Let and be two independent random variables, each following a uniform
distribution on [0, 1]. Let =+.
What is the support of ,(x,z)? Draw a plot.
What is probability density function of ?

The quadratic expression can be factorized to:

x*(x - 6)

Here we have the expression:

x^2 - 6x

To factorize this, first, we need to find the roots, which are the solutions of:

x^2 - 6x = 0

Notice that one of the solutions is trivial, and it is x = 0.

If now we assume that x ≠ 0 and divide both sides by x, we get:

x - 6 = 0

x = 6

That is the other solution.

Now, for a square polynomial with the roots a and b, the factorized form is:

(x - a)*(x - b)

In this case, the roots are 0 and 6, then:

x^2 - 6x = (x - 0)*(x - 6) = x*(x - 6)

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Answer: 2nd one down

Step-by-step explanation:

Step-by-step explanation:

a.b=0.6×0.75

=0.45

a/b= 0.6/0.75

=0.8

Answer:

all are correct

Step-by-step explanation:

The graph of s(x) = -6x + \(8x^2\) + 5x + 3 is concave up at the point with x-coordinate -1. Let us consider the second derivative.

To determine the concavity of a function at a specific point, we need to analyze the second derivative of the function. If the second derivative is positive, the graph is concave up, and if it is negative, the graph is concave down.

Given s(x) = -6x + \(8x^2\) + 5x + 3, let's find the second derivative:

s'(x) = -6 + 16x + 5

s''(x) = 16

The second derivative is a constant, 16, which is positive. Since it is always positive, the graph of s(x) is concave up for all values of x. Therefore, at the point with x-coordinate -1, the graph is also concave up.

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Answer:

True

Step-by-step explanation:

angle 3 and 6 are alternate angles.

alternate angles have the following characteristics:

1. they are inside the parallel lines

2. they are on opposite sides of the transversal

3. they are EQUAL

another example of alternate angles is angle 4 and angle 5

Answer:

True

Step-by-step explanation:

I took this in my class already

Answer:

4+(-11)

Step-by-step explanation:

you need to put the negative 11 in ()

The coterminal angles are given as follows:

a) 0º.

b) 120º.

The coterminal angle of a negative angle between 0 and -360º = -2pi is found adding 360º = 2pi to the angle, hence:

-2pi + 2pi = 0, which is the answer to item a.

The coterminal angle is found taking the remainder of the division of the angle by 360º.

The remainder of the division of 480º by 360º is of 120º, hence the coterminal angle of 480º is of 120º.

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Audric's average speed for the entire trip is 125 km/h.

The speed of Audric during his trip to San Pablo, Laguna from Quezon City is 10 km/h faster than his speed on his way back to Quezon City. His return trip took an hour.

Find Audric's average speed for the entire trip.

Audric drove 120 km from Quezon City to San Pablo, Laguna to attend their family reunion.

Let's assume the speed of Audric on his way to San Pablo, Laguna was x km/h.

So, his speed on his way back to Quezon City was (x - 10) km/h.

Using the formula:

speed = distance/time

We can calculate the time Audric took to reach San Pablo, Laguna and his time to return to Quezon City.

Audric's time to reach San Pablo, Laguna = 120/xAudric's time to return to Quezon City

= 120/(x - 10)

According to the problem, his return trip took an hour,

so we have:

120/(x - 10) = 1

Now we can solve for x as follows:

120 = x - 10120 + 10

= xx = 130 km/h

Therefore, Audric's speed on his way to San Pablo, Laguna was 130 km/h, and his speed on his way back to Quezon City was (130 - 10) = 120 km/h.

Now, we can find Audric's average speed for the entire trip as follows:

Average speed = total distance / total time

Total distance = 120 km + 120 km = 240 km

Total time = 120/130 + 120/120

= 0.92 + 1 hours

= 1.92 hours

Average speed = 240/1.92

= 125 km/h

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Answer:

Step-by-step explanation:

Sample Space

off  even numbers

= {2,4,6,8,10}.

There are 5 outcomes in the sample space,

F'(1) = 8/√5, f'(2) = 8/√6, and f'(4) = 4√2. the four-step process to find f'(x) and then find f'(1), f'(2), and f'(4). f(x) = 16Vx+4

to find the derivative of the function f(x) = 16√(x+4) using the four-step process, we can follow these steps:

step 1: identify the function and rewrite it if necessary.f(x) = 16√(x+4)

step 2: identify the composite function and its derivative.

let u = x + 4f(u) = 16√u

f'(u) = 8/√u

step 3: apply the chain rule.f'(x) = f'(u) * u'

      = (8/√u) * 1       = 8/√(x + 4)

step 4: simplify the derivative if necessary.

f'(x) = 8/√(x + 4)

now, let's find f'(1), f'(2), and f'(4) by substituting the respective values into the derivative function:

f'(1) = 8/√(1 + 4)      = 8/√5

f'(2) = 8/√(2 + 4)

     = 8/√6

f'(4) = 8/√(4 + 4)      = 8/√8

     = 8/(2√2)      = 4√2

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Yusef's financial advisor may have played a crucial role in the success of his budget by employing various effective strategies.

Firstly, the advisor could have helped Yusef create a comprehensive and realistic budget by thoroughly assessing his income, expenses, and financial goals. This would ensure that Yusef's budget is tailored to his specific needs and circumstances. Additionally, the advisor might have guided Yusef in establishing clear financial goals and breaking them down into manageable milestones, providing motivation and direction.

Regular monitoring and tracking of expenses would allow Yusef to stay on top of his spending and make necessary adjustments. The advisor could have also educated Yusef on the importance of saving and helped him develop a systematic savings plan. By instilling financial discipline, providing guidance, and fostering a proactive approach to budgeting, the financial advisor would greatly contribute to Yusef's success in managing his finances effectively and achieving his financial objectives.

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a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.

a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.

b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.

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an=20.5+2 5n

correct me if I'm wrong

Answer:

x = 2

Step-by-step explanation:

\(2log_5 x = log_5 4 \\ \\ log_5 {x}^{2} = log_5 4 \\ \\ \implies \: {x}^{2} = 4 \\ \\ \implies \: x = \pm \sqrt{4} \\ \\ \implies \: x = \pm 2 \\ \\ x = - 2, \: \: x = 2\)

Since, anti-logarithm must be greater than zero.

\( \therefore x\neq - 2\)

\( \implies x = 2\)

Answer:

yes because 0.5 is 50%

Step-by-step explanation:

The car was traveling at approximately 40 ft/s when the brakes were first applied.

To find the initial velocity of the car when the brakes were first applied, we can use the kinematic equation:

v^2 = u^2 + 2as

where:

v = final velocity (0 ft/s, as the car comes to a stop)

u = initial velocity (what we want to find)

a = acceleration (deceleration due to braking, -16 ft/s^2)

s = distance (skid marks, 200 ft)

Rearranging the equation, we have:

u^2 = v^2 - 2as

Substituting the given values, we get:

u^2 = 0^2 - 2(-16 ft/s^2)(200 ft)

u^2 = 6400 ft^2/s^2

Taking the square root of both sides, we find:

u = ±80 ft/s

Since we are looking for the initial velocity, we discard the negative value as it represents the opposite direction of motion. Therefore, the car was traveling at approximately 80 ft/s when the brakes were first applied.

Note: It's important to ensure consistent units throughout the calculations, and in this case, we used the unit of feet per second (ft/s) for velocity and feet (ft) for distance.

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Solving for M, we get M = 5. Therefore, Michael is currently 5 years old.

Let's represent Ana's age as "A" and Michael's age as "M". We know that A = 2M since Ana is twice as old as Michael. Three years ago, Ana's age was (A-3) and Michael's age was (M-3). We also know that (A-3) = (M-3)+2 since Ana was two years older than Michael is now.
Now we can simplify and solve for M:
A-3 = M-1
2M-3 = M-1
M = 2
Therefore, Michael is 2 years old.
To solve this problem, let's represent Michael's age with the variable M, and Ana's age with the variable A. We know that A = 2M and that A - 3 = M + 2.
Now, substitute A with 2M: 2M - 3 = M + 2. Solving for M, we get M = 5. Therefore, Michael is currently 5 years old.

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Answer:

It is a gift economy

Step-by-step explanation:

This is correct on playto, but let me give you an explanation. A gift economy is a explicit agreement between two parties that if a favor is given, it'd be returned at a later time. If a hunter shared meat with others, the hunter expects to get something later in returned. By defintion, this is the role of a gift economy.

Answer:

y = 5x -4 or you could also write y = 5x + -4

it's still the same thing.

Step-by-step explanation:

To determine the total amount in a percentage problem when given the percentage rate and the part of the total amount, you need to divide the part by the percentage rate and multiply the result by 100.

To find the total amount when you know the percentage rate and the part of the total amount, you can use the following formula:

Total Amount = (Part of Total Amount) / (Percentage Rate)

Let's break it down step by step:

1.Identify the given values:

Part of Total Amount: This represents the portion or fraction of the total amount that you know. Let's say it's denoted by P.

Percentage Rate: This is the rate or proportion expressed as a percentage. For example, if the rate is 20%, it would be written as 0.20 or 20/100.

2.Plug the values into the formula:

Total Amount = P / (Percentage Rate)

3.Calculate the total amount:

Simply divide the given part of the total amount by the percentage rate to find the total amount.

For example, let's say you know that the part of the total amount is $500 and the percentage rate is 25%. You can calculate the total amount as follows:

Total Amount = $500 / 0.25 = $2000

Therefore, the total amount would be $2000 in this case.

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The exact length of the apothem in this case is 4.33 units.

The apothem of a regular polygon is a line segment that extends from the centre of the polygon to the midpoint of one of its sides. In a regular polygon with side length s and radius r, the apothem has a length of a = r * cos(180/n), where n is the number of sides in the polygon.

In the case of a regular polygon with a radius of 5 units, we can use the formula above to calculate the length of the apothem. If the polygon is a regular hexagon (n = 6), then the apothem has a length of a = 5 * cos(180/6) = 5 * cos(30) = 5 * 0.866 = 4.33 units.

Alternatively, we could use the formula a = r * (1 - cos(180/n))/sin(180/n) to calculate the apothem. This formula also gives us a result of a = 4.33 units.

So, the exact length of the apothem in this case is 4.33 units.

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As per the given radius, the exact length of the apothem is 4.33 units.

Here we have given that Circle a has a radius with the length of 5 units.

And we need to find the exact length of the apothem,

Here let us consider that the regular hexagon can be divided into 6 equal equilateral triangle.

Then the ΔAED is an equilateral triangle.

=> ∠A = 60°

Then the an equilateral triangle, the altitude bisects the angle is calculated as,

=> ∠DAH = 60/2 = 30°

Now, according to the given radius the apothem is calculated as,

=> cos 30 = AE/AH

=> cos 30 = AE/5

Here we know that the value of cos 30 = √3/2, then the value of the apothem AE is calculated as.

=> AE = √3/2 x 5

=>  AE = 4.33

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The blanks in each statement about the line segment should be completed as shown below.

Since we know U is the midpoint, we can say TU=8x + 11 substituting in our values for each we get:

8x + 11 = 12x - 1

Solve for x

We now want to solve for x.

−4x+11=−1

−4x = -12

x= 3

Solve for TU, UV, and TV

This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.

TU=8x+11 We know that x=3 so let’s substitute that in.

TU=8(3)+11

TU= 35

We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.

UV=12x−1 We know that x=3 so let’s substitute that in.

UV=12(3)−1

UV= 35

Based on the segment addition postulate, we have:

TU+UV=TV

35+35=TV

TV= 70

Find the detailed calculations below;

TU = UV

8x + 11 = 12x - 1

8x + 11 - 11 = 12x - 1 - 11

8x = 12x - 12

8x - 12x = 12x - 12 - 12x

-4x = -12

x = 3

By using the substitution method to substitute the value of x into the expression for TU, we have:

TU = 8x + 11

TU = 8(3) + 11

TU = 24 + 11

TU = 35

By applying the transitive property of equality, we have:

UV = TU and TU = 15, then UV = 35

By applying the segment addition postulate, we have:

TV = TU + UV

TV = 35 + 35

TV = 70

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Answer:

No

Step-by-step explanation:

When \(x=2\), \(y=-6(2)=-12\), not \(4\).

Answer:

y = 5x + 4

Step-by-step explanation:

Hope it helps.

Step-by-step explanation:

We need to write the sum of 2x - 7 and the opposite of 2x

Opposite of 2x is (-2x)

Sum means to add the number :

2x-7 + (-2x)

Remove parentheses,

2x-7 - 2x

Taking like terms together,

2x-2x-7= 0-7

= -7

Hence, the answer is -7.