Suppose parametric equations for the line segment between (8,-2) and (9,-2) have the form:
{x(t)=a+bt
{y(t)=c+dt
If the parametric curve starts at (8,-2) when t=0 and ends at (9,-2) at t=1, then find a,b,c, and d. a= b=
c=
d=

From the given table, we can see a column of different car types, and a row of different colors. We are asked about the probability that a random chosen car would be a beige SUV

Answer:

\(Area = 153.938040026m^2\)

\(Circumference= 43.9822971503m\)

Step-by-step explanation:

Area

\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)

Circumference

\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)

Answer:

11 cups

Step-by-step explanation:

1.50x10=15 and that wouldn't be the answer because, he needs to cover all of his supplies.  1.50x11=16.5, and that is enough money to cover all of his supplies. So he would need 11 cups total.

Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

Designing an easy do-it-yourself compost bin:

Drawing and Description:

The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.

The bin can be placed directly on the ground or on a solid surface, depending on personal preference.

Materials Used:

Wood or wire mesh (depending on preference)

Nails or screws to assemble the structure

Size of the Bin:

The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.

Substances Used to Fill It:

To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.

Household Items That Can Go in It:

You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).

Time for Compost to Be Ready:

The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.

Using the Compost:

Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.

for similar questions on compost bin:

https://brainly.com/question/30423152

#SPJ11

Answer: A). 14,866.01 ft^2

Step-by-step explanation:

A=2πrh+2πr2=2·π·26·65+2·π·262≈14866.01644ft²

Answer:

Step-by-step explanation:

Number of electronic systems = 6

(a) Number of defected systems = 2

Probability of getting at least one system is defective

1 defective and 1 non defective + 2 defective

= (2 C 1 ) x (4 C 1) + (2 C 2) / (6 C 2)

= 3 / 5

(b) four defective

Probability of getting at least one system is defective

2 defective and 2 non defective + 3 defective and 1 non defective + 4 defective  

= (4 C 2 ) x (2 C 2) + (4 C 3 )(2 C 1) + (4 C 4) / (6 C 4)

= 1

Answer:

(a)P(At least one defective)\(=0.6\)

P(Both are defective)\(=0.067\)

(b)P(At least one defective)\(=14/15\)

P(Both are defective)\(=0.4\)

Step-by-step explanation:

We are given that

Total number of complex electronic system, n=6

(a)Defective items=2

Non-defective items=6-2=4

We have to find the  probability that at least one of the two systems tested will be defective.

P(At least one defective)=\(\frac{2C_1\times 4C_1}{6C_2}+\frac{2C_2\times 4C_0}{6C_2}\)

Using the formula

\(P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}\)

P(At least one defective)\(=\frac{\frac{2!}{1!1!}\times \frac{4!}{1!3!} }{\frac{6!}{2!4!}}+\frac{\frac{2!}{0!2!}\times \frac{4!}{4!}}{\frac{6!}{2!4!}}\)

Using the formula

\(nC_r=\frac{n!}{r!(n-r)!}\)

P(At least one defective)\(=\frac{2\times \frac{4\times 3!}{3!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}+\frac{1}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}\)

P(At least one defective)\(=\frac{2\times 4}{3\times 5}+\frac{1}{3\times 5}\)

P(At least one defective)\(=\frac{8}{15}+\frac{1}{15}=\frac{9}{15}\)

P(At least one defective)\(=\frac{3}{5}=0.6\)

Now, the probability that both are defective

P(Both are defective)=\(\frac{2C_2\times 4C_0}{6C_2}\)

P(Both are defective)=\(\frac{\frac{2!}{0!2!}\times \frac{4!}{4!}}{\frac{6!}{2!4!}}\)

P(Both are defective)\(=\frac{1}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}\)

P(Both are defective)\(=\frac{1}{3\times 5}\)

P(Both are defective)\(=0.067\)

(b)

Defective items=4

Non- defective item=6-4=2

P(At least one defective)=\(\frac{4C_1\times 2C_1}{6C_2}+\frac{4C_2\times 2C_0}{6C_2}\)

P(At least one defective)\(=\frac{\frac{4!}{1!3!}\times \frac{2!}{1!1!} }{\frac{6!}{2!4!}}+\frac{\frac{4!}{2!2!}\times \frac{2!}{2!}}{\frac{6!}{2!4!}}\)

P(At least one defective)\(=\frac{2\times \frac{4\times 3!}{3!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}+\frac{\frac{4\times 3\times 2!}{2!\times 2\times 1}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}\)

P(At least one defective)\(=\frac{2\times 4}{3\times 5}+\frac{2\times 3}{3\times 5}\)

P(At least one defective)\(=\frac{8}{15}+\frac{6}{15}=\frac{8+6}{15}\)

P(At least one defective)\(=\frac{14}{15}\)

P(Both are defective)\(=\frac{4C_2\times 2C_0}{6C_2}\)

P(Both are defective)\(=\frac{\frac{4\times 3\times 2!}{2\times 1\times 2!}\times \frac{2!}{2!}}{\frac{6\times 5\times 4!}{2\times 1\times 4!}}\)

P(Both are defective)\(=\frac{\frac{4\times 3\times 2\times 1}{2\times 1\times 2\times 1}}{3\times 5}\)

P(Both are defective)\(=\frac{6}{15}=0.4\)

P(Both are defective)\(=0.4\)

Answer:

B is the answer

Step-by-step explanation:

hope it helps

Answer:

54°

Step-by-step explanation:

The overall angle degrees of a trinangle 180°

Since we know that once of the angles is 72° we subract that from 180°

That equals 108°

Then we divide 108° since that is the sum of both the angles.

108/2= 54, so y= 54°

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

The correct dot plot represents this data set is shown in figure C.

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 data set is,

31, 35, 38, 31, 32, 38, 37, 39, 31, 35, 32, 38

Now, From data set;

31 is repeated by 3 times

32 is repeated by 2 times

35 is repeated by 2 times

37 is repeated by 1 times

38 is repeated by 3 times

Hence, The correct dot plot represents this data set is shown in figure C.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ7

10.

Consider the given function,

Solve for the critical points as,

Thus, the given function has an extrema at point x= -5.

Apply the second derivative test,

It is found that the function has a maxima at point x= -5.

Solve for the maximum value as,

Thus, the maximum value of the function is -5.

Now, apply the leading coefficient test to find the end behavior of the function.

It is observed that the leading coefficient is negative, so according to the test, the value of the function approaches negative infinity as 'x' approaches infinity.

So the minimum value of the function tends to negative infinity,

Now, solve for the ratio as,

Thus, the ratio approaches infinity.

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

Learn more about Probability,

https://brainly.com/question/29492440

#SPJ1

Answer:

Identity property on multiplication

Step-by-step explanation:

If you multiply any number by 1, you will get the same number.

15 * 1 = 15   ; 25* 1 = 25

By making x the subject of the formula in this equation u = cos(0.5x)​ gives x = 2cos⁻¹(u).

In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.

In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.

By taking the arc cosine of both sides of the equation, we have the following:

u = cos(0.5x)

cos⁻¹(u) = 0.5x

By multiplying both sides of the mathematical equation by 2, we have the following:

2 × cos⁻¹(u) = 0.5x × 2

x = 2cos⁻¹(u)

Read more on expression here: brainly.com/question/25767785

#SPJ1

The volume of the circular cylinder be,

⇒ 62.8 mm³

Given that,

For a circular cylinder,

Height = 5 mm

Radius = 2 mm

Then we have to find the volume of this circular cylinder

Since we know that,

The right circular cylinder is a cylinder with circular bases that are parallel to each other. It's a three-dimensional form. The axis of the cylinder connects the centers of the cylinder's two bases.

This is the most frequent sort of cylinder encountered in daily life. The oblique cylinder, on the other hand, does not have parallel bases and resembles a skewed construction.

volume of circular cylinder = πr²h

Here we have,

r = 2 mm

h = 5 mm

Now put the values into the formula we get,

Volume = π x 2² x 5

             = 62.8 mm³

To learn more about volume visit:

https://brainly.com/question/16860802

#SPJ1

Fractions such as 12 in/ 1 ft and 1 yd/ 3ft are called unit conversion fractions

Unit conversion fractions are used to convert between different units of measurement within the same quantity.

The fraction 12 in/1 ft represents the conversion factor from inches to feet, where 12 inches is equivalent to 1 foot.

This fraction allows us to convert a certain length measured in inches to an equivalent length in feet.

Similarly, the fraction 1 yd/3 ft represents the conversion factor from yards to feet, where 1 yard is equivalent to 3 feet.

This fraction allows us to convert a certain length measured in yards to an equivalent length in feet.

To learn more on Fractions click:

https://brainly.com/question/10354322

#SPJ1

Fill in each blank so that the resulting statement is true

Fractions such as 12 in/ 1 ft and 1 yd/ 3ft are called _________fractions

The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

Know more about volumes,

https://brainly.com/question/17101095

#SPJ1

9514 1404 393

Answer:

  5/32768

Step-by-step explanation:

This sequence does not have a common difference, but does have a common ratio of r = 10/40 = 1/4. The first term is a1 = 40.

The general term of a geometric sequence is ...

  an = a1·r^(n-1)

Then the 10th term is ...

  a10 = 40·(1/4)^(10 -1) = 40/4^9 = 5/32768

The profit function for a furniture company introducing a new line of lounge chairs is P(x) =\(-8.32x^2 + 1,248x - 36,400\), where x represents the number of chairs to be manufactured and sold.

The problem provides the revenue function and cost function for a furniture company introducing a new line of lounge chairs. To find the profit function, we need to subtract the cost function from the revenue function.

The revenue function R(x) is given as 1,248x - \(8.32x^2\), where x represents the number of chairs manufactured and sold. This function calculates the total revenue obtained by the company by multiplying the number of chairs sold (x) by the price of each chair (1,248 - 8.32x).

The cost function C(x) is given as 36,400 - 83.2x. This function calculates the total cost incurred by the company to manufacture x chairs, which includes both fixed and variable costs.

To find the profit function for the furniture company, we need to subtract the cost function C(x) from the revenue function R(x):

P(x) = R(x) - C(x) = (1,248x - \(8.32x^2\)) - (36,400 - 83.2x)

Simplifying this expression, we get:

P(x) =\(-8.32x^2\) + 1,248x - 36,400

Therefore, the profit function for the furniture company is P(x) = \(-8.32x^2\) \(+ 1,248x - 36,400\).

To learn more about cost function please click on below link        

https://brainly.com/question/31041336

#SPJ1

The sales tax rate is 10.45 percent.

The area of the first room is 11 x 12 = 132 square feet and the area of the second room is 25 x 13 = 325 square feet.

The cost of the carpet and padding for the first room is 132 x (3.50 + 0.75) = $593.25 and for the second room is 325 x (3.50 + 0.75) = $1294.75.

The total cost of the carpet and padding (before tax) is $593.25 + $1294.75 + $500 = $2388.

Now we can set up an equation to solve for the sales tax. We know that the total cost with tax is $2637.63. So, the equation would be:

Total cost with tax = Total cost before tax + Tax

2637.63 = 2388 + Tax

Tax = 2637.63 - 2388

Tax = $249.63

To find the sales tax rate, we can divide the tax by the total cost before tax.

Tax Rate = Tax / Total cost before tax

Tax Rate = 249.63 / 2388 = 0.1045 or 10.45%

Therefore, the sales tax rate is 10.45 percent.

To learn more about the sales tax visit:

brainly.com/question/27092799.

#SPJ1

Answer:

less than or equal to -11

Step-by-step explanation:

subtract 8 to both sides

k< or equal to -11

Answer:

Raul is 15 years old.

Step-by-step explanation:

The number of years from the start of the Great Depression to Nixon's election is six years less than three times Raul's age: 3r-6

If then Nixon's first election happened 39 years after the Great Depression, then: 3r-6=39

3r-6=39    Add six to both sides so the 6 on the left side gets canceled out (positive and negative cancel each other out) so the equation will now look like this: 3r=45

Then divide 3 on both sides (multiplication and division also cancel each other out), then the equation looks like this: r=15

And so, Raul is 15 years old.

Answer:

1. A≈ 78.54

2. A≈201.06

Step-by-step explanation:

1) A=πr2=π·52≈78.53982

2)

A=1

4πd2=1

4·π·162≈201.06193

Answer:

$3.25

Step-by-step explanation:

This is division

29.25 divided by 9

9 goes into 29.25 3 times

29.25-27=2.25

2.25 is 1/4 of 9

2.25*4=9 because 2*4=8 and .25*4=1 so 8+1=9

So the answer is 3 1/4 or $3.25

The correct option is,

The table represents a linear function because there is not a constant rate of change in the input and output values.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table is shown in figure.

Now,

For Table;

The equation of line is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - (-4) = (-2 - (-4)) / (- 1 - (-2))  (x - (-2))

⇒ y + 4 = 2/1 (x + 2)

⇒ y + 4 = 2 (x + 2)

⇒ y + 4 = 2x + 4

⇒ y = 2x

Thus, The table represents a linear function because there is not a constant rate of change in the input and output values.

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ1