The required polynomial long division is shown, and the solution of the expression is given as x + 1 + [2x+ 3] / (x² − 1).
What is synthetic division?It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.
Here,
x² − 1) x³ + x² + x + 2 ( x + 1
x³ - x
----------------------
x² + x + x
x² + 1
------------------------------
2x + 1 + 3
Thus, the required polynomial long division is shown, and the solution of the expression is given as x + 1 + [2x+ 3] / (x² − 1).
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I need help with these 4 questions
Only questions 1 2 3 4
Answer: 1: x = 2y - 1 This equation shows that the value of x is always 2 times the value of y minus 1.
2: y = 3x + 3 This equation shows that the value of y is always 3 times the value of x plus 3.
3: y = (x/4) - 1 This equation shows that the value of y is always the value of x divided by 4 minus 1.
4: y = x-5 This equation shows that the value of y is always the value of x minus 5.
The seventh grade class supplied bags of snacks and beverages for the school dance. They supplied 50 more beverages than bags of snacks. The dance was supplied with a total of 400 items. How many of each were supplied.
a) Define the variable(s)
b) Write a system of equations for the situation.
Answer:
a) let 's' = number of bags of snacks
b) let 's+50' = number of bags of beverages
s + s+50 = 400
Step-by-step explanation:
a) let 's' = number of bags of snacks
b) let 's+50' = number of bags of beverages
s + s+50 = 400
solve:
2s + 50 = 400
2s = 350
snacks = 175
beverages = 175+50 or 225
total = 400
if 250 ml cost 650 tk, then how much will cost 120 ml ?
Amy works for a company that produces plastic lids and cups for restaurants. She wants to use a one-sample zzz interval to estimate what proportion of lids produced in a day have a defect that makes them not fit the cups. She takes a random sample of 100100100 lids from the more than 1{,}0001,0001, comma, 000 total lids produced that day and finds 555 lids in the sample with this defect.
Amy can use a one-sample z-interval to estimate the true proportion of lids in the population of 1,000,000 that have the defect.
What is sample?Sample can refer to an example of a particular item or type of thing. It can also refer to a section of a population that is chosen in order to represent the whole group. When used in research, samples are used to make conclusions about a population as a whole. Samples are also often used to test products or services in order to assess their quality or performance.
First, she will calculate the sample proportion of lids with the defect by dividing the number of lids in the sample with the defect (555) by the total number of lids in the sample (100,000). This sample proportion is 0.00555.
Next, Amy will calculate the standard error of the sample proportion. This is calculated by taking the square root of the sample proportion multiplied by (1 - sample proportion) divided by the sample size. The standard error for this sample is 0.00023.
Finally, Amy can calculate the one-sample z-interval. This is done by subtracting the standard error from the sample proportion and adding it to the sample proportion. This gives a one-sample z-interval of 0.0053 to 0.0058.
This one-sample z-interval tells Amy that she can be 95% confident that the true proportion of lids with the defect in the population of 1,000,000 is between 0.0053 and 0.0058.
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Find X. Show your work.
2(x-6)=12
Answer:
x=6
Step-by-step explanation:
Expand brackets:
2x-12=12
This is because 2 times x=2x and 2 times -6= -12
Add 12 to the right side to cancel out the -12 on the left.
2x-12+12=12
Simplify to get 2x=12
Divide by 2 to get x=6
Help with geometry similar triangles. ABC ~ ___ by _____
Answer choices : EDC, ECD, DCE, CED, or None. Side Side Side, Side Angle Side, Angle Angle, or None.
The triangles ABC and CED are similar by none.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The figure in shown in image.
We know that;
Two triangles are similar if there corresponding sides are in proportion.
So, In triangles ABC and CED;
The ratio of corresponding sides are equal to each other.
Hence, By the options, we get;
The triangles ABC and CED are similar by none.
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SM1 PLEASE HELP ASAP TYSMM
Using commutative property of addition, the expression 3T 1,892 lb + 1,325 lb is equal 4.5T, 217 lb
What is Addition of ExpressionA mathematical procedure called adding expressions entails merging two or more expressions to create a new expression. A reduced version of the original expressions is produced by adding expressions, which works similarly to adding integers.
We merge similar phrases while adding expressions. When a variable is raised to the same power, terms are said to be like terms. Because they both have the same variable (x) raised to the same power, for instance, 2x and 3x are similar phrases (1).
It's crucial to remember that the commutative characteristic of addition ensures that the order of the terms has no impact on the outcome when adding or subtracting expressions.
In conclusion, adding expressions is a mathematical operation that combines two or more expressions to create a new expression; it is comparable to adding integers. We merge similar phrases while adding expressions. When a variable is raised to the same power, terms are said to be like terms. The commutative property of addition accounts for the fact that the outcome is unaffected by the order of the terms.
In this problem, we have two expressions which we need to add together.
NB;
T = tonslb = poundsSo, in the given expression;
3T 1,892 lb + 1,325 lb = 3T 3217lb
But 1 pounds = 0.5 ton
3000 pounds = 1.5 ton
3T 1,892 lb + 1,325 lb = 4.5T, 217 lb
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prove by the sum of arithmetic induction that the sum of the first n terms of a n arithmetic sequence
The sum of the first n terms of an arithmetic sequence can be proven using the principle of induction. We assume the formula holds for n = k, and then show it holds for n = k+1, thus showing it holds for all values of n.
The sum of the first n terms of an arithmetic sequence can be determined using the formula S_n = (n/2)(a_1 + a_n), where a_1 is the first term and a_n is the nth term.
We can prove this formula using the principle of induction.
Base Case: Let n = 1. Then S_1 = (1/2)(a_1 + a_1), which simplifies to S_1 = a_1. This is the same result we would get if we added the first term of the sequence.
Inductive Step: Assume that the formula holds for n = k.
Then S_k = (k/2)(a_1 + a_k).
Now consider n = k+1.
S_k+1 = (k+1/2)(a_1 + a_k+1)
= (k/2)(a_1 + a_k) + (1/2)(a_1 + a_k+1)
= S_k + (1/2)(a_k+1 - a_1)
= S_k + (1/2)(a_k+1 - a_k) + (1/2)(a_k - a_1)
= S_k + (1/2)(a_k+1 - a_k) + [S_k - (k/2)(a_1 + a_k)]
= (k+1/2)(a_1 + a_k+1)
= S_k+1
Therefore, we have shown that if the formula holds for n = k, then it also holds for n = k+1. By the principle of induction, the formula holds for all n.
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Now, write an expression using the two terms from parts C and D to represent the net change to Quiana’s loan as a result of her payments.
Part D's answer: -5
Part C's answer: -$247.43
info: Quiana took out a loan to pay for a new car. Initially, she owed the lender $15,234.68. She has repaid $247.43 of the loan each month for the past 5 months. What is the net change to the loan from Quiana’s perspective over the past 5 months?
Complete the steps below to help Quiana calculate the loan amount that she’s repaid to the lender.
From Quiana's perspective, the net change in the loan during the last 5 months is $1237.15.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.
Here,
15234.68-247.43*5=13997.53
Net change
= Initial loan amount - current balance
= $15,234.68 - $13,997.53
= $1237.15
The net change to the loan from Quiana’s perspective over the past 5 months is $1237.15.
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125 five pences in pounds?
Answer:
125 pounds = 2500 five pence
Answer:
Step-by-step explanation
£1.00=100p
125p=£1.25more workers what sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in exercise 36(b)? justify your answer.
On solving the provided question, we can say that the sample size would have to be multiple by 4 = 4048
what is sample size?The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.
the sample size would have to be multiple by 4
n = 1012
n X 4
= 1012 X 4
= 4048
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The US has a population of approximately 330 million people. Given that 0. 35 of the population have blue eyes, calculate the number of people in the US who do not have blue eyes.
The number of people in the US who do not have blue eyes is 214.5 million.
The given question has been solved using Probability. It is given that the number of people in the US is 330 million
for the time being, we let P=330 which represents the population of the US
also, it is given that the number of people having blue eyes is 0.35 times the Population
So, Pb= 0.35 × P
here, Pb represents the number of people having blue eyes
So the number of people that do not have blue eyes must be the number of people having blue eyes subtracted from those having blue eyes
i.e, Pnb=P-Pb
=P-(P × 0.35)
=P(1-0.35)
=330 (0.65 )
=214.5
Thereby, the number of people that do not have blue eyes is 214.5 million.
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Need help plsssssss!!!!!
Answer:
C. 8 : 1
Step-by-step explanation:
A unit rate is a ratio of a number to one.
To make both sides of the given ratio:
[tex]\dfrac{2}{5} : \dfrac{1}{20}[/tex]
whole numbers (and make the right side 1), simply multiply both sides by the Least Common Multiple (LCM) of the denominators.
To find the LCM of two numbers, list out their prime factorizations and then multiply the highest power of each distinct prime number present.
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5 = 5
20 = 4 * 5
LCM(5, 20) = 4 * 5 = 20
The LCM of 5 and 20 is 20.
Next, we need to multiply 20 by both sides of the ratio.
[tex]20\left(\dfrac{2}{5}\right) : \left(\dfrac{1}{20}\right)20[/tex]
Then, simplify.
[tex]\dfrac{40}{5} : 1[/tex]
[tex]8 : 1[/tex]
So, the unit ratio of [tex]\dfrac{2}{5} : \dfrac{1}{20}[/tex] is 8 : 1.
T/F. In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 16.
As per the concept of probability that it takes three rolls until the player rolls doubles is 0.11574 and this can be determined by using the given data.
In math the term probability of an event is defined as nothing but a number between 0 and 1 where zero shows the impossibility and one shows the certainty.
Here we have given that a certain board game, here the player rolls two fair six-sided dice until the player rolls doubles.
And here we know that the probability of rolling doubles with one roll of two fair six-sided dice is 1/6.
Here first we need to determine the probability of rolls to obtain doubles in each roll.
That can be calculated as ,
=> 1 - 1/6 = 5/6
Then the fails in the second roll is calculated as,
=> 1 - 1/6 = 5/6
Then the third roll the player rolls doubles that is calculated as,
=> 1/6
So, the probability of requiring 3 rolls until getting doubles will be calculated as
=> 5/6 x 5/6 x 1/6
=> 25/216
When we simplify this one then we get,
=> 0.115
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2x + 8 > x + 10 > 3x + 9
The solution of the linear inequality 2x + 8 > x + 10 > 3x + 9 is:
X>2 and X<1/2
What is linear inequalities?When two mathematical expressions or two numbers are compared in an unequal way, it is called an inequality in mathematics. Inequalities can generally be classified as either numerical, algebraic, or a combination of the two. A polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, which is the case in a linear inequality, which is an inequality involving at least one linear algebraic expression.
step1:
2x + 8 > x + 10 > 3x + 9
2x+8>x+10 and x+10>3x+9
2x + 8 > x + 10 :X>2
X+10>3X+9:X<1/2
Step2:
X>2 and X<1/2
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Give me a list of rational numbers that are not integers.
Answer:
Step-by-step explanation:
7.8, 7/29, 1234/21, 11.1212, 9.8, 76/1112
Integers can only be positive numbers, negative, non negative or 0.
What is the best approximation of the solution to the system to the nearest integer values X minus Y equals negative 65X plus 3Y equals 24
The best approximation of the solution to the system to the nearest integer values X minus Y equals negative 65X plus 3Y equals 24 are x = 43 and y = 22
How to determine the solutionFrom the information given, we have the expressions;
X minus Y equals negative 65X plus 3Y equals 24This is represented as;
x - y = -65
x + 3y = 24
Make 'x' the subject from equation 1
x = -65 + y
Now, substitute the expression into equation (2), we get;
-65 + y + 3y = 24
collect the like terms
4y = 24 + 65
Add the like terms
4y = 89
Divide the values by the coefficient of y
y = 89/4 = 22
Substitute the value in eqation3
x = -65 + 22
Add the values
x = 43
Hence, the values are 43 and 22
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7. Describe the rule for each of the tables below:
a.
Row 1
Row 2
Rule:
5
7
7
11
15
37
19
35
29
55
Answer:
Step-by-step explanation:
It is difficult to determine the rule for the table without further context or information. However, based on the pattern in the table, it appears that the rule for generating the second number in each row is to add 2 to the first number in that row. The rule for generating the third number in each row is to add 6 to the second number in that row. The fourth number is the sum of the first and the third number in that row.
Select the correct answer.
What is the value of x in the triangle?
The value of x is 7 from the given figure.
What is Triangle ?
Triangle can be defined in which three sides , three angles and the sum of three angles is always is 180 degrees.
From the given triangle ,
Let the triangle be ABC
where A = 60 and B = 30 and C = 90
CA = 7[tex]\sqrt{3}[/tex]
CB = x .
sin60 = 7[tex]\sqrt{3}[/tex] /x
[tex]\sqrt{3}[/tex] / 2 = 7[tex]\sqrt{3}[/tex] /x
1/7 = 2 * x
x = 7 * 2
x = 14
In triangle ABC ,
AC^2 + CB ^ 2 = AB ^2
7[tex]\sqrt{3}[/tex] ^2 + CB^2 = 14*14
CB^2 = 196 - 149
CB^2 = 49
CB = 7
Hence, The value of x is 7 from the given figure.
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Pls help!! URGENT!!
What is RU? Use the figure below.
Answer: 20 ( Choice A )
Step-by-step explanation: You can prove that triangle RTS and triangle RTU are the same using the Side-Angle-Side method, so ultimately, side RS should equal RU. Therefore, 8x = 6x + 5.
x should equal 2.5. The question is asking you how long side RU is, simply plug in 2.5 and you get 20.
A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given:50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45Which of the following histograms is the best representation of the data
Therefore , as a result, the answer to the provided median problem is that the median will range from 38.
Define median.The median value is the number that exactly lies in the middle of a dataset that has been arranged. The gap between the minimum and maximum 50% of the data is a maximum likelihood measure or average. Depending on whether you have an odd or possibly even amount of data points, different formulas are used to calculate the median and mode.
Here,
Given the values:
50,42,32,35,41,44,24,46,31,47,36,32,30,44,22,47,31,56,28,37,49,28.42,38 and 45
The following is what we have: => (50+42+32+35+41+44+24+46+31+47+36+32+30+44+22+47+31+56+28+37+49+28.42+38 + 45) /25 = 37.88
The median will reach around 38.
As a result, the answer to the provided median problem is that the median will range from 38.
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The complete question is "A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given: 50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 The following histogram is a representation of the data. Calculate the median ages"
What is the range of the following data set?
34 15 75 81 45 73 97 89 23
Answer: 45
Step-by-step explanation:
why is the answer here (-∞, 6)
why 6
Answer:
Step-by-step explanation:
Basically, because till x = 6, f(6) was less than 0.
They are asking the value of f(x), not x.
Thanks
Write an abolute value inequality comparing the ditance of the tour guide and the diver to eal level. Who i cloer to ea level? Explain how you know. Sea level = -18 ft
Tour guide = 5 ft
One diver = -11 ft
The diver is closer to sea level since their distance to sea level (7 ft) is less than the distance of the tour guide to sea level (23 ft).
As we know,
|Tour guide - sea level| < |One diver - sea level|
The distance between the tour guide and sea level is 5 - (-18) = 23 feet.
The distance between one diver and sea level is -11 - (-18) = 7 feet.
Since the absolute value of the difference between the tour guide and the sea level is greater than the absolute value of the difference between one diver and the sea level, we can conclude that the diver is closer to the sea level.
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the length of a rectangle is increasing at a constant rate of 3 cm/s, and its width is increasing at a constant rate of 0.5 cm/s. at the time the length is 5 cm and the width is 1.2 cm, how fast is the area of the rectangle increasing?
The area of a rectangle is increasing at a constant rate of 3.5 cm²/s when the length is increasing at a constant rate of 3 cm/s and the width is increasing at a constant rate of 0.5 cm/s.
The area of a rectangle is calculated as length multiplied by width (A = L x W). At the given time, the length is 5 cm and the width is 1.2 cm, so the area is 6 cm². When the length is increasing at a constant rate of 3 cm/s, and the width is increasing at a constant rate of 0.5 cm/s, then the area is increasing at a rate of 3.5 cm²/s. This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5). This is the rate of increase of the area and is expressed as 3.5 cm²/s This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5).
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ctice
For 12-13, use the figure. A bike path crosses
a road as shown. Solve for each indicated
angle measure or variable.
84°
Online
Assessment and
my.hrw.com Intervention
M
4x
G
Considering the diagram of the bike path crosses the angle measures are calculated to be
x = 21 degrees
< KMH = 96 degrees
How to find the angel measuresAccording to the diagram, the angle at the intersection of the road shows that
84 degrees = 4x
The angles are equal based on the vertical angle theorem
solving for x
84 degrees = 4x
4x = 84
x = 84 / 4 = 21
x = 21 degrees
solving for < KMH
< KMH and 84 are supplementary angles
< KMH + 84 = 180
< KMH = 180 - 84
< KMH = 96 degrees
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Sarah invested £16 000 in a unit trust five years ago. The value of the unit trust has increased by 6% per annum for each of the last 3 years. Before this, the price had decreased by 4% per annum. Calculate the current price of the unit trust. Give your answer to the nearest whole number of pounds.
Answer:
17562 pounds
Step-by-step explanation:
16000*96%=15360. 15360*96%=14745.6. 14745.6*106%=15630.336. 15630.336*106%=16568.1562. 16568.1562*106%=17562.2456. 17562.2456 approximately equals 17562 pounds.
Can somebody help me
Answer:
Look, I don't know how to tell the answers by looking at the squares but I can tell you how to do it.
a) Subtract the number on the left with the number on the top, pretty simple, i am sure u can do that.
b) After you have done that, count how many negative scores you got and divide that by 9.
c)Finally, count all the numbers more than 3 again and divide it by 9.
Note: 9 here is the total number of outcomes.
Thanks
What is a point that divides a line segment into 2 equal parts called?
Answer: Midpoint
Step-by-step explanation:
Paul usually makes the 100 km journey to visit his family. The trip involves three separate stages:
a) A stage of 20 km that is travelled on small roads at a constant speed of 30 km/h.
b) A stage of 50 km that is travelled on the highway at a constant speed of 100 km/h.
c) A stage of 30 km that is travelled on standard roads at a constant speed of 40 km/h.
The length of the section of roadworks was 121 km.
What is the concept of time and distance?
Time is directly proportional to distance. It means that speed remains constant, if we have two vehicles moving two distances for two different time duration then the time is directly proportional to the distance. Speed is directly proportional to distance.
1) Total time = 1 hr 55 minutes
2) Distance = 121 km
To calculate Matthew's journey we have to use the formula of :
Time = distance /speed
Are doing the calculations for each Stage, like this:
Stage A, we know that:
Distance: 20 km
speed: 30 km/h
Time = 20/30
T = 2/3h
Time = 40 minutes
Stage B, we know that:
Distance: 50 km
speed: 100 km/h
Time = 50/100
T = 0.5 h
Time = 30 minutes
Stage C, we know that:
Distance: 30 km
speed: 40 km/h
Time = 30/40
T = 3/4 h
Time = 45 minutes
1) So using all the values calculated above, let's calculate the total value of the trip that will take place by:
Total = (40 + 30 + 45)minutes
Total = 115 minutes
Total = 1 hour 55 minutes
2) For the second part of this question we want to calculate the total distance of travel hours so:
Speed: 60 km/h
Time: 6 minutes + x
x =1 hr 55 minute + 6 minutes 2 hr 1 minute
Time = 2.01666667
Distance = speed * time
Distance = 60 * 2.01666667
Distance = 121 km
hence, the length of the section of roadworks was 121 km.
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