If ten babies were crying. Then the nanny got 100 more crying babies and only 53 babies were not crying how many babies were crying?

To prove that triangle ABC is an isosceles right triangle, we need to show that two sides of the triangle are equal in length and one angle is a right angle.

Distance Formula:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the distance formula:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Using the distance formula, we can calculate the lengths of the three sides of the triangle:

Side AB: d₁ = √[(6 - (-2))² + (2 - 4)²] = √[8² + (-2)²] = √(64 + 4) = √68

Side BC: d₂ = √[(1 - 6)² + (-1 - 2)²] = √[(-5)² + (-3)²] = √(25 + 9) = √34

Side AC: d₃ = √[(-2 - 1)² + (4 - (-1))²] = √[(-3)² + 5²] = √(9 + 25) = √34

Slope Formula:

The slope between two points (x₁, y₁) and (x₂, y₂) is given by the slope formula: m = (y₂ - y₁) / (x₂ - x₁)

Using the slope formula, we can calculate the slopes of the three sides of the triangle:

Slope AB:

m₁ = (2 - 4) / (6 - (-2)) = (-2) / 8 = -1/4

Slope BC:

m₂ = (-1 - 2) / (1 - 6) = (-3) / (-5) = 3/5

Slope AC:

m₃ = (4 - (-1)) / (-2 - 1) = 5 / (-3) = -5/3

From the distances calculated and the slopes of the sides, we can see that side AB is equal in length to side BC (both √34), indicating that two sides are equal. Additionally, the slope of side AC (m₃ = -5/3) is the negative reciprocal of the slope of side AB (m₁ = -1/4), indicating that the two sides are perpendicular, and hence, one angle is a right angle.

Therefore, triangle ABC is an isosceles right triangle.

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The volume of the solid obtained by rotating the region bounded by the curves about the x-axis is π/77 (243 - 9sqrt(3)).

To find the volume of the solid obtained by rotating the region bounded by the curves about the x-axis, we can use the method of cylindrical shells. This involves integrating the circumference of a cylindrical shell times its height to obtain the volume of each shell, and then adding up the volumes of all the shells to get the total volume.

First, let's find the points of intersection of the two curves:

2/7 x^2 = 9/7 - x^2

9/7 = 9/7 x^2 + 2/7 x^2

9/7 = 11/7 x^2

x^2 = 9/11

x = ±sqrt(9/11)

The solid we obtain by rotating this region about the x-axis will have cylindrical shells with height dx, radius x, and circumference 2πx. Therefore, the volume of each shell will be:

dV = 2πx × h × dx

where h is the difference between the y-values of the curves at x:

h = (9/7 - x^2) - (2/7 x^2) = 9/7 - 9/7 x^2

Therefore, the total volume of the solid will be:

V = ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) 2πx * (9/7 - 9/7 x^2) dx

V = 2π/7 ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) x(9 - 9x^2) dx

We can simplify the integrand by setting u = 9x^2:

du/dx = 18x

dx = du/18x

Substituting:

V = 2π/7 ∫(from u = 9/11 to u = 81/11) (1/2)u^(1/2) (9/2) (du/18x)

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / x du

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / sqrt(9/11 - u/11) du

This integral can be evaluated using a trigonometric substitution. Let u = 9/11 sin^2 θ, then:

du/dθ = (18/11) sin θ cos θ dθ

Substituting:

V = π/7 ∫(from θ = π/6 to θ = π/2) (81/121) sin^3 θ dθ

V = π/7 [(81/121) * (3/4) - (9/121) × (sqrt(3)/2)]

V = π/77 (243 - 9sqrt(3))

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Answer: 628571%.

Step-by-step explanation:

To find the confidence interval statistical analysis such as hypothesis testing or regression analysis is used. However, it is impossible to calculate without data.

To estimate the difference in traffic between a rural and urban location with a 95% confidence level, you would need specific data or information about the traffic counts or relevant measurements from both locations. The confidence interval estimate can be obtained using statistical analysis techniques such as hypothesis testing or regression analysis.

Typically, the process involves collecting data on traffic counts or related variables from both the rural and urban locations. Then statistical methods are applied to calculate the confidence interval estimate based on the sample data. The specific formula or method used would depend on the nature of the data and the analysis approach chosen.

Without specific data or information about the traffic counts or measurements, it is not possible to provide a numerical estimate for the 95% confidence interval of the difference in traffic between a rural and urban location.

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Answer:

You earn 20$ for washing 4 cars.

You washed 9 cars to get 45$.

Hope this helps!

Step-by-step explanation:

If you earned 35$ for washing 7 cars, one car is 5$ ( 35 ÷ 7 ).

If one car is 5$, 4 cars is 20$ ( 5 * 4 ).

Because one car is 5$, the 45$ is 9 cars ( 45 ÷ 5 ) or ( 9 * 5 ).

Answer: See explanation

Step-by-step explanation:

x=-(2-2*the square root of 6)/5, about 0.58

or

x=-(2+2*the square root of 6)/5, about -1.38

The values of the x from equation  \(5x^2+4x-4=0\) are  x = 0.5798 and -1.38.

Given that:

Equation:  \(5x^2+4x-4=0\)

To find the values of x that satisfy the equation \(5x^2+4x-4=0\), use the quadratic formula:

\(x = \dfrac{ -b \± \sqrt{b^2 - 4ac}}{ 2a}\)

Compare the equation with \(ax^2 + bx + c = 0\).

Here, a = 5, b = 4, and c = -4.

Plugging in the values to get,

\(x = \dfrac{-4 \± \sqrt{4^2 - 4 \times 5 \times (-4)}}{2 \times 5} \\x = \dfrac{-4 \± \sqrt{16 +80}}{10} \\x = \dfrac{-4 \± \sqrt{96}}{10}\\x = \dfrac{-4 \± {4\sqrt6}}{10}\)

So the solutions for x are calculates as:

Taking positive sign,

\(x = \dfrac{-4 + {4\sqrt6}}{10}\\x = \dfrac{-4 + {9.798}}{10}\\\)

x = 5.798/10

x = 0.5798

Taking negative sign,

\(x = \dfrac{-4 - {4\sqrt6}}{10}\\x = \dfrac{-4 - {9.798}}{10}\\\)

x = -13.798/10

x = -1.38

Hence, the exact solutions for the equation  \(5x^2 + 4x - 4 = 0\)  are x = 0.5798 and -1.38.

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Answer:

If its -2x^2+17 the answer would be -183.

Step-by-step explanation:

-2(100)+17

-200+17

= -183

Answer:

Is this function inverse or symmetrical or what

Step-by-step explanation:

Answer:

76 degrees

Step-by-step explanation:

this special line is an angle bisected.

that means it splits the angle at its starting point in 2 halves. as these names indicate, both parts are of equal size (half of the general angle).

we know one part (2) of this split angle : 38 degrees.

the other part (1) had to be equally sized : 38 degrees.

so, the total angle at point R is the sum of both split angles:

TRS = 38+38 = 76 degrees.

Total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

As given in the question,

Macro earns commission rate of 6% for the first $6500

And 9% on sales over $6500

Out of $10,500

For first $6500 Commission =(6500 × 6)/ 100

                                            = $390

For $ (10,500 - 6,500 = 4000) commission = (4000 × 9)/ 100

                                                                   = $360

Total graduated commission on sales of $10,500 = $( 390 + 360)

                                                                             = $750

Therefore, total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.

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Answer:

c.

Step-by-step explanation:

Plz mark brainliest :)

The probability of two or more people sharing a birthday is greater than 50%.

The problem you're describing is known as the birthday problem or the birthday paradox. The probability of two or more people sharing a birthday in a group of $n$ people can be calculated using the following formula:

\($$P(\text{at least two people share a birthday}) = 1 - \frac{365!}{(365-n)!365^n}$$\)

This formula assumes that all birthdays are equally likely, and that there are 365 days in a year (ignoring leap years).

To find the smallest value of \($n$\) for which the probability of two or more people sharing a birthday is greater than 50%, we can solve the above equation for \($n$\) using numerical methods (e.g., trial and error, or using a computer program).

Here's some Python code that uses a loop to calculate the probability of two or more people sharing a birthday for groups of increasing size, and stops when the probability exceeds 0.5:

import math

\(prob = 0\\n = 1\)

while prob < 0.5:

\(prob = 1 - math.factorial(365) / (math.factorial(365-n) * 365**n)  \\n += 1\)

print(n-1)

The output of this code is 23, which means that in a group of 23 or more people, the probability of two or more people sharing a birthday is greater than 50%.

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Answer:

PART A: C = 10 +8h

PART B: what you do is plug in the number 9 to h. so then you get C = 10 +8(9). This simplifies to C = 10 + 72. The final answer is C = 82. So Jessica made $82 for babysitting for 9 hours.

Answer:

part A:

С = 10 + 8h

part B :

$10 + $8 · 9 = $82

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The average speed of the Ironman winner is given by S = 15.8 mph

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the average speed of the Ironman winner be represented as S

Now , the distance of the race for swimming = 2.4 miles

The distance of the race for biking = 112 miles

The distance of the race for running = 26.2 miles

So , the total distance D = 2.4 + 112 + 26.2 = 140.6 miles

Now , the time taken for the women's race T = 8.9 hours

So , Speed = Distance / Time

And , the average speed of the Ironman winner = 140.6 / 8.9

The average speed of the Ironman winner S = 15.797 miles per hour

The average speed of the Ironman winner S ≈ 15.8 miles per hour

Hence , the average speed of the winner is 15.8 mph

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The complete question is :

The Ironman triathlon is a speed and endurance race that combines swimming ( 2.4 miles ) , biking ( 112 miles ) and running ( 26.2 miles ). One famous Ironman competition occurs each year in Hawaii , where the race began in 1978

a) What is the total distance covered in an Ironman race?

b) The best women's time for the Hawaiian Ironman race is 8.9 hours. What was the average speed of that Ironman winner?

Answer:

y = x + 4  

Step-by-step explanation:

Slope intercept :  2x - 2y = 8  =  2x     2x  = 8 + 2y   =  2x = 8 +2y   = 2x-8 =2y is the sae as 2y = 2x -8 divide everything by 2  = 2x / 2 - 8/2  = 2y/2 = y = x-4    

The cost of ordering shirts for a club is 268 units.

Define Function.

A function, according to a technical definition, is a relationship between a set of inputs and a set of possible outputs, where each input is connected to precisely one output.

 This means that a function f will map an object x exactly to one object f(x) in the set of possible outputs if the object x is in the set of inputs (called the codomain).

The statement that f is a function from X to Y using the function notation f: X→Y

The function that represents the cost of the shirts(x) is f(x) = 8x+12

Now, for x = 32

 f(x) = 8x+12

f(32) = 8(32) + 12

        = 256 +12

f(32) = 268 units

.

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Answer:

The square root of 37 is approximately 6.0827. To determine which two integers it lies between, we can find the integers that are closest to the square root of 37.

The integer that is smaller than 6.0827 is 6, and the integer that is larger than 6.0827 is 7.

Therefore, the square root of 37 is between the integers 6 and 7.

Answer: 8:1

Step-by-step explanation:

To find the simplest ratio of 4 kg of metal to 500g of plastic, we need to convert both quantities to the same unit of measurement. Let's convert 4 kg to grams:

Now we have 4000 g of metal and 500 g of plastic. To simplify the ratio, we can divide both quantities by their greatest common factor (GCF), which is 500:

Therefore, the simplest ratio of 4 kg of metal to 500g of plastic is 8:1.

________________________________________________________

The total weight of metal and plastic in the ratio 8:1 is indeed 4.5 kg.

The total weight of metal and plastic is:

The simplest ratio of metal to plastic is found by dividing both quantities by their greatest common factor.

The greatest common factor of 4 kg and 0.5 kg is 0.5 kg. Dividing both quantities by 0.5 kg gives:

\(\therefore\) The simplest ratio of metal to plastic is 8:1.

To check, we can verify that:

So the total weight of metal and plastic in the ratio 8:1 is indeed 4.5 kg.

\(\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}\)

1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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The value of A has been illustrated, computed and proven based in the triangle given.

It should be noted that that a triangle is a shape that has three sides and the value of the addition of all the angles are equal to 180°.

Based on the information that's given, it should be noted that the value of angle A, angle B, and angle C will be equal to 180°.

In this case, the following can be deduced:

A = 5x

B = 90°

C = x + 10°

Therefore, A + B + C = 180° (sum of angles in a triangle)

5x + 90 + x + 10 = 180°

6x = 180° - 90° - 10°

6x = 80°

x = 80/6

x = 13 1/3

Therefore, the value of A will be:

= 5x

= 5 × 13 1/3

= 66 2/3

Therefore, A is 66 2/3.

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Type I error is formed when she concludes the town's unemployment rate is not 9% when it actually is, which is an option (a).

Given that:

A large nationwide poll recently showed an unemployment rate of 9% in the US.

The mayor of a local town wonders if this national result holds true for her town, so she plans on taking a sample of her residents to see if the unemployment rate is significantly different than 9% in her town.

Here the null hypothesis is taken as that the unemployment rate is 9%, whereas the alternative hypothesis is that it is not 9%.

Type I error is the error formed when the null hypothesis is rejected, but the hypothesis is actually true.

So, here the conclusion is that the unemployment rate is not 9%, but it actually is 9%.

Hence, the correct option is (a).

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If two quantities are proportional, the true statements about the graph showing the relationship between them are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant.

Now let us suppose there are two quantities x and y.

A graph between two quantities is plotted.

Suppose x is directly proportional to y.

Thus, these Two variable quantities have a constant ratio

So, we can write

y ∝ x

Applying constant of proportionality,

y = kx

Where k is the constant of proportionality.

It represents a straight line.

Now,the value of x = 0 then the value of y must be equal zero, then the line which represented the direct variation must be passes through the origin

Now  If two variable quantities have a constant ratio and since y = kx is a straight line and passes through origin therefore from the given options the correct answer are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

Thus, If two quantities are proportional, the true statements about the graph showing the relationship between them are-

D. The points of the graph form a straight line.

E. The points of the graph must include the origin.

F. The points must all form equivalent ratios.

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The three externalities, which can either be positive or negative are Pollution from a factory, as more electricity is consumed, more coal is burned in power plants and vaccinations, such as the flu shot, can be advantageous for third parties.

The three externalities, which can either be positive or negative are:

1. Pollution from a factory can affect a community's quality of life and lead to health issues for the population.

2. As more electricity is consumed, more coal is burned in power plants, which contributes to pollution and causes smog, acid rain, and global warming.

3. Vaccinations, such as the flu shot, can be advantageous for third parties since they stop the spread of the illness in the general population, which has positive externalities.

These externalities arise because they provide a benefit or incur a cost to a third party, who may be a society or a consumer who is not using the service. Government intervention can address some of these issues in two ways:

(a) Command and control rules that impose direct restrictions on behavior, such as restricting smokestack emissions or the amount of toxic waste and outlining specific cleanup processes.

(b) Market-based policies that can encourage favorable externalities by offering market players incentives to reach the socially optimal level In order to reduce costs or boost production to improve demand and supply, the government can either provide subsidies to buyers or producers.

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\(\\ \sf\longmapsto I=\dfrac{PRT}{100}\)

\(\\ \sf\longmapsto I=\dfrac{775(1.47)(8)}{100}\)

\(\\ \sf\longmapsto I=\dfrac{9114}{100}\)

\(\\ \sf\longmapsto I=91.14\)

Answer:

91.14  $

Step-by-step explanation:

We know,

Interest = Principle× Rate of Interest× Time

or, 775× 1.47/100× 8

or, 91.14

Therefore, Interest is 91.14 $.

a. The probability that the player will hit on the 1st throw and miss on the 2nd throw, expressed in probability language, is P(Hit 1st Throw ∩ Miss 2nd Throw) = 0.29 or 29%. b. The probability that the player will hit on at least one of the two free throws is P(Hit at least one Throw) = 0.91 or 91%, which is obtained by subtracting the probability of missing both throws from 1.

a. To write the probability of the player hitting on the 1st throw and missing on the 2nd throw in probability language, you can express it as the probability of the intersection of the two events.

In this case, it would be written as P(Hit 1st Throw ∩ Miss 2nd Throw). The calculated probability of 0.29 or 29% can be substituted, resulting in P(Hit 1st Throw ∩ Miss 2nd Throw) = 0.29.

b. To determine the probability that the player will hit on at least one of the two free throws, you can consider the complement of the event where she misses both throws.

The complement of an event A is written as A'. In this case, you need to find P(Hit at least one Throw) or 1 - P(Miss both Throws). Using the given probabilities, P(Miss both Throws) = 0.09. Therefore, P(Hit at least one Throw) = 1 - P(Miss both Throws) = 1 - 0.09 = 0.91 or 91%.

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result is 31+i in where 31 is real part and i is complex part as given i= √-1 and i²= -1

In mathematics complex number is an element which has two parts one is called real part and the remaining is termed as imaginary part. An example is 41+6i

here, 41 is real part, 6i is imaginary part

A real number cannot be added or subtracted with an imaginary number, but a real number can be multiplied or divided with an imaginary number.

We are given, (2+3i) (5-7i)

    at first, we expand it by removing parenthesis

2x5-2x7i+3ix5-3ix7i

10-14i+15i-21i²

now like term is added

10+i+21   as we are given i²= -1

    31+i

hence, we get 31+i

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If Pharma Plus wants to achieve the optimal staffing level, they need to hire 5 additional pharmacists and 16 additional technicians, which would increase the payroll cost by $9,576 per hour.

a) To determine a minimum-cost staffing plan for Pharma Plus,

we have the following optimization problem:

Min 48P + 12T

Subject to:

P + T > 251 (Employees required)

2P - T > 0 (Service quality guideline)

P > 90 (Pharmacists employed)

Using the graphical method, we can graph the lines of each constraint:

Figure 1 From Figure 1, we can see that the feasible region is the shaded region above the blue line (P + T = 251) and

to the right of the orange line (2P - T = 0),

and to the right of the green line (P = 90).

To obtain the optimal solution, we need to find the intersection point of two lines, where the total cost is minimized.

However, this region has infinite intersection points, which makes it difficult to find the optimal solution.

To overcome this challenge, we use the corner-point method, where we evaluate the objective function at each corner point and select the one that yields the lowest cost.

In this case, the corner points are A (90, 161), B (115, 136), and C (165.5, 85.5).

Using the objective function, we obtain the following values:

At point A: 48(90) + 12(161)

= $3,624

At point B: 48(115) + 12(136)

= $4,008

At point C: 48(165.5) + 12(85.5)

= $7,308

Hence, the optimal solution is at point A (90, 161), where the total cost is $3,624 per hour.

Therefore, Pharma Plus needs at least 90 pharmacists and 161 technicians to minimize the total payroll cost to $3,624 per hour.

b) Given the current staffing levels and expected attrition, Pharma Plus has 85 pharmacists and 175 technicians.

To reach the level recommended in part (a), they need 5 additional pharmacists and 16 additional technicians.

The additional cost of payroll is the difference between the cost at current staffing levels and the cost at the optimal solution.

Using the average salary for licensed pharmacists and technicians, we have the following calculations:

The payroll cost using the current levels of 85 pharmacists and 175 technicians is $60 x 85 + $12 x 175

= $13,200 per hour.

The payroll cost using the optimal solution in part (a) is $48 x 90 + $12 x 161 = $3,624 per hour.

The increase in payroll cost is $9,576 per hour.

Therefore, if Pharma Plus wants to achieve the optimal staffing level, they need to hire 5 additional pharmacists and 16 additional technicians, which would increase the payroll cost by $9,576 per hour.

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The percent of the time that Haddad will save by paying the extra $30.000 per month is d) 59%.

A percentage is a unit in 100, a part of a whole, or a ratio of one variable to the bigger variable.

Percentages show the quantity or value of the independent variable that is contained in a dependent variable.

Data and Calculations:

Total months to pay off a debt = 58 months

The additional amount required to reduce the payment period to 24 months = $30 per month

The savings in time = 59% (58 -24/58 x 100).

Thus, the percent of the time that Haddad will save by paying the extra $30.000 per month is d) 59%.

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