e) Find the local minimum and maximum values of f. f(x) = 2x² + 3x² - 36x %

Answer:

The correct answers are:

The variable p is the independent variable.

The number of hours spent reading causes a change in the number of pages read.

The variable p is the dependent variable.

Step-by-step explanation: Hope this helps :)))

These two statements are correct and applicable

(1) The number of hours spent reading causes a change in the number of pages read.

(2) The variable p is the dependent variable.

"A Variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables."

"A dependent variable is the variable that changes as a result of the independent variable manipulation."

"A Line graph is a graphical display of information that changes continuously over time. A line graph may also be referred to as a line chart. Within a line graph, there are points connecting the data to show a continuous change. A Line graph has two axes(X- axis and Y-axis)"

We have,

Kelvin read 35 pages per hour

According to the question,

Number of hours increasing, number of pages also increasing

∵ The table data shows linear graph

We can clearly say that from a line graph definition,

These two are correct and applicable to Kelvin's situation

(1) The number of hours spent reading causes a change in the number of pages read.

(2) The variable p is the dependent variable.

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Answer:

Large pizzas= 12 Medium= 8

Step-by-step explanation:

if you 12 by 5 and 8 by 6 and add them together you get 108

Answer:

8 laps in 70 seconds is faster.

Step-by-step explanation:

If we divide 70/8 and 98/12 we get the following:

70/8= 8.75

98/12=8.16

8.75>8.16

The unit rate is 1 lap in 8.75 seconds and 1 lap in 8.16 seconds

The resort has set clear guidelines for rowboat rentals, including a limit of four people per boat and a maximum weight capacity of 800 pounds. These rules help to provide a safe and enjoyable experience for customers using the rowboats.

The summer resort has a policy that restricts the number of people allowed in each rowboat to four. Additionally, each boat is designed to hold a maximum weight capacity of 800 pounds. This policy is likely in place to ensure the safety of the guests and to prevent any accidents or mishaps on the water. In terms of pricing and availability, it's possible that the resort may offer different rental options depending on the size of the party or the length of time they wish to rent the boat for.

It's important for customers to adhere to the rules and regulations set forth by the resort to ensure a fun and safe experience for all. The summer resort rents rowboats to customers with a maximum capacity of four people per boat. This is to ensure the safety and comfort of the customers using the boats. Each rowboat is designed to hold no more than 800 pounds in total weight. This weight limit is put in place to maintain the boat's stability and prevent any accidents from occurring due to overloading.

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Answer:

60

Step-by-step explanation:

180-120=60 so the answer is 60

The value for R in the table which is most likely to indicate an association between the conditional variables is 0.79.

The association between the conditional variables, exist when the relative frequencies between the two variables are not similar.

The more the difference in the values shows the stronger the association between two.

The table given in the problem is attached below. The given option for the R value in the table is, 0.09,  0.10,  0.13, and 0.79.

As it is known that the bigger the difference, gives the stronger the association. Here, the R value with 0.79 is the most opposite to the value above the R.

Hence, the value for R in the table which is most likely to indicate an association between the conditional variables is 0.79.

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Answer:

D)

Step-by-step explanation:

To find the probability P(X ≤ 3) for a binomial random variable with parameters n = 14 and p = 0.13 using Excel, you can utilize the BINOM.DIST function. The BINOM.DIST function calculates the probability of a specific number of successes in a binomial distribution.

In this case, you need to calculate the cumulative probability from 0 to 3 successes. Here's how you can use Excel to find the result:

1. Open Excel and enter the formula:

  =BINOM.DIST(3,14,0.13,TRUE)

  This formula calculates the cumulative binomial probability for 3 or fewer successes (X ≤ 3) in a binomial distribution with n = 14 and p = 0.13. The TRUE argument specifies that it calculates the cumulative probability.

2. Press Enter to get the result.

The resulting value will be the probability P(X ≤ 3) rounded to four decimal places.

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a. Optimal solution: X1 = 140, X2 = 0, X3 = 80, Objective Function Value = 4700.000.

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding.

c. The dual price for the second constraint is 2.333, indicating that for each unit increase in its right-hand side value, the objective function value increases by 2.333.

d. The objective function coefficient of X2 can vary between 30 and 40 without changing the optimal solution

a. The complete optimal solution is:

X1 = 140

X2 = 0

X3 = 80

Objective Function Value = 4700.000

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding because it has a slack/surplus value of 0.

c. The dual price for the second constraint (9X1 + 15X2 + 3X3 < 1500) is 2.333. This means that for each unit increase in the right-hand side value of the second constraint, the objective function value will increase by 2.333 units, assuming all other variables and constraints remain constant.

d. The objective function coefficient of X2 can vary between 30 and 40 before a new solution point becomes optimal. This means that as long as the coefficient remains within this range, the current solution will still be optimal. However, if the coefficient of X2 goes below 30 or above 40, a new optimal solution may be obtained.

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The p-value for testing H0 (null hypothesis) versus Ha (alternative hypothesis) is 0.0038. We need to determine whether H0 would be rejected at different significance levels: α = 0.10, α = 0.05, α = 0.01, and α = 0.001.

To make the decision, we compare the p-value with the chosen significance level. If the p-value is less than or equal to the significance level, we reject H0. Otherwise, we fail to reject H0.

At α = 0.10: Since the p-value (0.0038) is less than 0.10, we reject H0.

At α = 0.05: Since the p-value (0.0038) is less than 0.05, we reject H0.

At α = 0.01: Since the p-value (0.0038) is greater than 0.01, we fail to reject H0.

At α = 0.001: Since the p-value (0.0038) is greater than 0.001, we fail to reject H0.

In summary:

H0 would be rejected at α = 0.10 and α = 0.05.

H0 would not be rejected at α = 0.01 and α = 0.001.

Please note that the decision to reject or fail to reject the null hypothesis depends on the chosen significance level, and different levels of significance can lead to different conclusions.

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Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.

What is the combination?

In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter. The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set.

If none of the numbers can be repeated, Joaquin can choose from a total of 22 numbers (0 through 21), and he needs to select three of them for his locker combination. This is a classic example of a combination problem, as the order in which he chooses the numbers does not matter. The number of ways to choose three numbers from a set of 22 without repetition is given by the formula for combinations:

C(22,3) = 22! / (3!(22-3)!) = 222120/(321) = 2310

So, Joaquin can choose from 2310 different locker combinations if none of the numbers can be repeated.

The name "combination lock" is appropriate because it refers to the process of combining numbers in a specific order to open the lock. In this case, the order of the numbers selected does not matter.

If Joaquin could repeat a number, but not use the same number twice in a row, the number of mathematical combinations are possible is given by the formula for permutations:

A(22,3) = 222120 = 9, 612

Hence, Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.

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For the function f(x) = cx, where c is a nonzero real number:

A vertical asymptote occurs when the function approaches infinity or negative infinity as the input approaches a certain value. For the function f(x) = cx, this does not happen as the input can be any real number and the output will always be a real number multiplied by a constant factor.

The horizontal asymptote is the value that the function approaches as the input becomes very large or very small. For the function f(x) = cx, as x becomes larger and larger in magnitude, the value of cx becomes closer and closer to 0, regardless of the value of c. So, the horizontal asymptote is y = 0.

The domain of a function is the set of all input values for which the function produces a valid output. For the function f(x) = cx, the input can be any real number, so the domain is all real numbers.

The range of a function is the set of all output values for which the function produces a valid output. For the function f(x) = cx, the output will always be a real number multiplied by a constant factor. If c is nonzero, the output will always be a non-zero real number, so the range is all real numbers. However, if c = 0, the function will output y = 0 for every x and thus the range would be only {0}

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Answer:

4

Step-by-step explanation:

I think I'm not sure but please let me know if it is helpful

Your answer is:

A) 1,400 - 2,000

keep believing and dont give up.

if nobody loves you, i do

Option A is right.

Given that:

Mean = 1700

Standard deviation = 100

So, the range for 3 standard deviations to the right and to the left of the mean is:

\(\left(1700-3\left(100\right)\ ,\ 1700\ +\ 3\left(100\right)\right)\\=\left(1700-300,\ 1700\ +\ 300\right)\\=\left(1400,\ 2000\right)\)

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Answer:

Hello, I would need to see an image of the quadrilateral at hand to be able to answer your question.

Step-by-step explanation:

Just let me know, here to help!

Answer:

100

Step-by-step explanation:

Because everyone had one plate and one drink, we can combine those individual prices.

5 + 1 = 6

Now we divide 600, the total cost, by 6, the cost for one person.

600 ÷ 6 = 100

So now we know that 100 people went to the party, as there was nothing left over.

Answer:

1. 8,5a + 38

2.  5,5+b

Step-by-step explanation:

1. a) 9,5(a+4)-a= 9,5a + 38-a= 8,5a + 38

2. 8+b-2,5= 5,5+b

Answer:

here

Step-by-step explanation:

intoTo do this, you just have to plug the value of x or y into the equation and solve to get its corresponding x or y value. So,

*If x = 2

*If y = 3

*If x = 6

*If x = 0

*If x = 3

*If y = 0

*If y = 8

Therefore, the table would be

Now, to find the slope of the line you can solve for y in the equation because that way you will have the equation of the line in its slope-intercept form, that is

So,

Then, in this case

Therefore, the slope of the line is -3.

Answer:

POKEMON YEAH!

Okay, so you first want to take 2485, and subtract it from 4500, because that is the amount of money he has already collected.

4500 - 2485 = 2015

Now you need to find out how many time you can multiply 155, to get 2015, or higher. In this case, I am just gonna divide:

2015/155 = 13

It will take him 13 more weeks to have enough for the Pokemon cards!

Step-by-step explanation:

Hope it helps! =D

Hi! Based on the information provided, using homework 10 data with a significance level (α) of 0.05 and a p-value of 0.038, your conclusion is that you would reject the null hypothesis.

This is because the p-value (0.038) is less than the significance level (0.05), indicating that there is significant evidence to suggest that the alternative hypothesis is true. Therefore, the conclusion is made based on the evidence to suggest that there is a statistically significant difference between the groups being compared in the study analyzed in homework 10.

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a) The expected value of X is 5/8.

b) The expected value of Y-\(X^2\) is 1/16.

c) The variance of X is 21/64.

(a) The expected value of a discrete random variable X with possible values x1, x2, ..., xn and corresponding probabilities p1, p2, ..., pn is given by:

E(X) = Σ(pi \(\times\) xi) for i = 1 to n

Using this formula, we can calculate the expected value of X as follows:

E(X) = (1/8\(\times\)(-1)) + (2/8 \(\times\)0) + (5/8 \(\times\) 1) = 5/8

Therefore, the expected value of X is 5/8.

(b) To find the probability function of Y-\(X^2\), we need to find the possible values of Y-\(X^2\) and their corresponding probabilities.

Y takes values -1, 0, 1 with probabilities 1/8, 2/8, 5/8 respectively. Therefore, Y-X^2 takes values (-1 - \((-1)^2\)), (0 - \(0^2\)), (1 - \(1^2\)), which simplify to -2, 0, and 0, respectively.

The probabilities of Y-X^2 taking these values can be found by considering all possible combinations of the values of X and Y. For example, when X = -1 and Y = -1, we have Y-\(X^2\) = -1 - \((-1)^2\) = -2. The probability of this occurring is 1/8 \(\times\)1/8 = 1/64. Continuing in this way, we can find the probabilities for all possible values of Y-\(X^2\):

Y-\(X^2\) = -2 with probability 1/64

Y-\(X^2\) = 0 with probability 3/8

Y-\(X^2\) = 2 with probability 5/64

Now we can calculate the expected value of Y-\(X^2\) as follows:

E(Y-\(X^2\)) = (-2 \(\times\) 1/64) + (0 \(\times\) 3/8) + (2 \(\times\) 5/64) = 1/16

Therefore, the expected value of Y-\(X^2\) is 1/16.

(c) The variance of a discrete random variable X with possible values x1, x2, ..., xn and corresponding probabilities p1, p2, ..., pn is given by:

Var(X) = E(X^2) - [E(X)\(]^2\)

To calculate Var(X), we need to first calculate E(X^2). Using the formula for expected value, we have:

E(X^2) = (1/8 \(\times\)\((-1)^2\)) + (2/8 \(\times\) \(0^2\)) + (5/8 \(\times\) \(1^2\)) = 7/8

Now we can calculate Var(X) using the formula above:

Var(X) = E(\(X^2\)) - [E(X)\(]^2\) = 7/8 - (5/8\()^2\) = 21/64

Therefore, the variance of X is 21/64.

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Answer:

2^12=2*2*2*2*2*2*2*2*2*2*2*2=4*4*4*4*4*4=16*16*16=256*16=4096

Step-by-step explanation:

Answer:

16.9265381881

Step-by-step explanation:

Tangent = Opposite/Adjacent.

Thus, tan62 = x/9 --> tan62 = 1.88072646535, multiply by 9 to get x, 1.88072646535* 9 = 16.9265381881

Rounding to four decimal places, the rates of change of P at t = 1 and t = 10 are about 0.0274 and 0.0274, respectively.

The percent P of defective parts produced by a new employee t days after the employee starts work can be modeled by t + 1790 P = 50(t + 2).To find the rates of change of P at t = 1 and t = 10, we have to differentiate the given function with respect to t.

Therefore, t + 1790 P = 50(t + 2)P = (50t + 100 - t)/1790P = (49t + 100)/1790

Now, we will find the rates of change of P at t = 1 and t = 10: (i) At t = 1P = (49(1) + 100)/1790P = 0.065dP/dt = d/dt [(49t + 100)/1790]dP/dt = (49/1790) = 0.0274(ii) At t = 10P = (49(10) + 100)/1790P = 0.365dP/dt = d/dt [(49t + 100)/1790]dP/dt = (49/1790) = 0.0274.

Therefore, the rates of change of P at t = 1 and t = 10 are approximately 0.0274, rounded to four decimal places.

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The linear correlation coefficient between the variables X and Y is given by r = (Sxy / sqrt(Sxx * Syy)). To find the linear correlation coefficient, we need to calculate Sxy and Sxx first.

The formula for Sxy is Sxy = Σ(xi * yi) - (Σxi * Σyi) / n, where xi and yi are the individual values of X and Y, Σ denotes the sum, and n is the sample size.

Given that the slope of the regression line is 0.375, we can deduce that Sxy = b * Sxx, where b is the slope of the regression line. Therefore, Sxy = 0.375 * Sxx.

Next, we calculate Sxx using the formula Sxx = Σ(xi^2) - (Σxi)^2 / n.

Given that S = 80, we can substitute the values into the formula to find Sxx = (80^2) - (Σxi)^2 / n.

Using the information provided in the question, we have Syy = 54.75.

Now, we can substitute the values of Sxy, Sxx, and Syy into the formula for the linear correlation coefficient: r = (Sxy / sqrt(Sxx * Syy)).

By substituting Sxy = 0.375 * Sxx, Sxx from the previous step, and Syy = 54.75 into the formula, we can calculate the value of r.

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Answer:

x-intercept(s):  ( 4 /3 ,  0 )

y-intercept(s):  ( 0 ,  − 3/ 2 )

Step-by-step explanation:

To find the x-intercept, substitute in  0  for  y  and solve for  x .

To find the y-intercept, substitute in  0 for  x and solve for  y .

Answer: 3,9

Step-by-step explanation: divided it

according to question the linearization of f(x) = x^(2/3) at a = 64 is:

l(x) = 16 + (1/6) * (x - 64)

To find the linearization of a function f(x) at a point a, we need to use the formula:

l(x) = f(a) + f'(a) * (x - a)

where f(a) is the value of the function at the point a, f'(a) is the derivative of the function evaluated at a, and (x - a) is the difference between x and a.

First, we need to find the value of f(a):

f(a) = a^(2/3) = 64^(2/3) = 16

Next, we need to find the derivative of f(x):

f'(x) = (2/3) * x^(-1/3)

Now, we evaluate f'(a):

f'(a) = (2/3) * 64^(-1/3) = (2/3) * (1/4) = 1/6

Finally, we can plug in these values into the formula for the linearization:

l(x) = 16 + (1/6) * (x - 64)

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

1/10 in first row

1/20 in second row

1/5 in third row

Step-by-step explanation:

it is simple, take first row, and look what is required to get 1,

here 5*2 is 10, so to get 1 we need to divide with 10

in second row, 20*1 is 20, so we need to divide with 20

and in third row 10* ½ is 5, so we need to divide with 5