Answers
Here, we want to get the set resulting from the given set operations
a) This set is the complement of the intersection of the subsets C and D
The intersection refers to that set that has its members as the elements present in both subsets
The intersection here is;
[tex]\mleft\lbrace8\mright\rbrace[/tex]Now, the complement here are the other elemnts present in the universal set
We have this as;
[tex]\mleft\lbrace1,2,4,7\mright\rbrace[/tex]b) Here, we want to get a union
The complement of set C are the elements that not present in set C but are in the universal set
So, the union here is are the list of elements in both set, without no repetitions
[tex]\begin{gathered} C^{\prime}\text{ = }\mleft\lbrace2,4\mright\rbrace \\ D\text{ = }\mleft\lbrace2,8\mright\rbrace \\ C^{\prime}\text{ U D = }\mleft\lbrace2,4,8\mright\rbrace \end{gathered}[/tex]Related Questions
Help me please, I tried this one but immediately got lost
Answers
Given:
The general equation of a circle is,
[tex]7x^2+7y^2-28x+42y-35=0\text{ ------(1)}[/tex]The standard equation of a circle is given by,
[tex](x-h)^2+(y-k)^2=r^2\text{ ------(2)}[/tex]Here, (h, k) is coordinates of the center of the circle and r is the radius of the circle.
Equation (1) can be converted to the standard form by first dividing equation (1) by 7.
[tex]x^2+y^2-4x+6y-5=0\text{ }[/tex]Grouping the x's and y's in the above equation,
[tex]x^2-4x+y^2+6y=5[/tex]Complete the square of variables x and y by adding constants that create prefect square trinomials.
[tex]\begin{gathered} x^2-4x+4+y^2+6y+9=5+4+9 \\ x^2-2\times x\times2+2^2+y^2+2\times y\times3+3^2=18 \end{gathered}[/tex]Now, factor the perfect square trinomials in each variable.
[tex]\begin{gathered} (x-2_{})^2+(y+3)^2=(\sqrt[]{18})^2 \\ (x-2_{})^2+(y+3)^2=(3\sqrt[]{2})^2 \end{gathered}[/tex]So, the equation of the circle in standard form is,
[tex](x-2_{})^2+(y+3)^2=(3\sqrt[]{2})^2[/tex]Comparing the above equation with the standard form of the equation of a circle given in equation (2), we get
[tex]h=2,\text{ k=-3 and r=3}\sqrt[]{2}[/tex]Therefore, the center of the circle is at the point (2, -3) .
The radius of the circle is,
[tex]3\sqrt[]{2}[/tex]
I need to know the answer to this question please thank you
Answers
GIVEN:
To which number set(s) does the following number belong? 19
Required;
To select any/all correct options.
Step-by-step solution;
The number 19 first of all is a whole number, that is, an integer.
It also categorizes as a natural number, since we can actually identify the number in real life and not only in textbooks. Hence it categorizes too as a counting number.
Therefore, we have the number 19 as a member of the following sets of numbers;
ANSWER:
Real numbers
Integers
Counting or natural numbers
Whole numbers
Rational numbers
Find the Measure of an interior angle of regular hexagon (6 sides polygon).X=Hunt sum=(n-2)180
Answers
it is known that formula for the sum of the interior angles of a polygon is
sum = (n - 2) 180 (given )
here n is the number of side of a polygon
here we have 6 sides in a regular hexagon
so put n = 6
sum = (6 - 2) x 180
sum = 4 x 180 = 720 degrees.
the sum of all 6 interior angles is 720 degrees,
as all the interior angles are equal in a regular hexagon
so the measure of interior angle (x) is
x = 720/6
x = 120 degrees
so each interior angle is 120 degrees.
4. Which expression is equivalent to 9-^2•9^-35. The expression 2^3•4^26. Are (10^-3)^2 and (10^-2)3(NUMBER 4 & 5 & 6)
Answers
Answer
Question 4
Option A is correct.
9⁻⁵
Question 5
Option C is correct.
2⁷
Question 6
Option B is correct.
Yes, both expressions are equal to 10⁻⁶
Question 7
3⁰ + 3⁻² = 1 (1/9) = (10/9)
Explanation
To answer these questions, we will use the laws of indices.
- When a variable carries a power and is raised to an extra power, the answer is the variable carrying the product of these two powers.
- When a variable is raised to the power of a negative number, this is the same as 1 over that variable raised to the positive value of that power
- When the same variable, carrying different powers are multiplied with each other, then, the result is that same variable raised to the power of the sum of the two powers from before multiplication.
- When any number or variable is raised to the power of 0, the answer is 1.
Question 4
[tex]9^{-2}.9^{-3}=9^{-2}\times9^{-3}=9^{-2+(-3)}=9^{-2-3}=9^{-5}[/tex]Question 5
[tex]\begin{gathered} 2^3.4^2 \\ \text{But} \\ 4^2=(2^2)^2=2^{2\times2}=2^4 \\ 2^3.4^2=2^3\times2^4=2^{3+4}=2^7 \end{gathered}[/tex]Question 6
To know the answer to this, we will solve the two expressions
[tex]\begin{gathered} (10^{-3})^2=10^{-3\times2}=10^{-6} \\ (10^{-2})^3=10^{-2\times3}=10^{-6} \end{gathered}[/tex]We can see that both expressions are equal to 10⁻⁶
Question 7
3⁰ + 3⁻²
3⁰ = 1
3⁻² = (1/3²) = (1/9)
3⁰ + 3⁻² = 1 + (1/9) = 1 (1/9) = (10/9)
Hope this Helps!!!
find the area of the triangle show below.
Answers
Finding Area of Triangle.
[tex]\text{Area of a Triangle }=\frac{1}{2}bh[/tex]Where b = base = 16.7 inches , h = height = 22 inches
Substituting these values into the formula above, we get,
[tex]\begin{gathered} \text{Area=}\frac{1}{2}\times16.7\times22 \\ \text{Area}=16.7\times11=183.7inches^2 \end{gathered}[/tex]Hence, the correct answer is Area = 183.7 square inches
Consider the graph of F shown in the figure below
Answers
Given: the graph is given.
Find: average rate of change.
Explanation: average rate of change is equals to
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]here ,
[tex]x_1=2\text{ , y}_1=3\text{ , x}_2=6\text{ and y}_2=5[/tex][tex]\frac{y_2-y_1}{x_2-x_1}=\frac{5-3}{6-2}=\frac{2}{4}=0.5[/tex]Final answer: the required answer is 0.5
need answer with steps[tex] \sqrt{ - 81} [/tex][tex] \sqrt{ - 50} [/tex]
Answers
Gy, this is the solution to # 11 and # 12:
Let's recall that √-1 = i
11. √-81
√-1 * 81 (-1 * 81= -81)
9√-1
9i
12. √-50
√-2 * 25 (-2 * 25 = -50)
5√-2
5i√2
jake says that there should be a decimal point in the quotient 142.45 ÷7.4=1925 after the 2.which equation shows the best estimate for the quotient. a. 150÷10=15b. 140÷10=14c. 150÷5=30d. 140÷7=20part buse the drop down menus to explain whether jake is correct.jake correct because 192.5 close to the estimate. the decimal point belongs after the
Answers
We want to divide
142.45 ÷ 7.4
In order to find the best stimate, we round both numbers.
We have that 142.45 can be rounded to 140 or 150, since it is nearer to 140, then we round:
142.45 ≅ 140
Since 7.4 is near to 7, we can approximate it
7.4 ≅ 7
Then
142.45 ÷ 7.4 ≅ 140 ÷ 7
Since 140 ÷ 7 = 20, then
Answer- D
Part BWe have then, that the result for
142.45 ÷ 7.4
must be near to 20 (as we concluded on Part A).
142.45 ÷ 7.4 ≅ 20
Then, if we have 1925, then, the way of placing the decimal point that makes it nearer to 20 is
19.25
Jake says that it is 192.5 but it is farer from 20 than 19.25
Answer- Jake is not correct because 192.5 is far from the stimate. The decimal point belongs after the 9: 19.25
(-3x^2 - 9x + 5) - (-2^2 - 4x + 7)
Answers
In subtracting expressions, we can only apply addition and subtraction to like terms.
Which of the following systems of equations is an example of one where Substitution is the best method?A) {2x−8y=18 {−3x+7y=−27 B) {x=−4 {y=5 C) {y=23x +5 {2x−6y=−42 D) { 3x + 5y = 21 {- 2x+ 7y = 17
Answers
Solution:
The substitution method is best used when one of the equations is in terms of one of the variables.
From the system of equations given, the one where substitution is the best method is;
This is because the first equation is already in terms of the variable y.
Elisa won 57 lollipops playing basketball at the school fair. She gave two to every student in her math class. She has at least 7 lollipops left.
Answers
Let:
L(x) = remaining lollipops
x = Number of students in her math class
Part A
[tex]57-2x\ge L(x)[/tex]Since she has at least 7 lollipos left:
[tex]\begin{gathered} L(x)=7 \\ 57-2x\ge7 \end{gathered}[/tex]Part B
[tex]\begin{gathered} 57-2x\ge7 \\ \text{Solving for x:} \\ \text{Subtract 57 from both sides:} \\ 57-2x-57\ge7-57 \\ -2x\ge-50 \\ \text{Divide both sides by -2:} \\ -\frac{2x}{-2}\ge-\frac{50}{2} \\ x\le25 \end{gathered}[/tex]
Part C
[tex]\begin{gathered} 57-2x\ge7 \\ \text{ Since } \\ x\le25 \\ 57-2(25)\ge7 \\ 57-50\ge7 \\ 7\ge7 \end{gathered}[/tex]
Therefore the maximum number of students Elisa has in her class is 25.
The histogram below gives the ages of the children attending a summer science activity at the library. Children attending Frequency 5 7 Age.1. How many 6 years old are attending?2. How many children are attending the summer science activities?
Answers
The histogram show the number of children with age 5 to 8 years old that will attend the summer science activity.
Each bar represents the number of children of a certain age that will attend the science activities.
The frequency bar, shown on the left, indicates the number of children.
In the bottom is indicated the age of the children.
So the first bar indicates the number of 5 years old children that will attend the summer science activities. According to the histogram, 1 child with age 5 years old will attend the activities.
The second bar indicates the number of 6 years old children that will attend the summer science activities. The number of 6 years old children attending is 5
The third bar represents the number of 7 years old children attending. The histogram indicates that there are 6 7years old children attending.
The fourth bar represents the number of 8 years old children attending. There are 2 8years old children attending.
To determine the total number of children you have to add the observed frequencies for each age:
[tex]1+5+6+2=14[/tex]So 5 six years old children will attend the summer science activities and the total of children attending is 14.
You have to determine how many children are "at least" 7 years old.
This means that you have to determine how many children have 7 years or more.
In this sample, there are children that have 7 years old and 8 years old that meet the condition of being "at least" 7 years old. So you have to add the number of kids with ages 7 and 8:
[tex]6+2=8[/tex]8 children are at least 7 years old
The function c (x) = .5x + 70 represent the cost c(in dollars) of renting a truck from a moving company where x is the number of miles you drive the truck
Answers
For the given function c(x) = 0.5x +70 where c is the cost of renting a truck and x is the number of miles drive by truck , then domain and range of the function in inequalities are domain is x ≥ 0 and range is
y ≥70.
Graph is attached.
As given in the question,
Given function :
c(x) = 0.5x +70
where c is the cost of renting a truck and x is the number of miles drive by truck.
Graph of the function is attached.
c(x) represented on y-axis.
Values for the graph of the function c(x) = 0.5x +70 is,
x= 0
⇒ c(0) = 0.5(0) +70
⇒c(0) = 70
x =1
⇒ c(1) = 0.5(1) +70
⇒c(1) = 70.5
x=2
⇒ c(2) = 0.5(2) +70
⇒c(2) = 71
.... and so on.
Domain is x = 0,1,2,3,...
Range is c(x) = 70 , 70.5, 71, ....
In inequalities form:
Domain x ≥ 0
Range c(x) ≥ 70
Therefore, for the given function c(x) = 0.5x +70 where c is the cost of renting a truck and x is the number of miles drive by truck , then domain and range of the function in inequalities are domain is x ≥ 0 and range is y ≥70.
Graph is attached.
The complete question is :
The function c(x) = 0.5x+70 represents the cost c (in dollars) of renting a truck from a moving company, where x is the number of miles you drive the truck.
a. Graph the function and identify its domain and range. Write your answers as inequalities.
Learn more about function here
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6 in 10.9 in 6 in 5.1 in 18 in P= 40.9
Answers
The perimeter of the given trapezium is the sum of the side lengths of the trapezium.
Hence, the perimeter P is,
[tex]P=18+10.9+6+6=40.9\text{ in}[/tex]Therefore, the perimeter P of the given trapezium is 40.9 in.
Given, the altitude of the trapezium, h=5.1 in.
The length of parallel sides,
a=6 in.
b=18 in.
The area A of the trapezium is,
[tex]\begin{gathered} A=\frac{1}{2}\times sum\text{ of parallel sides}\times altitude \\ =\frac{1}{2}\times(a+b)\times h \\ =\frac{1}{2}\times(6+18)\times5.1 \\ =61.2\text{ sq.in.} \end{gathered}[/tex]Therefore, area A of the trapezium is 61.2 sq.in.
Simplify. eln 2x Enter just a standard polynomial in x
Answers
something we need to know in order to simplify this equation is when we have an exponential and a natural logarithm in the way we have in the question, they cancel themselves so the simplification for this equation is
[tex]e^{\ln \text{ 2x}}=\text{ 2x}[/tex]The length of the longer leg of a right triangle is 13 cm more than three times the length of the shorter leg. The length ofthe hypotenuse is 14 cm more than three times the length of the shorter leg. Find the side lengths of the triangle.
Answers
To answer this question we draw a diagram to help us:
In this diagram we let x be the length of the shorter leg, then we use the information given. Now using the pythagorean theorem we get the equation:
[tex](3x+14)^2=(3x+13)^2+x^2[/tex]Solving for x we have:
[tex]\begin{gathered} (3x+14)^2=(3x+13)^2+x^2 \\ 9x^2+84x+196=9x^2+78x+169+x^2 \\ x^2+78x+169-84x-196=0 \\ x^2-6x-27=0 \\ (x-9)(x+3)=0 \\ \text{then} \\ x=9 \\ or \\ x=-3 \end{gathered}[/tex]Since x is a lenght and lengths can't be negative we conclude that x=9. Once we know the value of x we plug it on the expression for the larger leg and the hypotenuse.
For the larger leg we have:
[tex]3(9)+13=40[/tex]For the hypotenuse we have:
[tex]3(9)+14=41[/tex]Therefore we conclude that:
Small leg is 9
Large leg is 40
Hypotenuse is 41
ASSIGNMENTSCOURSESAssignment 5. Conditional ProbabilityAct 1 of 3SECTION 2014Two number cubes are rolled for two separate events:Event A is the event that the sum of numbers on both cubes is less than 10.Event B is the event that the sum of numbers on both cubes is a multiple of 3Complete the conditional-probability formula for event B given that event A occurs first by writing A and B in the blepoza10NEXT QUESTIONASK FOR HELPTURNI
Answers
The total number for the sample space for two cubes rolled is 36
1,1; 1,2....; 1,6
2,1; 2,2..; 2,6
. .
. .
6,1; 6,2...; 6,6
Event A (less than 10; 1 - 9)
(1,1); (1,2); (1,3); (1,4); (1,5); (1,6)
(2,1); (2,2); (2,3); (2,4); (2,5); (2,6)
(3,1); (3,2); (3,3); (3,4); (3,5); (3,6)
(4,1); (4,2); (4,3); (4,4); (4,5)
(5,1); (5,2); (5,3); (5,4)
(6,1); (6,2); (6,3)
The sample space has 30 elements
[tex]Pr\text{ (<10) = }\frac{30}{36}\text{ = }\frac{5}{6}[/tex]P (A) = 0.83
Event B (sum of numbers on both cubes is a multiple of 3)
Event A already happened, we have Event B as:
(1,2); (1,5)
(2,1); (2,4)
(3,3); (3,6)
(4,2); (4,5)
(5,1); (5,4)
(6,3)
The sample space has 11 elements
[tex]Pr\text{ (multiple of 3) = }\frac{11}{30}\text{ = 0.367}[/tex]P (B|A) = 0.37
The figure below is a net for a triangular pyramid.6.06 ft-----------7 ftIf all the triangles are equilateral, what is the surface area ofthe pyramid, in square feet?
Answers
Given the net of a triangular pyramid:
As shown: all the triangles are equilateral triangles
The length of the side of the triangle = 7 ft
The height of the triangle = 6.06 ft
so, the area of one triangle =
[tex]\frac{1}{2}\cdot\text{base}\cdot\text{height}=\frac{1}{2}\cdot7\cdot6.06=21.21ft^2[/tex]The pyramid consists of 4 triangles
So, the surface area =
[tex]4\cdot21.21=84.84ft^2[/tex]so, the answer will be A = 84.84 ft^2
8) Order the numbers from greatest to least"10 points-17. TheTT- 2✓n-√7.-2, zTI V822-V7,-2Option 1Option 2TI V8-17,-2.22π V82.2.-2, – 7OOption 3Option 4
Answers
You have the values.
First I'll express the values as decimal numbers
[tex]-\sqrt{7}\cong-2.64[/tex][tex]\frac{\sqrt{8}}{2}\cong1.41[/tex][tex]\frac{\pi}{2}\cong\frac{3.14}{2}\cong1.57[/tex][tex]-2[/tex]The negative square root of 7 is less than -2.
And the square root of 8 divided two is less than pi divided by two.
The correct order is:
[tex]-\sqrt{7},-2,\frac{\sqrt{8}}{2},\frac{\pi}{2}[/tex]Option 1
Two sides of triangle measures 15 inches and 18 inches which of these is not apossible length for third side of the triangle
Answers
To determine the possible lenghts of the thir
Gasoline sells for 1.5 euros/liter in Bonn. What is the price in U.S. dollars per gallon? (1gal=3.785L)
Answers
1) Gathering the data
1.5 Euros / liter
2) Let's first convert the currency
Since it's in Germany, Foreign per Dollar
1 US$ = 0.9449
3) Converting Metric to Customary unit
1 gallon ----- 3.785 l
y ------------------ 1 l
y= 1/3.785 1 liter = 0.26 gallon
4)
1.5 euros ----------- 1 liter
x 0.26
x =
which expression is equivalent to -9(3y + 5) - 3y
Answers
There are many expressions that are equivalent to the given expression. Nevertheless, we can find a fully simplified equivalent expression by using the properties of real numbers.
Starting with the given expression:
[tex]-9(3y+5)-3y[/tex]Use the distributive property to expand the parenthesis:
[tex]\begin{gathered} -9(3y+5)-3y=-9(3y)-9(5)-3y \\ =-27y-45-3y \end{gathered}[/tex]Then, combine like terms -27y and -3y by adding their coefficients:
[tex]-27y-45-3y=-30y-45[/tex]Therefore, the given expression is equivalent to:
[tex]-30y-45[/tex]Suppose that an individual has a body fat percentage of 19.7% and weighs 167 pounds. How many pounds of her weight is made up of fat? Round your answerto the nearest tenth
Answers
Answer:
32.9 pounds of her weight is made up of fat.
Step-by-step explanation:
This question can be solved using a rule of three.
Her weight is of 167 pounds, which is 100% = 1. How much is 19.7% = 0.197?
167 pounds - 1
x pounds - 0.197
Applying cross multiplication
x = 167*0.197 = 32.9
32.9 pounds of her weight is made up of fat.
Find the GCF of 6 and 20
Answers
The factor of 6 = 3,2,6,1
and factor of 20 = 2,5,10,4, 1
GCF : The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.
2 is the largest common factor of 6 and 20
Answer : 2
In many epidemics, the cumulative number of cases grows exponentially, at least over a limited time. A recent example is the spread of the Influenza A (HIN1) virus, commonly called thwhich affected Mexico and the United States especially. On April 24, 2009, there were seven cumulative cases of swine flu in the United States reported to the World Health Organization.next two weeks, the cumulative number of cases in theUnited States increased by about 40% each day. If this growth rate had continued, what would have been the cumulative numberthe United States reported 20 days after April 24? (Round your answer to the nearest whole number.)cases
Answers
If the growth is exponential, it follows the formula:
P=Po*
5. Nicole is decorating a rectangular dining table for a party. The length of the table is 8 feet and the width is 6 feet. Nicole put a ribbon diagonally across the table. What is the length of theribbon, in feet?
Answers
From the problem, we have a rectangular table :
with dimensions 8 feet by 6 feet.
The diagonal is the hypotenuse of the formed triangles.
Using pythagorean theorem :
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, a and b are the measurements of two other sides.
That will be :
[tex]\begin{gathered} c^2=6^2+8^2 \\ c^2=36+64 \\ c^2=100 \\ c=\sqrt[]{100} \\ c=10 \end{gathered}[/tex]ANSWER :
10 feet
rewrite the equation in Ax +By=C use intergers for A,B,and C y+3=-4(x+5)
Answers
We will investigate how to represent an equation given in a general form given:
[tex]y\text{ + 3 = -4}\cdot(x\text{ + 5 )}[/tex]To represent the above equation in the required form:
[tex]Ax\text{ + By = C}[/tex]We will manipulate the terms of the given form by performing basic algebraic operators. We will start off with solving the parenthesis ( ) on the right hand side of the " = " sign:
[tex]y\text{ + 3 = -4x - 20}[/tex]We will then put all the variable terms involving " x and y" on left hand side of the " = " sign and cosntants on the other side:
[tex]\begin{gathered} y\text{ + 4x = -20 - 3} \\ 4x\text{ + y = -23} \end{gathered}[/tex]The equation is expressed in the required form above with the values of integers:
[tex]\begin{gathered} A\text{ = }4\text{ } \\ B\text{ = 1} \\ C\text{ = -23} \end{gathered}[/tex]The human body needs about 50 grams of protein daily. A hamburger contains about 20 grams of protein. What percent of the daily needs is the protein in the hamburger?
Answers
To answer this question, we can proceed as follows:
1. We have that the total of protein the human body needs daily is 50 grams.
2. A hamburger contains about 20 grams of protein.
Then, to find the asked percent, we can proceed as follows:
[tex]\begin{gathered} \frac{20}{50}\cdot100\%=\frac{2}{5}\cdot100\%=\frac{2\cdot100\%}{5}=2\cdot\frac{100\%}{5}=2\cdot20\%=40\% \\ \end{gathered}[/tex]Therefore, the hamburger has 40% of the protein we need daily.
You are dealt one card from a standard 52 card deck. Find the probability of being dealt a card greater than 3 and less than 7.
Answers
Given:
Total card = 52
Delta a card greater than 3 and less than 7.
Find-:
The probability of being dealt a card greater than 3 and less than 7.
Explanation-:
The probability formula is:
[tex]P(A)=\frac{\text{ Number of favourable outcome}}{\text{ Total number of favourable outcomes}}[/tex]The total number of favourable outcomes is 52.
The favourable outcome is:
Delta card greater than 3 and less than 7.
[tex]\text{ Total card }=3[/tex]So, the probability is:
[tex]P(A)=\frac{3}{52}[/tex]Then the probability is 3/5
Simplify -12qr^2+13rq^2