How do I evaluate P(3,3)

Answer:

15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

56-13=43............

Answer:

d = 43

Step-by-step explanation:

56 = 13 + d  Subtract 13 from 13 and subtract 13 from 56.

43 = d

Answer:

Solution given

4x+2=-13

subtract each term by 2

4x+2-2=-13-2

divide both side by 4

4x/4=-15/4

we get

x=-15/4

is a required answer.

Let's solve:

\(4x+2=−13\)

Step 1: Subtract 2 from both sides.

\(4x+2−2=−13−2 \\ 4x = - 15\)

Step 2: Divide both sides by 4.

\( \frac{4x}{4} = \frac{ - 15}{4} \)

Answer:

\( \frac{ - 15}{4} \)

          Both of these problems will be solved in a similar way, but with different numbers. First, we set up an equation with the values given. Then, we solve. Lastly, we plug into the original expressions to solve for the angles.

[23] ABD = 42°, DBC = 35°

(4x - 2) + (3x + 2) = 77°

4x+ 3x + 2 - 2  = 77°

4x+ 3x= 77°

7x= 77°

x= 11°

-

ABD = (4x - 2) = (4(11°) - 2) = 44° - 2 = 42°

DBC = (3x + 2) = (3(11°) + 2) = 33° + 2 = 35°

[24] ABD = 62°, DBC = 78°

(4x - 8) + (4x + 8) = 140°

4x + 4x + 8 - 8 = 140°

4x + 4x = 140°

8x = 140°

8x = 140°

x = 17.5°

-

ABD = (4x - 8) = (4(17.5°) - 8) = 70° - 8° = 62°

DBC =(4x + 8) = (4(17.5°) + 8) = 70° + 8° = 78°

Answer:

10

Step-by-step explanation:

just read to the first one

Answer:

iihi

Step-by-step explanation:

Answer:

h > 2

-------------------------

h < 3

Step-by-step explanation:

5h – 4 > 6

add 4 both sides

5h > 10

divide 5 both sides

h > 2

-------------------------

7h + 11 < 32

subtract 11 both sides

7h < 21

divide 7 both sides

h < 3

Answer:

65%

Step-by-step explanation:

4 + 3 = 7

7/20 = 35/100

100 - 35 = 65

I may be wrong but yknow

Answer: y + 2 = -7/6 ( x - 4 )

The shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units

The coordinates of the point = (9,1)

The equation of the line is

y = 2x + 3

Here the slope of the line is 2

The shortest distance between the point and the second line will be the perpendicular distance between the point and line

The perpendicular line slope will be -(1/m)

= -(1/2)

This perpendicular line will pass through the point (9, 1)

The point slope form is

y - 1 = -(1/2)(x - 9)

y - 1 = -(1/2x) + 9/2

y = -(1/2)x + 9/2 + 1

y = -(1/2)x + 11/2

Solve the equation

y = 2x + 3

y = -(1/2)x + 11/2

0 = (2 + 1/2)x -5/2

5/2 x = -5/2

x = -5/2 / 5/2

x = -1

Then

y = 2(-1) + 3

y = -2 + 3

y = 1

The distance between the point (9,1) and (-1, 1)

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

= \(\sqrt{(-1-9)^2+(1-1)^2}\)

= \(\sqrt{100}\)

= 10 units

Hence, the shortest distance from the point (9, 1) to the line y = 2x + 3 is 10 units

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Answer: 40%

Step-by-step explanation: all percents add to 100%, so 40%+20%=60%, and 100%-60%=40%

The number of plants Ethan has are 5.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of plants Ethan has.

Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.

If he starts with 32 ounces of water and ends up with 14.5 ounces

Total of 32 - 14.5 = 17.5 ounces of water.

As given the amount of water used is equal to the amount of water per plant times the number of plants:

3.5x = 17.5

Divide both sides by 3.5

x=5

Hence, , Ethan has 5 plants.

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Answer:

1,968

Step-by-step explanation:

Let x₁ and x₂, y₁ and y₂, and z₁ and z₂ represent the 3 pairs of siblings, and let;

Set X represent the set where the siblings x₁ and x₂ sit together

Set Y represent the set where the siblings y₁ and y₂ sit together

Set Z represent the set where the siblings z₁ and z₂ sit together

We have;

Where the three siblings don't sit together given as \(X^c\)∩\(Y^c\)∩\(Z^c\)

By set theory, we have;

\(\left | X^c \cap Y^c \cap Z^c \right |\) = \(\left | X^c \cup Y^c \cup Z^c \right |\) =  \(\left | U \right | - \left | X \cup Y \cup Z \right |\)

\(\left | U \right | - \left | X \cup Y \cup Z \right |\) = \(\left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)\)

Therefore;

\(\left | X^c \cap Y^c \cap Z^c \right | = \left | U \right | - \left (\left | X \right | + \left | Y\right | + \left | Z\right | - \left | X \cap Y\right | - \left | X \cap Z\right | - \left | Y\cap Z\right | + \left | X \cap Y \cap Z\right | \right)\)

Where;

\(\left | U\right |\) = The number of ways the 3 pairs of siblings can sit on the 7 chairs = 7!

\(\left | X\right |\) = The number of ways x₁ and x₂ can sit together on the 7 chairs = 2 × 6!

\(\left | Y\right |\) = The number of ways y₁ and y₂ can sit together on the 7 chairs = 2 × 6!

\(\left | Z\right |\) = The number of ways z₁ and z₂ can sit together on the 7 chairs = 2 × 6!

\(\left | X \cap Y\right |\) = The number of ways x₁ and x₂ and y₁ and y₂ can sit together on the 7 chairs = 2 × 2 × 5!

\(\left | X \cap Z\right |\) = The number of ways x₁ and x₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

\(\left | Y \cap Z\right |\) = The number of ways y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

\(\left | X \cap Y \cap Z\right |\) = The number of ways x₁ and x₂,  y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 2 × 4!

Therefore, we get;

\(\left | X^c \cap Y^c \cap Z^c \right |\) = 7! - (2×6! + 2×6! + 2×6! - 2 × 2 × 5! - 2 × 2 × 5! - 2 × 2 × 5! + 2 × 2 × 2 × 4!)

\(\left | X^c \cap Y^c \cap Z^c \right |\) = 5,040 - 3072 = 1,968

The number of ways where the three siblings don't sit together given as \(\left | X^c \cap Y^c \cap Z^c \right |\)  = 1,968

The point estimate of the population is 0.415 round to the nearest thousandth as needed the margin error is 0.189.

In statistics, for point estimation, an unknown population parameter (e.g. population mean). More formally, it is applying a point estimator to data to obtain a point estimate.

Point estimation can be contrasted with interval estimation. Such interval estimates are usually confidence intervals for frequentist inference and confidence intervals for Bayesian inference. More generally, point estimators can be contrasted with set estimators. An example is the confidence rate or confidence rate. Point estimators can also be contrasted with distribution estimators. Examples include confidence distributions, randomized estimators, and Bayesian posterior distributions.

Based on the question,

The confidence  interval of Lower bound is 0.226.

The confidence interval of Upper bound is 0.604.

X - E = 0.226.                     --------------------------- (1)

X + E = 0.604                     ---------------------------(2)

Adding equation (1) and (2),

    2X = 0.83

⇒  X = 0.83/2

⇒ X = 0.415

Putting X = 0.415 in equation (1),

0.415 + E = 0.604

⇒ E = 0.604 - 0.415

⇒ E = 0.189

Thus, the point estimate of the population is 0.415 round to the nearest thousandth as needed the margin error is 0.189.

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The area of the square increasing when the area of the square is 16 cm² by the rate of 48cm²/s.

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Here,

A = s²

(dA)/(dt)

(dA/ds)*(ds/dt)

(ds)/(dt) = 6 cm/s

When A = 16 cm²

16 = s²

s = √(16)

s = 4 cm

(dA)/(dt) = 2 × 4 × 6 = 48 cm²/s

When the square is 16 cm², its area grows by 48cm²/s, or one-fourth of its initial size.

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The intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

To show that a1 ≤ a2 ≤ ... ≤ an ≤ ..., we need to use the fact that the sequence of intervals is nested, meaning that each interval is contained within the next one.

First, we know that I1 contains I2, so every point in I2 is also in I1. That means that a1 ≤ a2 and b1 ≥ b2.

Now consider I2 and I3. Again, every point in I3 is also in I2, so a2 ≤ a3 and b2 ≥ b3.

We can continue this process for all the intervals in the sequence, until we reach In. So we have:

a1 ≤ a2 ≤ ... ≤ an-1 ≤ an

and

b1 ≥ b2 ≥ ... ≥ bn-1 ≥ bn

This shows that the endpoints of the intervals are ordered in the same way.

Given that I₁ ⊇ I₂ ⊇ ... In ⊇ ... is a nested sequence of intervals and In = [an; bn], we can show that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... as follows:

Since the intervals are nested, each subsequent interval is contained within the previous one. Mathematically, this means I₁ ⊇ I₂ ⊇ ... In ⊇ ... . Therefore, we have:

1. I₁ ⊇ I₂ implies [a₁; b₁] ⊇ [a₂; b₂], which means a₁ ≤ a₂ and b₁ ≥ b₂.
2. I₂ ⊇ I₃ implies [a₂; b₂] ⊇ [a₃; b₃], which means a₂ ≤ a₃ and b₂ ≥ b₃.

Continuing this pattern for all intervals in the sequence, we can conclude that a₁ ≤ a₂ ≤ ... ≤ an ≤ ... and b₁ ≥ b₂ ≥ ... ≥ bn ≥ ... .

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The answer is B. Quantitative, ratio, discrete.The data described, which is the number of inches of rain in a month, is quantitative data because it is numerical in nature.

The level of measurement for this data is ratio, which means that it has a true zero point and the ratios of the numbers have meaning. For example, if one month had 2 inches of rain and another had 4 inches of rain, we can say that the second month had twice as much rain as the first month.

In terms of whether the data is continuous or discrete, it is continuous because it can take on any value within a range. For example, it can rain 2.5 inches in a month, not just whole numbers like 2 or 3.

Therefore, the answer is B. Quantitative, ratio, discrete.

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The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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If the average waiting time in the line is 18 minutes, it is not possible to determine the number of customers at the carwash without additional information such as the service rate or arrival rate.

The number of customers at the carwash depends on various factors such as the service rate, arrival rate, and the distribution of service times. Without knowing these factors, it is not possible to accurately determine the number of customers at the carwash.

However, we can make some general observations. If the service rate is high, it is likely that the waiting time will be lower, and hence, the number of customers at the carwash will be lower. On the other hand, if the service rate is low, the waiting time will be higher, and hence, the number of customers at the carwash will be higher.

Similarly, if the arrival rate is high, the number of customers at the carwash will be higher, and if the arrival rate is low, the number of customers will be lower. Therefore, to determine the number of customers at the carwash, we need to know both the arrival rate and the service rate.

In conclusion, knowing only the average waiting time in the line is not sufficient to determine the number of customers at the carwash. Additional information such as the arrival rate and service rate is required to make an accurate estimation.

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If the lengths of all the sides of a polygon are tripled, but the angles remain the same, the area of the polygon will increase by a factor of 9. This is because the area of a polygon is directly proportional to the square of its side length. Therefore, tripling the side lengths will increase the area by a factor of 3^2, which is 9.

When the lengths of all the sides of a polygon are tripled while the angles remain the same, the new polygon will be similar to the original one but with larger sides. To determine what happens to the area of the polygon in this case, let's consider the following steps:

1. All the sides of the polygon are tripled. This means that each side's length is now 3 times its original length.

2. The angles of the polygon remain the same, so the overall shape is preserved.

3. To find the area of the new polygon, we can use the formula for the area of a similar polygon: (New area) = (scale factor)^2 * (Original area), where the scale factor is the ratio of the new side length to the original side length.

4. In this case, the scale factor is 3 (since the lengths of the sides are tripled). So, we have (New area) = (3)^2 * (Original area).

5. Therefore, the new area is 9 times the original area.

In conclusion, when the lengths of all the sides of a polygon are tripled and the angles remain the same, the area of the polygon increases by a factor of 9.

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A "required parameter" requires an assigned value for the argument used to call the method, while "optional parameters" do not need to be included in the method call and have a default value assigned to them.

The type of parameter that requires that the argument used to call the method must have an assigned value is a "required parameter".

Required parameters are parameters that must be included in the method call, and the argument passed for the required parameter must have a value assigned to it. If a required parameter is not included in the method call, or if the argument passed for the required parameter does not have a value assigned to it, an error will be thrown.

In contrast, there are also optional parameters, which are parameters that do not need to be included in the method call. If an optional parameter is not included in the method call, the method will use a default value assigned to the parameter.

In many programming languages, the syntax for specifying required and optional parameters in a method or function call is specified using different symbols, such as parentheses or square brackets.

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

The given system of differential equations is: dx/dt = 5x + 13y, dy/dt = -2x + 7y.

This system represents a system of first-order linear differential equations. The variables x and y are functions of t, representing the independent variable (usually time) and the dependent variables, respectively. In the first equation, dx/dt represents the rate of change of x with respect to t. It is equal to 5x + 13y, which means that the rate of change of x depends on both x and y. Similarly, in the second equation, dy/dt represents the rate of change of y with respect to t. It is equal to -2x + 7y, indicating that the rate of change of y also depends on x and y.

To analyze the behavior of this system, we can examine the coefficients of x and y in each equation. In the first equation, the coefficient of x is positive (5x), indicating that x has a positive effect on its own rate of change. Similarly, in the second equation, the coefficient of y is positive (7y), implying that y has a positive effect on its own rate of change.However, in the first equation, the coefficient of y is positive (13y), suggesting that y has a positive effect on the rate of change of x. In the second equation, the coefficient of x is negative (-2x), indicating that x has a negative effect on the rate of change of y.

The interdependence of x and y in these equations creates a system where the rates of change of x and y are influenced by both variables. The specific behavior and solutions of this system can be further analyzed by solving the differential equations using various techniques such as separation of variables, substitution, or matrix methods.

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To determine whether the variable is qualitative or quantitative, the reasoning for the following question will be:

a) qualitative, State of residence describes an attribute or characteristic, making the variable qualitative. Because the state of residence can be determined through measurement or counting, the variable is qualitative.

b) quantitative, The state of residence serves as a description of an attribute or characteristic, so the variable is quantitative. Since determining the state of residence requires measuring or counting, the variable is quantitative.

c) qualitative, Your variable will be quantitative if it is something like, say, your age or salary, which is typically something that can be discovered by counting or using mary-screw analysis. However, in this case, the state of residence is obviously a qualitative factor.

d) qualitative, If your variable is something like, say, your age or salary, or if it's something that is typically discovered by counting or Mary, then these kinds of variables are quantitative. But in this case, the state of residence is categorically important for this question.

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Answer:

the answer is 2, a randomly chosen study hall

Step-by-step explanation:

The gym after a game adds bias towards a sports event

The auditorium after a play is biased toward IMAX

The Nature Club is also possibly biased toward Imax

You have a project completion time of 60 days, and a non-critical path with 5 days of slack was delayed by 10 days. The correct answer is option ii. 65. The new project completion time after the delay of the non-critical task is 65 days.

To determine the new project completion time, follow these steps:

1. Determine the impact of the delay on the project completion time:

Since the non-critical path has 5 days of slack, it means that it can be delayed by up to 5 days without affecting the project completion time. However, the task was delayed by 10 days, which is 5 days more than its slack.

2. Calculate the new project completion time:

To find the new project completion time, add the extra delay (5 days) to the original project completion time (60 days).

New project completion time = Original project completion time + Extra delay
New project completion time = 60 days + 5 days
New project completion time = 65 days

So, the new project completion time is 65 days.

Based on the given options:
i. 60 - Incorrect, as the delay affects the project completion time.
ii. 65 - Correct, as calculated above.
iii. 70 - Incorrect, as the delay is not long enough to push the project completion time to 70 days.
iv. 55 - Incorrect, as the delay increases the project completion time, not decreases it.

Therefore, the correct answer is option ii. 65. The new project completion time after the delay of the non-critical path is 65 days.

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Discrete probability distribution is the events are those with a finite number of outcomes and the two conditions are that the each value is between 0 and 1, and the sum of all values is 1.

According to the statement

we have to explain all about the discrete probability distribution and its two conditions which determine that the this probability is a probability distribution.

So, For this purpose, we know that the

Discrete events are those with a finite number of outcomes

And this is other way that we defines that the A discrete probability distribution counts occurrences that have countable or finite outcomes. This is in contrast to a continuous distribution, where outcomes can fall anywhere on a continuum.

The main example of this is Binomial.

And the two conditions of the probability distribution is :

So, Discrete probability distribution is the events are those with a finite number of outcomes and the two conditions are that the each value is between 0 and 1, and the sum of all values is 1.

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Answer:

x = 52

Step-by-step explanation:

50+(2x +30)+ (2x +20) + X=360

Combine like terms

5x+100 =360

Subtract 100 from each side

5x+100-100 = 360 -100

5x = 260

Divide by 5

5x/5  = 260/5

x = 52

Answer:

x=52

Step-by-step explanation:

50+(2x +30)+ (2x +20) + X=360

First combine like terms

50+30+20=100

2x+2x+x=5x

combine

5x+100=360

subtract 100

5x=260

divide by GCF (5)

x=52

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The highest common factor of the numbers 210 and 308 is 4.

The highest factor of the two numbers which divides both the numbers is called as greatest common factor or HCF.

The highest common factor will be calculated by finding the factors of the two numbers. The factors of the two numbers are as follows:-

308   =  2 x  2   x  7  x  11

210   =  2  x  2   x  3  x  17

We can see that the 2  x  2  =  4 is the highest factor which is common between the two numbers 210 and 308. So 4 is the HCF which can divide both the numbers 210 and 308.

Therefore the highest common factor of the numbers 210 and 308 is 4.

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Answer:

A. y=2x-9

Step-by-step explanation:

A. Parallel lines have the same slope. That means the line y=2x+3 has the same slope as any line parallel to it. So the slope is 2.

Using m=2, substitute it and (4,-1) into the point slope form and simplify to find the y-intercept.