Let's call the event of flipping two tails in a row "success." The probability of success on any given flip is (1-p) ^2.
The number of flips required to get two tails in a row is a random variable, which we can calculate the expected value of. This expected value can be calculated as an infinite sum:
E = 1 * (1 - (1-p) ^2) + 2 * (1-p) ^2 * p + 3 * (1-p) ^2 * (p^2) + ...
This sum can be simplified using geometric series formula:
E = 1 / (1 - (1-p) ^2 * p)
So, the expected number of flips required to get two tails in a row with a biased coin with probability p of heads is given by the above formula.
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find the set of solutions for the linear system use x3, x2, etc. for the free variables if necessary. indicate if a variable is free by writing the same variable in the space (so if is free, write x1).
The set of solutions for the linear system is x1 = 6, x2 = 3, and x3 = -4.
The linear system is given as follows:
x1 + x2 - x3 = 6
2x1 + x2 + 2x3 = 8
3x1 + 2x2 + 3x3 = 14
To solve this system, we will use the Gauss-Jordan elimination method. First, we will subtract twice the first equation from the second equation and three times the first equation from the third equation.
2x1 + x2 + 2x3 = 8
- 2(x1 + x2 - x3 = 6)
2x1 + x2 + 2x3 = 8
3x1 + 2x2 + 3x3 = 14
- 3(x1 + x2 - x3 = 6)
0x1 + 3x2 + 5x3 = 6
Next, we will subtract three times the second equation from the third equation.
3x1 + 2x2 + 3x3 = 14
- 3(0x1 + 3x2 + 5x3 = 6)
3x1 + 2x2 - 2x3 = 8
Finally, we will divide the first equation by 1, the second equation by 3, and the third equation by -2.
x1 + x2 - x3 = 6
/ 1
x1 + (1/3)x2 + (5/2)x3 = 3
(-1/2)x1 + x2 + x3 = -4
The set of solutions for the linear system is x1 = 6, x2 = 3, and x3 = -4.
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Is this true or false?
Answer:
Step-by-step explanation:
you look it up, If that doesn't work, see if someone asked the same question on this, if not, I got nothing.
Suppose the average yearly salary of an individual whose final degree is a master's is $43 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn $110 thousand. Find the average yearly salary of an individual with each of these final degrees.
The average yearly salary of an individual with each of these final degrees is $22333 and $16666.6.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form
Ax + B = 0.
Given;
The average yearly salary of an individual whose final degree is a master's is $43000 less than twice that of an individual whose final degree is a bachelor's.
Combined, two people with each of these educational attainments earn $110 thousand.
Now, let the salary of bachelors be x
Then salary of masters= 2x-43000
x+2x-43000=110000
3x=67000
x=22333.33
2x-43000=16666.66
Therefore, by solving equations answer will be $22333 and $16666.6.
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A glass contains 320 cm³ of orange juice. The mass of the juice
is 370 g.
Calculate the density of the juice in kilograms per cubic metre
(kg/m³).
Give your answer to the nearest integer.
Therefore , the solution of the given problem of volume comes out to be density 1.15625 g/ cm³.
Describe volume.The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The amount of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.
Here,
Given:
Density = mass /volume
mass = 370 gm
volume = 320 cm³
Density = 370/320
=>Density = 1.15625 g/ cm³
thus , density 1.15625 g/ cm³
Therefore , the solution of the given problem of volume comes out to be density 1.15625 g/ cm³.
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Use the substitution u = 9x2 + 8 to find the following indefinite integral Check your answer by differentiation '18x sin (9x2 + 8) 18x sin (9x2 + 8) dx=
The value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.
Explain about the indefinite integral?A function that accepts the antiderivative of that other function is said to take an endless integral. Visually, it is shown as an integral indicator, a function, and finally a dx. It is simpler to represent taking the antiderivative using the indefinite integral.The given integral is;
y = ∫18x sin (9x² + 8) dx
Put u = 9x² + 8
Then, on differentiation
18x dx = du
substitute the values:
y = ∫ sin (u) du.
y = -cos u
Put u = 9x² + 8
y = -cos (9x² + 8) + c
c is the constant of integration.
Thus, the value of the given indefinite integral is found to be: y = -cos (9x² + 8) + c.
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surd in bracket √2(2+6)
The value of the expression given as √2(2+6) is 4
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
√2(2+6)
We start by evaluating the expression in the bracket
So, we have the following
√2(2+6) = √2(8)
Evaluate the products
This gives
√2(2+6) = √16
Lastly, we have
√2(2+6) = 4
Hence, the solution is 4
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Answer this question Please
(70 points)
A 130
The red line meets the measuring tool at 155 and 25 therefore we get:
155-25 = 130
answer the question for me
Answer: 1, 2, and 4.
Step-by-step explanation: Each must be wider than the angle than a "L" has.
Jen is packing a box for her brother at college. The package must weigh less than 12 pounds. The table shows the weight of items she has already placed in the box.
The only items she can add to the box to make it less than 12 pounds are; either the package of socks or the book
How to solve Inequality word problems?The list of items and their weight that she has already packed are;
Boots = 5.2 pounds
Jeans = 1.25 pounds
Sweater = 2.05 pounds
Running Shoes = 2.25 pounds
We are told that the package must weigh less than 12 pounds. Thus, let the weight of the additional item be x and as such we have the inequality;
5.2 + 1.25 + 2.05 + 2.25 + x < 12
10.75 + x < 12
Subtract 10.75 from both sides to get;
x < 1.25
The only item that is less than 1.25 pounds that she can carry is either the package of socks or the book
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Find the area of each triangle. Round to the nearest tenth.
The area of the triangle is 2. 6 square units
How to determine the area of the triangleThe formula for calculating the area of a triangle is expressed as;
A = 1/2bh
Given that the parameters are;
A is the area of the triangleb is the base of the triangleh is the height of the triangleusing the trigonometric identity, sine, we have;
sin 60 = h/4
substitute the values
0. 8660 (4) = h
h = 3.5
substitute the value
Area = 1/ 2 × 3. 5 × 1. 5
multiply the values
Area = 2. 6 square units
Hence, the value is 2. 6 square units
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Determine the area of each composite figure. Round to the nearest tenth if necessary.
The area of each composite figure is 828.96 cm².
What is Surface Area?A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.
Given:
Surface area = SA of Cone + SA of Hemisphere
Cone:
radius = 8 cm
slant height = 17 cm
So, SA of Cone = πrl
= 3.14 x 8 x 17
= 427.04 cm²
Hemisphere:
radius = 8 cm
So, SA of Hemisphere = 2πr²
= 2 x 3.14 x 8 x 8
= 401.92 cm²
Thus, the SA of figure = 427.04 + 401.92 = 828.96 cm²
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The dotplot below displays the number of math classes taken by a random sample of 35 students at a high school.
A dotplot titled Math Classes. A number line going from 2 to 6 is labeled number of math classes taken. 2, 1; 3, 6; 4, 18; 5, 7; 6, 1.
Which letter represents the approximate location of the mean number of math classes?
A. A
B. B
C. C
D. D
Answer:
Class B
Step-by-step explanation:
duh
Answer:
b
Step-by-step explanation:
true/false. the student knows that the relationship between the spring constant (k), the mass (m), and the period of oscillation (t) is given by the equation (19) this is not a linear equation, but it can be linearized using the same method used to linearize equation 10.
The statement “The relationship between the spring constant (k), the mass (m), and the period of oscillation (t) is given by the equation (19) this is not a linear equation, but it can be linearized using the same method used to linearize equation 10.” is true because equation 19 can indeed be linearized with the same method used to linearize equation 10.
Equation 10 is a non-linear equation and can be linearized by taking the natural logarithm of both sides. This will convert the equation into a linear form which can be used to calculate the parameters of the original equation.
Similarly, equation 19 can be linearized by taking the natural logarithm of both sides. The linearized form of equation 19 will also be useful in finding out the parameters of the original equation.
By linearizing the equations, it becomes easier to solve for the parameters of the equations. This is because linear equations are much simpler and can be solved using basic algebraic methods.
Linear equations can also be solved using matrix methods and can be used to solve for the parameters of the original equations more accurately.
Therefore, it is true that equation 19 can be linearized using the same method used to linearize equation 10. This will make it easier to solve for the parameters of the original equation.
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In this figure, h = 6, and r = 8.
What is the exact surface area of the cone?
Enter your answer in the box.
[answer] units²
Cone oriented with vertex on top and base on bottom. The perpendicular distance between the vertex and the base is labeled h. The radius of the circular base is labeled r.
[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=6\\ r=8 \end{cases}\implies SA=2\pi (8)(6+8) \\\\\\ SA=16\pi (14)\implies SA=224\pi \implies SA\approx 703.72~units^2[/tex]
the gourmet grill company manufactures and sells two types of grills: propane and electric. each propane grill sells for $320 and costs $220 to manufacture. each electric grill sells for $260 and costs $180 to manufacture. each grill goes through four operations in the manufacturing process. the hours required by each type of grill in each of these manufacturing processes are summarized as follows:
The Gourmet Grill Co. produces propane and electric grills with varying cost and hours required in 4 manufacturing processes. Aim is to maximize profit by determining the production plan using LP model, feasible region and level curves.
a. The LP model for this problem can be formulated as follows:
Maximize: $320P + $260E (profit from selling propane and electric grills)
Subject to:
2P + E <= 2400 (hours of machine press time available)
4P + 5E <= 6000 (hours of fabrication time available)
2P + 3E <= 3300 (hours of assembly time available)
P + E <= 1500 (hours of testing time available)
P, E >= 0 (non-negativity constraints)
Where P is the number of propane grills and E is the number of electric grills produced.
b. The feasible region for this problem is a polygon with vertices (0, 0), (600, 0), (300, 900), (0, 1200). This region represents the combination of P and E that satisfies all the constraints.
c. To determine the optimal solution using level curves, we can start by plotting the feasible region and then finding the level curve that represents the maximum profit. The level curve would be a straight line with slope equal to $320/$260 (the ratio of price per unit for the two types of grills). The intersection of this line with the feasible region would represent the optimal solution, which would be the combination of P and E that maximizes the profit.
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Roberto needs 6 feet and 8 inches of lumber to repair the deck. He has 54 inches of lumber. How many more inches of lumber does he need?
Answer:
26 inches, or 2 ft 2 in.
Step-by-step explanation:
1 ft = 12 in.
6 ft 8 in. = 6 ft + 8 in. =
= 6 ft × 12 ft / in. + 8 in.
= 72 in. + 8 in.
= 80 in.
He needs 80 inches.
80 - 54 = 26
Answer 26 inches or 2 ft 2 in.
Answer:
he needs 26 inches
Step-by-step explanation:
The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean 188 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl. For 14 - year - old boys, blood cholesterol levels follow a Normal distribution with mean170mg/dl and standard deviation 30 mg/dl. Now suppose we select independent SRS of 25 men aged 20 to 34 and 36 boys aged 14 and calculate the sample mean heights xM - xB. Describe the shape, center, and spread of the sampling distribution xM - xB. Find the probability of getting a difference in sample means xM - xB that's less than0 mg/dl. Show your work. Should we be surprised if the sample mean cholesterol for the 14 - year - olds exceeds the sample mean for the men?
The sampling distribution of xM - xB is normally distributed with a mean of 18 mg/dl and a standard deviation of 35.4 mg/dl.
The sampling distribution of xM - xB is a normal distribution. This can be calculated by subtracting the mean of the men (188mg/dl) from the mean of the boys (170mg/dl), which gives a mean of 18 mg/dl. To calculate the standard deviation, we first calculate the standard deviation of the men (41 mg/dl) and the boys (30mg/dl). Then we use the formula: standard deviation of xM - xB = sqrt(standard deviation of men^2 + standard deviation of boys^2). This gives us a standard deviation of 35.4mg/dl. To calculate the probability of getting a difference in sample means xM - xB that's less than 0 mg/dl, we use the z-score formula: z = (x-mean)/standard deviation. Plugging in x = 0, mean = 18 and standard deviation = 35.4 gives us a z-score of -0.5197. Using a z-table, this gives us a probability of 0.3085. It should not be a surprise if the sample mean cholesterol for the 14 - year - olds exceeds the sample mean for the men as the mean cholesterol level for the boys is lower than the men.
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Draw The Congruence markings on ΔXYZ, so that ΔABC≅ΔXYZ by ASA
Angle B is equal to angle Y and angle A is equal to angle X. And AB is equal to side XY.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ΔABC is congruent to the triangle ΔXYZ.
In triangles ΔABC and ΔXYZ, then we have
∠B = ∠Y (Corresponding angles)
∠A = ∠X (Corresponding angles)
AB = XY (Common side)
Angle B is equal to angle Y and angle A is equal to angle X. And AB is equal to side XY.
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find the slope of the line passing through the points (3, -9) and ( 1,-4)
Answer:
= [tex]-\frac{5}{2}[/tex]
= m = -2.5
Step-by-step explanation:
Hope it helps on your assignment/quiz/test/homework
Answer:-5/2
Step-by-step explanation:
(3,-9) and (1,-4)
(x1,y1) (x2,y2)
[tex]\frac{-4+9}{1-3\\}[/tex] = [tex]\frac{-5}{2}[/tex]
the range of x is the set {0,1,2,3,x}, where x is unknown. if each value is equally likely and the mean of x is 6, determine x.
If each value is equally likely and the mean of x is 6, x = 24.
The arithmetic mean (arithmetic average or simply the mean or average) in statistics is the sum of a collection of numbers divided by the count of numbers in the collection, which is is often a set of results from an experiment, a survey, or observational study.
The arithmetic mean A is defined to be the formula: [tex]A = \frac{1}{n} \sum_{i=1}^{n} a_i=\frac{a_1+ ... +a_n}{n}[/tex].
We're given a set of {0, 1, 2, 3, x} where x is unknown and the mean of x is 6. In order to find the value of x, we can plug all the known values in the formula first and then we're going to simplify the equation:
[tex]A = \frac{a_1+...+a_n}{n}\\\\6 = \frac{0+1+2+3+x}{5}\\\\6 = \frac{6+x}{5}\\\\30 = 6 + x\\\\30 - 6 = x\\\\x = 30 - 6\\\\x = 24[/tex]
We've confirmed that x is indeed equal to 24.
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Wrtie the slope intercept form of the inequality 9x-7y>-7
Answer:
Step-by-step explanation:
9x - 7y > -7
-7y > -9x - 7
y < 9/7x + 1
83 cmp cut from 1.3 metres 1.3metres
The remaining length when 85 cm is cut from 1.3 meters is 0.45 meters.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know, 1.3 meters = 1.3×100 cm = 130 cm.
Now, 83 cm is cut from it.
Therefore, The remaining length is,
= (130 - 85) cm.
= 45 cm.
And 45 cm is equal to (45/100) meters.
= 0.45 meters.
Q. 83 cm is cut from 1.3 meters what would the remaining length in meters?
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Simplify
a+b
a-b
a=5 and b= 3
Answer:
Step-by-step explanation:
The value of the given expression will be 4.
What will be congruence criterion
They are congruent by the by the Angle-Side-Angle (ASA) congruence criterion.
What is an Angle-Side-Angle (ASA) congruence criterion?Angle-Side-Angle (ASA) congruence criterion states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent. In this case, the angles angle E = angle I and EG=FI (a non-included side), so the triangles ADEF and AHIG are congruent by ASA.
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use the pythagorean theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle.
The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
Therefore, for the given values of 3, 4, and 5, these lengths can indeed form a right triangle. Specifically, this triangle is a 3-4-5 triangle, which is a special type of right triangle whose sides have integral lengths and whose angles are all multiples of 30°.
Mathematically, this can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the triangle and c is the length of the hypotenuse. The theorem is a fundamental result in geometry and has wide-ranging applications in mathematics, physics, engineering, and other fields.
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6. [3 marks ] Answer the question regarding the meaning of the given statement which contains a multiple negation. Stephen failed to avoid spoilers on the new Star Wars movie. Did Stephen see spoilers?
Answer: The statement "Stephen failed to avoid spoilers on the new Star Wars movie" contains a negative phrase "failed to avoid". When a sentence contains a negative phrase, it can sometimes be difficult to determine the meaning. However, in this case, the meaning of the sentence is that Stephen did see spoilers on the new Star Wars movie. The use of "failed to avoid" indicates that Stephen made an effort to avoid spoilers but was unsuccessful, which means that he saw them.
Step-by-step explanation:
find tr
a. 10
b. 25
c. 30
d.40
The solution is Option C.
The measure of TR of triangle STR is TR = 30
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔPQR
Let the second triangle be represented as ΔSTR
The measure of PR = 35
The measure of SR = 25
The measure of QR = 42
The measure of QT = x
The measure of TR = 42 - x
Now , PQ is similar to ST
Now , the triangles PQR and STR are similar triangles
And , corresponding sides of similar triangles are in the same ratio
Substituting the values in the equation , we get
SR / PR = TR / QR
25 / 35 = ( 42 - x ) / 42
On simplifying the equation , we get
Multiply by 42 on both sides of the equation , we get
( 42 - x ) = ( 25 x 42 ) / 35
On further simplification , we get
42 - x = 30
Adding x on both sides of the equation , we get
x + 30 = 42
Subtracting 30 on both sides of the equation , we get
x = 12
Now , the measure of TR = 42 - x
Substitute the value of x in the equation , we get
The measure of TR = 42 - 12 = 30
Hence , the measure of TR of triangle is 30
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show that the sum of residuals (error) for any first order simple linear regression least squares line is zero (0). that is pn i
The sum of residuals (error) for any first order simple linear regression least squares line is zero (0).
To show that the sum of residuals (error) for any first order simple linear regression least squares line is zero (0), we can use the following equation:
∑i = 1n (yi − (b0 + b1xi)) = 0Where b0 is the intercept and b1 is the slope of the line, and xi and yi are the x and y values of the ith data point. This equation can be expanded by substituting the least squares solution for b0 and b1 into the equation:
∑i = 1n (yi − (∑i = 1n yi)/n − (∑i = 1n xiyi − (∑i = 1n xi)(∑i = 1n yi))/(∑i = 1n xi2 − (∑i = 1n xi)2/n)) = 0
Simplifying both sides of the equation, we get:
∑i = 1n (yi − (∑i = 1n xiyi)/(∑i = 1n xi2)) = 0
Therefore, the sum of residuals (error) for any first order simple linear regression least squares line is zero (0).
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consider the following system below, assuming the pinion has negligible inertia. formulate two equations of motion in terms of x, theta, and theta a for the parameters shown. one should be written in terms of the rotational acceleration and the other in terms of the linear acceleration
The system shown consists of a rotational mass, a pinion, and a linear mass.
The equations of motion for this system can be formulated in terms of x, theta, and theta a in terms of rotational and linear acceleration.
The equation of motion for rotational acceleration is given by:
θ¨ = (1/J) * (T - (b*x¨))
Where J is the moment of inertia of the rotational mass, T is the torque applied to the pinion, and b is the coefficient of friction between the pinion and the linear mass.
The equation of motion for linear acceleration is given by:
x¨ = (1/m) * (T - (b*θ¨))
Where m is the mass of the linear mass, T is the torque applied to the pinion, and b is the coefficient of friction between the pinion and the linear mass.
The equations of motion for the system shown can be formulated in terms of rotational acceleration (θ¨) and linear acceleration (x¨) using the moment of inertia (J) and mass (m) of the rotational and linear masses, respectively, as well as the coefficient of friction (b) between the two.
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The Unit Rate means how much of something per 1 unit of something else. true or flase
Answer:
true
Step-by-step explanation:
A unit rate is a price for one unit of anything. This is written as a ratio with a denominator of one.