what is the probability that the distance between two randomly chosen points in a circle is less than the radius?

The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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The ratio of c:d:e is 1:3:2.

To find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.

A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.

You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.

It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.

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The duration it takes a teacher and the duration it takes a student to each paint the mural found using the combined work formula are;

The number of brushes and tubes of paints purchased are;

The time, Tₙ, it takes to do a work by two people combined, where the time it takes one person to do the work is T₁ and the time it takes the second person to do the same work is T₂, can be expressed as in the following combined work or rate of work formula equation;

[tex]\frac{1}{T_1}+\frac{1}{T_2} = \frac{1}{T_n}[/tex]

Let T represent the time it takes one teacher to paint the large mural, and let S represent the time it takes a student to paint the large mural, we get;

[tex]\frac{8}{T}+\frac{2}{S} = \frac{1}{10}[/tex]...(1)

[tex]\frac{6}{T}+\frac{8}{S} = \frac{1}{14}[/tex]...(2)

Multiplying equation (1) by 4 and subtracting equation (2) from the result, we get;

[tex]4\times \frac{8}{T}+\frac{2}{S} = \frac{32}{T}+\frac{8}{S} = \frac{4}{10} = \frac{2}{5}[/tex]

[tex]\frac{32}{T}+\frac{8}{S} = \frac{2}{5}[/tex]

[tex]\frac{32}{T}+\frac{8}{S} -\left(\frac{6}{T}+\frac{8}{S}\right) = \frac{2}{5} - \frac{1}{14} = \frac{23}{70}[/tex]

[tex]\frac{26}{T}+0 = \frac{23}{70}[/tex]

T = (70/23) × 26 = 1820/23 = 79 3/23

[tex]\frac{8}{T}+\frac{2}{S} = \frac{1}{10}[/tex], therefore;

[tex]\frac{2}{S} = \frac{1}{10} - \frac{8}{T}[/tex]

[tex]\frac{2}{S} = \frac{1}{10} - \frac{8\times 23}{1820} = -\frac{1}{910}[/tex]

S = -910 × 2 = -1820

Second question

The budget on tubes of paint and paintbrushes = $200

The cost of a tube = $4.00 and the cost of a paintbrush = $0.5

Number of brushes purchased = 2 × The number of tubes of paint purchased

Let x represent the number of paintbrushes purchased and let y represent the number of tubes of paint purchased, we get;

0.5·x + 4·y = 200

x = 2·y

Therefore; 0.5 × (2·y) + 4·y = 200

y + 4·y = 5·y = 200

y = 200/5 = 40

The number of tubes of paint purchased, y = 40

x = 2·y, therefore;

x = 2 × 40 = 80

The number of paintbrushes purchased, x = 80

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According to the regression model, approximately 71.46% of the audience will finish watching a documentary that is 85 minutes long.

Regression is a statistical method used to model the relationship between two variables.

In this case, the regression equation y = -0.414x + 106.55 is used to approximate the percent of people in an audience who finish watching a documentary, y, given the length of the film in minutes, x.

To find the best prediction for the percent of people who will finish watching a documentary that is 85 minutes long, we need to plug in 85 for x in the regression equation:

y = -0.414x + 106.55

y = -0.414(85) + 106.55

y = -35.09 + 106.55

y = 71.46

Therefore, the best prediction for the percent of people who will finish watching a documentary that is 85 minutes long is 71.46%.

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A measurable characteristic of an entire population is a parameter.

The population data is the real data for a certain attribute in the context of statistics, whereas the sample data is the representative data picked from the population. Metrics like mean, standard deviation, median, and mode are typically used to measure the characteristics of the sample and population.

Option B is the right response to the provided question.

A parameter is a quantity that affects a mathematical object's output or behavior yet is thought of as being held constant. Variables and parameters have a lot in common, and in some cases, the distinction is really one of perspective.

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There are 265 bottles in the first group, 285 in the second group, 505 in the third group, and 515 in the fourth group in both the ways.

Solution Method 1: With the aid of a diagram

We can make an outline to monitor the quantity of jugs in each gathering. We should dole out a variable to address the quantity of containers in the principal bunch, x.

Bunch 1: x containers

Bunch 2: x + 20 containers

Bunch 3: 2(x + 20) = 2x + 40 containers

Bunch 4: 2x + 50 containers

The complete number of containers is x + (x + 20) + (2x + 40) + (2x + 50) = 1700

Along these lines, 6x + 110 = 1700

Taking away 110 from the two sides: 6x = 1590

Separating the two sides by 6: x = 265

In this way, there are 265 jugs in the principal bunch, 285 in the subsequent gathering, 505 in the third gathering, and 515 in the fourth gathering.

Solution Method 2: With Algebraic Equations

We can address the quantity of containers in each gathering with factors:

Bunch 1: x containers

Bunch 2: y bottles

Bunch 3: z bottles

Bunch 4: w bottles

Considering that:

y = x + 20

z = 2y = 2(x + 20) = 2x + 40

w = z + 10 = 2x + 50

Also, the all out number of jugs is x + y + z + w = 1700

Subbing the upsides of y, z, and w:

x + (x + 20) + (2x + 40) + (2x + 50) = 1700

Working on the articulation:

6x + 110 = 1700

Taking away 110 from the two sides:

6x = 1590

Separating the two sides by 6:

x = 265

Thus, there are 265 containers in the principal bunch, 285 in the subsequent gathering, 505 in the third gathering, and 515 in the fourth gathering.

Connection between the two techniques:

The two techniques utilize similar conditions to address the quantity of jugs in each gathering, and they show up at a similar arrangement. The thing that matters is that the principal technique presents the arrangement in a diagram, which can be simpler for certain individuals to comprehend, while the subsequent strategy utilizes mathematical conditions, which can be more proficient for taking care of the issue. Notwithstanding, the two strategies depend on similar ideas and standards of polynomial math.

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the value of x will be either 1 or 3 for the condition f (x) = g (x).

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equations: f (x) = -x^2 + 3x - 2 and g (x) = -x + 1

To find the value of x for the  f (x) = g (x)

So,

-x^2 + 3x - 2 =  -x + 1

-x² + 4x -3 = 0

multiply by -1 in the equation

x² - 4x +3 = 0

x² - 3x - x +3 = 0

take (x-3 ) common

x(x -3)-1(x- 3) = 0

Thus,

x = 1 or 3

Therefore, the value of x will be either 1 or 3 for the condition f (x) = g (x).

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A real-world situation consistent with the data provided would be (a) the height of a balloon as it ascends in the air at a constant rate, (b) the speed of a car as it accelerates from a standstill to a constant speed, (c) the height of a soccer ball as it is kicked into the air (d) the velocity of a skydiver as they fall to the ground.

a. A real-world situation consistent with the data provided would be the height of a balloon as it ascends in the air at a constant rate. In this case, x can be the time elapsed in seconds, and y can be the height in meters.

The balloon's height will not change with time (f'(x) = 0), meaning the balloon is not accelerating, and the height remains constant as it moves from 0 to 3 seconds.

b. A real-world situation consistent with the data provided would be the speed of a car as it accelerates from a standstill to a constant speed. In this case, x can be the time elapsed in seconds, and y can be the speed in meters per second.

The speed of the car will increase at a constant rate (f'(x) = 50), meaning the car is accelerating, and the speed increases as it moves from 0 to 3 seconds.

c. A real-world situation consistent with the data provided would be the height of a soccer ball as it is kicked into the air. In this case, x can be the time elapsed in seconds, and y can be the height in meters.

The height of the ball will increase as time goes by (f'(x) is increasing as x increases), meaning the ball is moving upwards, and the height increases as it moves from 0 to 3 seconds.

d. A real-world situation consistent with the data provided would be the velocity of a skydiver as they fall to the ground. In this case, x can be the time elapsed in seconds, and y can be the velocity in meters per second.

The velocity of the skydiver will decrease as time goes by (f'(x) is decreasing as x increases), meaning the skydiver is falling faster and faster, and the velocity decreases as it moves from 0 to 3 seconds.

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--The given question is incomplete; the complete question is

"Describe different real-world situations (include the units of x and y) that would be consistent with the data provided:

a. f'(x)=0, 0 ≤ x ≤ 3

b. f'(x) = 50, 0 ≤ x ≤ 3

C. f'(x) is increasing as x increases, 0 ≤ x ≤ 3

d. f'(x) is decreasing as x increases, 0 ≤ x ≤ 3"--

(C) The corresponding value of x represents the expected y-value at each location on the least-squares regression line.

A straight line that depicts the relationship between a response variable (y) and an explanatory variable (x) is called a regression line (LSRL, or Least Squares Regression Line).

A mathematical model called the line is used to forecast the value of y given a value for x.

We need an explanatory and a response variable for regression.

The anticipated y-value at each position on the least-squares regression line is represented by the corresponding value of x.

One way to use linear regression is by using least squares. It enables us to identify abnormalities in our data and forecast results based on an existing collection of data.

Values that are either too wonderful or awful to be real or that are unique cases are known as anomalies.

Therefore, (C) the corresponding value of x represents the expected y-value at each location on the least-squares regression line.

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Gwen's walked 18.81 meters in her living room.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

We have to given that;

Gwen's living room is rectangular and measures 6 meters by 5 meters.

Now, Beginning in one corner, Gwen walks the length of her living room and then turns and walks the width.

Hence, Distance cover by him = 6 + 5

                                               = 11 meters

And, Finally, Gwen walks back to the corner she started in.

Hence, The distance cover to back to the corner she started in is,

⇒ d² = 6² + 5²

⇒ d² = 36 + 25

⇒ d = 61

⇒ d = 7.81 meters

Thus, The total distance cover by her by walking = 7.81 + 11

                                                                            = 18.81 meters

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The compound interest on $1240 at 8% for 2 years is $205.8

Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

The Amount on a compound interest is expressed as: A = P(1+r/100)^t

where P is the principal and r is the rate, t is the time

A = 1240( 1+8/100)²

A = 1240(1+0.08) ²

A = 1240(1.08)²

A = 1240× 1.166

A = $1445.8

A = P+I

I = A-P

I = 1445.8-1240

I = $ 205.8

therefore the interest on the $1240 compounded for 2 years is $205.8

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The probability of drawing a white marble is 2/15

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

4 white, 10 blue, and 16 red marbles

This means that

Total = 4 + 10 + 16

Total = 30

So, the probability of drawing a white marble is

P = White/Total

Substitute the known values in the above equation, so, we have the following representation

P =  4 / 30 = 2/15.

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Complete question

a jar contains 4 white, 10 blue, and 16 red marbles. if one marble is drawn at random from the jar, find the probability that a white marble is selected

Answer:

232 and 58

Step-by-step explanation:

bro just use a calc

Answer:

Part A: C, 129 & Part B: A, 58

Step-by-step explanation:

Part A:

36+ 51 + 42= 129

Part B:

152- 49 - 45= 58

To double check part B:

58 + 49 + 45 = 152

Step-by-step explanation:

(gof)(x) is basically g(f(x))

= 4 × (3x - 1)² + 9

= 4 × (9x² - 6x + 1) + 9

= 36x² - 24x + 4 + 9

= 36x² - 24x + 13

Answer:

16/4 = 4

1 block = 4 minutes

4 blocks = 16 minutes

to put this into a ratio it would be 1:4

The age of the oldest of the five friends is 19 years and the youngest is 12 years.

The given information is in a group there are five friends, the sums of the ages of each group of four of them are 58, 59, 61, 62 and 64.

The range of a data set is the difference between smaller values and a larger value in the set.

To find the age of the oldest person

Range=oldest age -the youngest age

[tex]oldest=\frac{Range-youngest age}{4}[/tex]

R=(64-58/4)+(64-59/4)+(64-61/4)+64-62/4)

R=1.5+1.241+0.75+0.5

R=3.991.

64/4=16.

O=16+3.991

Oldest=19 years.

Youngest=16-3.9=12 years.

Hence, the age of the oldest of the five friends is 19 years.

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Answer:

see below

Step-by-step explanation:

4/7*224 = 128

224 miles / 7 gallons = 32 miles per gallon

so given either factors, you'll be able to solve the other.

the problem will become how many gallons used to drive xxx miles.

Answer: (x+6)(x+4)

Step-by-step explanation: Search math w ay on the internet :)

Answer:

LCD = 30

Step-by-step explanation:

11/15 = 11/15 × 2/2 = 22/30

9/10 = 9/10 × 3/3 = 27/30

The statement W ⊂ J is true.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, and the complement of sets.

We have,

From the given information,

R ⊂ J

D ⊂ J

M ⊂ D ⊂ J

W ⊂ D ⊂ J _____(1)

Now,

⊂ means subset.

Example:

A = {1, 2, 3}

B = {1, 2, 3, 4}

So,

A ⊂ B since the element in A is also in B and B has one extra element.

So,

From (1),

W ⊂ J

Thus,

W is a subset of J.

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Appropriate values of equation with standard form:

2.D. A=4, B=0, C=9

3.B.5x-4y=9

A system of linear equations is one of the algebraic equations. This equation has the characteristic that each term contains a constant, or multiplication of a constant with a single variable.

This equation is said to be linear because this mathematical relationship can be described as a straight line in the Cartesian coordinate system, a system that uniquely assigns each point in a plane a series of numerical coordinates.

This system of linear equations generally has two main properties, namely:

For example l is a linear equation, then:

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The data displays be used to compare populations as

(i)they quickly illustrate measures of center

(ii)they show trends in data that can be compared.

Data Display is basically displaying of useful data which has been extracted from bundles of raw data or raw data points. That useful data can be used to compare two different datasets as well.

It says that it quickly illustrate measures of centre. True, because it presents you quick display so that everyone seeing the data in form of charts or tables easily catch the information to be conveyed.

It says, they show trends in data that can be compared. Yes again true. Data displays show you trends of different things in one clear picture and it can be compared with other datasets through the use of data displays.

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Before reading this article, my opinion of selfies is that they were easy and not very dangerous photographs to capture. When I read the article my perspective changed to be more careful when taking a selfie.

A selfie is a term that refers to a photograph that is taken autonomously of oneself. Now most devices include a front camera to take photos of yourself, the famous selfies.

My perspective before reading the article was that selfies were ordinary photos like any other. However, after reading the article I see that they have a high risk of accidents, so it is necessary to be careful not to be in a risky situation because of a photo.

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Check the picture below.

so by the "inscribed angle theorem" that means "c" is half of 70°, and by Thales Theorem "a" is a right-angle, btw that can also be derived by the "inscribed angle theorem", that makes angles "b" and "c" complementary angles.

The following expressions can be written as 12x+9 , 5y + 14 , -3c-10 and 11a+4b-5

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that consists of one or more variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to represent a wide range of mathematical situations, such as equations, inequalities, functions, and formulas.

(a) 5x + 7 + 6x + 2 = 11x + 9

(b) 7y + 4 - 2y + 10 = 5y + 14

(c) 6c - 2 - 9c - 8 = -3c - 10 (Rewrote subtraction as addition: 6c - 2 + (-9c) - 8)

(d) 1lx + 2y + 4x + 8y = 5x + 10y (Combined "like terms": lx and x are not the same, so they can't be combined)

(e) 3m + 2n - 5m + 11n = -2m + 13n

(f) -2w + 4z + 7w - 9z = 5w - 5z

(g) 15x + 2y + 7 + 6y + 4x + 2 = 19x + 8y + 9

(h) 3a + 7b - 9 + 8a - 3b + 4 = 11a + 4b - 5

Therefore, The following expressions can be written as 12x+9 , 5y + 14 , -3c-10 and 11a+4b-5

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The six algebraic equations are given below.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

AD, BE and CF intersect at point P.

And AD⊥CF.

The algebraic equations:

∠APC + ∠CPD = 180°  {Supplementary angles}

∠FPA + ∠CPA = 180°  {Supplementary angles}

∠EPA + ∠BPA = 180°  {Supplementary angles}

∠EPD = ∠BPA {opposite angle theorem}

∠APB + ∠CPB = ∠CPA {Angle addition postulate}

∠EPF + ∠EPD = ∠DPF {Angle addition postulate}

Therefore, 6 equations are given above.

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The total distance between Dylan and Mackenzie is reduced by x feet each time Dylan travels x feet, since Mackenzie travels 2x feet during that time. Therefore, their combined distance of travel is x + 2x = 3x feet.

Since their starting distance apart was 230 feet, and their combined distance of travel is 3x feet, we can write an equation to represent the situation:

230 = 3x

To find the distance each person travels, we can solve for x by dividing both sides of the equation by 3:

230 / 3 = 3x / 3

x = 230 / 3 = 76.67 feet

So, Dylan travels x = 76.67 feet and Mackenzie travels 2x = 2 * 76.67 = 153.33 feet.

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