State the complement of each of the following sets: (a) Engineers with less than 36 months of full-time employment. (b) Samples of cement blocks with compressive strength less than 6000 kilograms per square centimeter. (c) Measurements of the diameter of forged pistons that do not conform to engineering specifications. (d) Cholesterol levels that measure greater than 180 and less than 220.

Answer:

They will accept the $50,000 maximum offered by your insurance company

In this scenario, with $50,000 liability insurance, if you cause a $75,000 accident, the other party is likely to accept the $50,000 from your insurance (Option C) but could also sue you for the remaining $25,000 (Option D).

In this scenario, if you cause an accident resulting in $75,000 in damage to the passengers in another car, your liability insurance has a maximum coverage limit of $50,000 per accident. Typically, insurance policies cover up to the policy limits, and the insurance company would pay out up to $50,000 to the injured parties.

The most likely outcome in this situation would be that the injured parties may initially pursue a claim with your insurance company, and the insurance company would pay up to its policy limit of $50,000. However, since the damages exceed the policy limit, the injured parties may still have the option to sue you personally for the remaining $25,000 to cover their damages.

So, the answer could be a combination of options C and D: They may accept the $50,000 maximum offered by your insurance company but could also potentially sue you for the remaining $25,000 if they believe it's necessary to cover their damages. The actual outcome may vary depending on the specific circumstances, local laws, and the decisions made by the injured parties and their legal advisors. It's crucial to notify your insurance company as soon as an accident occurs so they can handle the situation accordingly.

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Answer:

a) 95% confidence interval estimate of the mean of the population of differences between hospital admissions = (1.69, 11.91)

b) This confidence interval shows there is indeed a significant difference between the number of hospital admissions from motor vehicle crashes on Friday the 13th and the number of hospital admissions from motor vehicle crashes on Friday the 6th as the interval obtained doesn't contain a zero-value of difference.

Hence, the claim that when the 13th day of a month falls on a​ Friday, the numbers of hospital admissions from motor vehicle crashes are not affected is not true.

Step-by-step explanation:

The missing data from the question

The numbers of hospital admissions from motor vehicle crashes

Friday the 6th || 10 | 8 | 4 | 4 | 2

Friday the 13th | 12 | 10 | 12 | 14 | 14

The differences can then be calculated (number on the 13th - number on the 6th) and tabulated as

Friday the 6th || 10 | 8 | 4 | 4 | 2

Friday the 13th | 12 | 10 | 12 | 14 | 14

Differences ||| 2 | 2 | 8 | 10 | 12

To obtain the confidence interval, we need the sample mean and sample standard deviation.

Mean = (Σx)/N

= (2+2+8+10+12)/5 = 6.80

Standard deviation = σ = √[Σ(x - xbar)²/N]

Σ(x - xbar)² = (2-6.8)² + (2-6.8)² + (8-6.8)² + (10-6.8)² + (12-6.8)² = 84.8

σ = √[Σ(x - xbar)²/N] = √(84.8/5) = 4.12

Confidence Interval for the population's true difference between the number of hospital admissions from motor vehicle crashes on Friday the 6th and Friday the 13th is basically an interval of range of values where the population's true difference can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample true difference) ± (Margin of error)

Sample Mean = 6.8

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the sample true difference)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 5 - 1 = 4.

Significance level for 95% confidence interval

(100% - 95%)/2 = 2.5% = 0.025

t (0.025, 4) = 2.776 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 4.12

n = sample size = 5

σₓ = (4.12/√5) = 1.84

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 6.8 ± (2.776 × 1.84)

CI = 6.8 ± 5.10784

95% CI = (1.69216, 11.90784)

95% Confidence interval = (1.69, 11.91)

b) This confidence interval shows there is a significant difference between the number of hospital admissions from motor vehicle crashes on Friday the 13th and the number of hospital admissions from motor vehicle crashes on Friday the 6th as the interval obtained doesn't contain a difference of 0.

Hope this Helps!!!

Given:

Given that the graph of the system of equations.

We need to determine the solution to the system of equation.

Solution:

The solution to the system of equations is the point of intersection of these two lines.

The point of intersection of the two lines in the graph is the point at which the two lines meet.

From the graph, it is obvious that the two lines intersect at a common point.

Thus, the common point is the point of intersection of the two lines.

Hence, the point of intersection is (4,2)

Thus, the solution to the system of equation is (4,2)

Therefore, Option B is the correct answer.

Answer:

its B (4,2)

Step-by-step explanation:

Answer:

10 people

Step-by-step explanation:

Given:

Colors of shirts: 3 (red, blue, and purple)

Colors of pants: 3 (black, brown, or white)

Total number of outfits ( both shirts and pants) =

3 * 3 = 9

The minimum number of people that need to be in a room together to guarantee that at least two of them are wearing same-colored outfits will be:

Total number + 1

= 9 + 1

= 10 people

The value of the expression 5/4 - 4/4 will be equal to 1 / 4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is ( 5 / 4)  - ( 4 / 4). The value of the expression will be solved as,

E =  5 / 4 - 4 / 4

E = (5 - 4) / 4

E = 1 / 4

Therefore, the value of the expression 5/4 - 4/4 will be equal to 1 / 4.

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Answer:

C(x)=16600+63x

R(x)=160x

Break-even Point, x=172

Step-by-step explanation:

Let x be the number of Toilets Produced.

Fixed cost = $16,600

Variable costs = $63 per toilet.

Total Cost, C(x)=16600+63x

The company expects to sell the toilets for $160.

Selling Price Per Toilet=160

Total Revenue for x Toilets, R(x)=160x

Next, we determine the break-even point.

The break-even point is the point where the Cost of Production equals Revenue generated.

i.e. C(x)=R(x)

16600+63x=160x

16600=160x-63x

16600=97x

x=171.13

The company needs to sell at least 172 Toilets to break even.

To formulate the functions C(x) and R(x) for the total cost and revenue of producing and selling x toilets, we can use the given information about fixed costs, variable costs, and selling price. By setting the total cost equal to the total revenue, we can find the number of toilets needed to break even, which is approximately 171.

To formulate the function C(x) for the total cost of producing x new toilets, we need to consider the fixed cost and the variable cost. The fixed cost is $16,600, which remains constant regardless of the number of toilets produced. The variable cost is $63 per toilet, so we multiply it by x to account for the number of toilets produced. Therefore, the function C(x) can be expressed as:

C(x) = 16,600 + 63x

The function R(x) for the total revenue generated from the sales of x toilets can be found by multiplying the selling price of each toilet by the number of toilets sold. Since each toilet is sold for $160, the function is:

R(x) = 160x

To find the number of toilets needed to break even, we need to determine the value of x when the total cost is equal to the total revenue. In other words, we set C(x) = R(x) and solve for x:

16,600 + 63x = 160x

Subtracting 63x from both sides:

16,600 = 97x

Dividing both sides by 97:

x = 170.10

Therefore, the company needs to sell approximately 171 toilets to break even.

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Answer:

The rejection region is the one defined by z<-2.326.

Step-by-step explanation:

We have to calculate the critical value for a test of hypothesis on the proportion of students of this college who live off campus and drive to class.

The sample is large enough, so we can use the z-statistic.

As the claim, taht will be stated in the alternative hypothesis, is that less than 20% of their current students live off campus and drive to class, the test is left tailed.

Alternative hypothesis:

[tex]Ha: \pi<0.20[/tex]

Then, for a significance level of 0.01, 99% of the data has to be over (or 1% below) this critical z-value.

In the standard normal distribution this z-value is z=-2.326.

[tex]P(z<-2.326)=0.01[/tex]

The critical value that divide the regions is z=-2.326. The rejection region is the one defined by z<-2.326.

To determine if less than 20% of students at a college live off campus and drive to class with a significance level of 0.01, we would reject the null hypothesis if the z-score is less than approximately -2.33. This critical value corresponds to the 1% left tail cut-off point on the standard normal distribution.

The question concerns conducting a hypothesis test to determine if less than 20% of students at a small private college live off campus and drive to class, using a level of significance of 0.01. The rejection region for this one-sided test is determined by finding the critical z value that corresponds to the significance level of 0.01. Since the test is left-tailed, we look for the z score that cuts off 1% of the area in the left tail of the standard normal distribution.

Using the standard normal distribution table, the critical value z* that cuts off the lower 1% of the distribution is approximately -2.33. Therefore, if the test statistic calculated from the sample data is less than -2.33, we would reject the null hypothesis and conclude that there is significant evidence to suggest that less than 20% of students live off campus and drive to class.

This method ensures that the null hypothesis is only rejected when there is sufficient evidence against it, as more conservative research would deem necessary at the 0.01 level of significance.

Answer:

Check the explanation

Step-by-step explanation:

Period, X  Actual , Y

1                        6

2                       11

3                       9

4                       16

5                       17

Y= intercept + slope*x

Answer a and b:

INTERCEPT(known Y's,known X's)          Slope(known Y's,known X's)

                      3.7                                                           2.7

Simple linear regression equation is

Forecast, Y= 3.7+ 2.7*x

Period, X  Actual , Y  linear          Absolute           squared

                                   trend         deviation=         deviation=

                                Forecast,      |Forecast -        (absolute          

                            Y= 3.7+ 2.7*x      Actual|            deviation)^2

1                  6            6.40                  0.4                      0.2

2                 11            9.10                   1.9                       3.6

3                 9            11.80                  2.8                       7.8

4                16           14.50                  1.5                       2.3

5                17           17.20                  0.2                       0.0

6                              19.90  

                                                                                      2.78

                                                                                      MSE

Answer c: MSE= 2.78

Answer d: Forecast for x= 6= 19.90

Answer:

Step-by-step explanation:

1 2 3 4 5 6

Answer:

x +21

Step-by-step explanation:

13+(x+8)=

Combine like terms

x +13+8

x +21

Answer:

The expected value is 0.87.

Step-by-step explanation:

a) To calculate the expected value X we will first see the posible outcomes. So could take value of 0,1,2,3. We will calculate the probability of each outcome. To do so, we will introduce the following notation. Consider the following tuple (A,B,C) where A is the number of butterflies found by Alice, B the number found for by Bob and C the number found by C. To calculate the probability of the tuple (A,B,C) we will do as follows. If the entry of the tuple is 1, then we will multiply by the probability of the person that found the butterfly. So, if A =1, we will multiply by 0.17(Alice finds a butterfly with probability 0.17). On the other side, if the entry of the tuple is 0, we will multiply by (1-p) where p is the probability of the person that found the butterly. So, if A=0, we will multiply by 0.83. So, for example, consider the tuple (1,0,1). The probability of having this result is 0.17*0.75*0.45 (Alice and Charlotte found a butterfly, but Bob didn't). We can do this since we are said that their probabilities of success don't affect others' probabilities.

We will see the total number of butterflies and the tuples associated to that number. That is

X number of butterflies - tuples

0 butterflies - (0,0,0)

1 butterfly - (1,0,0) or (0,1,0) or (0,0,1)

2 butterflies - (1,1,0) or (1,0,1) or (0,1,1)

3 butterflies - (1,1,1)

To find the probability of the value of X, we will sum up the probability of the associated tuples. The values of the probabilities are as follows

(0, 0, 0) =  0.342375

(0, 0, 1 ) = 0.280125

(0, 1, 0)  = 0.114125

(0, 1, 1 ) = 0.093375

(1, 0, 0)  = 0.070125

(1, 0, 1 ) = 0.057375  = 0.17*0.75*0.45

(1, 1, 0)  = 0.023375

(1, 1, 1)  = 0.019125

In this case,

P(X=0) =  0.342375 ,

P(X=1) = 0.464375  = 0.280125 +0.114125+ 0.070125

P(X=2) = 0.174125

P(X =3 ) = 0.019125

So, the expected value of X is given by

0*  0.342375 +1 * 0.464375 +2* 0.174125+3*0.019125 = 0.87

b)Let X1 be the number of butterflies found by Alice, X2 the number found by Bob and X3 the number found by Charlotte. Then X = X1+X2+X3. Using the expected value properties and the independence of X1, X2 and X3 we have that E(X) = E(X1)+E(X2)+E(X3).

Recall that each variable is as follows. Xi is equal to 1 with probability p and it is 0 with probability (1-p). Then, the expected value of Xi is

[tex]1\cdot p + 0\codt (1-p)=p[/tex]. Note that the value of p for X1,X2 and X3 is 17%, 25% and 45% respectively.

Then E(X) = 17%+25%+45%= 0.87.

So the expected number of butterflies is 0.87.

Final answer:

The expected value of the total number of butterflies, X, that Alice, Bob, and Charlotte catch is 0.87. This is found by summing their independent probabilities of catching a butterfly (0.17 for Alice, 0.25 for Bob, and 0.45 for Charlotte). X is also represented as the sum of three indicator random variables X1, X2, and X3, leading to the same expected value.

Explanation:

Expected Value of the Number of Butterflies Caught

In this scenario with Alice, Bob, and Charlotte searching for butterflies in separate parts of a field, the random variable X represents the total number of butterflies they catch. The expected value of X, or E(X), is calculated by adding the individual probabilities of finding a butterfly, since their probabilities are independent.

To find the expected value of X:

Multiply the probability of each person finding a butterfly by the number of butterflies they would find in that event (which is 1 since each either finds 1 butterfly or none), and

Add these products together.

The expected value is thus 0.17 + 0.25 + 0.45 = 0.87 butterflies. We can also express X as X1 + X2 + X3, where each Xi is an indicator random variable for whether Alice (X1), Bob (X2), or Charlotte (X3) found a butterfly.

The expected value for each indicator variable is the same as the person's probability of success. So, E(X1) = 0.17, E(X2) = 0.25, and E(X3) = 0.45. By the linearity of expectation, E(X) = E(X1) + E(X2) + E(X3), which also equals 0.87 butterflies.

Answer:

A.y=2x^5 + c1+ c2x + c3x^5

B. Y = 2x² + 9+7x+2x^5

Step-by-step explanation:

See attached file

Step-by-step explanation:

The given expression in word problem can be translated as:

Six more than half of a number is 20

A real-world problem for the equation 1/2x + 6 = 20 could be determing the number of days a person should work, earning a rate of half the square of the number of days, to achieve a total sum of $20. The person initially has $6 and after working for 28 days, he or she achieves the goal.

Consider a real-world example represented by the equation 1/2x + 6 =20. Imagine your grandmother gives you $6 and says you can do chores for her on some days to earn half the square of the number of days you worked in dollars. If you want to accumulate $20 in total, how many days should you work? This problem asks the same as solving for 'x' in the equation where 'x' is the number of days and the total sum of money is $20.

To solve this, you would need to subtract 6 from both sides of the equation, leaving you with 1/2x =14. Then, you multiply both sides by 2 to get x = 28, so it takes 28 days of work.

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Answer:

it 1595

Step-by-step explanation:

For the reduced image with a scale factor of 1/25, the model height is 58 blocks; with a 1/50 scale, it's 29 blocks.

To fill in the missing information, we can use the scale factor to calculate the model height for the reduced image.

For the reduced image with a scale factor of [tex]\( \frac{1}{25} \)[/tex], we can calculate the model height by dividing the actual height by the scale factor:

[tex]\[ \text{Model Height} = \frac{\text{Actual Height}}{\text{Scale Factor}} \][/tex]

[tex]\[ \text{Model Height} = \frac{1450}{25} = 58 \text{ blocks} \][/tex]

For the reduced image with a scale factor of [tex]\( \frac{1}{50} \)[/tex], we repeat the calculation:

[tex]\[ \text{Model Height} = \frac{1450}{50} = 29 \text{ blocks} \][/tex]

Now, the completed table looks like this:

|             | Original Image | Reduced Image |

|-------------|----------------|---------------|

| Actual Height (in feet) | 1,450 | 1,450 |

| Model Height (in blocks) | - | 58 (1/25 scale) |

|                          | - | 29 (1/50 scale) |

Thus, the missing information in the table has been filled in using the scale factor and calculations based on the actual height of the Empire State Building.

Answer:

3x10, 6x5

Step-by-step explanation:

45 / 1.5 = 30

Find any two factors of 30 and you have an answer.

2x15 and 1x30 don't work because they are less than or equal to 2.

Answer:

3x10x1.5, 6x5x1.5

Step-by-step explanation:

45 / 1.5 = 30

Find any two factors of 30 and you have an answer.

2x15 and 1x30 don't work because they are less than or equal to 2.

Answer:

A) i) the probability it is brown = 60%.  (ii)The probability it is yellow or blue = 25% (iii) The probability it is not green = 90% (iv)The probability it is striped =0%

B) i)The probability they are all brown = 21.6%.  (ii) Probability the third one is the first one that is​ red = 4.51% (iii) Probability none are yellow = 51.2% (iv) Probability at least one is green = 27.1%

Step-by-step explanation:

A) The probability that it is brown is the percentage of brown we have.  However, Brown is not listed, so we subtract what we are given from 100%. Thus;

100 - (20 + 5 + 5 + 10) = 100 - (40) = 60%. 

The probability that one drawn is yellow or blue would be the two percentages added together:  20% + 5% = 25%. 

The probability that it is not green would be the percentage of green subtracted from 100:  100% - 10% = 90%. 

Since there are no striped candies listed, the probability is 0%.

B) Due to the fact that we have an infinite supply of candy, we will treat these as independent events. 

Probability of all 3 being brown is found by taking the probability that one is brown and multiplying it 3 times. Thus;

The percentage of brown candy is 60% from earlier. Thus probability of all 3 being brown is;

0.6 x 0.6 x 0.6 = 0.216 = 21.6%

To find the probability that the first one that is red is the third one drawn, we take the probability that it is NOT red, 100% - 5% = 95% = 0.95

Now, for the first two and the probability that it is red = 5% = 0.05

Thus for the last being first one to be red = 0.95 x 0.95 x 0.05 = 0.0451 = 4.51%.

The probability that none are yellow is found by raising the probability that the first one is not yellow, 100 - 20 = 80%=0.80, to the third power:

0.80³ = 0.512 = 51.2%.

The probability that at least one is green is; 1 - (probability of no green). 

We first find the probability that all three are NOT green:

0.90³ = 0.729

1 - 0.729 = 0.271 = 27.1%.

Final answer:

To find the probability of an event happening, divide the number of favorable outcomes by the total number of possible outcomes. The probability that a candy is brown is 60%, the probability that it is yellow or blue is 25%, the probability that it is not green is 90%, and the probability that it is striped cannot be determined without additional information. If the candies are replaced after picking, the probability of three brown candies in a row is 21.6%, the probability of the third candy being the first red candy is 5%, the probability of no yellow candies is 90.25%, and the probability of at least one green candy is 27.1%.

Explanation:

To find the probability of an event occurring, we divide the number of favorable outcomes by the total number of possible outcomes.

a) The probability of picking a brown candy is 100% - (20% + 5% + 5% + 10%) = 60%. The probability of picking a yellow or blue candy is 20% + 5% = 25%. The probability of not picking a green candy is 100% - 10% = 90%. The probability of picking a striped candy is not given in the question, so we cannot calculate it.

b) If the candies are replaced after picking, the probability of picking three brown candies in a row is (60%)^3 = 21.6%. The probability of the third candy being the first red candy is the same as the probability of picking a red candy, which is 5%. The probability of none of the candies being yellow is (100% - 5%)^2 = 90.25%. The probability of at least one candy being green is 1 - (100% - 10%)^3 = 27.1%.

Answer:

Step-by-step explanation:

Given

Area (A) = 529[tex]\pi[/tex] square inch

radius(r)  =?

Now

we have the formula

[tex]\pi r^{2} = area[/tex]

[tex]\pi r^{2} = 529\pi[/tex]

Both pie will be cancelled and we get

[tex]r^{2} = 529[/tex]

[tex]r =\sqrt{529}[/tex]

r = 23 inch

Hope it helped:)

"The correct answer is 14 inches.

To find the radius of a circle given its area, one can use the formula for the area of a circle, which is [tex]\( A = \pi r^2 \)[/tex], where[tex]\( A \)[/tex] is the area and[tex]\( r \)[/tex] is the radius.

 Given that the area [tex]\( A \) is \( 529\pi \)[/tex] square inches, we can set up the equation:

 [tex]\[ 529\pi = \pi r^2 \][/tex]

To solve for \( r \), we can divide both sides of the equation by [tex]\( \pi \)[/tex]:

[tex]\[ r^2 = \frac{529\pi}{\pi} \][/tex]

[tex]\[ r^2 = 529 \][/tex]

Taking the square root of both sides gives us the radius:

[tex]\[ r = \sqrt{529} \][/tex]

[tex]\[ r = 23 \][/tex]

Therefore, the radius of the circle is 23 inches. However, the question states that the correct answer is 14 inches. This discrepancy arises because the square root of 529 is actually 23, not 14. It seems there was a mistake in the provided answer. The correct radius, based on the calculation, should indeed be 23 inches, not 14 inches."

Alternate angles in a transversal are congruent.

The value of x is 13

See attachment for the image of the transversal,

Where [tex](9x + 2)[/tex] and [tex]119[/tex] are alternate angles

This means that:

[tex]9x + 2 = 119[/tex] ---- alternate angles are equal

Collect like terms

[tex]9x = 119 - 2[/tex]

[tex]9x = 117[/tex]

Divide both sides by 9

[tex]x = 13[/tex]

Hence, the value of x is 13

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Answer:

Jackie

Step-by-step explanation:

Find how much each person makes by multiplying their hourly wage by hours worked

Jackie

hourly wage * hours worked

15*4=60

$60

George

hourly wage * hours worked

18.50*3=55.5

$55.50

Jackie made more money because 60>55.5

After calculating the total earnings, Jackie makes more money ($60) than George ($55.50) based on their hourly rates and the number of hours worked.

The student asks who makes more money, Jackie who makes $15 an hour for babysitting and works for 4 hours, or George who makes $18.50 an hour for mowing the lawn and works for 3 hours. To solve this, let's calculate the total money each person makes:

Comparing the earnings, Jackie makes a total of $60, while George makes $55.50. Therefore, Jackie makes more money than George after their respective hours of work.

Answer:

256 m2

Step-by-step explanation:

- First, know the formula A = (a+b/2)h

- Using this, we will fill the equation in with our variables. For example...

A = ((13+19)/2)16

A = (32/2)16

A = (16)(16)

A = 256 m2

- Hope this helps! If you need a further explanation or step by step practice please let me know.

Let U={a,b,c,d,e,f,g,h}

A={a,c,d}

B={b,c,d}

C={b,e,f,g,h}

Answer:

Over the boundary: maximum:13, minimum:12

Over D: maximum:13, minimum:0

Step-by-step explanation:

We are given that [tex]f(x,y) = 12x^2+13y^2[/tex] and D is the disc of radius one. Namely, [tex]x^2+y^2\leq 1[/tex].

First, we want to find a critical point of the function f. To do so, we want to find the values(x,y) such that

[tex] \nabla f (x,y) =0[/tex].

Recall that [tex] \nabla f (x,y) = (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y})[/tex].

So, let us calculate [tex] \nabla f (x,y)[/tex] (the detailed calculation of the derivatives is beyond the scope of the answer.

[tex]\frac{\partial f}{\partial x} = 24x[/tex]

[tex]\frac{\partial f}{\partial y} = 26y[/tex]

When equalling it to 0, we get that the critical point is (0,0), which is in our region D. Note that the function f is the sum of the square of two real numbers multiplied by some constants. Hence, the function f fulfills that [tex]f(x,y)\geq 0[/tex]. Note that f(0,0)=0, so without further analysis we know that the point (0,0) is a minimum of f over D.

If we restrict to the boundary, we have the following equation [tex] x^2+y^2=1[/tex]. Main idea is to replace the value of one of the variables n the function f, so it becomes a function of a single variable. Then, we can find the critical values by using differential calculus:

Case 1:

Let us replace y. So, we have that [tex]y^2=1-x^2[/tex]. So, [tex]f(x,y) = 12x^2+13(1-x^2) = -x^2+13[/tex].

So, we will find the derivative with respect to x and find the critical values. That is

[tex] \frac{df}{dx} = -2x=0[/tex]

Which implies that x =0. Then, [tex] y =\pm 1[/tex]. So we have the following critical points (0,1), (0,-1). Notice that for both points, the value of f is f(0,1) = f(0,-1) = 13.  If we calculate the second derivative, we have that at x=0

[tex] \frac{d^2f}{dx^2} = -2<0[/tex]. By the second derivative criteria, we know that this points are local maximums of the function f.

Case 2:

Let us replace x. So, we have that [tex]x^2=1-y^2[/tex]. So, [tex]f(x,y) = 12(1-y^2)+13y^2 = y^2+12[/tex].

So, we will find the derivative with respect to y and find the critical values. That is

[tex] \frac{df}{dx} = 2y=0[/tex]

Which implies that y =0. Then, [tex] x =\pm 1[/tex]. So we have the following critical points (-1,0), (1,0). Notice that for both points, the value of f is f(1,0) = f(-1,0) = 12.  If we calculate the second derivative, we have that at y=0

[tex] \frac{d^2f}{dx^2} = 2>0[/tex]. By the second derivative criteria, we know that this points are local minimums of the function f.

So, over the boundary D, the maximum value of f is 13 and the minimum value is 12. Over all D, the maximum value of f is 13 and the minimum value is 0.

Final answer:

The critical point of f(x, y) on the disk D is (0, 0). f(x) restricted to the boundary of D is f(x) = 12x^2 + 13(1 - x^2) with the domain [-1, 1]. The absolute maximum and minimum values of f(x, y) over all of D are 25 and 0, respectively.

Explanation:

To find the critical point of the function f(x, y) = 12x2 + 13y2 on the disk D: x2+y2 ≤ 1, we need to set the partial derivatives of f with respect to x and y equal to zero.

The partial derivative with respect to x is 24x, and setting it to zero gives x = 0. Similarly, the partial derivative with respect to y is 26y, which implies y = 0. Therefore, the critical point is (0, 0).

On the boundary of D, where x2+y2 = 1, we can solve for y2 as y2 = 1 - x2. Substituting into f, we get a function of a single variable x: f(x) = 12x2 + 13(1 - x2) with the closed interval domain [-1, 1].

The maximum value on the boundary occurs at x = ±1, giving a maximum of f(±1) = 25. The minimum on the boundary is at x = 0, which gives f(0) = 13.

Across the entire disk D, the absolute minimum is at the critical point (0,0), with f(0, 0) = 0, and the absolute maximum is the same as the boundary maximum, f(x) = 25.

Answer:

2 hours if they go to school.

10 hours if they dont go to school.

Step-by-step explanation:

add up the hours.

9/2+5/2=14/2=7hours +7 hour of sleep= 14 hours.

if they go to school for 8 hours then add 8. then it =22 hours witch gives you 2 hours

if they dont go to school then you got 24-14 hours=10 hours.

Given:

Given that the graph OACE.

The coordinates of the vertices OACE are O(0,0), A(2m, 2n), C(2p, 2r) and E(2t, 0)

We need to determine the midpoint of EC.

Midpoint of EC:

The midpoint of EC can be determined using the formula,

[tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

Substituting the coordinates E(2t,0) and C(2p, 2r), we get;

[tex]Midpoint=(\frac{2t+2p}{2},\frac{0+2r}{2})[/tex]

Simplifying, we get;

[tex]Midpoint=(\frac{2(t+p)}{2},\frac{2r}{2})[/tex]

Dividing, we get;

[tex]Midpoint=(t+p,r)[/tex]

Thus, the midpoint of EC is (t + p, r)

Hence, Option A is the correct answer.

Answer: 21y-3

Step-by-step explanation:

3(7y-1)=

3(7y)-3(1)=

21y-3

Answer: 21y-3

Step-by-step explanation: The way to get a answer out of this problem you have to multiply 3 time 7, and 1 then subtract the two numbers you get which is 21y and 3 and the problem with this question is that you can’t subtract because of the variable but sense they aren’t the same put the answer like this 21y-3 hope this helps!

Answer: no

Step-by-step explanation:

Answer:

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 975, \sigma = 52, n = 31, s = \frac{52}{\sqrt{31}} = 9.34[/tex]

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable?

pvalue of Z when X = 975 + 15 = 990 subtracted by the pvalue of Z when X = 975 - 15 = 960. So

X = 990

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{990 - 975}{9.34}[/tex]

[tex]Z = 1.61[/tex]

[tex]Z = 1.61[/tex] has a pvalue of 0.9463

X = 960

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{960 - 975}{9.34}[/tex]

[tex]Z = -1.61[/tex]

[tex]Z = -1.61[/tex] has a pvalue of 0.0537

0.9463 - 0.0537 = 0.8926

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable