monthly profit using the new reimbursement rate.

New total revenue per month = $65 * 1000 = $65,000

Profit (loss) = New total revenue per month - Fixed costs - (Variable costs per office visit * Number of office visits per month)

Profit (loss) = $65,000 - $25,000 - ($10 * 1000)

Profit (loss) = $30,000

Therefore, if the commercial insurance company changes the reimbursement rate to $65, the monthly profit would be $30,000.

D) Impact of all commercially insured patients being covered by a capitated contract:

i. Monthly revenue:

Revenue per patient per month = $2 (capitated payment per patient)

Monthly revenue = Revenue per patient per month * Number of office visits per month

Monthly revenue = $2 * 1000

Monthly revenue = $2,000

ii. Monthly profit/loss:

Profit (loss) = Monthly revenue - Fixed costs - (Variable costs per office visit * Number of office visits per month)

Profit (loss) = $2,000 - $25,000 - ($10 * 1000)

Profit (loss) = -$33,000

Therefore, if all commercially insured patients are covered by a capitated contract, the monthly profit would be a loss of $33,000.

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Answer:

The correct options are;

1. Definition of supplementary angles

2. m∠1 + m∠2 = m∠1 + m∠3

3. m∠2 = m∠3

4. Definition of congruent angles

Step-by-step explanation:

The two column proof is presented as follows;

Statement    \({}\)                                      Reason

1. ∠1 and ∠2 are supplementary \({}\)       Given

∠1 and ∠3 are supplementary \({}\)      

2. m∠1 + m∠2 = 180°     \({}\)                      (1) Definition of supplementary angles

m∠1 + m∠3 = 180°

3. (2) m∠1 + m∠2 = m∠1 + m∠3      \({}\)     Transitive Property

4. (3) m∠2 = m∠3     \({}\)                            Subtraction property of equality

5. ∠2 ≅ ∠3     \({}\)                                       (4) Definition of congruent angles

Given that angles ∠1 and ∠2 are supplementary, we have, ∠1 + ∠2 = 180°

Given that angles ∠1 and ∠3 are also supplementary, we also have, ∠1 + ∠3 = 180°

∴ ∠1 + ∠2 = 180° = ∠1 + ∠3

∠1 + ∠2 = ∠1 + ∠3

∠1 + ∠2 - ∠1 = ∠1 + ∠3 - ∠1

∴ ∠2 = ∠3

∴ ∠2 ≅ ∠3, by definition of congruent angles.

The value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

To answer the question, we will conduct a hypothesis test to at the 0.1 level to ascertain whether or not the manufacturer's MPG rating is incorrect.

We start by stating the null and alternative hypotheses:

\($H_0$\): The mean miles/gallon for the vans is 53.8

\($H_A$\): The mean miles/gallon for the vans is not 53.8

We choose a significance level $\alpha = 0.1$ and calculate the following test statistic:

\($z = \frac{\bar{x}-\mu}{\sigma/\sqrt{n}} = \frac{53.4-53.8}{1/\sqrt{16}} = -2.5$\)

With a standard normal table, we look for the area to the left of -2.5, which is 0.0062. Because this value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

Therefore, the value of 0.0062 is less that our significance level of 0.1, we reject the null hypothesis at the 0.1 level of significance and conclude with sufficient evidence that the manufacturer's MPG rating is incorrect.

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Answer:

B = 10

I hope this helps!

Answer:

b=40 I just took this quiz

Answer:b=40 a=100

Step-by-step explanato a line is 180 degrees, the outside of the triangle is 140 degrees so the inside must be 40 to make 180 and a is also 40 because the triangles sides are the same

to find a we now know that both angles on the bottom 40+40 will add up to 80 and to make a complete triangle we need 180 so the measure of a is 100 degrees

a=100

b=40

Considering the perimeter of the trapezoid, the set-builder representation of the possible values for the length of the sides labeled m is:

{m | m > 6}.

The perimeter of a polygon is calculated by the sum of the lengths of all the outer edges of the figure.

In the context of this problem, these measures of the outer edges are given as follows:

Hence the perimeter of the trapezoid is given as follows:

P = 6 + 10 + m + m = 16 + 2m.

The perimeter is greater than 28, hence the inequality is:

P > 28.

16 + 2m > 28. (replacing the equation for P into the inequality).

2m > 12

m > 12/2

m > 6.

The set-builder notation of this interval is:

{m | m > 6}.

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Answer:

divident

Step-by-step explanation:

The coordinates for point B are 7 = √(x - 5)² + (y - 4)².

What is the distance formula?

The distance formula is used to calculate the length of the line which joins the two points in an x−y plane. The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line.

Here, we have

Given: Segment AB Has point A located At (5, 4). If The Distance from A To B Is 7 units.

To find the distance between any two the following formula is used.

D = √(x₂ - x₁)² + (y₂ - y₁)²

7 = √(x - 5)² + (y - 4)²

Hence, the coordinates for point B are 7 = √(x - 5)² + (y - 4)².

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To find all real numbers a that satisfy the equation \(a^2\) = a - 2, we can rewrite the equation as\(a^2\) - a + 2 = 0 and solve for a using quadratic equation methods.

The quadratic equation is given by ax^2 + bx + c = 0, where in our case a = 1, b = -1, and c = 2. Substituting these values into the quadratic equation formula (-b ± √(b^2 - 4ac)) / (2a), we get:

a = (-(-1) ± √(\((-1)^2\) - 4(1)(2))) / (2(1))

  = (1 ± √(1 - 8)) / 2

  = (1 ± √(-7)) / 2

Since the square root of a negative number is not a real number, there are no real solutions for a that satisfy the equation \(a^2\) = a - 2. In other words, there are no real numbers that make the equation true.

This does not violate the exponential function property because the equation\(a^2\) = a - 2 does not involve raising a to a power. The property ax = ay if and only if x = y holds for exponential functions, but it does not apply to the equation in question. In this case, we are solving a quadratic equation, not dealing with exponentiation.

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To identify the values of a and r and determine if the sequence is convergent or divergent, we need to analyze each given geometric sequence.

1) Sequence: 3, 6, 12, 24, ...

  The common ratio (r) can be found by dividing any term by its preceding term. Here, r = 6/3 = 2. The first term (a) is 3. The general term (an) can be written as an = a * r^(n-1) = 3 * 2^(n-1). Since the common ratio (r) is greater than 1, the sequence is divergent, as it will continue to increase indefinitely as n approaches infinity.

2) Sequence: -2, 1, -1/2, 1/4, ...

  The common ratio (r) can be found by dividing any term by its preceding term. Here, r = 1/(-2) = -1/2. The first term (a) is -2. The general term (an) can be written as an = a * r^(n-1) = -2 * (-1/2)^(n-1) = (-1)^n.  Since the common ratio (r) has an absolute value less than 1, the sequence is oscillating between -1 and 1 and is divergent.

3) Sequence: 5, -15, 45, -135, ...

  The common ratio (r) can be found by dividing any term by its preceding term. Here, r = -15/5 = -3. The first term (a) is 5. The general term (an) can be written as an = a * r^(n-1) = 5 * (-3)^(n-1). Since the common ratio (r) has an absolute value greater than 1, the sequence is divergent. In summary, the first sequence is divergent, the second sequence is divergent and oscillating, and the third sequence is also divergent.

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