In order for an expression, such as x² + 4x + , to become a perfect square trinomial, it must be in the form of a² + 2ab + b².
What is perfect squares?Perfect squares are whole numbers that are the result of multiplying a given number by itself. For example, 4 is a perfect square because it is the result of multiplying 2 by itself. Similarly, 9 is a perfect square because it is the result of multiplying 3 by itself. Other examples of perfect squares include 16 (4x4), 25 (5x5), 36 (6x6), and so on.
To do this, you must factor the expression. In this case, the expression can be factored into (x + 2)².
Once the expression has been factored into a perfect square trinomial, it can be written as (x + 2)².
This is a perfect square trinomial because it represents the area of a square, as the length of each side is equal to (x + 2).
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Kelsie works at a bicycle shop as a salesperson. She records the number of bicycles she sells daily. Here is the probability distribution of B = the number of bicycles Kelsie sells on a randomly selected day, and T the time she spends filling out daily sales reports. 2 B = # of bicycles sold T = time (minutes) Probability 40 20 10 0. 05 0. 15 0. 50 0. 30
a) Calculate E(B)
b) Calculate the mean time she spends filling out daily reports.
c) Calculate the standard deviation for both random variables
The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.
What is meant by discrete distribution?If a random variable has a limited number of outcomes or a countable number, it is discrete (i.e. the integers are infinite, but are able to be counted).
The discrete distribution presented reveals that the expected value of Kelsie's time spent completing daily sales reports is 9.5 minutes.
The discrete distribution given is:
P(X = 0) = 0.3
P(X = 10) = 0.5
P(X = 20) = 0.15
P(X = 30) = 0.05
The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:
E(X) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5
Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.
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a. E(B) = 9.5
b. The amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.
c. Standard variable shows how much deviation from mean variable.
What do you understand by discrete distribution?In statistics, a discrete distribution is a probability distribution that estimates the probability of a certain discrete, finite outcome. Simply put, as opposed to a continuous distribution, the discrete probability distribution aids in determining the probabilities of the occurrence of a specific event expressed in terms of positive, non-decimal, or whole integers.
The discrete distribution given is:
P(X = 0) = 0.3
P(X = 10) = 0.5
P(X = 20) = 0.15
P(X = 30) = 0.05
The average of a discrete distribution is equal to the sum of each result times the probability associated with that outcome, so:
E(B) = 0(0.3) + 10(0.5) + 20(0.15) + 30(0.05) = 9.5
Therefore, the amount of time Kelsie should spend doing daily sales reports is 9.5 minutes.
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Find the number of the degree of this polynomial.(please)
Answer:
2 is the highest degree because it's the only exponent
We take a sample of 80 observations from a large population with a mean of 1460 and a standard deviation of 270. The probability that the sample mean is between 1300 and 1400 is:
The probability that the sample mean is between 1300 and 1400 is approximately 1.34%.
We can use the Central Limit Theorem and the standard normal distribution to calculate the probability that the sample mean is between 1300 and 1400. The Central Limit Theorem states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the distribution of the population.
Since we have a sample of 80 observations, we can assume that the sample mean follows a normal distribution with a mean of 1460 (the population mean) and a standard deviation of:
Standard deviation of the sample mean
= population standard deviation ÷ [tex]\sqrt {sample size[/tex]
[tex]= 270 \div \sqrt{80} = 27[/tex]
So the standard deviation of the sample mean is 27.
We can now standardize the interval between 1300 and 1400 by subtracting the mean and dividing it by the standard deviation of the sample mean.
[tex]Z_1[/tex] = (1300 - 1460) / 27 = -2.59
[tex]Z_2[/tex] = (1400 - 1460) / 27 = -2.22
We need to find the area under the standard normal distribution curve between Z1 and Z2.
Using a standard normal table or a calculator with the standard normal distribution function, we can find the probability that a random variable from the standard normal distribution is between -2.59 and -2.22. This probability is approximately 0.0134 or 1.34%.
Therefore, the probability that the sample mean is between 1300 and 1400 is approximately 1.34%.
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Robot Navigation Self-navigating robots are very useful in the real world. Reducing the risk of human error by having a computer do tasks can increase the safety of transportation: Airplanes have systems that automate takeoffs and landings. Some cars can parallel park themselves. Cargo ships have autopilots. Mazes offer a challenge that can be directly translated to these situations. In this task, you are developing navigation software for a company that makes robotic systems that can direct themselves. As a first-level test of the robot you are developing, you will have it navigate a maze. North West East South B:The arrow at the maze entrance indicates that the robot will be heading east when it enters the maze. When programming the robot, let the complex number d represent the direction the robot is facing. As the robot changes direction, the value of d will also change; so, the value of d is dependent on where the robot is in the maze. At the start of the maze, what is the value of d? C;While navigating the maze, the robot will need to be able to turn left and right. The first turn the robot will make is a left turn. What will the value of d be after the first turn?
The first left turn, the value of d will be -1i, indicating that the robot is now facing north.
What is value?Value is the worth of something, which can be measured in terms of money, time or importance. It is something that is sought after and desired. Value can also be seen in terms of a person's character, morals, beliefs, and principles. It is an intangible concept that is difficult to quantify, but it is often sought after and is an important aspect of life. Value is what makes something worthwhile and irreplaceable.
The robot will need to be able to detect walls. As it moves through the maze, it will need to be able to detect when it is about to hit a wall. This can be done using sensors. The sensors should be able to detect the wall and the distance from the wall. This will allow the robot to turn in the correct direction and avoid hitting the wall.
The robot will also need to be able to detect when it has reached the end of the maze. This can be done by programming the robot to recognize when it has come to a dead end, or when it has reached a certain point in the maze. Once the robot has reached the end, it can then turn around and exit the maze.
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The sum of two numbers is 50. the greater number is four less than five times the lesser number. Find the numbers
The required two numbers are 9 and 41.
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
Let x be the lesser number, and y be the greater number.
From the question, we know that:
x + y = 50 (Equation 1: The sum of the two numbers is 50)
y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)
The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.
Then, two numbers are x = 9 and y = 41.
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What is a equivalent ratio
Answer:
Step-by-step explanation:
In ratio and proportion , when we compare two ratios or we can say two fractions then they are said to be equivalent when both of them are same.
What is the variable in 2x 3 7?
The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms only x is the variable.
What is an equation?The meaning of such an equations in algebra is just a mathematical expression stating the equality between two mathematical terms. For instance, 6x + 5 = 11 is an equation where 6x + 5 and 11 are two expressions separated by the 'equal' sign.
Identity equations and conditional equations are the two types of equations. For just any value of both the variables, an equality remains true. Only such variables have values that make a condition expression true. Two expressions joined by an equals sign ("=") form an equation.
The variable in 2x + 3 = 7 is x because rest 2, 3 and 7 are constant terms.
if we solve the above equation, we get
2x + 3 = 7
or, 2x = 7 - 3
or, 2x = 4
or, x = 2
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Just look in the screenshot. :) And whoever helps me ty, the points will be 30!
The Triangle Similar to ΔABC is ΔDEF in which m <E = 80 and m <F = 35.
The Correct option is (A).
What is Angle Sum PropertyAccording to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
What is Similarity of Triangles?If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
Given:
In ABC, m<A= 65 and m<B= 80
Now, using Angle sum Property
m<A + m <B + m <C = 180
65+ 80 + m<C= 180
m <C = 180 - 145
m <C = 35
So, the similar Triangle will be DEF in which m <E = 80 and m <F = 35.
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Match each trig function with its corresponding trigonometric ratio.
Find Sin A, Sin B, Cos A, Cos B, Tan A, Tan B
The trigonometric ratios for the triangle in this problem are given as follows:
sin(A) = a/c.cos(A) = b/c.tan(A) = a/b.sin(B) = b/c.cos(B) = a/c.tan(B) = b/a.What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The sides are connect by the right angle, of 90 degrees, while the hypotenuse is the straight line segment that connects the endpoints of each of the sides.
Then the trigonometric ratios presented on the bullet points are used for angles A and B in this problem.
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a man left 1/2 of his money to his first son 3/8 to his second son, the rest 80,000 to his third son.how much did he he leave to his second son
As per the given conditions in the question, the amount of money that the second son was left with by the man is 2,40,000.
How do you add two fractions with different denominators?To add two fractions with different denominators, you must first find a common denominator. A common denominator is a number that is divisible by both denominators of the fractions. Once you have a common denominator, you can add the numerators of the fractions together and place the sum over the common denominator. Then simplify the fraction if possible.
What is the reciprocal of a fraction?The reciprocal of a fraction is another fraction whose numerator and denominator are flipped. For example, the reciprocal of the fraction 2/3 is 3/2. The product of a fraction and its reciprocal is always equal to 1. To find the reciprocal of a fraction, simply swap the numerator and denominator.
Considering the conditions given in the question,let us suppose that the third son was left with x part of the money,
so we can use the equation,
part of money left for fist son + part of money left for second son + part of money left for third son = total part of money
or, 1/2 + 3/8 + x = 1
therefore, x = 1/8
Also we know that the third son was left 80,000 ,
so 1/8 of total money = 80,000
therefore, total money = 80000 * 8 =6,40,000
Now the amount left for the second son is , 3/8 of total money
which is equal to , 3/8 of 6,40,000 = 2,40,000
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-x+3y=6 in slope intercept form pls i need to know!!!
Answer:
Below
Step-by-step explanation:
Slope - intercept form is y = mx + b you just need to manipulate the given equation to this form
-x +3y = 6 add 'x' to both sides of the equation
3y = x + 6 divide by 3
y = 1/3 x + 2 Done !
Last year there
were 620 7th grade
students. This year
enrollment has
increased by 105%.
How many 7th
grade students are
there this year?
Answer: 1271
Step-by-step explanation:
620 + (105% × 620) =
620 + 105% × 620 =
(1 + 105%) × 620 =
(100% + 105%) × 620 =
205% × 620 =
205 ÷ 100 × 620 =
205 × 620 ÷ 100 =
127,100 ÷ 100 =
1,271
Carlton is using the following data samples to make a claim about the house values in his neighborhood:House ValueA $100,000B $600,000C $650,000D $700,000E $900,000Based on the data, should Carlton use the mean or the median to make an inference about the house values in his neighborhood?He should use the median because there is an outlier that affects the mean.He should use the mean because there are no outliers that affect the mean.He should use the mean because it is in the center of the data.He should use the median because it is in the center of the data.
The option A "He should use the median because there is an outlier that affects the mean." is correct.
It is clear from the data that option E's house is much more expensive than those in the other options. A $9,00,000 price is therefore an outlier in this set of data.
In symmetrically distributed data, an inference is made using the mean. Due to the inclusion of an outlier, the data is not symmetrical. As a result, the mean won't accurately depict the data's centre. As a result, we shall refrain from drawing conclusions about the pricing of the residences using the mean.
Therefore, since the median is unaffected by outliers, we shall use it.
Therefore, since there is an outlier that influences the mean, we will utilise the median. The answer is (A).
Your sincere criticism is crucial for better outcomes.
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A soccer team earns 2 points for a win and 1 point for a tie. Let w represent the number of wins and t represent
the number of ties. Write an expression that describes the team’s total points
An expression that describes the team’s total points will be 2w + t.
How to calculate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator
In this case, the soccer team earns 2 points for a win and 1 point for a tie.
Let w represent the number of wins and t represent the number of ties.
The expression that describes the team’s total points will be:
= 2(w) + t
= 2w + t
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find the area of the rectangle whose length is 16cm and breath is 8am
Answer:128 cm^2
Step-by-step explanation:
11. Which of the following is a solution to the
inequality c + 4 <-7?
(1) -15
(2) -10
(3) -5
(4) O 0
(5) 10
Answer:
-15
Step-by-step explanation:
That's the answer because
-15+4=-11
-15+4=-11-11<-7
find the volume of this triangular prism.
The volume of the triangular prism is 120 cm cube.
How to find the volume of a triangular prism?A triangular prism is a three-sided prism. The volume of a triangular prism can be represented as follows:
volume of a triangular prism = 1 / 2 bhl
where
b = base of the triangular faceh = height of the triangular facel = height of the triangular prismTherefore,
b = 10 cm
h = 12 cm
l = 6 cm
Therefore,
volume of a triangular prism = 1 / 2 × 10 × 12 × 6
volume of a triangular prism = 1 / 2 × 120 × 6
volume of a triangular prism = 60 × 6
volume of a triangular prism = 120 cm³
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(Help within 5 minutes)
A small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded. The results showed that 150 of the adults who were parents and 40 of the adults who were not parents thought the park should be expanded.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table.
Should the park be expanded?
Yes No
Parents
Not parents
The park should be expanded based on the information as the majority want the expansion.
How to illustrate the information?From the information, on the small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded.
Also, the results showed that 150 of the adults who were parents and 40 of the adults who were not parents thought the park should be expanded.
Based on the above the number of people that wants the expansion will be:
= (150 + 40) / 250 × 100
= 190 / 250 × 100
= 76%
It should be expanded.
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Perry learned to play a total of 18 piece over the coure of 9 week of piano leon. After 12 week of piano leon, how many total piece will Perry be able to play? Solve uing unit rate
In a course of 12 weeks, Perry will be able to play a total of 25 pieces of the piano Leon.
A total of 18 pieces of piano are learnt by Perry in a course of 9 weeks.
By using simple algebra, we can find the number of pieces that will be played by Perry in one week,
So, we can write, The learing speed,
Number of piano pieces learnt = Weeks
19 pieces = 9 weeks
Learning speed = 19/9 Pieces per week
So, the number of pieces learnt in 12 weeks is,
Number of pieces learnt = 19/9 x 12
Number of pieces learnt = 25.22
Number of pieces learnt = 25
So, Perry will be able to play 25 pieces.
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3 chairs and 4 tables cost rs 7540. if the price of a chair is 220 find the price of table?
ans - 7120
Answer:
The price of a table is rs1720
Step-by-step explanation:
Let C and T be the individual prices of the tables and chairs.
We know that 3C + 4T = rs7540
We are then told that C = rs220, so we can enter that into the equation to find T:
3C + 4T = rs7540
3(220) + 4T = rs7540 [for C = rs220]
660 + 4T = 7540
4T = rs6880
T = rs1720
Check:
Do 3 chairs at 220 each and 4 tables at 1720 each add to a total of 7540?
Chairs: rs660
Tables: rs6880
Total = rs7540 YES
Solve the proportion: Men 45 : ? Women 50 : 10
Answer:
The answer to the proportion is 45:25.
Step-by-step explanation:
To solve this proportion, we can use cross multiplication. That is, we can multiply the numerator of the first ratio (45) by the denominator of the second ratio (10) and the numerator of the second ratio (50) by the denominator of the first ratio (?). This will give us
45 x 10 = 500 and 50 x ? = 500.
If we divide both sides of the equation by 50, we get
? = 25.
Therefore, the answer to the proportion is 45:25.
2 hrs 35 minutes
+ 3 hrs 40 minutes
please help asap thank you !!
There i a bag filled with 4 blue, 3 red and 5 green marble. A marble i taken at random from the bag, the colour i noted and then it i replaced. Another marble i taken at random. What i the probability of getting 2 blue?
The probability of getting 2 blue is 1/9.
You are choosing replacement marbles. The trials (marble selections) are independent from one another and follow the binomial distribution.
1/3 of the time, a blue marble will be the first one chosen.
(This is due to the fact that 4 out of 12 marbles are blue, therefore 4/12 equals 1/3.
A blue marble is 1/3 more likely to be chosen the second time.
The two probabilities can be multiplied to obtain the following results because the marble selections are independent:
The likelihood of receiving two blues is (1/3)2 =1/9.
Therefore, there is a 1/9 chance of obtaining two blues.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
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What do the following two equations represent? y+1= -4(x - 2) 2x8y = 16
On solving the provided question, we can say that the values of the equation here will be y +1 = 8X 8y = 16 => y = 9.455
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
y+1= -4(x - 2) 2x8y = 16
x = 0
y +1 = 8X 8y = 16
y = 9.455
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Can u please help?.........................
The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 2 to 3 is the ordered pair (3, 0).
How to determine the coordinates of point P?In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.
In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(2(9) + 3(-1))/(2 + 3)], [(2(6) + 3(-4))/(2 + 3)]
P(x, y) = [(18 - 3)/(5)], [(12 - 12)/5]
P(x, y) = [15/5], [0/5]
P(x, y) = [3, 0]
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Complete Question:
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-1, -4), B(9, 6); to 3. The coordinates of P are?
Students in a statistics class took their first test. The following are the scores they earned. Create a frequency distribution and histogram for the data using a lower class limit of 49.5 and a class width of 10. Describe the shape of the distribution Search Search Select an answer variable(s), the correct graph to make is a a) Since data were collected for? Select answer b) For this one the class width is given to be the following: class width Complete the frequency relative frequency table using the given class width. Round relative frequencies to 3 decimal places. Frequency Relative Frequency Classes 495 c) Which of the following is the correct histogram for the given data? Frey 495 595 695 795 Histogram for Test I Score 895 995 Q Search Search 5 Spring ZOO) Final El Pl E U M QUI PUUVITU 495 595 69.5 79.5 Histogram for Test / Score 89.5 99.5 Q a Frequency 49.5 595 695 795895995 Histogram for Test / Score Frequency 595 603 795 Histogram for Tere d) What shape is the histogram above? Select an ant Q Search Search LE
a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram
b) For this one the class width is given to be the following: class with = 10 . See the attachment for table
c) See the attachment for the graph
What is histogram ?
A histogram is a collection of rectangles with bases and the gaps between class boundaries. All of the rectangles are contiguous, and each rectangle bar represents some kind of data. Rectangles have heights that are proportionate to the corresponding frequencies for both related and dissimilar classes.
a) Since data were collected for "score quantitative" variable(s), the correct graph to make is a histogram
b) For this one the class width is given to be the following: class with = 10 . See the attachment for table
c) See the attachment for the graph
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Solve the proportion below. 7/x = 19/114 x=____
A. 8
B. 4
C. 28
D. 24
A taste test asks people from Texas and California which pasta they prefer brand A or brand B. This table shows the results. Brand A Brand B Total 125 150 105 275 45 Texas California Total 80 90 170 60 A person is randomly selected from those tested. What is the probability that the person is from California, given that the person prefers brand A? Round your answer to two decimal places
Therefore , the solution of the given problem of probability comes out to be thus brand A is more prefer by the person as probability of B IS 0.43.
Define probability.A probability is a number that represents the likelihood that a certain event will occur. Probabilities may be expressed as percentages
range from 0% to 100% or from 0 to 1.
Here,
Given :
Which brand of pasta do Texas and California prefer
Because brand B is preferred by 45 persons in Texas, the answer would be A.
There are 105 persons that favor brand B overall.
=> 45/105
=> 15/ 35
=> 0.42857...
So ,
rounded it would be 0.43,
thus brand A is more prefer by the person
Therefore , the solution of the given problem of probability comes out to be thus brand A is more prefer by the person as probability of B IS 0.43.
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Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it. What fraction of the voters voted in favor of the measure?
Enter the fraction in simplest form.
The fraction of the voters who voted in favor of the measure will be 1/5.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Ricardo's town recently voted on a new education funding package. Of the voters who voted for the bill, 20% voted for it.
The fraction of the voters who voted in favor of the measure will be given as,
⇒ 20%
⇒ 20 / 100
⇒ 1 / 5
The fraction of the voters who voted in favor of the measure will be 1/5.
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The figure below to the left is a graph of f(x), and below to the right is g(x).
The figure below to the left is a graph of f(x), a
(a) What is the average value of f(x) on 0≤x≤2? avg value = __________
(b) What is the average value of g(x) on 0≤x≤2? avg value = __________
(c) What is the average value of f(x)?g(x) on 0≤x≤2? avg value = _________
(d) Is the following statement true?
Average(f)?Average(g)=Average(f?g)
A. Yes
B. No
The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.
avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.
a)
Hence average value of f(x) on 0≤x≤2
= 1/2 ∫f(x) with 0 and 2 as intervals
Since integration is basically the area under the curve we get
avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]
Since from 0 to 1, the figure is a triangle and beyond that a straight line we get
1/2[1/2 X 1 X 1 + 0]
= 1/4 sq units
b)
Similarly, the average value of g(x) on 0 ≤ x ≤ 2
1/2[area from 0 to 1 + area from 1 to 2]
= 1/2[0 + 1/2]
= 1/4 sq units
c) here we need to find the average of f(x) . g(x)
Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1
Hence we see that on multiplying the functions, the resultant has to be a 0 function.
Hence its average value will be 0.
d)
Average(f) . Average(g) = 1/4 X 1/4
= 1/16
Average of (f.g) = 0
Hence the statement is false
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Complete Question
The figure attached to the left is a graph of f(x), and below to the right is g(x).
The figure below to the left is a graph of f(x), a
(a) What is the average value of f(x) on 0≤x≤2? avg value = __________
(b) What is the average value of g(x) on 0≤x≤2? avg value = __________
(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________
(d) Is the following statement true?
Average(f) . Average(g)=Average(f.g)
A. Yes
B. No