Can someone please explain this question. Please give a step by step explanation

average rate of change from 4 to 9 minutes is 2.25 min . division of the y-value change by the x-value change.

It represents the average change in the function's per-unit value during that time period. On the function's graph, it is generated from the slope of the line connecting the interval's ends.

the difference between the y- and x-values is divided. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity.

Given that

the change in y value occurred in 9 minutes and the change in x value occurred in 4 minutes, the average rate of change was 9 minutes by 4 minutes, or2.25 minutes.

9 min / 4 min

= 2.25 min

average rate of change from 4 to 9 minutes is 2.25 min . division of the y-value change by the x-value change.

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All three statement parametric equation are true so option D. all three are true is the correct option of the given statement.

In parametric form, the x and y coordinates are defined as functions of t, which represent angles in this form: x = r cos t and y = r sin t, and so map the whole circle. These parametric equations are known as polar equations.

The position of a point on a Ferris wheel, for instance, can be represented graphically using parametric equations. The parametric equations can be used to model every aspect, including height above the ground, spin direction, and speed.

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A general term for a sample selected in accordance with probability theory, which ensures that every person in the population has an equal chance of being selected for the sample, is known as Probability sampling.

A probability sampling method is an any method of sampling that utilizes some from of random selection. Probability sampling refers to the selection of a sample from a population, when the selection is based on the principle of randomization, that is random selection or chance.

In simple random sampling each sampling unit of a population has an equal chance of being included in the sample. Consequently, each possible sample also has an equal chance of being selected.

The advantage of simple random sampling is that it does not require any information on the survey frame other than the complete list of units of the survey population along with contact information. In a simple random sample, every number of the population has an equal chance of being selected.

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The credit card holder paid an additional D. $559.56 over the 12 months versus paying the balance in full before the end of the first month.

The additional payment made by the credit card holder results from paying installments instead of clearing the balance in the first month.

Installment plans attract finance charges at an annual percentage rate (APR), which increases the total amount paid.

Therefore, the additional payment is the difference between the total installment payments and the credit card balance at the beginning of the first month.

N (# of periods) = 12 months

I/Y (Interest per year) = 11.99%

PV (Present Value) = $6,299.59

PMT (Periodic Payment) = $-350

Results:

FV = $3,009.15

Sum of all periodic payments = $3,850 ($350 x 11)

Total Interest = $559.57

The total amount paid over the 12 months = $6,859.15 ($3,009.15 + $3,850)

The total amount paid in full in the first month = $6,299.59

Additional payment made via installments = $559.56 ($6,859.15 - $6,299.59)

Thus, for making installment payments, the credit card holder incurred the additional cost of Option D.

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4/7 is probability a two-way table to model this chance process.

What are examples and probability?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

                                The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

No events getting thick crust pizza and getting pizza with mushrooms are not disjoint as we can have pizza that has thick crust and mushroom both.

No events are not independent as

P(thick and having mushroom) is not equal to P(thick crust)*P(having mushroom)

P( thick and having mushroom) = 2/7

P(thick crust) = 3/7

P( having mushroom) = 4/7

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A weight training program for a friend that will increase his or her muscular endurance:

Legs: barbell back squats — 3 sets of 5 reps.

Chest: flat barbell bench press — 3 set of 5 reps.

Back: seated cable rows — 3 sets of 6–8 reps.

Shoulders: seated  shoulder press — 3 sets of 6–8 reps.

The ability of a muscle or group of muscles to perform repetitive contractions against a force for an extended period of time is referred to as muscular endurance. The more muscular endurance you have, the more repetitions you can do.

Muscular endurance is the ability to contract a muscle or group of muscles against resistance, such as weights or body weight, for an extended period of time. Increasing these muscles' performance means they can continue to contract and work against these forces.

The workouts should be done on Mondays, Wednesdays, Fridays, and Saturdays. That way, you can take a day off between upper-body-focused workouts. Each of the four weekly workouts consists of five moves that you will perform in straight sets.

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The number of units x that produces a maximum revenue is approximately 1890.56 units.

To find the number of units x that produces a maximum revenue R, you need to find the value of x that maximizes the function R = [tex]171x^2 - 0.06x^3.[/tex]

To do this, you can take the derivative of the function with respect to x and set it equal to 0. The derivative of a function gives us the slope of the function at a particular point, so setting the derivative equal to 0 will give us the points where the function is at a relative maximum or minimum.

The derivative of R with respect to x is:

R' = [tex]342x - 0.18x^2[/tex]

To find the value of x that maximizes R, we set R' equal to 0 and solve for x:

[tex]0 =[/tex] [tex]342x - 0.18x^2[/tex]

[tex]0.18x^2 = 342x[/tex]

[tex]x = \frac{342}{0.18}[/tex]

[tex]x = 1890.56[/tex]

Therefore, the number of units x that produces a maximum revenue is approximately 1890.56 units. Keep in mind that this is only a local maximum, and there may be other values of x that produce a higher revenue. To find the absolute maximum or minimum of the function, you would need to examine the behavior of the function over its entire domain.

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The required simplified equivalent fraction of 0.32 is 8/25. Option A is correct.

Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,

Here,
Given the terminating decimal value,
= 0.32
= 32/100
= 8/25

Thus, the required simplified equivalent fraction of 0.32 is 8/25. Option A is correct.

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The null hypothesis asserts that the data are well described by both your model and the model without independent variables.

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The required funds invested in Charles Schwab & co and Merrill lynch are 1200 and 2800 respectively.

Given that,
Make two separate investments for a total of $4000. The percent return on Charles Schwab & co. At the end of the year was 5% and the percent return on Merill lynch was 7%. The combined return on both funds was $256.

here,
let x be the invested amount on Charles Schwab & co and y be the invested amount on Merrill lynch.
According to the question,
x + y = 4000
x = 4000 - y   - - - - - (1)
And
0.05x +0.07y = 256 - - - - (2)
From equation 1 and 2
x=1200 and y=2800

Thus, the required funds invested in Charles Schwab & co and Merrill lynch are 1200 and 2800 respectively.

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Answer:

9 laps

Step-by-step explanation:

75% of something is the same as three-fourths, or multiplying by 0.75

12 x 0.75 = 9

or you can divide by 4 and then multiply by three if you know what to separate the original number into

12/4 = 3     3 x 3 = 9

Answer:

A, D, E, and F are all equivalent expressions.

Step-by-step explanation:

A. 1:

1 is already a simplified fraction, so there is nothing to do.D. 4:

4 is already a simplified fraction, so there is nothing to do.E. 1.

28.:

This expression is not a fraction, but rather a mixed number. To convert it to a fraction, we first need to rewrite it as an improper fraction. To do this, we take the whole number (1) and multiply it by the denominator (28), and then add the numerator (0):1.28 = 1 * 28 + 0 = 28Then we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4:28/4 = 7F. 1

22:

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:1/22 = 1/22

I hope this helps! Let me know if you have any questions.

Answer:

Chemical energy is changed to heat energy.

Step-by-step explanation:

The Central Limit Theorem establishes that the sampling distribution of the sample means of size n can be approximated to a normal distribution with mean and standard deviation s = /n for a normally distributed random variable X, with mean and standard deviation.

The Central Limit Theorem can also be used with skewed variables if n is at least 30.

The sampling distribution of the sample percentage for a proportion p in a sample of size n will be about normal, with mean and standard deviation s = p(1-p)/n.

The mean is the difference between the means when two normal variables are subtracted, and the standard deviation is the square root of the sum of the variances.

Average gas mileage (A): Mean 36, SD 6, sample size 50:

So, μA = 36, sA = 6/√50 = 0.8485

Gas mileage B: Mean 42, SD 8, and sample size of 50:

So, μB = 42, sB = 8/√50 = 1.1314

Arrangement of the difference:

Mean: 36 - 42 = -6 where A - B

Standard deviation: 1.4142

Locate the point estimate.

This is the mean difference, which is -6 mpg.

To determine our level, we must deduct 1 from the confidence interval and divide the result by two. So: 1 - 0.95/2 = 0.025

Now that z has a pvalue of, we must locate it in the Ztable.

Z = 1.96 since it has a pvalue of.

Identify the margin of error M as follows.

M = zs = 1.96 * 1.4142 = 2.77

2.77 mpg is the error margin.

The sample mean plus M determines the interval's upper end. Therefore, it is -6 + 2.77 = -3.23 mpg.

The difference between the population mean gas mileage for engines A and B and how to interpret the data, in mpg, have a 95% confidence interval of (-8.77, -3.23) means, whereas the standard deviation is the sum of the variances' square roots.

Average gas mileage (A): Mean 36, SD 6, sample size 50:

So, μA = 36, sA = 6/√50 = 0.8485

Gas mileage B: Mean 42, SD 8, and sample size of 50:

So, μB = 42, sB = 8/√50 = 1.1314

Arrangement of the difference:

Mean: 36 - 42 = -6 where A - B

Standard deviation: 1.4142

Locate the point estimate.

This is the mean difference, which is -6 mpg.

B. Determine the error margin.

By subtracting 1 from the confidence interval and dividing the result by 2, we can determine our level. So: 1 - 0.95/2 = 0.025

We must now locate z in the Ztable because it has a pvalue of

Z = 1.96 since that has a p value of.

Find the margin of error now. such that M

M = zs = 1.96 * 1.4142 = 2.77

The error margin is 2.77 mpg.

C. Build the 95% confidence interval for the difference between the population-mean fuel economy for engines A and B, then analyze the findings (5 pts)

The sample mean multiplied by M determines the interval's upper end. Consequently, it is -6 + 2.77 = -3.23 mpg.

The 95% confidence interval for the difference between population mean gas mileage for engines A and B and how to interpret the data, in mpg, is (-8.77, -3.23).

You should calculate the population standard deviation when the dataset you’re working with represents an entire population, i.e. every value that you’re interested in. The formula to calculate a population standard deviation, denoted as σ.

A % confidence interval (CI) for the population mean is given by Example 6.2 A meat inspector has randomly measured 30 packs of acclaimed 95% lean beef. The sample resulted in the mean 96.2% with the sample standard deviation of 0.8%.

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On solving the provided question we can say that - as the probability the result will be either a red- or green-colorblind individual.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1.

In the US, there are more males than women who are colorblind to red and green  = 0.07adults

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If a graph moves arbitrarily near to a line in one direction (without necessarily crossing it), then the line is a(n) asymptote of the graph.

An object that serves as the limit of another line or curve in mathematics. Asymptotic to an axis, or the asymptote of a curve, refers to a falling curve that approaches but does not reach the horizontal axis.

An asymptote is a value that you approach steadily but never quite achieve. An asymptote is a line that a graph skirts but never touches in mathematics. It can be horizontal, vertical, or slanted. A graph that approaches a line but does not cross it is said to be an asymptote.

An asymptote of a curve in analytical geometry is a line along which the angle between the curve and the line decreases when one or both of the x or y coordinates tend to infinity. A line that is tangent to a curve at a point at infinity is said to be the asymptote of the curve in projective geometry and similar contexts.

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(-9, 9) domain of the vector function. A vector valued function's domain is a subset of all real numbers at which the function is well-defined.

Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using a value for x, that chosen x-value is said to belong to f's domain.

A vector-valued function is a rule that gives each member of a subset of R1 a vector. A function's domain is the set of all possible inputs to the function. The domain of f(x)=x2 is all real numbers, for example, and the domain of g(x)=1/x is all real numbers except x=0.

r(t) = t − 1 t 1 i sin(t) j ln(81 − t2) k

Lets find the domain of  first which is given by,

t - 2 / t + 2

This function is defined at all values except, t equals to -2 as the function is not defined at,

t -= -2

Lets find the domain of  first which is given by,

sin(t),

Two trigonometry function sine and cosine defined for all real number

This function is defined at all real numbers. Hence the domain of component  j is.

Set the above argument greater than zero to find where the expression is defined.Thus,

(9 + t ) (9 - t) > 0

Therefore,

The domain of it should be (-9, 9)

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The solution of the given equation is:

[tex]\frac{log 9}{Log 2} - 1[/tex]  = 2.16992500144

Logarithm:

Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8. Similarly, 2 = log10 100 because 102 = 100. The latter kind of logarithm (that is, the base 10 logarithm) is called the ordinary logarithm or the Briggs logarithm and simply write log n.

Invented in the 17th century to speed up calculations, logarithms greatly reduced the time required to multiply large numbers. These were the basis of numerical computation for over 300 years until the mechanical calculator of the late 19th century and his 20th century computer sophistication made it obsolete for large-scale calculations. However, the natural logarithm (with base e ≅ 2.71828 and written ln n) continues to be one of the most useful functions in mathematics, being applied to mathematical models in the physical and biological sciences.

According to the question:

2ˣ=4.5

Take the logarithm of both sides of the equation

log2ˣ = log9 / 2

x . log2 = log9 − log2

divide both sides of the equation by log 2:

          [tex]\frac{x Log 2}{Log 2} = \frac{Log 9 - Log 2}{Log 2}[/tex]

⇒  x = [tex]\frac{log 9}{Log 2} - 1[/tex]

⇒ x = 2.16992500144.

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We relocate the decimal point such that there is just one non-zero digit in front of the decimal point to achieve "normal" scientific notation. 32 thus becomes 3.2.

What's standard form in math?

A number can be written in a certain style that adheres to regulations, which is known as its standard form.

Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 10^8.

32=3.2 × 10^1

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The statement that best describes Lucia's claim is at option (b), that is " Lucia's claim is incorrect since not all the rotations that are multiples of 45° carry a square onto itself".

It is given that, Lucia draws a square and plots the center of the square.

Lucia claims that " any rotation about the center of the square that is a multiple of 45° will carry the square onto itself".

To verify this claim, we need to construct a square (ABCD) as shown in the figure.

When the square ABCD is rotated about 45° where we can it is 1 × 45°, the square formed is A'B'C'D' is not the same as the actual one. So, they are not in symmetry after the rotation n this case.

If we rotate again, that is for the second multiple of 45° (2 × 45°), we get a square A''B''C''D''. But, now the square is similar to the actual one. So, they are in symmetry.

This means we can say that, not for all the multiples of 45° rotation, the square does not carry onto itself.

Therefore, we can conclude that "Lucia's claim is incorrect since not all rotations that are multiples of 45' carry a square onto itself".

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As per the given probability, the two action that the base station would takes are, 1) increasing the transmission power, and 2) reducing the transmission rate.

Probability:

In statistics, probability refers the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Given,

Here we need to find the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase.

Here we have given that, a mobile node gets farther and farther away from a base station,

And the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase will be solve by  increased transmission power and then reduce the rate.

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Answer:

Step-by-step explanation:

4/14

Divided both by 2

2/7

The amounts of pupils that gives each answer is given as follows:

The amounts are obtained by the multiplication of the decimal equivalent of each percentage by the total number of students, which is 40.

The percentages are given as follows:

Then the decimal equivalents of each of these percentages is given as follows:

Finally, the number of students that gave each student is given as follows:

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The first five terms of the given trigonometric series are (C) 0.5884, 0.5878.

A mathematical series where the sines and cosines of integral multiples of a variable angle are used to connect the components.

Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent are the six trigonometric functions.

Below is a graph of the first five terms in the trigonometric series of sin:

sinx = x - x³/3! + x⁵/5! - x⁷/7! + x⁹/9! .......

Insert x = 4π/5

sin4π/5 = 4π/5 - (4π/5)³/3! + (4π/5)⁵/5! - (4π/5)⁷/7! + (4π/5)⁹/9! .......

Upon resolution, we determine an approximate value of:

sin4π/5 = 0.5884

Find the true value now:

sin4π/5 = 0.5878

Therefore, the first five terms of the given trigonometric series are (C) 0.5884, 0.5878.

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Complete question:
Use the first five terms of the trigonometric series to approximate the value of sin to four decimal places. Then compare

the approximation to the actual value.

a. -0.9568, -0.9659

b. -0.9649, -0.9659

C. 0.5884, 0.5878

d. -0.9609, -0.9659

At some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)

Lola is making greeting cards, which she will sell by the box at an arts fair. She paid $50 for a booth at the fair, and the materials for each box of cards cost $8. She will sell the cards for $10 per box of cards.

We are going to use 50, 8 and 10 to find are answer.

Therefore, we are going to divide the numbers:

[tex]\boxed{50/10}[/tex]

First, we need to figure out 50/10:

[tex]\boxed{50/10=5}[/tex]

[tex]\boxed{8x5=40}[/tex]

[tex]5=40\\(50/10=5=8x5=40)[/tex]

Therefore, at some point, she will sell enough cards so that her sales cover her expenditures. So, the correct answer is ($40)

Answer:

40

Step-by-step explanation:

1. There are 80 Nickels, 120 dimes, and 300 quarters in the piggy bank.

2. The coins worth is $91

How many types of coins are there?

There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.

1 Quarter = 25 cent

1 dime = 10 cents

1 Nickel = 5 cents

1 penny = 1 cent

Assume that, the number of Nickel coins is x.

Given that, 2 nickles there are 3 dimes.

1 nickle there are 3/2 dimes.

x nickles there are 3x/2 dimes.

Also given that,

2 dimes there are 5 quarters.

1 dimes there are 5/2 quarters.

3x/2 dimes there are (5/2) × (3x/2) quarters = 15x/4.

There is 500 coins in the piggy.

Therefore, x + (3x/2) + (15x/4) = 500

(4x + 6x + 15x) /4 = 500

25x/ 4 = 500

x = 80.

The number of dimes is (3 × 80)/2 = 120

The number of quarters is (15 × 80)/4 = 300.

The total cost of 80 nickles, 120  dimes, and 300 quarters is

= [(80 ×  5) + (120 × 10) + (300 × 25)] cents

= 400 + 1200 + 7500 cents

= 9100 cents

= $(9100/100)

= $ 91

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The surd expression 1 + [√2 / (3 - √2)²]  can be simplified as (61 + 11√2/ 49) where a is 61/49 and b is 11/49

When evaluating an expression, the first step is to identify the operators and operands in the expression. The operators are the symbols that direct the operation. The operands are the values or variables that the operators act upon. Once the operators and operands are identified, the expression can be evaluated by applying the order of operations to the expression. This includes performing operations inside parentheses first, then multiplication and division, followed by addition and subtraction.

In the case of a surd expression, the same process should be followed. However, it is important to note that surds can be simplified using the rules of indices. This means that surds with the same base value can be combined using addition and subtraction.

In the give problem, we have

1 + [√2 / (3 - √2)²] can be written in the form a + b√2

1 + [√2 / (3 - √2)²] can be simplified using a calculator to give us a value of;

1 + [√2 / (3 - √2)²] = (61 + 11√2/ 49)

In this expression, a = 61/49, b = 11/49

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On solving the provided question, we cans ay that by standard deviation, [tex]SE = 0.1590 (approx.)[/tex]

Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed. Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed.

By sample standard deviation, we mean standard error. Hence, we have that:

Therefore, Standard deviation[tex]= 0.6929891[/tex]

The sample size [tex](n) = 19.[/tex]

Hence:

[tex]SE = 0.1589826.\\ SE = 0.1590 (approx.)[/tex]

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Answer:2.04.10/8

Step-by-step explanation:

Response:

2.04.10/8

Step by step explanation:

1. Write the number as a decimal

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204000000.0

2. Convert it to a new number between 1 and 10

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We move the decimal point so that 204000000.0 becomes a new number between 1 and 10. Since our number is greater than 10, we move the decimal point to the left. Remove trailing zeros. Keep count of amounts times we move the decimal point.

204000000.0 -> 2.04

Our new number is 2.04. We have moved the decimal point 8 times.

3. Define the power of 10

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Since our original number was greater than 10, the exponent of 10 is positive. Remember that we moved the decimal point 8 times, so the exponent is positive 8:

4.End result

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