In the above example, we divided the domain into 3 elements. By doing so, we reduce the problem to determining a finite number of temperature values. Later, we will see how to obtain these values from governing equations and/or boundary conditions. For now, answer the following question based on the concepts covered in the above video.Let's consider the case when we increase the number of elements to 5. How many temperature values will we need to obtain to determine the variation of temperature along the line?With 5 elements, we have a total of 6 nodes. We need to obtain the temperature at each of these 6 nodes.Increasing the number of elements is referred to as mesh refinement.

The reduced fraction is 7 using GCF method.The GCF is also known as the Highest Common Factor (HCF)

The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

The fraction = 14/66

The factors of 14 = 2×2×2×3

The factors of 28 = 11*3*2

The gcf is 2 × 2 = 4

Divide the denominator and numerator by 4

14 ÷2 = 7

14÷ 2 = 7

We get,

The fraction = 14/2 =7

To learn more about factors refer

https://brainly.com/question/29327147

#SPJ13

\(k > 1\)

Step-by-step explanation:

1) Subtract 11 from both sides.

\(12 - 11 < k\)

2) Subtract 12 - 11 to 1.

\(1 < k\)

3) Switch sides.

\(k > 1\)

Therefor the answer is, k > 1.

Answer:

no they are not equal just look at the picture carefully and you will realise it's not equal

(a)We have to use a continuous exponential growth model to write a formula relating to t and N(t), where t is the time (in years) since the initial population is introduced, and N(t) is the number of fish at time t. Continuous exponential growth models can be expressed as;
N(t) = N₀ * e^(kt)
where N₀ is the initial population, t is the time elapsed, k is the continuous growth rate, and e is Euler's number.

(b)Given that the initial population is introduced into a lake and it grows according to a continuous exponential growth model. The number of fish in the lake is 300 after 4 years. Using N(t) = N₀ * e^(kt);300 = N₀ * e^(4k)So, the formula relating to t and N(t) is;
N(t) = N₀ * e^(kt)
Putting the values into the formula;
N(t) = 300/ e^(4k)We know the number of fish in the lake after 4 years is 300.
Therefore;300 = N₀ * e^(4k)
Dividing by N₀; 300/N₀ = e^(4k)
We have; N(t) = N₀ * e^(kt)
Putting the values into the formula;
N(t) = N₀ * e^(kt)N₀ = N(t) / e^(kt)
At t = 0; N₀ = N(0) / e^(k*0)N₀ = N(0) / e^0
N₀ = N(0)
Now we can substitute the value of N₀ into the formula;
N(t) = N(0) * e^(kt)
Substituting the values in N(t) = N₀ * e^(kt);
N(t) = 1000 * e^(0.23t)

To know more about exponential growth refer here:

https://brainly.com/question/12490064

#SPJ11

Answer:

f(1)= 5

so x=1

f(5)= 5(5-1) = 20

The value of f(5) is 3125.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(1) = 5 and f(n) = 5f(n − 1)

Now, for finding the the 5 th term we have to find the remaining four term before the 5th term.

So, n=2

f(2) = 5f(1)

f(2)=  5(5)

f(2)=  25

Now, n=3

f(3) = 5f(2)

f(3)=  5(25)

f(3)=  125

Now, n=4

f(4) = 5f(3)

f(4)=  5(125)

f(4)=  625

Now, n=5

f(5) = 5f(4)

f(5)=  5(625)

f(5)=  3125

Hence, the value of f(5) is 3125.

Learn more about function here:

https://brainly.com/question/12431044

#SPJ2

Random variables can be either discrete or continuous.

Sample spaces need not consist of numbers.  In statistics, we are most often interested in numerical outcomes such as the "count" of an occurrence.  We call X a random variable because its values vary when the phenomenon is repeated.  We use capital letters near the end of the alphabet like X or Y.

A random variable is a variable whose value is a numerical outcome of a random phenomenon.  When a random variable describes a random phenomenon the sample space S just lists the possible values of the random variable.  There are two ways of assigning probabilities to the values of a random variable that will dominate our application of probability as we study statistical inference.

Random variables can be either discrete or continuous.  A discrete random variable X has a "countable number of possible values.  The probability distribution of X lists the values and their probabilities in table form.  The probabilities must satisfy two requirements:

1)  every probability pi is a number between 0 and 1

2) p1 + p2 +,,,+pk = 1.

The probability of any event is found by adding the probabilities pi of the particular values xi that makes up the event.

For more information on random variables click on the link below:

https://brainly.com/question/17217746

#SPJ4

Answer:

a

Step-by-step explanation:

Answer:

No solution is possible

Step-by-step explanation:

You didn't indicate the number of adults and children.

The maximum distance Frank can travel would be 10 miles.

What is maximum distance?

For maximum distance that is maximum range of a projectile, the angle of projectile should be 45°.

From given question,

taxicabs charge for first mile = $1.00

for each additional mile = $0.30

The cost for the first mile is $1, and for each additional mile it's $0.30, so for 10 miles it would be $1 + 9 * $0.30 = $4.70. Since Frank has only $3.50, he can travel a maximum of 10 miles.

Therefore, The maximum distance Frank can travel would be 10 miles.

To know more about maximum distance visit,

https://brainly.com/question/2497377

#SPJ1

Answer:

slope = 4

Step-by-step explanation:

.................

There is a significant effect of temperature and/or noise conditions on task performance, as well as any specific conditions that differ significantly from each other.

State the hypotheses: Before conducting any statistical analysis, it is important to state the null and alternative hypotheses.

In this case, the null hypothesis would be that there is no significant effect of temperature and noise conditions on task performance, while the alternative hypothesis would be that there is a significant effect.

Check assumptions: The validity of the ANOVA results relies on several assumptions being met, such as normality of the data, homogeneity of variance, and independence of observations.

These assumptions can be checked using statistical tests or graphical methods.

Conduct the analysis: To conduct a two-way ANOVA in a statistical software package, the data would be organized in a table with one column for the dependent variable (task performance),

Two columns for the independent variables (temperature and noise conditions). The software will then calculate the sum of squares, mean squares, and F-values for each main effect and the interaction effect, as well as the associated p-values.

Interpret the results: The ANOVA output will provide information on whether there are significant main effects of temperature and noise conditions, as well as whether there is a significant interaction effect.

If the p-value is less than the significance level (usually 0.05), then we can reject the null hypothesis and conclude that there is a significant effect. Post-hoc tests may be used to identify which specific conditions differ significantly from each other.

Report the results: The results of the ANOVA analysis should be reported in a clear and concise manner, including the F-value, degrees of freedom, and p-value for each effect.

It is also important to include any limitations or potential sources of error in the study.

For similar question on effect of temperature:

https://brainly.com/question/29439060

#SPJ11

Answer:

170 feet per second

Step-by-step explanation:

To answer the question you need to find the unit rate. To find the unit rate divide the denominator with the numerator in a way that the denominator becomes 1.

5,100/30 = 170

The skydiver falls at a rate of 170 feet per second before opening the parachute.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

It takes a skydiver 30 seconds to fall 5,100 feet before opening the parachute.

Hence, Height for this is,

⇒ 5100 / 30

⇒ 170 feet per second

Thus, the skydiver falls at a rate of 170 feet per second before opening the parachute.

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ2

The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is  0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.

Given that mean μ = 4.2 , standard deviation σ = 1.3

1. P(X >= 5) = P((X - μ)/σ >

                    = (5 - 4.2) /1.3

                    = P(Z ≥ 0.6154)

                    = 1 - P(Z < 0.6154)

                    = 1 - 0.7324

                    = 0.2676

The required probability is 0.2676.

2.Given that n = 8 then  \(\bar x\) = σ/\(\sqrt{(n)\)  = 1.3/√(8) = 0.4596

P(x-bar ≥ 5) = P((\(\bar x\) - μ)/σx-bar ≥ (5 - 4.2)/0.4596)

                        = P(Z ≥ 1.7406)

                        = 1 - P(Z < 1.7406)

                        = 1 - 0.9591

                        = 0.0409

The required probability is 0.0409.

Learn more about Probability;

https://brainly.com/question/16794285

#SPJ4

Answer:

Step-by-step explanation:

The starting amount of water in the tank = 19

She needs to add enough water to get 67L of water in the tank.

19 + 6*t ≥ 67                  Subtract 19 from both sides.

19-19 + 6t ≥ 67 -19

6t ≥ 68                           Divide by 6

t ≥ 68/6

t ≥ 11.33 minutes

The cosecant, secant, and cotangent functions are defined as the reciprocals of the sine, cosine, and tangent functions, respectively which have two parent trigonometric functions have a period of π and a range that consists of the set of all real numbers.

These functions also have a period of 2π and their ranges depend on the range of the corresponding parent function.

Therefore, correct answer will be a. sine, b. cosine and c. tangent.

The trigonometric functions are mathematical functions used to describe relationships involving lengths and angles of triangles. These functions include sine, cosine, tangent, cosecant, secant, and cotangent. Each of these functions has its own unique properties, including period and range.

Here you can learn more about trigonometric functions

https://brainly.com/question/6904750#

#SPJ11

We know that the number of flowers is proportional to the area of the garden

We observe that for a garden of 12 ft² it is recommended to plant 16 flowers,

we want to find a way of obtaining 16 out of 12.

There are two ways:

If we add 4 to 12:

12 + 4 = 16

If we divide 12 by 3 and multiply the result by 4:

We apply both ways to the second terms: a garden of 15 ft² it is recommended to plant 20 flowers.

First way: adding 4 to 15 ft²:

15 + 4 = 19

Second way: dividing by 3 and multiplying by 4:

We obtain 20 using the second method, since it has always the same proportion we can find all the number of flowers just by knowing the area of the garden. We just need to divide it by 3 and multiply it by 4.

Now we can find the recommended number of flowers for a garden of 24 ft²:

Using the formula they gave us:

Cost of shipping = 2.79 + 0.38(8)

Cost of shipping = 2.79 + 3.04

Cost of shipping = 5.83(currency unit)

3x+5=11

3x=6

x=2

Answer is x=2 Hope this helps

Answer:

B)  (-∞, 2)

Step-by-step explanation:

Given functions:

\(f(x)=x-3\)

\(g(x)=-0.5x\)

To find the interval for which (f - g)(x) is negative, set (f - g)(x) less than zero and solve for x:

\(\begin{aligned}(f-g)(x)& < 0\\f(x)-g(x)& < 0\\(x-3)-(-0.5x)& < 0\\x-3+0.5x& < 0\\1.5x-3& < 0\\1.5x& < 3\\x& < 2\end{aligned}\)

Therefore, the interval for which the composite function (f - g)(x) is negative is:

Answer:

Weight depends on the amount of gravity.

Step-by-step explanation:

Unlike mass, which remains constant, weight depends on the force of gravity that is exerted on it.

To conduct this simulation, we will first generate a random number between 0 and 1 for each of the four children in each trial. If the random number is less than 0.15, we will consider that child to have contracted the disease.Here is how we can do this using the random number table you provided:Trial 1:

Child 1: 0.14 (does not get the disease)

Child 2: 0.06 (gets the disease)

Child 3: 0.11 (does not get the disease)

Child 4: 0.13 (does not get the disease)Trial 2:

Child 1: 0.12 (does not get the disease)

Child 2: 0.08 (does not get the disease)

Child 3: 0.05 (gets the disease)

Child 4: 0.10 (does not get the disease)Trial 3:

Child 1: 0.09 (does not get the disease)

Child 2: 0.01 (gets the disease)

Child 3: 0.03 (gets the disease)

Child 4: 0.06 (gets the disease)...Trial 20:

Child 1: 0.14 (does not get the disease)

Child 2: 0.12 (does not get the disease)

Child 3: 0.05 (gets the disease)

Child 4: 0.07 (gets the disease)Based on this simulation, we can estimate the average number of children who will get the disease by taking the total number of children who got the disease across all 20 trials and dividing by the total number of trials. This comes out to be approximately 1.5 children.To calculate the probability of two of the children getting the disease, we count the number of trials where exactly two of the children got the disease, and divide by the total number of trials. In this simulation, this occurs in 5 trials out of 20, so the probability is 5/20 = 0.25.To calculate the probability of at least two of the children getting the disease, we count the number of trials where at least two of the children got the disease, and divide by the total number of trials. In this simulation, this occurs in 8 trials out of 20, so the probability is 8/20 = 0.4.

a) the probability of x being greater than or equal to 11, we subtract this area from 1 to obtain P(x ≥ 11) = 1 - 0.6915 = 0.3085. b) P(x ≤ 8.5) = 0.2266. c) The probability between these two values is 0.3129. d)  The probability between these two values is 0.9156.

(a) To find P(x ≥ 11), we first need to standardize the value using the Z-score formula: Z = (x - μ) / σ. Substituting the given values, we get Z = (11 - 10) / 2 = 0.5. Using the table of areas under the standardized normal curve, we find the corresponding area to be 0.6915. Since we're interested in the probability of x being greater than or equal to 11, we subtract this area from 1 to obtain P(x ≥ 11) = 1 - 0.6915 = 0.3085.

(b) To find P(x ≤ 8.5), we standardize the value: Z = (8.5 - 10) / 2 = -0.75. Referring to the table, we find the area corresponding to Z = -0.75 as 0.2266. Therefore, P(x ≤ 8.5) = 0.2266.

(c) For P(10.96 ≤ x ≤ 15.54), we standardize both values: Z1 = (10.96 - 10) / 2 = 0.48 and Z2 = (15.54 - 10) / 2 = 2.77. From the table, we find the area corresponding to Z1 as 0.6844 and Z2 as 0.9973. The probability between these two values is given by the difference: P(10.96 ≤ x ≤ 15.54) = 0.9973 - 0.6844 = 0.3129.

(d) To find P(4.86 ≤ x ≤ 12.82), we standardize both values: Z1 = (4.86 - 10) / 2 = -2.57 and Z2 = (12.82 - 10) / 2 = 1.41. Using the table, we find the area corresponding to Z1 as 0.0051 and Z2 as 0.9207. The probability between these two values is P(4.86 ≤ x ≤ 12.82) = 0.9207 - 0.0051 = 0.9156.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

The simplified power of the product (5w⁷)² is 25w¹⁴ and  (7w⁻⁹)⁻³ is 1/343 w²⁷

To simplify the expression (7w⁻⁹)⁻³ using Kelly's steps, we can follow the exponentiation rules:

Apply the power to each factor individually:

(7⁻³)(w⁻⁹)⁻³

Simplify each factor:

7⁻³ = 1/7³ = 1/343

(w⁻⁹)⁻³ = w⁻³⁻⁹ = w²⁷

Now, let's simplify the expression (5w⁷)²:

Apply the power to each factor individually:

(5²)(w⁷)²

Simplify each factor:

5² = 25

(w⁷)² = w¹⁴

Therefore, the simplified power of the product (5w⁷)² is 25w¹⁴

To know more about power click here :

https://brainly.com/question/28457639

#SPJ4

The question is incomplete the complete question is :

Kelly simplified this power of a product

(7w⁻⁹)⁻³

1. 7⁻³ (w⁻⁹)⁻³

2 1/343 w²⁷

use Kelly's steps to simplify this expression

(5w⁷)²

what is the simplified power of the product?

5w

10w¹⁴

25w

25w¹⁴

Opportunity cost is the price of giving up an option. An opportunity cost is the price you pay for selecting a particular option over another. Opportunity cost is the benefits you lose by choosing one alternative over another one.”

The value of the next-highest-valued alternative use of a resource is what economists mean when they talk about its "opportunity cost." You cannot, for instance, read a book at home during the time you would have spent seeing a movie and spend the money you would have spent on something else.

Opportunity cost is frequently referred to as the second-best option. The loss of benefit that would have been realized if a different option had been taken is sometimes referred to as the alternative cost. The loss of advantage as a result of a change in decision is another way to explain it.

Learn more about opportunity costs  to visit this link

https://brainly.com/question/13036997

#SPJ4

Answer:

The variance rounded to the nearest tenth is 691.8

Step-by-step explanation:

Xavier's bowling scores:

135, 140, 130, 190, 112, 200, 185, 172, 163, 151, 149

No. of observations n = 11

\(Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{135+140+130+190+112+200+185+172+ 163+ 151+149}{11}\\Mean =157\)

Formula of variance : \(\sigma^2=\frac{\sum(x_i-\bar{x})^2}{n}\)

\(\sigma^2=\frac{(135-157)^2+(140-157)^2+(130-157)^2+(190-157)^2+(112-157)^2+(200-157)^2+(185-157)^2+(172-157)^2+(163-157)^2+(151-157)^2+(149-157)^2}{11}\)

\(\sigma^2=\frac{7610}{11}\)

\(\sigma^2=691.81\)

Hence the variance rounded to the nearest tenth is 691.8

Steps to solve:

f(x) = 2x + 1

~Substitute

f(9) = 2(9) + 1

~Multiply

f(9) = 18 + 1

~Add

f(9) = 19

Best of Luck!

Answer:

19

Step-by-step explanation:

substitute 9 in x and you get 18 then add 1 so total u get 19

Hope that helps :)

Answer:

f=4

Step-by-step explanation:

so, when we do this problem notice that there is a variable this can mean a lot of things but in this case, it just means were solving for f so we first move the constant (5) to the right-hand side and change its sign then we subtract 33 from 5 to get 28 so the equation would look like 7f = 33-5

to get 7f = 28 and now for the last step you divide both sides of the equation to get f = 4

Hope this helped :)

Answer:  A. an incorrect decision when the null hypothesis is false

Explanation:

A type I error is when we reject the null, but the null was true.

A type II error is when we fail to reject the null, but the alternative was true.

Refer to the chart below to help organize things.

Answer:

x=27

Step-by-step explanation:

expanding the above expression we get

5x+5=4x+32

grouping numbers with coefficient of x at the left side and constant at the right side we get

5x-4x=32-5

x=27