15 (x-3)/5= 3 (2x-3) without the distributive property ( the / symbol is division)

As per the given joint density function, the marginal density function for y1 is f1(y1) = 1/y1, where y1 > 0.

Joint density functions are used to describe the distribution of two or more variables. They provide the probability of observing certain values for multiple variables at the same time.

For the given joint density function

[tex]= > f(y1, y2) = e^{-(y1 y2)}, y1 > 0, y2 > 0[/tex]

and 0 elsewhere, we are asked to find the marginal density function for y1, which is denoted by f1(y1).

Here the marginal density function of y1 is found by integrating the joint density function over all possible values of y2. It gives us the probability density for y1 alone, without considering the value of y2.

In order to find f1(y1), we integrate f(y1, y2) with respect to y2, from 0 to infinity:

=> f1(y1) = ∫ f(y1, y2)dy2

[tex]= > \int f(y1, y2) = \int {e^{-(y1 y2)},dy2}[/tex]

[tex]= -(1/y1)e^{-(y1 y2)}[/tex]

= −(1/y1) * 0 + (1/y1) = 1/y1

Here it is important to note that the marginal density function must always be non-negative, since it represents a probability density.

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At age of 25 years, the diameter would be 6.8612mm

At 50 years the diameter would be 5.422mm

What are the logarithms?

A logarithm is an exponent that indicates the power to which a certain number, called the base, must be raised to produce a given number.

d = 2.115Logₑa + 13.669

d = diameter of the pupil

a = number of years

Note : Logₑa = In a (check logarithmic rule)

d = 2.115Ina + 13.669

1. At 25 years,

d = -2.115In25 + 13.669

d = -2.115 × 3.2188 + 13.669

d = -6.807762 + 13.669

d = 6.8612mm

At 25 years, the pupil shrinks by 6.86mm

2. At 50 years,

d = -2.1158In50 + 13.669

d = -2.1158 * 3.912 + 13.669

d = -8.2770 + 13.699

d = 5.422mm

At 50 years, the pupil shirks by 5.422mm

Hence,

At age of 25 years, the diameter would be 6.8612mm

At 50 years the diameter would be 5.422mm

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The volume of the triangular prism is 168 cm³ while the surface area of the rectangular and triangular prism are 286 cm² and 270 ft² respectively

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The surface area of a solid figure is gotten by calculating each area of the surface and then summing.

a) For the rectangular prism:

Surface area = 2(9 * 7) + 2(9 * 5) + 2(7 * 5) = 286 cm²

b) For the triangular prism:

Surface area = 2(0.5 * 12 * 5) + (7 * 12) + (7 * 13) + (5 * 7) = 270 ft²

3) Volume  = (1/3) * base area * height = (1/3) *  (8 * 9) * 7 = 168 cm³

The volume of the triangular prism is 168 cm³

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The x-value gives the maximum area is 450 ft.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Given that, a rectangular corral is to be built using 900 ft of fencing.

Here, 900=2l+w

w=900-2l

b) Area = Length×width

So, area = l×(900-2l)

Let the length be x, we get

Area =900x-2x²

f(x)=900x-2x²

d) The x-value gives the maximum area is

900x-2x²=0

900x=2x²

x=450

Therefore, the x-value gives the maximum area is 450 ft.

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Answer:

The area of the rectangle is  [tex]8\sqrt{6}+\sqrt{18}[/tex]  ft².

Step-by-step explanation:

The formula for the area of a rectangle is length times width

[tex]A=lw[/tex]

We are given

[tex]l=8+\sqrt{3}[/tex]

[tex]w=\sqrt{6}[/tex]

Given this information we can solve for the area.

[tex]A=(8+\sqrt{3})*\sqrt{6}[/tex]

Use the Distributive Property to distribute [tex]\sqrt{6}[/tex] over [tex]8+\sqrt{3}[/tex].

[tex]A=8\sqrt{6}+\sqrt{6} \sqrt{3}[/tex]

We can simplify this to

[tex]A=8\sqrt{6}+ 3\sqrt{2}[/tex]  or  [tex]A=8\sqrt{6}+\sqrt{18}[/tex]

The number formed by 1 and 4 is 14 from the given informations.

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The digits be x and y

x + y = 6 ...........(i)

The number is 10x + y

The number formed by interchanging is 10y + x

10y + x - 10x - y = 36

⇒9y - 9x = 36

⇒y - x = 4 ..........(ii)

Sum of the two equations are

x+ y +y -x = 6 + 4

⇒2y = 10

⇒ y = 5

Now the value of x is 1.

The number is 10x + y = 10 + 4 = 14

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Answer:

[tex]4a^3b^2[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{20a^5b^3}{5a^2b}=\frac{20}{5}\cdot a^{5-2}\cdot b^{3-1}=4a^3b^2[/tex]

Answer:

4a^3b^2 ----> [tex]=4a^3b^2[/tex]  So (A)

Step-by-step explanation:

[tex]\frac{20a^5b^3}{5a^2b}[/tex]

[tex]\mathrm{Factor\:the\:number:\:}\:20=5\cdot \:4[/tex]

[tex]=\frac{5\cdot \:4a^5b^3}{5a^2b}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:5[/tex]

[tex]=\frac{4a^5b^3}{a^2b}[/tex]

Simplify

[tex]=\frac{4a^3b^3}{b}[/tex]

and simplify one more time!

[tex]=4a^3b^2[/tex]

hope this helps ~~wdfadss~~

Solving provided question, we can say that Using the Pythagorean theorem,  [tex]15^2 = h^2 + 5^2 \\[/tex] => h = 14.14 feet

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

Using the Pythagorean theorem,

[tex]15^2 = h^2 + 5^2 \\[/tex]

[tex]h^2 =\sqrt{200}[/tex]

h = 14.14 feet

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The value of segment BC = 9.8 and the value of BD = 7 in the given right triangle ABC.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Given that the length of the segment CA = 14.

As BD is the bisector of line CA we have:

CD = 7 and

DA = 7

Given that angle C = 45 degrees.

Then,

tan C = opposite side/ adjacent side

tan (45) = BD / 7

1 (7) = BD

BD = 7

Using the Pythagorean Theorem we have:

BC^2 = BD^2 + CD^2

Substituting the values of BD = 7 and CD = 7 we have:

BC^2 = 7^2 + 7^2

BC^2 = 49 + 49

BC = 9.8

Hence, the value of segment BC = 9.8 and the value of BD = 7 in the given right triangles ABC.

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The mean has increased due to the elimination of the minimum value from the data. It is highly affected by the extreme value while the median is not affected to a very high extent.

According to the question,

Observation 44 is removed from the data.

The arranged data is,

{44,45,46,47,48,56,59,60}

The mean and median will be given, as follows:

[tex]Mean = \frac{59 + 47 + 56+ 46 + 48 + 60 +45 }{7}[/tex]

            = 51.5714

[tex]Mead = \frac{N+1}{2} th term[/tex]

            [tex]= \frac{7 + 1}{2}[/tex]  term

            = 4th term

Median = 47

Hence, it is concluded that the mean has increased due to the elimination of the minimum value from the data. Thus, it is highly affected by the extreme value while the median is not affected to a very high extent.

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The complete question is:

A study examined music performance anxiety. Scores on the Performance Anxiety Inventory (PAI) scale for participants in eight different studies is reproduced in the following table.

59, 47,56,44, 46, 48,60,45

Suppose the PAI score of 44 results from a study involving development-delayed children; consequently, the researchers eliminated this data value from the analysis. What impact does this have on the value of the mean? The median?

The radius of the circle is 3√5 cm.

What is Pythagoras theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

Let O be the circle's centre and r its radius. Its chords are AB and CD, which have lengths of 6 cm and 12 cm, respectively.

Draw OM LAB which cuts CD at N AB||CD and ON ICD OM LAB AM = MB (*.* Perpendicular drawn from centre of circle bisects the chord).

AM = MB = 1/2AB

AM = 1/2 * 6 =3cm

Distance between chords AB and CDMN = 3cm.

Let ON = x cm.

In right angled AOCN, by Pythagoras theorem

OC² = ON² + CN2

(OC)² = (x)² +(6)²

(OC)² = x²+36.....(i)

(OC)² = (3)²+36

=9+36

= 45

OC = √45

OC = 3√/5cm.

Hence, The radius of the circle is 3√5 cm.

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The slope criteria for parallel and perpendicular lines is a useful tool for solving geometric problems because it helps you determine whether two lines are parallel, perpendicular or neither based on their slopes.

For parallel lines, the slope must be equal. If the slopes of two lines are equal, then the lines are parallel.

For perpendicular lines, the product of their slopes must be equal to -1.

If the product of the slopes of two lines is -1, then the lines are perpendicular.

To apply the slope criteria in a problem, you need to find the equation of the two lines, either in slope-intercept form (y = mx + b) or point-slope form (y - y1 = m(x - x1)). Once you have the equation, you can find the slope of each line by either finding the coefficient of x in the slope-intercept form or finding the value of m in the point-slope form. Then you can compare the slopes to determine whether the lines are parallel, perpendicular, or neither.

For example, consider two lines with equations y = 2x + 1 and y = -(1/2)x + 3. To determine whether they are parallel or perpendicular, you first find the slope of each line: 2 for the first line and -1/2 for the second line. Since their slopes are not equal, the lines are not parallel. But since the product of their slopes is equal to -1, the lines are perpendicular.

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1.102 pounds for an approximate result, divide the mass value by 453.6

453.592 grams equals one pound.As a result, you’ll frequently see that abbreviated to 453 grams. However, if you recall from elementary school math lesson, we usually round up when the first figure following a decimal point is five or greater, so you may also use 454 grams.

One pound is about equivalent to 0.45359237 kilos (kg). The provided pound value is multiplied by 0.45359237 pound, unit of avoirdupois weight, equivalent to 16 ounces, 7,000 grains, or 0.45359237 kg, and of troy and apothecaries’ weight, equal to 12 ounces, 5,760 grains, or 0.3732417216 kg. The acronym lb comes from the Roman predecessor of the contemporary pound.

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Based on the information in the statement, we can establish that the most accurate conclusion would be "we can draw conclusions about cause and effect for students like those in the study" (option B).

According to the information from the study, the conclusion that we can draw must be related to the students who participated in the study because this study only had an impact on these students. We cannot establish a conclusion in which a change occurs to other students because the other students in the school did not identify a change in their daily life.

So, the most appropriate conclusion would be "we can draw conclusions about cause and effect for students like those in the study" because they are the ones who noticed a change in their daily lives after participating in the study.

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The area at right end point is Rn=7.484 and area at left end points is Ln=7.476

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here f(x) = [tex]\frac{1}{x^3}[/tex] over the interval [1,5] and n=10 then

Δx = [tex]\frac{b -a}{n} = \frac{5-1}{10} = \frac{4}{10} = \frac{2}{5}[/tex]

Δx = 0.4

Then subinterval are, [0,0.4],[0.4,0.8],[0.8,1.2],[1.2,1.6],[1.6,2],[2,2.4],[2.4,2.8],[2.8,3.2],[3.2,3.6],[3.6,4]

Then, area using right end point is

Rn = Δx[f(0.4)+f(0.8)+f(1.2)+f(1.6)+f(2)+f(2.4)+f(2.8)+f(3.2)+f(3.6)+f(4)]

=> Rn = 0.4[[tex]\frac{1}{0.4^3} +\frac{1}{0.8^3} +\frac{1}{1.2^3} +\frac{1}{1.6^3} +\frac{1}{2^3} +\frac{1}{2.4^3} +\frac{1}{2.8^3}+\frac{1}{3.2^3} +\frac{1}{3.6^3}+\frac{1}{4^3}[/tex]]

=> Rn=0.4[18.71]

=> Rn= 7.484

Now area using  Left end point is

=>Ln = Δx[f(0)+f(0.4)+f(0.8)+f(1.2)+f(1.6)+f(2)+f(2.4)+f(2.8)+f(3.2)+f(3.6)]

=> Ln = 0.4[[tex]\frac{1}{0^3}+\frac{1}{0.4^3} +\frac{1}{0.8^3} +\frac{1}{1.2^3} +\frac{1}{1.6^3} +\frac{1}{2^3} +\frac{1}{2.4^3} +\frac{1}{2.8^3}+\frac{1}{3.2^3} +\frac{1}{3.6^3}[/tex]

=> Ln = 0.4[18.69]

=> Ln =7.476

Hence the area at right end point is Rn=7.484 and area at left end points is Ln=7.476

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The average speed for the whole journey is 25 mph.

Completed question :

Tim goes on a car journey. For the first 15 minutes his average speed is 40 mph. He then stops for 25 minutes. He then completes the journey at an average speed of 45 mph. The total journey time is 1 hour.

a) Draw a distance-time

graph for his journey.

b) What is the average

speed for the whole

journey?

mph

Given data :

1. Tim travels first 15 minutes = [tex]\frac{1}{4}[/tex] hour at average speed of 40 mph and passed :

40 x [tex]\frac{1}{4}[/tex]  = 10 miles.

2. Time stops for 25 minutes (distance traveled = 0 miles).

3. He then completes the journey at an average speed of 45 mph. The total journey time is 1 hour, then he was travelling at 45 mph for

60 - 15 - 25 = 20 minutes = [tex]\frac{1}{3}[/tex] hour

and covered

45 x  [tex]\frac{1}{3}[/tex]  = 15 miles.

The distance-time graph for his journey is attached.

Find the average speed for the whole journey:

Average speed = Total distance / Total time = [tex]\frac{10 + 15}{1}[/tex] = 25 mph.

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Answer:

72 sq ft

Step-by-step explanation:

The area of the square pool is 6ft * 6ft = 36 sq.ft.

The perimeter of the pool is 2 * (6ft + 6ft) = 24ft.

The length of the gravel path is equal to the perimeter of the pool, so 24ft.

The width of the gravel path is 3ft, so the total area of the gravel path is 24ft * 3ft = 72 sq.ft.

Since the corners of the path are rounded, we can assume that the loss of area is negligible and assume that the area of the gravel path is 72 sq.ft.

So, the approximate area of the gravel path is 72 sq.ft.

Jack is 100 ft away from the trail guide.

The angle of depression is the angle between the horizontal line and the  observation line of the object from the horizontal line.

Given is that Jack is one side of a 200 foot wide canyon and Jill is on the other side. Jack and Jill can both see the trail guide at angle of depression of 50 degrees.

From the figure, we can write -

tan (50) = OB/OC

OB = OC tan(50)                                   ......... { 1 }

and

tan (50) = OB/OA

OB = OA tan (50)                                  ......... { 2 }

Equation { 1 } and { 2 } -

OC tan(50) = OA tan(50)

OC = OA                                                   ...... { 3 }

Now -

AC = AO + OC

2OA = AC

2OA = 200

OA = 100 ft

Therefore, jack is 100 ft away from the trail guide.

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His mistake is the graph.

The correct graph is given below.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = (-1/2)x + 2

The coordinates on the graph will be:

When x = 0, 1, 2, 3

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

y = (-1/2) x 1 + 2 = -1/2 + 2 = 3/2 = 1.5

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

y = (-1/2) x 3 + 2 = -3/2 + 2 = 1/2 = 0.5

And so on....

Now,

The x-intercept.

i.e x = 0,

y = 2

The y-intercept.

i.e y = 0,
0 = (-1/2)x + 2

x = 4

Now,

The graph is given below.

We see there the y-intercept is at y = 2 and the x-intercept is at x = 4.

Thus,

The graph is a mistake.

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Answer:

Neither

Step-by-step explanation:

Parallel slopes are the same and perpendicular slopes are opposite reciprocals which would be like 2/3 and -3/2.

For each nth term of the sequence, we can multiply 3 by itself (n-1) times and then multiply that result by 23.The nth term of the sequence b1, b2, b3, … , which is bn = 3^(2n-1) × 23.

A geometric sequence is a sequence of numbers in which each term is found by multiplying the previous term by a constant. In this case, the constant is 3 and the first term is 23. An explicit rule for the nth term of the sequence is given by bn = 3^(n-1) * 23. This rule states that bn is equal to 3 to the power of n minus 1, multiplied by 23. Therefore, for each nth term of the sequence, we can multiply 3 by itself (n-1) times and then multiply that result by 23. This gives us the nth term of the sequence.

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Answer:

Step-by-step explanation:

I am preaty positve that it is 99

The electric field increases linearly with the position x along the x-axis.

The electric field E as a function of the position x can be found by taking the derivative of the electric potential V with respect to x:

E = -dV/dx = -d(-4x^2 + 3x - 8)/dx = 8x - 3

So the electric field E as a function of x is given by the equation:

E = 8x - 3

This means that the electric field increases linearly with the position x along the x-axis.

Therefore, The electric field increases linearly with the position x along the x-axis.

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Answer:

4800 liters fuel to travel 600 kilometers

Answer:

50L

Step-by-step explanation:

Given ,

To Find -

Now,

If Car travels 240 km in 20 L of petrol

Then,

The car travels 1 km in 20/240 L of petrol.

Then,

Petrol needed to travel 600 km

20/240 × 600

20/24 × 60

20/4 × 10

5 × 10

= 50 L

Hence, 50 L of petrol is needed to travel 600 km.

The ratio of liters of yellow paint to red paint will make the same shade of orange paint is 10 to 6

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

5 liters of yellow paint with every 3 liters of red paint

This means that

Ratio = 5 litres of yellow : 3 liters of red

Multiply the ratio by 2

So, we have

Ratio = 10 litres of yellow : 6 liters of red

Hence, the ratio is 10 : 6

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Kate need 3/4 cup of flour. She only ha two measuring cup, a 1/3 and a 1/8. The cup should Kate use is 1/8 .

The cup of flour she need is 3/4 that is 75% of the use.

There are two cups available 1/3 and 1/8

In percentages 1/3 can be 33.33%

And in percentages 1/8 can be 12.5%

The amount to be filled is 3/4 that is 75% so the cup that will be used for this is 1/8 that is 12.5% so that,

= 12.5 x 6

= 75

So we used 1/8 cup for 6 times we can get the 3/4 cup of flour.

A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fractio," which meaning "to break," is the source of the English term "fraction." The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilized fractions to solve because they were the first civilization to understand fractions.

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If the interest is compounded continuously, an investment account with the same initial investment and the same APR will have the highest APY.

APY (Annual Percentage Yield) is the effective annual rate of return after compounding. The higher the APY, the more frequently the interest is compounded.

Compounding yields the highest APY because it effectively provides an infinite number of compounding periods. Compounding daily, monthly, or annually yields lower APYs than compounding continuously.

An investment account is a type of financial product that allows people to save or invest money in the hopes of earning a profit. Individual retirement accounts (IRAs), brokerage accounts, savings accounts, and other types of investment accounts are available.

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Answer:

3(3+4n)

Step-by-step explanation:

3x3=9

3x4=12

so, gcf is 3

36.74098197 kg in 81 lbs. Likewise, the question how many pounds in 81 kilogram has the answer of 178.57443237 lbs in 81 kg.

81 kg * 2.2046226218 lbs / 1 kg= 178.57443237lbs

The weight of 81 kilograms is equivalent to 178.57443237 pounds (81kg = 178.57443237lbs). It is simple to convert 81 kg to lb. Simply use our calculator above or the method to convert 81 kg to pounds. To convert 81 kg to pounds, multiply the kilogram mass by 2.2046226218. The formula for converting 81 kilograms to pounds is [lb] = 81 * 2.2046226218. Thus, 81 kilos in pounds are 178.57443237 pounds.

One pound is about equivalent to 0.45359237 kilos (kg). The pound to kilogram conversion is accomplished by multiplying the provided pound value by 0.45359237. In addition, one kilogram is about equal to 2.2046226218 pounds.

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