The graphs of the functions f(x)

The third option best describes a stratified sample of customers. The Option C.

To form a stratified sample, the analyst divides the customers into six groups based on their mortgage amounts. This ensures that customers from different mortgage amount ranges are represented in the sample.

Then, the analyst randomly selects 13 customers from each group. By stratifying the sample based on mortgage amounts and selecting customers at random within each group, the analyst ensures that the sample is representative of the overall population of mortgage customers.

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Step-by-step explanation:

a) The mode is 7, because it appears three times, which is more than any other number in the list.

b) To find the median, we need to arrange the numbers in order from smallest to largest:

2 3 4 5 7 7 7 8 18

The median is the middle number, which in this case is 7, since there are an equal number of values on either side of it.

c) To calculate the mean, we add up all the numbers and then divide by the total number of values:

(3 + 7 + 2 + 4 + 7 + 5 + 7 + 18 + 8) / 9 = 61 / 9 ≈ 6.78

So the mean is approximately 6.78.

d) The range is the difference between the largest and smallest numbers in the list:

18 - 2 = 16

So the range is 16.

Answer:

The numbers are 9 in total

Step-by-step explanation:

a) Mode 7

7 is the most occuring number.

b) Rearrange the numbers to find median

2, 3, 4, 5, 7, 7, 7, 8, 18

median=7

middle number is the median

c) Mean=2+3+4+5+7+7+7+8+18/9

mean=6.7

d) Range= Highest number - lowest number

18-2=16

I hope this helps a lot!

Answer:

Step-by-step explanation:

Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.

The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:

P = 2(3x + 2x)

40 = 2(5x)

Now, let's solve for x:

40 = 10x

x = 40/10

x = 4

Now that we have the value of x, we can find the length of the rectangle:

Length = 3x = 3(4) = 12

Therefore, the length of the rectangle is 12.

The equation after completing the square is (x+2)²=3. Consider the equation: 0=x²+4x+1. To rewrite the equation by completing the square, we need to complete the square by adding and subtracting the square of half of the coefficient of the x.

Let's see how to complete the square: 0 = x² + 4x + 1(1)

We'll take the constant term (1) to the right-hand side of the equation, so it becomes negative. 0 = x² + 4x - 1(2)

To complete the square, we add and subtract the square of half of the coefficient of x. (a) Half of the coefficient of x is 4/2 = 2.

(b) We'll add and subtract 2² = 4. 0 = x² + 4x + 4 - 4 - 1(3)

The first three terms can be expressed as the square of the quantity x+2: (x+2)² = 0 + 4 - 1(4)This simplifies to: (x+2)² = 3

Thus, the equation after completing the square is (x+2)²=3.

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Answer:

Step-by-step explanation:

To determine the percentage of adults who had 2 children, we need to first find the total number of adults questioned.

Looking at the bar graph, we can see that the bar representing 2 children has a height of 2.5. This means that 2.5 adults indicated having 2 children.

Let's assume the total number of adults questioned is "m". According to the bar graph, the sum of the heights of all the bars represents the total number of adults questioned.

From the bar graph, we can see the following:

The bar representing 4+ children has a height of 4.

The bar representing 3- children has a height of 3.5.

The bar representing 2- children has a height of 2.5.

The bar representing 1- children has a height of 1.5.

The bar representing 1 child has a height of 1.

The bar representing 0.5- children has a height of 0.5.

The bar representing 0 children has a height of 0.

To find the total number of adults questioned (m), we sum up the heights of all the bars:

m = 4 + 3.5 + 3 + 2.5 + 2 + 1.5 + 1 + 0.5 + 0

m = 18

Therefore, the total number of adults questioned is 18.

To find the percentage of adults who had 2 children, we divide the number of adults with 2 children (2.5) by the total number of adults questioned (18) and multiply by 100:

Percentage = (2.5 / 18) * 100

Percentage ≈ 13.9 (rounded to 1 decimal place)

Therefore, approximately 13.9% of the adults questioned had 2 children.

Answer:

52% used.

Step-by-step explanation:

13/25=52/100=52%

When going from left to right, the item goes up, it increases, and when it goes down, it decreases

Step-by-step explanation:

When we simplify the expression, we get:

0.0048 * 0.81 / 0.027 * 0.04 = (0.0048 / 0.027) * (0.81 / 0.04)

Using a calculator to evaluate the two fractions separately, we get:

0.0048 / 0.027 ≈ 0.1778

0.81 / 0.04 = 20.25

Substituting these values back into the original expression, we get:

(0.0048 / 0.027) * (0.81 / 0.04) ≈ 0.1778 * 20.25

Multiplying these two values together, we get:

0.1778 * 20.25 ≈ 3.59715

To express the answer in standard form, we need to write it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point three places to the left, since there are three digits to the right of the decimal point:

3.59715 ≈ 3.59715 × 10^(-3)

Therefore, the final answer in standard form is approximately 3.59715 × 10^(-3).

Answer:On a coordinate plane, a straight line with positive slope goes through points (3, 3) and (4, 4).

Step-by-step explanation:

Answer:

when substituting x = -0.5, 0, and 1 into the equation, we get the results -8, -7, and -5, respectively.

Step-by-step explanation:

Part A:

To solve the equation 5 + x - 12 = 2x - 7, follow these steps:

Combine like terms on each side of the equation:

-7 + 5 + x - 12 = 2x - 7

-14 + x = 2x - 7

Simplify the equation by moving all terms containing x to one side:

x - 2x = -7 + 14

-x = 7

To isolate x, multiply both sides of the equation by -1:

(-1)(-x) = (-1)(7)

x = -7

Therefore, the solution to the equation is x = -7.

Part B:

Now let's substitute the given values of x and evaluate the equation:

For x = -0.5:

5 + (-0.5) - 12 = 2(-0.5) - 7

4.5 = -1 - 7

4.5 = -8

For x = 0:

5 + 0 - 12 = 2(0) - 7

-7 = -7

For x = 1:

5 + 1 - 12 = 2(1) - 7

-6 = -5

Answer:

Step-by-step explanation:

To simplify the expression (5x - 2) / (x - 2) - (4x), we can follow these steps:

First, let's simplify the numerator:

5x - 2

Now, let's distribute the negative sign to the term (4x):

-4x

Next, let's combine the terms in the numerator:

(5x - 2) - 4x = 5x - 2 - 4x = x - 2

Now, let's rewrite the expression:

(x - 2) / (x - 2) - 4x

Since we have (x - 2) as both the numerator and denominator, we can simplify further by canceling out the common factor:

1 - 4x

Therefore, the simplified form of the expression (5x - 2) / (x - 2) - (4x) is 1 - 4x.

Answer: O (4, -4)

Step-by-step explanation:

To solve the system of equations using elimination, we can multiply the second equation by -3 to eliminate the y term:

Original equations:

5x + 3y = 8 (Equation 1)

4x + y = 12 (Equation 2)

Multiply Equation 2 by -3:

-3(4x + y) = -3(12)

-12x - 3y = -36 (Equation 3)

Now we can add Equation 1 and Equation 3 to eliminate the y term:

(5x + 3y) + (-12x - 3y) = 8 + (-36)

Simplifying:

5x - 12x + 3y - 3y = 8 - 36

-7x = -28

Divide both sides by -7:

x = -28 / -7

x = 4

Now substitute the value of x back into either of the original equations, let's use Equation 2:

4(4) + y = 12

16 + y = 12

y = 12 - 16

y = -4

Therefore, the solution to the system of equations is x = 4 and y = -4.

To find an object's maximum height, we need to find the vertex of this quadratic equation.

Answer: 5.50 seconds

Terms to know:

Quadratic function: A quadratic function is a polynomial function of degree 2, which means the highest power of the variable in the equation is 2.

Vertex: The vertex of a quadratic function is the point on the graph where the function reaches its highest or lowest point. In the case of a quadratic function in the form f(x) = ax^2 + bx + c, the vertex is given by the coordinates (x, f(x)).

Step-by-step explanation:

The vertex of a quadratic equation can be represented as [tex](\frac{-b}{2a}, f(\frac{-b}{2a})[/tex]

Since we only are looking at the time it takes to reach maximum height we will only look at the x value.

[tex]x= \frac{-176}{2(-16)}[/tex]

[tex]x= 5.50[/tex]

The difference table for the sequence (-1, 6, 24, 56, 105, 174, 266) reveals a cubic pattern, where the third differences are constant at 3. Based on this pattern, the next term in the sequence is predicted to be 289.

The difference table for the given sequence (-1, 6, 24, 56, 105, 174, 266):

Term     |   First Difference   |   Second Difference   |   Third Difference

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

-1

6                         7

24                    18                                  11

56                   32                                 14                                   3

105                  49                                17                                   3

174                 69                                 20                                  3

266                92

To construct the difference table, we start by writing down the given sequence. Then, in the first column, we calculate the differences between consecutive terms. In the second column, we calculate the differences between the values in the first difference column. Similarly, in the third column, we calculate the differences between the values in the second difference column.

Analyzing the difference table, we observe that the third differences are constant at 3. This indicates a cubic pattern in the sequence, where the difference between consecutive terms is increasing by a constant amount each time.

To predict the next term, we take the last term of the sequence (266) and add the next difference (23) to it:

Next term = 266 + 23 = 289

Therefore, based on the pattern observed in the difference table, the next term in the sequence is predicted to be 289.

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The perimeter of the square and the area of the shaded part are 48cm and 454.16cm² respectively²

The formula for calculating the area of a circle is expressed as;

Area = πr²

Now, substitute the value, we have;

Area = 3.14 × 12²

Find the square and multiply the values, we have;

Area = 3.14(144)

Multiply the values

Area = 452. 16 cm²

Perimeter of a square take the formula;

Perimeter = 4a

Substitute the value

Perimeter = 4(12) = 48 cm

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Answer:

C.  [7.6, 10.6]

Step-by-step explanation:

To calculate the confidence interval for the mean number of misspelled words in the student population, we can use the confidence interval formula:

[tex]\boxed{CI=\overline{x}\pm z\left(\dfrac{s}{\sqrt{n}}\right)}[/tex]

where:

Given values:

The standard deviation is the square root of the variance:

[tex]s=\sqrt{s^2}=\sqrt{12.25}=3.5[/tex]

The empirical rule states that approximately 99.7% of the data points will fall within three standard deviations of the mean.

Therefore, z-value for a 99.7% confidence level is z = 3.

Substituting these values into the formula, we get:

[tex]CI=9.1\pm 3\left(\dfrac{3.5}{\sqrt{49}}\right)[/tex]

[tex]CI=9.1\pm 3\left(\dfrac{3.5}{7}\right)[/tex]

[tex]CI=9.1\pm 3\left(0.5\right)[/tex]

[tex]CI=9.1\pm 1.5[/tex]

Therefore, the 99.7% confidence limits are:

[tex]CI=9.1-1.5=7.6[/tex]

[tex]CI=9.1+1.5=10.6[/tex]

Therefore, the confidence interval for the mean number of misspelled words in the student population is [7.6, 10.6].

Answer:

12

Step-by-step explanation:

[tex]\frac{3}{4}[/tex](x - 3) - [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]

We are looking at the denominators of 4, 2 and 3.  We are looking for the least common multiple.  If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.

4,8,12

2,4,6,8,10,12

3,6,9,12

the lowest number that we see on all three lists is 12.

Answer:

Step-by-step explanation:

To recover your investment in 5 years or less, you would need to earn enough to cover the cost of going to school ($30,000) as well as make up for the lost salary over the 2 years of schooling ($45,000/year * 2 years = $90,000).

Therefore, the minimum salary you would need to earn upon earning your degree is the sum of the cost of going to school and the lost salary:

Minimum salary = $30,000 + $90,000 = $120,000.

In order to recover your investment in 5 years or less, you would need to earn a minimum salary of $120,000 per year.

To recuperate the total cost of $120,000 ($30,000 tuition + $90,000 forgone salary) over 5 years, you would need to earn $24,000 more per year on top of your original $45,000 salary. This implies that the minimum salary you need to earn after graduating is $69,000 per annum.

To determine the minimum salary, we first need to calculate your total forfeiture over the 2 years of school, which equates to real costs and opportunity costs. Firstly, the real cost is the tuition of $30,000. Secondly, the opportunity costs are the 2 years of salary you're forgoing, best understood as the wages you would've made if you hadn't gone to school. Assuming the salary of $45,000 per year, the total opportunity cost for the 2 years would be $90,000.

Therefore, the total investment is calculated as the sum costs of tuition and forgone salary i.e. $30,000 (tuition) + $90,000 (forgone salary) = $120,000. So to recover this investment in 5 years, you would need to earn an addition of $120,000 above your original salary. Meaning, you will have to recover $120,000 / 5 years = $24,000 per year on top of your initial salary to recover your total costs in the stated timeframe.

Therefore, the minimum salary you need to earn after earning your degree is equal to your original salary plus recovered investment per year: $45,000 (original salary) + $24,000 (increase) = $69,000. Hence, upon completion of your degree, you will have to earn at least $69,000 per year to recover your total investment within 5 years.

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Answer:

The smallest number is 40.

Step-by-step explanation:

Let the number be x. Then the next 4 number will be x+2, x+4, x+6, x+8

.°. x+x+2+x+4+x+6+x+8 = 220

5x + 20 = 220

5x = 200

x = 40

Therefore the smallest of the five consecutive numbers is 40

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The probability of the union of events A and B, P(A U B), is 0.824.

To find the probability, we can use the formula:

P(A U B) = P(A) + P(B) - P(A ∩ B)

Given that P(A) = 0.450, P(B) = 0.680, and P(A U B) = 0.824, we can substitute these values into the formula:

0.824 = 0.450 + 0.680 - P(A ∩ B)

To find the probability of the intersection of events A and B (P(A ∩ B)), we rearrange the equation:

P(A ∩ B) = 0.450 + 0.680 - 0.824

P(A ∩ B) = 1.130 - 0.824

P(A ∩ B) = 0.306

Therefore, the probability of the intersection of events A and B, P(A ∩ B), is 0.306.

We can also calculate the probability of the union of events A and B, P(A U B), by substituting the given values into the formula:

P(A U B) = P(A) + P(B) - P(A ∩ B)

P(A U B) = 0.450 + 0.680 - 0.306

P(A U B) = 0.824

Therefore, the probability of the union of events A and B, P(A U B), is 0.824.

In summary, we have found that the probability of the intersection of events A and B, P(A ∩ B), is 0.306, and the probability of the union of events A and B, P(A U B), is 0.824, based on the given probabilities.

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These are general considerations, and specific experiences may vary depending on geographical location, cultural practices, and individual preferences.

On days when the temperature was less than 58 degrees, it indicates that the weather was relatively cool. This could imply various conditions and experiences depending on the context and location. In general, some possible scenarios on such days may include:

Cooler outdoor activities: People might engage in activities such as hiking, jogging, or outdoor sports that are more enjoyable in cooler temperatures.

Layered clothing: Individuals may choose to wear warmer clothing, including jackets, sweaters, or scarves, to stay comfortable in the cooler weather.

Indoor activities: Cooler temperatures may encourage people to spend more time indoors, engaging in activities such as reading, watching movies, or pursuing hobbies.

Increased energy consumption: Cold weather often leads to an increased need for heating systems, resulting in higher energy consumption to maintain indoor comfort.

Changes in vegetation: Cooler temperatures can affect plant growth and flowering patterns. Certain plants may thrive in cooler conditions, while others may enter a dormant phase.

Changes in animal behavior: Some animals may adapt to cooler temperatures by seeking shelter or adjusting their activities and migration patterns.

Possible health effects: Cooler temperatures may impact individuals with certain health conditions, such as respiratory issues or joint pain, requiring them to take appropriate measures to stay comfortable.

These are general considerations, and specific experiences may vary depending on geographical location, cultural practices, and individual preferences.

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a. The interval of time between eruptions if the previous eruption lasted 4 minutes is 86.51 minutes.

b. The residual for this cycle is 2.07 minutes.

c. The interval of time between eruptions lasted for 2.07 minutes than the regression line equation predicted.

d. The slope of the regression line means that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

e. No, the value of the y-intercept doesn't have meaning in the context of the problem.

Based on the information provided above, the relationship between the duration of the previous eruption (x in minutes) and the interval of time between eruptions (y in minutes) is modeled by this regression line equation:

ÿ = 33.35 + 13.29x

Part a.

When x = 4 minutes, the value of is given by:

ÿ = 33.35 + 13.29(4)

ÿ = 86.51 minutes.

Part b.

The residual for the given cycle can be calculated as follows;

Residual = y - ÿ

Residual = 62 - (33.35 + 13.29(2))

Residual = 62 - 59.93

Residual = 2.07 minutes.

Part c.

Based on the calculation above, we can logically deduce that the interval of time between eruptions lasted for 2.07 minutes than the equation of regression line predicted.

Part d.

The slope of the regression line is equal to 13.29 and it implies that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

Part e.

In the context of the problem, we can logically deduce that the value of the y-intercept doesn't have any meaning because the duration of the previous eruption cannot be equal to 0 minutes.

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First, we need to convert the length of the ribbon to centimeters to match the length of the ribbon pieces we plan to cut:

4m 20cm = (4 x 100)cm + 20cm = 420cm

Next, we can divide the total length of the ribbon by the length of each piece to find how many pieces we can cut:

420cm ÷ 70cm = 6

Therefore, we can cut 6 smaller ribbons, each 70cm long, from the 4m 20cm length of ribbon we have.

The boundaries of the 99% confidence interval are

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

Selected, x = 28021

Sample, n = 38433

This means that the proportion, p is

p = 28021/38433

p = 0.729

The 99% confidence interval is then calculated as

CI = p ± z * √(p * (1 - p)/n)

Where

z = 2.576 i.e. the z-score at 99% confidence interval

So, we have

CI = 0.729 ± 2.576  * √(0.729 * (1 - 0.729)/38433)

Evaluate

CI = 0.729 ± 0.0058

Evaluate

CI = (0.7232, 0.7348)

Hence, the confidence interval is (0.7232, 0.7348)

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Step-by-step explanation:

1 job divided by the sum of the rates = 3 hours

1 / ( 1/5 + 1/x )  = 3  

x = 7.5 hrs    for assistant alone

The correct answer is Yearly income assessable income: Rs 7,75,974

Taxable income of Amar: Rs 7,66,796

To find Amar's yearly income, we'll consider his monthly salary and additional benefits:

Yearly Income:

Monthly salary = Rs 58,786

Yearly salary = Monthly salary * 12 = Rs 58,786 * 12 = Rs 7,05,432

Additional benefits:

One month salary for festival expense = Rs 58,786

EPF contribution per month (deducted from salary) = 10% of monthly salary = 0.10 * Rs 58,786 = Rs 5,878

Government's EPF contribution = Rs 5,878

Total additional benefits per year = One month salary + EPF contribution + Government's EPF contribution = Rs 58,786 + Rs 5,878 + Rs 5,878 = Rs 70,542

Yearly income assessable income = Yearly salary + Total additional benefits = Rs 7,05,432 + Rs 70,542 = Rs 7,75,974

Taxable Income:

To calculate the taxable income, we deduct certain deductions from the assessable income.

Deductions:

EPF contribution per month (deducted from salary) = Rs 5,878

Life insurance per month = Rs 3,300

Total deductions per year = EPF contribution + Life insurance = Rs 5,878 + Rs 3,300 = Rs 9,178

Taxable income = Assessable income - Total deductions = Rs 7,75,974 - Rs 9,178 = Rs 7,66,796

Income Tax:

To determine the income tax paid, we need to apply the applicable tax rate to the taxable income. Since tax rates can vary based on the country and specific rules, I am unable to provide the exact income tax amount without additional information.

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Answer:

Where lines cross over each other. The lines have a common point.