Use the definition of ""f(x) is O(g(x))"" to show that x4 + 9x3 + 4x +7 is o(x4).

The length of Alice’s step is 0.6 m.

The length of Basil’s step is 0.8 m.

Since Basil takes 100 fewer steps than Alice to walk 240 m;

the number of steps Basil takes = (240/A) - 100.

Basil's step is 20 cm longer than Alice's step;

B = A + 0.2

The distance each person walks is calculated as;

A(240/A) = (A + 0.2) [(240/A) - 100]

240 = 240 - 100A + 48/A - 20

0 =  - 100A + 48/A - 20

100A - 48/A = -20

100A² - 48 = -20A

100A² + 20A - 48 = 0

Solve for A using formula method;

A = 0.6 m

Basil's step length:

B = 0.6 + 0.2

B = 0.8 m

Learn more about length here: https://brainly.com/question/28108430

#SPJ1

By definition two quantities are proportional of each other if it can be express like:

where k is the constant of proportionality.

Now, by definition a line is a set of points that have the same rate of change between them, no matter which points we take.

Thus we can argue that a line always have a constant rate but they don't necessarily represent proportional quantities.

Their are 12  different ways can you score 24 points as required by problem .

what is score ?

Score generally refers to the number of points earned or accumulated in a game, competition, or test. In sports, for example, score typically refers to the number of goals, runs, or points a team or individual has earned during a game or match.

what is competition?

Competition refers to a situation in which individuals or groups of people compete against each other in order to achieve a specific goal, such as winning a prize, achieving a certain level of performance, or gaining recognition

In the given question,

To find all the different ways to score 24 points in a football game, we can use a combination of the given scoring rules. We can start with the highest-scoring play, a touchdown, and then see how many field goals, safeties, and extra point conversions we need to reach a total of 24 points.

Here are all the possible ways to score 24 points:

4 touchdowns + 4 extra point conversions

3 touchdowns + 2 field goals + 3 extra point conversions

2 touchdowns + 4 field goals + 2 extra point conversions

1 touchdown + 6 field goals + 3 extra point conversions

2 touchdowns + 1 field goal + 4 extra point conversions

1 touchdown + 3 field goals + 6 extra point conversions

8 field goals + 3 extra point conversions

2 touchdowns + 2 safeties + 2 extra point conversions

1 touchdown + 4 field goals + 1 safety + 3 extra point conversions

3 field goals + 2 safeties + 3 extra point conversions

2 field goals + 4 safeties + 2 extra point conversions

1 field goal + 6 safeties + 3 extra point conversions

Note that there may be other ways to score 24 points depending on the specific game situation and the rules of the league.

To know more about score, visit:

bhttps://brainly.com/question/12905637

#SPJ1

Answer:

one solution?

Step-by-step explanation:

The probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7 is 28.43%. Correct option is D.

To calculate the probability that a score will be greater than 82 in a normal distribution with a mean of 78 and a standard deviation of 7, we need to use the standard normal distribution and the z-score.

First, we can find the z-score for 82 using the formula:

z = (x - mu) / sigma

where x is the value of interest (in this case, 82), mu is the mean (78), and sigma is the standard deviation (7).

z = (82 - 78) / 7

z = 0.57

Next, we can use a z-table or a calculator to find the area under the standard normal curve corresponding to a z-score of 0.57. The area represents the probability that a score will be greater than 82.

Using a standard normal table, we find that the area to the right of z = 0.57 is 0.2843 or approximately 28.43%. Therefore , correct option is D.

In conclusion, by calculating the z-score and using a standard normal distribution table, we can find the probability that a score will be greater than a certain value in a normal distribution with a known mean and standard deviation.

To learn more about probability click on,

https://brainly.com/question/23665017

#SPJ4

Complete question is:

A normal distribution with a mean of 78 and a standard deviation of 7, what is the probability that a score will be greater than 82?

group of answer choices

A. 23.89%

B. 26.11%

C. 76.11%

D. 28.43%

E. 52.22%

The options are analyzed as follows:

1: The overline 0.729 means:

This is a non- terminating recurring decimal hence it is rational.

2: The nuumber 0.0195347... is a non terminating and non recurring decimal hence it is irrational.

3. The number -12 is rational since it is an integer.

4.The number 4.565656... is a non terminating recurring decimal hence it is rational.

5. The number given by:

Since square root of 2 is irrational and 3 is rational the product is irrational.

Also the decimal is non terminating non recurring hence it is irratonal.

So the options 2 and 5 are irrational.

Answer:

5.2

Step-by-step explanation:

The probability that a used radio will be working after an additional 8 years, given that the number of years a radio functions is exponentially distributed with parameter λ = 1/8, is approximately 0.3679.

To find the probability that the used radio will be working after an additional 8 years, we can utilize the exponential distribution with the given parameter λ = 1/8. The exponential distribution is characterized by the probability density function f(x) = λe^(-λx), where x represents the number of years.

To calculate the probability, we need to find the survival function or complementary cumulative distribution function (CCDF). The survival function is defined as S(x) = 1 - F(x), where F(x) is the cumulative distribution function (CDF).

For the exponential distribution, the CDF is F(x) = 1 - e^(-λx). Substituting the given parameter λ = 1/8 and x = 8 into the CDF, we have F(8) = 1 - e^(-1/8 * 8) = 1 - e^(-1) = 1 - 1/e ≈ 0.6321.

Finally, the survival function or CCDF for x = 8 is S(8) = 1 - F(8) = 1 - 0.6321 ≈ 0.3679. Hence, the probability that the used radio will be working after an additional 8 years is approximately 0.3679.

To know more about exponential distribution refer here:

https://brainly.com/question/30669822#

#SPJ11

Answer:

c = 14.9

Step-by-step explanation:

use the pythagorean thereom:

a² + b² = c²

a² = 11 × 11 = 121

b² = 10 × 10 = 100

c² = 121 + 100 = 221

now find the square root of 221:

√221 = 14.866...

round to the nearest tenth:

the 6 next to the 8 means round up.

so the hypotenuse is 14.9

Answer:

whats goin on homie

Step-by-step explanation:

Answer:

sup

Step-by-step explanation:

Answer: 1/6

Step-by-step explanation:

Since Sam has to memorize 1/2 of his lines and he memorizes 1/3 of his lines today, the fractions of his lines that he has left to memorize will be gotten by subtracting 1/3 from 1/2. This will be:

= 1/2 - 1/3

= 3/6 - 2/6

= 1/6

Therefore, he has 1/6 of his lines left to memorize.

Answer:

1/6

Step-by-step explanation:

The fractions of his lines will he have left to memorize is calculated as:

Number of lines he has to memorize - Number of line he memorized today

Number of lines he has to memorize = 1/2

Number of line he memorized today = 1/3

Hence,

= 1/2 - 1/3

Lowest Common Denominator = 6

= 3 - 2/6

= 1/6

The equation, which represents a circle that is concentric with the circle shown and has a radius twice as large of that circle, is (x-4)²+(y-6)²=16.

The equation of the circle is the equation which is used to represent the circle in the algebraic equation form, with the value of center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

\((x-h)^2+(y-k)^2=r^2\)

Here (h,k) is the center of the circle and (r) is the radius of the circle.

On a coordinate plane, a circle has a center (4, 6) and has a radius of 2 units.

The equation of another circle which is concentric with the circle has to be found out. Two circles are concentric if they have the same center.

Thus, the center of this circle is also (4,6). Now, this circle has a radius that is twice as large. Thus, the radius of this circle is,

\(r=2\times2\\r=4\)

The equation of this circle with center (4,6) and radius 4 is,

\((x-4)^2+(y-6)^2=(4)^2\\(x-4)^2+(y-6)^2=16\)

Thus, the equation, which represents a circle that is concentric with the circle shown and has a radius twice as large as that circle, is (x-4)²+(y-6)²=16.

Learn more about the equation of circle here;

https://brainly.com/question/1506955

Answer: (x – 4)2 + (y – 6)2 = 16

Step-by-step explanation: i took the test n got it correct :)

- The vertical asymptote is x = 3/2.
- The horizontal asymptote is y = -5/2.

To graph the vertical and horizontal asymptotes of the rational function \[ f(x)=\frac{-10 x+11}{4 x-6} \], we need to determine the behavior of the function as x approaches positive or negative infinity.

1. Vertical asymptotes:
Vertical asymptotes occur when the denominator of a rational function equals zero, leading to an undefined value. In this case, the denominator is \((4x-6)\). Setting it equal to zero and solving for x, we find:
\[ 4x-6 = 0 \]
\[ 4x = 6 \]
\[ x = \frac{6}{4} \]
\[ x = \frac{3}{2} \]

Therefore, the vertical asymptote of the function is x = 3/2.

2. Horizontal asymptotes:
To determine the horizontal asymptote, we compare the degrees of the numerator and denominator of the function. The degree of the numerator is 1, and the degree of the denominator is also 1. Since the degrees are the same, we divide the leading coefficient of the numerator by the leading coefficient of the denominator.

The leading coefficient of the numerator is -10, and the leading coefficient of the denominator is 4. Therefore, the horizontal asymptote is given by:
\[ y = \frac{-10}{4} \]
\[ y = -\frac{5}{2} \]

So, the horizontal asymptote of the function is y = -5/2.

To summarize:
- The vertical asymptote is x = 3/2.
- The horizontal asymptote is y = -5/2.

By graphing the function, you will see that it approaches the vertical asymptote at x = 3/2 as x gets larger or smaller, and it approaches the horizontal asymptote at y = -5/2 as x approaches positive or negative infinity.

Know more about horizontal asymptote here:

https://brainly.com/question/30176270

#SPJ11

Statistics help present data precisely and draw meaningful conclusions. While presenting data, one should be aware of using adequate statistical measures.

Readers are generally interested in knowing the variability within the sample, descriptive data should be precisely summarized with SD. The use of SEM should be limited to computing CI which measures the precision of population estimate. Journals can avoid such errors by requiring authors to adhere to their guidelines.

Studying the entire population is time and resource-intensive and not always feasible; therefore studies are often done on the sample, and data are summarized using descriptive statistics. These findings are further generalized to the larger, unobserved population using inferential statistics.

For example, to understand the cholesterol levels of the population, the cholesterol levels of the study sample, drawn from the same population are measured.

To learn more about individual variability visit,

https://brainly.com/question/23320848

The result of 490 divided by 7 is 70.

To calculate 490 divided by 7, we can perform long division as follows:

        70

   __________

7  |  490

   -  49  (7 times 7)

   _______

         0  (no remainder)

In the first step, we divide 7 into the first digit of 490, which is 4. The quotient is 0, and we bring down the next digit, which is 9.

Next, we divide 7 into 49. The quotient is 7, and there is no remainder.

Therefore, the answer to 490 divided by 7 is 70.

To know more about divided, refer here:

https://brainly.com/question/15381501

#SPJ6

According to the textbook, polygraph testing (lie detection) screening is prohibited as a condition of employment outside of government jobs, which means option (a) is correct.

The use of polygraph testing, also known as lie detection, as a screening tool for employment purposes is generally restricted. The rationale behind this restriction is based on concerns regarding the reliability and validity of polygraph tests in accurately detecting deception. Polygraph testing has been found to have limitations, as false positives and false negatives can occur, leading to inaccuracies in the results.

Due to these concerns, many jurisdictions have implemented legal restrictions on the use of polygraph testing in employment settings. It is important to note that there may be certain exceptions to this general prohibition. In some cases, such as certain high-security government positions or jobs that involve protecting the public from potential harm, polygraph testing may be permitted based on a countervailing need.

However, in the broader context of employment screening, polygraph testing is generally prohibited outside of government jobs.

Learn more about polygraph testing here:

https://brainly.com/question/15681821

#SPJ11

So the first digit could be 0-9.

second is the same 0-9

And the 3rd 0-9 and lastly the 4th 0-9

There is a \(\frac{1}{10} *\frac{1}{10} *\frac{1}{10}* \frac{1}{10}\) chance that they will get it right by guessing.

So that means a \(\frac{1}{10000}\) chance that they will get it right.

So their are 10000 possible codes.

The number of ways the student can answer the questions in either true or false for 8 questions is:  256 ways

Permutations and combinations are basically the various ways that we select objects from a particular set generally without any replacement, to form subsets. This selection of subsets is referred to as a permutation when the order of selection is a factor. However, it is referred to as a combination when order is not a factor.

In this question, we are to find the number of ways in which this question can be answered when there are 8 true/false questions in an examination.

So, we have the number of ways for a single question to select the answer as 2 which is true or false.

Thus,  the expression for the number of ways to answer the question in either true or false for 8 questions is:

2⁸ = 256 ways

Read more about permutation and combination at: https://brainly.com/question/4658834

#SPJ1

Answer:

1.07=x-780/28

Step-by-step explanation:

Miss credit score: 810

Answer:

810

Step-by-step explanation:

Answer:

Volume of cone = 40 in³

Step-by-step explanation:

Given:

Volume of cylinder = 120 in³

Height of cylinder = Height of cone

Radius of cylinder = Radius of cone

Find:

Volume of cone

Computation:

Volume of cylinder = πr²h = 120 in³

Volume of cone = (1/3)πr²h

So,

Volume of cone = (1/3)(120)

Volume of cone = 40 in³

Answer:

The step Hazel made the mistake in was step 2. She made the mistake of subtracting 3t-3. You cannot do this because they are not like terms. To be like terms, the second 3 would have to have a t on it as well.

Step-by-step explanation:

We are asked that how could we determine the number of feet per second a squirrel can run?

Recall that rate (also known as speed) is given by

Where d is the distance in feet.

t is

Answer:

a) during the 3rd season the populations will be the same

b) after 11 1/4 seasons the second species of fish will be eliminated

Step-by-step explanation:

1)  y = 25x + 255

2) y = -40x + 450

the above linear equations model the statements from the problem

we can find out when the two populations will have the same amount by graphing them and finding the point of intersection or by setting them equal to each other:

25x + 255 = -40x + 450

add 40x to each side to get:

65x + 255 = 450

subtract 255 from each side to get:

65x = 195

x = 195/65

x = 3

To find the season when the second species is eliminated we can use the second equation and set 'y' equal to zero and solve for 'x':

0 = -40x + 450

subtract 450 from each side to get:

-450 = -40x

x = -450/-40

x = 11.25

The diagonal measurement of the rectangle is approximately 74.44 inches.

To find the diagonal measurement of a rectangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides. In this case, the length of the rectangle is 60 inches and the width is 44 inches. So, we can consider these two sides as the legs of a right triangle and the diagonal as the hypotenuse. Using the Pythagorean theorem, we have:Diagonal^2 = Length^2 + Width^2; Diagonal^2 = 60^2 + 44^2 ; Diagonal^2 = 3600 + 1936; Diagonal^2 = 5536.

Taking the square root of both sides, we find: Diagonal = √5536 ≈ 74.44 inches. Therefore, the diagonal measurement of the rectangle is approximately 74.44 inches.

To learn more about diagonal click here: brainly.com/question/14735698

#SPJ11

If data shows that overweight children do not suffer from diabetes as predicted in the model that links child obesity and diabetes (i.e., data shows a lower than 80% probability), then the next step would be to review the model's assumptions and revise the model as necessary.

This may involve analyzing additional data or changing the model's structure or parameters, to better reflect the observed relationships between child obesity and diabetes. It is important to ensure that the model is based on accurate and reliable data, as this will help to ensure that the model's predictions are useful and informative.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

137

Step-by-step explanation:

The number of ways we can choose three different numbers in order for a unique code for this case is 2730

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

We can use combinations for this case,

Total number of distinguishable things is m.

Out of those m things, k things are to be chosen such that their order doesn't matter.

This can be done in total number of ways,

⇒ \(^{m} C_{k} =\) m! / (m - k)! k!

If the order matters, then each of those choice of k distinct items would be permuted k! times.

So, total number of choices in that case would be:

⇒ \(^{m} P_{k} =\) m! / (m - k)!

This is called permutation of k items chosen out of m items (all distinct).

Given that:

The considered lock as a 3 number code

There are 15 numbers available.

None of the number can repeat.

In a lock, the order of the way numbers are arranged matters.

Because of no repetition allowed, we can simulate this situation as:

The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.

And we have:

The number of ways we can choose 3 numbers out of 15 numbers with order is,

⇒  \(^{m} P_{k} =\) m! / (m - k)!

⇒  \(^{15} P_{3} =\) 15! / (15 - 3)!

            = 15! / 12!

            = 2730

Thus, The number of ways we can choose three different numbers in order for a unique code for this case is 2730

Learn more about combinations and permutations here:

brainly.com/question/16107928

#SPJ3

Answer:

1. SSS

2. SAS

3. SAS

4. 1?

5. SSS

Step-by-step explanation: