A radar tends to overestimate the distance of an aircraft, and the error is a normal random variable with a mean of 50 meters and a standard deviation 100 meters. What is the probability that the measured distance will be smaller than the true distance?.

Answer:

If I am understanding the question correctly, every 6 feet in real life will be equivalent to 1 inch "on paper", or in the blueprint. Using dimensional analysis, which is a methodology for converting from one unit to another, we have:

18 feet * 1 inch / 6 feet = 3 inches

On the other axis,

24 feet * 1 inch / 6 feet = 4 inches

Therefore, the blueprint for this 18x24 foot room, with a scale of 6 feet:1inch, should be 3x4 inches.

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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7.36 for each cap

$36.80 is the cost for 5 caps. if we divide the cost of the pack to the individual number of idems (caps), the equation (36.80÷5) will come out to $7.36, meaning $7.36 is the cost for each individual cap.

Answer:

sqrt 5 = 2.23606798

Step-by-step explanation:

Thank you for telling us the 2 is squared that really helps!

x^2 - 5 = 0

(add 5 both sides)

x^2 = 5

(sqrt both sides) (sqrt stands for square root)

x = sqrt 5

(Usally they just want sqrt 5 as an answer but if they want decimals its)

x = 2.23606798

Answer:

x=\(\sqrt{5}\)

Step-by-step explanation:

f(x)=\(x^{2}\)-5

\(x^{2}\)-5=0

Add 5 to both sides.

\(x^{2}\)=5

To get rid of the square of x, put the square root thingie so that it will cancel out. BTW, if you put it on one side, you have to put it on the other side.

\(\sqrt{x^{2} }\)=\(\sqrt{5}\)

x=\(\sqrt{5}\)

Hope this helps! Plz give brainliest!

Answer:

c i believe sorry if its wrong

Step-by-step explanation:

Answer:

3. A.

4. 136

Step-by-step explanation:

3. Find the surface area:

2 * 1  = 2

3 * 2.2 = 6.6

2 * 3 = 6

3 * 1 = 3

2 + 6.6 + 6 + 3 =  17.6

4. Find the surface area:

5 * 7 * 2 = 70

6 * 4 = 24

7 * 6 = 42

70 + 24 + 42 = 136

Answer:

Where is point A and B. Confusing -.-

Step-by-step explanation:

Answer:

I think it's 3 steps

Step-by-step explanation:

Answer:2

Step-by-step explanation:

The unit vector in the same direction will be equal to  (6 i/5.1 - 3 j/5.1).

A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity.

A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.

As per the given data in the question,

The unit vector is calculated as:

\(\vec u_a=\frac{\vec a}{||\vec a||}\)

\(\vec a= x \vec i+y \vec j\)

Now, calculate the magnitude of the vector,

\(\vec a\) = √(x² + y²)

\(|\vec a|\) = √6² - 3²

= √36 - 9

= 5.1

So, the unit vector will be,

\(\vec u_a\) = (6 i - 3 j)/5.1

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Answer:

t = 3s

Step-by-step explanation:

The equation t = 3s can be used to calculate the total cost.

The slope of the line is 2/5 and to represent the "rise" and "run" on the line, a vertical line and a horizontal line are drawn to show the change in y and x, respectively.

To find the slope of the line, we can choose two points on the line and use the formula:

slope = (change in y)/(change in x)

Let's choose the points (-2, 3) and (3, 5) on the line. The "rise" is the change in y and the "run" is the change in x between these two points:

Rise = change in y = 5 - 3 = 2

Run = change in x = 3 - (-2) = 5

So the slope of the line is:

slope = (change in y)/(change in x) = 2/5

Therefore, the slope of the line in simplest form is 2/5.

To represent the "rise and run" on the line, we can draw a vertical line going from the point (-2, 3) to the point (-2, 5) to represent the "rise" of 2 units, and a horizontal line going from the point (-2, 5) to the point (3, 5) to represent the "run" of 5 units.

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Answer:

504.

Step-by-step explanation:

multiplication is just repeated addition. so it would be 84+84+84+84+84+84. multiply all 6 80's first to get 480. then multiply all 6 4's to get 24. 480+24=504

Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.

To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.

The ratio of cost to the quantity of visitors for $9 and four visitors is:

$9/4 visitors = $2.25/ visitors

The ratio of value to the quantity of visitors for $18 and eight visitors is:

$18/8 visitors = $2.25/ visitors

We are able to see that both ratios are equal to $2.25 per visitor.

Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.

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Answer:

C

Step-by-step explanation:

The problem states:

"The second anthill has one and one-third the amount of ants of the first hill."

Answer: C

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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a. To compute the confidence interval, use a t-distribution.

b. With 90% confidence, the population mean number of pounds per person per week is between 32.382 pounds and 35.418 pounds.

c. If many groups of 196 randomly selected members are studied, approximately 90% of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week, while about 10% will not contain the true population mean number of pounds of trash generated per person per week.

(a) To compute the confidence interval, we use a t-distribution since the sample size is less than 30 and the population standard deviation is unknown.

(b) With 90% confidence, the population mean number of pounds per person per week is between [32.674, 35.126] pounds. Here, we use the formula for the confidence interval:

CI = xbar ± (t * (s / √n)),

where xbar is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution corresponding to the desired confidence level.

Using the given information, the lower bound of the confidence interval is 33.9 - (1.645 * (8.3 / √196)) ≈ 32.674, and the upper bound is 33.9 + (1.645 * (8.3 / √196)) ≈ 35.126.

(c) If many groups of 196 randomly selected members are studied, approximately 90% of these groups' confidence intervals will contain the true population mean number of pounds of trash generated per person per week, while approximately 10% will not contain the true population mean. This means that in repeated sampling, about 90% of the calculated confidence intervals will capture the actual population mean, providing a measure of accuracy for the estimation process. The remaining 10% will not include the true population mean, representing the possibility of estimation error or uncertainty in those particular intervals.

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Answer:

A sequence is a chain of numbers all related. In this case, they are related by the rule "f(n + 1) = –10f(n)". Each number is called a term. Here is what the rule in this sequence means:

Since f(n + 1) is the "next" term and f(n) is the "current" term, to get to the next term, you take the current term and multiply by -10.

When they say f(1) = 1 it means that the first term (term number 1) is 1. When they ask "What is f(3)?", they are asking, "What is the 3rd term?"

Since term #1 is 1, then to find term #2, we multiply 1 by -10. So term #2 is -10. To find term #3, we take term #2 and multiply it by -10, so -10 x -10 = 100. So term #3 is 100

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Mean= add up all the numbers, then divide by how many numbers there are. 0+3+6=9

9/3=3

When an increase in one variable is associated with an increase in a second variable, the two variables are known as positively correlated. The correlation coefficient is the measure of the degree of the relationship between two variables.

The correlation coefficient ranges from -1 to 1. A positive correlation coefficient indicates a positive relationship between two variables, while a negative correlation coefficient indicates an inverse relationship between two variables.

A positive correlation coefficient signifies that as one variable increases, the other variable also increases. For instance, the correlation between a person's height and weight is positive because as their height increases, so does their weight.

In the same way, as a person's income increases, so does their level of expenditure. Positive correlations can be either strong or weak.A strong correlation is indicated by a correlation coefficient close to 1, while a weak correlation is indicated by a correlation coefficient closer to zero.

For example, the correlation between a person's weight and the number of hours they exercise per week is strong. When a person's exercise time increases, so does their weight loss. In conclusion, when an increase in one variable is associated with an increase in a second variable, the two variables are positively correlated.

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Answer:

On the y axis

Step-by-step explanation:

If x is zero, it automatically has to be on the y axis because x=0 is where the x and y axis intersect.

For a triangle with base of 10 inches and altitude of 16 inches, its area will be 80 in² (third option).

Calculation For the Area of the Triangle:

It is given that,

The base of the triangle, B = 10 inches

The altitude from the base of the triangle or height, H = 16 inches

Now, the formula used for finding the area of a triangle is given as follows,

Area, A = (1/2) × B × H

Substituting the given values of B and H in the above formula for area, we get,

A = (1/2) × (10 inches) × (16 inches)

A = 5 × 16 inches²

A = 80 inches²

Thus, the area of the triangle have base 10 inches and altitude 16 inches is 80 square inches.

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The value of the absolute percent error for week 3 is 25.00%.

To calculate the absolute percent error for week 3, we need to find the absolute difference between the forecasted value and the actual value, and then divide it by the actual value. Finally, we multiply the result by 100 to convert it to a percentage.

To find the absolute percent error for week 3, we'll use the formula:

Absolute Percent Error = |(Actual Value - Forecasted Value) / Actual Value| * 100

For week 3:

Actual Value = 4.00

Forecasted Value = 3.00

Absolute Percent Error = |(4.00 - 3.00) / 4.00| * 100

= |1.00 / 4.00| * 100

= 0.25 * 100

= 25.00

Therefore,For week three, the absolute percent error value is 25.00%.

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Answer:

1) Four coplanar points are points, J, K, L, and M which are points on the plane Z

2) A point non-coplanar with the planar with the plane Z is the point R

3) The intersection of the plane JPS and the plane Z is the line JM

Step-by-step explanation:

Two or more points are said to be coplanar if they are located on the same plane

A point that is non-coplanar to a plane is a point not located on the plane

The intersection of two planes is a line, given that a plane is defined as a two-dimensional figure or flat surface, such as the surface of a smooth door intersecting with a smooth wall happens only along a line.

Answer:79°

Step-by-step explanation:

Given the 124° angle, the other angle formed by that line and the top side of the square must be 56°, as they are supplementary angles (they must add up to 180°). This means that the angle formed by that same line and the bottom side of the square is also 56° since it is a corresponding angle and the top and bottom sides of a square are parallel. The angle that a diagonal of a square forms with the sides of a square is always 45°.

So now we have a triangle (in red in my diagram) with angles of 45°, 56°, and x°. The sum of the angles of a triangle must always equal 180°, so we solve for x:

56 + 45 + x = 180

x = 180 - 56 - 45 = 79

So angle x must be 79°.

The probability that, out of a random sample of 10 internet users, 6 are concerned about the privacy of their e-mail can be calculated using the binomial probability formula.

The binomial probability formula allows us to calculate the probability of a specific number of successes (concerned internet users) in a given number of trials (random sample of 10 internet users), given the probability of success in a single trial (95% or 0.95 in this case).

Using the binomial probability formula, we can calculate the probability as follows:

\(P(X = 6) = C(n, x) * p^x * (1 - p)^(n - x)\)

P(X = 6) is the probability of exactly 6 internet users being concerned about privacy,

n is the total number of trials (10 in this case),

x is the number of successful trials (6 in this case),

p is the probability of success in a single trial (0.95 in this case), and

C(n, x) is the number of combinations of n items taken x at a time.

Plugging in the values, we have:

\(P(X = 6) = C(10, 6) * 0.95^6 * (1 - 0.95)^(10 - 6)\)

Calculating this expression will give us the probability that exactly 6 out of the 10 internet users in the random sample are concerned about the privacy of their e-mail.

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Answer:

\(2\sqrt{10}\) units

Step-by-step explanation:

The distance formula states that \(D(x_{1} ,y_{1})(x_{2},y_{2} )=\sqrt{(x_{2} } -x_{1} )^2+(y_{2}-y_{1} )^2\\\).

We then plug in our points and compute.\(\sqrt{(4-(-2))^2+(3-1)^2} =\sqrt{6^2+2^2} =\sqrt{36+4} =\sqrt{40} =\sqrt{2^2*2*5} =2*\sqrt{2*5} =2\sqrt{10}\)

The * represents multiplication.