What is the value of x in the triangle?
10
10
X
10√2
О А.
OB. 10
OC. 20
OD. 2012
OE. 10√3

The marginal density functions of the joint probability density functions, X and Y (a) \(f(x) = \frac{2x-1}{6}, f(y) = \frac{2}{9} (6-y)\)

                                   (b) P(X>2, Y>1.5 ) = 0.3194

                                   (c) X and Y are not independent

The given function is :

\(f(x) =\frac{3x-y}{9} , 1 < x < 3 , 1 < y < 2 and 0 , eleswhere\)

(a) Marginal Density Functions of X and Y are

\(f_{x}(x) =\int\limits^2_1{f(x,y)} \, dy =\int\limits^2_1{\frac{3x-y}{9} } \, dy =\frac{1}{9} [2xy -\frac{y^{2} }{2} ]^{2} _{1} = \frac{1}{9}(3x-\frac{3}{2}=\frac{2x-1}{6} , 1 < x < 3\\ f(x) = \frac{2x-1}{6}, 1 < x < 3\)

\(f_{y}(y) = \int\limits^3_1{f(x,y)} \, dx = \int\limits^3_1{\frac{3x-y}{9} } \, dx =\frac{2}{9}(6-y)\\ f_{y}(y) = \frac{2}{9}(6-y) , 1 < y < 2\)

(b) P(X>2, Y>1.5)

 \(=\int\limits^2_\frac{3}{2} \int\limits^3_2 {f(x,y)} \, dxdy \\ =\int\limits^2_\frac{3}{2} {[\int\limits^3_2 {\frac{3x-y}{9} } \, dx }] \, dy \\=0.3194\)

(c) To check whether X and Y are independent, we have:

\(f_{x}(x) =\frac{2x-1}{6} ,f_{y} (y) =\frac{2(6-y)}{9} \\ X,Y are independent if \\f_{xy} =f_{x}*f_{y} = \frac{2x-1}{6}*\frac{2(6-y)}{9} \\=\frac{1}{27}(12x+y-2xy-6)\\ \neq f(x,y)\)

Therefore, X and Y are not independent.

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The angle, which is on the third quadrant, is 233.13°

Here we want to find an angle whose terminal side passes through the point (-3/5, -4/5)

Notice that both coordinates are negative, thus, this is on the third quadrant.

To get the angle we need to take the inverse tangent of the quotient between the y-coordinate and the x-coordinate.

angle = Atan(-4/5/-3/5)

angle = 53.13°

And the angle is on the third quadrant, so we need to add 180°, then we will get:

angle = 53.13° + 180° = 233.13°

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The absolute maximum of f on the given interval is at x = 8.

We have,

a.

To determine the absolute extreme values of f(x) = 2x³ - 30x² + 126x on the interval [2, 8], we need to find the critical points and endpoints.

Step 1:

Find the critical points by taking the derivative of f(x) and setting it equal to zero:

f'(x) = 6x² - 60x + 126

Setting f'(x) = 0:

6x² - 60x + 126 = 0

Solving this quadratic equation, we find the critical points x = 3 and

x = 7.

Step 2:

Evaluate f(x) at the critical points and endpoints:

f(2) = 2(2)³ - 30(2)² + 126(2) = 20

f(8) = 2(8)³ - 30(8)² + 126(8) = 736

Step 3:

Compare the values obtained.

The absolute maximum will be the highest value among the critical points and endpoints, and the absolute minimum will be the lowest value.

In this case, the absolute maximum is 736 at x = 8, and there is no absolute minimum.

Therefore, the answer to part a is

The absolute maximum of f on the given interval is at x = 8.

b.

To confirm our conclusion, we can graph the function f(x) = 2x³ - 30x² + 126x using a graphing utility and visually observe the maximum point.

By graphing the function, we will see that the graph has a peak at x = 8, which confirms our previous finding that the absolute maximum of f occurs at x = 8.

Therefore,

The absolute maximum of f on the given interval is at x = 8.

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positive correlation :relationship between the number of hours a student studies and their grade point average (GPA).

negative correlation :relationship between the number of hours a student spends watching television and their grade point average (GPA).

Correlation is a statistical term that describes the relationship between two variables. When two variables are positively correlated, it means that as one variable increases, the other variable also increases. When two variables are negatively correlated, it means that as one variable increases, the other variable decreases.

An example of a positive correlation is the relationship between the number of hours a student studies and their grade point average (GPA). As the number of hours a student studies increases, their GPA also tends to increase. This is a positive correlation because both variables are increasing together.

An example of a negative correlation is the relationship between the number of hours a student spends watching television and their grade point average (GPA). As the number of hours a student spends watching television increases, their GPA tends to decrease. This is a negative correlation because one variable is increasing while the other is decreasing.

It's important to note that correlation does not imply causation. Just because two variables are correlated it does not mean that one variable causes the other. It could be that some other variable is causing both variables to change, or that the relationship is not causal at all.

In summary, correlation is a statistical term that describes the relationship between two variables. Positive correlation means that as one variable increases, the other variable also increases.

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The original cost of the bike is $20

What is percentage ?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," the percent sign, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

A fraction of 100 is represented as a number or ratio known as a percentage. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

Let x be the discount

20/100 = x / 25

1/5 = x/25

x = 25/5

x = 5

The discount is 5

The original cost is

$25 - $5

= $20

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Answer: Is there any answer choices?

Step-by-step explanation:

Answer:

a) 1/2 of an energy bar

b) 42 pieces

Step-by-step explanation:

a) Here, Franklin are 3/4 of an energy bar while Trey are 2/3 of what Franklin ate

The fraction are by Trey is 2/3 * 3/4 = 6/12 = 1/2

b) To find the number of pieces of wood present, we will need to divide the height of Colin’s stack by the thickness of each piece of wood

Mathematically, that will be;

57 3/4 divided by 1 3/8

= 231/4 * 8/11 = 42 pieces

Answer:

kejorrerprpfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

a. the exact value of arcsin(sin(13π/12)) is **π/12**. b. the value of arccos(cos(8π/5)) is **UNDEFINED**. c. the exact value of arctan(tan(11π/9)) is **5π/9**.

(a) To find the exact value of arcsin(sin(13π/12)), we need to determine the angle whose sine is equal to sin(13π/12). However, it's important to note that the range of the arcsin function is [-π/2, π/2].

The reference angle for 13π/12 is π - (13π/12) = π/12, which lies in the range of the arcsin function. Furthermore, the sine function is positive in both the first and second quadrants, so the angle will be positive.

Therefore, the exact value of arcsin(sin(13π/12)) is **π/12**.

(b) For arccos(cos(8π/5)), we need to find the angle whose cosine is equal to cos(8π/5). The range of the arccos function is [0, π].

The reference angle for 8π/5 is 8π/5 - 2π = -2π/5, which is negative and not within the range of the arccos function. Hence, the expression is undefined.

Therefore, the value of arccos(cos(8π/5)) is **UNDEFINED**.

(c) In the case of arctan(tan(11π/9)), we are looking for the angle whose tangent is equal to tan(11π/9). The range of the arctan function is (-π/2, π/2).

The reference angle for 11π/9 is 11π/9 - 2π = 5π/9, which is within the range of the arctan function. Therefore, the exact value of arctan(tan(11π/9)) is **5π/9**.

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Answer:number D

Step-by-step explanation:

50 55 and keep going up

Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

Answer:

Yes they are same shape but different size

Step-by-step explanation:

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the y-axis , horizontal translation

and vertical translation

1. If point (x , y) is reflected across the y-axis, then its image is (-x , y)

2. If point (x , y) is translated h units to the right, then its image is

  (x + h , y), if translated h units to the left, then its image is (x - h , y)

3. If point (x , y) is translated k units up, then its image is (x , y + k),

  if translated k units down, then its image is (x , y - k)

∵ The vertices of triangle BCD are (1 , 4) , (1 , 2) , (5 , 3)

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The x-coordinates of the vertices of Δ B'C'D' have the same

  magnitude of x-coordinates of Δ BCD and opposite signs

∴ Δ B'C'D' is the image of Δ ABC after reflection across the y-axis

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The vertices of triangle B''C''D'' are (5 , -1) , (5 , -3) , (1 , -2)

∵ The image of -1 is 5 and the image of -5 is 1

∴ The x-coordinates of the vertices of triangle B'C'D' are added by 6

∵ The image of 4 is -1 , image of 2 is -3 and the image of 3 is -2

∴ The y-coordinates of the vertices of triangle B'C'D' are subtracted

  by 5

∴ Δ B"C"D" is the image of Δ B'C'D' by translate 6 units to the right

 and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

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The composition of transformations that maps BCD to B"C"D" is described by the following rule:

Composition translation of 6 units x, negative 5 units y across the y-axis last response

Let us rewrite the y-axis reflection, horizontal translation, and vertical translation.

1. If point (x, y) is mirrored across the y-axis, the image of that point is (-x , y)

2. If point (x, y) is translated h units to the right, its image is (x + h, y), and if it is translated h units to the left, its image is (x + h, y) (x - h , y)

3. If point (x, y) is translated k units up, its image is (x, y + k), but if it is translated k units down, its image is (x , y - k)

∵ Triangle BCD has (1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. Triangle B'C'D' has (-1, 4) vertices, (1, 2) vertices, and (5, 3) vertices. The x-coordinates of the B'C'D' vertices have the same magnitude as the x-coordinates of BCD and opposite signs. B'C'D' is the picture of ABC after it has been reflected across the y-axis.

The vertices of triangle B'C'D' are (-1, 4), (-1, 2), (-5, 3), (1, -2)

The vertices of triangle B"C"D" are (5, -1), (5, -3), (1, -2)

The x-coordinates of the triangle B'C'D' vertices are added by 6.

The image of 4 is -1, the image of 2 is -3, and the image of 3 is -2.

The y-coordinates of triangle B'C'D' vertices are subtracted by 5.

∴ Δ B"C"D" is the image of Δ B'C'D' by translating 6 units to the right

and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

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Answer:  x=55, y=65

Step-by-step explanation:

hope this helps! feel free to clarify if unsure

Green, Inc.'s qualifying research expenditures for the year can be calculated by adding the in-house research expenditures to the payments made to a qualified research organization, such as the Blue Foundation.

Using this formula, we can calculate the qualifying research expenditures for the year as follows:

$60,000 + $30,000 = $90,000

Therefore, the answer is (d) $90,000.

In-house research expenditures, such as wages, supplies, and computer time, qualify as research expenditures for tax purposes. Payments made to a qualified research organization also qualify as research expenditures. To determine the total qualifying research expenditures for the year, these two types of research expenditures must be added together.

In the given scenario, Green, Inc. incurred $60,000 in in-house research expenditures and paid $30,000 to the Blue Foundation for research. Adding these two amounts together, the qualifying research expenditures for the year are $90,000.

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Answer:

Static

Step-by-step explanation:

By process of elimination, static is the only one that would work.

Answer:

static.

Step-by-step explanation:

\(\\ \leq \int\limits^a_b {x} \, dx x^{2} \sqrt{x} \sqrt[n]{x} \leq \geq \neq \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx \left \{ {{y=2} \atop {x=2}} \right.\)

13) The scientific notation is        1.4354125 * 10⁸. 14) The scientific notation is        1.4354125 * 10⁻¹. 15) The scientific notation is 22366.0992. 16) The scientific notation is 1.55 * 10¹⁰.

Let's solve the given expressions and write the answers in scientific notation:

13) \((6.125*10^3) * (2.345*10^4)\)

To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:

\((6.125 * 2.345) * (10^3 * 10^4) = 14.354125 * 10^(3 + 4) = 14.354125 * 10^7 = 1.4354125 * 10^8\)

\(= 1.4354125 * 10^8\)

14) \((6.1258*10^3) * (2.345*10^{-4})\)

To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:

\((6.125 * 2.345) * (10^3 * 10^{-4}) = 14.354125 * 10^{3 - 4} = 14.354125 * 10^{-1} = 1.43541258* 10^{-1}\)

\(= 1.4354125 * 10^{-1}\)

15) \(3700.13 * (6.04*10^4)\)

To multiply a decimal number and a number in scientific notation, we simply multiply the decimal by the coefficient of the scientific notation:

3700.13 × 6.04 = 22366.0992

Since the answer does not need to be expressed in scientific notation, the result is 22366.0992.

= 22366.0992

16) \((6.2*10^4) / (0.4*10^{-5})\)

To divide numbers in scientific notation, we divide the coefficients and subtract the exponents:

\((6.2 / 0.4) * (10^4 / 10^{-5}) \\= 15.5 * 10^{4 - (-5}) \\= 15.5 * 10^9 \\= 1.55 * 10^{10}\\= 1.55 * 10^{10}\)

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Answer:

The midpoint is (1, 3) and the length of the segment (let's call it AB) is 6.32

Step-by-step explanation:

Answer:

A) (1, 3)

B) \(2\sqrt{10}\\\)

Step-by-step explanation:

A) We are finding the averages of the x and y values. The midpoint formula is as so:

(x1 + x2/2, y1 + y2/2)

(-2+4/2 , 4+2/2)

(2/2 , 6/2)

(1.3)

With distance, the formula is\(\sqrt{(x_{1} -x_{2})^{2} + (y_{1} -y_{2})^{2}\)

\(\sqrt{(4-(-2))^{2} + (2-4)^{2}\)

\(\sqrt{(6)^{2} + (-2)^{2}\)

\(\sqrt{36 + 4}\)

\(\sqrt{40}\)

\(2\sqrt{10}\)

THIS FORMULA OPTION GAVE ME THE HARDEST TIME-

Answer: \(h=8.33\ cm\)

Step-by-step explanation:

Given

The length of a cuboid is \(l=15\ cm\)

breadth is \(b=12\ cm\)

Total surface area is \(S.A.=900\ cm^2\)

Surface area is given by \(2(lb+hl+bh)\)

Insert the values

\(\Rightarrow 900=2(15\times 12+15h+12h)\\\Rightarrow 450=225+27h\\\Rightarrow 225=27h\\\Rightarrow h=8.33\ cm\)

Answer:

  5

Step-by-step explanation:

You want the length of the line segment between (-2, 2) and (2, -1).

The relation between the side lengths of a right triangle is given by the Pythagorean theorem. It tells you ...

  c² = a² +b²

where c is the hypotenuse of the triangle, and 'a' and 'b' are the legs.

When you plot the points on a grid, you can identify the vertical and horizontal distances between them by counting grid squares, or by finding the difference of coordinates:

  AB = B -A = (2, -1) -(-2, 2) = (2 +2, -2 -2) = (4, -3)

The point on the right is 4 horizontal units and 3 vertical units from the point on the left.

The above relation tells us the segment length is ...

  c² = 4² +3² = 16 +9 = 25

  c = √25 = 5

The length of the line segment is 5 units.

__

Additional comment

The integer triple of segment lengths that form a right triangle is called a "Pythagorean triple." The one relevant to this problem is {3, 4, 5}. Others often seen in algebra, trig, and geometry problems are ...

  {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

and multiples of these. If you become familiar with these triples, you can often write down the answer to a question like this simply by recognizing the dimensions involved.

Answer:

A. 3.75 pounds

Step-by-step explanation:

16 ounces = 1 pound

converting 60 ounces to pounds

Let x = number of pounds

60 ounces = x pounds

Find the proportion

16 / 1 = 60 / x

Cross product

16 * x = 1 * 60

16x = 60

Divide both sides by 16

x = 60/16

x = 3.75

Therefore,

60 ounces = 3.75 pounds

If \($x$\) is an element of the set \($\{ -1, 1, 2 \}$\) and \($y$\) is an element of \($\{ -2, -1, 0, 1, 2 \}$\), the number of distinct values of \($x^y$\) that are positive is 5.

When the base is positive, the exponent produces positive powers.

Now, let's evaluate the power for each possible combination of \($x$\) and \($y$\):

For \($x = -1$\) and \($y$\) being an even number, we get a positive power. Here are the possible even values for \($y$\):
\($y = -2$\) and \($y = 0$\).  Therefore, \($x^y$\) is positive for two possible combinations: \($(-1)^{-2} = 1$\) and \($(-1)^{0} = 1$\).

For \($x = 1$\) and any value of \($y$\), the power of \($x$\) is always positive, and the value of \($x$\) is always 1. Therefore, there's only one possible combination: \($1^y = 1$\).

For \($x = 2$\) and \($y$\) being an even number, we get a positive power. Here are the possible even values for \($y$\):
\($y = -2$\) and \($y = 0$\). Therefore, \($x^y$\) is positive for two possible combinations: \($2^{-2} = 1/4$\) and \($2^{0} = 1$\)

For \($x = 2$\) and \($y$\) being an odd number, we get a negative power. Here are the possible odd values for \($y$\):
\($y = -1$\) and \($y = 1$\). Therefore, \($x^y$\) is positive for zero possible combinations.

Therefore, the total number of distinct values of \($x^y$\) that are positive is \($2+1+2 = 5$\).

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Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

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Answer:

A and 1/3

Step-by-step explanation:

Answer:

We conclude that the  standard form of the given function is:

\(f(x)=-9x^2-90x-221\)

Hence, option B is correct.

Step-by-step explanation:

We know that the standard form of the quadratic function is of the form

\(f\left(x\right)\:=\:ax^2\:+\:bx\:+\:c\)

Given the function

\(f(x)=-9\left(x\:+\:5\right)^2\:+\:4\)

as (x+5)² = x² + 10x + 25

\(f(x)=-9\left(x^2+10x+25\right)+4\)

Expanding  -9(x² + 10x + 25) = -9x² - 90x - 225

\(f\left(x\right)\:=-9x^2-90x-225+4\)

simplifying

\(f(x)=-9x^2-90x-221\)

Therefore, we conclude that the  standard form of the given function is:

\(f(x)=-9x^2-90x-221\)

Hence, option B is correct.

Answer:

Hope this helps!

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Answer:

I will do

Step-by-step explanation:

length of balcony: 14 feet

Breadth of balcony:6 feet

area of rectangular balcony: length ×breadth

answer 14ft × 6ft = 84ft²

BREADTH MEANS WIDE

option C is correct because a line bisecting parallel lines makes the same angle on each line at the point of intersection

so they all will make 61°

Answer:

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

Let the amount deposited be x. It is assumed we are talking about simple interest.

After 4 years the interest amount is:

95% of this amount is Rs 4940:

Mrs Majhi deposited Rs 20000.

Mrs. Majhi deposited Rs 20000 in her bank account. This was calculated by first finding the total interest (before tax) and then using the formula for simple interest to determine the principal amount.

The question is based on the concepts of Simple Interest and taxation. We know that Mrs Majhi received Rs 4940 as net interest after 4 years and this amount is 95% of the total interest (since 5% was paid as income tax). The total interest can be calculated as (4940 / 95) * 100 = Rs 5200.

The rate of interest is given as 6.5% per annum. Thus, the money deposited (Principal) by her can be calculated using the formula for simple interest (I = PRT/100), where P is the Principal, R is the rate of interest, and T is the time. Re-arranged to calculate the Principal (P), it becomes P = I / (R*T) = 5200 / (6.5*4) = Rs 20000.

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