There is no intersection and no solution to the system since the region above the line y=2x+2/3 and the region below the line y=2x+1/3 are the solutions to the inequalities y>2x+2/3 and y<2x+1/3, respectively.
In the given question, we have to find the solution of the system Y>2x+2/3 and y<2x+1/3 change.
We firstly draw the two lines y=2x+2/3, and y=2x+1/3.
They are parallel and the line y=2x+2/3 is located over the line y=2x+1/3.
There is no intersection and no solution to the system since the region above the line y=2x+2/3 and the region below the line y=2x+1/3 are the solutions to the inequalities y>2x+2/3 and y<2x+1/3, respectively.
The solution of y2x+2/3 is the region below the line y=2x+2/3, and the solution of y>2x +1/3 is the region above the line y=2x+1/3 when the inequality sign of both inequalities is reversed. This implies that the area between the two lines is where the system's solution lies.
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The right question is:
How will the solution of the system Y>2x+2/3 and y<2x+1/3 change? If the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?
suppose the estimated regression equation is given by . what are the predicted value of y and the residual when x is 2 and y is observed to be 9?
The predicted value and residual for y is 9.4 and -0.4 respectively.
In statistics, a regression equation is used to determine whether or not there is a relationship between two sets of data. If you measure a child's height every year, you might discover that they grow about 3 inches per year. A regression equation can be used to model that trend (growing three inches per year). In fact, most things in the real world (from gas prices to hurricanes) can be modelled mathematically, allowing us to forecast future events.
Regression equations can assist you in determining whether your data can be fit to an equation. This is extremely useful if you want to make predictions based on your data, whether they are future predictions or indications of past behaviour.
Given,
Regression equation is y=11-038x
Observed value of y = 9
predicted value of y can be determined by substituting x=2 in the equation
y=11-0.8(2)=11-1.6=9.4
The residual can be calculated by formula,
residual = observed value - predicted value
residual = 9 - 9.4
residual = -0.4
Thus, the predicted value is 9.4 and residual is -0.4.
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Your question is incomplete, here is the complete question.
suppose the estimated regression equation is given by y=11-0.8x . what are the predicted value of y and the residual when x is 2 and y is observed to be 9?
what is the difference between descriptive statistics and inferential statistics?
A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.
Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.
The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.
The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.
Hence we get the required answer.
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suppose that the rural wage is $2 per day. urban modern sector employment can be obtained with a probability of 0.24 and pays $4 per day. the urban informal sector pays $1 per day. using this information, and making assumptions as needed, predict whether there will be any rural-to-urban or urban-to-rural migration? explain your reasoning, stating explicitly any simplifying assumptions, and show all your work.
The solution to given problem is since E(Wu) < Wr, there will be no migration from rural areas .
What does probability theory entail?
The subject of probability in mathematics is concerned with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, with 1 typically signifying certainty and 0 typically signifying impossibility.
Here,
Since ,the rural wage is $2 per day. Urban modern sector employment can be obtained with .24 probability and pays $4 per day. The urban traditional sector pays $1 per day.
As long as the rural pay (Wr) differs from the anticipated urban wage (E(Wu)), according to the Harris-Todaro model, there will be movement between rural and urban areas.
Here, Wr equals $2.00.
Determine the anticipated urban wage now.
E(Wu) = p
*Wum+(1-p)
*Wut
Where p is the likelihood of finding employment in the urban modern sector, which is 0.25, and Wum is the wage for such employment, which is $4.00.
Wut = $1.00 in wages for jobs in the typical urban sector.
Hence, E(Wu) = 0.24*$4.00+0.76*$1.00 = $1.72
Since E(Wu) < Wr, there will be no migration from rural areas .
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you draw a two-card hand from a standard deck of 52 cards. what is the probability of drawing a hand that contains exactly 2 face cards (a face card is a king, queen, or jack)?
By using the concept of probability, it can be calculated that -
Probability that a two-card hand from a standard deck of 52 cards contains exactly 2 face cards (a face card is a king, queen, or jack) = [tex]\frac{11}{221}[/tex]
What is probability?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur.
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Number of face card = 12
Total number of cards = 52
Probability that a two-card hand from a standard deck of 52 cards contains exactly 2 face cards (a face card is a king, queen, or jack) = [tex]\frac{{12 \choose 2}}{{52 \choose 2}}[/tex]
= [tex]\frac{66}{1326}[/tex]
= [tex]\frac{11}{221}[/tex]
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8,3, -i
what is the polynomial function for these numbers
Answer:
f(x) = x⁴ - 11x³ + 25x² - 11x + 24---------------------------------
It is assumed the provided numbers are the zero's of the polynomial function.
We know complex zero's come in pairs if function has rational constants.
So we should have zero's: 8, 3, -i and i.
Find the polynomial:
f(x) = (x - 8)(x - 3)(x + i)(x - i) = (x² - 11x + 24)(x² + 1) = x⁴ - 11x³ + 25x² - 11x + 24Help please! I’m struggling:(
Answer:
B
Step-by-step explanation:
The median is the mid point value. Basically the median is whatever number is in the middle.
the different geometries that a molecule can attain by bond rotations and bends are called conformations. True/False ?
TRUE: A molecule can adopt a variety of geometries known as conformations by the rotation and bending of its bonds.
Conformational isomerism, often known as stereoisomerism, is a type of stereoisomerism in chemistry in which the isomers can be changed to one another simply by rotations about formally single bonds. Different conformations refer to any two arrangements of atoms in a molecule that differ by rotation about a single bond, whereas conformations that correspond to local minima on the potential energy surface are more specifically known as conformational isomers or conformers.
As a result, conformational isomers differ from other classes of stereoisomers (such as configurational isomers), where interconversion entails the necessary breaking and reformation of chemical bonds.
Thus, the statement, The different geometries that a molecule can attain by bond rotations and bends are called conformations is TRUE
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What is the difference between addition and subtraction of polynomials?
The difference between addition and subtraction of polynomials is that addition involves like terms and subtraction involves taking one polynomial away from another.
A polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).In addition to polynomials, the like terms are included whereas, in subtraction, the like terms are subtracted. The addition of polynomials involves combining like terms to form a single expression, while subtraction involves taking one polynomial away from another. In addition, when subtracting polynomials, the sign of each term in the second polynomial needs to be changed (from positive to negative, or from negative to positive).
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in a stopwatch time study, the number of cycles that must be timed is a function of: (i) the variability of observed times. (ii) the desired accuracy for the estimated job time. (iii) the desired level of confidence for the estimated job time.
To calculate the number of cycles we need above 3 options
Stop Watch Time Study:
Stop Watch Time Study is one of the equipment used for Time Study. It is employed for measuring the time taken by an operator to complete the work. Stop watch used for time study purpose should be very accurate and preferably be graduated in decimals so that it can recover even up to 0.01 minute.
A large hand in the stop watch is revolved at a speed of one revolution per minute. The dial of the stop watch is divided into 100 equal divisions. The small hand inside the stop watch revolves at a speed of one revolution in 30 minutes.
Given that
In a stopwatch time study, the number of cycles that must be timed is a function of:
options are
(i) the variability of observed times.
(ii) the desired accuracy for the estimated job time.
(iii) the desired level of confidence for the estimated job time
To calculate the number of cycles we need above 3 options
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What is the value of x?
Enter your answer as a decimal to the nearest tenth in the box.
Answer:3
Step-by-step explanation:
6.Which of these statements is correct? Select all that apply.
Responses
the built-in math function is square root or cube root.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
The correct options are:
A solution to the equation x2=81 is x=9.
A solution to the equation x3=125 is x=5.
A solution to the equation x3=216 is x=6.
Hence the built-in math function is square root or cube root.
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What is the equation of the line through 1 2 which makes equal intercepts on the axis?
The equation of the line through [tex](1,2)[/tex] which make equal intercepts on the axis [tex]x+y=3[/tex]
The equation of the line through (1,2) makes an equal intercept on the axis
The formula of the intercept form is
[tex]\frac{x}{a} +\frac{y}{b} =1[/tex]
If they make an equal intercept
[tex]a=b\\\frac{x}{a} +\frac{y}{a} =1\\x+y=a[/tex]
Put the value of the point in the axis, and we get.
[tex]1+2=a\\a=3[/tex]
Put the value in the equation, and we get.
[tex]x+y=3[/tex]
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the wait time to ride the ferris wheel at a state fair is 15 minutes when 75 people are in line. at this rate, how long is the wait time when 200 people are in line?
The wait time required for 200 people are in line would be 40min.
Given that:
wait time to ride the ferris wheel for 75 people is 15 minutes.
we have given 200 people that are in line to ride.
for each person in line from the beginning is an additional 0.2 wait time.
so, the number of people in line n times = 0.2 = wait time.
Therefore,
[tex]\frac{15\ min}{75 \ people}=0.2\frac{min}{people} \\\\wait \ time = n*0.2\frac{min}{people} \\\\wait\ time = (200)*0.2\frac{min}{people}\\\\wait\ time = 40 min[/tex]
Hence, The wait time required for 200 people are in line would be 40min.
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if the probability of a dancing lady accepting an invitation to dance is 0.18, find the expected number of ladies you would have to ask before one accepts.
If the probability of a dancing lady accepting an invitation to dance is 0.18.The accepted number of ladies asked before is 7.14 .
Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).
According to the above discussion:
P{x(bar) (0.18)} = 0.07142371
= 7.14%
Therefore, the expected number is 7.14%.
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Find the number x, If 11/3 of x is 55
The missing number of the algebraic expression is; x = 15
How to solve algebraic word problems?We are given the algebraic expression that we should find the number x, If 11/3 of x is 55.
This can be expressed as;
(11/3)x = 55
Multiply through by 3 to get;
(11/3)x * 3 = 55 * 3
11x = 165
Divide both sides by 11 to get;
11x/11 = 165/11
x = 15
Which we conclude that 15 is the missing number.
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Identifying Products Resulting in a Sum or Difference of
Cubes
Sum of cubes:
(a + b)(a²-ab + b²) = a³ + b³
Difference of cubes:
(a-b)(a² + ab + b²)=a³-b³
4) Intro
Which products result in a sum or difference of cubes?
Check all that apply.
(x-4)(x2+4x-16)
□ (x-1)(x²-x+1)
(x-1)(²+x+1)
(x+1)2+x-1)
(x+4)(x²-4x+16)
□ (x+4)(x2 + 4x + 16)
The products result in a sum or difference of cubes are
(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).
What is sum or difference of cubes?
The term "sum of cubes" refers to a polynomial with the formula a^3 + b^3. The term "difference of cubes" refers to a polynomial with the form
a^3 - b^3.
The formulas for sum of cubes and difference of cubes are given:
Sum of cubes: (a + b)(a²-ab + b²) = a³ + b³
Difference of cubes: (a-b)(a² + ab + b²)=a³-b³
We have to check which products result in a sum or difference of cubes.
Consider,
(1) (x - 4)(x^2 + 4x - 16)
(x - 4)(x^2 + 4x - 16) = x^3 - 8x^2 + 32x - 64
It is not a sum or difference of cubes.
(2) (x-1)(x²-x+1)
(x - 1)(x² - x + 1) = x^3 - 2x^2 + 2x - 1
It is not a sum or difference of cubes.
(3) (x - 1)(x² + x + 1)
(x - 1)(x² + x + 1) = x^3 - 1
This is the difference of cubes.
(4) (x + 1)(x^2 + x - 1)
(x + 1)(x^2 + x - 1) = x^3 + 2x^2 - 1
It is not a sum or difference of cubes.
(5) (x + 4)(x² - 4x + 16)
(x + 4)(x² - 4x + 16) = x^3 + 64
This is the sum of cubes.
(6) (x + 4)(x^2 + 4x + 16)
(x + 4)(x^2 + 4x + 16) = x^3 + 8x^2 + 32x + 64
It is not a sum or difference of cubes.
Hence, the products result in a sum or difference of cubes are
(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).
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Find the slope between the following points: (-4,7), and (4,—10)
Answer:
-17/8
Step-by-step explanation:
-10-7 -17
---------- = -------
4-(-4) 8
How do you determine a linear function?
The function is linear when the highest degree the the function is 1 .
In the question ,
we have been asked about when a function is called as linear .
By the definition ;
the Linear function is the function that has the highest degree as 1 and
On the coordinate plane the linear function represents the straight line .
the general form of the linear function is f(x) = mx + d ,
the slope is "m" and the y intercept is "d" .
The Examples of Linear Function are
f(x) = 3x + 2 ,
f(x) = -6x + 7
f(x) = 8 .
Therefore , the characteristic for the function to be linear is explained above.
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using the information in q8, what is the optimal number of cookies to make? 2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen
By using probability, it can be calculated that-
the optimal number of cookies to make is 2400 dozens
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Here
Each dozen of cookies is sold for $1.99 and cost $0.99
Shortage = $(1.99 - 0.99) = $1
Cookies that are not sold at the end of the day are reduced to $0.49
Overage = $(0.99 - 0.49) = $0.5
Service = [tex]\frac{1}{1 + 0.5}\\[/tex]
[tex]=\frac{1}{1.5}\\\\=\frac{2}{3}\\\\=0.67[/tex]
Now the table is
Demand Probability of demand Cumulative probability
(Dozen)
1800 0.05 0.05
2000 0.15 0.2
2200 0.2 0.4
2400 0.3 0.7
2600 0.2 0.9
2800 0.1 1
Here the closest to service is 0.7
So the optimal number of cookies to make is 2400 dozens
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Complete Question
Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are specialty of his shop. Each dozen sells for $1.99 and costs $0.99, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.49 and sold the following day as day-old merchandise. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand he estimates demand for cookies as
Demand Probability of demand Cumulative probability
(Dozen)
1800 0.05
2000 0.15
2200 0.2
2400 0.3
2600 0.2
2800 0.1
Using the information in q8, what is the optimal number of cookies to make? 2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen
2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen
Which table represents a linear function?
the table:4 represents a linear function.
What is system of linear equations?
The intersections or meetings of the lines or planes that represent the linear equations are known as the solutions of linear equations. The set of values for the variables in every feasible solution is a solution set for a system of linear equations.
Not a Solution
If there is no intersection of any lines, or if the graphs of the linear equations are parallel, then the system of linear equations cannot be solved.
An Endless Number of Options
A set of infinite points exists for which the L.H.S. and R.H.S. of an equation become equal, indicating that a system of linear equations has an infinite number of solutions.
Unique fixing a series of linear equations
For table 4: The slope will be (8-6)/(3-5) = 2/-2 = -1
and (10-8)/(1-3) = 2/-2 = -1
Hence, the table:4 represents a linear function.
For a function to be linear the slope of all the segments should be same.
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What is an example of a function equation?
The example of the function equation is f(x+3) = x² + 8x + 16 .
In the question ,
we have been asked to give an example of the function equation .
The Function Equation is defined as equations where the unknowns are functions, rather than a traditional variable.
For Example :
If f(x+3) = x² + 8x + 16 , then what is f(x)?
the above question is an example of function equation .
to find the solution ,
we let ,y = x + 3; then x = y - 3 .
Substituting the value of x in f(x+3) we get ,
f(y) = 2y² + 2y + 1 .
hence f(x) = 2x² + 2x + 1 that is = (x + 1)² .
Therefore , the example is f(x+3) = x² + 8x + 16 .
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the measure of ∠1 is 50 degrees. what is the measure of ∠6 ?
If the measure of angle 1 is 50° then the measure of angle 2 is 30°.
We know that line l ∥ line m and line p is the transversal.
Let's label the diagram as follows.
Now, by the vertically opposite angles theorem,
we have angle 1 = ∠TPQ = 50°
now ∠P and ∠Q form interior angles,
Hence, by the interior angles theorem, we have
∠P + ∠Q = 180°
The sum of the interior angles of the angles formed by the transversal is 180°.
50° + ∠Q = 180°
subtracting 50° on both sides we get,
∠Q = 180° - 50°
∠Q = 30°
Hence, the measure of angle 2 is 30°.
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The complete question is -
In the given figure, line l and line m are parallel and line p is transversal If the measure of 1 is 50 degrees what is the measure of 2?
(7x³ + x² + x) ÷ (x² + 1)
Answer:
7x + 1 Remainder -6x - 1
or
7x + 1 - (6x + 1)/(x² + 1)
Step-by-step explanation:
(7x³ + x² + x) ÷ (x² + 1)
7x + 1
---------------------
x² + 1 | 7x³ + x² + x
7x³ + 0 + 7x
------------------------
x² - 6x
x² + 0x + 1
--------------------
-6x - 1
(7x³ + x² + x) ÷ (x² + 1) = 7x + 1 Remainder -6x - 1
or
(7x³ + x² + x) ÷ (x² + 1) = 7x + 1 - (6x + 1)/(x² + 1)
A shoe company packs boxes of shoes in crates, divide to complete the table
Answer:
2/ 95
3/ 72
4/ 453
Step-by-step explanation:
2/ Take 2185 divided by 23 = 95
3/ Take 3888 divided by 54 = 72
4/ Take 7248 divided by 16 = 453
Kaylee is going to a carnival that has games and rides. Each game costs
$1.25 and each ride costs $2.50. Kaylee spent $12.50 altogether at the
carnival and the number of rides she went on is twice the number of
games she played. Graphically solve a system of equations in order to
determine the number of games Kaylee played, x, and the number of
rides Kaylee went on, y.
Based on the graph, a solution for the system of equations is 2 and 4.
The number of games Kaylee played is equal to 2 games.The number of rides Kaylee went on is equal to 4 rides.How to write and solve the system of equations graphically?In order to write a system of linear equations to describe this situation, we would assign variables to the number of games Kaylee played and number of rides Kaylee went on, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of games Kaylee played.Let the variable y represent the number of rides Kaylee went on.Since each game costs $1.25 and each ride costs $2.50, and Kaylee spent $12.50 altogether, we have;
1.25x + 2.50y = 12.50. ..........equation 1.
Additionally, the number of rides she went on is twice the number of
games she played;
y = 2x ..........equation 2.
Next, we would use an online graphing calculator to graphically solve the system of linear equations. Therefore, the required solution for the given system of linear equations is the point of intersection of the two (2) lines on the graph, which is given by this coordinate (2, 4).
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what is the x intercept of y = x + 3
and how do you get the answer
Answer: i believe it is
x-intercept(s): (−3,0) y-intercept(s): (0,3)
and
Step-by-step explanation:
substitute in 0 for y and solve for x and do that for the other just 0 for x and solve for y
There are 24 members of a kayaking club this summer. Next year, Owen hopes the number of members will be 125% of this number.
Write a percent equation in the form part = percent • whole that can be used to find 125% of 24. Use p to represent the part and represent the percent as a decimal.
The percent equation in the form of p = percent x whole is
p = 1.25 x 24
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of members in the club = 24
Number of members in the club next year = 125% of 24
The percent equation of 125% of 24.
p = 125/100 x 24
p = 1.25 x 24
p = 5/4 x 24
p = 5 x 6
p = 30
Thus,
The percent equation is p = 1.25 x 24
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Finn shows his work in finding the solution to 4x+6=2+3(x+2). After checking his answer in the original equation, he found that it did not work. Where did he make a mistake?.
Finn had solved the bracket in an incorrect way because of which he got a wrong answer.
Here we see that the equation is
4x + 6 = 2 + 3(x + 2)
Here we see that Finn has opened the brackets to write
4x + 6 = 2 + 3x + 2
Here is the point where he made a mistake.
When we have a term that needs to be multiplied by the terms in a bracket, we need to multiply it with every term inside the bracket.
This means, that 3 needs to be multiplied with x as well as 2.
Hence we get
4x + 6 = 2 + 3x + 6
Now if we deduct 3x from both sides we will get
x + 6 = 8
Now deducting 6 from both sides gives us
x = 2
Hence the value of x is 2
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Find the value of X
(Please help)
Answer: x = 19
Step-by-step explanation:
Let's start with what we know. The area of a trapezoid is:
(B1 + x) * H /2 = Area
So here we have:
(25 + x)* 7 /2 = 154.
We multiply by 2 on both sides:
(25 + x)*7 = 308
Divide by 7 on both sides:
25 + x = 44
Subtract 25 from both sides:
x = 19.
So x = 19.
Answer: 19 inches
Step-by-step explanation:
The shape is a trapezium. (You can tell as there is one pair of parallel sides.) Therefore, to find the area, the following formula is needed:
Area of a trapezium = [tex]\frac{a + b}{2} * h[/tex]
a and b represent the parallel sides
Next, plug in the given values:
[tex]154 = \frac{x + 25}{2} * 7[/tex]
Rearrange the equation to get x on its own:
[tex]154 = \frac{x+25}{2} * 7\\\\\frac{154}{7} = \frac{x+25}{2} \\\\22 = \frac{x+25}{2} \\\\22*2 = x + 25\\\\44 = x + 25\\\\44-25 = x\\\\x = 19\\\\[/tex]
Therefore, the answer is 19 inches. Remember your units!
A shoe store sells sneakers, loafers, and boots in narrow, medium, and wide widths. They are available in sides 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, and 10.5. Find the number of pairs of shoes available. Then find the probability of selecting a size 8 in medium width sneakers. Is it likely or unlikely that the size would be chosen?
Answer:
1/90
Step-by-step explanation: