A computer uses the numbers 1,2 or 3 at random to make three digit numbers. Show on a three diagram all possible outcomes that computer can print calculate the probability of getting

Answer:

The method of moment (MOM) estimator as:  \(\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}\)

\(\overline X = \dfrac{4}{9}\)

\(\mathbf{\hat {\theta} =\dfrac{16}{25} }\)

Step-by-step explanation:

From the question, the correct format for the probability density function is:

\(fx(x ; \theta) = \left \{ {{\sqrt{\theta x}^{\sqrt{\theta}-1}}\ \ 0 \leq x \leq 1 \atop {0} \ \ \ \ \ \ \ otherwise } \right.\)

where θ > 0 is an unknown parameter.

(a) The MOM estimator can be calculated as follows:

\(E(X) = \int ^1_0x. \sqrt{\theta} \ x^{\sqrt{\theta}-1} \ dx\)

\(E(X) = \int ^1_0 \sqrt{\theta} \ x^{\sqrt{\theta}} \ dx\)

\(E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 } ( x ^{\sqrt{\theta}+1})^1_0\)

\(E(X) = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }\)

suppose E(X) = \(\overline X\)

Then;

\(\overline X = \dfrac{\sqrt{\theta} }{\sqrt{\theta} +1 }\)

\(\dfrac{1}{\overline X} = \dfrac{\sqrt{\theta} +1 }{\sqrt{\theta}}\)

\(\dfrac{1}{\overline X} =1 + \dfrac{1}{\sqrt{\theta}}\)

making \(\dfrac{1}{\sqrt{\theta}}\) the subject of the formula, we have:

\(\dfrac{1}{\sqrt{\theta}} =\dfrac{1}{\overline X} - 1\)

\(\dfrac{1}{\sqrt{\theta}} =\dfrac{1-\overline X}{\overline X}\)

\(\sqrt{\theta} =\dfrac{\overline X}{1-\overline X}\)

squaring both sides, we have:

The method of moment (MOM) estimator as:  \(\mathbf{\hat {\theta} =(\dfrac{\overline X}{1-\overline X})^2}\)

b) If the observations are \(\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{2}\)

Then,

\(\overline X = \dfrac{\dfrac{1}{2}+ \dfrac{1}{3}+\dfrac{1}{2}}{3}\)

\(\overline X = \dfrac{\dfrac{3+2+3}{6}}{3}\)

\(\overline X = \dfrac{\dfrac{8}{6}}{3}\)

\(\overline X = \dfrac{8}{6} \times \dfrac{1}{3}\)

\(\overline X = \dfrac{8}{18}\)

\(\overline X = \dfrac{4}{9}\)

Finally, the point estimate of the estimator \(\theta\) is

\(\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{1-\dfrac{4}{9}} \end {pmatrix}^2}\)

\(\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}} \end {pmatrix}^2}\)

\(\mathbf{\hat {\theta} =\begin {pmatrix} \dfrac{4}{5} \end {pmatrix}^2}\)

\(\mathbf{\hat {\theta} =\dfrac{16}{25} }\)

The correct answer is, Cougars; they have a larger median value of 22 inches.

Calculating the median and mean for each data set, we get:

Cougars:

Median = 22 inches

Mean = 22.3 inches

Panthers:

Median = 22.5 inches

Mean = 22.2 inches

Since the median of the Cougars data set is larger than the median of the Panthers data set, we can conclude that the Cougars have the largest overall size hat for their players.

Therefore, the correct answer is, Cougars; they have a larger median value of 22 inches.

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Step-by-step explanation:

1) zeros of the given function:

6x²-3=0; ⇔ 6(x²-0.5)=0; ⇔ x²=0.5; ⇔

\(\left[\begin{array}{ccc}x=-\sqrt{0.5} \\x=\sqrt{0.5} \end{array}\)

2) relationship:

if to see the equation x²-0.5=0 (ax²+bx+c=0 is standart form!), then the sum of the zeros is '0' (it is 'b' of the standart form), the product of equation roots is '-0.5' (it is 'c' of the standart form).

\({\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}\)

★ The polynomial

f(x) = 6x² - 3

\({\large{\textsf{\textbf{\underline{\underline{To \: find :}}}}}}\)

★ Zeroes of the polynomial f(x) = 6x² - 3

\({\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}\)

We have,

\(f(x) = \tt 6 {x}^{2} - 3\)

Which can also be written as

\( \implies f(x) = \tt {(\sqrt{6} x)}^{2} - { (\sqrt{3}) }^{2} \)

Using a² - b² = (a - b) (a + b)

\( \implies f(x) = \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} )\)

To find the zeroes, solve f(x) = 0

\( \longrightarrow \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} ) = 0\)

either \( \tt \sqrt{6} x - \sqrt{3} = 0 \: or \: \sqrt{6} x + \sqrt{3} = 0\)

\( \implies \tt \sqrt{6} x = \sqrt{3 \: } \: or \: \: \sqrt{6} x = - \sqrt{3}\)

\( \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{6} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{6} }\)

\( \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} }\)

\(\implies \tt x = \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} } \: or \: x = - \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} }\)

\(\implies \tt x = \dfrac{1}{ \sqrt{2} } \: \: or \: \: - \dfrac{1}{ \sqrt{2} }\)

Hence, the zeroes of f(x) = 6x² - 3 are:

\( \tt \alpha =\sf \boxed {{ \red{ \dfrac{1}{ \sqrt{2} } } }}\: \: and \: \: \beta =\sf \boxed {{ \red{ - \dfrac{1}{ \sqrt{2} } } }}\)

• Verification

Sum of zeroes = \( ( \alpha + \beta )\)

\( = \tt \dfrac{1}{ \sqrt{2} } + \bigg(- \dfrac{1}{ \sqrt{2} } \bigg)\)

\( = \tt \dfrac{1}{ \sqrt{2} } + - \dfrac{1}{ \sqrt{2} } \)

\(= \tt 0\)

and, \(\tt - \dfrac{Coefficient \: of \: x}{Coefficient \: of \: {x}^{2} }\)

\( \tt = - \dfrac{0}{6} \)

\( \tt = 0\)

\( \therefore \tt \: Sum \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Coefficient \: of \: x}{ \tt Coefficient \: of \: {x}^{2}}}}}\)

Also,

Product of zeroes = \( \alpha \beta \)

\( = \dfrac{1}{ \sqrt{2} } \times - \dfrac{1}{ \sqrt{2} } \)

\( = - \dfrac{1}{ 2 } \)

and, \(\tt - \dfrac{Constant \: term}{Coefficient \: of \: {x}^{2} }\)

\( \tt = \dfrac{ - 3}{6} \)

\( \tt = \dfrac{ - 1}{2} \)

\( \therefore \tt \: Product \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Constant \: term}{ \tt Coefficient \: of \: {x}^{2}}}}}\)

\(\rule{280pt}{2pt}\)

Answer:

4.7 * 10^8

Step-by-step explanation:

Using exponential properties, it is found that the equivalent expression to the frequency of any pitch is given by:

\(f = 440\sqrt[12]{2^{10}}\)

It happens according to the following rule, with the denominator as the root and the numerator as the exponent:

\(a^{\frac{n}{m}} = \sqrt[m]{a^n}\)

The rule for the frequency is given by:

\(f = 440(2)^{\frac{10}{12}}\)

Hence the equivalent expression to f is given by:

\(f = 440\sqrt[12]{2^{10}}\)

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Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

Step-by-step explanation:

wait a person was about to report it sorry ;/

had to take it off

Answer/Step-by-step explanation:

==>Given:

=>Rectangular Pyramid:

L = 5mm

W = 3mm

H = 4mm

=>Rectangular prism:

L = 5mm

W = 3mm

H = 4mm

==>Required:

a. Volume of pyramid:

Formula for calculating volume of a rectangular pyramid us given as L*W*H

V = 5*3*4

V = 60 mm³

b. Volume of prism = ⅓*L*W*H

thus,

Volume of rectangular prism given = ⅓*5*3*4

= ⅓*60

= 20mm³

c. Volume of the prism = ⅓ x volume of the pyramid

Thus, 20 = ⅓ × 60

As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.

The radian measure of an angle is directly proportional to the length of the arc intercepted by that angle on the unit circle.

Proportional is a mathematical concept that describes the relationship between two or more values that have a constant ratio. It is commonly used to describe the relationship between two or more variables, such as the size of an object in relation to another or the amount of a certain item in relation to the total amount. In proportionality, the ratio of the amounts remains consistent, no matter what the size of the values.

This means that as the angle increases, so does the length of the arc. This is because the length of an arc is determined by the angle measure of the central angle created by the arc, and the radian measure of an angle is the ratio of the arc length to the radius of the circle. Therefore, if the angle measure increases, so does the arc length.

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Answer: Answer choice 'B'

Step-by-step explanation:

4.00 + 0.75 + 0.40 + 0.03 = $5.18. This is Jill's amount.

3.00 + 0.40 + 0.02 = $3.42. This is Mark's amount.

To find out how much more money Jill has in comparison to how much mark has, we need to subtract Jill's money by Mark's money ($5.18 - $3.42)

if done correctly, your answer should be $1.76 (answer 'B')

Answer:

MPG is miles per gallon so we just need to divide the miles by the gallons

345/16=21.56

so i guess a?

i mean thats rounded wrong but its the closes one

a

Hope This Helps!!!

Here we have an arithmetic sequence with a common difference of 6, so the recursive formula is:

Tₙ = Tₙ₋₁ + 6

Where T₁ = 4.

Here we have the following sequence:

4, 10, 16, 22, ...

This seems to be an arithmetic sequence, to check this, we need to take the difference between consecutive terms and see if this is constant.

10 - 4 = 6

16 - 10 = 6

22 - 16 = 6

So yes, this is an arithmetic sequence and the common difference is 6, this means that each term is 6 more than the previous one, so the recursive formula is:

Tₙ = Tₙ₋₁ + 6

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Answer:

\(D = 72.2\ yd\)

Step-by-step explanation:

Given

\(Length\ (L)= 58\ yd\)

\(Width \ (W)= 43\ yd\)

Required

Determine the diagonal (D)

The relationship between D, L and W can be gotten using Pythagoras Theorem:

\(D^2 = L^2 + W^2\)

Substitute values for L and W

\(D^2 = 58^2 + 43^2\)

\(D^2 = 3364 + 1849\)

\(D^2 = 5213\)

Take Square root of both sides

\(D = \sqrt{5213}\)

\(D = 72.2011080247\)

\(D = 72.2\ yd\) (Approximated)

Answer: A

Step-by-step explanation:

Volume= LxWxH so we get 20x28x24 as given.

Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.

13,440-10,500= 2,940 Cubic Inches

Option A

Answer:

Part A:  13440 cubic inches.

Part B: A - 2940 cubic inches.

Step-by-step explanation:

The volume of the box = 24x20x28 = 13440 cubic inches.

The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.

13440-10500 = 2940 cubic inches. The answer is A.

Answer:

1,000 units^3 of water

Step-by-step explanation:

20•10•5 =1,000

Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

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The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Answer:

16. 150ft

17. 120ft

18. 14sq in

19. 12ft

20. 100miles

21. 87ft

22. 24in        23. 31in

Step-by-step explanation:

brainliest?

The numerical value of x in the similar pair of triangle is 10.

A ratio is simply the relation between two amounts showing how many times a value is contained within another value.

From the diagram,

Side A of the small triangle = 10

Side B of the small triangle = x + 2

Side A of the Big triangle = 10 + x

Side B of the big triangle = x + 14

Hence;

Ratio of Side A to Side B of the small triangle = 10 / x + 2

Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14

Since the triangle area similar, equate the two ratio and solve for x.

10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )

Cross multiply

10( x + 14 ) = ( 10 + x )( x + 2 )

Expand using FOIL method

10x + 140 = 10x + 20 + x² + 2x

10x + 140 = x² + 12x + 20

x² + 12x + 20 = 10x + 140

x² + 12x + 20 - 10x - 140 = 0

x² + 2x - 120 = 0

Factor the left side of the equation

( x - 10 )( x + 12 ) = 0

Hence;

x - 10 = 0 and x + 12 = 0

x = 10 and x = -12

Since the dimension of the triangle cannot be negative,

x = 10

Therefore, the value of x is 10.

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On first evening she receives 19 calls and on second evening  she receives 11 calls while on 3rd evening she receives 38 calls.

A mathematical equation is a fοrmula that joins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences oοn either side of a letter is described by a mathematical formula. Often, there is οnly one variable, which alsο serves as the symbol, fοr instance, 2x – 4 = 2.

X, Y, and Z represents the 1st , 2nd, and 3rd evenings

X + Y + Z = 68

⇒ X = Y + 8

⇒ Z = 2(Y + 8)

⇒ Y + Y + 8 + 2(Y + 8) = 68

Y = 11 calls

And

X = (11)+ 8 = 19 calls

Z = 2((11) + 8) = 38 calls

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Proved that Triangle ABD ≅ Triangle CBD

Consider the triangle ABD and the triangle CBD

The length of the side AB = The length of the side BC

The length of the side AD = The length of the side cd

The third side is common

According to the SSS rule congruent . If the three side of the triangle is equal to the three sides of the another triangle then the both triangles are congruent

Then three sides of the triangle ABD is equal to the three sides of the triangle CBD, Therefore the triangle ABD and triangle CBD are congruent

Hence, proved that Triangle ABD ≅ Triangle CBD

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Gillian earned  $42.75 last week.

Arithmetic operators are used to perform mathematical operations like addition, subtraction, multiplication and division.

...

There are 7 arithmetic operators in Python :

Addition.

Subtraction.

Multiplication.

Division.

Modulus.

Exponentiation.

Floor division.

Gillian work

2.2 hours+3.5 hours= 5.7 hours

5.7 hours× $7.50 =  $42.75

Therefore Gillian earned $42.75

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The properties applied in the steps are distributive property, additive property and the division property

The equation is given as

2(10 - 13x) + 9x = -34x + 60.

This means that preliminary step is

Given: 2(10 - 13x) + 9x = -34x + 60.

Next, we apply the distributive property

So, we have

Step 1: Apply the distributive property

20 – 26x + 9x = -34x + 60.

Next, we evaluate the like terms

So, we have

Step 2: Evaluate the like terms

-17x = -34x + 40

Next, we evaluate the like terms

So, we have

Step 3: Evaluate the like terms

17x = 40

Lastly, we apply the division property of equation

So, we have

Step 4: Division property of equation

X = 40/17.

Hence, the properties applied in the steps are distributive property, additive property and the division property

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Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Answer:

the distance between the 2 points is 6.4 units.

Step-by-step explanation:

point 1 has the coordinates (-4, -2).

point 2 has the coordinates (1, 2).

the distance between both points is the Hypotenuse of the right- angled triangle of the coordinate difference lines in parallel to x- and y-axis.

so, how long is the difference in x dimension ?

and his long is the difference in y dimension ?

these are the sides of the triangle.

the difference in x dimension :

1 - -4 = 1 + 4 = 5

the difference in y dimension :

2 - -2 = 2 + 2 = 4

P1P2² = 4² + 5² = 16 + 25 = 41

P1P2 = sqrt(41) = 6.4

Answer:

a

Step-by-step explanation:

sorry if wrong

To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201

The given parameters are:

This means that

df = 11 and t = 1.910

To calculate the t value,

We check the row where the heading of the degree of freedom is 11

i.e. df = 11

On this row, the t value 1.910 would be between 1.796 and 2.201

This is because 1.910 is greater than 1.796 and it is less than 2.201

Hence, the complete statement is

To determine where the given t-value would fall, we look for the row with heading d.f. =11. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t = 2.201

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The expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Therefore, the expression equivalent to (p - q)(x) is (x² - 1) - 5(x - 1).

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Answer:

It is given that

p(x) = x² - 1

q(x) = 5(x - 1)

We have to find (p - q)(x)

We know that

(p - q)(x) = p(x) - q(x)

Substituting the values

= (x² - 1) - 5(x - 1)

Step-by-step explanation: