Suppose that z= x3y2, where both x and y are changing with time. At a certain instant when x= 1 and y=2, x is decreasing at the rate of 2 units/s, and y is increasing at the rate of 3 units/s. How fast is z changing at this instant?

Answer:

5

Step-by-step explanation:

Answer:

1.2

Step-by-step explanation:

For this, everything after 8 doesn't matter.

Because 8 is bigger than 5, we will round the number to the left up.

It is because 8 is the hundreth.

=1.2

Using it's formula, the distance between the points A(13,2) and B(7,10) is of 10 units.

Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

In this problem, the points are A(13,2) and B(7,10), hence the distance is given by:

\(D = \sqrt{(13 - 7)^2+(2 - 10)^2}\)

D = sqrt(100)

D = 10 units.

The distance between the points A(13,2) and B(7,10) is of 10 units.

More can be learned about the distance between two points at https://brainly.com/question/18345417

#SPJ1

Answer:

See below.

Step-by-step explanation:

The solution to this set of equations would be (3,5).

-hope it helps

Answer:

Son -- 10

Dad -- 30

Step-by-step explanation:

5  years ago the dad was 15 years older than his son.15 / 3 = 5. The son was 5 five years ago he would be 10 now because 5 years ago he was 5. Since the son is 10 the dad must be 30. I know this because the dad is 20 years older than his son.

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

Learn more about probability here

https://brainly.com/question/32117953

#SPJ4

The volume of a cylinder can be found using the formula V = πr^2h, where r is the radius (half of the diameter) and h is the height.

Since the diameter is given as 2 feet, the radius is 1 foot. The height is given as 4 feet. Substituting these values into the formula, we get:

V = π(1 ft)^2(4 ft) ≈ 12.57 cubic feet

Therefore, the approximate volume of the cylindrical storage container is approximately 12.57 cubic feet. It is important to note that this is an approximation since the actual value of π is an irrational number that cannot be expressed exactly as a decimal. However, using the value of π ≈ 3.14 is commonly accepted as a good approximation in many cases.

To know more about volume of a cylinder visit:

https://brainly.com/question/16134180

#SPJ11

Answer:

40

Step-by-step explanation:

7 = 17.5% × Y

STEP 2 7 =

17.5

100

× Y

Multiplying both sides by 100 and dividing both sides of the equation by 17.5 we will arrive at:

STEP 3 Y = 7 ×

100

17.5

STEP 4 Y = 7 × 100 ÷ 17.5

STEP 5 Y = 40

The probability that a randomly selected fish is a large, red fish is 0.25 or 25%.

To find the probability that a randomly selected fish is a large, red fish, we need to consider both the probability of selecting a large fish and the probability of selecting a red fish among the large fish.

Assuming an equal number of large and small fish, the probability of selecting a large fish is 0.5 (or 1/2).

Among the large fish, the probability of selecting a red fish is also 0.5 (or 1/2).

To find the overall probability, we multiply the probabilities of the individual events:

Probability of selecting a large, red fish = Probability of selecting a large fish × Probability of selecting a red fish among the large fish

Probability of selecting a large, red fish = 0.5 × 0.5

Probability of selecting a large, red fish = 0.25

Therefore, the probability that a randomly selected fish is a large, red fish is 0.25 or 25%.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ4

Explanation:

Ashton wants to divide 6 pounds of pecans between 5 neighbors. We have to divide 6 by 5 and write it as a mixed number, because we'll get an improper fraction:

Answer:

The correct option is C 1 1/5 pounds

Answer:

2-1 = 1

Step-by-step explanation:

Hopefully help......

Answer:

1

Step-by-step explanation:

say you have two apples, if you eat one, it subtracts one from the whole (2) and leaves you with one apple!1!!

i—

(a) The percentage of weeks with between 218 and 246 defective cars is 15.74%.

(b) The percentage of weeks with more than 246 defective cars is 0.13%.

(c) The percentage of weeks with between 162 and 218 defective cars is  84.00%.

(d) The cutoff for the fewest 16% of defective cars produced in a week is approximately 189 cars.

(e) The cutoff for the greatest 2.5% of defective cars produced in a week is approximately 231 cars.

To solve these problems, we'll use the properties of the normal distribution.

(a) To find the percentage of weeks with between 218 and 246 defective cars, we need to calculate the area under the normal curve between these two values. We'll use the z-score formula:

z = (x - μ) / σ

where z is the z-score, x is the value, μ is the mean, and σ is the standard deviation.

For 218 defective cars:

z1 = (218 - 204) / 14 = 14 / 14 = 1

For 246 defective cars:

z2 = (246 - 204) / 14 = 42 / 14 = 3

Now, we'll use a standard normal distribution table or a calculator to find the percentage associated with these z-scores.

Using a standard normal distribution table, the percentage for z = 1 is 0.8413, and the percentage for z = 3 is 0.9987.

The percentage of weeks with between 218 and 246 defective cars is:

0.9987 - 0.8413 = 0.1574 or 15.74%.

(b) To find the percentage of weeks with more than 246 defective cars, we need to calculate the area under the normal curve to the right of 246.

Using the z-score formula:

z = (246 - 204) / 14 = 42 / 14 = 3

Using a standard normal distribution table or a calculator, the percentage associated with z = 3 is 0.9987.

The percentage of weeks with more than 246 defective cars is:

1 - 0.9987 = 0.0013 or 0.13%.

(c) To find the percentage of weeks with between 162 and 218 defective cars, we'll follow a similar process as in part (a).

For 162 defective cars:

z1 = (162 - 204) / 14 = -42 / 14 = -3

Using a standard normal distribution table or a calculator, the percentage for z = -3 is 0.0013.

The percentage of weeks with between 162 and 218 defective cars is:

0.8413 - 0.0013 = 0.8400 or 84.00%.

(d) To find the cutoff for the fewest 16% of defective cars, we need to find the z-score associated with this percentile.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to a percentile of 16%.

The z-score for a percentile of 16% is approximately -0.994.

Now, we can use the z-score formula to find the corresponding defective car value:

-0.994 = (x - 204) / 14

Solving for x:

x = -0.994 * 14 + 204

x ≈ 189.04

The cutoff for the fewest 16% of defective cars produced in a week is approximately 189 cars.

(e) To find the cutoff for the greatest 2.5% of defective cars, we'll follow a similar process as in part (d).

The z-score for a percentile of 97.5% (100% - 2.5%) is approximately 1.96.

Using the z-score formula:

1.96 = (x - 204) / 14

Solving for x:

x = 1.96 * 14 + 204

x ≈ 231.44

The cutoff for the greatest 2.5% of defective cars produced in a week is approximately 231 cars.

To learn more about area visit:

brainly.com/question/31849536

#SPJ11

SQUARES BECAUSE THEY ARE IN THE MIDDLE DUMMY

Answer:

C. 25 square cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

yes

Answer:

$240 extra

Step-by-step explanation:

1/3(7200) + 12(420) = 2400 + 5040 = 7440

7440 - 7200 = 240

The customer had to pay 1720 extra.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A car is priced at $7200.

If the deposit is one third = 7200/3

                                          = 240

The amount after 12 payments will be

= 240 x 12

= 2880

total cost will be

= 2880 + 2400

= 5280

and, The customer had to pay extra amount

= 7200 - 5280

= 1720

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ5

The procedure the researcher will use is called stratification sampling.

A stratified sample is created by separating a population into similar subpopulations (strata) and taking a representative sample from each. Stratified sampling is used by researchers to ensure that specific subgroups are represented in their samples. Additionally, it helps them estimate the characteristics of each group precisely. This method is used in many surveys in order to better understand the differences between subpopulations. The term stratified sampling is also used to refer to stratified random sampling.

To Learn more about stratified sampling:

https://brainly.com/question/14675869

#SPJ4

Answer:

Sorry! There is no attatched picture or complete information

The total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.

To find the total cost of repayment, we need to calculate the total amount that Marvin will pay over the course of 5 years. Since he is making monthly payments, we need to first find the total number of payments he will make:

Total number of payments = 5 years x 12 months/year = 60 payments

The total amount Marvin will pay is then:

Total amount = 60 payments x $128.95/payment = $7,737.00

To find the total interest Marvin will pay, we need to subtract the original amount of the loan from the total amount he will pay:

Total interest = Total amount - Loan amount

Total interest = $7,737.00 - $6,800.00

Total interest = $937.00

Therefore, the total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.

To know more about costs , refer here :

https://brainly.com/question/14725550#

#SPJ11

Answer:

B is the answer

Step-by-step explanation:

Answer:

NULL ; TRUE

Step-by-step explanation:

The sampling distribution is on the assumption that the null hypothesis is true .

The null hypothesis is a general statement that states that there

is no relationship between two phenomenon's under

consideration or that there is no association between two groups.

#SPJ4

Learn more about on

https://brainly.com/question/23056080

The sampling distribution is based on the assumption that the null hypothesis is TRUE.  

A null hypothesis is a general statement that something is. There is no relationship between the two phenomena under or consider that there is no relationship between the two groups.  

The sampling distribution is based on the assumption that the null hypothesis is TRUE.

Learn more about sampling distribution here

https://brainly.com/question/15713806

#SPJ4

The real solutions of the given quadratic equation 2x² + 5x - 2 are (-5 ±√41)/4. Yes, the equations have real solutions because the discriminant of the given equation is positive.

We can solve the equation 2x² + 5x - 2 = 0 using the quadratic formula

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 2, b = 5, and c = -2, so we have:

x = (-5 ± √(5² - 4(2)(-2)) / 2(2)

x = (-5 ± √41) / 4

So the solutions are

x = (-5 + √41) / 4

x = (-5 - √41) / 4

These are both real solutions, since the discriminant (b² - 4ac) is positive. Therefore, the equation 2x² + 5x - 2 = 0 does have real solutions.

To know more about quadratic equation here

https://brainly.com/question/29164877

#SPJ4

The value of y=34 makes the equation true.

Given the equation is √34×√y=34.

An equation is a mathematical statement with the symbol "equal" between two expressions of equal value.

The given equation is √34×√y=34.

We have to find value of y which makes the equation true.

Firstly, we will divide both sides by √34, we get

(√34×√y)/√34=34/√34

√y=34/√34

Now, we will rationalize the right side by multiplying the numerator and denominator by √34, we get

√y=(34×√34)/(√34×√34)

√y=(34×√34)/34

√y=√34

Further, we will do squaring on both sides, we get

y=34

Hence, the value of y which make the equation √34×√y=34 true is y=34.

Learn more about the equation from here brainly.com/question/2972832

#SPJ9

a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

Learn more about empty set here: https://brainly.com/question/13553546

#SPJ11

Answer:

Solution given:

sin y = -4/5

p/h=4/5

p=4

h=5

b=√{5²-4²)=3

cos y = b/h=-3/5

again

cos x=12/13

b/h=12/13

b=12

h=13

p=√(13²-12²)=5

sin x=p/h=5/13

now

sin[x-y]=sinxcosy-cosxsiny

=5/13×-3/5-(12/13×-4/5)=33/65 is your answer.

The sign of the expression \(-3 * \frac{4}{(-7)}^{105\) is positive

From the question, we have the following parameters that can be used in our computation:

\(-3 * \frac{4}{(-7)}^{105\)

From the above, we have

Negative * Negative

When evaluated, we have

Negative * Negative = Positive

This means that the sign of the expression is positive

Read more about expression at

https://brainly.com/question/31819389

#SPJ1

Question

What is the sign of \(-3 * \frac{4}{(-7)}^{105\)

Answer:

The rate of change is 1/2

Step-by-step explanation:

Formula:

y-y/x-x

The two points i chose were (-1,1) and (1,1)

You plug them in:

1-0/ 1 - (-1)

leaving you with 1/2

Answer:

the last one.                       -0.5<t≤3.

Step-by-step explanation:

the black circle means including so 't' is less than or equal to 3

the white circle means not including so 't' is more than -0.5

Answer:

D

Step-by-step explanation:

Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica