Let Y1 and Y2 have joint pdf
f(y1,y2)=3y1
, if 0≤y2≤y1≤1
0, otherwise.
a) Find the marginal density function for Y2.
b) For what values of y2 is the conditional density f(y1|y2)
defined?

Answer:

The answer is Sin B

Step-by-step explanation:

I remember in 8th grade doing this

We have shοwn algebraically that the sοlutiοns tο the system οf equatiοns F(x) = g(x) are [tex](-2, -3)[/tex] and [tex](1, 0)[/tex].

A system οf equatiοns in algebra is made up οf twο οr mοre equatiοns that are sοlved tοgether. "A grοup οf equatiοns satisfied by the same set οf variables are called a system οf linear equatiοns. Finding the values οf the variables emplοyed in the system οf equatiοns is the first step tοwards sοlving it.

While maintaining the balance οf the equatiοns οn bοth sides, we cοmpute the values οf the unknοwn variables. Finding a variable whοse value makes the cοnditiοn οf all the given equatiοns true is the primary gοal οf sοlving an equatiοn system.

Tο prοve that these cοοrdinate pοints are sοlutiοns, we need tο substitute them intο bοth equatiοns and verify that they satisfy the equatiοns. Let's start with (-2, -3):

[tex]F(-2) = (-2)^2 + 2(-2) - 1 = 4 - 4 - 1 = -1[/tex]

[tex]g(-2) = (-2) - 1 = -3[/tex]

We can see that [tex]F(-2) = g(-2)[/tex] , sο[tex](-2, -3)[/tex]is a sοlutiοn.

Nοw let's check (1, 0):

[tex]F(1) = 1^2 + 2(1) - 1 = 2[/tex]

[tex]g(1) = 1 - 1 = 0[/tex]

Again, we can see that F(1) = g(1), sο (1, 0) is alsο a sοlutiοn.

Therefοre, we have shοwn algebraically that the sοlutiοns tο the system οf equatiοns F(x) = g(x) are (-2, -3) and (1, 0).

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The team jogged longer in the afternoon because they covered a distance of 6 eighths of a mile, which is greater than the 3 eighths of a mile they covered in the morning.

To compare the distance jogged in the morning and afternoon, we need to find the common unit for both. We can convert both fractions to have the same denominator by finding the least common multiple (LCM) of 8 and 4, which is 8.

So, in terms of eighths of a mile, the distance jogged in the morning is:

3/8 miles = 3 eighths of a mile

And the distance jogged in the afternoon is:

3/4 miles = 6 eighths of a mile (since 3/4 = 6/8)

Therefore, the team jogged longer in the afternoon because they covered a distance of 6 eighths of a mile, which is greater than the 3 eighths of a mile they covered in the morning.

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Answer:

Step-by-step explanation:

You can start by drawing a diagram.  Then, you need to pick the shorter side and designate it as "x".  The longer side must be "x+8".

The formula for area of a rectangle is A=l*w.  Since the area is 84, then you can use the A=l*w formula.  84 = x(x+8) would be the equation to solve for x.

Now, you need to put the equation in standard form.  So, x2 + 8x - 84 = 0.

Since you can't solve this quadratic using factoring, you need to complete the square.

To complete the square you need to add 84 to both sides.  Now you have x2 + 8x = 84.  Take the coefficient for the x term (8) and divide by 2.  Now square it.  That would be 42, so 16.  Now you have x2 +8x +16 = 100.

Factor x2 +8x +16, so (x+4)2 = 100

If you use the square root property, you have x+4 = 10.  Therefore, x = 6 (the short side) and 14 is the long side.

I hope that helps.

Answer:

80.925

Step-by-step explanation:

124.5 x 0.35 = 43.575

124.5 - 43.575 = 80.925

Answer:

yes 10 to the 3rd power is 1,000 so try to go from there if more info is needed please comment "more info"

Step-by-step explanation:

Answer:

-b = √(3a+28)

Step-by-step explanation:

3a = -28 + b²

3a + 28 = b²

√(3a + 28) = √b²

negative solution:

-b = √(3a+28)

Answer:

Step-by-step explanation:129412515968569028414 m

The intercepted arcs of the inscribed angle are in proportion to the inscribed angle itself. In other words, the larger the inscribed angle, the more significant the intercepted arc it cuts, and vice versa. So, in an equilateral triangle, each of the inscribed angles of the circle measures 60°, which is half of the central angle of 120° that intercepts the same arc.

The angle measure and intercepted arcs of inscribed angles in an equilateral triangle inscribed in a circle are related, and the relationship between inscribed angles and central angles in a circle is that the inscribed angles are half of the central angle. Let us have a more in-depth understanding of these two angles.An inscribed angle is an angle that has its vertex on the circle and is formed by two chords that intersect at that point. It is half of the central angle that intercepts the same arc.A central angle is an angle whose vertex is at the center of the circle, and the sides of the angle pass through any two points on the circumference of the circle.

For an equilateral triangle inscribed in a circle, each angle measures 60°, and the central angle measures 120°. So, each of the two inscribed angles measures half of the central angle, i.e., 60°.The relationship between inscribed angles and intercepted arcs.

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By answering the presented question, we may conclude that As a result, the darkened zone has an area of 88 square units.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

We must determine the size of the darkened zone.

The bigger rectangle (with the frame) has a surface area of (12+2) x (10+2) = 14 x 12 = 168 square units.

The smaller rectangle (with the frame) has an area of (8+2) x (6+2) = 10 x 8 = 80 square units.

The frame's area is equal to the difference between the two areas: 168 - 80 = 88 square units.

As a result, the darkened zone has an area of 88 square units.

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Answer:

x = - 8

Step-by-step explanation:

(3x - 1)(x + 1) - 3x(x + 1) = 7 ← factor out (x + 1) from each term

(x + 1)(3x - 1 - 3x) = 7

(x + 1)(- 1) = 7 ( multiply both sides by - 1 )

x + 1 = - 7 ( subtract 1 from both sides )

x = - 8

Answer:

Step-by-step explanation:

[tex]\bf (3x -1 ) (x+1)- 3x(x+1)=7[/tex]

Expand:-

[tex]\bf 3x^2+2x-1-3x\left(x+1\right)[/tex]

[tex]\bf 3x^2+2x-1-3x^2-3x[/tex]

Combine like terms:-

[tex]\bf (3x^2-3x^2)+(2x-3x)-1[/tex]

[tex]\bf -x-1=7[/tex]

Add 1 to both sides:-

[tex]\bf -x-1+1=7+1[/tex]

[tex]\bf -x=8[/tex]

Divide both sides by -1:-

[tex]\bf \cfrac{-x}{-1}=\cfrac{8}{-1}[/tex]

[tex]\bf x=-8[/tex]

_________________________

Hope this helps!

Answer:

3

Step-by-step explanation:

The range of the normal curve representing 95% of the scores fall is equal to 40.2 to 59.8.

The range within which 95% of the scores fall,

Calculate the z-scores corresponding to the 2.5th and 97.5th percentiles of the normal distribution.

The z-score corresponding to the 2.5th percentile is -1.96.

And the z-score corresponding to the 97.5th percentile is +1.96.

Using the formula for the z-score, we can calculate the corresponding raw scores as,

Lower bound is equal to,

z = (X - μ) / σ

⇒-1.96 = (X - 50) / 5

⇒X = 40.2

Upper bound is equal to,

z = (X - μ) / σ

⇒ +1.96 = (X - 50) / 5

⇒ X = 59.8

Therefore, 95% of the scores fall within the range of 40.2 to 59.8.

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The value of x is 8. So correct is C.

In mathematics, a triangle is a geometric shape that consists of three line segments that intersect at three endpoints. These endpoints are called vertices, and the line segments are called sides.

Triangles are one of the most basic shapes in geometry and are used in many areas of mathematics, science, engineering, and everyday life. They can be classified based on the length of their sides and the measure of their angles.

Some common types of triangles include:

Equilateral triangle: A triangle in which all three sides are equal in length.

Isosceles triangle: A triangle in which two sides are equal in length.

Scalene triangle: A triangle in which all three sides have different lengths.

Right triangle: A triangle in which one angle measures 90 degrees (a right angle).

To find the value of x, we can use the trigonometric ratios of a right-angled triangle. Let's call the base of the triangle "b".

We know that the angle between the hypotenuse and the base is 45 degrees, which means that the other acute angle is also 45 degrees. Therefore, we can use the trigonometric ratio for the sine of 45 degrees to relate the hypotenuse and the perpendicular as follows:

sin(45 degrees) = opposite/hypotenuse

where the opposite side is the perpendicular, which is given as 4√2.

sin(45 degrees) = 4√2/x

Simplifying this equation gives:

x = 4√2 / sin(45 degrees)

We know that sin(45 degrees) = 1/√2, so substituting this value into the equation above gives:

x = 4√2 / (1/√2) = 4√2 * √2 = 8

Therefore, the value of x is 8.

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Answer:

[tex]\boxed{-\frac{1}{8} }[/tex]

Step-by-step explanation:

De acuerdo al inverso multiplicativo se cumple lo siguiente:

[tex]a\times \frac{1}{a}= \frac{a}{a}=1[/tex]

Por lo tanto:

[tex]-8 \times \frac{1}{-8}=1[/tex]

El número que cumple con el enunciado es [tex]-\frac{1}{8}[/tex]

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer:

a) Account 2 will pay Lewis more interest after 15 years because it pays compound interest, which means that the interest is calculated on both the initial deposit and the accumulated interest from previous years. On the other hand, Account 1 pays simple interest, which means that the interest is calculated only on the initial deposit.

b) To calculate the amount of interest paid by each account, we can use the following formulas:

For Account 1: I = P × r × t, where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years.

I = 3100 × 0.07 × 15 = £3255

For Account 2: A = P × (1 + r/n)^(n × t), where A is the amount of money at the end of the investment period, P is the principal, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

In this case, n = 1 (compounded annually), so the formula simplifies to:

A = 3100 × (1 + 0.05)^15 = £5569.62

The interest earned by Account 2 is the difference between the final amount and the initial deposit:

I = A - P = £5569.62 - £3100 = £2469.62

Therefore, Account 2 will pay £2469.62 - £3255 = -£785.38 less in interest than Account 1 after 15 years.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

the number of zeroes is defined by the highest exponent of the variable in the functional expression.

The cost of materials for the cheapest container is 69.6 dollars.

Let's first express the dimensions of the rectangular container in terms of a single variable. Let the width of the base be x meters, then the length of the base is 2x meters, and the height of the container is 10/(2x^2) = 5/x^2 meters, since the volume of the container is 10 cubic meters.

The area of the base is x * 2x = 2x^2 square meters, so the cost of the base is 10 * 2x^2 = 20x^2 dollars.

The area of each side of the container is (2x)(5/x^2) = 10/x square meters, so the cost of the four sides is 4 * (10/x) * 6 = 240/x dollars.

The total cost C of the materials is the sum of the cost of the base and the cost of the sides:

C = 20x^2 + 240/x

To find the value of x that minimizes this expression, we can take its derivative with respect to x and set it equal to zero:

dC/dx = 40x - 240/x^2 = 0

Solving for x, we get:

x^3 = 6

x = (6)^(1/3)

Substituting this value of x back into the expression for C, we get:

C = 20(6)^(2/3) + 240/(6)^(1/3) ≈ 69.6 dollars

Therefore, the cost of materials for the cheapest rectangular container is approximately 69.6 dollars.

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Answer: 1.061

Step-by-step explanation:

1). Based on conditions, formulate: 1+6.1%

2). Then convert to a decimal: 1.061

Answer:

Select the one at the lowest point on the right of the y-axis. This point has an x value (horizontal) of 1 and 1/2, with a y value (vertical) of -5.

Hoped this helped.

Step-by-step explanation:

The y-axis is where x = 0 ....so the y-axis intercept occurs at x = o

 put  in   '0' for 'x'

y = 0^2 + 2(0) + 10       <===== 10 is the y-axis intercept

The amount of caster sugar used in the first attempt is given as follows:

340 g.

The amount of caster sugar used in the first attempt is obtained applying the proportions in the context of the problem.

The expressions for each attempt are given as follows:

The amount used on the third attempt was of 376.38 g, hence the amount used on the first attempt is obtained as follows:

1.107x = 376.38

x = 376.38/1.107

x = 340 g.

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Answer:

sin Θ = [tex]-\frac{3}{5}[/tex]

tan Θ = [tex]-\frac{3}{4}[/tex]

csc Θ = [tex]-\frac{5}{3}[/tex]

cot Θ = [tex]-\frac{4}{3}[/tex]

Step-by-step explanation:

We know that this triangle is a 3-4-5 triangle since we know the cos of the angle. We also know this angle is located in Quadrant IV (4) since cos is positive and tan is negative.

Based off this info we can find the rest of the trig functions

sin Θ = [tex]-\frac{y}{r}[/tex]

tan Θ = [tex]-\frac{y}{x}[/tex]

csc Θ = [tex]-\frac{r}{y}[/tex]

cot Θ = [tex]-\frac{x}{y}[/tex]

If Cody was 10 %, percent taller than he was on the first day of school last year then he was 150 cm tall on the first day of school last year.

 To find out the height of Cody on the first day of school last year, we need to perform a calculation as follows:

           Let's say their height of Cody on the first day of school last year is 'x'.

           His height of Cody on the first day of school this year is 165 cm.

           Cody is 10% taller than he was on the first day of school last year, so:

                      165 = x + (10% of x)

    Simplifying this equation will give

                        165 = x + 0.1 x 165

                               = 1.1xx

                               = 150

           Therefore, Cody was 150 cm tall on the first day of school last year.

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So the measures of the angles in the isosceles obtuse triangle are 20 degrees, 80 degrees, and 80 degrees.

What is triangle ?

Three straight ends and three angles make up a closed triangle, a two-dimensional geometric object. A triangle's angles add up to 180 degrees in all cases. Based on their side lengths and angle measurements, triangles can be categorized in a variety of ways. Typical categorizations comprise: Triangle having no equal sides is referred to as a scalene triangle. Isosceles triangle: A triangle with two sides of equal length. A triangle having an equilateral shape is one with three equal sides. Triangle that has all angles that are less than 90 degrees is referred to as an acute triangle. Triangle with one angle that is precisely 90 degrees is referred to as a right triangle. A triangle that has a side that is more acute than 90 degrees is said to be obtuse.

given

In the isosceles obtuse triangle, let x represent the measurements of each equal angle.

One of the equal angles is bigger than 90 degrees since the triangle is obtuse. As a result, we have:

x + x + 20 = 180 (sum of angles of a triangle) (sum of angles in a triangle)

When we simplify this equation, we obtain:

2x + 20 = 180

2x = 160

x = 80

Hence, each of the equal angles is 80 degrees in length. As a result, there are three different ways to measure the angles in the isosceles obtuse triangle, which has one angle that is 20 degrees, as follows:

20-80-80 degree range

80-20-80 degree range

80-80-20 Celsius

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The calculated surface area of the cuboid has a value of 192 square feet.

The surface area of a cuboid is the sum of the areas of all six faces.

In this case, the dimensions of the cuboid are 8 ft by 8 ft by 2 ft. So we can calculate the surface area as follows:

Therefore, the total surface area of the cuboid is:

= 2(64 sq ft) + 2(16 sq ft) + 2(16 sq ft)

= 128 sq ft + 32 sq ft + 32 sq ft

= 192 sq ft.

So the surface area of the given cuboid is 192 square feet.

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Therefore, they took in $43.10 selling watermelons that day.

Describe the dollar sign($)?

The dollar sign, also referred to as the peso sign, is a symbol that looks like a capital "S" crossed with one or two vertical strokes ($ or Cifro symbol depending on typeface), and it's used to denote the unit of many different currencies around the world, including the majority of currencies denominated in "pesos" and "dollars." The Portuguese word for the specifically double-barred Cifro symbol is cifro.

The sign is also present in a number of compound currency symbols, including those for the Nicaraguan córdoba (C$) and the Brazilian real (R$).

If they sold 5/6 of the watermelons, then they sold 8/6 of the watermelons. So, they sold 4/3 of the watermelons.

If they sold 4/3 of the watermelons for $5.75 each, then they sold each watermelon for $4.31.

They sold 5/6 of the watermelons for $5.75 each,

so they sold

5/6 × 4/3

= 20/18 = 10/9 of the watermelons for $4.31 each.

$4.31 * 10 = $43.10 That day.

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Required value of N is 1

This is a problem of simplification which is major part of Algebra.

Some Algebra's formulas:

[tex]{(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \\ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \\ {(x + y)}^{3} = {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} \\ {x}^{3} + {y}^{3} = {(x + y)}^{3} - 3xy(x + y) \\ {x}^{3} - {y}^{3} = {(x - y)}^{3} + 3xy(x - y) \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ {x}^{2} + {y}^{2} = {(x - y)}^{2} + 2xy \\ {x}^{2} - {y}^{2} = {(x + y)}^{2} - 2xy \\ {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2} ) \\ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )[/tex]

Given equation is [tex] - 3(8 \times N) = - 24[/tex]

We want to Simplify both side.

Multiplying (-3) and (8×N),

-24N = -24

Now we are dividing (-24) by (-24),

N = -24/-24

N = 1

Therefore, required value of N is 1.

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[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} t_1=0.5\\ t_2=0.75 \end{cases}\implies \cfrac{f(0.75)-f(0.5)}{0.75 - 0.5}\implies \cfrac{7.744-6.275}{0.75-0.5} \\\\\\ \cfrac{1.469}{0.25}\implies 5.876~\frac{meters}{second}[/tex]

You roll a number cube two times. The theoretical probabilities are accurate is P(even number then odd number)= 1/4

Probability:

Probability is the likelihood of something happening. When we are unsure of the outcome of an event, we can talk about the likelihood of certain outcomes - how likely are they to occur. The analysis of events governed by probability is called statistics.

According to the Question:

Let P(E), P(H), and P(E and H) be the probabilities of rolling an even number on a die, heads on a coin, and heads, respectively.

We know,

P(E and H) = P(E)×P(H)

Now, to find P(E and H), we have to find P(E) and P(H).

Total number of possible results of a die roll = 6

Favorable results of an event E = {2, 4, 6}

∴ Number of favorable results of an event E = 3

Therefore,

P(E) = number of favorable results of an event event E / possible results The total number of

⇒ P(E)=3/6=1/2

There are two possibilities for tossing a coin = {H, T}

∴ Probability of heads on a flip coin = P(H)= 1/2

Finally, the probability that

Lewis gets an even number and flips heads =

1/2×1/2 = 1/4

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