Let X and Y be uniformly distributed in the triangle with vertices at (0, 0), (2,0), (1,2). Find P(X ≤ 1|Y = 1).

Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

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Answer:

second line plot

Step-by-step explanation:

It is the second line pot because...

d-4>-3

so what you do is you make it a equation

d-4=-3

you transfer the -4 to the other side by adding it on both sides

d=1

therfore d can 1 and any number above 1

I hope this helped

The amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares, and counted the number of trees with diameters exceeding 12 inches in each square is 16.67

In order to estimate the amount of lumber in a tract of timber, an owner will use a technique called sample size estimation.

By using this data, the owner can then calculate an estimate of the total amount of lumber present in the tract of timber.

In this case, the sample size is 70, the square size is 2500 square feet, and the diameter of the trees is 12 inches. Therefore, the formula becomes:

=> Total Trees = (Number of Trees in Sample / 70) x (2500 / 12).

If we plug in the number of trees counted in each square, we can find the total estimated number of trees in the tract of timber.

If the owner counted 7 trees in the first square, the formula would be

=> (7 / 70) x (2500 / 12) = 16.67.

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Complete Question:

To estimate the amount of lumber in a tract of timber, an owner randomly selected seventy 50-by-50-foot squares and counted the number of trees with diameters exceeding 12 inches in each square. The data are listed here.

7 9 8 10 3 7 7 9 9 11 7 9 5 5 10 10 9 8 2 8 5

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Explanation:- When they had asked, Round 468986 to the nearest thousand, You should know that :-

Th H T O

4 6 8 9 8 6

So, Here In Thousand place we have 8.

Then see the all numbers after 8 That is :-

8986

So 8986 is nearest to 9000

Therefore, answer will be 469000.

the answer is 469000 hope it help's

The rate of change of the surface area when the radius is 12 cm is approximately -0.033 cm^2 per minute.

To find the rate of change of the surface area when the radius is 12 cm, follow these steps:

1. Find the relationship between the volume (V) and the radius (r) of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3.

2. Differentiate V with respect to time (t) to find the rate of change of volume (dV/dt): dV/dt = 4πr^2(dr/dt).

3. We know the rate of change of volume (dV/dt) is -5 cm^3 per minute (gas is escaping, so the rate is negative). Plug this value into the equation: -5 = 4π(12^2)(dr/dt).

4. Solve for the rate of change of the radius (dr/dt): dr/dt = -5/(4π(12^2)).

5. Find the relationship between the surface area (A) and the radius (r) of the sphere. The formula for the surface area of a sphere is A = 4πr^2.

6. Differentiate A with respect to time (t) to find the rate of change of surface area (dA/dt): dA/dt = 8πr(dr/dt).

7. Plug in the known values (r = 12 cm and dr/dt from step 4) into the equation: dA/dt = 8π(12)(-5/(4π(12^2))).

8. Simplify and calculate the rate of change of the surface area: dA/dt ≈ -0.033 cm^2 per minute.

So, the rate of change of the surface area when the radius is 12 cm is approximately -0.033 cm^2 per minute.

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Rate of change of the surface area when the radius is 12 cm and the gas is escaping at a rate of 5 cm³/min is approximately -0.65 cm²/min.

We are given that the rate of gas escaping the spherical balloon is 5 cm³/min. This means that the rate of change of volume, dV/dt, is -5 cm³/min (since the volume is decreasing).

The formula for the volume of a sphere is:

V = (4/3)πr³

Differentiating with respect to time, we get:

dV/dt = 4πr²(dr/dt)

where dr/dt is the rate of change of the radius with respect to time.

Solving for dr/dt, we get:

dr/dt = (dV/dt) / (4πr²)

Substituting the given values, we get:

dr/dt = (-5 cm³/min) / (4π(12 cm)²) = -0.00215 cm/min (Note that the negative sign indicates that the radius is decreasing.)

Now, we need to find the rate of change of surface area, dA/dt. Using the formula for the surface area of a sphere, A = 4πr², we can differentiate with respect to time using the chain rule:

dA/dt = dA/dr * dr/dt

where dA/dr is the rate of change of surface area with respect to the radius.

Differentiating A = 4πr² with respect to r, we get:

dA/dr = 8πr

Substituting the given value, we get:

dA/dr = 8π(12 cm) = 301.59 cm²

Finally, substituting both values into the chain rule equation, we get:

dA/dt = (301.59 cm²) * (-0.00215 cm/min) ≈ -0.65 cm²/min

Therefore, the rate of change of the surface area when the radius is 12 cm and the gas is escaping at a rate of 5 cm³/min is approximately -0.65 cm²/min.

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Following are the mathematical operations for the numerics.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. Image: The basic mathematical operation symbols. A set of numbers and operations make up a mathematical expression.

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Answer:

I think its the one on the bottom right

Step-by-step explanation:

Answer:

bottom right is the answer i think

Answer:

A possible solution is she should by 6 bags of popcorn and 10 drinks

Step-by-step explanation:

The price of each bag of popcorn = $7.50

The price of each drink = $4.50

The amount Sarah has to spend = $90

The number of bags of popcorn and drinks Sarah must buy = 16 bags of popcorn and drinks

Let the number of bags of popcorn purchased be represented by x and the number of drinks purchased be represented by y

Therefore, we have;

x + y ≥ 16.....(1)

x × 7.5 + y × 4.5  ≤ 90

Which gives;

7.5·x + 4.5·y ≤ 90....(2)

Rewriting the inequalities as a function of y, gives;

From inequality (1), x + y ≥ 16, we have;

y = ≥ 16 - x

From inequality (2), 7.5·x + 4.5·y ≤ 90, we have;

7.5·x + 4.5·y ≤ 90

4.5·y ≤ 90 - 7.5·x

y ≤ 90/4.5 - 7.5/4.5·x

y ≤ 20 - 5/3·x

Please find attached, the plot of the inequalities

A possible solution is given as the value of x = 6, where y = 10

Therefore, she should by 6 bags of popcorn and 10 drinks.

The vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

To find a vector parallel to the line of intersection of the planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7, we first need to find the direction vector of the line of intersection.

We can find the direction vector by taking the cross product of the normal vectors of the two planes. The normal vector of the plane 2x - 3y + 5z = 2 is <2, -3, 5>, and the normal vector of the plane 4x + y - 3z = 7 is <4, 1, -3>. Taking the cross product of these two vectors, we get:

<2, -3, 5> × <4, 1, -3> = <-16, 22, 11>

This vector <-16, 22, 11> is the direction vector of the line of intersection of the two planes.

To find a vector parallel to this line, we can simply multiply the direction vector by a scalar. For example, we can choose a scalar of 2 to get:

2<-16, 22, 11> = <-32, 44, 22>

Therefore, the vector <-32, 44, 22> is parallel to the line of intersection of the two planes given by the equations 2x - 3y + 5z = 2 and 4x + y - 3z = 7.

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if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

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The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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Given:

A figure of an angle.

To find:

The parts of the angle.

Solution:

From the given figure, it is clear that the vertex point of the given angle is I.

The starting point of two rays is point I.

First ray is starting from the point I and passes through the point J. So, the name of ray is \(\overrightarrow{IJ}\).

Second ray is starting from the point I and passes through the point H. So, the name of ray is \(\overrightarrow{IH}\).

Two parts of the given angle are \(\overrightarrow{IJ}\) and \(\overrightarrow{IH}\).

Therefore, the correct options are D and F.

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A sample size of approximately 37 is needed to estimate the mean hemoglobin level of 11-year-old boys with a margin of error no greater than 0.5 g/dl and a 95% confidence level.

a) In order to estimate the mean hemoglobin level (μ) of 11-year-old boys with a margin of error no greater than 0.5 g/dl and a 95% confidence level, we need to determine the sample size. The margin of error is calculated by multiplying the critical value (z*) with the standard deviation (σ) divided by the square root of the sample size (n). Given that the standard deviation is 1.2 g/dl, we can rearrange the formula to solve for n:

Margin of Error = z* * (σ / sqrt(n))

We want the margin of error to be no greater than 0.5 g/dl, so we can plug in the values:

0.5 = z* * (1.2 / sqrt(n))

To find the appropriate critical value (z*) for a 95% confidence level, we can refer to the standard normal distribution table or use a calculator. Assuming a z* value of approximately 1.96, we can substitute the values and solve for n:

0.5 = 1.96 * (1.2 / sqrt(n))

By squaring both sides of the equation and solving for n, we find that the sample size needed is approximately 37.

b) To estimate the mean hemoglobin level (μ) with a margin of error of 0.5 g/dl and a 99% confidence level, we follow a similar approach. The only difference is the critical value (z*) for a 99% confidence level. Assuming a z* value of approximately 2.58, we can substitute the values into the formula:

0.5 = 2.58 * (1.2 / sqrt(n))

By squaring both sides of the equation and solving for n, we find that the sample size needed is approximately 90.

In summary, a sample size of approximately 37 is needed to estimate the mean hemoglobin level of 11-year-old boys with a margin of error no greater than 0.5 g/dl and a 95% confidence level. Alternatively, a sample size of approximately 90 is required to achieve the same margin of error but with a higher confidence level of 99%.  

The explanation for determining the sample size involves using the formula for margin of error and rearranging it to solve for the sample size (n). By plugging in the given values of the standard deviation and the desired margin of error, we can calculate the critical value (z*) for the specific confidence level. Using this critical value, we can substitute the values back into the formula and solve for n. In the first scenario, where a 95% confidence level is desired, a z* value of approximately 1.96 is used. In the second scenario, with a 99% confidence level, a z* value of approximately 2.58 is utilized. The resulting equations are then squared to isolate n and determine the required sample size.  

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Answer:

30 and 21

Step-by-step explanation:

Answer: 6000 milligrams

Step-by-step explanation:

Multiply 6 by 1000

Answer:

Step-by-step explanation:

60

11/12 - 3/4 = 1/6

1/2 + 4/9 = 17/18

11/12 - 3/4

= 11-9/12

= 2/12

= 1/6

1/2 + 4/9

= 9+8/18

= 17/18

Hence the solution to the expression in it's simplest form is 1/6 and 17/18

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Answer:

1/6and 17/18

Step-by-step explanation:

11/12-3/4

find the l.c.m

11/12-3/4=11-9/12=2/12=1/6

1/2+4/9=9+8/18=17/18

hope it helps please mark brainliest

A hotel has a rectangular shaped meeting room that is 13.4 yards wide and 15.1 yards long. If the carpenter cost $ 1.71 per feet² what would be the cost of carpenting the room ?

Given :

Need to find :

Solution :

THIS QUESTION IS BASED ON MEANSURATION TO SOLVE THIS QUESTION FIRST WE WILL CALCULATE THE AREA OF THE MEETING ROOM AND THEN WE WILL CALCULATE THE COST OF CARPENTING THE MEETING ROOM.

Calculating the area of the meeting room

\( \star \: \large \boxed{\sf{ Area_{(rectangle)} = Length × Breadth }}\)

\( \large\rm{ Area_{(rectangle)} = (15.1 × 13.4) yard² = 202.34 \: yards²}\)

Area of the meeting room = 202.34 yard²

Calculating the cost of carpenting the meeting room

First we will convert yards into feet

We know,

1 yard = 3 feet

202.34 yard = 202.34 × 3 = 607.02 feet

Now calculating the cost of carpenting the meeting room

Rate of carpenting = $ 17.1 per feet²

Cost of carpenting = $ ( 17.1 × 607.02) = $10,380.04

Final Answer -

\( \rule{180pt}{3pt}\)

By direct evaluation of the exponential function f(x) = a · 2ˣ we conclude that the proposition "f(0) = 3 when a = 3" is the only true. (Correct choice: B)

Herein we should analyze an exponential function of the form f(x) = a · 2ˣ and find what proposition is true by direct evaluation:

x = 0

2 = a · 2⁰

a = 2

x = 0

3 = a · 2⁰

a = 3

x = 1

9 = a · 2

a = 9/2

By direct evaluation of the exponential function f(x) = a · 2ˣ we conclude that the proposition "f(0) = 3 when a = 3" is the only true. (Correct choice: B)

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Answer:

.31

Step-by-step explanation:

the United States Air Force has 19 women for every 81 men enlisted in a squadron has 750 member approximately how many women round your answer to the nearest whole number ​

we have that

Let

x -----> the number of women

y ----> the number of men

so

x+y=750 -------> equation A

x/y=19/81--------> y/x=81/19

y=(81/19)x ------> equation B

substitute equation B in equation A

x+(81/19)x=750

solve for x

(100/19)x=750

x=(750*19)/100

x=142.5

therefore

Answer:

\( {a}^{6} {b}^{2} \)

solution

\( {a}^{3} \times b \times {a}^{3} \times b \\ = {a}^{3 + 3} \times {b}^{1 + 1} \\ = {a}^{6} {b}^{2} \)

hope this helps...

Good luck on your assignment..

Answer:

\(a^{6}b^{2}\)

Step-by-step explanation:

\(a^3 \times b \times a^3 \times b\)

If there are no exponents written, then the exponent is 1.

\(a^3 \times b^1 \times a^3 \times b^1\)

When multiplying two powers that have the same base, you can add the exponents.

\(a^{3+3} \times b^{1+1}\)

\(a^{6} \times b^{2}\)

Answer:

Below

Step-by-step explanation:

35 choices for first number

34 choices for second number (because it cannot be same as first)

34 choices for third number  ( because it cannot be same a second)

35 x 34 x 34 = 40 460 combos

Answer:

There will need to be 2 and 1/3 cups of flour according to the recipe

Step-by-step explanation:

Given the recipe, we can say that for each 2 and 2/3s cups of milk, one cup of flour is used. We can write this as ( 2 + 2/3)  cups of milk / (1) cup of flour.

We can also write 2 + 2/3 as 2*(3/3) + 2/3 = 6/3 + 2/3 = 8/3, making our ratio

(8/3) / 1

The ratio stays the same, no matter how many cups of milk or flour are used. Therefore, (8/3) /1 = (4 + 2/3) / cups of flour

Writing our final cups of flour as c, we can say

(8/3) / 1 = (4+2/3) / c

(4+2/3)/c = (12/3 + 2/3) /c = (14/3) /c

(8/3)/1 = (14/3) /c

anything divided by 1 is equal to itself

(8/3) = (14/3)/c

multiply both sides by c to make the variable not a denominator

(8/3) * c = 14/3

multiply both sides by 3 to remove the denominators

8 * c = 14

divide both sides by 8 to isolate the c

c = 14/8 = 7/3 = 6/3 + 1/3 = 2 + 1/3

There will need to be 2 and 1/3 cups of flour according to the recipe

Answer:

1/3

Step-by-step explanation:

First find the LCD or least common denominator. The least common denominator is the number that both of the denominators are divisible by.

In this case, 2 and 3 are both divisible by 6.

Convert both fractions into a fraction with a denominator of 6.

1/2 = 3/6 (multiply numerator and denominator by 3)

2/3 = 4/6 (multiply numerator and denominator by 2)

Now you can multiply as they have the same denominator.

3/6 × 4/6 = 12/36

Simplify.

12/36 = 1/3 (numerator and denominator are divisible by 12)

Hope that helps.

Answer:

113.081 mm²

Step-by-step explanation:

A semicircle is the half part of a circle. And we know that the semicircle have 24 mm of diameter, and the radius is 24/2 = 12 mm. The small circle is inside the semicircle, so its diameter is equal to the radius of the semicircle, and its radius is 12/2 = 6mm

Now, consider π = 3.141, the area of the small circle is:

π•6² = 3.141 • 36 = 113.076 mm²

The area of the semicircle is (π•12²)/2 = (3.141•144)/2 = 226.151 mm²

Now, you just subtract the areas:

226.151 - 113.076 = 113.081 mm²

Marginal Revenue is negative, the firm should consider reducing its output to increase its total revenue.

Therefore, correct answer will be a. increase.

Marginal Revenue (MR) is a crucial concept in economics that measures the change in a firm's total revenue as a result of selling one additional unit of output. MR is used by firms to make decisions about how much output to produce and what price to charge.

In a linear (inverse) demand function, MR is negative when the elasticity of demand is less than one, meaning that the demand for a product is relatively inelastic. In other words, as the firm increases output, the price will decrease, causing total revenue to decline.

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Data collected over several time periods are called time series data.

Time series data refers to data that is collected over several time periods. It captures a sequence of observations of a variable of interest over time, such as sales figures, stock prices, temperature, and so on. The observations are usually taken at regular intervals, such as daily, weekly, monthly or yearly, and the data reflects the changes in the variable over time.

Time series data is useful for identifying trends, patterns, and seasonality in the data, and for making predictions about future values. It's often used in economic forecasting, weather forecasting, and other fields where understanding how a variable changes over time is important.

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1 yard = 3 feet

3ft * 2 yards = 6 feet

$1.26 / 6ft = $0.21 / ft