consider the process of throwing $m$ balls into $n$ bins, where each ball is thrown into a uniformly random bin, independent of other balls. what is the expected number of balls in a particular bin $b$?

the dimensions will minimize the amount of paper used is with length 4 inch and a width 12 inch.

What is the area of the rectangle?

The area of a rectangle (A) is the product of its length 'a' and width or breadth 'b'. So, Area of Rectangle = (a × b) square units.

We have given

Johnny is designing a rectangular poster to contain 12 in² of printing with a 1-in margin at the top and bottom and a 3-in margin at each side.

Let,

l be the length and w be the width.

Area is A = l * w

Johnny is designing a rectangular poster to contain 12 in² of printing

i.e. Area of the inner printed section 12 = lw  .........(1)

A 1-in margin at the top and bottom and a 3-in margin at each side.

i.e. l'=l+2 and w'=w+6

The total Area of the Poster is

A = (l+2) + (w+6) ...........(2)

Substitute the value of l from (1) in (2),

A = (12/w + 2) (w + 6)

A = 12 + 72/w + 2w + 12

A = 24 + 72/w + 2w

Differentiate w.r.t w,

A' = -72/w² + 2

For critical value put A'=0,

-72/w² + 2 = 0

2 = 72/w²  

w² = 72/2

w² = 36

w = 6

Differentiate again w.r.t w,

A''(w) = 2(72/w²)

A''(6) = 2(72/(6)²)

A''(6) = 2(72/36)

A''(w) = 2*2 = 4>0

It is minimum at w=6.

Substitute in (1),

12 = lw  

l = 2

The dimensions required are

l' = l + 2

= 2+2

= 4 inch

w'=w + 6

= 6 + 6

= 12 inch

Hence, the dimensions will minimize the amount of paper used is with a length 4 inch and a width 12 inch.

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The hose will take 28.27 minutes to fill the second aquarium.

Given,

Rectangular Aquarium - 1

Length = 12 inches

Width = 13 inches

Height = 14 inches

Time taken by a hose to fill the aquarium = 3 minutes

Rectangular Aquarium - 2

Length = 21 inches

Width = 28 inches

Height = 35 inches

We have to find the time taken by the same hose to fill the aquarium 2.

Volume of Aquarium 1 = length × width × height

= 12 × 13 × 14 = 2184 inch³

To fill 2184 inch³, the hose will take 3 minutes.

Now,

Volume of Aquarium 2 = length × width × height

= 21 × 28 × 35 = 20580 inch³

Here,

The time taken by the hose to fill a volume of 20580 inch³;

= 3 × 20580 / 2184 = 28.27 minutes

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Answer: 11.9 pounds

Step-by-step explanation:

142.5 - 130.6 = 11.9

Reducing the variation of a process will increase the width of a given confidence interval relative to that process.

Option C is correct .

In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as a confidence interval. By employing the dimensions of values used in the computation of the intervals, it is simple to establish the link between components of two confidence intervals. The width is a fundamental component in these range estimates, which are affected by sample size, etc.

Hence, reducing the variation of a process will increase the width of a given confidence interval relative to that process is false.

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The new position of the anchor is 7 1/5 below the surface of the ocean

Initially the anchor is located 15 3/5 m below the surface of the ocean, this is same as = -15 3/5 m

The anchor is further lowered and the position now is

=   -15 3/5 m - 4 1/5 m

= -99 /5 m

Then the anchor is pulled up 12 3/5 m  the new position now is

= -99 /5 m + 12 3/5 m

= -36/5

= -7 1/5

= -7.2

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please look in down below all in there

A test's standard deviation is 5 and its mean is 85. scores is within one standard deviation of the mean is 25/n^12.

The square root of the variance of a random variable, sample, mean ,statistical population, data set, or probability distribution is that variable's standard deviation. Although less robust in practice, it is algebraically simpler than the average absolute deviation.The fact that the standard deviation is expressed in the same unit as the data, as opposed to the variance, is a useful characteristic of the statistic.

variance = 5^2 = 25

standard deviation of the mean = ( variance / n )^1/2

= (25/n)^1/2

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The operator used in the statement a > b is a comparison operator. In this case, true will be returned if the value of a is greater than the value of b, whereas false if the value of a is less than the value of b.

Code decisions require comparison operators. Comparison operators are used in the statement a > b. Using a and b as variables, it compares their values, returning true if a is greater than b, and false otherwise.

By comparing the values of two variables, the program can make decisions. Coders should understand how comparison operators work since they are used frequently in programming.

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The required function of the line would be y = 2x + 1.

The slope-intercept form is one rule to represent linear function rules.

f(x) = mx+b is sometimes used. In any scenario, m and b describe the line's overall features. The slope is denoted by m, while the y-intercept is denoted by b.

Linear equations, or straight-line equations, can be quickly recognized as they have no terms with exponents in them. For example, you will find an x or a y , but never an x². Each linear equation describes a straight line, which can be expressed using the slope intercept form equation.

According to the given question,

The coordinates of the y-intercept would be (0, 1).

The value of the x-coordinate is 1 when y-coordinate is 3.

Here the line passes through points (0, 1) and (1, 3).

Let the required linear function would be

     y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = 1

x₂ = 1, y₂ = 3

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 3 = (3 - 1)/(1 - 0 )[x -1]

⇒ y - 3 = (2)[x -1]

⇒ y - 3 = 2x - 2

⇒ y = 2x - 2 + 3

⇒ y = 2x + 1

Therefore, the required function of the line would be y = 2x + 1 which is shown in the given question.

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The expression that has a value of 40 when x = 10.8. is (C) (x² ÷ 18) + 33.52

The complete question is added at the end of this solution

From the question, we have the following expressions that can be used in our computation:

A 4,320 ÷ x

B 288/x + 16

C (x² ÷ 18) + 33.52

D (1,752 ÷ x) – 162/29

F x/12 + 36

The value of x is given as

x = 10.8

So, we evaluate the expressions at this value of x

Expression A: 4,320 ÷ x

4,320 ÷ 10.8 = 400 --- false

Expression B 288/x + 16:

288/10.8 + 16 = 42.7 --- false

Expression C (x² ÷ 18) + 33.52:

(10.8² ÷ 18) + 33.52 = 40 --- true

Expression D (1,752 ÷ x) – 162/29:

(1,752 ÷ 10.8) – 162/29 = 156.6 --- false

Expression F x/12 + 36:

10.8/12 + 36 = 36.9 --- false

Hence, the only expression is (x² ÷ 18) + 33.52

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Complete question

Select all the expressions that have a value of 40 when x = 10.8.

A 4,320 ÷ x

B 288/x + 16

C (x² ÷ 18) + 33.52

D (1,752 ÷ x) – 162/29

F x/12 + 36

Answer:

1. $105

2. $144

Step-by-step explanation:

For the first question:

4.20 × 25 = 105

For the second question:

4.80 × 30 = 144

Could you please give me brainliest for this? Thank you!

No, this sample is not representative of all high school seniors in the US as the sample is selected by an optional web survey, which is not a good sampling technique as non-response bias is introduced.

90% confidence interval for a population proportion.

= 0.55 ± 1.645 *  √0.55(1-0, 55)/1509

= 0.55 ± 0.0211

= (0.5289, 0.5711)

We are 90% confident the true proportion of high school seniors who are fairly certain they will participate in a study abroad program in college lies between 52.89% to 57.11%b

90% confidence means if we select 100 samples, 90 of them will have their sample statistic within the 90% confidence interval. Or otherwise, we can be 90% certain that the population parameter will fall within the 90% confidence interval.

Yes, as the lower limit of the confidence interval is greater than 50%, there is strong evidence to support the claim that the majority of high school seniors are fairly certain that they will participate in a study abroad program in college.

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Answer:

1.41 inches per hour

Step-by-step explanation:

volume of water for 3 hrs=4.23 inches

v of water for 1 hours=4.23/3=1.21inches

Answer:

It would be the third option, because the square root of 85 is 9.22, and 28/3 is 9.33 repeated.

Hope this helps, have a great day! :D

Step-by-step explanation:

The percentage error is 8.3%

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction.

Given that, Akira is redecorating her bedroom. She misread the markings on her ruler and thought a picture frame she bought was 5.2 centimetres wide. The frame's actual width was 4.8 centimetres.

Percentage Error = ((Estimated Number – Actual Number)/ Actual number) x 100.

= (5.2-4.8)/4.8x100 = 8.3%

Hence, The percentage error is 8.3%

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If the R is an equivalence relation then for every a and b in set R , if a = b then aRb exists.

If R is an equivalence relation on set A, a and b are in A and [a]=[b]

By the definition of the equivalence relation we can say that R is reflexive

Hence aRa and so by definition of equivalence class a ∈ [a] .

Since [a] = [b] and a ∈ [a] we can say that a ∈ [b] by the definition of set equality.

Now we will use the definition of equivalent class we can say that aRb .

An equivalence relation is a reflexive, symmetric, transitive binary link. The relationship of equipollence between line segments in geometry is one example of an equivalence relation.

Each equivalence relation separates the underlying set into distinct equivalence classes. Two items in the given set are only comparable to one another if and when they belong to the same equivalence class.

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A graph which best represents the polynomial function f(x) = (x + 1)(x − 1)(x − 4) is: D. Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 1, 1, and 4. The graph intersects the y axis at a point between 0 and 5.

In Mathematics, a polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations.

This ultimately implies that, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

In this context, we can reasonably and logically deduce that the zeros of a polynomial function are all of the values (x-intercepts) on the x-coordinate that makes this polynomial function equal to zero and these include the following on a graph:

Zeros = (-1, 0)

Zeros = (1, 0)

Zeros = (4, 0)

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Answer:

O Your friend. If f is a function, then the line is not vertical.

Step-by-step explanation:

If you are given that the equation is a linear function, it can't have any undefined values.

Answer:

Your friend. If ƒ is a function, then the line is not vertical.

Step-by-step explanation:

I just had this question, and I solved it and got it right, see the picture

The value of E(XY) is equivalent or equal to -1 according to the joint pdf having function f(x, y) = xe^−x(1 + y) x ≥ 0 and y ≥ 0 0.

Given that:

f(x,y) = xe^-x(1+y), where x ≥ 0 and y ≥ 0 0.

E(XY) = ∫∞ ∫∞ xy. xe^−x(1 + y) dx dy

            0   0

E(XY) = ∫∞ ∫∞ x^2y . e^−x(1 + y) dx dy

            0   0

E(XY) = ∫∞ x^2 . e^−x (∫∞ y e^-xy dy) dx

             0                     0

E(XY) = ∫∞ x^2 . e^−x (-1/x) dx

             0

E(XY) = - ∫∞ x . e^−x dx

               0

E(XY) = - 1

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y are equal to i.e. E(XY) = -1.

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The correct answer for the question that is being presented above is this one: "D.The distributions are somewhat similar; C.The distributions are similar." Data Set 1 has a mean of 84 and a MAD of 6. Data Set 2 has a mean of 78 and a MAD of 8. You conclude about the two distributions: .The distributions are somewhat similar; The distributions are similar.

The system of equation - 7x + y = 19 and - 2x + 3y = - 9 have solution at

(-101/9, -3318/19).

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given, A system of equations - 7x + y = 19 and - 2x + 3y = - 9.

Now, multiplying eqn(i) by 2 and eqn(ii) by 7 we get,

- 14x + 2y = 38...(iii) and - 14x + 21y = - 63...(iv)

Now, subtracting eqn(iii) from eqn(iv) we get,

 (- 14x + 21y = - 63)

- (- 14x + 2y = 38)

_______________

           19y = - 101.

               y = - 101/19

and putting the value of y in eqn(iv) we get x = - 3318/19.

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If f is continous on [a,b], then f attains an absolute maximum value f(c) and absolute minimum value f(d) at some numbers c and d in [a,b] then it is a true statement

What is an absolute maximum?

An absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.

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The measure of angle < HEB = 60 degrees.

Given:

if you draw square abcd and extend the sides by equal lengths to form square efgh.

so that the area of abcd is half the area of efgh.

Let AB = x and HA = x

so area of square ABCD = x * x

= x^2

< HEB = 60 so < BHE = 30

EB = y

HE = 2y

HB = x + y

so x + y = [tex]\sqrt{3}[/tex] y

x = [tex]\sqrt{3}[/tex] y - y

x = ([tex]\sqrt{3}[/tex] - 1 ) y

y = x /  ([tex]\sqrt{3}[/tex] - 1 )

squaring on both sides

y^2 =  x^2 /  ([tex]\sqrt{3}[/tex] - 1 )^2

= x^2 / 3 - 1

= x^2 / 2

Area of EFGH = (2y)^2 = 4y^2 = 2x^2 = 2 * area of ABCD.

Therefore < HEB = 60 degrees.

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In order to estimate the population proportion within 5%, a sample size of at least 384 is needed.

The number of individuals or observations included in a study is referred to as the sample size. Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.

This can be calculated using the formula:

n = (z^2 * p * (1-p)) / (e^2)

where z is the z-score corresponding to a 95% confidence level, p is the estimated proportion of people in favor of legalizing marijuana, and e is the margin of error (5%).

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The correct options are: Polygon P is similar to polygon P′ and The angle measurements of polygon P are equal to the corresponding angle measurements of polygon P′

The dilation of a figure is enlargement or reduction of its original image to final image by a certain scale factor.

Given that, Polygon P is dilated from the origin by a scale factor other than 1 to create polygon P′

We know that, in dilation, both figures are similar not congruent, because they get enhanced or reduced by a certain scale factor, if scale factor is 1 then they can be congruent also.

Since, both figure are similar, therefore, their corresponding angles are congruent.

Hence, correct options are ; Polygon P is similar to polygon P′ and The angle measurements of polygon P are equal to the corresponding angle measurements of polygon P′.

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Answer: The answer is 27

Answer:

27

Step-by-step explanation:

I hope its helpful to you.

The 4 different types of items will be selected.

What is the combination?

Combinations are mathematical operations that count the number of possible configurations for a set of items where the order of the selection is irrelevant. In combinations, you can select the items in any order.

[tex]nCr = \frac{n!}{(n - r)! \ r!}[/tex]

This formula to find the number of combinations by using r objects from the n objects is also referred as the ncr formula.

so, we have 4 items and a person randomly selects 3.

[tex]nCr = (n, r) = (4, 3)[/tex]

[tex]= \frac{4!}{3!(4 - 3)!}[/tex]

= 4! / 3!

= 4

Hence, The 4 different types of items will be selected.

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The number of defectives follows binomial distribution with parameters (n,p) and if n>30 then binomial distribution goes to the Normal' approximation.

Given that,

We have to find which of the following approximation approaches is adequate in a test of the equality of the percent defectives from two populations when the sample sizes are big (> 30).

We know that,

The normal curve is roughly followed by the sample distribution of averages or proportions from numerous independent experiments. The population value that corresponds to a sample proportion or average is its expectation.

Therefore, the number of defectives follows binomial distribution with parameters (n,p) and if n>30 then binomial distribution goes to the Normal' approximation.

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This enabled the borrower to obtain 90 percent financing while avoiding the additional cost of pmi. these loans are more commonly referred to as  piggyback mortgage loans.

A loan is the lending of cash via one or more individuals, organizations, or different entities to other individuals, corporations, etc. The recipient incurs a debt and is normally susceptible to pay hobby on that debt till it is repaid as well as to repay the foremost amount borrowed.

A mortgage is a shape of debt incurred by using an character or different entity. The lender—commonly a business enterprise, economic organization, or authorities—advances a amount of money to the borrower. In return, the borrower agrees to a sure set of phrases together with any finance charges, hobby, repayment date, and different situations.

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Answer:

I don’t know

Step-by-step explanation: