question content area top part 1 a pair of dice is rolled. what is the probability of getting a sum less than 5​?

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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If a right triangle's height is 5 times the length of its base and the area of the triangle is 160, then the height of the triangle is 40 units

A right triangle's height is 5 times the length of its base

Consider the length of the base as b and the height as h

h = 5b

The area of the triangle = 160 square units

The area of the triangle = 1/2 × b × h

Where b is the base of the triangle

h is the height of the triangle

Substitute the values in the equation

1/2 × b × h = 160

1/2 × b × 5b = 160

1/2 ×5b^2 = 160

5b^2 = 320

b^2 = 320/5

b^2 = 64

b = [tex]\sqrt{64}[/tex]

b = 8 units

Then the height of the triangle h = 5b

= 5 × 8

= 40 units

Therefore, the height of the triangle is 40 units

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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 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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Answer: 3.6

Step-by-step explanation:

Step 1:  30/100 = x/12

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

In order to calculate the correlation between two variables related to the same sample you need to calculate first the mean of each variable.

Before determining the correlation, the covariance of the two variables in the issue must always be computed. The standard deviation of each variable is then needed. The correlation analysis is calculated by dividing the covariance even by combination of a standard deviations of two or more variables.

A correlation is a statistical measurement of the two-variable connection. The measure works best with parameters that have a linear connection with one another.

The degree of the relationship between two variables is examined using correlation. To get the correlation between two variables, divided the covariance value by the standard deviation of both variables. Correlation analysis for two variables in the same sample should be performed. If you run a survey with two factors, a responder should be able to answer both variables at a glance. Furthermore, other participants' replies to the parameter might be evaluated for a correlation test.

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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

Adjacent angles of a parallelogram are supplementary.

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

The blanks in this two-column proof should be completed (filled) as follows:

Statements                              Reasons_______________

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.

In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent i.e AD ≅ CD.

Additionally, HL is an acronym for hypotenuse leg and it states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.

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Answer:

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

Step-by-step explanation:

or what the  guy said on top :D

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.

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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Each corner of a triangle can form an exterior angle of the triangle by extending one side of the triangle. As we can see in above picture, where 'w' is exterior angle of angle 'z'.

The measure of the exterior angle to ∠d is 126°. So, the correct option is option (D).

We have given that,

A ∆DEF such that m∠d = (2x + 19)°,

m∠e = (3x + 24)°, and m∠f = 87°.

we have to find out the degree measure of the exterior angle to ∠d.

As we know that sum of angles of triangle is equal to 180° .

so, m∠d + m∠e + m∠f = 180°

=> (3x + 24)° + (2x + 19)° + 87° = 180°

=> (5x + 24 + 19 + 87)° = 180°

=> 5x + 130° = 180°

=> 5x = 50°

=> x = 10°

plug this value in angle d , angle e we get ,

m∠d = (3 ×10 + 24 )° = 54°

We can see that adding the angle measurement d and the exterior angle measurement gives d = 180 degrees. This is because they are a pair of adjacent angles and both lie on a straight line.

measure of Exterior angle of ∠d + measure of ∠d = 180°

Measure of exterior angle of ∠d

= 180° - m∠d

= 180° - 54° = 126°

Hence, the measure of exterior angle of d is 126°.

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Greater than 100. 700% of 6 is 42.

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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Answer: 2y4 + 4y2

Step-by-step explanation:

2y3 + 4y2

2y4 + 4y2✔

1/2y3 + 1y2

1/2y4 + 4y2

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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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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#1= 36

#2=81

#3= 32

#4=125

⇒ 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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Answer:

C ≈ 241.9 cm

Step-by-step explanation:

the circumference (C) of the circle is calculated as

C = πd ( d is the diameter )

here d = 77 , then

C = π × 77 ≈ 241.9 cm ( to 1 dec. point )

Answer:

7%

Step-by-step explanation:

When trying to figure out percentages, we can try to use a proportional relationship. Percent means out of a hundred, and since we don't know the percentage on top,  we can mark it as ?.

21/300 = ?/100

To figure this out quickly, we can try figuring out how many times we need to multiply or divide to get to the next number. Between 21 and ?, we can't do anything because we are unsure of what ? is.

Between 300 and 100, we can notice that to get to 100, we must divide by 3. 300/3 = 100

This means that the first ratio is three times the amount of the second ratio, which means that the second ratio is 1/3 of the first.

We can multiply 21 by 1/3 (or divide by 3), which will get us to 7.

7/100 = 0.07 = 7%

Answer:

50,000

Step-by-step explanation:

1,750 x 2 = 3,500

25,000 x 2 = 50,000

The volume of the composite shape is 38mm³(nearest whole number)

A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes.

The volume of a the composite solid above = volume of cone + volume of cylinder

volume of cone = 1/3πr²h

=1/3×3.14×2²×3

= 12.56mm³

volume of the cylinder = πr²h

= 3.14×2²×2

= 25.12mm³

therefore the volume of the shape = 12.56+25.12

= 37.68mm³

= 38mm³( nearest whole number)

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Answer:

5 chairs per table.

Step-by-step explanation:

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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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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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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