the quartiles of a dataset are the three values that divide the data into four equal groups, each group representing 25% of the data. the first quartile (q1), also known as the lower quartile, is the value that separates the lowest 25% of the data from the rest of the data. the second quartile (q2), also known as the median, is the value that separates the lowest 50% of the data from the highest 50% of the data. the third quartile (q3), also known as the upper quartile, is the value that separates the lowest 75% of the data from the highest 25% of the data. together, the three quartiles can give a sense of the distribution of the data and the spread of the values

By equation for the graph y = 2 cos (x − π 12)  this  we get  

x            f (x)

π /2        2

π            0

3π / 2     -2

2π           0

5π / 2      2.

y = 2 cos (x − π 12)

Find the parameters necessary to calculate the amplitude, period, phase shift, and vertical shift using the formula a cos (b x c ) + d.

a = 2

b= 1

c = π /2

d = 0

locate | a |'s amplitude.

Dimension: 2

Calculate the duration of 2 cos (x 2 ).

2 | b | can be used to determine the period of the function.

2π / |b|

In the formula for the period, swap out b for 1.

2π  /  |1 |

What separates a number from zero is its absolute value. 0 to 1 are separated by a distance of 1 and 2 units.

1

Subtract 2 from 1 to get 2.

Use the cb formula to get the phase shift.

From c b, one may get the phase shift of the function.

c b: Phase Shift

The equation for phase shift should have the values of c and b changed.

Changing phases: 2 1

Take 2 and divide it by 1.

Shift in Phase: 2

Name the trigonometric function's attributes.

Two-second period with amplitude two

Phase Change: 2 (rightward by 2).

Vertical Shift: null

To graph, choose a few points.

To continue, tap the screen.

x          f ( x )

π /2         2

π             0

3π /2      − 2

2 π           0

5π / 2       2

Amplitude, period, vertical shift, phase shift, and points can all be used to graph the trig function.

Dimension: 2

Two (2) years

Phase Change: 2 (rightward by 2).

Vertical Shift: null

x            f (x)

π /2        2

π            0

3π / 2     -2

2π           0

5π / 2      2.

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3rd image is translations are rigid transformations that do not change the orientation of the original image.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

3rd image is translations are rigid transformations that do not change the orientation of the original image.

2 and 4 are rotations and 5 is a dilation.

Hence, 3rd image is translations are rigid transformations that do not change the orientation of the original image.

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The limit does not exist because the function is not defined at (x,y) = (0,0)You can see this by plugging in (x,y) = (0,0) into the function, you get 3(0^2) * 0 / (0^2 + 0^2) = 0 / 0 which is an indeterminate form.

In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Calculus and mathematical depend on limits, which are also used to determine integrals, derivative, and continuity.

There are each limits (left- and proper limits), infinite limits, and limitations at infinity in addition to regular, two-sided limits.

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Answer:12 fives 2 10's

Step-by-step explanation:

So, the two balls are located on the same plane, the x-y plane, with the baseball at <3,5,0>m and the tennis ball at <-3,-1,0>m, with the vector pointing from baseball to the tennis ball is <-6,-6,0>m.

The position vector of the baseball is <3,5,0>m. The position vector of the tennis ball is <-3,-1,0>m.

The position vector of the tennis ball relative to the baseball is the vector pointing from the baseball to the tennis ball and it is calculated by subtracting the position vector of the baseball from the position vector of the tennis ball: <-3,-1,0>m - <3,5,0>m = <-6,-6,0>m

So the two balls are located on the same plane, the x-y plane, with the baseball at <3,5,0>m and the tennis ball at <-3,-1,0>m, with the vector pointing from baseball to the tennis ball is <-6,-6,0>m.

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Answer:

-12 < -5

Step-by-step explanation:

its simple math. -12 is less than -5 because its more negative.

The coldest temperature recorded in Vostok station in Fahrenheit is -89.2°F

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

The coldest temperature recorded in Vostok station in Fahrenheit is:

= -22.3 × 4

= -89.2°F

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Every month of the year has

The numerical value of the expression 3a - 5b when a = -3 and b = -2 is 1.

Given the expression in the question;

3a - 5b

To determine the value of the expression, replace a with -3 and b with -2 for all occurrence of a and b in the expression.

3a - 5b

Plug in a = -3

3( -3 ) - 5b

Plug in b = -2

3( -3 ) - 5( -2 )

-9 -+ 10

10 - 9

Subtract 9 from 10

1

Therefore, the value of the expression is 1.

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The number 480,000 in scientific notation is 4.8 * 10⁵

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

Number = 480,000

Multiply the number by 1

So, we have the following representation

Number = 480000 * 1

Express 1 as 10⁵/10⁵

Som we have

Number = 480000 * 10⁵/10⁵

This gives

Number = 4.8 * 10⁵

Hence, the expression is 4.8 * 10⁵

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Answer:

Step-by-step explanation:

8 - (-5) - 4(-7)

8- (-5) - (-28)

8 + 5 + 28

13 + 28

41

Answer:

8 - (-5) - 4(-7) = 41

Step-by-step explanation:

Given problem,

→ 8 - (-5) - 4(-7)

Let's solve the problem,

→ 8 - (-5) - 4(-7)

→ 8 + 5 - (4 × -7)

→ 13 - (-28)

→ 13 + 28

→ 41 => final answer

Hence, the answer is 41.

After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score. These measurements must come from a ratio scale

A ratio scale is a type of measurement scale that allows for the comparison of two or more values by using division. After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score.

In this case, the researcher is comparing Bob's score to Jane's score, and the comparison involves division (Bob's score is three times greater than Jane's score).

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A one-sample z-test for a population proportion requires that n po > 10 and n(1-Po) > 10 for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size.

1. Calculate the sample size, n, needed for the test.

2. Check that npo > 10 and n(1 - Po) > 10 for both the sample and population proportions, Po.

3. Check that each sample proportion is less than or equal to 0.5.

4. Check that the sample size is more than 10 times the population size.

5. Check that the population size is more than 10 times the sample size.

6. Check that the population distribution is approximately normal.

A one-sample z-test for a population proportion is used to evaluate the difference between a sample proportion and a population proportion. Before conducting the test, it is important to check for independence, which is done by ensuring that certain conditions are met. First, npo > 10 and n(1-Po) > 10 must be true for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size. Lastly, the population distribution must be approximately normal. These conditions must be met in order for the test to be valid and reliable. If any of these conditions are not met, the test results may be inaccurate.

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The given tax rates are as follows: Drew’s tax due is 4,519.50 and his effective tax rate is 11.6%. Option A is correct.

You will determine your total taxable income based on your tax slab by subtracting all eligible deductions from the gross taxable income. Senior citizens pay a different slab rate.

An income tax system's tax base is referred to as taxable income. That is, the amount of income that was subject to taxation by the government. In most cases, some or all of the income is included, and expenses and other deductions reduce it.

                      Single Taxpayers: Income Brackets

Tax Income                  Rate Bracket             Tax Owed              

0 to 9,525                       10%                     10% of taxable income

9,526 to38,700               12%        $952.50 plus 12% of  38,700 the excess                                                                                        over

$38,701 to 82,500          22 %                $4,453.50 plus 22% of 38,701                                                                                     the excess over

82,501 to 157,500          24%      $14,089.50 plus 24% of the excess over

                                                                                                         157,500

157,501 to  200,000       32%      $ 32089.50  plus 32% of the excess over

200,001 to   500,000     35%      45,689.50 plus 35% of excess over

500,000 >                        37%      $150,689.50 plus 37% of 500,000 of the    

                                                             excess over

The taxable income lies in the tax rate range of   $38,701 to 82,500.

Therefore the tax would be  :

                                  $4,453.50 + 22% of (39,000-38,701=299)

                                           = $4,453.50 + 22% of 299

                                                  =  $4,453.50 + 65.78

                                                  = $ 4519.28

The taxable income lies in the tax rate range of  $38,701 to 82,500. Due and effective tax rate is $4,453.50 plus 22% of 38,701 the excess over.

The calculated tax is $ 4519.28

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The statement a(x-b)-c = ax-(ab+c) is true because it follows the rules of algebraic operations and the distributive property.

On the left side of the equation, we have a(x-b)-c.

Here, a is a constant and it is being multiplied by (x-b). According to the distributive property, we can rewrite this as:

ax-ab-c.

On the right side of the equation, we have ax-(ab+c)

Here, we have a constant a being multiplied by x and then we have another constant ab and c being subtracted, which we can also rewrite as:

ax - ab -c

As you can see, both sides of the equation are equivalent and the statement is true.

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The model's graph, y = 10770/x2 - 0.37, 5 x 100 demonstrates that the resistance will be about halved when the wire's diameter is doubled. This is brought on by the inverse square relationship between wire resistance and diameter.

1. Graph the model y = 10770/x² - 0.37, 5 ≤ x ≤ 100 using a graphing utility.

2. Find the resistance when x is 5.

y = 10770/5² - 0.37 = 2104.1 ohms

3. Find the resistance when x is 10.

y = 10770/10² - 0.37 = 526 ohms

4. Divide 2104.1 by 526 to find the factor by which the resistance is changed when the diameter of the wire is doubled.

2104.1/526 = 4

The graph of the model y = 10770/x² - 0.37, 5 ≤ x ≤ 100 shows that the resistance of the wire decreases as the diameter of the wire increases. Doubling the diameter of the wire will roughly halve the resistance, as can be seen by comparing the resistance when x is 5 (2104.1 ohms) to the resistance when x is 10 (526 ohms). Thus, the resistance is changed by a factor of 4 when the diameter of the wire is doubled.

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False. Undifferentiated schizophrenia is a type of schizophrenia where a person displays general symptoms of the disorder such as hallucinations and delusions, but does not meet the criteria for any of the other subtypes of schizophrenia.

A person exhibiting a mixture of schizophrenic symptoms would likely be diagnosed with schizophrenia, but not as specifically undifferentiated schizophrenia.This disorder is characterized by a mixture of positive and negative symptoms, including delusions, hallucinations, disorganized speech, disorganized behavior, lack of emotion, and social withdrawal. However, a person who exhibits a mixture of schizophrenic symptoms could have any type of schizophrenia, not just undifferentiated schizophrenia. For example, a person could have paranoid schizophrenia, disorganized schizophrenia, or catatonic schizophrenia. To diagnose schizophrenia, a doctor must analyze the patient's symptoms and determine which type of schizophrenia they have.

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No, there is not. We do not have sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000.

To test the hypothesis that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000, we can use a two-proportion z-test. The null hypothesis is that the proportion of U.S. adults who are aware of the investment's outcome is equal to or greater than 40%, and the alternative hypothesis is that the proportion is less than 40%.

The test statistic is calculated as:

z = (p1 - p2) / √(p(1-p)(1/n1 + 1/n2))

where p1 is the proportion of U.S. adults in the sample who are aware of the investment's outcome (374/1010), p2 is the proportion assumed in the null hypothesis (0.4), and n1 and n2 are the number of observations in the sample and population, respectively.

Using these values, the test statistic is:

z = (0.369 - 0.4) / √(0.4(1-0.4)(1/1010)) = -1.08

Using a two-sided test with a significance level of 0.05, we can look up the critical value in a standard normal table or using software and find that the critical value is ±1.96. Since -1.08 is between -1.96 and 1.96, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000.

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Answer: In order to solve for x, we will have to use the logarithmic properties to isolate x.

f(x) = 3 - 4 In (x-2)

To solve for x, we will have to get x alone on one side of the equation by using the logarithmic property that logb(a^c) = c*logb(a).

4 In (x-2) = 3

In (x-2) = 3/4

To find x, we will raise e to the power of both sides

x-2 = e^(3/4)

x = e^(3/4) + 2

So the solution of x is e^(3/4) + 2

It's important to notice that the natural logarithm (ln) and log base e (In) are same and the solution is valid for both.

Step-by-step explanation:

The sum of expression 1/2 + 2/(1/2) is obtained to be option B: 4.

What is sum?

The outcome of adding two or more numbers or phrases is known as the sum in mathematics. The sum is a method of bringing things together as a result. To put it another way, adding two or more numbers together results in a new result or total.

The fractional expression is - 1/2 + 2/(1/2)

Apply the fraction reciprocal rule -

If there is a fraction in denominator then it is reciprocated and multiplied.

= 1/2 + 2/(1/2)

= 1/2 + 2(2/1)

= 1/2 + 4

Now, take the LCM and multiply it with the numerators -

= 1/2 + 4

Find the sum of the numbers -

= (1 + 8)/2

= 9/2

= 4.5

When estimated and rounded the number is equivalent to 4.

Therefore, the fractional expression results in 4.

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Estimate the sum. Round the number.

1/2 + 2/(1/2)

The sum is approximately -

A: 0

B: 4

C: -4

D: 8

Answer:

70

Step-by-step explanation:

The time that should take her to run each mile is approx 11.5 minutes.

Given that,

She runs 5 miles in 57 and a half minutes.

Based on the above information,

The time that should be taken by her is

= 57.5 ÷ 5 miles

= 11.5 minutes.

Therefore we can conclude that the time that should take her to run each mile is approx 11.5 minutes......

Time cross-sectional data is data collected from a sample of subjects at a single point in time.

This data can be used to measure the characteristics of a population at a given point in time. For example, a population can be surveyed to measure the percentage of people who own a car, the median age of the population, or the percentage of people who have a college education.

Time series data is data collected from the same sample of subjects over a period of time. This data can be used to measure the changes in a population over time. For example, a population can be surveyed to measure the percentage of people who own a car over a five-year period, the median age of the population over the same five-year period, or the percentage of people who have a college education over the same five-year period.

Time controlled data is data collected from the same sample of subjects at different points in time but with a controlled variable. For example, a survey can be conducted to measure the percentage of people who own a car at the start of the school year, the median age of the population at the start of the school year, and the percentage of people who have a college education at the start of the school year in different cities.

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Emily Janson should receive the scholarship offer because she has the higher batting average over the combined junior and senior years.

The batting average of a player is calculated by dividing the number of hits they have by the total number of at-bats. This can be expressed as a formula: Batting Average = H/AB.

For Allison Fealey, her junior year batting average can be calculated by dividing the number of hits (15) by the total number of at-bats (40), which is 0.375. Emily Janson’s junior year batting average can be calculated by dividing the number of hits (74) by the total number of at-bats (204), which is 0.363

For Allison Fealey, her senior year batting average can be calculated by dividing the number of hits (79) by the total number of at-bats (254), which is 0.310. Emily Janson’s senior year batting average can be calculated by dividing the number of hits (35) by the total number of at-bats (120), which is 0.292.

When the data from the junior and senior years were combined and aggregated, Allison Fealey’s combined two-year batting average can be calculated by dividing the number of hits (94) by the total number of at-bats (294), which is 0.320. Emily Janson’s combined two-year batting average can be calculated by dividing the number of hits (109) by the total number of at-bats (324), which is 0.336.

Based on this analysis, Emily Janson should receive the scholarship offer because she has the higher batting average over the combined junior and senior years.

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The true statement is " A and B must point in the same direction."

Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by A + B = C. Which one of the following statements concerning these vectors is true?

According to the question

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Answer:

A line that is perpendicular to the line y=-2x+1 will have a slope that is the negative reciprocal of -2, which is 1/2.

The equation of a line in point-slope form is:

y - y1 = m(x - x1)

Where m is the slope of the line, and (x1, y1) is a point on the line.

Given that the point (-4,3) lies on the line, we can substitute those values for x1 and y1:

y - 3 = 1/2(x + 4)

Which is the equation of a line that is perpendicular to y=-2x+1 that passes through the point (-4,3).

Alternatively, you can also write the equation of a line in slope-intercept form y = mx + b,

The slope of a line perpendicular to y=-2x+1 is 1/2, therefore m = 1/2

We can substitute the point (-4,3) in the equation y = mx + b,

3 = (1/2)(-4) + b

b = 3.5

Therefore the equation of the line is y = 1/2x + 3.5

The interest rate that Mr. Mogi borrowed the money, given the amount borrowed and the amount repaid, is 17. 8%

To find the interest rate that Mr. Mogi borrowed the money at, first find the amount he paid per year:

= Total payment / Number of years

= 20, 000 / 10

= $ 2, 000 per year

You can then use the RATE function on Spreadsheet to find the interest:

NPER = 10 years

PMT = $ 2, 000

PV = 9, 000

FV = $ 20, 000

The interest rate would be 17. 8%

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The area of the figure given, which is composed of a rectangle and two semicircles, is 154. 27 units ²

First, find the area of the rectangle in the composite shape which is :

= Length x Width

= 13 x 8

= 104 units ²

The area of a semi - circle is:

= ( π x r ² ) / 2

Seeing as there are two semi - circles, the area is:

= π x r ²  

= π x 4 ²

= 50. 27 units  ²

The area of the composite shape is therefore:

= 50. 27 + 104

= 154. 27 units ²

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Answer:

Four hundred thirdy seven and six hundred and eight thousandths.

437.068

Step-by-step explanation:

Hope it helps! =D

The number formed by these terms is 437.068.

To solve this problem, we first need to understand the place value system and what each term represents.

As per the place value system used in decimals:

- Hundreds: It is the third digit to the left of the decimal point and each unit represents 100.
- Tens: It is the second digit to the left of the decimal point and each unit represents 10.
- Ones: It is right next to the decimal point, all the digits to the left of it are the ones. Each unit represents 1.
- Hundredths: It is the second digit to the right of the decimal point and each unit represents 0.01.
- Thousandths: It is the third digit to the right of the decimal point and each unit represents 0.001.

In the given context, we know that there are 4 hundreds, 3 tens, 7 ones, 6 hundredths, and 8 thousandths.

To start, we calculate each term separately:

- 4 hundreds = 4 x 100 = 400
- 3 tens = 3 x 10 = 30
- 7 ones = 7 x 1 = 7
- 6 hundredths = 6 x 0.01 = 0.06
- 8 thousandths = 8 x 0.001 = 0.008

After evaluating each term separately, we sum them up together for the final answer:

- Sum = 400 + 30 + 7 + 0.06 + 0.008 = 437.068

Hence, the number formed by these terms is 437.068.

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lim [f(x) - g(x)] is9.

Generally, In mathematics, a limit is a value that a function "approaches" as the input of the function "approach" some value.

More formally, given a function f(x) and a value L, we say that "the limit of f(x) as x approaches a is L" if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a, but not equal to a.

In other words, the limit of a function describes the behavior of the function as the input gets arbitrarily close to a particular value, but doesn't necessarily equal that value

The limit of the difference between the two functions is the difference of their individual limits. So,

lim [f(x) - g(x)] = lim f(x) - lim g(x)

= 7 - (-2)

= 9.

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The total number of animals in the farm is given by 200

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here: The number of cows is 30 and they form 15% of the total animals on the farm.

Let the number of animals in the form be x then

15% of x=30

x=30×100/15

x=200

Hence, The total number of animals in the farm is given by 200

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