A fruit basket holds x2 x2 – 3 x x + 12 apples. Maha takes out 4 x− x− 6 of them. How many apples are left in the basket?
p.s Please explain how you solve this question!

Markov's inequality says that for a positive random variable X and any positive real number a, the probability that X is greater than or equal to a is less than or equal to the expected value of X divided by a.

(i) Let X be the number of automobiles sold next week. We have E(X) = 16, and we want to find an upper bound to P(X > 18).

Using Markov's inequality, we have:

P(X > 18) <= E(X)/18 = 16/18 = 8/9

Therefore, an upper bound to the probability that next week's sales exceed 18 is 8/9.

(ii) Let X be the number of automobiles sold next week. We have E(X) = 16 and Var(X) = 9.

By Chebyshev's inequality, we have:

P(|X-E(X)| < k*sqrt(Var(X))) >= 1 - 1/k^2

We want to find a lower bound to P(10 ≤ X ≤ 22).

First, we standardize X by subtracting the mean and dividing by the standard deviation:

Z = (X - E(X))/sqrt(Var(X)) = (X - 16)/3

We want to find P(10 ≤ X ≤ 22), which is equivalent to finding P(-2 ≤ Z ≤ 2). Using Chebyshev's inequality with k=2, we have:

P(-2 ≤ Z ≤ 2) >= 1 - 1/2^2 = 3/4

Substituting back for X, we get:

P(10 ≤ X ≤ 22) = P(-2 ≤ (X - 16)/3 ≤ 2) >= 3/4

Therefore, a lower bound to the probability that next week's sales are between 10 and 22, inclusively, is 3/4.

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Answer:

436g

Step-by-step explanation:

1kg=1000g

3kg=3000g

3000+52=3052

3052÷7=436

Answer:

Points are (3, 1) and (6, 2) ....

Step-by-step explanation:

When y is 1

[tex]{ \tt{1 = \frac{1}{3}x }} \\ \\ { \tt{x = 3}}[/tex]

Point: (3, 1)

When y is 2;

[tex]{ \tt{2 = \frac{1}{3}x }} \\ \\ { \tt{x = 6}}[/tex]

Point: (6, 2)

The required points are (0,2) and (0,-2) respectively.

The equation of the ellipse is 4x² + y² = 4. Find the points on the ellipse that are farthest away from the point (1,0). (Round your answers to the nearest hundredth.)Solution:The given equation of the ellipse is 4x² + y² = 4.Let (x, y) be a point on the ellipse.The square of the distance between (x, y) and (1,0) is given by:(x - 1)² + y²The maximum and minimum of (x - 1)² + y² occur at the same point where the maximum and minimum of [(x - 1)² + y²] is equal to the maximum and minimum of [4x² + y² - 4] and also where the gradient of both functions is perpendicular.Thus, we need to find the maximum and minimum of the function f(x, y) = (x - 1)² + y² subject to the constraint 4x² + y² = 4.Maximize and minimize the function f(x, y) subject to the constraint 4x² + y² = 4 using Lagrange multipliers.Let g(x, y) = 4x² + y² - 4 = 0 be the constraint equation.Let L be the Lagrange functionL(x, y, λ) = f(x, y) + λg(x, y)Therefore, L(x, y, λ) = (x - 1)² + y² + λ[4x² + y² - 4]Now differentiate L(x, y, λ) partially with respect to x, y and λ.Lx = 2(x - 1) + 8λxLy = 2y + 2λydL/dλ = 4x² + y² - 4 = 0From the equation dL/dλ = 0, we get4x² + y² = 4 ⇒ x²/1 + y²/4 = 1Thus, the ellipse can be represented as:x = cosθ; y = 2sinθwhere 0 ≤ θ ≤ 2πThus, Lx = 2(x - 1) + 8λx = 0⇒ 2cosθ - 2 + 8λcosθ = 0Ly = 2y + 2λy = 0⇒ 2sinθ + 2λ(2sinθ) = 0dL/dλ = 4x² + y² - 4 = 0⇒ 4cos²θ + 4sin²θ - 4 = 0⇒ cos²θ + sin²θ = 1∴ 4λsinθ + cosθ - 1 = 0Solving the equations obtained above, we get(1) θ = 0: (x, y) = (1,0)(2) θ = π: (x, y) = (-1,0)(3) θ = π/2: (x, y) = (0,2)(4) θ = 3π/2: (x, y) = (0,-2)The points on the ellipse that are farthest away from the point (1,0) are (0,2) and (0,-2).(0,2) has the largest y-value, and (0,-2) has the smallest y-value.Therefore, the required points on the ellipse are:(0, 2) (larger y-value)(0, -2) (smaller y-value)Hence, the required points are (0,2) and (0,-2) respectively.

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Answer:

143°

When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.

Answer:

12

Step-by-step explanation:

6=a/4+2

L.C.M=4

4(6)=a+6(2)

24=a+12

24-12=a

a=12

The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).

The probability of Z > 0.75 is 1 - 0.77337 = 0.22663

The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968

Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).

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The matrix A does not eigenvector v corresponding to the given eigen value.

λ.A = [ -11  60 ]

v = [ 1   3λ ]

v is an eigenvector of A calculate corresponding eigenvalue,

A × v = λ × v

where A is the given matrix.

v is the given vector.

λ is the corresponding eigenvalue.

× denotes matrix multiplication.

Let's first calculate A × v we have,

A × v

= [-11 60] × [ 1 3λ]

= [-11-33λ    60+ 180λ]

Check A× v is equal to λ × v ,

λ × v =

λ × [ 1 3λ]

= [λ  3λ^2]

Set these two vectors equal to each other and get the following system of equations ,

-11-33λ = λ  __(1)

60+ 180λ = 3λ^2  ___(2)

From equation (1) we get,

⇒34λ = -11

⇒ λ = -11/34

Substituting this value of λ into the second equation, we have,

60+ 180λ = 3λ^2

⇒ 60 + 180(-11/34) = 3(-11/34)^2

⇒ (2040 -1980)/ 34 = 3(-11/34)^2

⇒ 60/34 = 3( 11/34)^2

⇒ 60 × 34 = 3 × 11 × 11

⇒20× 34 = 11 × 11

Which is not true.

so the value of λ does not satisfies both equations.

Therefore, v is not an eigenvector of A with corresponding eigenvalue λ.

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The above question is incomplete, the complete question is:

Check whether v is an eigen vector of A  if yes find the corresponding eigen value.

λ.A = [ -11  60 ]

v = [ 1   3λ ]

The perimeter of the non-shaded region in the figure can be calculated to be 14 inches.

Given a figure.

The middle portion of the figure is not shaded.

It is required to find the perimeter of the non-shaded region.

It is given that:

The whole area of the shaded region = 78 inches²

The area of the small square which is situated at the bottom is:

Area of small square = 2 × 4

                                  = 8 inches²

So, the area of the rest of the shaded area = 78 - 8

                                                                       = 70 inches²

Now, the area of the whole region without the small square is:

Area = 10 × (10 - 2)

        = 80 inches²

So, the area of the non-shaded region = 80 - 70

                                                                = 10 inches²

The width of the non-shaded rectangle is 2 inches.

So, length = 5 inches.

So, the perimeter is:

P = 2(5 + 2)

  = 14 inches

Hence, the perimeter is 14 inches.

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The figure is given below.

In data analytics, a population refers to all possible data values in a certain dataset.

Data analytics is a set of procedures and processes for examining datasets in order to draw conclusions from the information they contain, often aided by specialized systems and software. Organizations use data analytics to aid decision-making, increase efficiency, and evaluate outcomes.

The population and sample are two concepts in statistics. The population and sample are two concepts in statistics. The population is the entire set of objects or individuals being studied, while the sample is a subset of the population that is chosen for analysis. The sample is a subset of the population, chosen at random or according to some other criteria in order to represent the population as a whole.

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Answer:

B

Step-by-step explanation:

1. Notice all the LHS answers are (0,-6) so that's definitely an answer

2. Substitute out the y so 2nd equation becomes x-6=x^2-6; so x^2-x=0; therefore x=0 or x=1

3. x=1 so y=-5 and that's the second answer hence B

Answer:

The answer is B.

Step-by-step explanation:

hope this helps

so he got them for £10 all 24 bars, then he went and sold each for 50c, so hmmm 24 at £0.50 that's (24)(0.5) = 12, so he bought them for £10 and sold them for £12, he's got a surplus or profit of £2.

now, if we take 10(origin amount) as the 100%, what's 2 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 10 & 100\\ 2& x \end{array} \implies \cfrac{10}{2}~~=~~\cfrac{100}{x} \\\\\\ 5 ~~=~~ \cfrac{ 100 }{ x }\implies x=\cfrac{100}{5}\implies x=20[/tex]

Answer:

105 degrees

Step-by-step explanation:

sum of angles in triangle is 180 degrees

11x-5+6x+5+x = 180

simplify this to get 18x=180

180/18 = 10 = x

plug in 10 for x

11(10) - 5

110-5

105

Answer: Differential Equation Initial Condition y' + y tan x = sec X + 9 cos x y(0) ... linear differential equation for x > 0 that satisfies the initial condition.

Step-by-step explanation:

Answer:  The geometric series is convergent and the value is 16.

Step-by-step explanation:

How to illustrate the information?

Recall that the sum of an infinite geometric series, S, given first term, t_1, and common ratio, r, is given by:

S = t_1/(1 - r)

Note that:

3 = (4)(3/4)

9/4 = (3)(3/4

27/16 = (9/4)(3/4)

So this a geometric series with t_1 = 4 and r = 3/4. Therefore:

4 + 3 + 9/4 + 27/16 + ... = 4/(1 - 3/4) = 4/(1/4) = 16

The correct option is 16.

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum 4+3+ 9/4 +27/16 +???

choices are

1. 3/4

2. 12

3. 4

4. divergent

5. 16

As per the unitary method, Arun's mother would be 36 years old if Arun is 3 years old.

Let Arun's age be m years.

Let Arun's mother's age be n years.

From the problem statement, we know that n = 4m + 6. This means that Arun's mother's age is directly proportional to Arun's age, with a constant ratio of 4 and a constant difference of 6.

To solve for n, we can use the unitary method. We can set up a proportionality between the two ages as follows:

n / m = (4m + 6) / m

To solve for n, we can cross-multiply to get:

n = m x (4m + 6)

Expanding the right-hand side of the equation, we get:

n = 4m² + 6m

Therefore, Arun's mother's age is 4m² + 6m years. We can simplify this expression by factoring out 2m:

n = 2m(2m + 3)

This gives us a simpler form of the equation for Arun's mother's age. To find her age, we simply substitute Arun's age (m) into this expression and simplify.

If Arun is 3 years old (m = 15), then his mother's age would be:

n = 2m(2m + 3) = 2(3)(2(3) + 3) = 2(3)(6) = 36

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Answer: graph is attached

Step-by-step explanation:

your equation is y = -3.5x + 50

your slope is - 3.5, your y intercept is 50

to graph it yourself using a line tool

start your first point at the y intercept of 50

put your first point

next, your slope is - 3.5 this means y/x for slope is -3.5 / 1

rise is -3.5 down and run is over right +1

because we want a straight line and the slope is a fraction, make a table and you can use points that are on exact numbers instead of fractions.

at x = 0, y = 50

at x = 1, y = 46.5 ( 50 - 3.5)

at x = 2, y = 43  (46.5 - 3.5)

at x = 3, y = 39.5 ( 43 - 3.5)

at x = 4, y = 36  ( 39.5 - 3.5)

you can graph the even numbers and draw your line.

see attached graph and table.

Answer:

Ans = 8

Step-by-step explanation:

because -- is + and  −−√70 is positive

so square root =8.366600265340757

and 8 is bigger as 8.366600265340757 is a decimal number.

Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

Greek number prefixes are employed in the naming of molecular (covalent) substances.

Greek number prefixes are employed in the naming of molecular (covalent) substances. Prefixes are always combined in order of size (left-to-right in the table below). For instance, "heptadecatetracta" (7 + 10 + 400) would be the prefix for the number 417.

We utilise prefixes (mono-, di-, tri-, etc.) at the beginning of each element in molecular compounds to denote the element's subscript, but we only use the prefix mono- for the compound's second element.

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Answer:

It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).

Step-by-step explanation:

The normalized form of the equation

(x+2)^2= - 16

x^2 + 4x + 4 = - 16

x^2 + 4x + 20 = 0

We have in the form ax^2 + abx + c = 0

a = 1

b = 4

c = 20

Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64

Discriminant is negative, therefore, no Real solutions.

You walked a total of 4576 yards to get to the basketball court.

In order to represent amounts in a more practical or acceptable unit of measurement, unit conversions are crucial for addressing mathematical issues. In this task, for instance, we were given distances in miles but had to translate them into yards to get the overall distance travelled. We wouldn't be able to compare or combine values that are stated in various units without unit conversions. When working with formulae or equations that contain physical quantities with multiple units, unit conversions are also crucial.

Given that, the distance walked is 1.5 miles and 1 1/10 miles.

Coverting into yards we have:

1.5 miles is equal to 1.5 x 1760 = 2640 yards

1 1/10 miles is equal to (1 + 1/10) x 1760 = 1936 yards

Total distance is:

2640 + 1936 = 4576 yards

Hence, you walked a total of 4576 yards to get to the basketball court.

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The algebraic representation of the statement subtract 4 times the positive square root of z from thrice of x is 4√z - 3x.

A mathematical expression is composed of term. A coefficient is an integer that is either multiplied by the variable it is associated with or put alongside the variable. A coefficient is, in other words, the numerical component of a phrase that contains both constants and variables. For instance, the coefficient in the expression 2x is 2.

The algebraic representation of the given statement is:

4 times the positive square root of z: 4√z

4 times the positive square root of z: 4√z - 3x

Hence, the algebraic representation of the statement subtract 4 times the positive square root of z from thrice of x is 4√z - 3x.

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Step-by-step explanation:

a. f(x) = s(q(x))

b. f(x) = q(s(q(x)))

d. f(x) = g(p(h(x)))

f. f(x) = q(s(x))

i. f(x) = h(r(x))

n. f(x) = h(g(s(x)))

not sure about h and p tho

hope this helps

Table C represents a linear relationship that is also proportional. This is because the ratio of the output (y) to the input (x) is always constant, which is a characteristic of proportional relationships.

What is a linear equation?

A linear equation is an algebraic equation that represents a straight line on a graph. In general, a linear equation takes the form:

y = mx + b

A linear relationship between two variables, x and y, is one in which the change in y is directly proportional to the change in x. This means that for any change in x, there is a corresponding change in y that can be expressed as a constant multiple of x.

For example, if we have a linear relationship y = mx + b, where m is the slope of the line and b is the y-intercept, then if we increase x by 1 unit, y will increase by m units. This relationship holds true for all values of x and y along the line.

A proportional relationship, on the other hand, is a special case of a linear relationship in which the ratio of y to x is always the same constant. This means that if we increase x by 1 unit, y will increase by a constant multiple of x. In other words, the relationship between x and y is one of scaling, where the size of y is always a fixed multiple of the size of x.

Therefore, Table C represents a linear relationship that is also proportional. This is because the ratio of the output (y) to the input (x) is always constant, which is a characteristic of proportional relationships.

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The net price is $4,060.75 and the trade discount amount is $ 1,042.25.

Chain discounts = 9/8/5

Total number of snow boards = 21

Calculate the trade discount:

Trade discount = List price x Discount rate

= 5,103 x 0.09

= 459.27

Calculating the net price after the first discount:

= List price - Trade discount

= 5,103 - 459.27

= 4,643.73

Calculating the net price after the second discount:

= Net price after first discount x (1 - Discount rate)

= 4,643.73 x (1 - 0.08)

= 4,274.47

Calculating net price after the third discount:

= Net price after second discount x (1 - Discount rate)

= 4,274.47 x (1 - 0.05)

= 4,060.75

Calculating the trade discount amount -

= 459.27 + 379.26 + 203.72

= 1,042.25

Complete Question:

Sam’s Ski Boards. com offers 9/8/5 chain discounts to many of its customers. The Ski Hut ordered 21 ski boards with a total list price of $5,103. What is the net price and trade discount amount?

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Answer: Yes Leah Is Correct.

Step-by-step explanation: Leah is correct because if you have a rectangle divided into 4 parts than if you will be asked how much parts will you need to make this fraction a whole you’ll say 4 since if you say for example six you will be wrong since six is too much so if you shade one part in than it’s 1/4 ths now let’s say you shaded in 3/4th you will see 3 shaded and one more left not shaded in which gives the fraction the name 3/4.

hope this made sense.

Answer:

you need to show the numbers

Step-by-step explanation:

The given data is quantitative, The data is discrete and The highest level of measurement for this data is ratio

The given data is quantitative, as it involves measuring the number of defective circuits per CPU for a sample of 100 CPUs.

The data is discrete, since we are counting the number of defective circuits, which can only take integer values.

The highest level of measurement for this data is ratio, since the data involves measuring the number of defective circuits per CPU, and the ratio of one measurement to another is meaningful (for example, a CPU with 2 defective circuits has twice as many as a CPU with 1 defective circuit).

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If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle. Also if a circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long then length of the arc subtended by the angle's rays 8.4 cm. Another circle is centered at the vertex of the angle then arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.

a.) To find the fraction of the circle's circumference subtended by the angle's rays, we divide the angle measure by 360 degrees:

fraction of circle's circumference = 140/360

Simplifying this fraction, we get:

fraction of circle's circumference = 7/18

To find the length of the arc subtended by the angle's rays, we multiply the fraction of the circle's circumference by the circumference of the circle. Let's call the circumference of the circle "C":

length of arc = (7/18)*C

We're also told that the length of 1/360th of the circumference is equal to 0.06 cm. So, we can write:

(1/360)*C = 0.06

Multiplying both sides by 360, we get:

C = 360*0.06 = 21.6 cm

Now, we can substitute this value of C into the expression for the length of the arc:

length of arc = (7/18)*C

length of arc = (7/18)*(21.6)

length of arc = 8.4 cm (rounded to one decimal place)

Therefore, the length of the arc subtended by the angle's rays is 8.4 cm.

b.) We're given that 1/360th of the circumference of the circle is 0.06 cm long. To find the length of the arc subtended by the angle's rays, we need to multiply 140/360 by 0.06:

length of arc = (140/360)*0.06

length of arc = 0.0233 cm (rounded to four decimal places)

Therefore, the length of the arc subtended by the angle's rays is approximately 0.0233 cm.

c.) We're told that the length of the arc subtended by the angle's rays is 70 cm. To find the circumference of the circle, we need to find the length of 1/360th of the circumference first. We can do this by dividing 70 by 1/360:

(1/360)*C = 70

Multiplying both sides by 360, we get:

C = 70*360 = 25,200 cm

Therefore, the circumference of the circle is 25,200 cm. We can also verify this by dividing the length of the arc by the fraction of the circumference subtended by the angle's rays:

length of arc = (7/18)*C

C = (18/7)*length of arc

C = (18/7)*70

C = 180 cm (rounded to one decimal place)

This is a different value than we got earlier, so we need to check our calculations. It turns out that the previous calculation was incorrect - we made a mistake when multiplying 7/18 by 21.6. The correct calculation gives us:

length of arc = (7/18)*C

length of arc = (7/18)*(21.6)

length of arc = 8.4 cm (rounded to one decimal place)

Now, we can calculate the circumference of the circle:

length of arc = (7/18)C

C = (18/7) *length of arc

C = (18/7) *70

C = 180 cm (rounded to one decimal place)

Therefore, the circumference of the circle is 180 cm.

Also, If an angle of measurement of 140° then; a circle is centered at the vertex of the angle, then the arc subtended by the angle's rays is 0.0233 cm times as long as 1/360th of the circumference of the circle.

b. A circle is centered at the vertex of the angle, and 1/360th of the circumference is 0.06 cm long.The length of the arc subtended by the angle's rays 8.4 cm

c. Another circle is centered at the vertex of the angle.

The arc subtended by the angle's rays is 70 cm long,Therefore the circumference of the circle is 180 cm.

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