Let (Y, Y2) have the joint pdf f(41, 42) = { 2e-(4+92) 0 < y1 < y2 < 0 0 otherwise (a) Find the marginal density of Y1. (b) Find the conditional density of Y2 given Y1 = y1. (c) Are Y1 and Y2 independent? In the same setting as Q5 above, (a) Find E(Y2|Y1 = yı). (b) Find V(Y2|Y1 = yı).

We can be reasonably confident that our estimate adequate sample size of 67% is within 2.5% of the true proportion.

To determine if a sample size of 1,400 is adequate for estimating a proportion of 67%, we need to calculate the margin of error and compare it to the given tolerance level of 0.025.

We can use the following formula to calculate the margin of error:

[tex]E = z \sqrt{\frac{(p (1-p)}{n} )[/tex]

where:

Plugging in the values, we get:

[tex]E = 1.96 \sqrt{(0.67 (1-0.67)/1400)[/tex]

≈ 0.025

Thus, the error margin is around 0.025. This indicates that there is a 95% chance that the real percentage will be within 0.025 of the estimated proportion.

We may infer that a sample size of 1,400 is sufficient for predicting a proportion of 67% with the provided degree of confidence and tolerance as the computed margin of error is equal to the required tolerance level. As a result, we can say with some degree of assurance that our estimate of 67% is within 2.5% of the actual proportion.

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Answer:

[tex] \frac{x {}^{2} }{9} - 11[/tex]

Answer:

C. (1, 1)

Step-by-step explanation:

first lets find how much fencing he has used between the three sides they gave us.

between E and F, there is 2 units.

between F and G, there is sqrt(3^2 + 4^2) = 5 units.

so, lets try option C.

between E and C, there is 4 units.

between C and C and G, there is 5 units.

2 + 5 + 4 + 5 = 16, which is how much fencing he has.

yes, it is C. (1, 1)

Answer:

x = -10/3

Step-by-step explanation:

6(2x – 1) – 12 = 3(7x + 4)

12x - 6 - 12 = 21x + 12

12x - 18 = 21x + 12

-9x - 18 = 12

-9x = 30

x = -30/9

x = -10/3

Answer:

Step-by-step explanation:

[tex]6(2x -1) - 12 = 3(7x + 4)[/tex]

   [tex]12x-6-12=21x+12[/tex]         (multiplied to remove brackets)

         [tex]12x-18=21x+12[/tex]        

                 [tex]12x=21x+30[/tex]          (+18 to both sides of the equation)

                 [tex]-9x=30[/tex]                   (-21x both sides)

                      [tex]x=-\frac{30}{9}=-\frac{10}{3}[/tex]    (÷-9 both sides and then simplified the

                                                    fraction)

None of the answers are correct

a) The numbers that can be decomposed in the form 2A + 1 are the ones that are odd when subtracted by 1 and then divided by 2. So, we can check each number to see if it satisfies this condition:

6: (6 - 1)/2 = 2.5 (not a natural number)

8: (8 - 1)/2 = 3.5 (not a natural number)

11: (11 - 1)/2 = 5

16: (16 - 1)/2 = 7.5 (not a natural number)

19: (19 - 1)/2 = 9

22: (22 - 1)/2 = 10.5 (not a natural number)

23: (23 - 1)/2 = 11

So, the three numbers that can be decomposed in the form 2A + 1 are 11, 19, and 23.

b) The numbers in part a) have in common that they are odd.

The required shape of the attached histogram of the prices of the books is given as bell shaped.

General characteristics of histograms ,based on some general observations are,

If the histogram is roughly symmetric around its center, then the distribution is likely to be approximately normal (bell-shaped).

If the histogram has a peak on one side and a long tail on the other, then the distribution is likely to be skewed (either positively or negatively skewed).

If the histogram has multiple peaks or modes, then the distribution is likely to be multimodal.

Based on these observations,

The shape of the distribution in the bookstore's inventory is bell shaped.

As here in the attached histogram is symmetric around its center.

It is almost symmetric between 100 to 150 dollars.

Therefore, the shape of the distribution of the prices of books is bell shaped in the attached histogram.

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The above question is incomplete, the complete question is:

A bookstore took an inventory of the prices of its books and created a histogram to show the results. what shape does the distribution have?

Diagram is attached.

Answer:

x = y = 5

Step-by-step explanation:

This triangle and its markings show that the acute angles are equal. Given that it is a right triangle, this is a 45-45-90 triangle. This also means that the values of x and y are equal. Note that for any triangle, if two angles are equal, then their corresponding side lengths are also equal. The side lengths for this type of triangle follow the pattern s - s - s√2 where the first two are side lengths and last value is the length of the hypotenuse. (s represents the length of a side)

We want to find x and y, so we need the value of s.

s√2 = 5√2
s = 5

Therefore, x = 5, y = 5.

m/EFH = 109° and m/EFG = 18°. Angles in a straight line sum to 180°. Since m/GFH is 71°, the remaining angle measures must add up to the remaining 109°. Therefore, m/EFH must be 109° and m/EFG must be 18°.

To find m/EFH and m/EFG, we need to use the fact that angles in a straight line sum to 180°. We can use this fact to work out the missing angle measures.

First, we note that m/GFH is 71°. This means that the remaining angles must add up to the remaining 109°.

We can then calculate m/EFH by subtracting m/GFH from 180°. m/EFH is therefore 180° - 71° = 109°.

Next, we can calculate m/EFG by subtracting m/EFH from 180°. m/EFG is therefore 180° - 109° = 18°.

Therefore, m/EFH = 109° and m/EFG = 18°.

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The length of the best that is with the contact of rim of the pulley is (5/18)π cm.

The shaded region is 10√5 - (5/18)π cm.

To find the length of the belt that is in contact with the rim of the pulley, we need to find the length of the arc of the circle with radius 5 cm that is between the points O and P.

The circumference of a circle with radius 5 cm is 2πr = 10π cm. So the fraction of the circle between O and P is 10/360 = 1/36 of the total circumference. Therefore, the length of the arc OP is (1/36) x 10π = (5/18)π cm.

To find the shaded region, we need to subtract the length of the belt in contact with the pulley from the length of the belt pulled to point P.

The belt pulled to point P is the hypotenuse of a right triangle with legs 5 cm (the radius of the pulley) and 10 cm (the distance from the center of the pulley to point P). Using the Pythagorean theorem, we can find the length of the belt pulled to point P:

h² = 5² + 10²

h² = 125

h = √125 = 5√5 cm

So the length of the belt pulled to point P is 2(5√5) = 10√5 cm.

Therefore, the length of the shaded region is 10√5 - (5/18)π cm. This is the length of the part of the belt that is not in contact with the pulley.

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Answer:

Step-by-step explanation:

Mason subtracted 5 from each side instead of adding 5.

x - 5 < 11

x - 5 + 5 < 11 + 5

x < 16

The number line will have an open circle at 16 since it does not include

16.  It will be shaded to the left from that open circle as it includes

all values less than 16.  

The statement which most closely summarizes the data is that about 80 necklaces have more than 28 beads. The solution has been obtained by using the standard deviation.

What is standard deviation?

The standard deviation measures how skewed the data are with respect to the mean. Data are said to be more densely grouped around the mean and more dispersed, respectively, when the standard deviation is low and large.

We are given that the mean for the normal distribution is 24 beads and the standard deviation is 4 beads.

Now,

⇒ P (X ≥ 28) = 1 - P (X < 28)

⇒ P (X ≥ 28) = 1 - P ([tex]\frac{X-24}{4}[/tex] < 1)

⇒ P (X ≥ 28) = 1 - P (Z < 1)

⇒ P (X ≥ 28) = 1 - 0.84

⇒ P (X ≥ 28) = 0.16

Now, since the total necklaces are 500, the necklaces which have more than 28 beads are as follows:

⇒ 500 * 0.16

⇒ 80 necklaces

Hence, the third option is the correct answer.

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Question: The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads. Which sentence most closely summarizes the data?

A )About 24 necklaces have more than 28 beads.

B )About 48 necklaces have more than 28 beads.

C)About 80 necklaces have more than 28 beads.

D)About 96 necklaces have more than 28 beads.

To find the percentage increase in price from yesterday's price to today's price, we can use the following formula:

Percentage Increase = ((New Value - Old Value) / Old Value) x 100

Plugging in the given values, we get:

Percentage Increase = ((2.75 - 2.40) / 2.40) x 100

Percentage Increase = (0.35 / 2.40) x 100

Percentage Increase = 0.1458 x 100

Percentage Increase = 14.58%

Therefore, the percentage increase in price from yesterday's price to today's price is 14.58%, rounded to the nearest tenth of a percent.

7/8 is greater than -0.50, greater than -15/16, and less than -1/4. All of these inequalities are true except for 7/8 being less than -0.60.

To solve the inequality 7/8 < -0.60, we need to manipulate it to get it in the form of an equation. First, we can multiply both sides of the inequality by 8, to get 7 < -8(0.60). Next, we can distribute the negative sign on the right side to get 7 < -4.80. Finally, we can subtract 7 from both sides of the equation to get 0 < -4.80 - 7, which equals 0 < -11.80. This means that 7/8 is not less than -0.60, which is the answer to the inequality.

To confirm this answer, we can also solve the inequality 7/8 > -0.50. Again, we can multiply both sides of the inequality by 8 to get 7 > -8(0.50). We can then distribute the negative sign to get 7 > -4. Now, if we subtract 7 from both sides of the equation, we get 0 > -4 - 7, which equals 0 > -11. This means that 7/8 is indeed greater than -0.50.

To further confirm our answer, we can solve the inequality 7/8 > -15/16.

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Answer:

Step-by-step explanationThere are more than 800 species of June bugs known to science and more are discovered every year. Adult beetles are usually blackish or reddish brown in colour, and tend to be very hairy on their fronts:

Step-by-step explanation:

To find the vertices of triangle ABC after the translation T = (2/3), we can use the following formula:

(x', y') = (x + 2/3, y + 2/3)

where (x, y) are the coordinates of the original point and (x', y') are the coordinates of the translated point.

Using this formula, we can translate each vertex of triangle A'B'C' back to its original position:

Vertex A:

x = 3 - 2/3 = 7/3

y = 1 - 2/3 = 1/3

Therefore, the coordinates of vertex A in triangle ABC are (7/3, 1/3).

Vertex B:

x = 1 - 2/3 = 1/3

y = -2 - 2/3 = -8/3

Therefore, the coordinates of vertex B in triangle ABC are (1/3, -8/3).

Vertex C:

x = 1 - 2/3 = 1/3

y = 2 - 2/3 = 4/3

Therefore, the coordinates of vertex C in triangle ABC are (1/3, 4/3).

Therefore, the vertices of triangle ABC are (7/3, 1/3), (1/3, -8/3), and (1/3, 4/3).

Answer:

Let A(x1, y1), B(x2, y2), and C(x3, y3) be the vertices of triangle ABC.

Under the translation T, each point (x, y) is mapped to the point (x + 2/3, y), which means that the new coordinates of A, B, and C will be:

A' = (x1 + 2/3, y1)

B' = (x2 + 2/3, y2)

C' = (x3 + 2/3, y3)

We are given the coordinates of A' (3, 1), B' (1, -2), and C' (1, 2), so we can set up a system of equations to solve for the coordinates of A, B, and C:

x1 + 2/3 = 3 => x1 = 2 1/3

y1 = 1

x2 + 2/3 = 1 => x2 = 1/3

y2 = -2

x3 + 2/3 = 1 => x3 = 1/3

y3 = 2

Therefore, the vertices of triangle ABC are A(2 1/3, 1), B(1/3, -2), and C(1/3, 2).

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The independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$". The relationship is linear, with $ = 3s + 15.

A rate is a measure of the amount of change of one quantity with respect to another quantity, often expressed as a ratio or a fraction. It tells us how much one quantity changes per unit of time or per unit of another quantity. Examples of rates include speed, velocity, acceleration, interest rate, and growth rate

In the given table, the independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$".

The relationship between the number of snacks purchased and the total cost is a linear relationship, where the total cost increases by $3 for every additional snack purchased.

We can write the equation for the relationship between the two variables as:

$ = 3s + 15

Here, the constant term 15 represents the fixed cost or the cost of buying zero snacks. The coefficient 3 of the independent variable "s" represents the additional cost incurred for each additional snack purchased.

Therefore, The independent variable is the number of snacks purchased, denoted by "s", and the dependent variable is the total cost, denoted by "$". The relationship is linear, with $ = 3s + 15.

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The given statement " The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate " is false because the allowable range for an objective function coefficient assumes that the original estimates for other coefficients are approximately correct

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are approximately correct, but not necessarily completely accurate. The allowable range takes into account the potential variability or uncertainty in the estimated values of the other coefficients, as well as the impact of any errors or discrepancies in the data used to estimate the model.

Therefore, the allowable range provides a range of values within which the objective function coefficient can vary while still producing a valid and useful model. It does not assume that the other coefficients are completely accurate or that this is the only coefficient whose true value may differ from its original estimate.

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Step-by-step explanation:

Based on the information you provided, an actuary earns $94,740 per year while a nurse practitioner earns $89,960 per year. The difference in their annual salaries is $4,780. Over 20 years, an actuary would earn $95,600 more than a nurse practitioner (20 years * $4,780/year = $95,600).

Answer:

x < 3

Step-by-step explanation:

4x -7 < 5

4x < 12

x < 3

Answer:x < 3

Step-by-step explanation:4x -7 < 5

4x < 12

x < 3

Answer:

Step-by-step explana add

The area οf the playgrοund is 1264 square yards. Hence, οptiοn B is cοrrect.

Geοmetry is a branch οf mathematics that deals with the study οf shapes, sizes, pοsitiοns, angles, and dimensiοns οf οbjects in space.

Tο find the area οf the playgrοund, we need tο divide it intο twο triangles and οne rectangle, and then find the area οf each and add them tοgether.

The rectangle has a length οf 12 yards and a width οf 20 yards, sο its area is:

40 x 20 = 800 square yards.

Area of Triangle 1 with base 40 yd and height 12 yd:

= 1/2 × 40 × 12

= 240 square yards.

Area of Triangle 2 with base (12 + 20) yd and height 14 yd:

= 1/2 × 32 × 14

= 224 square yards.

Adding all the areas:

= 800 + 240 + 224

= 1264 square yards.

Thus, the area of the playground is 1264 square yards. Hence, option B is correct.

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Complete question:

A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.

What is the area of the playground?

1,728 square yards

1,264 square yards

864 square yards

800 square yards

The probability that the child must wait at least 9 minutes on a given morning is approximately 0.2231.

Let X be the waiting time at the bus stop. We know that X is exponentially distributed with mean 6 minutes. Therefore, the probability density function (PDF) of X is given by:

f(x) = 1/6 * e^(-x/6) for x >= 0

To find the probability that the child must wait at least 9 minutes, we need to calculate the following probability:

P(X >= 9) = integral of f(x) from 9 to infinity

= integral from 9 to infinity of (1/6 * e^(-x/6)) dx

Using integration by substitution, let u = x/6, du = 1/6 dx, so that:

P(X >= 9) = integral from 3/2 to infinity of e^(-u) du

= [e^(-u)] evaluated from 3/2 to infinity

= e^(-3/2)

≈ 0.2231

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Answer:

x=0,[tex]\frac{9}{2}[/tex]   Decimal Form: 0, 4.5

Step-by-step explanation:

1 )Move all terms to one side.

56[tex]x^{2}[/tex]-252x=0

2 )Factor out the common term 28x.

28x(2x−9)=0

3 )Solve for x

x=0,[tex]\frac{9}{2}[/tex]   Decimal Form: 0, 4.5

Answer: 243.617

Step-by-step explanation:

300 = [tex]x[/tex] x (1 + 7/100/4)^(4 x 3)

300 = [tex]x[/tex] x (1.0175)^12

300 = [tex]x[/tex] x 1.231

[tex]x[/tex] = 300/1.231

[tex]x[/tex] = 243.617

Answer: Geometric and common difference is 1/3

Step-by-step explanation:

Answer:

f = 3.74

Step-by-step explanation:

f sin 42° = 2.5

f = 2.5 (sin 42° = 0.669)

sin 41°

= 3.736

= 3.74 (2.d.p.)

The value of f in the given equation is 3.74.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given equation is,

f sin 42° = 2.5

Dividing both sides of the equation by sin 42°,

f = 2.5 / sin 42°

f = 3.74

Hence the value of f is 3.74.

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The rate of change between 75 and 125 miles is calculated by dividing the difference between the fuel cost at 125 and 75 miles by the distance traveled. The fuel cost at 75 miles is $3.85, while the fuel cost at 125 is $6.35. The rate of change is $0.05 per mile.

To calculate the rate of change between 75 and 125 miles, subtract the fuel cost at 125 miles from the fuel cost at 75 miles and divide the difference by the distance travelled:

Rate of change = (fuel cost at 125 miles - fuel cost at 75 miles) / (125 - 75)

First, we need to find the fuel cost at 75 miles:

() = 0.1 + 0.05x

() = 0.1 + 0.05(75)

() = 3.85

The fuel cost at 75 miles is $3.85.

Next, we need to find the fuel cost at 125 miles:

() = 0.1 + 0.05x

() = 0.1 + 0.05(125)

() = 6.35

The fuel cost at 125 miles is $6.35.

Now we can substitute these values into the rate of change formula:

Rate of change = (6.35 - 3.85) / (125 - 75)

Rate of change = 2.5 / 50

Rate of change = 0.05

The rate of change of the cost of fuel when the car travels from 75 miles to 125 miles is $0.05 per mile.

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The complete question is: If a car travels x miles, the cost of fuel used is given by the function () = 0.1 + 0.05x dollars. What is the rate of change of the cost of fuel when the car travels from 75 miles to 125 miles?

Answer:

B is correct

Step-by-step explanation:

The shaded region is below both lines, and the boundary line y = 2x - 1 is dashed because the inequality is strict. The solution can be described as: y < 5 - 3x and y < 2x - 1.

Inequality is a mathematical statement that compares two values or expressions. It uses symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to indicate the relationship between the two expressions. Inequalities are used to represent a range of possible values, rather than just a single value as in an equation.

Here,

We have the system of inequalities:

y + 3x < 5

2x - y > 1

To solve this system, we can start by isolating y in each inequality:

y < 5 - 3x

y < 2x - 1

Now we can graph each inequality on the coordinate plane and shade the region that satisfies both inequalities.

For the first inequality y < 5 - 3x, we can start by graphing the line y = 5 - 3x. This line has a y-intercept of 5 and a slope of -3. Since the inequality is y < 5 - 3x, we need to shade the region below the line.

For the second inequality y < 2x - 1, we can start by graphing the line y = 2x - 1. This line has a y-intercept of -1 and a slope of 2. Since the inequality is 2x - y > 1, we need to shade the region below the line.

The solution to the system is the region that is shaded by both inequalities. Here is a graph of the solution:

   |         /

 5 |- - - -/---- - - - - - - -

   |     /  |             /

   |  /     |          /

 2 |- - - - -/------- - - - -

   | /      |        /

   |/       |     /

-1 | - - - - - - - - - - - - -

   0       1       2       3

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