25 points. Please show working out!

The zeros at the end of a number can be significant if it contains decimal point only if the digit next to or at the end of the number (of decimal point) is a significant number.

Significant numbers of a given number are those digits that can convey the meaning of the number or what it stands for (measures as) according to its accuracy.

All non-zero numbers are significant numbers irrespective of the fact where they are positioned, that is they can be positioned before or after a decimal (also before or after a zero).

All zeros are not significant numbers and whetehr they are to be called significant numbers or depend on the fact where they are positioned and whether they convey any meaning (or value ) of the number. If the zeros are between two non zero significant digits then zero is also considered as a significant number.

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A graph of the function,

f(x) = log₃(x - 1) + 2 is given in the image below.

The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

Given:

A function,

f(x) = log₃(x - 1) + 2.

let y = f(x) = log₃(x - 1) + 2.

To find the y-intercept:

y = log₃(-1) + 2

y = 1.111

Therefore, the graph of the function is given in the attached image.

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You cannot compare two marginal distributions to see if the corresponding two variables are related.

Therefore the answer is False.

Comparing two marginal distributions only provides information about the individual variables, not their relationship. Marginal distributions represent the frequencies or probabilities of each variable independently of the other variables in the dataset. To determine the relationship between two variables, a joint distribution or a statistical test such as correlation or regression analysis should be used. These methods allow for a deeper understanding of the relationship between the variables and can provide insights into their direction and strength of association. Therefore the given statement "You can compare two marginal distributions to see if the corresponding two variables are related." is False.

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The slope of the line passing through the points (2, 8) and (2, -4) is undefined.

The slope of the line passing through the points (-7, 8) and (2, 8) is zero.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-4 - 8)/(2 - 2)

Slope, m = (-12)/0

Slope, m = undefined.

Since the change in the y-axis equals to zero, the slope of this line is equal to zero:

Slope, m = (8 - 8)/(2 - (-7))

Slope, m = 0/9

Slope, m = 0

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Answer:

The probability of landing on less than two sections when the spinner is spun once is 0.25.

Answer: it will be 0.25 hope this helped have a nice day :)

20h⁵ - 35h⁴ is the simplified and dispersed expression.

What does math's distribution mean?

Something is divided, shared, or given away when it is "distributed." What does this mean for the distributive property of mathematics? Basic arithmetic operations like addition and subtraction are used to divide the results of multiplication according to the distributive property of the law of multiplication.

We may utilize the distributive property of multiplication, which asserts that a(b + c) = ab + ac, to distribute and simplify 5h³(4h² - 7h).

The 5h³ is first distributed to both words inside of the parenthesis as follows:

5h³(4h² - 7h) is equal to 5h³ * 4h² - 5h³ * 7h.

Secondly, by multiplying the coefficients and adding the exponents, we simplify each term:

20:5 + 5:3 + 4:2 + 5:3 + 7:4 = 35:4

When we add everything together, we get the following: 5h³(4h² - 7h) = 20h⁵- 35h⁴.

Hence, 20h⁵ - 35h⁴ is the simplified and dispersed expression.

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The next step would be to draw an arc with the compass centered at the endpoint.

This arc should intersect the segment at two points.

We have,

After Jessica places the compass on one endpoint of the segment and opens it to a width larger than half of the segment, her next step would be to draw an arc with the compass centered at the endpoint.

The concept used in Jessica's next step is the compass-and-straightedge construction method.

By opening the compass wider than half of the segment and drawing an arc with the compass centered at one endpoint, she creates two points of intersection between the arc and the segment.

These points will divide the segment into two equal halves, allowing her to bisect the segment.

Thus,

The next step would be to draw an arc with the compass centered at the endpoint.

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The value of weight of 73 kg when converted to pounds is  160.93726 pounds.

kilogram is the standard unit of mass in the International System of Units (SI), while pounds are a common unit of mass used in the United States and other countries.

To Know how to convert between different units of measurement is essential for accurate calculations and comparisons. convert 73kg to pounds, you can use the formula: 1 kilogram is equal to 2.20462 pounds.

Therefore, to convert 73kg to pounds, you would multiply 73 by 2.20462.

73 x 2.20462 = 160.93726 pounds

So, weight of 73kg is equivalent to 160.93726 pounds

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20 kg is approximately equal to 44.0925 pounds ( rounded to four decimal places )

The conversion factor to convert kg to pounds is 2.20462

1 kg = 2.20462 pounds

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in pounds = The mass in kg × conversion factor

Substitute the values in the equation

1 kg = 2.20462 pounds

20 kg =  20 × 2.20462

Multiply the numbers

= 44.0925 pounds  ( rounded to four decimal places )

Therefore, 20 kg is 44.0925 pounds

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To convert  90% confidence interval, add and subtract the margin of error from the sample mean

A 90% confidence interval is a range of values that is likely to contain the true population parameter with 90% probability. Here's how you can calculate a 90% confidence interval:

Collect a sample of data that is representative of the population

Calculate the sample mean and the sample standard deviation (s).

Determine the sample size (n).

Use a t-distribution table or calculator to find the critical t value for a 90% confidence level and (n-1) degrees of freedom.

Calculate the margin of error by multiplying the critical t value by the standard error of the mean, which is s/ [tex]\sqrt{n}[/tex].

margin of error = t-value × (s / [tex]\sqrt{n}[/tex])

Determine the upper and lower bounds of the confidence interval by adding and subtracting the margin of error from the sample mean.

Lower bound = Sample mean - margin of error

Upper bound = sample mean + margin of error

The resulting interval will be the 90% confidence interval for the population mean.

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1) r base number is 3.

2)This is an exponential growth function

3) the Y interception is (0,2)

4)The purple line in the graph is a Horizontal asymptote and it has an equation 1.

5)The domain of the function is all real numbers.

6) The range of the function is all the real numbers >1

What is exponential growth function ?

A process called exponential growth sees a rise in quantity over time. When a quantity's derivative, or instantaneous rate of change with respect to time, is proportionate to the quantity itself, this phenomenon takes place.

This is an exponential growth function so

Our base number is 3.

For statement 2 as explained, it is a growth function.

As far we get in X-axis higher is the value.

For statement 3 the Y interception is (0,2) as sowed below.

For statement 4 The purple line in the graph is a Horizontal asymptote and it has an equation 1.

For statement 5 The domain of the function is all real numbers.

For statement 6 The range of the function is all the real numbers >1. Because we do not include the asymptote.

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The converted value of the units 3000 meters to the required miles is given by 1. 8641 miles ( round up to four decimal places ) .

Standard form to Convert meters and miles is equal to :

1 meter = 0.000621371 miles

Now,  the value of 3000 meters in miles we get by multiplying it by 0.000621371 we get,

3000 meters = ( 3000 ) × ( 0.000621371 ) miles

                      = ( 1.864113 ) miles

                      = ( 1.8641 ) miles ( round up to four decimals places )

Therefore, the value of 3000 meters to miles is equal to ( 1.8641 ) miles ( round up to four decimals places ) .

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The value of 104 kg into lbs can be converted by multiplying kilogram by 2.204622  so the answer is 229.3 pounds.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

The SI unit of mass is the kilogramme (kg). It has the same mass as the international kilogramme prototype. The International Bureau of Weights and Measures maintains a platinum-iridium international prototype similar to this one. A kilogramme is about equivalent to 2.20462262184878 pounds.

The legal definition of a pound, or the international avoirdupois pound, is 0.45359237 kilogrammes.

Pounds = kilograms × 2.20462262184878

= 104 x 2.20462262184878

= 229.3 pounds or lbs.

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The nominal GDP in 2012 is $3,450.00.

The GDP deflator is a price index that measures the average price level of goods and services produced in an economy. It is calculated as the ratio of nominal GDP to real GDP, multiplied by 100.

Nominal GDP (Gross Domestic Product) is a measure of the total value of all goods and services produced within a country's borders during a given period of time, usually a year, using current market prices

To use the GDP deflator formula to answer the question, we need to rearrange the formula and solve for nominal GDP:

Nominal GDP = Real GDP × (GDP deflator / 100)

Plugging in the given values, we get:

Nominal GDP = $2,300.00 × (150.00 / 100) = $3,450.00

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The given question is incomplete, the complete question is:

: The GDP deflator formula can be used in a variety of ways. Use it to answer the questions that follow. Round final answers to two decimal places, as needed. Real GDP $2300.00 GDP deflator 150.00 .what is the nominal GDP in 2012 ?

Regression is a statistical procedure for determining the linear relationship between a number of variables. A simple regression model has one dependent variable and one independent variable [tex](y)[/tex]

It is used to forecast the amount of a dependent variable according to the results of one independent variable. [tex](x)[/tex]

The estimated least-squares line has the following shape :[tex]y=bo+b1x[/tex].

In this case, the dependent variable is, the independent variable is, the intercept is, and the slope coefficient is.

The slope of a linear regression describes how a unit change in x changes the y value.

When, the intercept represents the expected mean value of Y. When X never equals zero, the intercept has no intrinsic meaning.

Step  (1) The process of estimating the linear relationship between two or more variables is known as regression. Only if there is a linear relationship between both variables can a regression equation be used to predict future.

Linear regression is the most fundamental a kind of regression and is the most widely used proposed model. A regression line can be used to predict dependent variables based on independent variables.

Step: (2) Outliers have a significant impact on the slope of the regression line. Influential points are also referred to as outliers in regression analysis.

Outliers can have a significant impact on the regression equation, so remove any outliers that are recognized errors. Consider the effects of any known inconsistencies that are outliers.

Step 3: Because outliers can have a large impact on the regression line, they are also referred to as important and powerful points.

An outlier is a data point that is located far away first from remaining pieces of data. These are additionally known as influencing points. Outliers have a significant influence on the slope of something like the regression line.

For linear associations, regression models can be utilized.

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Answer:

See explanation below

Answer is 1/8

Step-by-step explanation:

The expression is:

[tex]\left(\dfrac{1}{512}\right)^{\dfrac{1}{3}}[/tex]

A number x raised to the power [tex]\dfrac{1}{3}[/tex] means it is the cube root of that number or [tex]\mbox{\large \sqrt[3]{x} }[/tex]

Also [tex]\left(\dfrac{1}{x}\right)^a = \dfrac{(1)^a}{x^a}[/tex]

Combining these two facts we get
[tex]\left(\dfrac{1}{512}\right)^{\frac{1}{3}} = \dfrac{1^{\frac{1}{3}}}{512^\frac{1}{3}}= \dfrac{\sqrt[3]{1} }{\sqrt[3]{512} } = \dfrac{1}{\sqrt[3]{512} }[/tex]

[tex]\sqrt[3]{512} = 8[/tex]

So
[tex]\left(\dfrac{1}{512}\right)^{\dfrac{1}{3}} = \dfrac{1}{8}[/tex]

The FRF method is a common technique for analyzing the dynamics of structures and systems, it is typically not used as a primary method for determining a system damping ratio by field measurements.

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There are 142,506 different committees of 5 students that can be selected from a group of 30 students.

The number of different committees that can be formed by selecting 5 students from a group of 30 students can be calculated using the formula for combinations, which is:

n C r = n! / r!(n - r)!

where n is the total number of items (in this case, the number of students) and r is the number of items to be selected (in this case, 5).

Substituting the values, we get:

30 C 5 = 30! / (5! * (30 - 5)!)

= (30 * 29 * 28 * 27 * 26) / (5 * 4 * 3 * 2 * 1)

= 142,506

Therefore, there are 142,506 different committees of 5 students that can be selected from a group of 30 students.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is a measure of the chance or likelihood of an event happening, expressed as a number between 0 and 1. A probability of 0 means the event will not occur, and a probability of 1 means the event will definitely occur.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability, and it assumes that all outcomes are equally likely.

There are also other types of probability, including empirical probability (based on observations and data), subjective probability (based on personal judgment and beliefs), and conditional probability (the probability of an event given that another event has occurred).

Probability has applications in many fields, including statistics, science, finance, and engineering. It is used to model and predict the occurrence of events, to make decisions under uncertainty, and to design systems and processes that can minimize risk and maximize the chances of success.

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Answer: The other angle would be 60 degrees.

Step-by-step explanation:

To find the minimum score you would need to be in the top 4%, we need to use the standard normal distribution and the given z-score.

First, we find the z-score corresponding to the top 4% using a standard normal distribution table or a calculator:

z = invNorm(1 - 0.04) = invNorm(0.96) = 1.7507 (rounded to four decimal places)

The minimum score needed to be in the top 4% is the score that corresponds to this z-score in the distribution of exam scores. We can use the formula for standardizing a normal random variable to find this score:

z = (X - μ) / σ

where X is the exam score, μ is the mean of the exam scores, and σ is the standard deviation of the exam scores.

Solving for X, we get:

X = zσ + μ = 1.75076.1 + 76.4 = 87.46

Therefore, the minimum score you would need to be in the top 4% is approximately 87.46 points.

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Answer: The correct digits for the combination lock are 1, 5, and 8, in that order.

Step-by-step explanation:

Based on the given clues, we can deduce the correct digits for the combination lock as follows:

From the clue "128 One digit is right and in its place," we know that one of the digits is 1.

From the clue "157 One digit is right, but in the wrong place," we know that either 5 or 7 is a correct digit, but in the wrong position. Since we already know that one of the digits is 1, the correct digit must be 5. Therefore, the second digit is 5 and it is in the wrong place.

From the clue "841 Two digits are right but both are in the wrong place," we know that the digits 8 and 4 are correct, but they are both in the wrong position. Therefore, the last digit must be 4 or 8. However, we also know from the clue "624 One digit is right, but in the wrong place" that the last digit is not 4. Therefore, the correct third digit is 8.

So, the correct digits for the combination lock are 1, 5, and 8, in that order.

Therefore, the combination for the lock is 158.

Answer:

35.35 seconds

Step-by-step explanation:

The volume of the cylindrical glass can be calculated as:

V = πr²h

where r is the radius (half of the diameter), h is the height, and π is the mathematical constant π (approximately 3.14).

Since the diameter is 3 inches, the radius is 1.5 inches. The height is 10 inches. Therefore, the volume of the glass is:

V = π(1.5)²(10) ≈ 70.69 cubic inches

To fill the glass 50%, we need half of the volume:

V/2 ≈ 35.35 cubic inches

The faucet dispenses water at a rate of 1 cubic inch per second, so the time it takes to fill the glass 50% is:

t = (V/2) / (1 cubic inch per second) ≈ 35.35 seconds

Therefore, it takes approximately 35.35 seconds to fill the glass 50%. Rounded to two decimal places, the answer is 35.35 seconds.

The number round to the nearest hundredth according to the rules is 7.11.

The steps to round the digits to nearest hundredth are as follows -

Step 1 - Firstly read the number and analyse the number at the position hundredth. We see that 0 is present at the hundredth position.

Step 2 - Now check the number on the right hand side of the number. We see that it is 9.

Step 3 - If the number is greater than 5, then add one to the prior digit (the one at hundredth position).

Step 4 - Write the final number using above points. The number will be 7.11. The number 3 will be dropped as we are directed to shorten the number.

The rounded number is 7.11.

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The maximum number of people who can go to the amusement park is 6.

To determine the number of people who can go to the amusement park, use the following equation:

Total cost = Parking cost + Admission cost

The total cost cannot exceed $86, the amount of money the friends have. The parking cost is $5 and the admission cost per person is $13.50. Therefore, we can write the following equation:

86 ≥ 5 + 13.5x

To solve for x,  subtract 5 from both sides of the inequality and then divide both sides by 13.5. This gives us the following equation:

x ≤ (86 - 5) / 13.5

x ≤ 6

Therefore, the maximum number of people who can go to the amusement park is 6.

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Step-by-step explanation:

-Multiply inside the brackets

-Add like terms ( Or in this case move it to the others side to find p)

-Add

- Then do some substitution to check for the answers

Answer: the answer is 48

Step-by-step explanation:

Answer: 48

Step-by-step explanation: A triangles formula is base x height divided by 2, therefore we will do first 8 x 12 which equals 96, and divide by 2, giving us 48.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

What is an angle of depression?

If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle formed between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.

There is an angle of elevation from point R to S. Thus point R is lie above S.

The angle of depression from point R to point S is ∠1.

The angle of elevation from point S to point R is ∠2.

∠2 is the angle of elevation from S to R.

∠1 is the angle of depression from point R to point S.

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