Find the Slope of the line that passes through the given points: (5, 2) and (6, 6).

Using the concepts of probability, we got 0.5 is the probability of drawing the sum $20 or more when  two bills are drawn randomly without replacement.

We have an envelope contains 8 bills;

Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.

When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.

Total  outcomes = 2 x 2 x 2 x 2 = 16

Total possible outcomes, more than 20;

(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases

That is,

The total possible outcomes is 8.

Now,

The probability of bill to be $20 or more = Possible outcome / Total outcome

Probability = 8/16 = 1/2=0.5

Hence, When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 0.5.

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(Complete question)

an envelope contains eight bills: 2 ones, 2 fives, 2 tens, and 2 twenties. two bills are drawn at random without replacement. what is  the probability that their sum is $20 or more?

Answer:

$ 30.66

Step-by-step explanation:

434/31=14 x 2.19=30.66

To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v)

The joint distribution of (u, v), where u and v are defined as

\(u = \frac{x}{{\sqrt{x^2 + y^2}}}\)  and \(v = \frac{y}{{\sqrt{x^2 + y^2}}}\), is given by:

\(f_{U,V}(u,v) = \frac{1}{{2\pi}} \cdot e^{-\frac{1}{2}(u^2 + v^2)}\)

To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v):

\(J = \frac{{du}}{{dx}} \frac{{du}}{{dy}}\)

\(\frac{{dv}}{{dx}} \frac{{dv}}{{dy}}\)

Substituting u and v in terms of x and y, we can evaluate the partial derivatives:

\(\frac{{du}}{{dx}} &= \frac{{y}}{{(x^2 + y^2)^{3/2}}} \\\frac{{du}}{{dy}} &= -\frac{{x}}{{(x^2 + y^2)^{3/2}}} \\\frac{{dv}}{{dx}} &= -\frac{{x}}{{(x^2 + y^2)^{3/2}}} \\\frac{{dv}}{{dy}} &= \frac{{y}}{{(x^2 + y^2)^{3/2}}}\)

Therefore, the Jacobian determinant is:

\(J &= \frac{y}{{(x^2 + y^2)^{\frac{3}{2}}}} - \frac{x}{{(x^2 + y^2)^{\frac{3}{2}}}} \\&= -\frac{x}{{(x^2 + y^2)^{\frac{3}{2}}}} + \frac{y}{{(x^2 + y^2)^{\frac{3}{2}}}} \\J &= \frac{1}{{(x^2 + y^2)^{\frac{1}{2}}}}\)

Now, we can find the joint density function of (u, v) as follows:

\(f_{U,V}(u,v) &= f_{X,Y}(x,y) \cdot \left|\frac{{dx,dy}}{{du,dv}}\right| \\&= f_{X,Y}(x,y) / J \\&= f_{X,Y}(x,y) \cdot (x^2 + y^2)^{\frac{1}{2}}\)

Substituting the standard normal density function

\(f_{X,Y}(x,y) &= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(x^2 + y^2)} \\f_{U,V}(u,v) &= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(x^2 + y^2)} \cdot (x^2 + y^2)^{\frac{1}{2}} \\&= \frac{1}{2\pi} \cdot e^{-\frac{1}{2}(u^2 + v^2)}\)

Therefore, the joint distribution of (u, v) is given by:

\(f_{U,V}(u,v) &= \frac{1}{2\pi} \cdot \exp\left(-\frac{1}{2}(u^2 + v^2)\right)\)

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To find the joint density function, we need to calculate the Jacobian determinant of the transformation from (x, y) to (u, v)

The joint distribution of (u, v) is a bivariate normal distribution with mean (0,0) and variance-covariance matrix

\(\begin{bmatrix}2 & 0 \0 & 2\end{bmatrix}\)

The joint distribution of (u, v) can be found by transforming the independent random variables x and y using the following formulas:

\( u = x + y\)
\( v = x - y \)

To find the joint distribution of (u, v), we need to find the joint probability density function (pdf) of u and v.

Let's start by finding the Jacobian determinant of the transformation:

\(J = \frac{{\partial (x, y)}}{{\partial (u, v)}}\)

\(= \frac{{\partial x}}{{\partial u}} \cdot \frac{{\partial y}}{{\partial v}} - \frac{{\partial x}}{{\partial v}} \cdot \frac{{\partial y}}{{\partial u}}\)

\(= \left(\frac{1}{2}\right) \cdot \left(-\frac{1}{2}\right) - \left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right)\)

\(J = -\frac{1}{2}\)

Next, we need to express x and y in terms of u and v:

\(x = \frac{u + v}{2}\)

\(y = \frac{u - v}{2}\)

Now, we can find the joint pdf of u and v by substituting the expressions for x and y into the joint pdf of x and y:

\(f(u, v) = f(x, y) \cdot |J|\)

\(f(u, v) = \left(\frac{1}{\sqrt{2\pi}}\right) \cdot \exp\left(-\frac{x^2}{2}\right) \cdot \left(\frac{1}{\sqrt{2\pi}}\right) \cdot \exp\left(-\frac{y^2}{2}\right) \cdot \left|-\frac{1}{2}\right|\)

\(f(u, v) = \frac{1}{2\pi} \cdot \exp\left(-\frac{u^2 + v^2}{8}\right)\)

Therefore, the joint distribution of (u, v) is given by:

\(f(u, v) = \frac{1}{2\pi} \cdot \exp\left(-\frac{{u^2 + v^2}}{8}\right)\)

In summary, the joint distribution of (u, v) is a bivariate normal distribution with mean (0,0) and variance-covariance matrix

\(\begin{bmatrix}2 & 0 \0 & 2\end{bmatrix}\)

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Answer:

82in

Step-by-step explanation:

brainliest?

The set {p, q, r, s} is linearly dependent if `a = -31` is found for the given linear combination of functions.

A set of functions is said to be linearly dependent if one or more functions can be expressed as a linear combination of the other functions.

Consider the given functions:

`p(x) = x³x²+2x+3,

q(x) = 3x³ + x²-x-1,

r(x) = x³ + 2x + 2`, and

`s(x) = 7x³ + ax² + 5`.

To show that these functions are linearly dependent, we need to find constants `c₁, c₂, c₃, and c₄`, not all zero, such that

`c₁p(x) + c₂q(x) + c₃r(x) + c₄

s(x) = 0`.

Let `c₁p(x) + c₂q(x) + c₃r(x) + c₄s(x) = 0`... (1)

We can substitute the given functions in this equation and obtain the following:

`c₁(x³x²+2x+3) + c₂(3x³ + x²-x-1) + c₃(x³ + 2x + 2) + c₄(7x³ + ax² + 5) = 0`... (2)

Let's simplify and rearrange the above equation to obtain a cubic equation in terms of `a`.

This is because we need to find the value of `a` for which there are non-zero values of `c₁, c₂, c₃, and c₄` that satisfy this equation.

`(c₁ + c₂ + c₃ + 7c₄)x³ + (c₁ + c₂ + 2c₄)x² + (2c₁ - c₂ + 2c₃ + ac₄)x + (3c₁ - c₂ + 5c₄) = 0`

The coefficients of this cubic equation should be zero for all `x` in the domain.

So, we have:

`c₁ + c₂ + c₃ + 7c₄ = 0` ...(3)

`c₁ + c₂ + 2c₄ = 0` ...(4)

`2c₁ - c₂ + 2c₃ + ac₄ = 0` ...(5)

`3c₁ - c₂ + 5c₄ = 0` ...(6)

Solving equations (3) to (6), we obtain:`

c₁ = -7c₄`

`c₂ = -2c₄`

`c₃ = -13c₄`

`a = -31`

Hence, the set {p, q, r, s} is linearly dependent if `a = -31`.

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The equivalent expression after combining like terms is (-8n + 7)/7.

To combine like terms in the expression (1/7) - 3((3/7)n - (2/7)), we will distribute the -3 to the terms inside the parentheses:

(1/7) - 3 * (3/7)n + 3 * (2/7)

Simplifying each term:

1/7 - 9/7n + 6/7

Now, let's combine the fractions:

(1 - 9n + 6)/7

Combining the numerators:

(-8n + 7)/7

Therefore, the equivalent expression after combining like terms is (-8n + 7)/7.

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Answer: Angle C

Step-by-step explanation:

Answer: See the graph below.

Yes her plan to construct a square inscribed in a circle is her plan correct.

Let's check if her plan is correct:

In order to construct a square inscribed in a circle,

the following steps should be followed

STEP 1:Draw a circle and its centre, O.

STEP 2:Draw a diameter PQ through the centre of the circle.

STEP 3:Mark the midpoint R of PQ.

STEP 4:Draw a perpendicular bisector of PQ, it should pass through R

STEP 5:It cuts PQ at right angles at R. Label the point where the perpendicular bisector cuts PQ as T.

STEP 6:Connect OT and RT to intersect the circle at points S and U respectively.

Now we have a square INSIDE the circle, where O is the center, and the square's diagonal is the circle's diameter, while the square's sides are the circle's radii.

So, Molly's plan is correct.

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Length of paper left is 5 m.

What is length?

Distance is measured by length. Length is a quantity having the dimension distance in the International System of Quantities. Most measuring systems use a base unit for length from which all other units are derived. The metre is the basic unit of length in the International System of Units (SI). The greatest extended dimension of a stationary item is typically believed to be its length. This is not always the case, as it may depend on the location of the item. Height, sometimes known as vertical length or vertical extent, and width, breadth, or depth are all words used to describe the length of a stationary object. When length is the longest dimension, width or breadth generally refer to the shorter one.

Length of paper left = 20-(1.5x10) = 20-15 = 5 m.

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Answer:

1 2 4 5 7 8 is not divisible by 2 ,3

Answer:

Its 175

Step-by-step explanation:

175

Given that:

Stacy bought 7 pounds of bananas at $0.69 a pound

and 9 pounds of guavas at $0.99 a pound.

She gave two $10 bills. We have to find the change she got while buying fruits.
So the total cost of 7 pounds of bananas = $0.69 × 7 = $4.83

Total cost of 9 pounds of guavas = $0.99 × 9 = $8.91

Now, the total amount Stacy gave for the fruits = 2 × $10 = $20

Therefore, the total cost of the fruits = $4.83 + $8.91 = $13.74

Now, the change she got = Total amount given – Total cost of fruits= $20 – $13.74= $6.26

The change Stacy got if she gave two $10 bills is $6.26.

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For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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Answer:

$592,395

Step-by-step explanation:

Because $1,623 x 365= $592,395 in a year

A study group of five people wants to track the root growth of sweet potatoes. To achieve this, the group should create a table to keep track of the data and then use the data to create the appropriate charts. To answer this question, we must first understand what root growth is and why it is important.

Root growth refers to the lengthening and thickening of roots over time. Root growth is essential for the survival of plants, as it allows them to absorb water and nutrients from the soil. Sweet potatoes are particularly interesting because they are root vegetables, meaning that the part of the plant that we eat is the root itself.
To track root growth, the study group should create a table that records the length and thickness of the sweet potato roots over time. The group should measure the roots at regular intervals, such as once a week, and record the measurements in the table. The table should also include the date and any other relevant information, such as weather conditions or soil quality.
Once the study group has collected enough data, they can use it to create appropriate charts. Line charts are ideal for showing how root length and thickness change over time, while bar charts are ideal for comparing the root growth of different sweet potato varieties or under different growing conditions.
In conclusion, tracking root growth is an essential part of understanding how sweet potatoes grow and develop. To do this, the study group should create a table to keep track of the data and then use the data to create appropriate charts. The table should include the date, root length, root thickness, and any other relevant information, while the charts can be used to visualize the data and draw conclusions.

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The total deduction for Thomas Schmitt per week is $319.5.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

The total weekly salary of Thomas = $526/week

Gross pay = $9912/year

Since,

1 year = 12 months

And,

1 month = 4 weeks

So,

1 year = 12 × 4 = 48 weeks.

So,

Gross pay per week = $9912/48 weeks

Gross pay per week = $206.5/week.

Now,

Deduction = 526 - 206.5 = $319.5

Hence "The total deduction for Thomas Schmitt per week is $319.5".

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Answer:

x=3 y=-1

Step-by-step explanation:

y=2x-7

2x+y=5

___________________

2x+2x-7=5

4x-7=5

4x=12

x=3

___________________

2(3)-7=y

6-7=y

-1=y

Answer:

c = 3

Step-by-step explanation:

Hope it helps and have a great night! =D

~shining stars~

The value of 'c' in the 32^{2c} = 8^{c+7}\(32^{2c} = 8^{c+7}\) is, 3.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An expression \(32^{2c} = 8^{c+7}\).

Now, To equate the exponents we have to change the bases to the same value.

Therefore, \(32^{2c} = 8^{c+7}\) ⇒ \((2^5)^{2c} = (2^3)^{c+7}\).

5(2c) = 3(c + 7).

10c = 3c + 21.

7c = 21.

c = 3.

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Answer:

Half Dozen Donuts: $6.59

Donut Holes: $4.89

2 Vanilla Lattes: $6.98

Subtotal: $18.37

Tax: $1.47

Total: $19.84

Step-by-step explanation:

It finally worked. So I guess it only shows on computers, not mobile.

Answer:

(675°F − 32) × 5/9 + 273.15 = 630.372K

Hope it's right if not so sorry :)

The percentage mark-up of the goods is 69 percent.

The mark-up percentage is calculated by subtracting the unit cost from the selling price, dividing by the unit cost and multiplying times 100.

Therefore, the buyer for a chain of stores purchased tables in bulk, paying $200 each. The stores will sell each table for $338.

Hence, the percentage mark-up can be calculated as follows:

percentage mark-up = 338 - 200 / 200 × 100

percentage mark-up = 138 × 100 / 200

percentage mark-up = 13800 / 200

percentage mark-up = 138 / 2

percentage mark-up = 69 %

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Let:

(x1,y1) = (0,4)

(x2,y2) = (4,0)

The slope m is:

Using the point slope equation:

Answer:

21

Step-by-step explanation:

1, 1, 2, 3, 5, 8, 13, 21

The required eighth number in the Fibonacci sequence is 21.

Given that,
1, 1, 2, 3, 5, and 8 are the first six numbers of the Fibonacci sequence. what is the eighth number is to be determined

The sequence is defined as the specific pattern of numbers in which they are arranged.

Here,
given Fibonacci sequence is 1, 1, 2, 3, 5, 8

The Fibonacci numbers, sometimes known as Fn, are a set of numbers in mathematics where each number is the sum of the two numbers before it.
According to the above definition,
7 th number = 5th number + 6th number =
7 th number = 5 + 8 = 13
8th number = 8 + 13 = 21

Thus, the required eighth number in the Fibonacci sequence is 21.

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Answer:

301.44 cm ^ 2

Step-by-step explanation:

We have that the total surface area of a cone would be the sum of the base area and the lateral surface area.

the area of the base, being a circle is pi * r ^ 2

the lateral area would come being the multiplication between the inclined height, the radius and the number pi, that is to say pi * r * l

the inclined height is calculated using the Pythagorean theorem, the legs being the radius and the altitude, thus:

l ^ 2 = 6 ^ 2 + 8 ^ 2

l ^ 2 = 100

l = 10

Therefore, we can replace:

A = 3.14 * 6 ^ 2 + 3.14 * 10 * 6

A = 301.44

It means that the total surface area is 301.44 cm ^ 2

3)  since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.

(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:

Total payment A = Monthly installment * Number of installments

              = $375 * 36

              = $13,500

Therefore, Adrian paid a total of $13,500 over the course of 36 months.

(2) In the simple interest formula I = Prt, the letters used represent the following variables:

I: Interest (the amount of interest paid)

P: Principal (the initial amount, or in this case, the car worth)

r: Rate of interest (expressed as a decimal)

t: Time (in years)

(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:

r = (I / Pt) * 100

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Answer:

See below.

Step-by-step explanation:

They invested in a ratio of Julie:Kristen of 5:12.

5 + 12 = 17

Julie invested 5/17 of the amount, and Kristen invested 12/17 of the mount.

a.

Julie: 5/17 * $51,000 = $15,000

Kristen: 12/17 * $51,000 = $36,000

b.

Kristen owns 12/17 of the business.

As a percent, 12/17 = 12/17 * 100% = 70.6%

c.

The percent of the business each owns does not change with the amount the company is worth.

Kristen owns 70.6%, so Julie owns 100% - 70.6% = 29.4%

Answer:

well 6.75 is actually real and if u times it by 2.89 you should get ur answer sir (:

Step-by-step explanation:

jK

A single triangle is 180 degrees.

As you can see. Triangle A, as it is shown in the bad drawing. It is an isosceles triangle because two sides are equal to one another, indicated with the lines. Angle A is given as 57. By the isosceles triangle theorem, Angle A equals to Angle B. Calculating the missing angle: 180 - 57 (given) - 57 (because of the isosceles triangle theorem type of thing. I forgot) = 66

You can see it is a verticle angle so angle C is equal to angle D, therefore angle D is 66.

Again it is an isosceles triangle so Angle F is 66. 180 - 66(angle D) - 66(angle F) = 48 = angle x

Angle A = 57 degrees. Given

Angle A = Angle B. isosceles triangle theorem

Angle B = 57 degrees. Substitute

Angle A + Angle B + Angle C = 180. Definition of Triangle (I forgot what it was called)

57 + 57 + Angle C = 180. Substitution

Angle C = 66. Subtraction

Angle C = Angle D. Verticle angle theorem.

Angle D = 66. Substitution

Angle F = Angle D. isosceles triangle theorem

Angle F = 66. Substitution

Angle D + Angle F + Angle X = 180. Definition of Triangle?

66 + 66 + Angle X = 180. Substitution

Angle X = 48. Subtraction