By using the concept of set operation, the result obtained is
[tex]n(A \cap B) = 2[/tex]
What is a set?
Set is a well defined collection of distinct objects. The members of a set are called elements of a set. Set can be empty as well as non empty.
Set can be finite as well as infinite.
The number of elements inside a set is known as cardinal number of the set
Operations on set are union, intersection, set difference and symmetric difference
Concept of set operation has been used here
n(A)=5 n(B)=7 and n(AUB)= 10
[tex]n(A \cap B) = n(A) + n(B) - n(A \cup B)[/tex]
[tex]n (A \cap B) = 5 + 7 -10\\n(A \cap B ) =2[/tex]
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Translate (in terms of x) then solve the algebraic equation:
Nine is subtracted from twice some number and the result is the sum of the number
and 7.
The Algebraic Equation is correct
What is Algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.
Two times a certain quantity
When a number is divided by two, ten is subtracted: 2x-9
The equal sign is a result.
The number and its sum equals 7+x.
Put everything together (except for the first 2x, that was used to find the second part).
2x-9=7+x
Get all of your like terms on the same side first. Because dealing with a negative variable can result in an additional step at the end, I personally dislike dealing with them. As a result, I'll take the n on the right and shift it to the 2x on the left.
2x-9=7+x
x-9=7
The -9 must now be positioned on the other side of the equal sign.
x = 7 + 9
x=16
Connect the 16 to the original equation to make sure you're doing it correctly.
2(16)-9=7+(16)
32-9=7+16
23=23
It is accurate.
Hence, The algebraic equation is correct
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explain the error
rational numbers
3.4
integers
-1.2
whole numbers
-2 3
Answer: -2 isn’t a whole number and -1.2 isn’t a integer.
Use Figure 1 to evaluate each trigonometric function of angle A . The side adjacent to angle A has length 4 and the side opposite angle A has length 10.
The trigonometric ratios for angle A are measured below.
What is triangle?
A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a right angled triangle as shown in the image attached.
The six trigonometric ratios are -
sin (A) = 10/√116
cos (A) = 4/√116
tan (A) = 10/4
cosec (A) = √116/10
sec (A) = √116/4
cot (A) = 4/10
Therefore, the trigonometric ratios for angle A are measured above.
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Calculate the simple interest and maturity value.
Note: Do not round intermediate calculations. Round your answers to the nearest cent.
S
Principal
19,500
Interest rate
6 1/2 %
Time
20 month
Simple interest
< Prev
C
a
2 of 14
Maturity value
Next >
DELL
The simple interest is 2112.5 and the maturity value is 21,612.5
In the given question,
We have to find the simple interest and maturity value.
The given principal amount (P)= 19,500
The interest rate (r)= 6 1/2%
We write the interest in improper fraction. We can write it as 6 multiple with 2 then adding the result of multiplication with 1.
So the simplest form (r)=13/2%
Time = 20 months.
Now converting the months into years.
As we know that in one year have 12 months.
So the Time = 20/12
Time (T)= 5/3
The formula of simple interest is
I = P*R*T/100
Now putting the value
I = 19,500*(13/2)*(5/3)/100
Simplifying
I = 19,500*13*5/100*2*3
I = 1,267,500/600
I = 2112.5
Hence, the simple interest is 2112.5.
Now finding the maturity value(MV).
MV=P+I
MV=19,500+2112.5
MV=21,612.5
Hence, the maturity value is 21,612.5
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Two car owners are in need of car repairs. Elise will need to pay the mechanic $1 per
minute for labor, plus $350 to cover the cost of new parts. Kayla will need to pay $200
for parts and $2 per minute for labor. Depending on how long each repair takes, the
two jobs might end up costing the same amount ?
Answer:
yes, if the labor takes 150 minutes (or 2h 30 minutes)
Step-by-step explanation:
m + 350 = 2m + 200
2m - m = 350 - 200
m = 150
Use the given equivalents, along with dimensional analysis, to convert the given unit to the unit indicated.
65 lb to g
The conversion of the measurement of 65 lb will be 29483.5 g.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
In this case, we need to convert 65 lb to g
It should be noted that we have to multiply the weight value by 453.5
Therefore, it should be noted that 65 lb will be:
= 65 x 453.5
= 29483.5 g.
Therefore, it should be noted that the conversion of the measurement of 65 lb will be 29483.5 g.
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(7x-7)
63°
(3x +45)
(9-4)
Find x and y
The value of x is 33 and y is 39.
What is parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.As, (7x- 7) = 3x+ 45 (corresponding angles)
4x = 52
x= 13
Now, 7x- 7 + w + 63 = 180 (linear pair)
w= 180- 147
w= 33 degree.
y-6 = 33 (Alternate interior angle)
y= 39
Hence, the value of x is 33 and y is 39.
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HOME Realty claims that it can sell a detached, residential house faster than any other realty company. With the aim of examining HOME's claim, you sample 20 customers who sold a detached, residential house through HOME and record the selling times (in days) of the houses. Your data are summarized below:
Selling Time Frequency
0 10 3
10 20 4
20 30 6
30 40 4
40 50 3
Find the proportion of selling times in the sample that are less than 20 days claims that it can sell a detached, residential house faster than any other realty company.
The proportion of selling times is 0.35
From the question, we have
Selling Time___ Frequency
0 10____________3
10 20__________ 4
20 30__________ 6
30 40__________ 4
40 50__________ 3
Proportion of selling times in sample above that are less than 20 days :
total frequency = (3 + 4 + 6 + 4 + 3) = 20
Selling time which is less Than 20 days :
(0 - 10) = 3
(10 - 20) = 4
Total = (3 + 4) = 7
Proportion = selling time less Than 20 days / total frequency
= 7 / 20
= 0.35
Addition:
The phrase "the addition" refers to combining two or more numbers. Adding two numbers is indicated by the plus sign (+), therefore adding three is written as three plus three. Additionally, the number of times the plus symbol (+) is used is up to you. For example, 3 + 3 + 3 + 3. Mathematical addition is a crucial component of the learning curriculum for kids. In primary school, students learn simple addition sums such as one-digit facts, Math addition sums, and double-digit Math addition sums. One of the most fundamental and interesting Math concepts for elementary school children is addition sums. Math is a fascinating subject, and children first learn basic mathematical concepts like adding numbers in their early years.
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Match each number with its divisibility numbers.
3. 60
4. 48
5. 81
A. 3,9
B. 2,3
C.
2, 3, 5, 10
The numbers matched with its divisibility numbers is
for 60 the divisibility numbers are 2,3,5,10 .
for 48 the divisibility numbers are 2,3 and
for 81 the divisibility numbers are 3,9 .
In the question ,
three numbers are given as 60 , 48 and 81
we need to match them with their , respective divisibility numbers that are given in the option
For the first number 60 ,
we see that 60 is divisible by 2 , 3 , 5 and 10 because
30*2 [tex]=[/tex] 60 , 3*20 [tex]=[/tex] 60 , 5*12 [tex]=[/tex] 60 and 10*6 [tex]=[/tex]60 ,
So, for 60 the divisibility numbers are 2,3,5,10
that is option(c)
For the second number 48 ,
we see that 48 is divisible by 2 and 3 because
2*24 [tex]=[/tex] 48 , 3*16 [tex]=[/tex] 48 ,
So , for 48 the divisibility numbers are 2,3
that is option(b)
For the third number 81
we see that 81 is divisible by 3 and 9 because
3*27 [tex]=[/tex] 81 , 9*9 [tex]=[/tex] 81
So , for 81 the divisibility numbers are 3 an 9
that is option(a)
Therefore , The numbers matched with its divisibility numbers is
for 60 the divisibility numbers are 2,3,5,10 .
for 48 the divisibility numbers are 2,3 and
for 81 the divisibility numbers are 3,9 .
The given question is incomplete , the complete question is
Match the numbers 60 , 48 and 81 with its divisibility numbers
(a) 3,9
(b) 2,3
(c) 2,3,5,10
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Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.
What property did Bill use?
The addition property used by Bill in finding the actual December temperature is the commutative property of addition.
According to the question,
We have the following information:
Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.
We know that are five properties of addition: closure property, commutative property, associative property, additive identity property of addition and additive inverse property.
The commutative property of addition means that if two numbers are added and their order is inversed then the result of addition will always be the same.
For example, we get -2 by adding -5+3 and 3+(-5). The change in order of digits does not affect the final result.
Hence, the addition property used by Bill in finding the actual December temperature is the commutative property of addition.
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(−3,y) and (x,2).
y=4x+6
orderd pair
for questions 4-6: The table below shows
e average price of a gallon of gasoline.
Year
2000
2004
2010
2012
2015
Price
2.02
2.32
3.02
3.64
2.45
4. Find the rate of change from 2004 to 2010.
5. Find the rate of change from 2000 to 2012.
6. Find the rate of change from 2012 to 2015
Answer:6/13/3
Step-by-step explanation:look at how the year’s difference are
Use the graph of the following function (x) to find the value.
f(1)
From the graph of the given function , the value of f(1) = -1.
As given in the question,
From the graph of the given function,
Two coordinates from the graph are as follow:
( x₁ , y₁) = (1, -1)
( x₂ , y₂ ) = ( 0, -3 )
Equation of the line representing the function is given by:
(y - y₁) /(x-x₁) = ( y₂ -y₁)/ (x₂ -x₁)
⇒(y +1)/ (x-1) = (-3 +1)/ (0-1)
⇒ (y +1)/ (x-1) = 2
⇒y +1 = 2x -2
⇒ y = 2x -3
To get the value of x we have,
y = f(x)
⇒f(x) = 2x -3
⇒f(1) = 2(1) -3
⇒f(1) = -1
Therefore, from the graph of the given function , the value of f(1) = -1.
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16 2/3-15 1/6+1.3/2.5x1.56x0.4
HELP ASAP
Answer:
Step-by-step explanation:
The answer would be 1.82448
A director of reservations believes that 9% of the ticketed passengers are no-shows. If the director is right, what is the probability that the proportion of no-shows in a sample of 789 ticketed passengers would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of no-shows in a sample of 789 ticketed passengers would differ from the population proportion by less than 3% is 0.9968
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 9% = 0.09
sample size, n = 789
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.09(1 - 0.09)) / 789}
= √{(0.09 * 0.91) / 789}
= 0.0102
The probability
differ from the population proportion by less than 3%
|X - 0.09| < 0.03
X < 0.12 OR X > 0.06
0.06 < X < 0.12
P(z < 0.12) - P(z < 0.06 )
z score for z < 0.06
z = (0.06 - 0.09) / 0.0102
= -2.9412
p value for z < -2.9412 = 0.0016
z score for z < 0.12
z = (0.12 - 0.09) / 0.0102
= 2.9412
p value for z < 2.9412 = 0.9984
The probability required = 0.9984 - 0.0016 = 0.9968
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Rewrite polynomial in standard form
The standard form of polynomial is x^2 + 9x - 1/10
To write the equation in standard form, look at the degree of highest term and then rewrite the equation in decreasing order of degree i.e. from highest to lowest.
The given polynomial is
⇒ x^2 + 9x - 1/10
The standard form of the polynomial is
⇒ x^2 + 9x - 1/10
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The green basilisk enclosure will include a rectangular pond in one corner. The width of the
pond will be 3 inches less than the width, w, of the enclosure.
W-3
The area of the water's surface is given by this expression: w² - w - 6.
Question
Question 1
Factor the area expression, w² - w - 6.
Replace the values of A and B to write the expression in factored form.
(w - A) (w + B)
After factorization we get the two terms ( w - 3 ) ( w + 2 )
And the values of A and B as 3 and 2 respectively .
That is A = 3 and B = 2.
The given expression is w² - w - 6.
This question can be calculated easily by middle term split
First step is to multiply the first and the last term
which will give us - 6
thus now we have to look for two number which when either added or subtracted will give us - 1
Thus we can write it as :
w² - 3 w + 2 w - 6
Now take the terms which are common
and we will get
w ( w - 3 ) + 2 ( w - 3 )
( w - 3 ) ( w + 2 )
Thus if we compare it with (w - A) (w + B)
we will get the values of A and B as
3 and 2 respectively .
That is A = 3 and B = 2
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What is an equation of a line, in point-slope form, that passes through (1, -7) and has a slope of -2/3?
O y-7= -2/3( x + 1)
Oy+7= -2/3(x - 1)
Oy+7=2/3(x + 1)
O y-7=2/3(x-1)
Answer:
second option
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{2}{3}[/tex] and (a, b ) = (1, - 7 ) , then
y - (- 7) = - [tex]\frac{2}{3}[/tex] (x - 1) , that is
y + 7 = - [tex]\frac{2}{3}[/tex] (x - 1)
Select all possible solutions to the equation (x - 5)² - 6 = 0.
The two possible solutions of the given quadratic equation are -
x = +√6 +5 and x = -√6 +5
What is defined as the solution of equation?Finding the value that a variable expresses is the process of solving an equation. The solution of the equation is the value that was discovered. The collection of all values which, when substituted for unknowns, cause an equation to hold true is known as the solution. Two fundamental algebraic rules using the additive property as well as the multiplicative property are utilised to determine the solutions for equations having an unique unknown raised to a power of one.For the given question;
(x - 5)² - 6 = 0
Bring constant on other side.
(x - 5)² = 6
Taking square root both side.
√ (x - 5)² = √6
(x - 5) = ±√6
Separate the constant and variables.
x = ±√6 +5
There are two possible solution.
x = +√6 +5 and x = -√6 +5
Thus, the two possible solutions of the given quadratic equation are -
x = +√6 +5 and x = -√6 +5.
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You pick a card at random.
5678
What is P(not divisor of 45)?
Write your answer as a percentage.
%
As a percentage, a card at random 5, 6, 7, 8 9, 7.5, 6.42, 5.62. Per cent is derived from the Latin adverbial phrase per centum, which means "by the hundred." The Latin phrase made its way into English in the 16th century.
What is meant by percentage?A percentage is a number or ratio that is expressed as a fraction of one hundred. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct.," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement. Percentage = (Original number/Another number) x 100 is the formula for calculating the percentage of one number from another. A percentage is a value or ratio that represents a fraction of 100 in mathematics. Percentage means one hundred percent. There are no units in it. A percentage is a number that tells us how much out of 100 we are talking about, and it can also be written as a decimal or a fraction - three for the price of one.Therefore,
45/5 = 9
45/6 = 7.5
45/7 = 6.42
45/8 = 5.62
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how much is 1191 less than 1111
Answer: If you mean how much is 1111 less than 1191, then your answer is
80.
Step-by-step explanation: 1191 - 1111 = 80.
Question 5 (1 point), You are making your friend a triangular fabric decoration for their home. It has ripped so you need to go buy new fabric. The fabric you are buying is $3 per square foot. Using the dimensions below, how much money do you need to buy enough fabric?
Answer:
1). True
2). x = 16.4 m^2
3). A = 24, h = 4
4). A = 18.39
5). 162
Step-by-step explanation:
I took this quiz on K12 and got everything correct! Brainliest welcome! :)
A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the high-quality version is 4.5 MB. Yesterday, there were 1450 downloads of the song, for a total download size of 5629 MB. How many downloads of the standard version were there?
The number of downloads that were standard version were 560 songs.
How many downloads of the standard version were there?The first step is to form a system of equations:
2.9s + 4.5h = 5629 equation 1
s + h = 1450 equation 2
Where:
s = number of standard songs downloaded h = number of high quality songs downloadedMultiply equation 2 by 4.5:
4.5s + 4.5h = 6525 equation 3
Subtract equation 3 from equation 1:
896 = 1.6s
Divide both sides of the equation by 1.6:
s = 560
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A shoe store is offering a series of markdowns for its customers due to its need for quick cash. The shoe store is offering the markdowns in the following order: 35%, 20%, and 10%. What would be the sale price of a pair of boots, if it originally costs $165.00?
The final price of the shoes after successive discounts is $77.22.
What is a discount?
A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.
Main Body:
Sale price = Original price - discount
The formula for successive discount is given by=
Cost price*(1 - discount₁/100)*(1 - discount₂/100)*(1 - discount₃/100)
Now calculating:
According to the question , Cost price = $165
sale price = 165*(1-0.35)*(1-0.20)*(1-0.10)
= 165*0.65*0.8*0.9
= $77.22
Hence the answer to sale price of the shoe would be $77.22
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Two buses leave a station at the same time and travel in opposite directions. On bus travels 17 km/h faster than the other. If the two buses are 836 kilometers apart after 4 hours, what is the rate of each bus
Step-by-step explanation:
speed = distance / time
to get distance, we have to multiply by time.
the speed the 2 busses are moving seat from each other is
x + (x + 17) = 2x + 17
x = the speed of one bus
x + 17 = the speed of the other bus.
so, after 4 hours the distance between them is
(2x + 17) × 4 = 836
2x + 17 = 209
2x = 192
x = 96 km/h
bus 1 travels at 96 km/h.
bus 2 travels at 96+17 = 113 km/h.
6th grade problem i need help
Answer:
Step-by-step explanation:
1. First multiply to get the number of hours for 5 painters.
5*21= 105 minutes for 5 painters.
2. Divide by 7 for hours taken for the 7 painters!
105/7=15
3. Answer=15 hours
26% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive.
Answer:
a) p(X =2) = 0.261
b) P(x>2) = 0.566
c) P(2<x<5) = 0.334
Step-by-step explanation:
Given 24% of U.S. adults say they are more likely to make purchases during a sales tax holiday
Probability 0f U.S. adults say they are more likely to make purchases during a sales tax holiday (p) = 0.24
n = 10
By using Poisson distribution
mean number of make purchases during a sales tax holiday
λ = np = 10 X 0.24 = 2.4
a)
The probability of getting exactly '2'
The probability
b) The probability of getting more than '2'
= 0.090 + 0.2177+0.261 = 0.566
P(x>2) = 0.566
c) The probability of getting between two and five
P( 2<x<5) = P(x=3)+p(x=4) =P(2<x<5) = 0.2090 + 0.125 = 0.334
hope this helps
Which of the following equations does the graph below represent?
A. 3x + 7y = 21
B. -3x + 7y = 21
C. x + 7y = 21
D. -3x + y = 21
Answer:
B
Step-by-step explanation:
if x = 0 ; y = 3
if x = -7 ; y = 0
A 0 + 7(3) = 21
0 + 21 = 21
21 = 21 (ok)
3(-7) + 0 = 21
-21 = 21 (false)
B
0 + 21 = 21
21 = 21 (ok)
(-3)(-7) + 0 = 21
21 = 21 (ok)
PLEASE HELP Use the substitution method to solve the sysytem of linear equations. Enter your answer as an ordered pair. There are four different question with these equations
1. Y=2x+5 X=1
2. Y=2x+1 Y=6x-1
3. Y=2(x-7) X+y=4
4. 3x-y=6 X+3y=12
The solutions to these system of equations are given as follows:
1. x = 1, y = 7.
2. x = 0.5, y = 2.
3. x = 6, y = -2.
4. x = 3, y = 3.
What is a system of equations?A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of a problem.
For item 1, it is already stated that the solution for x is x = 1, hence the solution for y is obtained as follows:
y = 2(1) + 5 = 7.
For item 2, we are given two equations for y, hence the solution for x is obtained as follows:
2x + 1 = 6x - 1
4x = 2
x = 2/4
x = 0.5.
Hence the solution for y is:
y = 2(0.5) + 1 = 1 + 1 = 2.
For item 3, from the second equation, we have that:
y = 4 - x.
Then the solution for x will be of:
2(x - 7) = 4 - x
2x - 14 = 4 - x
3x = 18
x = 18/3
x = 6.
The solution for y is:
y = 4 - 6 = -2.
For item 4, from the first equation, we have that:
y = 3x - 6.
Then, replacing on the second equation, the solution for x is obtained as follows:
x + 3(3x - 6) = 12
x + 9x - 18 = 12
10x = 30
x = 3.
Then the solution for y is:
y = 3x - 6 = 3(3) - 6 = 9 - 6 = 3.
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Willy is an avid fisherman of the world. As he travels, he goes fishing 2 times on every mainland Country he visits and goes fishing 5 times on every Island he visits.
As far as he remembers, Willy went fishing 65 times in the total of the 25 unique Countries and Islands he visited.
How many Countries and Islands did Willy visit? (Where and represent the countries and islands)
The number of mainland countries is 20 and the number of island countries is 5 countries that Willy visited.
How to calculate the value?Let the number of mainland be represented by m
Let the number of island be represented by x.
This will be illustrated as:.
m + x = 25 .... i
2m + 5x = 65 .... ii
From equation i, m = 25 - x.
Put this into equation ii
2m + 5x = 65
2(25 - x) + 5x = 65
50 - 2x + 5x = 65
3x = 65 - 50
3x = 15
Divide
x = 15 / 3
x = 5
Island countries = 5
Since m + x = 25
m = 25 - 5 = 20
Mainland countries = 20
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