probability of rolling a 6 with two dice one with values 1, 2, 2, 3, 3, 4 and 1, 3, 4, 5, 6, 8

31.41 feet of fence to you need to go around the building.

What is circumference of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

The radius of the circle given is = 50/2 feet.

So the clearance of 20 feet will be there all way.

So total effective radius will be 25-20 5 feet.

the circumference is 2πr = 2*π*5 = 31.41 feet

Hence, 31.41 feet of fence to you need to go around the building.

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Answer:

10

Step-by-step explanation:

if u got up 10 from (9,-2) you will get to (9,8)

Answer: 2y4 + 4y2

Step-by-step explanation:

2y3 + 4y2

2y4 + 4y2✔

1/2y3 + 1y2

1/2y4 + 4y2

Answer: A and C is incorrect, the middle is 14. The minimum is 13. The max is 16.

Step-by-step explanation: B is correct

there is no 12

Answer: 3.6

Step-by-step explanation:

Step 1:  30/100 = x/12

Step 2: Multiply 12x30 and then divide it by 100

f-1(x)=1\5x-11

Step-by-step explanation:

The distance AC to be covered for the given triangle will be  429.94 meters.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.

As per the given triangle,

By cosine law,

Cos∠ABC = (220² + 430² - AC²)/(2 × 220 × 430)

Cos∠ABC = (233300 - AC²)/189200

Cos(180° - 75°) = (233300 - AC²)/189200

(233300 - AC²) = -48968.56

AC² = 184331.4367

AC = 429.94 meter

Hence "The distance AC to be covered for the given triangle will be  429.94 meters".

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Answer:

50,000

Step-by-step explanation:

1,750 x 2 = 3,500

25,000 x 2 = 50,000

If Noah earns £160 a week and pays £55 in tax, he has £160 - £55 = £160-£55 = £105 to spend.

Subtraction is a mathematical procedure that includes subtracting one number from another. For example, if we have five apples and subtract three of them, we are left with two apples. Beginning with the bigger number and deducting the smaller number from it is how subtraction is done. Subtraction is denoted by the minus symbol (-). A difference is the outcome of a subtractive operation.

We may better grasp how to solve issues requiring the removal of one or more elements from a set by understanding the fundamental mathematical formula of subtraction. It is employed in many different scenarios, such as when we need to subtract incomes on a regular basis.

How to solve?

The formula for the money Noah has to spend each week is m = w - t.

£160 - £55 = £160 - £55 = £105

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Adjacent angles of a parallelogram are supplementary.

[tex]x+2x=180 \\ \\ 3x=180 \\ \\ x=\boxed{60}[/tex]

The random sample study's standard error, which measures the energy usage in a major metropolis, is 0.275.

The formula used to compute standard error is as follows:

standard error = standard deviation / √sample size

For  the data given in question-

Thus,

Standard error = 4.68 / 17

Standard error  = 0.275

Thus, the standard error for the mean of the sample is found as 0.275.

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Answer:20 ft

Step-by-step explanation:

Using Pythagoras' Theorem:

[tex]h^{2} = a^{2} +b^{2} \\h^{2} = 16^{2} +12^{2} \\h^{2} = 256+144h^{2} = 400\\\\[/tex]

Now you want to get h alone. To do that you need to get rid of the squared by finding the square root of 400.

[tex]h=\sqrt{400}\\h=20[/tex]

The point estimate of the population standard deviation is Select one is 5.4558.

Given data

9,13,15,15,21,24

We have to find first mean

Here n=6

[tex]$\begin{aligned} \text { mean } \bar{x} & =\frac{\sum x_i}{n} \\ & =\frac{9+13+15+15+21+24}{6} \\ & =\frac{97}{6} \\ & =16.166\end{aligned}$[/tex]

[tex]$\therefore$[/tex] Standard deviation

[tex]S=\sqrt{\frac{\sum\left(x_i-x\right)^2}{n-1}}$$[/tex]

S= root (9-16.(66)^2+(13-16.166)^2+(15-16.166)^2+(15-16.166)^2+(21-16.166)^2+(25- 16.166)^2/(6-1)

[tex]\begin{aligned}& =\sqrt{\frac{148.833336}{5}} \\& =\sqrt{29.7666} \\& =5.4558\end{aligned}[/tex]

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Answer:

Step-by-step explanation:

b) 7.688 The point estimate of the population standard deviation is 7.688. The point estimate of a population parameter is the estimate of the population parameter based on a single sample. In this case, the point estimate of the population standard deviation is the sample standard deviation, which is a measure of the spread or variability of the sample data. To calculate the sample standard deviation, we need to first calculate the sample mean, which is the average of the values in the sample. In this case, the sample mean is (9 + 13 + 15 + 15 + 21 + 24)/6 = 14.5. We can then use this value to calculate the sample standard deviation, which is √(((9-14.5)² + (13-14.5)² + (15-14.5)² + (15-14.5)² + (21-14.5)² + (24-14.5)²)/6) = 7.688. This is the point estimate of the population standard deviation. The other answer choices are not the sample standard deviation.

On solving the provided question, we got that - 0.000005178 as the P-value,the null hypothesis is a common statistical theory that contends that no statistical relationship

Using a single observed variable to compare two sets of observed data and measured phenomena, the null hypothesis is a common statistical theory that contends that no statistical relationship and significance exists.

h0; no change in beverage preferences

h1: alterations in drink preferences

alpha = 0.05

We find the test statistics' solution.

The attachment underwent the chsquare test.

Chi-square: (O-E)2/E

Chi square is 32.30188.

[tex]number of degrees of freedom = n-1 = 6-1 = 5[/tex]

I determined the p value using the chi distribution tool in Excel.

CHIDIST(3.20188, 5) =

0.000005178 as the P-value

We reject the null hypothesis since the pvalue is less than 0.05 and come to the conclusion that there is enough evidence to support the shift in drink preferences.

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From a sample of 100 leading world companies we can estimate the residual value is 4,762.9054 .

It is given that,

Regression equation net income = 2277+0.0307

From a sample of 100 leading world companies we can estimate the revenue.

(a-1)

for the (x,y) pair, x = $41,078 and y = $8,301 or it is represented as ($41,078 , $8,301)

then the above (x,y) pair's residual value is e = y - ÿ

ÿ = 2277+0.307x

= 2277+0.0307(41078)

= 2277+1261.0946

= 3538.0946

Thus, e = y - ÿ

so, e = 8301 - 3538.0946

= 4762.9054

Hence, the residual value = 4,762.9054                                                                                  

To calculate the correlations between a dependent variable and one or more independent variables, a statistical technique grouping together several statistical techniques known as regression analysis is utilized. Revenue is the entire amount of money received from the sale of goods or services related to a company's main operations. Revenue, also known as gross sales, is often referred to as the "top line" because it appears at the top of the income statement. The residual value, also known as salvage value, is the estimated value of a fixed asset at the end of its useful life or lease term.

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Answer:

5 chairs per table.

Step-by-step explanation:

The slope (-8) of the linear equation that is represented by the table, is the amount Austin pays each week, which is $8.

A linear equation which is given as y = mx + b, has a slope value which represents the change in y over a change in x and is given by the value of m in the linear equation.

If a table is said to represent a linear equation, the slope of the linear equation, which can also be called the unit rate, can be found by using two pairs of values from the table to calculate the change in y over the change in x.

Given that the table above represents a linear equation where L is dependent on the value of t, it means that slope of the linear equation represents the amount Austin paid back each week.

Find the slope using two points, (2, 24) and (4, 8):

Slope (m) = (24 - 8) / (2 - 4)

m = 16/-2

m = -8

Therefore, this means that Austin pays $8 every week.

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The value of x from the given five integers is 34.

Here we have to find the value of x.

Data given:

Five positive number = 31, 58, 98, x, x

The mean is 1.5 times the mode.

Mean = (31 + 58 + 98 + x + x) / 5

         = (187 + 2x) / 5

Mode = x

As the mean is 1.5 times the mode so from this we have:

mean = 1.5 × mode

(187 + 2x)/ 5 = 1.5x

187 + 2x = 7.5x

5.5x = 187

x = 34

Therefore the value of x is 34.

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The mistake are shown below and the correct steps are shown below.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60

And, All the steps are;

⇒ 6 (8 - 3x ) = - 3 (9x - 1 ) + 60

⇒ 54 - 18x = −27x − 3 + 60

⇒ 54 - 18x = −27x + 57

⇒ -18x = -27x + 3

⇒ 9x = 3

⇒ x= 1/3

Now,

Since, The expression is,

⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60

Cleary, In the second step 2; your partner doing mistake.

So, All the correct steps are;

⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60

⇒ 48 - 18x = - 27x + 3 + 60

⇒ 48 - 18x = - 27x + 63

⇒ 27x - 18x = 63 - 48

⇒ 9x = 15

⇒ x = 15/9

⇒ x = 5/3

Thus, The correct value is;

⇒ x = 5/3

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The shortest distance Louisa is from her school is 107.7 feet

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

East = 100 feet

South = 40 feet

The shortest distance from her school is calculated using the following theorem

Shortest distance = √(East² + South²)

Substitute the known values

Shortest distance = √(100² + 40²)

Evaluate

Shortest distance = 107.7

Hence, the shortest distance = 107.7 feet

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The dimensions of a right circular cylinder of maximum volume are

[tex]5\sqrt{6}[/tex] and [tex]10\sqrt{3}[/tex].

Given the radius of sphere is 15 cm.

Let's assume radius of right circular cylinder = r

height of right circular cylinder = h.

Since the cylinder is inscribed in the sphere, their centers will coincide. As a result, the height is divided into two equal portions from the sphere's center. Therefore, we can apply Pythagoras' Theorem to get the cylinder's half-height in terms of radius.

[tex]R^2 = r^2 + (h/2)^2.[/tex]

[tex]r^2 = R^2 - h^2/4.[/tex]

Volume of cylinder = [tex]\pi*r^2*h.[/tex]

Now we can substitute value of [tex]r^2[/tex] in volume of cylinder.

V =  [tex]\pi*( R^2 - h^2/4)*h[/tex]

taking  R = 15 .

V = [tex]\pi*(225 - h^2/4)*h[/tex]

V = [tex]\pi*225*h - \pi*h^3/4[/tex]

For maximum volume we have to do derivative of volume  = 0

derivative with respect to h.

V' = [tex]\pi*225 - 3*\pi*h^2/4[/tex]

V' = 0

[tex]\pi*225 - 3*\pi*h^2/4[/tex]= 0

[tex]3*h^2/4 = 225[/tex]

[tex]h^2 = 75*4.[/tex]

h = 10[tex]\sqrt{3}[/tex]

put the value of h in [tex]r^2 = 225 - h^2/4[/tex]

[tex]r^2[/tex] = 225 - (300/4)

[tex]r^2[/tex] = 150

r = [tex]\sqrt{150}[/tex]

r = 5[tex]\sqrt{6}[/tex].

So the dimensions of a right circular cylinder are 10[tex]\sqrt{3}[/tex] and 5[tex]\sqrt{6}[/tex].

Given Question is incomplete, Complete Question here:

find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. what is the maximum​ volume?

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Answer:

x=9/5 − 4y/5

x = 7 + y/2

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

#1= 36

#2=81

#3= 32

#4=125

She may thus combine 21 pounds of tea priced at $3 and 14 pounds of tea priced at $2 to create tea that costs $2.6 per pound.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Here,

Let 3x be the pounds of tea for $3 and 2x be the pounds of tea for $2.

Total required pounds=35

3x+2x=35

x=35/5

x=7

So, She can add 21 pounds of tea for $3 and 14 pounds of tea for $2 to make the tea that is $2.6 per pound.

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Expression a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)   is an identity, by left-hand term and right-hand term property.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)  

To prove that the given expression is an identity,

Solve left-hand term,

Substitute a² = x, b² = y

a⁶ + b⁶

= x³ + y³

Use formula x³ + y³ = (x + y)(x²  - x y + y²)

= (x + y)(x²  - x y + y²)

Again substitute x = a², y = b², expression will be,

= (a² + b²)(a⁴ - a²b² + b⁴)  

Hence, a⁶ + b⁶ =  (a² + b²)(a⁴ - a²b² + b⁴)  

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The value of f(t) are 48000, 52200, 54300, 56400, and g(t) are 48000, 49776, 51617.71, and 53527.56.

She was given a starting wage of $48,000 from Company A, with annual raises of $2100.

The formula for Company A is

f(t) = 48000 + 2100t

She was given a starting wage of $48,000 from Company B, with an annual rise of 3.7%.

The formula for Company B is

g(t) = 48000 × [tex](1 + 0.037)^t[/tex]

The value of f(t) and g(t),

t ------- f(t) ------- g(t)

0 ----- 48000 ----- 48000

1 ------ 52200 ----- 49776

2 ----- 54300 ----- 51617.71

3 ----- 56400 ----- 53527.56

The graphical representation of both the linear equations of company A and company B.

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There are 0 lines, 1 regions, and no line junctions. There are always k+1k+1 regions and kk intersections added whenever a line is added and crosses k other lines.

Another perspective is that k+1k+1 areas are added for each line and k intersections added (the number of added lines and intersections).Consequently, the total number of regions is 1 plus the sum of the number of lines and junctions.The number of intersections is 1 + the number of lines. There are (n2) (n2) crossovers with nn lines (if no two lines are parallel and no three lines are coincident). Therefore, there are (n2) +n+1=n(n1)/2+n+1=n2+n+2/2 areas instead of (n2) +n+1=n(n1)/2+n+1=n2+n+2/2).

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⇒ Yes X+Y and X-Y are independent

What is covariance?

Covariance is a measure of the combined variability of two random variables used in probability theory and statistics. The covariance is positive if the greater values of one variable primarily match the greater values of the other variable, and the same is true for the lesser values.

Define U=X+Y,  V=X−Y

Then, [tex]x=\frac{(U+V)}{2}[/tex], and

[tex]Y=\frac{(U-V)}{2}[/tex]

Find the Jacobian J for the transformation.

Then, fU,V(u,v)= fX(x=(u+v)/2) fY(y=(u−v)/2)|J|

You will find that fU,V(u,v) factors into a function of u alone and a function of v alone. Thus, by the Factorization thm, U and V are independent.

b) Yes X+Y and X-Y are independent

a) Since , X+Y and X-Y are independent,

COV(X+Y , X-Y) = 0 Answer

Cov(X+Y , X-Y) = 0

b)

Yes these are independent

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Greater than 100. 700% of 6 is 42.