The simplification of the complex fraction is found as 11/14.
Define complex fraction/mixed fraction?A mixed fraction is a fraction that is created by fusing a fraction with a whole number. An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that. Step 1: Multiply the mixed fraction's denominator by the whole number component.Step 2: Increase the product from Step 1 by the numerator.Step 3: In the numerator/denominator form, write the improper fraction using the total from Step 2.For the given question, the expression is-
-2/7 + 1 1/3
To convert mixed fraction 1 1/3 i improper fraction, multiply 3 with 1 and add 1.
1 1/3 = 1 x 3 + 1 /3
1 1/3 = 4/3 Put in main equation.
-2/7 + 4/3
Simplify the expression.
= -2 x 3 + 4 x 7/ (7 x 4)
= -6 + 28 / 28
= 22/28
Divide both with 2
= 11/14
Thus, the simplification of the complex fraction is found as 11/14.
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The correct question is
Simplify the complex fraction.
-2/7 + 1 1/3
1. The cost of bell peppers varies directly with the weight of bell peppers, as shown in the table. Write a direct variation equation to represent this relationship. Then identify the constant of variation and interpret its meaning.
The constant of variation is 1.75 for every unit increase in x (weight), and the cost(y) value increases by $ 1.75.
What is the equation?
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The difference between two consecutive entries is constant, as we can see = 1.75
⇒ 7 - 5.25 = 1.75
⇒ 8.75-7 = 1.75
⇒ Slope(m) = 1.75
The slope represents the variable's rate of change.
y - 3 = m(x - 5.25)
y - 5.25 = 1.75(x-3)
y = 1.76x
Thus, the constant of variation is 1.75
This indicates that for every unit increase in x (weight), the cost(y) value increases by $ 1.75.
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The question seems to be incomplete the correct question has been attached
[tex]4x^{2} +12x+8=0[/tex]
Step-by-step explanation:
4x² + 12x + 8 = 0
this has the same solutions as
x² + 3x + 2 = 0
as we simply divided everything by 4. 0/4 = 0.
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case that is
x = (-3 ± sqrt(3² - 4×1×2))/(2×1) =
= (-3 ± sqrt(9 - 8))/2 = (-3 ± sqrt(1))/2
x1 = (-3 + 1)/2 = -2/2 = -1
x2 = (-3 - 1)/2 = -4/2 = -2
so, the 2 solutions are
x = -1
or
x = -2
A rectangular ground is 121/4m long and 41/2 m broad. Find the perimeter and area of the ground.
Answer:
Thank you,Hope you like it and it will help you
The height of a building is proportional to the number of floors The figure shows the height of a building with 9 floors
a. Reasoning write the ratio of height of the building to the number of floors. Then find the unit rate, and explain what it means in this
b. How tall would the building be if it had 15 floors
THIS IS FOR MIDDLE SCHOOL 7TH GRADE
Answer: B
Step-by-step explanation:
it has to do with simallar mathematics of 12th grade so you can do the sum
its pretty ez cuz im a 12th grader
what is meter × meter
[tex]meter^{1`} *meter^{1} \\=meter^{1+1} \\=meter^{2}[/tex]
⇒Mote I used the laws of exponents : [tex]=x^{m} *x^{n} \\=x^{m+n}[/tex]
The area of a rectangular garden is 224 square meters. The width is 6 meters longer than one-half of the length. Find
the length and the width of the garden. Use the formula, area = length • width.
Pls help
[tex]\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ A=224\\ w=\stackrel{\textit{half-length plus 6}}{\frac{L}{2}+6~\hfill } \end{cases}\implies 224=L\left( \cfrac{L}{2}+6 \right)\implies 224=\cfrac{L^2}{2}+6L[/tex]
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(224)=2\left( \cfrac{L^2}{2}+6L \right)}\implies 448=L^2+12L \\\\\\ 0=L^2+12L-448\implies 0=(L-16)(L+28)\implies \boxed{L= \begin{cases} -28\\\\ 16 ~~ \textit{\LARGE \checkmark} \end{cases}} \\\\\\ \stackrel{\textit{since we know that}}{w=\cfrac{L}{2}+6}\implies w=\cfrac{16}{2}+6\implies \boxed{w=14}[/tex]
now, let's notice, "L" has two valid values but for this case "L" cannot be negative.
The expression $25 + $10h gives the amount of money that Stephanie earns per day, where h is the number of hours she works. How much does she earn if she works 4 hours?
Answer:
25+10(4)= 65
Step-by-step explanation:
think of it as she makes 10 dollars an hour plus then she gets a 25 dollar bonus so you multiply the number of hours by 10 then and the bonus
Answer: $65
Step-by-step explanation:
25+10h h=4
25+10x4=
25+40=
65
ASAP
10 yellow, 6 green, 9 orange, and 5 red cards facedown. Once a card selected, NOT replaced.
a. P(two cards that are not orange)
b. P(two cards that are neither red nor green)
The probability of selecting two cards that are not orange, is 0.483 and the probability of selecting two cards that are not red and green, is 0.393.
In the given question we have to find the probability.
From the question it is given that,
10 yellow, 6 green, 9 orange, and 5 red cards facedown.
Total number of cards = 10+6+9+5
Total number of cards = 30
Once a card selected, NOT replaced.
a.) Now finding the probability of selecting two cards that are not orange.
There are total orange cards = 9
The number of cards except orange card = 21
Then the probability of selecting one card except orange = 21/30
Then the probability of selecting other card except orange = 20/29
Then the probability of selecting two cards that are not orange is
P(O) = 21/30 * 20/29
P(O) = 420/870
P(O) = 0.483
Then the probability of selecting two cards that are not orange, is 0.483.
(b) Now finding the probability of selecting two cards that are neither red nor green.
The total number of cards except red and green card = 19
Then the probability of selecting one card except red and green card = 19/30
Then the probability of selecting other card except red and green card = 18/29
Then the probability of selecting two cards that are not red and green card is
P(RG) = 19/30 * 18/29
P(RG) = 342/870
P(RG) = 0.393
Then the probability of selecting two cards that are not red and green, is 0.393.
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the product of a number and 12 increased by two
After solving the formed equation from the question, the result will be equal to 4.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
The given statement of the question in the equation form will be,
5x + 12 = 32
5x = 20
x = 4
Therefore, the value of x will be equal to 4.
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Your complete question must be like this:
The product of a number and 5 is increased by 12 the result is 32 to find the number.
Students in two classrooms were given a mathematics test. The first classroom had 25 students and their average score was 86%. The second classroom had 15 students and their average score was 94%. If the teacher combined the test scores of students in both classes, what is the average score for both classes?
Answer:
Step-by-step explanation:
The temperature went from 13o C at 3PM to -5o C at midnight that evening.
Which statement best describes the rate of change of the temperature
during this period of time?
The rate of change of the temperature on the time interval is -2°C. This means that, in average, for each hour that passes the temperature decreases by 2 degrees Celcius.
What is the rate of change on the temperature?A rate of change is defined as the quotient between the difference in some measure (in this case it will be the difference between the final temperature and the initial temperature) and the time interval in which it happens.
Here we know that:
final temperature = -5°C
Initial temperature = 13°C
And this change goes from 3 P.M. to midnight, so the change happens on an interval of 9 hours.
Then the rate of change of the temperature is:
r = (-5°C - 13°C)/9h = -2°C/h
So for each hour, the temperature decreases by 2°C.
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Need help with This also
Answer:
Step-by-step explanation:
8.5 inches divided by 2 = 4.25 inches which is the base of the triangle with a height of 5.8 inches. Area of that triangle is 1/2 x base x height = 1/2 x 4.25 inches x 5.8 inches = 12.325 inches squared. Two of the triangles make 1 full isoceles triangle= 2 x 12.325 inches squared = 24.65 inces squared. But there are 5 isoceles triangles in a pentagon, so 5 times 24.65 inches squared = 123.25 inches squared.
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 122.
A rectangle has a width of x and a length of x plus 4.
The inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.
According to the question,
We have the following information:
The perimeter of the rectangle is less than 122.
A rectangle has a width of x and a length of x plus 4.
Now, the expressions for the width and length of the rectangle are given below:
Width = x units
Length = (x+4) units
We know that the following formula is used to find the perimeter of rectangle:
2(length+width) < 122
2(x+4+x) < 122
2(2x+4) < 122
Dividing by 2 on both sides:
2x+4 < 122/2
2x+4 < 61
Subtracting 4 from both sides:
2x < 61-4
2x < 57
Dividing by 2 on both sides:
x < 57/2
x < 28.6
Hence, the inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.
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A plumber who is just starting out offers low rates to attract new customers. He charges $35 to visit a client's home, plus an additional $20 per hour. If the plumber charges a customer $45 for a visit, how long was it?
If the plumber charges a customer $45 , then the visit was 0.5 hours long .
In the question ,
it is given that
the fixed charge to visit a client's home is = $35
additional per hour charge of plumber is = $20 .
let the time taken by plumber in the customer house be "x" .
So , according to the question
the equation for total charge is
total charge = 35 + 20x
given the customer paid $45 ,
So , 45 = 35 + 20x
20x = 45 - 35
20x = 10
x = 10/20 = 0.5
Therefore , If the plumber charges a customer $45 , then the visit was 0.5 hours long .
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Emma wrote one hundred thousand as 1,000,000. Explain what she did wrong.Then write the number correctly
Answer:
she wrote 1 million. It's 100,000
Step-by-step explanation:
she wrote 1 million. It's 100,000
-4x=76 x equals _-____________________________________________________________________________________________________________________________________________________________--
The value of x in the equation -4x = 76 is 19.
What is equation?The equals sign is used in equations to indicate the equality of two expressions in a formula.
Given:
-4x = 76,
-x = 76 / 4,
x = -19
Therefore, the value of x in the equation -4x = 76 is 19.
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In chapters 5-8 of Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm. What causes these feelings
A. A visit from his father
B. A letter from Elizabeth
C. The arrival of Henry Clerval
D. An award for creating the monster
Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm, An award for creating the monster causes these feelings.
How does Victor first react to the monster and what happens to both after the first encounter?Victor is the first to enter and is relieved to see no evidence of the creature. But, exhausted by months of labour and the horror of the creature he has created, he becomes ill with a nervous fever that lasts several months.Victor begins to grasp, for the first time, that what he has made is not only the scientific result of an experiment in animated matter, but a genuine living entity with needs and desires.He informs Victor that all of his horrible deeds stemmed from his desperate loneliness. He offers to take his new friend to South America, where they will hide in the bush away from human interaction. He claims that with the sympathy of a fellow monster, he will no longer be compelled.'Frankenstein,' by Mary Shelley, is the narrative of Victor, who creates a monster with the goal of generating life. He was a genius in college, and he created a monster. His own creation was a failure.To learn more about Frankenstein, refer,
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Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm, An award for creating the monster causes these feelings.
How does Victor first react to the monster and what happens to both after the first encounter?Victor is the first to enter and is relieved to see no evidence of the creature. But, exhausted by months of labor and the horror of the creature he has created, he becomes ill with a nervous fever that lasts several months.Victor begins to grasp, for the first time, that what he has made is not only the scientific result of an experiment in animated matter, but a genuine living entity with needs and desires.He informs Victor that all of his horrible deeds stemmed from his desperate loneliness. He offers to take his new friend to South America, where they will hide in the bush away from human interaction. He claims that with the sympathy of a fellow monster, he will no longer be compelled.'Frankenstein,' by Mary Shelley, is the narrative of Victor, who creates a monster with the goal of generating life. He was a genius in college, and he created a monster. His own creation was a failure.To learn more about Frankenstein, refer,
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Calculate: (Round your final answers to the nearest cent.) Units Unit Cost Beg. Inventory Jan. 1 20 $ 8.00 May 10 15 $ 11.00 June 30 17 $ 20.00 Dec. 10 12 $ 21.00 24 units not sold LIFO FIFO Weighted-Average Cost of Ending Inventory A C E Cost of Goods Sold B D F
1. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:
LIFO FIFO Weighted-Average
Ending inventory $425 $691 $573
Cost of goods sold $492 $226 $344
How do the inventory methods differ?FIFO (First-in, First-out) assumes that the physical flow of goods sold follows the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
The weighted-average method uses the average cost of goods to compute the ending inventory and the cost of goods sold.
LIFO:
Ending inventory = $425 ($917 - $492)
Cost of goods sold = $492 (12 x $20 + 12 x $21)
FIFO:
Ending inventory = $691 (9 x $11 + 17 x $20 + 12 x $21)
Cost of goods sold = $226 ($917 - $691)
Weighted Average:
Ending inventory = $573 (40 x $14.33)
Cost of goods sold = $344 (24 x $14.33)
Inventory Table:Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 20 $8.00 $160
May 10 Purchases 15 $11.00 $165
June 30 Purchases 17 $20.00 $340
Dec. 10 Purchases 12 $21.00 $252
Total 64 $917
Units sold 24
Ending inventory 40 (64 - 24)
Average cost = $14.33 ($917/64)
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How many times greater is 5.96 × 10^4 then 2.98 × 10^3?
A. 20
B. 500
C. 50
D. 200
The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ , the correct option is (a) .
In the question ,
it is given that
the number is 5.96 × 10⁴ ,
we have to find that how many times greater is 5.96 × 10⁴ then 2.98 × 10³ .
to find that the number is how many times greater ,
we divide 5.96 × 10⁴ by 2.98 × 10³ .
So , on dividing the numbers we get
= ( 5.96 × 10⁴ ) / ( 2.98 × 10³ )
= 5.96/2.98 × 10⁴⁻³
= 2 × 10¹
= 20 times
Therefore , The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ .
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In which quadrant does the point (10, -9) lie?
Answer:Qadrant 4
Step-by-step explanation:
What is the coefficient of the 7th term of (3x² - 2)14?
13492928512 is the last term (7th term )of binomial expansion of the given expression so therefore it has no coefficient .
What is binomial expansion ?The binomial theorem is a way to bring the formulation to a finite power.
The binomial theorem is a effective extension device with packages in algebra, probability, and more. A binomial is an algebraic expression containing wonderful terms.
Calculationit has been attached below b'coz' that was not possible to type here
hope that image is clear .
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Linda estimates the number of questions she answered correctly on a test. She answered 8 correctly with probability 0.6, 15 correctly with probability 0.3, and 20 correctly with probability 0.1. What is the expected value of the number of questions Linda answered correctly?
Linda' number of questions has an expected value of 11.3
How to determine the expected value of number of questions?The given parameters in the question are:
8 questions with probability 0.6,
15 questions with probability 0.3
20 questions with probability 0.1
The expected value is then calculated as
E(x) = Sum of (number of questions * probability)
Substitute the known values in the above equation, so, we have the following representation
E(x) = 8 * 0.6 + 15 * 0.3 + 20 * 0.1
Evaluate
E(x) = 11.3
Hence, the expected value is 11.3
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Hello, I need help with this math exercise.
John buys 7 apples and 4 pears for $7.25. At the same prices, Hayley buys 5 apples and 9 pears for $10.40. What is the price of one pear? Use Cramer’s Rule to solve.
The price of one pear is $0.85
How to use Cramer’s Rule to solve the price of one pear?
Cramer's rule is one of the useful methods used for solving a system of equations. In this method, the values of the variables in the system are to be calculated using the determinants of matrices. Thus, Cramer's rule is also known as the determinant method.
Given that: John buys 7 apples and 4 pears for $7.25 and at the same prices, Hayley buys 5 apples and 9 pears for $10.40
We will use this given information to form equations in matrices form. Let a and p represent the prices of one apple and one pear respectively.
The equation is:
7a + 4p = 7.25
5a + 9p = 10.40
The matrix formed is:
[tex]C=\left[\begin {array}{ccc}7&4\\5&9\end{array}\right][/tex] , [tex]b=\left[\begin {array}{ccc}7.25\\10.40\end{array}\right][/tex]
Find the determinants,
D = (7 x 9) - (5 x 4) = 43
Da = (7.25 x 9) - (10.40 x 4) = 23.65
Dp = (7 x 10.40) - (5 x 7.25) = 36.55
a = Da/D = 23.65/43 = 0.55
p = Dp/D = 36.55/43 = 0.85
Since p = 0.85. Therefore, the price of one pear is $0.85
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x+13
2x +1
x-8
Find x
X = 43.5 .............
if p is false,which row represents when p v(q^r) is true?
E
F
G
H
Answer:
f and g 231
Step-by-step explanation:
James shares 5/8 of a cake between 6 people.
What fraction of the cake do they each receive?
Answer:
5/48
Step-by-step explanation:
The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48.
What is a fraction?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
In another word, if we divide two numbers by each other then the upper word is called the numerator, and the lower word is called the denominator.
As per the given,
James shares 5/8 of a cake between 6 people.
Now, 1/6 of 5/8 will be as,
1/6(5/8) = 5/48
Hence "The fraction of people getting cake will be 1/6 of 5/8 thus it will be 5/48".
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According to the general equation for conditional probability, if P(AB) =3/7 and P(B)=7/8,
what is P(AIB)? O A. O B. O c. O D. 16 49 32 24 49
Answer:
(d) 24/49
Step-by-step explanation:
You want to know P(A|B) when P(AB) = 3/7 and P(B) = 7/8.
Conditional probabilityThe general equation for conditional probability tells you ...
P(A|B) = P(AB)/P(B)
P(A|B) = (3/7)/(7/8) = (3/7)·(8/7)
P(A|B) = 24/49
The cost to produce x units of wire is C= 45x + 450, while the revenue is R= 70x. Find the interval where the product will at least break even.
The interval where the product will be at least break even equals to 18 units.
What is a break even point?In accounting, the break-even point refers to the production level at which total revenues equal total expenses.
Given data
Cost is given as C = 45x + 450
Revenue is given as: R = 70x
In this case, the point of breakeven will be:
Cost = Revenue
45x + 450 = 70x
We will collect like terms:
70x - 45x = 450
25x = 450
We will divide both side by 25:
25x/25 = 450/25
x = 18
Therefore, the interval where the product will be at least break even equals to 18 units.
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Point M is the midpoint of AB. If the coordinates of A are ( -3 , 6 ) and the coordinates of M are ( -5 , 2 ), what are the coordinates of B? (reference sheet on the left side)
The coordinates of B are (-7,-2).
What do you mean by x and y coordinates?
The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.
According to the given data in the question,
if M is the location where line segment AB meets its midpoint.
Then, we will using the midpoint formula,
[tex](-5,2)=(\frac{-3+x}{2},\frac{6+y}{2})..............(1)[/tex]
Putting the x-coordinates in (1),
[tex]-5=\frac{-3+x}{2}\\ -10=-3+x\\-10+3=x\\x=-7[/tex]
Similarly, putting the y-coordinates in (1),
[tex]2=\frac{6+y}{2} \\4=6+y\\4-6=y\\y=-2[/tex]
Hence, the coordinates of B are (-7,-2).
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For f(x)=3x+18, what is the value of x for which f(x) =21
a. x=2
b. x=5
c. x=1
d. x=-1
Answer:
I believe the answer is C
Step-by-step explanation:
a. would = 24b. would = 33c. would = 21d. would = 15 :)