Let X 1
​
,X 2
​
,…,X 18
​
be a random sample of size 18 from a chi-square distribution with r=1. Recall that μ=1 and σ 2
=2. (a) How is Y=∑ i=1
18
​
X i
​
distributed? (b) Using the result of part (a), we see from Table IV in Appendix B that P(Y≤9.390)=0.05 and P(Y≤34.80)=0.99. Compare these two probabilities with the approximations found with the use of the central limit theorem.

Answer:

x=20

Step-by-step explanation:

How I did it was I divided 3/12 to get .25 and 5 divided by .25 is 20. So x is equal to 20.

We have a vertical and a horizontal lines, the equations are:

Line A: x = -5  (vertical one)

Line B: y = -5  (horizontal one)

Remember that the general linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Now, line A passes through  (–5, –2), (–5, 7), then the slope is:

a = (7 + 2)/(-5 + 5) = 9/0

Notice that if we divide by zero, the slope tends to infinity, so we have a vertical line.

In this case, the line A will be x = -5.

Now line B passes through points: (7, –5), (–2, –5)

Then the slope is:

a = (-5 + 5)/(-2 - 7) = 0/-9 = 0

Then the line is:

y = 0*x + b

And passes through (7, –5), then:

-5 = 0*7 + b

-5 = b

So this line is y = -5.

Concluding, we have:

Line A: x = -5

Line B: y = -5

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Answer:

Line A: no slope

The equation of line A is x = -5

Line B has a slope of 0

The equation of line B is y = -5

Step-by-step explanation:

I did it already :)

The selling price for the given cost price and profit percentage is ₹420.5.

The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.

Given that, the cost price of a bag of almonds is ₹290 and it is sold with a profit of 45%.

We know that, Selling price = (100+Profit%)/100 ×CP

Here, Selling price = (100+45)/100 ×290

= 145/100 ×290

= 1.45×290

= 420.5

Therefore, the selling price is ₹420.5.

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Answer:

y = 3x + 1

Step-by-step explanation:

The equation for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

Answer:

-5m - 10

Step-by-step explanation:

1/3(3m+6)-2(3m+6)

= 1m + 2 - 6m - 12

= -5m - 10

So, the answer is -5m - 10

Answer:

-5(m+2)

Step-by-step explanation:

1/3(3m+6)-2(3m+6)

combine like terms

-5/3(3m+6)

Distribute

-5m - 10

common factor

-5(m+2)

The slope of the least squares line, also known as the regression coefficient or beta coefficient (b1), is calculated using the covariance between the two variables (x and y) and the variance of x. The formula for calculating the slope of the least squares line is: False.

b1 = Cov(x, y) / Var(x)

In the given statement, it is mentioned that the covariance of x and y is 26.16, and the standard deviation of x is 32.7. However, the variance of x is needed to calculate the slope of the least squares line, not the standard deviation.

Therefore, without knowing the variance of x, we cannot determine the slope of the least squares line with the given information. The statement "b1 = 0.80" is not correct as it is not supported by the information provided.

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Answer:

13= hypotenuse

12=adjacent

5=opposite

The exact value of sin(π/6) is 1/2.

To find the exact value of sin(π/6), we can use the unit circle or the trigonometric identity for the sine function. In the unit circle, π/6 corresponds to an angle of 30 degrees, which lies in the first quadrant.

At this angle, the y-coordinate of the corresponding point on the unit circle is 1/2. Since sin(θ) represents the ratio of the opposite side to the hypotenuse in a right triangle, for an angle of 30 degrees, sin(π/6) is equal to 1/2.

Alternatively, we can use the trigonometric identity sin(θ) = cos(π/2 - θ). Applying this identity, we have sin(π/6) = cos(π/2 - π/6) = cos(π/3). Now, π/3 corresponds to an angle of 60 degrees, which lies in the first quadrant.

At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2. Therefore, cos(π/3) = 1/2. Substituting this value back into sin(π/6) = cos(π/3), we get sin(π/6) = 1/2.

In both approaches, we find that the exact value of sin(π/6) is 1/2, indicating that the sine function of π/6 radians is equal to 1/2.

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the perimeter of the equilateral triangle with a side length of 12√3 is 36√3 units.

In order to find the perimeter of the given triangle, we have to find the side of the triangle. The altitude of the triangle  = 18 inches. Let us assume the side of the triangle as a. The formula for calculating the altitude of an equilateral triangle is : Altitude  =√3/2×a  (side)

18 =√3/2 × a

a = 18 × 2√3

a = 36√3

a = 36 ×√3 / √3×√3

a =36√3/3

a = 12√3 inches.

If the side of an equilateral triangle is 12√3, then all three sides of the triangle are of equal length, since it is an equilateral triangle. Therefore, the perimeter of the triangle is simply the sum of the lengths of its three sides. Since each side of the triangle has a length of 12√3, the perimeter is: Perimeter = 3 x (12√3) = 36√3.

Therefore, the perimeter of the equilateral triangle with a side length of 12√3 is 36√3 units.

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The correct solution to the arithmetic expression (2 8)/2*9/3 using the order of operations as employed by Oracle 12c when solving equations is 4.

According to the Order of Operations, the first step is to evaluate expressions inside parentheses, then perform any multiplications or divisions, and finally perform any additions or subtractions. In this expression, the first step would be to evaluate the expression inside the parentheses: (28)/2. This evaluates to 14.

Next, the expression becomes 14 * 9/3. According to the Order of Operations, we need to perform the multiplication first, so 14 * 9 = 126. Finally, we perform the division: 126/3 = 42.

So, the correct solution to the expression (2 8)/2 * 9/3 is 42.

Order of operations is a set of rules used to determine the sequence in which arithmetic operations should be performed in a mathematical expression to obtain the correct result. The rules ensure that operations are performed in a consistent and predictable manner.

The order of operations is typically represented by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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Answer:

No

Step-by-step explanation:

Without even answering 218*12 it is obvious this is the wrong answer

the last digit of each number determines the last digit in the answer

218 has 8 as the last number and 12 has 2

multiply them together

2*8 is 16

the last digit is 6 and not 1

Answer:

No- 218 * 12 = 2616.

Multiply with an algorithm and add the partial products up to check. You don't get 5,521 when you multiply 218 * 12.

Nul(A) = Nul(B) , Col(A) = Col(B) in integer matrices.

Describe matrix using an example?

A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements.

                                 In addition to many other areas of mathematics, matrices have extensive applications in the fields of engineering, physics, economics, and statistics.

The null space of any matrix A consists of all the vectors

 X  such that Ax = 0

And the column space of a matrix A is the span of its column vectors.

Let  A = \(\left[\begin{array}{ccc}1&0&0 \\0&1&0\\0&0&1\end{array}\right]\)

Therefore, Nul(A) = {(0,0,0,w ) w∈ Z }

 Col(A) = span{ (1,0,0), (0,1,0) , (0,0,1) }

By using definition of Null space of matrix and column space of matrix.

 Let B = \(\left[\begin{array}{ccc}1&1&0\\0&1&0\\0&0&1\end{array}\right]\)        

Nul(A) = {(0,0,0,w ) w∈ Z }

 Col(A) = span{ (1,0,0), (0,1,0) , (0,0,1) }

Hence Nul(A) = Nul(B) , Col(A) = Col(B)

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a) 20% 60 of  is 12

b) 25% of 24 is 6

c) 4% of 600 is 24

Here the problem we are dealing with is related to percentage, which could be a division or a proportion in which the value of the entire is continuously 100. is represented by the symbol "%".

a) let us consider the missing number to be x

so, the problem will be 20% of  x= 12

=> 20/1000* x= 12

=>20x= 12*100

=> x= 12*100/20 = 60

b) let the percentage be x

so, the problem will be x% of 24 =6

=>x/100* 24= 6

=>24x=600

=>x=600/24 =25

c)  here, we are given  4% of 600=?

=4/100* 600

=24

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Answer: You will need to know how many members there are and then divide 2,000 by the amount of members that will then give u ur answer

Step-by-step explanation:

Answer:

Answer is B

Step-by-step explanation:

\(12x - y = 25 \\ 9x + y = 17 \\ x = \frac{17 - y}{9} \\ 12( \frac{17 - y}{9} ) - y = 25 \\ \)

\(\frac{204}{9} - \frac{12}{9} y - y = 25 \\ \frac{204}{9} - \frac{21y}{9} = 25 \\ - \frac{21y}{9} = 25 - \frac{204}{9} \\ - \frac{21y}{9} = 2.33 \\ - 21y = 20.997 \\ y = - 0.99\)

\(y = - 1 \\ x = \frac{17 - y}{9} \\ x = \frac{17 - - 1}{9} = \frac{18}{9} \\ x = 2\)

Answer:

c

Step-by-step explanation:

I just did this question for my math class and i got it right

There were 682 children's and 332 adults were admitted when the entrance charge to an park is $4 for adults and $1.50 for children.

Given that,

The entrance charge to an amusement park is $4 for adults and $1.50 for children. 351 persons visited the park on one particular day, and 1014 dollars in entrance fees were collected.

We have to find how many people and kids were allowed inside.

We know that,

We get equations as,

1.5x+4y=351 ----->equation(1)

The other equation is

x+y=1014 ----->equation(2)

Take the equation(2)

x+y=1014

y=1014-x

Substitute y=1014-x in equation(1)

1.5x+4y=351

1.5x+4(1014-x)=351

1.5x+2056-4x=351

1.5x-4x=351-2056

-2.5x=-1705

2.5x=1705

x=1705/2.5

x=682

Substitute x=682 in equation(2)

y=1014-x

y=1014-682

y=332

Therefore, There were 682 children's and 332 adults were admitted when the entrance charge to an amusement park is $4 for adults and $1.50 for children.

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(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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Answer:

160 min or 2.66666667 hours per a week

Step-by-step explanation:

its very simple

40*4=160

hope I helped :)

The average student headcount for the spring terms is: 10700

A graph is a non-linear kind of data structure made up of nodes or vertices and edges. The edges connect any two nodes in the graph, and the nodes are also known as vertices. This graph has a set of vertices V= { 1,2,3,4,5} and a set of edges E= { (1,2),(1,3),(2,3),(2,4),(2,5),(3,5),(4,50 }.

We have the information:

From the graph,

Number of headcounts for spring '0.2 - 0.3' = 10900

Number of headcounts for spring '0.3 - 0.4' = 10500

Number of headcounts for spring '0.4 - 0.5' = 10700

The average student headcount for the spring terms is:

= 1/3 (10900 + 10500 + 10700)

= 10700

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For complete question, to see the attachment.

On solving the provided question, we can say that 1 degree = 3600 arc seconds and 1 degree = 60 arc minutes.

A 160 degree angle is measured in arc minutes, often known as arcmin, arcmin, arcmin, or arc minutes (represented by the sign '). One minute is equal to 121600 revolutions, or one degree, hence one degree equals 1360 revolutions (or one complete revolution). A degree, also known as a complete angle of arc, angle of arc, or angle of arc, is a unit of measurement for plane angles in which a full rotation equals 360 degrees. A degree is sometimes referred to as an arc degree if it has an arc of 60 minutes. Since there are 360 degrees in a circle, an arc's angles make up 1/360 of its circumference.

1 degree = 3600 arc seconds

1 degree = 60 arc minutes

A. 2 degree 18'36 = 2 + 18/60 + 36 / 2600 = 231 / 100 degree

B. 36 ′ 18 ′′ = 36/60 + 18/2600 = 121 / 200 degree

C. 7 degrees 59′ 59′′ = 7 + 59 / 60 + 59 / 3600 = 28799 / 3600 degree

D. 1' = 1/60 degree

F. 1" = 1/3600 degree

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Answer:

C.  Every integer is a rational number

Step-by-step explanation:

Integers are whole numbers which could be positive or negative and zero. Examples of integers are 330, 21, 10,052, 0, -425, -879, etc. Fractions are not integers.  Rational numbers are numbers that are expressed as the ratio of two integers. So numbers that have integers as their numerators and denominators can be rightly said to be rational numbers. Examples are, 5/7, 10,111/880, -365/15.

Since both the numerators and denominators are whole numbers, the entire figures can be said to be rational numbers. So, fractions are rational numbers.    

9514 1404 393

Answer:

  B.  22 to 26

Step-by-step explanation:

Multiply each value in the ratio by 2/3 to see an equivalent that is among the choices.

  33 : 39 = (2/3)(33) : (2/3)(39) = 22 : 26

In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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Answer:

53%

53/100

Step-by-step explanation:

Answer:

Regular = $0.21 per ounce, Family = $0.19 per ounce

Step-by-step explanation:

Regular

16oz = $3.36

                         Divide by 16 on both sides

1oz = $0.21

Family

40oz = $7.20

                          divide by 40 both sides

1oz = $0.19

Answer:

9 tickets

Step-by-step explanation:

If two tickets cost 14 dollars, then each ticket will cost 7 dollars

63/7=9

You can buy 9 tickets

Answer:

You can buy about 31 tickets

Step-by-step explanation: