Use Chebyshev's inequality to bound P(X - Y > 1). We can say that P(X - Y > 1) is less than or equal to 27/23(9).
Using Markov's inequality, we have:
P(X - Y > 1) <= E(X - Y) / 1
We know that E(X - Y) = E(X) - E(Y) = 10/3 - 1/3 = 3, and plugging this in gives:
P(X - Y > 1) <= 3 / 1 = 3
Therefore, we can say that P(X - Y > 1) is less than or equal to 3.
Using Chebyshev's inequality, we have:
P(|X - E(X)| > k*σ) <= 1/k^2
Since we want to find an upper bound for P(X - Y > 1), we can rewrite the expression as:
P(X - Y - E(X - Y) > 1) <= P(|X - E(X)| + |Y - E(Y)| > 1)
Using the triangle inequality, we have:
P(|X - E(X)| + |Y - E(Y)| > 1) <= P(|X - E(X)| + |Y - E(Y)|) / 1
Now, we need to find the variance of X - Y. Since X and Y are independent, Var(X - Y) = Var(X) + Var(Y) = (10/3)(2/3) + 1/9 = 23/27. Therefore, σ = sqrt(23/27), and plugging in k = 3 gives:
P(X - Y - E(X - Y) > 1) <= P(|X - E(X)| + |Y - E(Y)| > 1) <= P(|X - E(X)| + |Y - E(Y)|) / 3 <= 27/23(3^2)
Simplifying the expression, we get:
P(X - Y > 1) <= 27/23(9)
Therefore, we can say that P(X - Y > 1) is less than or equal to 27/23(9).
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Using Chebyshev's inequality, we can say that P(X - Y > 1) is less than or equal to 9/25.
Markov's inequality states that for any non-negative random variable X and any t > 0, we have:
P(X ≥ t) ≤ E(X) / t
In this case, we want to find an upper bound for P(X - Y > 1). Using Markov's inequality, we have:
P(X - Y > 1) ≤ E(X - Y) / 1
Now, let's find the expected value E(X - Y):
E(X - Y) = E(X) - E(Y)
The expected value of a binomial distribution with parameters n and p is given by E(X) = np, so we have:
E(X - Y) = E(X) - E(Y) = (10)(1/3) - (1/3) = 3 - 1/3 = 8/3
Substituting this into the inequality, we have:
P(X - Y > 1) ≤ (8/3) / 1
Simplifying, we get:
P(X - Y > 1) ≤ 8/3
Therefore, using Markov's inequality, we can say that P(X - Y > 1) is less than or equal to 8/3.
Now let's use Chebyshev's inequality:
Chebyshev's inequality states that for any random variable X with finite mean μ and finite variance σ^2, and any positive constant k, we have:
P(|X - μ| ≥ kσ) ≤ 1 / k^2
In this case, we want to find an upper bound for P(X - Y > 1). First, we need to find the mean and variance of X - Y.
The mean of X - Y is given by:
E(X - Y) = E(X) - E(Y) = (10)(1/3) - (1/3) = 3 - 1/3 = 8/3
The variance of X - Y is given by the sum of the variances of X and Y, since they are independent:
Var(X - Y) = Var(X) + Var(Y)
The variance of a binomial distribution with parameters n and p is given by Var(X) = np(1 - p), so we have:
Var(X - Y) = Var(X) + Var(Y) = (10)(1/3)(2/3) + (1/3^2) = 20/9 + 1/9 = 21/9 = 7/3
Now, let's apply Chebyshev's inequality:
P(X - Y > 1) = P((X - Y) - (8/3) > 1 - (8/3))
= P((X - Y) - (8/3) > -5/3)
= P(|X - Y - (8/3)| > 5/3)
Since the variance of X - Y is 7/3, we can use Chebyshev's inequality with k = 5/3:
P(|X - Y - (8/3)| > 5/3) ≤ 1 / (5/3)^2
= 1 / (25/9)
= 9/25
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Can anyone help me with this question?
Solve -2x^2 + 5x + 12 > or = 0
Answer: its 3.7 but you have to round.
Step-by-step explanation:
Determine the type of dilation shown and the scale factor used.
Enlargement with scale factor of 1.5
Enlargement with scale factor of 2.5
Reduction with scale factor of 1.5
Reduction with scale factor of 2.5
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Ratio of side of bigger rectangle to that to corresponding side of smaller rectangle (as they are similar) is :
[tex]\qquad \sf \dashrightarrow \: \dfrac{15}{6} [/tex]
[tex]\qquad \sf \dashrightarrow \: 2.5[/tex]
So, the bigger rectangle is a scaled up version of the smaller version with a scale factor of 2.5
So, our required answer will be :
Enlargement with scale factor of 2.5
Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 262626 thousand dollars and 222 thousand dollars, respectively. Suppose we select one of these cars at random. Let x=x=x, equals the sale price (in thousands of dollars) for the selected car. Find p(26
The probability of P(26 < X < 30) is 0.48.
In this case, the given parameters are:
Mean μ = 26
Standard deviation σ = 2
So, the probability P(26 < X < 30) will be represented as:
P(26 < X < 30)
= P(z1 < z < z2)
where:
z = (X – μ) / σ
Thus, now we have:
P(26 < X < 30)
= P((26 – 26) / 2 < z < (30 – 26) / 2)
= P(0 / 2 < z < 4 / 2)
= P(0 < z < 2)
= P(z < 2) – P(z < 0)
For z-score of probabilities, we have:
P(26 < X < 30)
= P(z < 2) – P(z < 0)
= 0.97725 – 0.5
= 0.47725
= 0.48
Hence, the probability of P(26 < X < 30) is 0.48.
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Although part of your question is missing, you might be referring to this full question: Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively. Suppose we select one of these cars at random. Let X represent the sale price (in thousands of dollars) for the selected car. Find P(26< X<30).
Solve each equation: Be sure to check the solutions:
1. X^2+17x+42=0
2. t^2-26t=56
3. y^2-84=5y
4. 17r+r^2=-52
PLEASE ANSWER QUICK!!!!!!!!!
Answer:
(1)... x1 = -14, x2 = -3
(2)... t1 = -2, t2 = 28
(3)... y1 = -7, y2 = 12
(4)... r1 = -13, r2 = -4
Step-by-step explanation:
Answer:
1.
[tex] {x}^{2} + 17x + 42 = 0 \\ using \: quadratic \: equation \: formula \\ x = \frac{ - 17± \sqrt{ {17}^{2} - 4 \times 1 \times 42 } }{2 \times 1} \\ x = \frac{ - 17±11}{2} \\ for \: x = \frac{ - 17 + 11}{2} \\ x = - 3 \\ for \: x = \frac{ - 17 - 11}{2} \\ x = - 14[/tex]
Answer for 1 : x=-3, x=-14
2.
[tex]t^2-26t=56 \\ also \: using \: quadratic \: equation \\ t = 28 \: or \: t = - 2[/tex]
Answer for 2: t=28, x=-2
3.
[tex]y^2-84=5y \\ {y}^{2} - 5y - 84 = 0 \\ applying \: quadratic \: equation \\ y = 12 \: or \: y = - 7[/tex]
Answer for 3: y=12, y=-7
4.
[tex]17r+r^2=-52 \\ {r}^{2} + 17r + 52 = 0 \\ r = - 4 \: or \: r = - 13[/tex]
Answer for 4: r=-4, r=-13
What is the coefficient of 3x²?
So on solving the provided question we can say that here, coefficient of 3x² is 3
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of 3x² is 3
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A triangular park with ide 115m, 81. 63m and 69. 27 m, ha to be fenced. Find the cot of fencing at the rate of ₹18. 50 per metre
The cost of fencing the triangular park at the rate of ₹18.50 per meter is ₹4903.65
To find the cost of fencing a triangular park with sides measuring 115m, 81.63m, and 69.27m, we first need to calculate the perimeter of the triangle. The perimeter of any two-dimensional figure is defined as the distance around the figure. We can calculate the perimeter of any closed shape just adding up the length of each of the sides.
Perimeter of triangle= Sum of the three sides
To do this, we add up the lengths of all three sides: 115m + 81.63m + 69.27m = 265.9m.
We can then multiply the perimeter by the cost per meter of fencing to find the total cost: 265.9m * ₹18.50/m = ₹4903.65.
So the cost of fencing the triangular park at the rate of ₹18.50 per meter is ₹4903.65
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An angle bisector of a triangle divides the opposite side of the triangle into segments 7 cm and 9 cm long. A second side of the triangle is 22.5 cm long. Find all possible lengths for the third side of the triangle
The other possible length for the third side of the triangle is 15 cm.
What is an Angle Bisector Theorem?
An angle bisector of a triangle divides the opposite side of the triangle into segments that are in the same ratio as the other two sides of the triangle. This is called the Angle Bisector Theorem.
Given that the angle bisector divides the opposite side into segments of 7 cm and 9 cm, the ratio of the other two sides of the triangle must also be 7:9.
Since the second side of the triangle is 22.5 cm, the third side must be:
x = (22.5 * 9) / 7 = 27 cm
So, the third side of the triangle is 27 cm.
The other side can be calculated by using the Pythagorean theorem.
c^2 = a² + b²
b = √(c² - a²)
b = √((27)² - (22.5)²)
b = √(729 - 506.25)
b = √222.75 = 15cm
Hence, The other possible length for the third side of the triangle is 15 cm.
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Segment JK has endpoints J(2,4) and K(6,2). You dilate the segment using a dilation centered at the origin with a scale factor of 1/2 and then reflect the image over the x-axis. Where is the final image of K?
The location of the point k after dilation and reflection over the x-axis is (3,-1).
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that Segment JK has endpoints J(2,4) and K(6,2). You dilate the segment using a dilation centered at the origin with a scale factor of 1/2 and then reflect the image over the x-axis.
Dilation of the point will be,
J(2,4) = j'(1,2
K(6,2) = k'(3,1)
The reflection over the x-axis of point k is,
k'(3,1) = ( 3,-1)
Hence, the point k will be (3,-1)
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What is the roots of the equation x² 7x 10?
Answer:
-5 and -2
Step-by-step explanation:
is this ordered pair a (-1,3) a solution to the inequality
Yes, The ordered pair (-1,- 3) is a solution to the inequality y > -5x⁴ + 7x³ + 8.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ y > -5x⁴ + 7x³ + 8.
And, The point is (- 1, - 3).
Now, We can substitute the value of (x, y) = (- 1, - 3) in given inequality and check as;
⇒ y > -5x⁴ + 7x³ + 8.
⇒ -3 > -5(-1)⁴ + 7(-1)³ + 8
⇒ -3 > -5 + 7 × - 1 + 8
⇒ - 3 > - 5 - 7 + 8
⇒ - 3 > - 4
This is true.
Thus, The ordered pair (-1,- 3) is a solution to the inequality
y > -5x⁴ + 7x³+ 8.
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The complete question is this,
The ordered pair (-1,- 3) is a solution to the inequality y >-5x⁴ + 7x³ + 8.
1) True
2) False
Work out the perimeter of a semicircle the radius 3cm give you answer I’m terms of pi
The perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.
What is perimeter of a semicircle?The complete length of a semicircle's boundary is referred to as the circumference of a semicircle, which is another name for its perimeter. The diameter's length and one-half of the original circle's circumference are added to determine it. Linear units such as "inches," "feet," "metres," or "centimetres," etc. are used to indicate the circle's circumference.
Given that the radius of the semicircle is 3cm.
The formula for the perimeter of a semicircle is:
P = pi(r) + 2r
Substituting the value of r = 3 we have:
P = pi(3) + 2(3)
P = 6 + 3pi
Hence, the perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.
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Calculate The length of a staircase that is 3.2m and has a standard height of 4.7 m
answer: hello
Step-by-step explanation:
If you get the answer then tell me
Ix time a number le 20 i the ame a four time the number increaed by 6. Find the number
The number is 14. Dividing both sides by 4 gives -4 = 4 × number, which can be further simplified to number = -4 ÷ 4. This means that the number is 14.
20 = 4 × (number + 6)
20 = 4 × number + 24
20 - 24 = 4 × number
-4 = 4 × number
number = -4 ÷ 4
number = -1
The equation provided is 20 = 4 × (number + 6). Rearranging this equation gives 20 = 4 × number + 24. Subtracting 24 from both sides gives 20 - 24 = 4 × number. Dividing both sides by 4 gives -4 = 4 × number. Dividing both sides by 4 once again gives number = -4 ÷ 4. Therefore, the number is 14.
To find the number in the equation given, we can first rearrange the equation so it is in the form of 20 = 4 × number + 24. Then, subtracting 24 from both sides gives us 20 - 24 = 4 × number. Dividing both sides by 4 gives -4 = 4 × number, which can be further simplified to number = -4 ÷ 4. This means that the number is 14.
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A fair die has its faces numbered from 1 to 6. Let random variable f represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3. 5 and standard deviation 1. 7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded.
A fair dice has its faces numbered from 1 to 6. Let random variable f represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3. 5 and standard deviation 1. 7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded. The mean of the distribution of sample means is 3.5 and the standard deviation of the distribution of sample means is 0.0854.
The mean of the distribution of sample means
μ = 3.5
The standard deviation of the distribution of sample means can be calculate as follows:
σₓ = σ/√n
σₓ = 1.7078/√400
σₓ = 0.0854
Thus, the right answer is provided by the data of Mean 3.5 and Standard Deviation 0.0854.
Your question is incpmplete but most probably your full question was
fair die has its faces numbered from 1 to 6. Let random variable F represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5
and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 imes, and the mean of the 5 values landing face up is recorded.
The mean and standard deviation of the results of the simulation should be
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Please help cause this is due tmrw and I don’t know it
The dimensions of the rectangle are y - 4y−4 for the length and 3y3y for the width
What is area of a rectangle?To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.We calculate the area of a rectangle to find the area occupied by the rectangle within its perimeter.In geometry, area of rectangle is the region covered by the rectangle in a two-dimensional plane. A rectangle is a type of quadrilateral, a 2d shape that has four sides and four verticesThe area of the rectangle is the region occupied by the sides of the rectangle. The area of the rectangle based on its dimensions is:3y(y-4)-3y²-12yThe dimensions of the rectangle are y - 4y−4 for the length and 3y + 53y+5 for the width. The area of the rectangle based on its dimensions is:(3y+5)(y-4)-3y²-7y-20To learn more about area of a rectangle refers to:
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FIRST WITH RIGHT ANSWER GETS BRAINIEST
(100 Points)
Select all that are true.
(Picture Below)
Answer:
C and D----------------------------------
Simplify each product and compare with the right side:
A)
3/8 × 54 = 3/4 × 27 = 81/4 = 20 1/4, incorrectB)
5/12 × 26 = 5/6 × 13 = 65/6 = 10 5/6, incorrectC)
11/15 × 20 = 11/3 × 4 = 44/3 = 14 2/3, correctD)
3/8 × 48 = 3 × 6 = 18, correctE)
7/12 × 48 = 7 × 4 = 28, incorrectAnswer:
3 and 4
Step-by-step explanation:
Evaluate each given expression.
Expression 1
[tex]\begin{aligned} \implies \dfrac{3}{8} \times 54 & =\dfrac{3\times54}{8}\\\\&=\dfrac{162}{8}\\\\&=\dfrac{162 \div 2}{8 \div2}\\\\&=\dfrac{81}{4}\\\\&=20\; \rm r\;1\\\\&=20\frac{1}{4}\end{aligned}[/tex]
Therefore, as 20⁵/₆ ≠ 20¹/₄ the equation is not true.
Expression 2
[tex]\begin{aligned} \implies \dfrac{5}{12} \times 26 & =\dfrac{5 \times 26}{12}\\\\&=\dfrac{130}{12}\\\\&=\dfrac{130\div2}{12\div2}\\\\&=\dfrac{65}{6}\\\\&=10\;\rm r\;5\\\\&=10\dfrac{5}{6}\end{aligned}[/tex]
Therefore, as 9³/₄ ≠ 10⁵/₆ the equation is not true.
Expression 3
[tex]\begin{aligned}\implies \dfrac{11}{15} \times 20 & =\dfrac{11 \times 20}{15}\\\\&=\dfrac{220}{15}\\\\&=\dfrac{220\div5}{15\div5}\\\\&=\dfrac{44}{3}\\\\&=14\; \rm r \;2\\\\&=14\dfrac{2}{3}\end{aligned}[/tex]
Therefore, as 14²/₃ = 14²/₃ the equation is true.
Expression 4
[tex]\begin{aligned} \implies\dfrac{3}{8} \times 48 & =\dfrac{3\times 48 }{8} \\\\& =\dfrac{144}{8} \\\\& =\dfrac{18 \times \diagup\!\!\!\!8}{\diagup\!\!\!\!8}\\\\&=18\end{aligned}[/tex]
Therefore, as 18 = 18 the equation is true.
Expression 5
[tex]\begin{aligned} \implies\dfrac{7}{12} \times 48 & =\dfrac{7\times 48 }{12} \\\\&=\dfrac{336}{12}\\\\&=\dfrac{28 \times 12}{12}\\\\&=28\end{aligned}[/tex]
Therefore, as 21 ≠ 28 the equation is not true.
2n>20 Solve the inequality. Graph the solution.
Answer:
n>10
Step-by-step explanation:
2n>20
n>20/2
n>10
What kind of a triangle it is if the lengths of the sides are 6cm 10cm and 13cm respectively?
one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.
An obtuse triangle is a triangle that has one angle which measures greater than 90 degrees. In order to determine if a triangle is an obtuse triangle, we need to calculate its angles.
To calculate the angles of the triangle, we can use the following formula:
Angle 1 = arccos ( (b2 + c2 - a2) / 2bc )
Angle 2 = arccos ( (a2 + c2 - b2) / 2ac )
Angle 3 = arccos ( (a2 + b2 - c2) / 2ab )
In this case, a = 6cm, b = 10cm, and c = 13cm. Substituting these values into the formula, we get:
Angle 1 = arccos ( (102 + 132 - 62) / 2 x 10 x 13 ) = 89.99 degrees
Angle 2 = arccos ( (62 + 132 - 102) / 2 x 6 x 13 ) = 110.01 degrees
Angle 3 = arccos ( (62 + 102 - 132) / 2 x 6 x 10 ) = 89.99 degrees
Since one of the angles measures greater than 90 degrees (110.01 degrees), this is an obtuse triangle.
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Is it possible to make a right angled triangle with the given sides 2.5 cm 6.5 cm 6 cm justify your answer if possible which is the hypotenuse?
It is possible to construct a triangle whose sides are 2.5 cm 6.5 cm and 6 cm because the sum of two sides are greater than three sides. 6.5 is the hypotenuse of the triangle because it is the largest length.
In the given question, we have to check that it is possible to construct a triangle whose sides are 2.5 cm 6.5 cm and 6 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 2.5 and 6.5
2.5 + 6.5 > 6
9 > 6
Now we add 2.5 and 6
2.5 + 6 > 6.5
8.5 > 6.5
Now we add 6.5 and 6
6.5 + 6 > 2.5
12.5 > 2.5
It is possible to construct a triangle whose sides are 2.5 cm 6.5 cm and 6 cm because the sum of two sides are greater than third sides.
As we know that the largest length is the hypotenuse of the triangle. So 6.5 is the hypotenuse of the triangle because it is the largest length.
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Solve for x.
8 = 2x+ 4
what does x=
Answer: x = 2
Step-by-step explanation:
8 = 2x + 4
2x = 8-4
= 4
x = 4 ÷ 2
= 2
x = 2
What it would look like if it was an actual equation :
8 = 2₂ + 4
Answer:
x = 2
Simple Algebraic EquationsTerminology
Variable: Any letter than stands for a value than can be solved and change value.
Coefficient: The number right before a variable (without being separated by an operator). It is a multiplication factor for a variable. Basically, it's just a way to express what you are multiplying a variable by,
If the coefficient is 1, it means [variable] * 1. 1[variable]
If the coefficient is 3, it means [variable] * x. 3[variable]
etc.
Constant: A fixed value (i.e. 3, 8, 1928). A variable is not a constant because if you were to add a coefficient (not including 0) to the start of a variable, the result would change depending on the value of the variable.
How to Solve
To solve, you must isolate the variable. It means moving the variable and it's coefficient to the other side of the equation with only the same variable on the same side with all the constants on the other side.
Do this with this rule that is extremely important in ALL of math beyond per-algebra and algebra.
Rule
If you multiply, divide, add, subtract, square root, exponent both sides of the equation by the same value, that end value stays the same. That is how you solve for it.
Q)Subtract 4 on both sides to isolate the variable.
8 - 4 = 2x + 4 - 4
Simplify by combining like terms.
4 = 2x
Divide 2 on both sides to solve for x as the coefficient is currently 2.
[tex]\frac{4}{2} =\frac{2x}{2}[/tex]
Simplify.
x = 2
Please Help me!!!! Sorry for the small picture!!
Answer:
Please see attached.
Step-by-step explanation:
what is 1+1+6+5+8+(+(+8+*8766735
Answer:
your answer is 561,072,052
A square has an area of 100square meters. What is the perimeter of the square?
The perimeter of a square with an area of 100 square meters is calculated to be 40 m
How to find the perimeter of the squareThe perimeter of a square is calculated using the formula 4 * length
Some necessary properties of a square
A square is a four sided polygon otherwise known as quadrilateral
All the sides are equal hence Length = width or breadth
The angles at which each side intersect is at 90 degrees
The area of a square is Length² hence
Length² = 100
Length = √100
Length = 10
plugging in Length = 10 to the perimeter
P = 4 * length
P = 4 *10
P = 40 m
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Is a coordinate plane 2 dimensional?
Yes, a coordinate plane 2 dimensional
A coordinated plane is an area formed by the intersection of two lines and so is called 2-Dimensional. The horizontal line is called X-axis and the vertical line is called Y-axis. The intersection point of these two lines is called origin.
Coordinates are set of two numbers used to locate a specific point on the plane. They are represented in form of (x,y). The points can be positive zero or negative. They are used to plot graphs pin points draw lines etc.
A coordinated plane has 4 quadrants. A quadrant can be defined as a region on a plane where both X,Y axis is perpendicular. They are:
First quadrant: x > 0, y > Second quadrant: x < 0, y > 0Third quadrant: x < 0, y < 0Fourth quadrant: x > 0, y < 0.To know more about the coordinated plane visit:
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Which of the following best describes a chord?
A. A line segment from the center of a circle to any point on the circle
B. A line segment that intersects a circle at exactly one point
C. A line segment that is on the outside of a circle
D. A line segment that has both endpoints on a circle
Chord of a circle is a straight line segment whose endpoints both lie on the circle.
Which line is referred to as a chord?A chord is a line segment that connects any two locations on the circle’s circumference.A straight line segment that connects and includes two points on a circle. A straight line connecting two points on a curve. 3.: an unique mood or temperament. I hit a responsive chord.
A chord is a line segment that connects two points on a curve in plane geometry. The word is frequently used to denote a line segment with endpoints on a circle. A chord is a line segment that connects two points on any curve, such as an ellipse. The diameter of a circle is defined as a chord that goes through its center point. The word chord is derived from the Latin chorda, which means bowstring.
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evaluate the integral (3 to 0) ( x2 + 9)^0.5 dx
The value of the expression: [tex]\int\limits^0_3 {( x^2 + 9)^{0.5}} \, dx[/tex] will be: [tex]\frac{1}{1.5} [18^{1.5}\times 36][/tex]
We have to determine the value of the expression: [tex]\int\limits^0_3 {( x^2 + 9)^{0.5}} \, dx[/tex]
First solving the expression without using the values of Limits:
As we can write the above as:
[tex]\int {( x^2 + 9)^{0.5}} \, dx \\\frac{1}{0.5+1}[( x^2 + 9)^{0.5+1}] \times \frac{x^3}{3} +9x[/tex]
As we know, [tex]\int{x^n} \, dx =\frac{1}{n+1}x^{n+1}[/tex], where, n is any number.
So we can write the above as:
[tex]\\\frac{1}{1.5}[( x^2 + 9)^{1.5} \times \frac{x^3}{3} +9x][/tex]
Now we will put the value of limits in the above expression:
First putting the lower limit, i.e. the value of x = 3
We will get it as:
[tex]\frac{1}{1.5}[( 3^2 + 9)^{1.5} \times (\frac{3^3}{3} +9\times 3)]\\\frac{1}{1.5} [18^{1.5}\times (9+27)]\\\frac{1}{1.5} [18^{1.5}\times 36][/tex]
Now putting the value of lower limit, i.e the value of x = 3,
We will get it as:
[tex]\frac{1}{1.5}[( 0^2 + 9)^{1.5} \times ({\frac{0^3}{3} +9\times 0)}]\\\frac{1}{1.5} [9^{1.5}\times ({0+0})]\\\frac{1}{1.5} [9^{1.5}\times 0]=0[/tex]
Now, for detemining the value of the expression,
We will subtract the value of lower limit from upper limit
We will get it as; [tex]\frac{1}{1.5} [18^{1.5}\times 36][/tex]
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When Han makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup. Here is a table that shows how to make batches of different sizes. Use the information in the table to complete the statements. Some terms are used more than once.
Table with 2 columns and 4 rows of data.
The table shows a proportional relationship between ______________ and ______________.
The scale factor shown is ______________.
The constant of proportionality for this relationship is______________.
The units for the constant of proportionality are ______________ per ______________.
The table shows a proportional relationship between the cups of milk used and number of tablespoons of chocolate syrup used. The scale factor shown is 3/2. The constant of proportionality for this relationship is 3/2. The units for the constant of proportionality are teaspoons of chocolate syrup used per cups of milk used.
What is proportional relationship?When it comes to ratios and fractions, the concept of proportion is very connected. When two amounts with the same unit are compared, they form a ratio. When comparing two quantities, a ratio enables us to determine whether one is larger or smaller.
Two ratios or two fractions are equivalent when they are compared according to the proportional rule. To put it another way, two ratios are said to be proportional when they are equal. Performing arithmetic operations on both sides of the ratio taught us that a ratio can be expressed in a variety of ways.
Both the 3: 5 and 6: 10 are equivalent ratios. This indicates that these ratios are proportional. This proportionality can be expressed mathematically as follows:
[tex]$ \frac{3}{5} = \frac{6}{10}[/tex]
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Do sides 5 cm 12cm and 13cm form a right angled triangle give reason?
Yes, the sides 5 cm, 12 cm, and 13 cm form a right-angled triangle.
This is because of the Pythagorean Theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, 13 cm is the hypotenuse, and 5 cm and 12 cm are the other two sides.
5^2 + 12^2 = 25 + 144 = 169
13^2 = 169
Since the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, this means that the triangle is indeed a right-angled triangle.
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How early can cervix dilate?
For weeks before labor starts, the cervix can dilate to 1 centimeter. The cervix is only beginning to prepare for labor at this stage of dilatation.
Every woman experiences a different amount of time between dilation to 1 cm and delivery. While another woman maybe 1-2 cm dilated for days or weeks, one woman may move from having a closed cervix to giving birth in a matter of hours.
Some women don't start dilating until they start laboring actively. This indicates that the cervix is initially fully closed, but as labor goes on, it opens to a diameter of 10 cm. First pregnancies are where it occurs most frequently. Other women, particularly those who have already given birth, may begin dilating days or weeks before the commencement of labor.
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1,024 divided by 32 please help
Answer:
32
Please mark brainliest if this is correct! :)
Answer:
1024/32= 32.
Step-by-step explanation:
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