(20 POINTS) Perfect Pizza Has 15 Toppings Listed On Their Menu. How Many Ways Could A Customer Choose (2024)

(a) The interpret the p-value in context of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower.

(b) The conclusion would make if a 0.05 is rejected because the p-value (0.0016) is less than the significance level.

If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01.

Anemia Study Results

(a) The p-value of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower, assuming that the true population mean is 12 g/dl (or higher), is only 0.0016. This suggests that the observed difference between the sample mean and the hypothesized population mean is statistically significant and unlikely to be due to chance alone.

(b) If using a significance level of 0.05, the null hypothesis (that the true population mean is 12 g/dl or higher) would be rejected because the p-value (0.0016) is less than the significance level. Therefore, it can be concluded that the sample provides evidence that the true population mean hemoglobin level is lower than 12 g/dl.

If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01. In this case, the evidence is even stronger, and the conclusion that the true population mean is lower than 12 g/dl would be even more robust.

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It will take John about 48 minutes of driving with a speed of 100km/h to catch Karabo on the Highway.

Karabo and John are at the same stop alongside the highway.

Karabo started driving along the highway with a constant speed of 80 km/h. After an hour, John also started driving in the same direction of the highway and at a constant speed of 100km/h.

Here, the distance covered by Karabo in one hour will be 80 km because his speed is 80km/h.

So, the distance D between John and Karabo is now 80 km.

John will have to cover this distance of 80 km to reach Karabo, so,

Time = Distance/Speed

Distance = 80 km,

Speed = 100km/h

Putting values,

Time = 80/100

Time = 0.8 hour.

This time will be 48 minutes, so, the time required by John is 48 minutes.

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The length QN on the triangle is 54 units

How to determine the length QN

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

Point P = Centroid

Also, we have

QP = 18

The centroid divides each median into the ratio 2:1.

Using the above as a guide, we have the following:

QN = 3 * QP

Substitute the known values in the above equation, so, we have the following representation

QN = 3 * 18

Evaluate

QN = 54

Hence, the length is 54 units

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c. Moon, d. Triangle, e. Square, h. Heart morphologies are synapomorphic from building your tree in the clade race.

In order to help businesses conduct sales transactions, employ marketing techniques, and manage their finances, inventory, and personnel, Square offers a variety of products and services. The Square app can currently be used to accept card payments in the US, Canada, Australia, Japan, the UK, Republic of Ireland, France, and Spain. With Square Payments, you can easily and safely accept all forms of payment. You can collaborate with customers rather than competing with them when it comes to how they want to pay for goods and services when you use Square Payments. Through Square, you can accept credit cards, Apple Pay, Android Pay, and a lot of other payment options.

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To determine the number of rows, we need to divide the total number of people by the number of people in each row. Using the information given, we have:

Number of people in the marching band = 45

Number of people in each row = 5

So the equation that shows the number of rows, denoted by "r", is:

r = 45/5

Simplifying the equation, we get:

r = 9

Therefore, there are 9 rows in the marching band.

The answer is (B) 45 ÷ 5 = 9.

As per the provided information, we can calculate and find that there are in total25girls present in the classroom.

We know that the total number ofstudentsis 90 and 45 of them are boys. So, the number of girls in the class is:

girls = total students -boys

= 90 - 45

= 45

Total no. of students=90Out of which 45 are boys which means 45 are girls.

We also know that 50% of the total studentssecuredgrade 'a'. So, the totalnumberof students who secured grade 'a' is:

total grade a = total students / 2

= 90 / 2

= 45

Now, Students who gotAgrade = 90×50/100

= 45

Now, Students who gotAgrade = 90×50/100

= 45

So, 45 students got Agrademarks.

Out of which 20 are boys which means girls who got A grade = 45-20=25

Hence, 25 Girls got A grade.

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Brandon purchased the phone for $500 , if the value of a phone decreases by 25% each year, it will take approximately 2.77 years for the value of the phone to decrease to $100.

To find the number of years it will take for the value of the phone to decrease to $100, we can use the formula:

years = log(initial value / final value) / log(1 - rate of decrease)

where log is the natural logarithm function, and rate of decrease is the percentage decrease in value each year as a decimal. In this case, the rate of decrease is 25%, or 0.25 as a decimal.

Plugging in the values, we get:

years = log(500 / 100) / log(1 - 0.25)

Taking the natural logarithm of both sides and simplifying, we get:

years = 2.7725887222

Rounding to two decimal places, the answer is 2.77 years.

It will take approximately 2.77 years for the value of the phone to decrease to $100.

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The measure of side LJ would be 88 + 11 = 99. Round to the nearest tenth, LJ is 99.0.

To find the measure of side LJ, we need to use the concept of similarity between triangles.

If two triangles are similar, then the ratio of their corresponding side lengths is equal.

In this case, triangle GHI is similar to triangle JKL.

Let's assume the measure of side GH is x.

Then, the measure of side GI would be 8x and the measure of side HI would be 41x.

The measure of side JK would be x and the measure of side KL would be 8x.

By using the ratios of the side lengths,

we can set up an equation:

x/8x = JK/KL

Solving for x, we get x = 11. So, the measure of side KL is

8x = 8 * 11 = 88

The measure of side LJ would be 88 + 11 = 99. Round to the nearest tenth, LJ is 99.0.

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The statistics related to the use of social media is as of 2023, there are approximately 8 billion individuals on the planet, and 4.9 billion of them use social media.

Social media analytics is the process of gathering information about a specific brand, good, or service from social media websites and then evaluating that information to make smarter, more knowledgeable business decisions. These analysis' insights are frequently utilized to assess consumer sentiment about a particular brand or item. In all areas of operation, statistical data is crucial for any organization. Without the knowledge, businesses risk missing out on prospective marketing opportunities or fresh trends that are altering how consumers see a specific brand. Utilizing social media has a significant impact on a company's ability to expand. Adolescents who use social media for more than three hours a day are more likely to experience mental health issues. 32% of 12- to 17-year-old children express anxiety, and 13% report depression. 25% of those aged 18 to 25 report having a mental illness.

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Answer:

Step-by-step explanation:

question must be f(x)=5x-2/6

fog(x)= [5(6x+2/5)-2]/6 = [6x+2-2] /6 = x

gof(x)= [6(5x-2/6) +2]/5 = [ 5x-2+2]/5 = x

hence fog(x)=gof(x)

Abigail needs 550 beads to make 50 necklaces with 11 beads each. She needs 18 bags of beads, since each bag has 30 beads. This can be verified by multiplying 18 bags x 30 beads per bag = 540 beads. She may need to buy an extra bag to ensure she has enough beads.

The total number of beads Abigail needs is 550 (50 necklaces x 11 beads per necklace = 550 beads). Since each bag has 30 beads, Abigail needs 18 bags (550 beads/30 beads per bag = 18 bags of beads). To verify this calculation, Abigail can multiply 18 bags x 30 beads per bag = 540 beads, which is close enough to the total number of beads needed (550 beads). The remaining 10 beads can be taken from another bag, or Abigail can buy an extra bag to make sure she has enough beads.

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Using the normal distribution, it is found that:

a) 1.39% of teenagers use their phone less than 5 hours per day.

b) 3.59% of teenagers use their phone more than 10 hours per day.

c) 49.85% of teenagers use their phone between 6 to 8 hours per day.

d) The 75th percentile of the distribution is of 8.59 hours.

What is Normal Probability Distribution?

The Z-score of a measure X of a variable that has mean represented by μ and standard deviation represented by σ is given by the fraction presented as follows:

Z = (X - μ) / σ

The mean and the standard deviation of the daily amounts they use their phone are given as follows:

μ = 7.75 and σ = 1.25

a)

The proportion that use their phone for less than 5 hours a day is given by the p-value of Z when X = 5, hence:

Z = (X - μ) / σ

Z = (5 - 7.75) / 1.25

Z = -2.2

Z = -2.2 has a p-value of 0.0139.

Thus the percentage is of 1.39%.

b)

The proportion that use their phone for more than 10 hours a day is one subtracted by the p-value of Z when X = 10, hence:

Z = (X - μ) / σ

Z = (10 - 7.75)/1.25

Z = 1.8

Z = 1.8 has a p-value of 0.9641.

1 - 0.9641 = 0.0359 = 3.59% (percentage).

c)

The proportion between 6 and 8 hours a day is the p-value of Z when X = 8 subtracted by the p-value of Z when X = 6, hence:

X = 8:

Z = (X - μ) / σ

Z = (8 - 7.75)/1.25

Z = 0.2

Z = 0.2 has a p-value of 0.5793.

X = 6:

Z = (X - μ) / σ

Z = (6 - 7.75)/1.25

Z = -1.4

Z = -1.4 has a p-value of 0.0808.

0.5793 - 0.0808 = 0.4985 = 49.85% (percentage).

d)

The 75th percentile is X when Z = 0.675, hence:

Z = (X - μ) / σ

0.675 = (X - 7.75)/1.25

X - 7.75 = 0.675 x 1.25

X = 8.59 hours.

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The complete question is as follows:

Smartphones come with an app that keeps track of the amount of time that the phone is being used. For teenagers, the distribution of amount of time they use their phone is approximately normal with mean = 7.75 hours per day and standard deviation = 1.25 hours per day.

(a) What percent of teenagers use their phone less than 5 hours per day?

(b) What percent of teenagers use their phone more than 10 hours per day?

(c) What proportion of teenagers use their phone between 6 to 8 hours per day?

(d) What is the 75th percentile of this distribution?

Answer: C

Step-by-step explanation: Because c is just 2*5, not 2^5

The width of the planter box needs to be 2 meters, calculated by dividing the area of 15 1/2 [tex]m^{2}[/tex] by the length of 7 3/4 m.

To find the width of the planter box, we need to use the formula for the area of a rectangle:

A = lw

where A is the area, w is the width, l is the length.

We know the area is 15 1 2 m 2 15 2 1 ​ m 2 15, start fraction, 1, divided by, 2, end fraction, start text, m, end text, squared, and the length is 7 3 4 m 7 4 3 ​ m7, start fraction, 3, divided by, 4, end fraction, start text, m, end text long. Here is the equation to follow:

15 1 2 m 2 = 7 3 4 m × w

To solve for w, we'll isolate it on one side of the equation by dividing both sides by 7 3 4 m 7 4 3 ​ m7, start fraction, 3, 4 divided by start text, m, end text long, end fraction:

w = 15 1 2 m 2 ÷ 7 3 4 m = 2 m

So the width of the planter box needs to be 2 meters.

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Answer:

852

Step-by-step explanation:

If it has to be the largest 3 digit number, this would be it

Answer:

What is net income?

Net income is the total amount of money your business earned in a period of time, minus all of its business expenses, taxes, and interest. It measures your company’s profitability. You can learn more in our guide on net income meaning. For now, we’ll get right into how to calculate net income using the net income formula.

Net income formula

Net income is your company’s total profits after deducting all business expenses. Some people refer to net income as net earnings, net profit, or simply your “bottom line” (nicknamed from its location at the bottom of the income statement). It’s the amount of money you have left to pay shareholders, invest in new projects or equipment, pay off debts, or save for future use.

The formula for calculating net income is:

Revenue – Cost of Goods Sold – Expenses = Net Income

The first part of the formula, revenue minus cost of goods sold, is also the formula for gross income. (Check out our simple guide for how to calculate cost of goods sold).

So put another way, the net income formula is:

Gross Income – Expenses = Net Income

Or, if you really want to simplify things, you can express the net income formula as:

Total Revenues – Total Expenses = Net Income

Net income can be positive or negative. When your company has more revenues than expenses, you have a positive net income. If your total expenses are more than your revenues, you have a negative net income, also known as a net loss.

Using the formula above, you can find your company’s net income for any given period: annual, quarterly, or monthly—whichever timeframe works for your business.

Answer: take the total amount of money you have earned, and subtract taxes, insurance, and retirement

Step-by-step explanation:

The bill for a meal was $33.75. The customer left $40.00, the percentage of the bill the tip was, 18.51%

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To calculate the tip, we need to subtract the cost of the meal from the amount left by the customer. In this case, the tip would be

⇒ $40.00 - $33.75

⇒ $6.25.

To calculate the tip as a percentage of the bill, we need to divide the tip amount by the cost of the meal and multiply by 100:

⇒ ($6.25 / $33.75) x 100

⇒ 18.51%

So the tip was 18.51% of the bill.

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The heights of statistics students were obtained by the author as part of an experiment conducted for class.

Last Digits of Heights: 0, 8, 4, 6, 8, 0, 3, 1, 7, 5

Frequency Distribution:

Class Frequency

0-9 4

10-19 3

20-29 1

30-39 1

40-49 0

50-59 0

60-69 0

70-79 1

80-89 2

90-99 0

Based on the frequency distribution, the heights appear to be reported rather than actually measured. This suggests that the accuracy of the results may be questionable, as it is possible that the heights were rounded or estimated.

The heights of statistics students were obtained by the author as part of an experiment conducted for class. From the frequency distribution, it appears that the heights were reported rather than actually measured, suggesting that the accuracy of the results may be questionable.

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Suppose A is n*n and the equation Ax=0 has only the trivial solution. Then there are no free variables in this equation, thus A has in pivot columns.

If the equation Ax = 0 has only the trivial solution, there is a pivot in every column.

If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.

Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.

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This question is incomplete. Following question is complete.

Suppose A is n*n and the equation Ax=0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In

Choose the correct answer below.

A. Suppose A is n*n and the equation Ax=0 has only the trivial solution. Then there are no free variables in this equation, thus A has in pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the n × n identity matrix, In

B. Suppose A is n × n and the equation Ax=0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the n × n identity matrix. In

C. Suppose A is n*n and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the n × n identity matrix. In

Using your angle sum formula, you can see that this is sin(A+B).

3 theta is your A, 2 theta is your B.

To combine these, plug them into the simple sin(A+B) formula.

sin(3theta + 2theta)

sin(5theta) is your answer.

The factor of 2x² + 5x - 7 is (2x + 7)(x + 1).

What is a factor of a polynomial?

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, A quadratic expression 2x² + 5x - 7.

Now, Two numbers multiply to - 14 and add to + 5 is + 7 and - 2.

Therefore, The factor of 2x² + 5x - 7 is,

2x² + 7x - 2x - 7.

= x(2x + 7) + 1(2x + 7).

= (2x + 7)(x + 1).

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The domain of a function is the set of all possible input values (x-values) for which the function is defined and produces a valid output (y-value).

In this case, the function has a fraction with a square root in the denominator, so the domain is all real numbers except for those values of x that would make the denominator equal to zero.

The denominator of the fraction is √(x^2 - 4x + 5), which is equal to zero when x^2 - 4x + 5 = 0. This is a quadratic equation that can be solved using the quadratic formula, which gives us two solutions: x = (4 ± √(4^2 - 4(1)(5))) / (2 * 1) = (4 ± √(-16)) / 2 = (4 ± 4i) / 2

Since the square root of a negative number is not a real number, the solutions are not real numbers. This means that the denominator is not equal to zero when x = 4 ± 4i. Therefore, the domain of the function is all real numbers except x = 4, which is the only excluded value. So, the domain of the function is (-∞, 4) U (4, ∞).

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At Times Square, they plan to spend 55 minutes, which is equivalent to 0.92 hours. To calculate the latest time Tiana's family can start their tour, we need to add the time they plan to spend at each location.

Tiana is on a tour of New York City with her family. They want to visit the Empire State Building, Central Park, and Times Square before their dinner reservations at 6:15 P.M.

They have planned to spend specific amount of time at each place.

At the Empire State Building, they plan to spend 1 hour and 5 minutes, which is equivalent to 1.0833 hours.

At Central Park, they plan to spend 2 hours and 30 minutes, which is equivalent to 2.5 hours.

At Times Square, they plan to spend 55 minutes, which is equivalent to 0.92 hours. Therefore, the total time they plan to spend on the tour is 1.0833 + 2.5 + 0.92 = 4.5133 hours.

To arrive at the dinner reservation on time, they need to start the tour by 6:15 P.M - 4.5133 hours = 1:34 P.M. This is the latest time they can start their tour and still make it to dinner on time.

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Answer and Step-by-step explanation:

To prove the identity:

1/tan(x) + tan(x) = sec(x)csc(x)

We will use the following trigonometric identities:

tan(x) = sin(x)/cos(x)sec(x) = 1/cos(x)csc(x) = 1/sin(x)

Substituting (1) into the left-hand side of the given identity, we get:

1/tan(x) + tan(x) = 1/(sin(x)/cos(x)) + sin(x)/cos(x)

Simplifying the expression on the left-hand side, we get:

1/tan(x) + tan(x) = cos(x)/sin(x) + sin(x)/cos(x)

Now, we will obtain a common denominator of cos(x)sin(x) on the right-hand side:

1/tan(x) + tan(x) = (cos^2(x) + sin^2(x))/(cos(x)sin(x))

Using the identity cos^2(x) + sin^2(x) = 1, we can simplify this expression to:

1/tan(x) + tan(x) = 1/(cos(x)sin(x))

Substituting (2) and (3) into the right-hand side of the identity, we get:

1/tan(x) + tan(x) = sec(x)csc(x)

Therefore, we have shown that the given identity is true.

Answer:

The given identity is valid. Please see the steps below.

Step-by-step explanation:

Given

[tex]\frac{1}{\tan x}+\tan x=\sec x \csc x[/tex]

Lets prove the identity.

Write [tex]\tan x[/tex] as a fraction with a denominator of 1 .

[tex]\frac{1}{\tan x}+\frac{\tan x}{1}=\sec x \csc x[/tex]

To write [tex]\frac{\tan x}{1}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{\tan x}{\tan x}[/tex].

[tex]\frac{1}{\tan x}+\frac{\tan x}{1}*\frac{\tan x}{\tan x}=\sec x \csc x[/tex]

Multiply [tex]\frac{\tan x}{1}*\frac{\tan x}{\tan x}[/tex].

[tex]\frac{1}{\tan x}+\frac{\tan x\tan x}{\tan x}=\sec x \csc x[/tex]

Combine the numerators over the common denominator.

[tex]\frac{1+\tan x\tan x}{\tan x}=\sec x \csc x[/tex]

Multiply [tex]\tan x \tan x[/tex].

[tex]\frac{1+\tan^2 x}{\tan x}=\sec x \csc x[/tex]

Apply the Pythagorean identity to

[tex]\frac{\sec^2 x}{\tan x}=\sec x \csc x[/tex]

Convert everything to sines and cosines.

Apply the reciprocal identity to [tex]\sec x[/tex].

[tex]\frac{\left(\frac{1}{\cos x}\right)^2 }{\tan x}=\sec x \csc x[/tex]

Apply the quotient identity to [tex]\tan x[/tex].

[tex]\frac{\left(\frac{1}{\cos x}\right)^2 }{\frac{\sin x}{\cos x} }=\sec x \csc x[/tex]

Apply the product rule to [tex]\left(\frac{1}{\cos x}\right)^2[/tex].

[tex]\frac{\frac{1^2}{\cos^2 x}}{\frac{\sin x}{\cos x} }=\sec x \csc x[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]{\frac{1^2}{\cos^2 x}*\frac{\cos x}{\sin x} }=\sec x \csc x[/tex]

Combine the fractions.

[tex]{\frac{1^2 \cos x}{\cos^2 x \sin x}=\sec x \csc x[/tex]

Factor [tex]\cos x[/tex] out of [tex]\cos^2 x \sin x[/tex].

[tex]{\frac{1^2 \cos x}{\cos x\cos x \sin x}=\sec x \csc x[/tex]

Cancel the common factor of [tex]\cos x[/tex].

[tex]{\frac{1^2}{\cos x \sin x}=\sec x \csc x[/tex]

One to any power is one.

[tex]{\frac{1}{\cos x \sin x}=\sec x \csc x[/tex]

Rewrite [tex]{\frac{1}{\cos x \sin x}[/tex] as a product.

[tex]{\frac{1}{\cos x}*{\frac{1}{\sin x}=\sec x \csc x[/tex]

Apply the reciprocal identity to [tex]{\frac{1}{\cos x}[/tex].

[tex]\sec x*{\frac{1}{\sin x}=\sec x \csc x[/tex]

Apply the reciprocal identity to [tex]{\frac{1}{\sin x}[/tex].

[tex]\sec x*\csc x=\sec x \csc x[/tex]

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The ratio of the number of people playing badminton in Hotel West Bay to the number of people swimming in Hotel East Bay pool is 30/40, or 3/4.

What is Ratio?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

let's find the number of people who arrive late to Hotel West Bay and have to play badminton:

70 people in total - 40 people capacity = 30 people playing badminton

let's find the number of people who arrive late to Hotel East Bay and have to play golf:

100 people in total - 80 people capacity = 20 people playing golf

The ratio of the number of people playing badminton in Hotel West Bay to the number of people swimming in Hotel East Bay pool:

30 people playing badminton / (70 people in total - 30 people playing badminton)

3/4

Hence, the ratio of the number of people playing badminton in Hotel West Bay to the number of people swimming in Hotel East Bay pool is 30/40, or 3/4.

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Answer: 30:80 which can reduced to 3:8

Step-by-step explanation: The number of people arriving late at Hotel West Bay and playing Badminton instead of swimming is equal to 70-40= 30 people

our system of equations correctly models the fair race.Our answer was correctly verified by substituting the values of x and y into the equations.

Let x represent the distance the rabbit can travel and let y represent the distance the turtle can travel. The system of two linear equations can be expressed as:

x + y = 2000 (the total distance of the race)

x = 7y (the rabbit can travel 7 times as fast as the turtle)

Solving the system, we get x = 1400 and y = 600. This means that the rabbit can travel 1400 meters and the turtle can travel 600 meters in the race.

To check our answer, we can substitute the values of x and y into the equations:

x + y = 1400 + 600 = 2000 (the total distance of the race)

x = 7y = 7(600) = 4200 (the rabbit can travel 7 times as fast as the turtle)

Therefore, our system of equations correctly models the fair race.

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To find the number of students in your class who pack a lunch, divide 20 by 5 and then multiply that quotation by 3. Option B

What are fractions?

Fractions are simply defined as part of a whole variable, number or element.

There are different types of fractions. They include;

Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractions

From the information given, we have that;

Total number of students in the class is 20Those that packed their lunch are 3/5

Then, we have;

20 × 3/5

60/5

Divide the values

12 students

Hence, the value is 12

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Based on these calculations, approximately 51% of the customers received a 25% discount, which is close to the manager's goal of having half of the customers receive this discount.

The relative frequency for each discount can be calculated by dividing the number of customers who received each discount by the total number of customers (500).

For a 10% discount:

Number of customers who received the discount = 47 + 45 + 44 = 136

Relative frequency = 136 / 500 = 0.272

For a 25% discount:

Number of customers who received the discount = 52 + 58 + 50 + 46 + 49 = 255

Relative frequency = 255 / 500 = 0.51

For a 40% discount:

Number of customers who received the discount = 58 + 51 = 109

Relative frequency = 109 / 500 = 0.218

Based on these calculations, approximately 51% of the customers received a 25% discount, which is close to the manager's goal of having half of the customers receive this discount. However, it is unclear if this method is appropriate or not without further information about the manager's goals and the target population.

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Solution of the given equation 7 ( x + 20 ) = 210 by solving different way for each Emmanuel and Mauricio is equal to x = 10.

Completion of the solution of the equation :

7 ( x + 20 ) = 210

Solving by Emmanuel way is:

7(x+20) = 210

Open the parenthesis to simplify the equation we get,

⇒ 7x + 140 = 210

⇒ 7x = 210 -140

⇒ 7x = 70

⇒ x = 10

Solving by Mauricio way is:

7(x+20) = 210

Divide both the side by 7 we get,

⇒ x + 20 = 210 /7

⇒ x + 20 = 30

⇒ x = 30 - 20

⇒ x = 10

Therefore, the solving the given equation by Emmanuel and Mauricio way gives the solution x = 10.

The above question is incomplete , the complete question is:

Emmanuel and Mauricio are solving the equation 7(x+20) = 210 by different way of writing steps.

Emmanuel Mauricio

7(x+20) = 210 7(x+20) = 210

7x + 140 = 210 x + 20 = 30

Finish solving each equation.

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