Let f(x,y)=3y​x​ (a) Find f(4,8),f2​(4,8), and fy​(4,8). (b) Use your answers from part (a) to estimate the value of ​3.99​/3√8.02.

You can use the fact that at the zeros of a function, the function evaluates to 0.

For the given scenario, the following statements are correct:

Option A: The scenario can be represented by the function h(x) = -0.25(x)(x-5)

Option B: The vertex is on the line x = 2.5

If function can be written in all factored form with form as (x+a), then we can one by one equate them to zero to get the zeros of given function. If not, then we will have to find them by other methods.

Since the given scenario has zeros at 0 and 5, thus two factors of the function h(x) would be (x-0)(x-5) = (x)(x-5). Since at x = 4, the function outputs 1, thus we have: h(x) = a(x)(x-5)( here a is other factor with two already known factors of function h(x) which might represent the scenario (assuming that scenario given can be represented or modeled using quadratic equation) such that:

a(4)(4-5) = 1,

or

\(a(4)(4-5) = 5\\ a(4)(-1) = 5\\ a = -\dfrac{5}{4} = -0.25\\ \)

Thus, the function for given scenario is represented by

\(h(x) = a(x)(x-5) = -0.25(x)(x-5)\)

Finding the first and second rate of function to get the maxima or minima:

\(h(x) = -0.25(x)(x-5) = -0.25x^2 + 1.25x\\ h'(x) = -0.5x + 1.25\\ h''(x) = -0.5\)

Putting h'(x) = 0 gives:

\(-0.5x + 1.25 = 0\\\\ x = \dfrac{1.25}{0.5} = 0.25\)

For all x, the second rate is negative, showing that at x = 2.5, there is maxima. Thus the vertex is on the line x =2.5 and the greatest height water achieves is at x = 2.5

Thus,

Option A: The scenario can be represented by the function h(x) = -0.25(x)(x-5)

Option B: The vertex is on the line x = 2.5; are correct options.

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Answer:

A&C

Step-by-step explanation:

Scores on one variable plotted against scores on a second variable.

The correct answer is (b)

Now, According to the question:

Let's know:

A scatterplot shows:

A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.

Hence, The correct answer is (b) i.e.,

Scores on one variable plotted against scores on a second variable.

Given,

In the question:

A scatterplot shows:

a. the average value of groups of data.

b. scores on one variable plotted against scores on a second variable.

c. the frequency with which values appear in the data

d. the proportion of data falling into different categories.

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To multiply the given expressions (8.65 x 10^3) and (9.3 x 10^-23), we can apply the laws of exponents. In multiplication, we multiply the coefficients and add the exponents.

First, we multiply the coefficients:

8.65 * 9.3 = 80.295

Next, we add the exponents:

10^3 * 10^-23 = 10^(3 + (-23)) = 10^-20

Combining the coefficient and the exponent, we get:

80.295 x 10^-20

Thus, the final result of the multiplication is 80.295 x 10^-20.

In scientific notation, this can be written as 8.0295 x 10^-19, where the coefficient is 8.0295 and the exponent is -19.

This means that the product of (8.65 x 10^3) and (9.3 x 10^-23) is approximately 8.0295 x 10^-19. This result represents a very small value due to the negative exponent, indicating that the product is much smaller than 1.

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Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles

40 of these small cubes are painted red on at least two faces.

To determine the number of small cubes that are painted red on at least two faces, we need to consider the cubes at the corners and edges of the large cube.

The large cube consists of 8 corner cubes, each having 3 faces painted red, and 12 edge cubes, each having 2 faces painted red. These corner and edge cubes are the ones that have the potential to be painted on at least two faces.

Number of corner cubes = 8

Number of faces painted red on each corner cube = 3

Total number of faces painted red on corner cubes = 8 * 3 = 24

Number of edge cubes = 12

Number of faces painted red on each edge cube = 2

Total number of faces painted red on edge cubes = 12 * 2 = 24

Now, we need to subtract the double-counted faces where the corner and edge cubes overlap. Each corner cube shares one painted face with three edge cubes, so there are 8 * 1 = 8 double-counted faces.

Therefore, the total number of small cubes painted red on at least two faces is:

Total number = Total number of faces painted red on corner cubes + Total number of faces painted red on edge cubes - Double-counted faces

Total number = 24 + 24 - 8 = 40

Hence, there are 40 small cubes out of the 1000 congruent cubes that are painted red on at least two faces.

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Systematic sampling is a type of probability sampling method where every nth item in a population is selected for inclusion in the sample.

For example, if a researcher wanted to select a systematic sample of 100 students from a school population of 1,000 students, they would randomly select one of the first 10 students (1/10th of the population) and then select every 10th student thereafter until they reach 100. Systematic sampling is often used when the population is too large to enumerate and it is more efficient than simple random sampling. However, it is important to ensure that the sampling interval is not biased in any way, otherwise the sample may not be representative of the population.

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Systematic sampling is a relatively easy and quick method of sampling, as it requires less effort and time than other methods such as stratified or cluster sampling.

The starting point is truly random, and that the interval selected does not create any bias in the sample.

Systematic sampling is a method of selecting a sample from a population using a system or a pattern.

It involves selecting every nth item or person from the population after a random starting point has been determined.

To perform systematic sampling, the first item or individual in the sample is randomly selected from the population.

Then, the remaining items or individuals are selected at regular intervals, such as every 10th or 20th item or individual.

The interval is calculated by dividing the population size by the desired sample size.

A researcher wants to select a sample of 100 from a population of 1000, the interval would be. \(1000/100 = 10.\)

The researcher would randomly select the first item or individual from the population, and then select every 10th item or individual thereafter until the desired sample size is reached.

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Answer:

x = -2

Step-by-step explanation:

Let the number be x

12 -2x = 8x +32

Add 2x to each side

12 -2x +2x = 8x+32+2x

12 = 10x+32

Subtract 32 from each side

12-32 = 10x+32-32

-20 =10x

Divide each side by 10

-20/10=10x/10

-2 =x

Answer:

x = 8

Step-by-step explanation:

6.5x + 1.4y = 59

If y = 5, then plug in 5 for y

6.5x + 1.4(5) = 59

Isolate variable (x)

6.5x + 7 = 59

6.5x = 59 - 7

6.5x = 52

x = 52 ÷ 6.5

x = 8

True

A triangle with all the three sides equal equilateral

Hope this helped you- have a good day bro cya)

The required value of the given expression at z = 6 is 51.

Given that,
The value of the expression z² + 3z - 3 is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= z² + 3z - 3
Put z = 6 and simplify the expression,
= 6² + 3(6) - 3
= 36 + 18 - 3
= 54 - 3
= 51

Thus, the required value of the given expression at z = 6 is 51.

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It is not impossible to construct a frame for a finite population or a target population, but it is impossible to construct a frame for a sampled population.

A frame is a list or map of all the units in a population, which is used to select a sample for a survey or study. If a population is finite, it is possible to list all the units in the population and create a frame. Similarly, if the target population is well-defined and can be identified, a frame can be constructed.

However, if the population is sampled, the frame cannot be constructed because the population is unknown and constantly changing. Therefore, it is impossible to construct a frame for a sampled population.

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The complete question is :

Is it impossible to construct a frame for a sampled population, a finite population, or a target population?

The inequality can be used to determine the number is 0.4x > x/2 - 15

The term inequality means the unequal relationship between the two or more expressions.

Here we have given that Forty percent of a number is greater than one-half the number decreased by 15.

And we need to find the number that is used to determine the inequality.

While we looking into the given question, let us consider x be that unknown  number.

Then based on the given statement, we have divide it into two parts.

First, forty percent of the number and it can be written as 40%x or 0.4x.

Next is one-half the number is 1/2 x or x/2

When we combine the whole statement,

Then we get the inequality,

=> 0.4x > x/2 - 15

Therefore option (c) is correct.

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9514 1404 393

Answer:

  (-1, 1)

Step-by-step explanation:

Find the differences between an f(x) value and the previous one

  3 -18 = -15

  0 -3 = -3

  3 -0 = 3

  6 -3 = 3

  3 -6 = -3

Where the differences are positive, the function is increasing on the interval. Here, it is increasing on the intervals (-1, 0) and (0, 1). Then the longest increasing x-interval is (-1, 1).

The Central Limit Theorem can also be used to investigate unusual events. An unusual event is one that occurs with a probability of less than 1%

The Central Limit Theorem can be used to investigate unusual events by calculating the probability of a sample mean being a certain number of standard deviations away from the population mean.

If we assume that the population is normally distributed, then we can use the normal distribution to calculate the probability of observing a sample mean that is a certain number of standard deviations away from the population mean.

An unusual event is typically defined as an event that occurs with a low probability, usually less than 5% or 1%. So, if we observe a sample mean that is more than 2 standard deviations away from the population mean, we can say that this is an unusual event that occurs with a probability of less than 5%. Similarly, if we observe a sample mean that is more than 3 standard deviations away from the population mean, we can say that this is an unusual event that occurs with a probability of less than 1%.

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Hugh poured 100 kilograms of water into 10 kg of salt. He made 110 kilograms of 9.09 % salt solution.

To find the mass of the solution add the mass of salt and the mass of the solution. To find the concentration of the solution divide the salt mass by the total mass of the solution and multiply by 100.

Here we have  

Hugh poured 100 kilograms of water into 10 kg of salt.

After adding 100 kilograms of water to 10 kg of salt.  

The total mass of the solution = 100 + 10 = 110 kg

The concentration of salt

= [ Mass of salt/ Mass of solution] × 100

= [ 10/110] × 100 = 9.09%      

Therefore,

Hugh poured 100 kilograms of water into 10 kg of salt. He made 110 kilograms of 9.09 % salt solution.  

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To determine the values of \(\(p\)\) for which the series \(\(\sum_{n=1}^{\infty} \frac{9(1+n^{10})^p}{n}\)\) converges, we can use the p-series test.

The p-series test states that for a series of the form \(\(\sum_{n=1}^{\infty} \frac{1}{n^p}\), if \(p > 1\),\) then the series converges, and if \(\(p \leq 1\),\) then the series diverges.

In our case, we have a series of the form \(\(\sum_{n=1}^{\infty} \frac{9(1+n^{10})^p}{n}\).\)

To apply the p-series test, we need to determine the exponent of \(\(n\)\) in the denominator. In this case, the exponent is 1.

Therefore, for the given series to converge, we must have \(\(p > 1\).\) In other words, the values of \(\(p\)\) for which the series is convergent are \(\(p > 1\) or \(p \geq 1\).\)

To summarize:

- If \(\(p > 1\)\), the series converges.

- If \(\(p \leq 1\)\), the series diverges.

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Answer:

cos = adjacent/hypotenuse

3/square root13

now you do square root 13 x3 divided by square root 13^2

= 3square root13/13

hope that answers your question

cost = $187.60

20% down

4 months of $39.40

1.- Calculate the 20%

187,6 ------------------- 100

x -------------------- 20

x = (20 x 187.6) / 100

x = 3752/100

x = 37.52

2.- Calculate the final price

Price paid = 37.52 + 4(39.40)

Price paid = 37.52 + 157.6

= $195.12

2.- Finance charge

= 195.12 - 37.52

= $157.6

Answer:

80

Step-by-step explanation:

5x8 hats=40/8 yard which equals 5 yards cause 40/8=5

So you know that 5 yards can make 8 hats.

Then do 5x16 because 10 yards is double the size as 5 to get 80.

false :) thats ur answer

The y-intercept of the line is -7. The equation of the line: y = 2x - 7

The slope of a line is a measure of its steepness.

The formula to find the slope between 2 coordinates of a line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

To find the y-intercept of the line, we need to use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

We know that the slope of the line is 2, so we can substitute that in:

y = 2x + b

To find the value of b, we can use the point (5/2,-2) that the line passes through. We substitute the x and y values of this point into the equation, and solve for b:

-2 = 2(5/2) + b

-2 = 5 + b

b = -7

So the y-intercept of the line is -7.

Putting this together with the slope, we get the equation of the line:

y = 2x - 7

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Answer:

Step-by-step explanation:

Let x be the number.

(x + 13)/2

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

Equations are mathematical statements with the equals (=) sign on each side and two algebraic expressions in the center.

Coefficients, variables, operators, constants, terms, and the equal to sign are just a few of the components that make up an equation. The "=" symbol and terms on both sides are always needed when writing an equation.

calculation

Let s = brittany 's age now

Let t = steve's age now

s = 3t

s + 9 = 2 (t+9)

s + 9 = 2t + 27

s = 2t + 27 - 9

s = 2t + 18

Substitute 3t for s and find t

3t = 2t + 18

3t - 2t = 18

t = 18 yrs is steve's age

then

s = 3(18)

s = 54 yrs is brittany's age

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

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Answer:

x=6

Step-by-step explanation:

6x+4=2x+28

4x=24

x=6

Answer:

\(DF = 38\)

Step-by-step explanation:

Given

\(DE = 2x\)

\(EF = 2x - 6\)

\(DF = 3x + 5\)

Required

Determine EF

Since E lies on DF, then

\(DF = DE + EF\)

Substitute values for DF, DE and EF

\(3x + 5 = 2x + 2x -6\)

Collect Like Terms

\(3x -2x -2x = -6 -5\)

\(-x = -11\)

Solve for x

\(x = 11\)

Recall that

\(DF = 3x + 5\)

Substitute 11 for x

\(DF = 3 * 11 + 5\)

\(DF = 38\)

Answer:

Alternate Exterior Angles theorem

Answer:

alternate exterior angles

Step-by-step explanation:

alternate exterior angles are when two angles are on the far side of two lines and are not on the same side of the line cutting through the two parallel lines

Hope this is not redundunt or anything because I thought maybe I should just explain it so you would understand it next time :)

Answer:

C.

\(x = 2( \sqrt{ {6}^{2} - {4}^{2} } ) \\ x = 2( \sqrt{20} ) \\ x = 8.9\)

Answer:

................... Sam should sell 25 chocolate

Step-by-step explanation:

hahaha

To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.

In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.

Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.

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There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.

Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.

It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.

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Answer:

d. 13 raise power 3/5

Step-by-step explanation: