(1 point) Find the maximum and minimum values of the function f(x, y, z) = yz + xy subject to the constraints y² + z2 = 169 and xy = 1. Maximum value is Minimum value is

Answer:

DEF is a right angle

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.

数学思维是如何建立的？ 怎样才能有数学思维？

In my opinion the answer it either A or C because they make the most sense if you calculate.

Answer:

Set B has a greater speed ,because it has greater range

Answer:

The pool manager pay for each item is $60.6.

Step-by-step explanation:

Given:

A pool manager balances the ph level of a pool.

The price of a bucket of chlorine tablets is $90, and the price of a ph test kit is $11.

The manager uses a coupon that applies a 40% discount to the total cost of the two items.

Now, to find the money the pool manager pay for each item.

The price of a bucket of  chlorine tablets is = $90.

The price of a ph test kit = $11.

So, to get the total price of both items we add both prices:

Total cost of two items = $101.

As, given a coupon that applies a 40% discount to the total cost of the two items.

Now, to get the total cost by applying discount:

Thus, the pool manager pay = $60.6.

Therefore, the pool manager pay for each item is $60.6.

To improve the experimental design, it would be beneficial to increase the sample size, include a control group, and ensure that all vehicles experience similar conditions of use.

The experimental design mentioned in the question has a few issues. Firstly, the sample size is relatively small, with only 100 Toyota Highlanders fitted with brand A wipers and 100 Chevrolet Equinoxes fitted with brand B wipers. A larger sample size would provide more accurate and reliable results.

Additionally, the experiment lacks a control group. A control group would involve using the same type of wipers on a set of vehicles under normal conditions. By comparing the wear of brand A and brand B wipers to the control group, it would be possible to determine if any wear differences are due to the wipers themselves or other factors.

Furthermore, the experiment does not account for differing conditions of use. It is unclear if both sets of vehicles were subjected to the same driving conditions and weather patterns. These factors could significantly impact the wear and lifespan of the windshield wipers.

In conclusion, to improve the experimental design, it would be beneficial to increase the sample size, include a control group, and ensure that all vehicles experience similar conditions of use.

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Answer:

arc EI = 103°

arc EGI = 257°

Step-by-step explanation:

arc HI = 77° because they are alternate angles

arc EI = (360° - 77° - 77°)/2 = 103°

arc EGI = 360° - 103° = 257°

Answer:

Listed

Please mark me as the brainliest and thanks

Answer:

\(\boxed{\mathrm{view \: explanation}}\)

Step-by-step explanation:

1. Relations are the set of y (output) and x (input) values that are related. A function is when each input has a relation with one output.

2. The mathematical formula is the formula of Pythagoras theorem. Where the length c (hypotenuse) is equal to the square root of the sum of the legs squared.

Answer:

A heptagon has 7 sides, so we take the hexagon's sum of the interior angles and add 180 to it getting us, 720+180= 900 degrees

Step-by-step explanation:

The formula for calculating the sum of the interior angles of a regular polygon is: (n-2) x 180 degrees. N is the number of sides

Answer:

Step-by-step explanation:

The 6x^2 because 6  is not a perfect square.

Answer:

6x^2

Step-by-step explanation:

6 isn't a perfect square

Answer:

D.

Hope this helps

The mean of the following data 0,5,30,25,16,18,19,26,0,20,28 is 17.

Hence option D is the correct option.

Mean is the average value of a given set of data. It is calculated by the formula,

Mean =  {Summation of all the values in the data set} / {Number of observations is the data set}

That is, Mean = {Σ all values in the data set} / {number of observations}

The given data set is as follows,

0,5,30,25,16,18,19,26,0,20,28

The number of observations in the data set is 11.

The summation of all the values in the data set is = {0 + 5 + 30 + 25 +
16 + 18 + 19 +26 + 0 + 20 + 28} = 187

Therefore, by applying  the formula of Mean we get

Mean = 187/ 11 = 17

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a.)Gross pay = $400

b.) Total deductions = $89.25

c .) Net pay = $310.75

For question a.) The gross pay of Omark is calculated as thus:

The number of days per week = 7 days

The of working hours per week = 50 hours.

The amount paid per hour = $10

Therefore gross payment for a week = 40×10 = $400

For question b.)

The total deductions = 9.25+15.25+48.50+9.50+2.75+4.00 = $89.25

For question c )

Omark net payment = gross payment - total deductions = 400- 89.25 = $310.75

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P(F|T) is not equal to P(F), the two events are dependent. The correct answer is no, because P(F ∩ T) ≠ P(F) • P(T).

To determine if two events are independent, you need to determine if P(F|T) = P(F) and P(T|F) = P(T).

If both of these are true, then the events are independent. If either one of them is not true, then the events are dependent.Let event F be a fire drill and event T be a tornado drill.

There is a 75% probability of having a fire drill, a 50% probability of a tornado drill, and a 25% probability of having both drills.

We need to find out if the two events are independent or not.

P(F) = 0.75, P(T)

      = 0.50 P(F ∩ T)

      = 0.25

We can calculate P(F|T) as follows:

P(F|T) = P(F ∩ T) / P(T)P(F|T)

         = 0.25 / 0.50 P(F|T)

         = 0.50

Since P(F|T) is not equal to P(F), the two events are dependent.

Therefore, the correct answer is no, because P(F ∩ T) ≠ P(F) • P(T).

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the predict() function takes as input a linear regression model and a set of predictor variables (in this case, the students' GPA) and returns a set of predicted response values (in this case, the number of hours exercised per week) based on the fitted model.

The specific value that the predict() function would predict for each student's number of hours exercised per week would depend on the coefficients and intercept of the linear regression model that was fitted to the data. These coefficients reflect the relationship between the predictor variable (GPA) and the response variable (number of hours exercised per week) and determine how changes in the predictor variable are associated with changes in the response variable.

The intercept represents the predicted value of the response variable when the predictor variable is zero. Therefore, the predict() function would use these coefficients and intercept to predict the number of hours exercised per week for each student based on their GPA.

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The median price from the given data is 648,303.

To find the median price from the given data, we need to arrange the prices in ascending order and then locate the middle value. If there is an odd number of data points, the median will be the middle value. If there is an even number of data points, the median will be the average of the two middle values.

Let's arrange the data in ascending order:

181,386,243,922,355,008,406,791,542,820,648,303,782,200,845,053,924,494,1,089,774,1,175,704,1,274,928,1,308,954

There are a total of 13 data points, which is an odd number. So, the median price is the middle value.

The middle value is the 7th value:

Median Price = 648,303

Therefore, the median price from the given data is 648,303.

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The inverse of f,  f^-1 = 8x / (x + 3)

To find the inverse function, let's consider the following steps:

Step 1: Replace f(x) with y. y = x/8x - 3

Step 2: Swap the x and y variables. x = y/8y - 3

Step 3: Solve for y. x(8y - 3) = y x 8y - 3x = y y = f⁻¹(x) = 8x / x + 3

Therefore, f⁻¹(x) = 8x / (x + 3)

The domain of f⁻¹ is all real numbers except -3, as it is not defined for x = -3.

Hence the domain is (-∞, -3) U (-3, ∞).

The range of f⁻¹ is also all real numbers except 0, as it is not defined for x = 0. Hence the range is (-∞, 0) U (0, ∞).

Thus, the domain and range of f⁻¹ are (-∞, -3) U (-3, ∞) and (-∞, 0) U (0, ∞) respectively, in interval notation.

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Answer:

x/8 + 9 =5

Step-by-step explanation:

Quotient is division and I decided to use x as my number so the first part is x/8. Then you do the nine more because more is addition to whatever is after it in our case it is x/8 so now you have x/8 + 9. Then it says equals 5 so the equation is x/8 + 9 = 5

I hope this helps!

Answer:3:3:1

Step-by-step explanation:divide by 3

The Laplace transform of y(t) is: \(Y(s) = (2 + d/ds[e^{(-5t)}]) / (s + 2)\)

What is laplace transform?

The Laplace transform is a mathematical operation that transforms a function of time into a function of complex frequency. It is named after Pierre-Simon Laplace, a French mathematician.

To find the Laplace transform of y(t) for the given differential equation, we can directly apply the Laplace transform to the equation and use the initial condition. The Laplace transform of the differential equation is given by:

\(L(dy/dt) + 2L(y) = L(t'e^{(5t)})\)

Using the properties of the Laplace transform, we have:

\(sY(s) - y(0) + 2Y(s) = L(t'e^{(5t)})\)

Substituting the initial condition y(0) = 2 and the Laplace transform of \(t'e^{(5t)} = -d/ds[e^{(-5t)}]\), we get:

\(sY(s) - 2 + 2Y(s) = -d/ds[e^{(-5t)}]\)

Rearranging the equation, we have:

\((s + 2)Y(s) = 2 + d/ds[e^{(-5t)}]\)

Taking the Laplace transform of both sides, we get:

\(Y(s) = (2 + d/ds[e^{(-5t)}]) / (s + 2)\)

Therefore, the Laplace transform of y(t) is:

\(Y(s) = (2 + d/ds[e^{(-5t)}]) / (s + 2)\)

Note: The expression is left in symbolic form without further simplification or expansion into partial fractions, as per the request.

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Thus, the probability that two custard-filled donuts are selected in a row) 11/46.

sampling without replacement is the process of selecting a subset of observations at random; once an observation is chosen, it cannot be chosen again. sampling with replacement, whereby one observation may be chosen more than once and a subset of observations is chosen at random.

Given data:

two-dozen (24) donuts

probability = favourable outcome / total outcome

probability (1st custard-filled donut) = total custard-filled donut / total donuts

probability (1st custard-filled donut) = 12/24

probability (1st custard-filled donut) = 1/2

Now,1 is already taken, now total donuts left are 23 with 11 custard-filled donut.

probability (2nd custard-filled donut) = total custard-filled donut / total donuts

probability (2nd custard-filled donut) = 11/23

Now,

probability (two custard-filled donuts in a row) = 1/2 * 11/23

probability (two custard-filled donuts in a row) = 11 / 46

Thus, the probability that two custard-filled donuts are selected in a row) 11/46.

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Answer:

Student 2 only

Step-by-step explanation:

Given that:

The written antiderivatives formulas by the students for k sin (kx), where  k > 1 are:

Student 1 : \(\int (k \ sin (kx)) \ dx= k^2 \ cos (kx) + C\)

Student 2: \(\int (k \ sin (kx) ) \ dx = - cos (kx) + C\)

The student that wrote the correct anti-derivate formula is Student 2 only.

This is because:

Suppose:

\(I = \int (k \sin (kx) ) \ dx\) where; k > 1

This implies that:

\(I = \int (k \sin (kx) ) \ dx\)

\(I =k \bigg ( \dfrac{-cos (kx)}{k} \bigg) + C\)   because \(\int sin (ax) \ dx = \dfrac{-cos (ax)}{a}+C\)

here;

C = constant of the integration

∴

I = - cos (kx) + C  which aligns with the answer given by student 2 only.

‘B’ had a better college entrance exam score due to the higher value of Z-Score.

The Z-score of an observation is the number of standard deviations it falls above or below the mean. Standard deviation is a statistic that is used to measure the dispersion of a dataset relative to its mean and is calculated by doing the square root of the variance.

\(Z=\frac{(observation-mean)}{standard deviation}\)

By putting the values as given in the question,We get,

A's score is (600 - 500) / 200 = 0.5 standard deviation i.e. above the mean.

B's score is (25 - 20) / 5 = 1 standard deviations i.e. above the mean.

Thus ‘B’ had a better score.

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The probability of light being green ,yellow, not red ,and not green are 11/17, 1/17, 12/17 and 6/17 respectively.

Traffic light is red for 25 sec

Traffic light is yellow for 5 sec

Traffic light is green for 55 sec

Total of 85 seconds

The probability of the light being yellow when you reach it, all other things being equal, is 5 / 85 = 1/17

The probability of the light being green when you reach it, all other things being equal, is 55/ 85 = 11/17

The probability of the light being not red when you reach it, all other things being equal, is 5+55/ 85 = 60/85 = 12/17

The probability of the light being not green when you reach it, all other things being equal, is 5+25/ 85 = 30/85 = 6/17

As a result, the odds of a light being green, yellow, not red, or not green are respectively 11/17, 1/17, 12/17, and 6/17.

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The solution for x of the expression 3x - 4 + 6x = 112 is given as follows:

x = 12.89.

The expression for this problem is defined as follows:

3x - 4 + 6x = 112

The first step is combining the like terms at the left side of the expression, hence:

3x + 6x = 9x.

Then the expression is given as follows:

9x - 4 = 112.

Isolating the variable x, the solution for x of the expression is given as follows:

9x = 116

x = 116/9

x = 12.89.

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Answer:

Step-by-step explanation:

Finding final velocity.

\(\boxed{v_{f}=v_{i} + at}\\\\v_{f} -- > final \ velocity\\\\v_{i} -- > Initial velocity\)

a -> accelaration

t ---> time

\(v_{i} = 7 \ m/s\)

a = 2 m/s²

t = 5 s

\(v_{f}= 7 + 2*5\)

     = 7 + 10

     = 17 m/s

10) h = 5 m

g = -10m/s²

\(t =\sqrt{\dfrac{2*h}{g}}\\\\ =\sqrt{\dfrac{2*5}{10}}\\\\= \sqrt{\dfrac{10}{10}}\\\\= 1\)

t = 1 sec