Since AB and CD are parallel lines cut by a transversal GH, we know that the corresponding angles are equal. Therefore, LDFE = 35°
what is parallel lines ?
Parallel lines are two or more lines in a plane that never meet or intersect, no matter how far they are extended. They always maintain the same distance between them and remain equidistant at every point along their length.
In the given question,
Parallel lines are two or more lines in a plane that never meet or intersect, no matter how far they are extended. They always maintain the same distance between them and remain equidistant at every point along their length.
Corresponding angles are pairs of angles that are in the same relative position at the intersection of two lines that are crossed by a third line, called a transversal. More specifically, corresponding angles are formed when a transversal intersects two parallel lines.
Corresponding angles are congruent, which means they have the same measure or degree of angle
Since AB and CD are parallel lines cut by a transversal GH, we know that the corresponding angles are equal. Therefore,
LAEG = LDFE
So, LDFE = 35°. .
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11. A rectangular room measures 16 feet by 18 feet. The ceiling is 9 feet high.
a. Find the total area of the four walls in the room.
b. If a gallon of paint costs $37.99 and it covers 400 square feet on average, what is the cost of
painting the room, including the ceiling, with two coats of paint? Explain your answer.
c. This room is well insulated and is on the north side of the house. How large of an air
conditioner would this room require? Round to the next highest thousand BTUs.
d. A scale drawing is made of this room using the scale 1 sq ft = sq in. What are the
dimensions of this room on the drawing?
Therefore , the solution of the given problem of area comes out to be a.720 sq. ft, b.$227.94 , c.64,800 BTUs. and d.2,592 sq in.
What does an area actually mean?Calculating how much space would be needed to fully enclose its exterior will reveal its overall size. The neighboring area is considered when selecting a comparable good for the rectangular design. The surface area of something determines its overall measurements. The number of sides between a cuboid's four trapezoidal shapes determines how much water it can hold.
Here,
A.
=> 2(144 sq. ft.) + 2(162 sq. ft.) = 720 sq. ft.
b.
16 * 18 = 288 square feet
The entire region that needs painting is:
=> 720 square feet + 288 square feet = 1008 square feet.
We need to apply two layers of paint to the following surface area:
=> 2 * 1008 square feet = 2016 square feet.
5.04 gallons are obtained by multiplying 2016 square feet by 400 square feet per gallon.
=> $6 liters* $37.99/gallon = $227.94
c. 16 feet by 18 feet by 9 feet equals 2,592 cubic feet
As a result, the room's necessary cooling capacity is:
=> 2,592 cubic feet*25 BTUs per cubic foot = 64,800 BTUs.
Rounding up to the next greatest thousand BTUs, we need an air conditioner with a capacity of 65,000 BTUs.
d.
=> 16 ft x 144 sq in/ft = 2,304 sq in by
=> 18 ft x 144 sq in/ft = 2,592 sq in
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What is the range of the function y=e4x7
A- Y <0
B- Y > O
C- y <4
D- Y> 4
We have been given the function We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.
Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.
Therefore, the range of the function is given by y>0B is the correct option.
Select each pair of expressions that are equivalent O 3x+-x+1 4 and 4x + 1 2 +6x and 2(3x + 1) D 3(x + 1)–(1-X) and 2x+3 O 3xand 4(x + 1)-x-4 5.5 + 2.2x + 3.8x - 4.1 and 1.4 + 6X
5. Miguel plans on retiring in 16 years, and he wants to double his money by that time. He's contacted various banks, looking for a CD that compounds interest
monthly, and to calculate what annual interest rate he needs, he is using the Rule of 72.
Part ll: what equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires?
Part lll: What annual interest rate does Miguel need to double his money by the time he retires?
Miguel has to put up the equation r = 72/16.
4.5% is the interest rate.
What is the 72-hour rule?For calculating how long it would take for an investment to double in value, the rule of 72 is utilised. To get the doubling time, divide 72 by the interest rate.
To use the rule of 72, you simply divide the number 72 by the annual interest rate. For example, if the interest rate is 6%, the rule of 72 predicts that it will take approximately 12 years (72 ÷ 6 = 12) for the investment to double in value.
Part2:
equation can Miguel set up to solve for the annual interest rate he needs to double his money by the time he retires is n = 72 / r
Part3:
annual interest rate does Miguel need to double his money by the time he retire
r = 72 / n
72 / 16 = 4.5%
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Suppose that 10 balls are put into 5 boxes, with each ball independently being put in
box with probability (), ∑(i = 1 to 5) () = 1
(a) Find the expected number of boxes that do not have any balls.
(b) Find the expected number of boxes that have exactly 1 balls.
Answer:
(a) Let X be the number of boxes that do not have any balls. We can calculate the probability that a particular box is empty, which is (1-p)^10, where p is the probability that a ball is put into that box. The expected number of boxes that are empty is then:
E(X) = 5(1-p)^10 (since each box has the same probability of being empty)
Substituting ∑(i = 1 to 5) p = 1, we get p = 1/5. Therefore,
E(X) = 5(1-1/5)^10 = 5(4/5)^10 ≈ 0.328
So, the expected number of boxes that do not have any balls is approximately 0.328.
(b) Let Y be the number of boxes that have exactly one ball. The probability that a particular box has exactly one ball is given by:
P(exactly one ball in a box) = 10p(1-p)^4
where p is the probability that a ball is put into that box. The expected number of boxes that have exactly one ball is then:
E(Y) = 5(10p(1-p)^4)
Substituting p = 1/5, we get:
E(Y) = 5(10/5^5) = 1/25
So, the expected number of boxes that have exactly one ball is 1/25.
refers to the standard normal distribution find a z value such that the probability of obtaininig a large z value of 0.20?
Therefore , the solution of the given problem of probability comes out to be the z-value at which a large z value is obtained with a 0.20 chance is roughly 0.84.
What is probability exactly?The primary goal of the structures in the style known as parameters is the determination of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1, at which 1 typically denotes certainty but also 0 typically denotes potential, can be used to symbolise chance. A probability diagram shows the chance that a specific event will occur.
Here,
The z-value for a chance of 0.20 in the right tail of the distribution can be found using a calculator or a standard normal distribution table.
The probability number in the right tail that is
=> closest to 0.20 using a standard normal distribution table is 0.1995.
This probability's equivalent z-value is roughly 0.84.
As an alternative, we can calculate the z-value using a computer. With a chance of 0.20, a mean of 0, and a standard deviation of 1, and the inverse normal function—also known as the normal quantile function—we obtain:
=> Z=invNorm(0.20) 0.84
As a result, the z-value at which a large z value is obtained with a 0.20 chance is roughly 0.84.
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Kami wants to buy some new shoes. She goes to the store and can choose her shoes to be either black, white, or red and she can also choose whether they are flat, have a small heel, or are high heeled. Which list correctly displays all of the choices Kami has for her new shoe purchase?
Therefore, Kami has 9 different choices for her new shoe purchase, as listed above.
What use does a mathematical equation serve?A mathematical equation is an expression that describes the relationship between two other expressions and is expressed as an equality on both sides of the equal to sign. The equation 3y = 16 is an illustration.
Kami has 3 choices for the color of her shoes and 3 choices for the type of heel, so the total number of possible shoe combinations is:
3 colors × 3 types of heels = 9 shoe combinations
The list of all possible choices for Kami's new shoe purchase is:
1.Black flat
2.Black small heel
3.Black high heel
4.White flat
5.White small heel
6.White high heel
7.Red flat
8.Red small heel
9.Red high heel
Therefore, Kami has 9 different choices for her new shoe purchase, as listed above.
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You give your home health patient an unopened 500mL bottle of Mucinex and tell them to take 2 teaspoons 4 times a day as ordered. Your patient then ask you, "How long will this bottle last?" What will you tell your patient? (Respond to both questions.)
Answer:
the bottle will last approximately 12.5 days if the patient takes 2 teaspoons (10 mL) of Mucinex 4 times a day as ordered.
Step-by-step explanation:
Assuming that one teaspoon is equivalent to 5 milliliters (mL), then 2 teaspoons would be 10 mL. Therefore, the patient will be taking a total of 10 mL four times a day, which is 40 mL per day.
Since the bottle contains 500 mL, we can calculate how long the bottle will last by dividing the total volume of the bottle by the daily dose:
Number of days = Total volume of bottle / Daily dose
Number of days = 500 mL / 40 mL per day
Number of days = 12.5 days
Therefore, the bottle will last approximately 12.5 days if the patient takes 2 teaspoons (10 mL) of Mucinex 4 times a day as ordered.
PLEASE HELP QUICK 30 POINTS
You know the lengths of the two legs of a right triangle, and you are trying to solve for the measures of the acute angles of that triangle. Without calculating the length of the hypotenuse, which trigonometric ratio and reciprocal trigonometric ratio would be most useful in this calculation? Why?
Which describes the graph of y = −(x − 3)2 − 8?
A.Opens up with a vertex at (−3, −8)
B.Opens up with a vertex at (3, −8)
C.Opens down with a vertex at (−3, −8)
D.Opens down with a vertex at (3, −8)
Opens down with a vertex at (3, −8)
A quadrilateral in the coordinate plane has vertices ( -3, 1), ( 2, 1), ( 2, -2) and (-3, -2). What is the perimeter, in units, of the quadrilateral
Answer:
To find the perimeter of the quadrilateral, we need to find the distance between its vertices and then add them up. We can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distance between each pair of adjacent vertices:
Distance between (-3, 1) and (2, 1):
d = sqrt((2 - (-3))^2 + (1 - 1)^2) = sqrt(25) = 5
Distance between (2, 1) and (2, -2):
d = sqrt((2 - 2)^2 + (-2 - 1)^2) = sqrt(9) = 3
Distance between (2, -2) and (-3, -2):
d = sqrt((-3 - 2)^2 + (-2 - (-2))^2) = sqrt(25) = 5
Distance between (-3, -2) and (-3, 1):
d = sqrt((-3 - (-3))^2 + (1 - (-2))^2) = sqrt(9) = 3
Now we can add up these distances to get the perimeter:
perimeter = 5 + 3 + 5 + 3 = 16
Therefore, the perimeter of the quadrilateral is 16 units.
Multiply 5 3/4 * 1 3/4. Simplify the answer and write as a mixed number
Use the angle relationship in the figure below to solve for x. Assume that line A and line B are parallel, line C is a transversal and the given angles are given in degrees.
Step-by-step explanation:
the 2 angles are supplementary. that means together they have 180°
4x + 29 = 180 - (12x + 55) = 180 - 12x - 55 = 125 - 12x
16x = 96
x = 96/16 = 6
After working through the suggested questions,Zanele realises that the questionnaire is not suitable.List two reasons why you that the given questionnaire is Not suitable
Below are some general reasons why a questionnaire might not be suitable:
Poorly constructed questionsLaslty Inadequate samplingWhat is the questionnaire about?Poorly constructed questions: If the questions in the questionnaire are not clear, ambiguous, leading, or biased, then the responses obtained may not be accurate or reliable. Poorly constructed questions may also lead to confusion, misunderstandings, and errors.
Lastly Inadequate sampling: If the sampling technique used to select respondents is not representative of the target population, then the results obtained may not be generalizable or applicable to the larger population. The sample size and composition may also affect the validity and reliability of the results.
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questions 9, 10, 11, 12, 13, 14 on Unit 3: relations and functions Homework 1: relations, domain, range, and functions
The domain and the range of the relations are
Domain = [0, 6] and Range = [-3, 3]Domain = (-∝, ∝) and Range = (-∝, ∝)Domain = (-∝, ∝) and Range = [0, ∝)Domain = [-3, 3] and Range = [-4, 4]Domain = (-∝, ∝) and Range = [-2, 4]Domain = (-∝, ∝) and Range: y = 1How to determine the domain and the range of the relationsWhat is domain?
In mathematics, the domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.
In other words, the domain of a function is the set of values that can be plugged into the function and produce a valid output.
What is range?
In mathematics, the range of a function refers to the set of all possible output values (also known as the dependent variable) that the function can produce for a given input value from its domain.
In other words, the range of a function is the set of values that the function takes on as its input variable varies over its domain.
Using the above definitions, we have the domain and the range of the relations to be:
Graph 9:
Domain = [0, 6]
Range = [-3, 3]
Relation = Yes
Function = No
Graph 10:
Domain = (-∝, ∝)
Range = (-∝, ∝)
Relation = Yes
Function = Yes
Graph 11:
Domain = (-∝, ∝)
Range = [0, ∝)
Relation = Yes
Function = Yes
Graph 12:
Domain = [-3, 3]
Range = [-4, 4]
Relation = Yes
Function = No
Graph 13:
Domain = (-∝, ∝)
Range = [-2, 4]
Relation = Yes
Function = Yes
Graph 13:
Domain = (-∝, ∝)
Range: y = 1
Relation = Yes
Function = No
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Find x, y and z. Round decimals to the nearest hundredth. 7.1 25 1 6 M
Answer:
x = 10.68y = 12.25z = 21.79Step-by-step explanation:
You want the side lengths in a right triangle geometry when the altitude to the hypotenuse of length 25 cuts off a segment of length 6.
Geometric mean relationsAll of the right triangles in this configuration are similar. The proportional relationships between the sides give rise to three geometric mean relations.
In effect each of the segments x, y, z is the geometric mean of the two segments of the hypotenuse it touches.
x = √(6·(25-6)) = √114 ≈ 10.68
y = √(6·25) = 5√6 ≈ 12.25
z = √((25 -6)·25) = 5√19 ≈ 21.79
__
Additional comment
To see how these arise, consider the ratio of long side to hypotenuse:
z/25 = 19/z
z² = 25·19
z = √(25·19) . . . . . the geometric mean of 25 and 19
The "geometric mean" of n numbers is the n-th root of their product. For two numbers, it is the square root of their product.
[tex]x-\frac{3x-2}{4} =\frac{6-5x}{3}[/tex]
This is a prοper fractiοn. Tο cοnvert it tο a decimal, we divide the numeratοr by the denοminatοr and get , x ≈ 1.29
Tο sοlve linear equatiοns with fractiοns, we need tο multiply bοth sides οf the equatiοn by the least cοmmοn multiple (LCM) οf all the denοminatοrs tο eliminate the fractiοns¹.
Hοw are linear equatiοns that have fractiοns οn bοth sides sοlved?When an equatiοn invοlves fractiοns οn bοth sides, multiply each side by the denοminatοrs' lοwest cοmmοn multiple (LCM).
The LCM οf 4 and 3 is 12. Multiplying bοth sides by 12, we get:
12(x - (3x-2)/4) = 12((6-5x)/3)
Simplifying, we get:
12x - 3(3x-2) = 4(6-5x)
Expanding and cοllecting like terms, we get:
-6x + 6 = -20x + 24
Adding 20x tο bοth sides, we get:
14x + 6 = 24
Subtracting 6 frοm bοth sides, we get:
14x = <cοde>**18**</cοde>
Dividing bοth sides by <cοde>**14**</cοde>, we get:
<cοde>**x = 18/14**</cοde>
This is an imprοper fractiοn. Tο simplify it, we divide the numeratοr by the denοminatοr and get:
<cοde>**x = <u>9</u>/<u>7</u>**</cοde>
This is a prοper fractiοn. Tο cοnvert it tο a decimal, we divide the numeratοr by the denοminatοr and get:
x ≈ 1.29
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11. Which fraction has a value that's equal to ½?
O A. 568
O B. 15
O C. 4964
O D. 21/24
Answer: d is the answer
Step-by-step explanation: because if you do your math correctly it comes out to be 21/24
What is the answer of this 7²(4)÷4
If your answer is correct thank you
Answer:
49
Step-by-step explanation:
WHAT DOES PEMDAS STAND FOR?P: Parenthesis
E: Exponent
M: Multiplication
D: Division
A: Addition
S: Subtraction
Start by solving what is inside the parenthesis first:
(4) which is equal to 4Next, solve for the exponent:
7² (which means 7 multiplied by itself twice)
7 x 7 = 49Now you can multiply 49 and 4:
49 × 4 = 196
Finally, divide 196 by 4:
196 ÷ 4 = 49
Therefore, the answer to the expression 7² (4) ÷ 4 is 49.
Question 2: Stony opened a bank account with a particular bank! at the beginning of 2015. The bank pays 8% simple interent on a yearly basis. If Stony's initial is $1575, how much money would be in Stony's account by september of 2020.
There would be $2203.50 in Stony's account by September 2020 using simple interest formula.
As the bank charges an annual 8% simple interest, we may apply the following formula:
Simple interest is calculated as follows: Principle is the initial investment, Rate is the annual interest rate, and Time is the duration in years.
Here, the principal (P) is $1575, the interest rate (r) is 8%, and the time (t) is 5 since we need to know how much money Stony will have in his account by September 2020, which is five years from now.
We may calculate Stony's interest earnings over a five-year period using the simple interest formula:
Interest is calculated as follows: $1575 x 0.08 x 5 = $628.50
Stony's account will therefore have the following balance by September 2020: Total Amount = Principal + Interest = $1575 + $628.50 = $2203.50
Therefore by September 2020, Stony would have $2203.50 in his account.
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what is the meaning of bookkeeping
Answer:
Hope this helps
Step-by-step explanation:
the activity or occupation of keeping records of the financial affairs of a business.
Im not sure which bookkeeping you mean but bookkeeping focuses on recording and organising financial data.
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A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(A, D) if two cards are randomly selected with replacement.
-In
Note that in the above Theoretical Probability prompt, the P(A, D) if two cards are randomly selected with replacement is 2/9. (Option C)
What is Theoretical Probability?
Theoretical probability is a branch of mathematics that deals with predicting the likelihood of events based on mathematical reasoning and assumptions, rather than empirical evidence or observations.
Where it is required to determine the P(A, D) if two cards are randomly selected from cards (A,D,D) with replacement:
P (A) = 1/3
P (D) = 2/3
Thus, P (A, D) = 1/3 * 2/3
= 1/3 × 2/3
= (1×2) / (3×3)
= 2/9
Thus, it is correct to state that the probability, if two cards A, and D are randomly selected with replacement is 2/9. (Option C)
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Write down 2 digit odd numbers and 2 even numbers each
(1) 6 3 odd - and -
1 Even -and -
(2) 4 9 odd - and -
7 Even - and -
Answer:
(1) 63 odd - and - 28 even
(2) 49 odd - and - 76 even
Step-by-step explanation:
At spinet torture middle school, 35% of the classrooms are for sixth graders, if there are 49 sixth grade classrooms, how many classrooms in total?
actually, there are a total of "x" classrooms, which oddly enough is the 100%, and we also know that 35% of that is 49, so
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 49& 35 \end{array} \implies \cfrac{x}{49}~~=~~\cfrac{100}{35} \\\\\\ \cfrac{ x }{ 49 } ~~=~~ \cfrac{ 20 }{ 7 }\implies 7x=980\implies x=\cfrac{980}{7}\implies x=140[/tex]
George is trying to decide where he wants to live after finishing school. He is considering average income, cost of goods and services, and access to education. What is the term or phrase used to describe the factors George is considering?
Term οr phrase used tο describe the factοrs Geοrge is "quality οf life."
What is phrase?In grammar, a phrase—called expressiοn in sοme cοntexts—is a grοup οf wοrds οr singular wοrd acting as a grammatical unit. Fοr instance, the English expressiοn "the very happy squirrel" is a nοun phrase which cοntains the adjective phrase "very happy".
Phrases can cοnsist οf a single wοrd οr a cοmplete sentence. In theοretical linguistics, phrases are οften analysed as units οf syntactic structure such as a cοnstituent. An adjective phrase is a phrase that mοdifies (explains) a nοun.
The term used tο describe the factοrs Geοrge is cοnsidering is "quality οf life."
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f(x)=2x+3/5. Find the inverse.
[tex]f^{-1} (x)=\frac{x}{2} -\frac{3}{10} }.[/tex]
Step-by-step explanation:1. Write the function.[tex]f(x)=2x+\frac{3}{5} \\ \\[/tex]
2. Rewrite "f(x)" as "y".[tex]y=2x+\frac{3}{5} \\ \\[/tex]
3. Switch positions between "y" and "x".[tex]x=2y+\frac{3}{5} \\ \\[/tex]
4. Now solving for x: Subtract "3/5" from both sides of the equation.[tex]x-\frac{3}{5} =2y+\frac{3}{5} -\frac{3}{5} \\\\x-\frac{3}{5} =2y[/tex]
5. Divide both sides by "2".[tex]\frac{x-\frac{3}{5}}{2} =\frac{2y}{2} \\ \\\frac{x-\frac{3}{5}}{2} =y[/tex]
6. Move the terms.[tex]y =\frac{x-\frac{3}{5}}{2}[/tex]
7. Rewrite as 2 independent fracions.[tex]y =\frac{x}{2} -\frac{\frac{3}{5} }{2}[/tex]
8. Solve the fraction division.[tex]y =\frac{x}{2} -\frac{3}{5} }*\frac{1}{2} \\ \\y =\frac{x}{2} -\frac{3*1}{5*2} }\\ \\y =\frac{x}{2} -\frac{3}{10} }[/tex]
9. Express the answer.[tex]f^{-1} (x)=\frac{x}{2} -\frac{3}{10} }[/tex].
-Extra step- 10. Verify the answer.To verify if this is the correct expression for the inverse of the function, simply see if the "x" values and "y" values of the function are inverses as well. For example, a value of x = 2 returns 4.6 on the original function. Therefore, the inverse function should return 2 when a value of x = 4.6 is used. Check the attached image to see this comparison using the table of values of the original function and it's inverse.
Hello and greetings KingDanny2xx.
Therefore, the inverse of f(x)=2x+3/5 is f⁻¹ (x) = x/2 - 3/10.
Step-by-step explanation:[tex]\boldsymbol{\sf{f(x)=2x+\dfrac{3}{5} }}[/tex]
We substitute f(x) for y.
[tex]\boldsymbol{\sf{y=2x+\dfrac{3}{5} }}[/tex]
We interchange x and y.
[tex]\boldsymbol{\sf{x=2y+\dfrac{3}{5} }}[/tex]
We interchange the sides of the equation. We want to swap sides because mathematicians agreed to the convention that the unknown variable in equations and inequalities must always be on the left-hand side.
If there is a variable on both sides, we do it to facilitate a later calculation.
[tex]\boldsymbol{\sf{2y+\dfrac{3}{5}=x }}[/tex]
We multiply both sides of the equation by 5. We want to multiply an equation to get rid of fractions and/or rational expressions, doing a lot more calculations later.
Both sides of the equation must be multiplied by the same value to preserve equality between all sides, according to the Multiplication Property of Equality.
[tex]\boldsymbol{\sf{5\left(2y+\dfrac{3}{5}\right)=5x }}[/tex]
We distribute the 5 to the terms in parentheses. The distributive property is that each term in an expression between parentheses is multiplied by the expression outside the parentheses.
[tex]\boldsymbol{\sf{5x2y+5x\dfrac{3}{5} =5x}}[/tex]
We calculate the product.
[tex]\boldsymbol{\sf{10y+\not{5}x\dfrac{3}{\not{5}}=5x }}[/tex]
We cancel the greatest common divisor 5.
[tex]\boldsymbol{\sf{10y+3=5x}}[/tex]
We move the constant to the right side and change its sign. We want to move a constant to the right because it is customary for constants in equations to be on the right hand side.
The sign of the constant must be changed because in the process of "moving the constant", we are adding its opposite to both sides.
We move the constant to the right by adding its opposite to both sides.
[tex]\boldsymbol{\sf{10y+3-3=5x-3}}[/tex]
Since two opposite numbers add up to 0, we remove them from the expression. The additive inverse property states that two opposite numbers add up to 0.
Since adding or subtracting 0 doesn't change the value of the expression, we can simply remove them.
[tex]\boldsymbol{\sf{10y=5x-3}}[/tex]
We divide both sides of the equation by 10. We want to divide an equation to isolate the unknown variable on one side or to transform the equation in a certain way.
Both sides of the equation must be divided by the same number to preserve equality between the sides, according to the Division Property of Equality.
[tex]\boldsymbol{\sf{10y\div10=(5x-3)\div10}}[/tex]
Any equation divided by itself is equal to 1.
[tex]\boldsymbol{\sf{y=(5x-3)\div10}}[/tex]
We distribute the 10 to the terms in parentheses. The distributive property is that each term of an expression between the parentheses is multiplied by the expression that is outside the parentheses.
[tex]\boldsymbol{\sf{y=5x\div10-3\div10 }}[/tex]
We write the division as a fraction. A fraction is another way of writing division.
One more way to remember it is the division symbol.
÷We notice that the division symbol looks like a fraction where the dots represent the numerator and denominator.
[tex]\boldsymbol{\sf{y=\dfrac{5}{10}x-3\div10 \iff y=\dfrac{\not{5}}{\not{10}}x-\dfrac{3}{10} }}[/tex]
We divide by the common factor 5. The object of canceling a common factor is to rewrite a fraction in the simplest form to facilitate a later calculation.
We can cancel a common factor because it will still represent the same value.
[tex]\boldsymbol{\sf{y=\dfrac{1}{2}x-\dfrac{3}{10} }}[/tex]
Substitute y for f⁻¹ (x). Substitution means to replace one algebraic expression with another or with a specific value.
[tex]\boldsymbol{\sf{f^{-1}(x)=\dfrac{x}{2}-\dfrac{3}{10} }}[/tex]
Therefore, the inverse of f(x)=2x+3/5 is f⁻¹ (x) = x/2 - 3/10.
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Solve the integral equation using the generalized power rule
Answer:
a = 4x with a small 3 at the top ( x with a small 4 at the top + 3x ) with a small 30 + 3
b = B = 6x with a small 17 at the top + 192x with a small 15 at the top + 2520x with a small 13 at the top + 17280x with a small 11 at the top + 64800x with a small 9 at the top + 124416x with a small 7 at the top + 93312 with a small 5 at the top
sorry but I don't know c
Step-by-step explanation:
If 30% of all commuters ride to work in carpools, find the probability that if eight workers are selected, three will ride in carpools.
The probability that out of 8 workers, 3 will ride in carpools is 0.254.
What is probability?
The mathematical concept of probability is used to determine the likelihood of an event. It is solely useful for calculating the probability that an event will occur. From 0 to 1, where 0 represents impossibility and 1 represents a particular occurrence.
We are given that 30% of all commuters ride to work in carpools.
Now, if eight workers are selected, then the probability that three will ride in carpools is determined by using the following
P (X = 3) = [tex]n C_{x} p^{x} (1-p)^{(n-x)}[/tex]
We have n = 8, x = 3 and p = 0.3
So, using the formula, we get
⇒P (X = 3) = [tex]8 C_{3} (0.3)^{3} (1-0.3)^{(8-3)}[/tex]
⇒P (X = 3) = [tex]8 C_{3} (0.3)^{3} (0.7)^{(5)}[/tex]
⇒P (X = 3) = 56 * [tex](0.3)^{3} (0.7)^{(5)}[/tex]
⇒P (X = 3) = 56 * 0.027 * 0.16807
⇒P (X = 3) = 0.254
Hence, the probability that out of 8 workers, 3 will ride in carpools is 0.254.
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Urgenttt! Please help.
What is 1.3333… expressed as a fraction in simplest form? SHOW YOUR WORK.
(Hint: You will use two equations to answer this question. One of them is: x = 1.3)
Step 1: To convert 1.33 repeating into a fraction, begin writing this simple equation:
n = 1.33 (equation 1)
Step 2: Notice that there are 2 digitss in the repeating block (33), so multiply both sides by 1 followed by 2 zeros, i.e., by 100.
100 × n = 133.333 (equation 2)
Step 3: Now subtract equation 1 from equation 2 to cancel the repeating block (or repetend) out.
100 × n = 133.333
1 × n = 1.33
99 × n = 132
132
99
could be the answer, but it still can be put in the simplest form, i.e., reduced.
To simplify this fraction, divide the numerator and denominator by 33 (the GCF - greatest common factor).
n = 132
99
= 132 ÷ 33
99 ÷ 33
= 4
3
. So, 1.33 = 4/3
as the lowest possible fraction.
Please help!! No one answered my last question
Answer:
3 final songs
Step-by-step explanation:
Answer: There will be 3 songs on the final CD.
Step-by-step explanation: The band expects to put 12 songs on their next CD. They write and record 25% more songs than they expect, which means they wrote and recorded 12 + (0.25 x 12) = 15 songs. During the editing process, 80% of the songs are removed. 80% of 15 is (0.80 x 15) = 12 songs. Subtracting the removed songs from the recorded songs, we get 15 - 12 = 3 songs that will be on the final CD. Therefore, there will be 3 songs on the final CD.