Binomial Distribution - Algebra 2B

A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?

The double integral of (xy y^(-2)) over the region R is equal to 0.

What is double integral ?

The term integral in math is defined as a method of adding or summing up the parts to find the whole and it is basically used to find the volume, area and the central values of many things. Double integrals are a two-dimensional integration method.

The given expression is the integrand of a double integral over the region R defined by the constraints 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2. To calculate this double integral, we would evaluate the following expression:

∬(xy y^(-2)) dA = ∬(xy y^(-2)) dx dy over the region R

We can evaluate this double integral using a change of variables, such as polar coordinates, or using rectangular coordinates.

In rectangular coordinates, we can evaluate the double integral using the following steps:

Evaluate the bounds of integration:

x: 0 to 2

y: 0 to 2

Evaluate the integral with respect to y first, keeping x fixed:

∬(xy y^(-2)) dx dy = ∫(x ∫(y y^(-2)) dy) dx, from 0 to 2

Evaluate the inner integral with respect to y:

∫(y y^(-2)) dy = -y^(-1) = -ln(y) + C, where C is an arbitrary constant

Substitute the solution for the inner integral back into the outer integral:

∫(x (-ln(y) + C)) dx = x(-ln(y)) - xC + D, where D is another arbitrary constant

Evaluate the outer integral with respect to x:

∫(x(-ln(y)) - xC + D) dx = (-x^2/2)ln(y) - (x^2/2)C + xD + E, where E is yet another arbitrary constant

Evaluate the constants of integration C, D, and E using the boundaries of integration for x and y:

-ln(2) - 0C + 0D + E = 0

-2ln(2) - 2^2/2 C + 2D + E = 0

Solving the system of equations, we find C = 2ln(2), D = 0, and E = 0

Substitute the values of C, D, and E back into the solution:

(-x^2/2)ln(y) - (x^2/2)C + xD + E = (-x^2/2)ln(y) - x^2ln(2)

Finally, evaluate the integral over the region R by substituting the bounds of integration for x and y:

(-2^2/2)ln(2) - 2^2ln(2) = -4ln(2) + 4ln(2) = 0

So, The double integral of (xy y^(-2)) over the region R is equal to 0.

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The probability of getting 15 or more heads is :

P (Z > -0.18) = 1 - 0.4289 =  0.5714

Now, According to the question:

Normal Approximation to Binomial:

The normal distribution is used to approximate for the binomial distribution. The condition when binomial distribution is approximated to normal is that n should be large and probability should be close to 0.5

"Information available from the question"

n = 30

Probability, p(heads) = 1/2

Since sample size is large, we check for normal approximation.

np = 30(1/2) = 15

and, n(1 - p) = 30(1 - (1/2)) = 15 both are greater than 5, we use normal approximation.

Mean, μ = np = 30(1/2) = 15

Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]

Standard deviation, σ = [tex]\sqrt{30(1/2)(1-1/2)}[/tex]

Standard deviation, σ =2.739

We have to find P (X ≥ 15). Using continuity correction, we deduct 0.5

P(X ≥ 15) = P(X > 14.5)

The respective Z-score with X = 14.5 is

Z = (x - μ)/ σ

Z = (14.5 - 15)/2.739

Z = -0.18

Now, we use z-tables to find probability greater than -0.18

P (Z > -0.18) = 1 - 0.4289 =  0.5714

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The fully factored form of the equation is 2x(x + 3) (2x - 1) that is option B.

Synthetic division and the rational root theorem can be used to demonstrate this. According to the rational root theorem, p must divide the constant term and q must divide the leading coefficient if p/q is a rational root of the polynomial f(x). The constant term in this example is -6, the leading coefficient is 4, and the potential rational roots are 1, 2, 3, and 6.

When we divide 4x3 + 10x2 - 6x by 2x - 1 using synthetic division, we arrive at the following result:

4x^3 + 10x^2 - 6x = (2x - 1) (2x^2 + 8x + 6)

We can then factor the remaining quadratic, 2x^2 + 8x + 6, as (x + 3)(2x + 2).

Thus, the completely factored form of 4x^3 + 10x^2 - 6x is:

4x^3 + 10x^2 - 6x = 2x(x + 3)(2x - 1)

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X = 1 means that we roll exactly 6 in the 3 trials. This means that the probability of rolling a 6 in this situation is 3(0.4)(0.6)2.

The probability of rolling a 6 in any given trial is 0.6 since Mrs. Chauvet's cube is unfair. The probability of getting a 6 in two of the three trials is 3(0.4)(0.6)2, while the probability of rolling a 6 in all three trials is 1(0.6)3. This means that the chance of rolling a 6 in any combination among three trials is the sum of the probabilities of rolling a 6 in each trial (0.6 + 0.6 + 0.6 = 1.8).

The probability of rolling a 6 exactly once in three trials is 3(0.4)(0.6)2, which is the probability of getting a 6 in one of the three trials and not getting a 6 in the other two.

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Answer:

ab means a multiplied by b, a(b+c) means add b and c together, then multiply by a, and (a+b)(c+d) means first add a and b

Step-by-step explanation:

ab means product, a(b+c) means product of a and sum of b & c and (a+b)(c+d) product of sum of a & b and c & d.

The result of multiplying two or more numbers together is the sum. The product of two or more numbers is what results from multiplication.

In mathematics, "ab" typically represents the product of two numbers, a and b.

"a(b+c)" represents the product of a and the sum of b and c, where a, b, and c are numbers.

"(a+b) (c+d)" represents the product of the sums of a and b and the sums of c and d.

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The equation in x and y whose graph is the path of the particle is y = (x - 4)2 + 5. The velocity vector at t= 4 is v(4) = i + 8j.

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.

Given r(t) as r(t) = x(t)i + y(t)j

Thus, this means that:

x = t+ 4         y = t2 + 5      

We see that we can solve t as:            

t = x - 4, thus:

y = (x - 4)2 + 5

v(t) is given by r'(t).

r'(t) = v(t) = i + 2tj                      

at t = 4:

v(4) = i + 8j

The acceleration is given by:  r"(t).

a(t) = r"(t) = 0i + 2j

The acceleration at t = 4 is:

a(4) = 0i + 2j

Hence, the equation in x and y whose graph is the path of the particle is y = (x - 4)2 + 5. The velocity vector at t= 4 is v(4) = i + 8j.

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The inequality equation is y ≤ -2x + 1 and the graph is plotted

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y ≤ -2x + 1   be equation (1)

when the inequality is solved ,

y = -2x + 1 , where the slope of the line is m = -2

Therefore , the value of A is -2x + 1 and the graph is plotted

Hence , the inequality equation is y ≤ -2x + 1

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Using the graph of the function f, the relative maxima of function is at x = 3 and is equal to 6.

The graph of the function f is given below:

A relative maximum occurs at an x-coordinated position when the function value is higher than it is compared to nearby places. At that time, the function value is at its relative maximum (y coordinate).

A relative minimum occurs at an x-coordinated location where the function value is the lowest in relation to its neighbors.

The Relative maximum is determined by y's maximum value.

In the graph we can see that;

The greatest value of the y value for x = 3 is 6.

As a result, the function's relative maximum is at x = 3 and is equal to 6.

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The complete question is:

The graph of a function f is given. Use the graph to find each of the following.

The​ numbers, if​ any, at which f has a relative maximum. What are these relative​ maxima?

Answer: The answer is 3.

Step-by-step explanation:

It follows that continuity at infinity is provided by having the same limit while approaching it from either side, i.e., the limit towards + and, which makes sense based on your understanding.

When a function can be extended to P1, it is said to be "continuous at infinity" (R).

Calculus's idea of the limit describes how a function behaves as its input gets closer to a particular value. As long as the limit is present, the value that f(x) approaches as x moves closer to c is represented by the notation lim(x -> c) f(x), which stands for the limit of a function at the point x = c.

You must demonstrate that all three of the following conditions are true in order to prove that a function f is continuous on an interval:

Every point in the interval has f specified, and the interval has f's bound.

For each and every > 0, there is a corresponding > 0 such that |x - c| implies |f(x) - f(c)| for all x and all c in the interval.

F is considered to be continuous on the interval if these requirements are met.

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2x＝ 3 -5√x using log form, x = log(2x + 5√x) = log(3)

To convert the equation 2x = 3 - 5√x into logarithmic form, we need to isolate the radical expression on one side of the equation. We can do this by adding 5√x to both sides:

2x + 5√x = 3

Next, we'll take the square root of both sides to eliminate the radical:

√(2x + 5√x)^2 = √(3^2)

Expanding the left side and simplifying:

2x + 5√x = 3

Finally, we'll take the logarithm of both sides to get x in logarithmic form:

log(2x + 5√x) = log(3)

To solve for x, we'll need to use logarithmic properties and/or exponential functions to isolate x on one side of the equation. log(2x + 5√x) = log(3)

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Answer: y = 3x + 0 OR y = 3x

Step-by-step explanation:

M = slope. rise/run. compare the points on the line by how much they rise and how much they run. In this case it is 3/1 (3). the B = the y-intercept. (the point where the line meets the y line, in this case the line meets at the origin which is 0.)

Answer: x = 104

Step-by-step explanation:

The solution to the exponential inequality in this problem is given as follows:

x < 1.72.

The exponential inequality for this problem is defined as follows:

3^(4x - 5) < 8.

The number 8 is not a base of 3, hence the way to isolate the variable x is applying the log of base 3 to both sides, as follows:

log3(3^(4x - 5)) = log3(8)

4x - 5 = log3(8)

The logarithm of base 3 of 8 can be obtained applying the change of base property, as follows:

log3(8) = log(8)/log(3)

log3(8) = 1.893.

Hence the inequality is solved as follows:

4x - 5 < 1.895

4x < 6.896

x < 6.896/4

x < 1.72.

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0.2 pizzas were consumed during the party.

What are the arithmatic calculations?

Arithmetic is the branch of mathematics that deals with basic operations such as addition, subtraction, multiplication, and division, and their properties and applications. Arithmetic calculations are mathematical operations that involve one or more numbers and result in a numerical answer.

To find the number of pizzas consumed during the party, we need to subtract the number of pizzas left at the end of the party from the number of pizzas at the beginning of the party.

At the beginning of the party, there was 1 pizza.

At the end of the party, there were 4/5 pizzas left.

So, the number of pizzas consumed during the party can be calculated as:

1 - 4/5 = 1 - 0.8 = 0.2

Therefore, 0.2 pizzas were consumed during the party.

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Domain : { x ∈ R : x ≥ 7 }

Range: { f ∈ R : f ≥ 9 }

Given function is:

f(x) =

Firstly find the domain of the given function.

Domain is set of all real x's values where given function is defined.

In other words, we exclude all the x's values from all real values where function is undefined.

In case of square root function, inside the square root given expression must be greater or equal to zero.

So,

x - 7 ≥ 0

Solve for x

x ≥ 7

So, domain is all real x when x ≥ 7.

Now find the Range of this function.

Range is set of all output values.

So, lowest value of out put is 9 when x is 7

and maximum value of the function is infinite.

So, Range is all real f's values when f ≥ 9.

Answer:

1.59375

Step-by-step explanation:

51 divided by 32 which is 1.59375

to check if you are right you do 1.59375 times 32 which equals to 51

The sample standard deviation is A. 5.9

What is Standard Deviation ?

It is a measure of how evenly distributed numbers are. It is the square root of the Variance, which is the average of the squared deviations from the Mean.

To find the sample standard deviation, first, we have to find the mean of the data, then subtract each data point from the mean, square each deviation, sum them, divide by the sample size minus 1, and then take the square root of the result.

Here's the calculation:

Mean = (1 + 5 + 12 + 16 + 15 + 12 + 19 + 5 + 10) / 9 = 11

Deviations = [-10, -6, 1, 5, 4, 1, 8, -6, -1]

Squared deviations = [100, 36, 1, 25, 16, 1, 64, 36, 1]

Sum of Squared deviations = 239

Sample Variance = Sum of Squared deviations / (Sample size - 1) = 239 / (9 - 1) = 239 / 8 = 29.875

[tex]Sample \ Standard\ Deviation=\sqrt{(Sample Variance)} \\\\Sample \ Standard\ Deviation=\sqrt{29.875}\\\\ Sample \ Standard\ Deviation= 5.9[/tex]

So, The sample standard deviation is 5.9 (rounded to one decimal place).

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An expression for the volume V of the rectangular prism in terms of its width w is V = ( 3W³ + 12W² ) Units³

Given data :

we know that

The volume of a rectangular prism is equal to

V = LWH ------> Equation A

where

L is the length

W is the width

H is the height

we know that

L = 3W ----> Equation B

H = W + 4 ------> Equation C

substitute equation B and equation C in equation A

V = ( 3W ) (W) ( W + 4 )

Apply distributive property

V = ( 3W³ + 12W² ) units³

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Answer:

Below

Step-by-step explanation:

68 x 157 = 10 676      to the nearest 100 would be 10700 ....the '7' next to the 6 in the 100s place dictates that you round the 6 UP to 7

Answer: 7/2

Step-by-step explanation: An easy way to calculate slope with two given points is to count the rise (y) between the points (7). Then count the run (x) between the points (2). Then put the rise over the run. 7/2

(a) The value of k is 64.

(b) The value of k is 25.

(c) The value of k is 25/4.

What is a trinomial?

An algebraic expression with three terms is called a trinomial. One or more terms in an algebraic expression each have variables and constants. These expressions use separators like +, -, ÷, and × that are symbols or operations. This algebraic expression includes a trinomial, a monomial, a binomial, and a polynomial.

(a)

Given trinomial is x² - 16x+k.

The algebraic identity is (a-b)² = a² -2ab + b²

Now equate  a² -2ab + b² with x² - 16x + k.

x² - 16x + k = a² -2ab + b²

Compare both sides:

x² = a², 16x = 2ab, k = b².

16 = 2b

b = 8

Taking square on both sides:

b² = 64

(b)

Given trinomial is x² + 10x + k.

The algebraic identity is (a+b)² = a² +2ab + b²

Now equate  a² -2ab + b² with x² + 10x + kk.

x² + 10x + k = a² + 2ab + b²

Compare both sides:

x² = a², 10x = 2ab, k = b².

10 = 2b  [Since x = a]

b = 5

Taking square on both sides:

b² = 25

(c)

Given trinomial is x² - 5x + k.

The algebraic identity is (a-b)² = a² -2ab + b²

Now equate  a² -2ab + b² with x² - 5x + k.

x² - 5x + k = a² -2ab + b²

Compare both sides:

x² = a², 5x = 2ab, k = b².

5 = 2b [Since x = a]

b = 5/2

Taking square on both sides:

b² = 25/4

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The distance between the ice cream parlor from the movie theater is 5 km.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

            School      

       |                       \

       |                          \

       |                              \   13 km

     12 km                          \

       |                                     \

Ice cream parlor                    Movie theater

Using Pythagorean theorem.

The distance between the ice cream parlor from the movie theater = x

Now,

13² = 12² + x²

169 = 144 + x²

x² = 169 - 144

x² = 25

x = 5

Thus,

The ice cream parlor from the movie theater is 5 km away.

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Answer:

Step-by-step explanation:

Assuming the oatmeal raisin and sugar cookies have an equal probability, it is less likely that a chocolate chip cookie will be picked since the other two cookies have a 37.5% chance of being picked. Despite this, it is still both likely and unlikely since it is only a small difference.

To conclude, it depends on what your teacher or textbook think. If they think a 12.5% difference between the other two cookies means that chocolate chip is unlikely, then it's unlikely. In my opinion, it is not equally but near equally likely and unlikely.

Answer:

y = 8

Step-by-step explanation:

6y+2 = 8y-14

2 = 2y - 14

16 = 2y

y = 8

5.385 is the length of each line segment according to the Pythagoras theorem and distance formula.

The basic Geometric mathematical relationship between one right triangle's three sides is termed as the Pythagorean Theorem, or simply the Pythagorean Theorem. This rule states that the areas with squares with the two parts added together equal the area of the square well with hypotenuse side. The Pythagorean Theorem says that the square that crosses the tangent of a right angled triangle opposite the right angle equals the total of the squares that span the sides of something like a right triangle. It is sometimes written as the generic geometric notation a2 + b2 = c2.

given

A2 + B2 = C2 is a Pythagorean theorem.

Let C be the point (-2,1)

A two-unit line segment AC would be required.

The length of line segment BC would be 5 units.

Incorporate the line segment length into the Pythagorean theorem by adding

2^2 + 562

= 4 + 25

= 29

≅5.385.

5.385 is the length of each line segment according to the Pythagoras theorem and distance formula.

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The volume of the cylinder 1 = 25.12 cubic centimeters.

The volume of the cylinder 2 = 100.48 cubic centimeters.

The volume of the cylinder 3 = 226.08 cubic centimeters.

A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.

Given:

3 cylinders have a height of 8 cm cylinder one has a radius of 1 cm cylinder 2 has the radius of 2 cm cylinder 3 has a radius of 3 cm.

The volume of the cylinder 1,

= πr²h

= (3.14)(1)(8)

= 25.12 cubic centimeters.

The volume of the cylinder 2,

= πr²h

= (3.14)(4)(8)

= 100.48 cubic centimeters.

The volume of the cylinder 3,

= πr²h

= (3.14)(9)(8)

= 226.08 cubic centimeters.

Therefore, the volume of each cylinder is given above.

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According to the consecutive interior angles theorem, when two lines are parallel, the consecutive interior angles are supplementary to each other.

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The second graph is correct

Answer:

second graph

Step-by-step explanation:

just wanted to help the first person who answered get brainlist