a drawer contains 20 socks. 10 are black. 6 are blue. 4 are red. two socks are taken out at random. what is the probability that one is blue and one is red?

The area of the figure that is given in the image below is: 26.13 ft².

To find the area of a composite figure, find the area of each of the shapes that make up the composite figure, then add their areas together.

Given the composite figure as shown in the diagram below, it consists of a triangle and a half circle (semicircle). To find the area of the composite figure, find the area of the triangle and that of the semicircle.

Area of triangle = 1/2 × base × height = 1/2 × 6 × 4

Area of triangle = 1/2 × 24

Area of triangle = 12 ft²

Area of semicircle = 1/2 × π × r² = 1/2 × 3.14 × 3²

= 14.13 ft²

Area of the composite figure = 12 + 14.13 = 26.13 ft².

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The purpose of controlling is to monitor performance and take corrective action as needed to ensure that objectives are met.

Performance refers to how effective or successful someone or something is in doing something. The capacity of a corporation to adopt optimal organization with the goal of providing a product or service that satisfies the expectations of consumers and customers determines business performance, which is strongly related to commercial effectiveness. Employee Engagement and Productivity are Improved by Performance Management. Employees who are actively involved in their work environments stay longer and produce better outcomes. Increasing employee engagement is essential to increasing output and maximizing return on investment.

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Answer:87 degrees

Step-by-step explanation:

113 degrees-26degrees= 87degrees.

The nearest 1000 is 160000.

Answer:

Step-by-step explanation:

The 160138 to the nearest 1000 is 160000

The value of the variable 'x' by simplifying the equation (x + 12) / (x + 5) = (x + 5) / x will be 12.5.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Then the equation is given as,

(x + 12) / (x + 5) = (x + 5) / x

Simplify the equation, then we have

(x + 12) / (x + 5) = (x + 5) / x

x² + 12x = (x + 5)²

x² + 12x = x² + 10x + 25

12x - 10x = 25

Further, simplify the equation, then we have

2x = 25

x = 25/2

x = 12.5

The value of the variable 'x' by simplifying the equation (x + 12) / (x + 5) = (x + 5) / x will be 12.5.

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The main advantages of using a random forest versus a single decision tree is that Random forest algorithm avoids and prevents overfitting by using multiple trees.

Random forest replaces the data used to build the tree and also the explanatory variables are bootstrapped so that partition is not done on the same important variable whereas  decision trees do not follow this algorithm. Bootstrapping reduces bias and variance both which makes the model more robust and accurate.

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Using Simple Speed formula,

To travel the distance of 75m with an airplane will need five gallons of fuel .

We have given that,

An airplane, fuel burn speed = 3 gallons of fuel per hour

ground speed of airplane = 45mph

distance = 75m

Speed = distance /time = 45 mph

=> 45 m distnce in one hour

fuel consumption of airplane = 3gallons/h

from above discussion we get,

fuel consumption for 45 m is equal to 3 gallons .

we have to calculate the quantity of fuel need to travel 75 m .

Now, 45 m distnce implies 3 gallons fuel consumption

1 m distance implies 3/45 gallons of fuel consumption

fuel consumption for 75 m =( 3/45)×75 = 5 gallons

Hence, 5 gallons fuel we need to travel 75 m .

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(a) The break-even point in units for the proposal by Vendor A = 6250 units

(b) The break-even point in units for the proposal by Vendor B = 6667 units.

In the question ,

it is given that ,

the fixed cost for proposal A [tex]=[/tex] $50000

the fixed cost for proposal B is = $80000

the  variable cost for proposal A is = $14

the variable cost for proposal B is = $10

the revenue generated by each unit is = $22

So , the break even points for both the proposal can be calculated using the formula ,

break even point = (fixed cost)/(contribution margin)

Substituting the values from above ,

we get  ,

Break even point for proposal A is

break even point [tex]=[/tex] 50000/(22 - 14)

= 50000/8

= 6250

Break even point for proposal B is

break even point [tex]=[/tex] 80000/(22 - 10)

= 80000/12

= 6667

Therefore , break even point for proposal A is 6250 units and for proposal B is 6667 units .

The given question is incomplete , the complete question is

Cortez Manufacturing intends to increase capacity by overcoming a bottleneck operation by adding new equipment. Two vendors have presented proposals. The fixed costs are $50,000 for proposal A and $80,000 for proposal B. The variable cost is $14.00 for A and $10.00 for B. The revenue generated by each unit is $22.00.

(a) The break-even point in units for the proposal by Vendor A =       units (b) The break-even point in units for the proposal by Vendor B =       units.

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The slope of a line perpendicular to the line whose equation is 3x+3y=18 is 1.

Given:

3x+3y=18

3y = 18 - 3x

3y = -3x + 18

divide by 3 on both sides

3y/3 = -3x/3 + 18/3

y = -3x/3 + 18/3

y = -1*x + 6

compare with y = mx+c

m = -1

slope of perpendicular line = -1/m

= -1/-1

= 1/1

= 1

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Age 38 most closely resembles the stage of adulthood known as "Becoming One's Own Man," (BOOM) according to Levinson. As a result, choice (A) is the best way to respond.

What is the men's boom phase?

Becoming One's Own Man, or BOOM is the name of Levinson's model's fourth stage. The man currently feels confined by the power brokers in their world. The person desires greater autonomy, dominance, and vocal authenticity.

Before the novice stage of adulthood ends, this transition gives people the chance to fix the problems with the first life structure they've created and make it closer in line with their young ideals and Dream.

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The values of the variables and numbers in radical form are presented as follows;

43a) x > -5

40a) a > 0

44b) x < 0

47e) x > 0

43b) x = The set of all real numbers

44a) The set of all numbers

45 a) x = 14

45 b) x = 0

45 c) x = -1

45 d) x = -4

45 e) x = 1

42 d)x = 5/196

9 e) x = 4

9 f) x = 8

9 a) √(0.6/36) ≈ 0.13

9 h) √((4 - 10)/(0.01)) = i·10·√6

A radical also known as a root is represented using the square root or nth root symbol and is the opposite of an exponent.

43 a) [tex]\sqrt{x + 5}[/tex]

x + 5 > 0

Therefore, x > -5

40a) ∛a

a > 0

44b) √(-5·x)³

-5·x < 0

x < 0

47e) √(13 - (13 - 2·x))

(13 - (13 - 2·x)) > 0

13 > (13 - 2·x)

0 > -2·x

x > 0

43b) √|x| + 1

x = All real numbers

44 a) √(-2·x)²

√(-2·x)² = -2·x

x = Set of all numbers

45 a) √(x - 5) = 3

(x - 5) = 3² = 9

x = 9 + 5 = 14

45b) √(2·x + 4) = 2

2·x + 4 = 2²

2·x = 2² - 4 = 0

x = 0/2 = 0

45c) √(x·(x + 1)) = 0

(x·(x + 1)) = 0

(x + 1) = 0

x = -1

45 d) √(x + 5) = -1

(x + 5) = (-1)²

x + 5 = 1

x + 5 = 1

x = 1 - 5 = -4

x = -4

45e) √x + x² = 0

√x = -x²

(√x)² = (-x²)² = x⁴

x  = x⁴

1 = x⁴ ÷ x = x³

x = ∛1 = 1

x = 1

42d) [tex]\sqrt{\dfrac{5}{x} } +3= 17[/tex]

[tex]\sqrt{\dfrac{5}{x} }= 17-3 =14[/tex]

[tex]\dfrac{5}{x} }=14^2=196[/tex]

[tex]x = \dfrac{5}{196}[/tex]

9e) [tex]\sqrt{\dfrac{4}{x} } = 1[/tex]

[tex]\dfrac{4}{x} } = 1^2[/tex]

x × 1² = 4

x = 4

19f) ∛x - 2 = 0

∛x = 2

x = 2³ = 8

9a) [tex]\sqrt{\dfrac{0.6}{36} }[/tex]

[tex]\sqrt{\dfrac{0.6}{36} }[/tex] = [tex]\sqrt{\dfrac{1}{60} }= \dfrac{\sqrt{15}}{30} \approx 0.13[/tex]

9h) [tex]\sqrt{\dfrac{4-10}{0.01} }[/tex]

[tex]\sqrt{\dfrac{4-10}{0.01} }[/tex]= √(-600) = √(-1)·√(600) = i·10·√6

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For the given problem the p - value is 0.0697.

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: Dean Halverson recently read that full-time college students study 20 hours each week.

She decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week.

A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks.

It was found that the average number of hours that the 35 students studied each week was 21.1 hours.

The sample standard deviation of 4.3 hours.

H0: μ = 20

H0: μ > 20

n = 35

X bar = 21.1

s = 4.3

Test statistics = t = (X bar - μ) / (s / √n)

                            = (21.1 - 20) / (4.3 / √35)

                          t = 1.5134

P value = df = n - 1 = 35 - 1 = 34

P([tex]t_3_4[/tex] > 1.5134) = 0.0697

Hence, the p - value is 0.0697.

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Cross-sectional pattern is not present in a time series. A time series is a sequence of data points measured at equally spaced time intervals.

A pattern is a repeat or uniformity in a collection of items or events. It is the typical manner in which something is carried out or occurs. Visual patterns, behavioral patterns, and language patterns are only a few examples of patterns. In the context of data analysis, patterns relate to regularities or trends in the data that may be utilized to anticipate outcomes or pinpoint connections between various variables. For instance, a time series of stock prices may show a definite upward trend, demonstrating the stock's increasing worth. To forecast the stock's future performance and guide investment choices, a pattern in this data may be found.

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The slope of line  y = - 2x is found to be -2 by comparing it with the equation of line.

The given equation is y = - 2x.

Comparing it with the equation of line y = mx, we get,

Slope(m) = -2

Therefore, the slope of line  y = - 2x is found to be -2 by comparing it with the equation of line.

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By using addition, it can be calculated that

Amount of money Walter should subtract from his bank account =

$(150 + 1.5) = $151.5

What is addition?

Suppose there are many numbers and the sum of the numbers have to be calculated. To find the sum of all the numbers, addition is used

This is a problem on addition

Walter used his bank's ATM to withdraw $150.

This was the sixth time he used the ATM in June.

His bank does not charge for the first five ATM use each month. After that, the fees is $1. 50 for each use.

Amount of money Walter should subtract from his bank account =

$(150 + 1.5) = $151.5

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Answer:10:05

Step-by-step explanation:

subtract 45 from 50!

Answer:

She started the test at 10:05 am

Step-by-step explanation:

Take the end time and subtract the time of the test

10:50-45 = 10:05

She started the test at 10:05 am

The number of ways to chose a president, vice president, secretary, and treasurer of the club, where no person can hold more than one office is 11880.

If the person cannot hold more than one office.

Then the number of ways of selecting a president, vice president, secretary and treasurer of the club from the club consisting of 12 member is given by the permutation ¹²P₄.

Because we have to select four member out of 12,

So, solving further,

= ¹²P₄

= 12!/(12-4)!

= 12!/8!

= 12 x 11 x 10 x 9

= 11880.

So, there are a total of 11880 ways to chose the members.

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Complete question - A club has 12 members A president, a vice president, a secretary, and a treasurer are to be chosen from these members. A member cannot serve for more than one position. In how many ways can this be down?

The linear system of equation y = -12x and 4x+2y= -8 has only one solution at 0.4,-4.8) .

The linear equation is  y = -12x and 4x+2y = -8

Now we solve the equations by substitution:

Using the value of y from the first equation and substituting in the second equation we get:

4x+2y = -8

or, 4x + 2(-12x)= -8

or, 4x -24x = -8

or, -20 x = -8

or, x = 0.4

At x=0.4 , y = -4.8

Hence solution is (0.4,-4.8) which represents the point of intersection of the two lines.

The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." Unknown variables are used as one or more variables in linear equations to model real-world issues.

The solutions are the points at which the lines or planes used to describe the linear equations intersect or meet. The set of values for each variable in a system of linear equations is known as the solution set.

Disclaimer: the complete question is :

How many solutions does this linear system have y = -12x and 4x+2y= -8 have?

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If the length of the room in drawing is 3 inches, then the actual length of the room is 24 feet

The scale of the drawing of a hotel = 1 inch : 8 feet

The length of the room in the hotel in the drawing = 3 inches

Consider the actual length of the room as x

Then the proportion will be

1 inch / 8 feet = 3 inches / x feet

Cross multiply the terms and find the value of x

1 × x = 3 × 8

Multiply the numbers

x = 24 feet

Hence, if the length of the room in drawing is 3 inches, then the actual length of the room is 24 feet

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Point (-3,5) is a solution to the system of inequalities

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

For this case, what we must do is find a point that meets both inequalities.

y> -2

x + y <4

We have then:

For (0,4):

First inequation:

4> -2 (correct)

Second inequality:

0 + 4 <4 (incorrect)

For (1,4):

First inequation:

4> -2 (correct)

Second inequality:

1 + 4 <4 (incorrect)

For (-3,5):

First inequation:

5> -2 (correct)

Second inequality:

-3 + 5 <4 (correct)

Point (-3,5) is system solution

For (-2,-3):

First inequation:

-3> -2 (incorrect)

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The Two-Sample Z-Tests remain valid because the two mistakes offset each other.

The Two-Sample Z-Tests is used to compare the means of two samples to determine whether it is feasible that they come from the same population. The null hypothesis is: the population means are equal.

A Z-Test can only be used when the population standard deviation is known and the sample size is 30 data points or larger. If not, a T-Test should be used.

Practically, the Two-Sample Z-Tests is not used often, because the two population standard deviations σ 1 and σ 2 are usually unspecified. Alternately, sample standard deviations and the T‐distribution are used.

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Each month we have to deposit 1389 of amount and we get interest of 30000

percentage, a relative value indicating hundredth parts of any quantity.

Given 500000 to be in our account in retirement of 30 years.

We need to find how much we have to deposit each month.

We know that in a year there are 12 months.

For 30 years the number of months are 12×30=360

So Now divide 500000 by 360 to find each month deposit

500000/360=1388.8

So each month one has to deposit 1389 into account.

Now if account earns 6% of interest. We need to find how much amount we earned.

6% is converted to decimal by dividing 6 by 100

0.06

Now multiply with 500000

0.06×500000

30000

Hence, each month we have to deposit 1389 of amount and we get interest of 30000.

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Three digit number:
    ABC

"if the digits are reversed, the number is unchanged":

    A=C, so our number is ABA

"the sum of the digits is 14":

    A + B + A = 14    or    2A + B = 14

"the tens digit is two more than the ones digit":

    B = A + 2

We have two equations:   

    2A + B = 14

    B = A + 2

Using substitution, we have:

     2A + A+2 = 14

     3A + 2 = 14

     3A  = 12

     A = 4

Going back to B = A + 2:

    B = 4 + 2

    B = 6

The number, ABA is 464.

Probability sampling procedure is the way researcher adhere closely to precise selection procedures to ensure that the results are projectable to the population under study.

What is Probability Sampling ?

Using this methodology based on probability theory, probability sampling is the strategy in which the research fellows selects samples from the larger population. A participant must be chosen at random if they are to be used as a probability as a sample.

As in this question researcher must follow Probability sampling, a participant must be chosen at random if they are used as a probability as the sample.

So, the required answer will be Probability sampling, as it helps researcher to precise selection procedures.

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The concept to graph a linear equation is explained below.

To make a line you really want two focuses. Then you can define a boundary through those two focuses. The x and y factors in the direct condition address the x and y facilitates on a diagram. In the event that you plug in a number for x, you can compute the relating number for y.

As examined, direct chart frames a straight line and indicated by a situation; y=mx+c. where m is the slope of the diagram and c is the y-block of the chart. The angle between any two focuses (x1, y1) and (x2, y2) are any two focuses on the direct or straight line

Steps to graph linear equation,

Step 1: Find the line slope and the y-intercept form of the line

Step 2: Graph the y-intercept of linear equation

Step 3: Find another point on the linear line using the slope

Step 4: Draw a linear equation of line that passes through the points

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Answer:

Explanation:

First step is to multiply the expression in brackets on the left side by 0.5

0.5(x+8)=x−4

Now we can move the unknown x to left side and the numbers to right side

x+4=x−4

The last equality is false, so the original equation has no solutions.

x−x=−4−40=−8

The equation represents the total cost for one month as y= 25 + 2x.In January she did 15 calls. In March, she owes $35.The graph of the function has been drawn below.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

A)

Total cost = fixed cost + 2 x number of calls

y = 25 + 2x

B)

In January y = 55

55 = 25 + 2x

x = 15

C)

In march x = 5

y = 25 + 2 x 5 = 35

D) The graph has been drawn below.

Hence "The equation represents the total cost for one month as y= 25 + 2x.In January she did 15 calls. In March, she owes $35.The graph of the function has been drawn below".

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Equation which represents a line that has a slope of 1/3 and passes through the point (-2,1) is:

[tex]y=\frac{1}{3} x+\frac{5}{3}[/tex]

What is the Equation of a Line?

The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.

Let the equation of line be y=mx+c

Where m is the slope and c is the y-intercept

⇒ m=1/3

and The line passes through (-2,1)

Putting it in the equation

[tex]\begin{aligned}&1=\frac{1}{3} \times-2+c \\&c=1+\frac{2}{3} \\&c=\frac{5}{3}\end{aligned}[/tex]

Hence,

An equation that represents a line that has a slope of 1/3 and passes through the point (-2,1) is: [tex]y=\frac{1}{3} x+\frac{5}{3}[/tex]

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(a) The equation that estimates the population t years after 2010 is

P(t) = 5655(1.014)^t.

(b) Population of the town in 2022 is 6,681.

We have given that the population of a town was 5655 in 2010.

And the population grow at a rate of 1.4% annually.

(a) We have to find equation that estimates the population t years after 2010.

We know the formula for exponential growth,

P(t) = P₀(1 + r)^t

where P₀ is the initial population,

r is the relative growth rate,

t is the time unit.

Putting the values in above equation we get,

P(t) = 5655(1 + 0.014)^t

P(t) = 5655(1.014)^t

(b) Now we have to find population of the town in 2022.

Here t = 2022 - 2010 = 12

Therefore equation of growth will become,

P(12) = 5655(1.014)^12

P(12) = 6681

Hence the population of the town in 2022 is 6,681.

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