what two requirements do you need for the chi square goodness of fit test

Answer: it cost 14 dollars

Step-by-step explanation:

Answer:

x = -324

Step-by-step explanation:

\( - 36 = \frac{x}{9} \\ - 36 \times 9 = \frac{x}{9} \times 9 \\ - 324 = x\)

Answer:

D or DD was not given any factor, but A was given which is 1, ADD= 1 multipltied by D

Answer:

w=40b

Step-by-step explanation:

Answer:

200

Step-by-step explanation:

You multiply 40 by 5.

Answer:

The new mean will be 20.

Step-by-step explanation:

The Mean Value of a Data Set

The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:

\(\displaystyle \bar x=\frac{\sum x_i}{n}\)

Where xi is the value of each data and n is the total number of values.

The mean of n=30 numbers is \(\bar x=18\). If each observation is increased by 2, then xi'=xi+2 and the new mean value will be:

\(\displaystyle \bar x'=\frac{\sum x'_i}{30}\)

\(\displaystyle \bar x'=\frac{\sum x_i+2}{30}\)

\(\displaystyle \bar x'=\frac{\sum x_i}{30}+\frac{\sum 2}{30}\)

The sum of 30 times 2 is 60, thus:

\(\displaystyle \bar x'=18+\frac{60}{30}=18+2=20\)

The new mean will be 20.

Answer:

equation: 10.00+2.50h=7.00+4.00h

10+2.5h-4h=7

10-1.5h=7

-1.5h=7-10

1.5h/1.5=-3/1.5

h=2

Answer:

2

Step-by-step explanation:

If you use rise over run, you should get to. From one point to the other, the rise is 2 and the run to the right is 1. So, you do 2 divided by 1, which is 2. So, the slope would be 2.

Answer: Yes you can use the HL theorem

Explanation:

HL = hypotenuse leg

The tickmarks tell us about the congruent hypotenuse sides. This takes care of the "H" from "HL".

The "L" portion is because BC = BC (reflexive property) which are the congruent legs.

So we have enough info to use the HL theorem to prove the triangles are congruent.

Note: The HL theorem only works for right triangles.

Answer:

\( \frac{1}{3} ( {21}^{2} ) \sqrt{ {23}^{2} - {10.5}^{2} } \)

\( = 3008.1\)

The volume of this square pyramid is about 3,008.1 mm^2.

Answer:

24x1.35=32.4

He should have recieved $32.40 in change.

Answer:

Percentage change = (14000-11200) / 11200 * 100

= 280000 / 11200

= 25%

So, your final answer is 25%

Hope this helps!

Step-by-step explanation:

Step-by-step explanation:

i guess it helps..if yuh need step by step explanation.comment i try to explain in worda

D. The set W would be a subspace of set of real numbers R cubed.

For a set to be considered a vector space, it must satisfy the following conditions:

1. It contains the zero vector (the additive identity).

2. It is closed under vector addition.

3. It is closed under scalar multiplication.

Since the set W is a subset of R cubed, it inherits the properties of R cubed, including the zero vector. Therefore, option C is not true.

Options A and B are not necessarily true for all subsets of R cubed. They may hold for some specific subsets, but they are not general properties that apply to all subsets.

Option D is the correct answer because it states that the set W would be a subspace of R cubed. A subspace is a subset of a vector space that is itself a vector space, satisfying all the properties of a vector space. Since W is a subset of R cubed, it would be a subspace if it satisfies the three conditions mentioned above.

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Answer:

(F.g(x))=x^2-10x+24

Step-by-step explanation:

when when we have a composition function, like f of g of x, we put the second function g of x in place of every x in f of x,

so f(x)=x^2-6x+8

and we will put x-2 which is g(x) in the place of every x

so f(g(x))=(x-2)^2-6(x-2)+8

so we ca n simplify that into f(g(x))=x^2-4x+4-6x+12+8

which simplifies to f(g(x))=x^2-10x+24

Answer:

x=20

Step-by-step explanation:

By the Triangle Sum Theorem, the angles of a triangle add up to 180. So we can set up the equation like this:

2x-10+70+4x=180

Combine Like terms

6x+60=180

Subtract 60 from both sides

6x=120

Divide by 6 to isolate the variable

x=20

Answer:x= 20

Step-by-step explanation:

As the equation of three angles of a triangle is 180°,

Then, 2x-10+70+4x=180

6x=120

So,x= 20

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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The points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

The points on the graph of f(x) = log9x can be calculated by substituting the given values of x in the equation. For example,

f(-1/81) = log9(-1/81) = log9(-1) - log9(81) = undefined

f(20) = log9(20) = log9(2*2*2*5) = log9(2) + log9(2) + log9(2) + log9(5) = 1 + 1 + 1 + 1.5 = 4.5

f(11/9) = log9(11/9) = log9(11) - log9(9) = 1.041393 - 0.954210 = 0.087183

f(-13) = log9(-13) = log9(-1) - log9(13) = undefined

f(2439) = log9(2439) = log9(3*13*37) = log9(3) + log9(13) + log9(37) = 0.477121 + 1.11394 + 1.579789 = 3.168910

f(181) = log9(181) = log9(3*3*7*7) = log9(3) + log9(3) + log9(7) + log9(7) = 0.477121 + 0.477121 + 0.84509 + 0.84509 = 2.55231

f(2) = log9(2) = log9(2) = 1

Hence, the points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

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Answer: no solution

Step-by-step explanation:

2× (7-2)>9+6

Calculate the sum or difference

2×5>9+6

Calculate the sum or difference

2 × 5 > 15

2×5>15

Calculate the product or quotient

10 > 15

10 > 15

The solution of the inequality

no solution

The z value for  a 97.8% confidence interval estimation is determined as 2.29.

The z value for  a 97.8% confidence interval estimation is calculated as follows;

The find the Z score, go to a Z lookup table which is found in a textbook or on an internet source. z table is created to give the possibility in a one-tailed analysis.

A confidence interval is a two-tailed examination,  in order to prepare the z score for 97.8%, look up the probability of 98.9%.

The value of 98.9% is

= (0.978 + 1 )/ 2

= 0.989 or 98.9%.

This implies that the z score of the date is 2.29.

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Answer:

They will each get 7 trout.

Step-by-step explanation:

Since there are two people (Nancy and Jason), take the 14 trout, and divide it amongst the two, so, they each get 7 fish.

Answer:

Step-by-step explanation:

\(\frac{480+24(x-40)}{x}\)

The numerator of the rational expression the money he earned for 'x' hours

The rate at which William is paid for each hour in excess of 40 hours 24.

x = 50 hours = (40 + 10 ) hours

The amount paid for excess 10 hours = 24 *10 = 240

Total amount earned for the week = 480 + 240 = 720

Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148. We may answer this question by using the definition of logrithmic.

Mathematical operations that relate to a number's logarithm are known as logarithmic functions. The power that a given basis must be increased in order to obtain a particular number is known as the logarithm of the number.

Although 10 (also known as the common logarithm) is the base that is most frequently used, logarithms can be calculated in relation to any positive base higher than 1. If the base is 10, the logarithm of such an integer x with regard to a base b is written by log(base b)(x), or just log(x).

We can compress the given logarithm via the logarithmic identity log(base a)(bc) = c * log(base a)(b):

Sqrt(3.5.11) = Log((3.5.11)(1/2), 9) = Log((3.5.11)*(1/2), 9) = (1/2) * Log (3.5.11, 9)

We must now calculate that logarithm of 9 in base 3.5.11. This can be changed to a log with a more recognisable column, such as base 10 or base e, using the change-of-base formula. Using the base 10 scale

3.5.11, 9) = 9)/log (3.5.11)

We can calculate this using a calculator:

log(9) = 0.9542 (reduced to 4 decimal places)

log(3.5.11) = log(3) + log(5) + log(11) = 0.4771, 0.6978, and 1.0414, respectively, yielding 2.2174. (rounded to 4 decimal places)

Therefore:

sqrt(3.5.11),9 = (1/2) log(3.5.11,9) = (1/2) log(9)/log(3.5.11)) = (1/2) log(0.9542/2.2174) = 0.2148 log(3.5.11,9) = (1/2) log(3.5.11, 9) = (1/2) 

Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148.

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The expanded form of the logarithm is:

log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)

What is logarithm?

A logarithm is a mathematical function that tells us what exponent is needed to produce a given number, when that number is expressed as a power of a fixed base. In other words, logarithms tell us how many times we need to multiply the base by itself to get the desired number.

We can use the property of logarithms that says:

log base b (a * c) = log base b (a) + log base b (c)

to expand the logarithm.

Therefore, we have:

log base 9 √(3.5.11) = log base 9 √(3 * 5 * 11)

= log base 9 (3) + log base 9 (5) + log base 9 (11)

So, the expanded form of the logarithm is:

log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)

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a) f(n) = 3n^2 is not O(g(n))

b) f(n) = 4n is O(g(n))

c) f(n) = 6nlog(n) + 5n is O(g(n))

d) f(n) = (log(n))^2 is not O(g(n))

1. Proof of the identity ∑[i=1 to n] ∑[j=1 to i] 2 = n(n+1)/2:

Let's evaluate the double sum on the left-hand side:

∑[i=1 to n] ∑[j=1 to i] 2

We can rewrite this as:

∑[i=1 to n] (2i)

Now, let's simplify the right-hand side of the equation:

n(n + 1)/2

Expanding the expression, we get:

\((n^2 + n)/2\)

To prove the identity, we need to show that the double sum on the left-hand side is equal to the expression on the right-hand side.

Let's evaluate the double sum:

∑[i=1 to n] (2i) = 2(1) + 2(2) + ... + 2(n)

Using the formula for the sum of an arithmetic series, we have:

∑[i=1 to n] (2i) = 2(1 + 2 + ... + n) = 2[(n(n + 1))/2] = n(n + 1)

We have shown that the left-hand side is equal to n(n + 1), which matches the expression on the right-hand side. Therefore, the identity is proven.

2. Solution to the recurrence T(1) = 4c, T(n) = 2cn + T(n/2):

To solve the recurrence relation, we can use the method of recursion tree and prove the solution by induction.

Step 1: Guess the solution: We assume that the solution to the recurrence relation is T(n) = knlogn for some constant k.

Step 2: Base case: T(1) = 4c (given). Plugging in n = 1 in the assumed solution, we have:

T(1) = k(1)log(1) = k(0) = 4c

From this, we can deduce that k = 4c.

Step 3: Inductive step: Assume that the solution holds for T(n/2), i.e., T(n/2) = (4c)(n/2)log(n/2).

Now, let's compute T(n) using the given recurrence relation:

T(n) = 2cn + T(n/2) = 2cn + (4c)(n/2)log(n/2)

Simplifying further, we get:

T(n) = 2cn + 2cnlog(n/2) = 2cn(1 + log(n/2))

Using log property, we can write log(n/2) as log(n) - log(2) = log(n) - 1.

Substituting this back into the equation, we have:

T(n) = 2cn(1 + log(n) - 1) = 2cnlog(n)

We have shown that T(n) = 2cnlog(n), which matches our assumed solution.

Step 4: By induction, we have proven that the solution to the recurrence relation T(1) = 4c, T(n) = 2cn + T(n/2) is T(n) = 2cnlog(n).

3. Proving or disproving f(n) = O(g(n)) for the given functions:

a) \(f(n) = 3n^2\)

To prove or disprove f(n) = O(g(n)), we need to show that there exist constants c and n0 such that f(n) <= c * g(n) for all n >= n0.

Let g(n) = nlog(n). Let's evaluate the limit of f(n)/g(n) as n approaches infinity:

\(lim (n- > ∞) (3n^2 / (nlog(n))) = lim (n- > ∞) (3n / log(n))\)

Using L'Hôpital's rule, we differentiate the numerator and denominator:

lim (n->∞) (3 / (1/n)) = lim (n->∞) (3n) = ∞

Since the limit is not finite, we can conclude that \(f(n) = 3n^2\) is not O(g(n)).

b) f(n) = 4n

Similarly, let's evaluate the limit of f(n)/g(n) as n approaches infinity:

lim (n->∞) (4n / (nlog(n))) = lim (n->∞) (4 / log(n))

Again, using L'Hôpital's rule:

lim (n->∞) (0 / (1/n)) = lim (n->∞) (0) = 0

Since the limit is finite, we can conclude that f(n) = 4n is O(g(n)).

c) f(n) = 6nlog(n) + 5n

Evaluating the limit:

lim (n->∞) ((6nlog(n) + 5n) / (nlog(n))) = lim (n->∞) ((6log(n) + 5) / log(n))

Using L'Hôpital's rule:

\(lim (n- > ∞) ((6 / (1/n)) / (1/n)) = lim (n- > ∞) (6) = 6\)

Since the limit is finite, we can conclude that f(n) = 6nlog(n) + 5n is O(g(n)).

d) \(f(n) = (log(n))^2\)

Evaluating the limit:

\(lim (n- > ∞) (((log(n))^2) / (nlog(n))) = lim (n- > ∞) ((2log(n)/n) / (1/n)) = lim (n- > ∞) (2log(n)) = ∞\)

Since the limit is not finite, we can conclude that \(f(n) = (log(n))^2\)  is not O(g(n)).

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the probability that at most 3 complaints will be received during the next 4 hours is 0.2381 or approximately 23.81%.

Let X be the number of complaints received in 4 hours. Then X follows a Poisson distribution with mean λ = 0.5 complaints/hour × 4 hours = 2 complaints.

To find the probability that at most 3 complaints will be received during the next 4 hours, we can use the Poisson probability formula:

P(X ≤ 3) = e^(-λ) * [λ^0/0! + λ^1/1! + λ^2/2! + λ^3/3!]

P(X ≤ 3) = e^(-2) * [1/1 + 2e^(-2)/1! + 4e^(-2)/2! + 8e^(-2)/3!]

P(X ≤ 3) = 0.2381

what is number?

A number is a mathematical object used to quantify and measure things. It can be used to represent quantities such as size, amount, distance, time, and many other things. Numbers can be integers, fractions, decimals, or irrational numbers, and they can be positive, negative, or zero. In mathematics, numbers are used to perform calculations and solve problems in various fields such as science, engineering, economics, and more.

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The total number of red marbles in the vase are 10.

A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.

The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.

Now, according to the question;

Let 'x' be the red marbles in the vase.

Let 'y' be the orange marbles in the vase.

The total number of marbles in the vase are 60

x  + y = 60 (equation 1)

The ratio of red marbles to orange ones is 1:5.

Thus, x/y = 1/5

cross multiplying;

5x = y

or y = 5x

substitute the value of y in equation 1;

x  + y = 60 (equation 1)

x  + 5x = 60

6x = 60

x = 10  (red marbles)

Thus, the number of red marbles in the vase are 10.

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Answer: The bench would cost about 396$

hope I helped you :D

Answer:

the bench costs $350

Step-by-step explanation:

Let's assume cost of table be T and bench be B

therefore,                 T+B= 746        ...........(1)

while we are given    T= B+46     ............(2)

                                  using (2) in (1)

                              [B+46] + B =746

                               2B= 700

                        B=350

So, cost of bench= $350

To estimate the unknown parameter λ using maximum likelihood, given X₁ = 3, X₂ = 4, X₃ = 5, we need to find the value of λ that maximizes the likelihood function based on the observed data. The likelihood function represents the probability of observing the given data for different values of λ.

The likelihood function L(λ) is defined as the product of the probability density function evaluated at each observed data point. In this case, we have L(λ) = f(3) * f(4) * f(5), where f(x) is the given probability density function.
Substituting the values into the likelihood function, we have L(λ) = ((λ - 1)/3^λ) * ((λ - 1)/4^λ) * ((λ - 1)/5^λ).
To find the maximum likelihood estimate of λ, we need to maximize the likelihood function. Taking the natural logarithm of the likelihood function (ln L(λ)), we can simplify the problem to finding the value of λ that maximizes ln L(λ).
Taking the derivative of ln L(λ) with respect to λ and setting it to zero, we can solve for the maximum likelihood estimate of λ.
By solving the equation, we can obtain the estimate for λ based on the observed data X₁ = 3, X₂ = 4, X₃ = 5.

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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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