Answers
DEFINITIONS
The union of two sets contains all the elements contained in either set (or both sets). The union is notated A ⋃ B.
The intersection of two sets contains only the elements that are in both sets. The intersection is notated A ⋂ B.
Using a Venn Diagram, the union and intersection of two sets can be seen below:
GIVEN
The sets are given to be:
[tex]\begin{gathered} S=\mleft\lbrace1,2,3,\ldots,18,19,20\mright\rbrace \\ A=\mleft\lbrace3,4,8,9,11,13,14,15,20\mright\rbrace \\ B=\mleft\lbrace4,7,13,14,16,18,19\mright\rbrace \end{gathered}[/tex]QUESTION
1) (A ∪ B): The terms of the two sets contained in either set or the two sets are
[tex](A\cup B)=\mleft\lbrace3,4,7,8,9,11,13,14,15,16,18,19,20\mright\rbrace[/tex]2) (A ∩ B): The elements that are in both sets are
[tex](A\cap B)=\mleft\lbrace4,13,14\mright\rbrace[/tex]
Related Questions
X) *11.4.14 Find the volume of the cylinder in terms of it and to the nearest tenth. 2 in 1 in The volume in terms of it is V= in3
Answers
We can calculate the volume of the cylinder as the product of the area of the base and the height of the cylinder.
[tex]V=A_b\cdot h[/tex]The area of the base is equal to:
[tex]A_b=\pi r^2=\pi\cdot2^2=4\pi[/tex]Then, the volume becomes:
[tex]V=A_b\cdot h=4\pi\cdot1=4\pi\approx12.6\text{ in}^3[/tex]Answer:
The volume in function of π is V = 4π in^3.
The volume rounded to the nearest tenth is 12.6 in^3.
A reflection across which line(s) carries the trapezoid onto itself?
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If we reflect about x =2, it is a mirror image on each side ( left and right). There is no other line where we can have a mirror image on each side.
Ronda ate 2/5 of the pie. Connor ate .375 of the pie. How much did they eatcombined? (Express your answer either as a fraction or decimal)
Answers
To convert 2/5 to a decimal;
[tex]undefined[/tex]Rick buys a $4,500 stove with an installment plan that requires 12% down. How much
is the down payment?
O $540
O $375
O $250
O $125
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Answer: 540
Step-by-step explanation: 12% of 4500 is 540
I’ve already done this problem, but I’m being told it’s wrong and I need to simplify but I don’t know how to do it with this question.
Answers
Permutation/combination In how many ways can five people line up to get on a bus? (Hint: all 5 people are lining up)
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We have to calculate in how many ways can five people line up to get on a bus.
This is a permutation of 5 in 5 without repetition, so it can be calculated as:
[tex]P(5,5)=5!=120[/tex]Answer: in 120 ways.
what is a unit rate for meter per second if a car travels 274 m in 17 seconds
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The rate is 274m/17s = 16.1176m/s
160 is what percent of the sum of 100 and 120 and 160
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42.105%
1) Let's first add thosse numbers up: 100 +120+160 =380
2) Now we can write out the following ratio, to find out what percentage is equivalent to 160 out of that 380:
[tex]\begin{gathered} 160----x \\ 380----100 \\ \frac{160}{380}=\frac{x}{100} \\ 380x=16000 \\ \frac{380x}{380}=\frac{16000}{380} \\ x=42.105\% \end{gathered}[/tex]Note that we had to cross multiply that.
3) Hence, the answer is 160 is approximately 42.105% of 380
I’ve been trying to figure out how to solve this and was wondering how to do this correctly!
Answers
SOLUTION
To solve this we will use the form for exponential growth to determine the formula to use.
Exponential growth has the form
[tex]\begin{gathered} P=P_0e^{rt} \\ P=\text{population after timer t} \\ P_0=\text{ initial population growth } \\ r=\text{ percent growth rate} \end{gathered}[/tex]Now the frogs tripple in population after 9 days. Initially they were 21. So in 9 days they become
[tex]21\times3=63\text{ frogs }[/tex]Applying the formula, we have
[tex]\begin{gathered} P=P_0e^{rt} \\ 63=21e^{9r} \\ 3=e^{9r} \\ \text{taking ln of both sides } \\ \ln 3=\ln e^{9r} \\ \ln 3=9r \\ r=\frac{\ln3}{9} \end{gathered}[/tex]The time for the frogs to get to 290 becomes
[tex]undefined[/tex]there are 14 square and 18 rectangles. what is the simplest ratio of squares to rectangles?
Answers
The simplest ratio of squares to rectangles can be obtained as follows:
There are 14 squares and 18 rectangles. The ratio of squares to rectangles is:
[tex]\frac{14}{18}=\frac{7}{9}[/tex]Then, the simplest ratio is 7/9 because 7 is a prime number and the ratio cannot be simplified any more. To obtain 7/9 we divided the numerator by 2 and the denominator also by 2.
There are 39 chocolates In a box call identically sheet dear 16 off filled with nuts 13 with caramel and 10 are solid chocolate you randomly select one piece eat it and then select a second piece find the probability of selecting to solid in a row
Answers
The probability of selecting two solid chocolates in a row is 0.0607 .
In the question ,
it is given that
there are total 39 chocolates in the box .
number of chocolates filled with nuts = 16
number of chocolates filled with caramel = 13
number of chocolates filled with solid = 10
Probability of selecting first chocolate as a solid is 10/39.
Now , there are 38 chocolates , with 9 solid chocolates ,
hence the probability of selecting second chocolate as a nut is = 9/38
So, the probability of selecting two solid chocolates in a row = 10/39×9/38
= 90/1482
= 0.0607
Therefore , the probability of selecting two solid chocolates in a row is 0.0607 .
The given question is incomplete , the complete question is
There are 39 chocolates in a box, all identically shaped. There 16 are filled with nuts, 13 with caramel, and 10 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row.
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What is the greatest common factor of 9 and 72?
Answers
The Greatest Common Factor of 9 and 72 is: 9
SOLUTION
Problem Statement
The question asks us to find the greatest common factor of 9 and 72.
Method
In order to solve this question, we just need to follow these steps:
1. Write out the prime factors of 9 and 72
2. Choose the common factors from both expressions.
3. Multiply the common factors.
Implementation
1. Write out the prime factors of 9 and 72:
[tex]\begin{gathered} 9=1\times3\times3 \\ \text{The common factors of 9 are: 3 and 3} \\ \\ 72=1\times2\times2\times2\times3\times3 \\ \text{Common factors of 72 are: 1,2, 2, 2 and 3, 3} \end{gathered}[/tex]2. Choose the common factors from both expressions.:
We need to examine the two expressions for 9 and 72 above. Choose the common values.
[tex]\begin{gathered} 3\times3\text{ is common to both 9 and 72} \\ i\mathrm{}e\text{.} \\ 9\text{ is common to both 9 and 72} \\ 3\text{ is common to both 9 and 72 as well} \\ 1\text{ is also common to both 9 and 72} \end{gathered}[/tex]3. Multiply the common factors.:
[tex]\begin{gathered} \text{Thus, choosing the greatest values from 1,3 and 9.} \\ \therefore\text{The Greatest Common Factor = 9} \end{gathered}[/tex]Final Answer:
The Greatest Common Factor of 9 and 72 is: 9
3 A free diver can dive at a rate of -0.75 meters per second. About how long would it take to reach a depth of -145 meters?
Answers
Answer:193.33s or 3.2 mins
Step-by-step explanation:
Here the diver dives at -0.75 constant velocity. So we can use the formula s = vt
from there we can find out the time when s = -145 m and v = -0.75m/s
Laverne created a painting with an area of 72 square inches and a length of 9 inches. They create a second painting with an area of 56 square inches. It has the same width as the first painting. What is the length of the second painting?
Answers
Answer: 7
Step-by-step explanation:
As our first step, we can divide 72 by 9 to discover the width of the first AND second painting. 72÷9=8
Now that we have discovered the width of the second painting, we will now solve the mathematical expression 56÷8.
Because 56 divided by 8 equals 7, the length of the second painting is 7 inches.
The graph shows the projections in total enrollment at degree granting institutions from Fall 2003 to Fall2012The linear model, y= 0.2145x + 15.79, provides the approximate enrollment, in millions, between the years 2003 and 2012, where x = 0 corresponds to 2003, x = 1to 2004, and so on, and y is in millions of students.(a) Use the model to determine projected enrollment for Fall 2008.The projected enrollment for Fall 2008 is millions.(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
In order to find the projected enrollment for 2008, we need to use the value of x equal to 5, because x represents the number of years after 2003.
Then, using the linear model with x = 5, we have:
[tex]\begin{gathered} y=0.2145\cdot5+15.79\\ \\ y=1.0725+15.79\\ \\ y=16.8625 \end{gathered}[/tex]Rounding to the nearest tenth, we have y = 16.9.
9) The temperature outside feels like - 3°C on Thursday. When the temperature is taken, it is actually 16°C. Howmany degrees lower does the temperature feel?
Answers
The temperature feels
[tex]16-(-3)=19[/tex]degrees lower from the actual.
Sean johnson 1. The angles of a triangle are described as follows: angle A is the largest angle: its measure is twice the measure of angle B. The measure of angle C is 2 less than half the measure of angle B. Find the measures of the three angles in degrees.
Answers
Explanation
Let
angle A is the largest angle
[tex]m\measuredangle A=m\measuredangle A[/tex]its measure is twice the measure of angle B,( in other words you have to multiply angle b by 2, to get angle A)
[tex]2(m\measuredangle B)=m\measuredangle A[/tex]Factor the expression. 12y + 14
Answers
Answer:
2(6y+7)
Explanation:
To factor the expression:
[tex]12y+14[/tex]First, find the greatest whole number that divides 12 and 14.
The number = 2, therefore:
[tex]\begin{gathered} 12y+14=2\mleft(\frac{12y}{2}+\frac{14}{2}\mright) \\ =2(6y+7) \end{gathered}[/tex]Four more than three times a number, is less than 30. Which of the following is not a solution?61278
Answers
Solution
- To solve the question, we simply need to interpret the question line by line.
- Let the number be x.
- "Four more than three times a number" can be written as:
[tex]\begin{gathered} \text{ Three times a number is: }3x \\ \text{ For more than three times a number becomes: }4+3x \end{gathered}[/tex]- "Four more than three times a number is less than 30" can be written as:
[tex]4+3x<30[/tex]- Now, we can proceed to solve the inequality and find the appropriate range of x. This is done below:
[tex]\begin{gathered} 4+3x<30 \\ \text{ Subtract 4 from both sides} \\ 3x<30-4 \\ 3x<26 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}<\frac{26}{3} \\ \\ \therefore x<8\frac{2}{3} \end{gathered}[/tex]- This means that all correct solutions to the inequality lie below 8.666...
- This further implies that any number greater than this is not part of the solutions of the inequality.
- 12 is greater than 8.666
Final Answer
The answer is 12
Robin is saving money to buy a 720$ phone. she has 105$ saved, and each week she adds 30$ to her savings. write an equation to find the number of weeks (w) until she has enough savings to buy the phone.
Answers
Let call w the number of weeks she has been saving.
Then, we can write the expression for her saving in function of the number of weeks as:
[tex]S(w)=105+30\cdot w[/tex]We now have to find the number of weeks it will take for her savings to reach $720.
We can find it by calculating w for S(w)=720:
[tex]\begin{gathered} S(w)-105+30w=720 \\ 105+30w=720 \\ 30w=720-105 \\ 30w=615 \\ w=\frac{615}{30} \\ w=20.5\approx21 \end{gathered}[/tex]Answer: it will take her 21 weeks to have enough savings.
7 singles, 13 fives, 4 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
Answers
So,
The probability to obtain one bill of the four, is 1/4.
So, the expected value is:
[tex]\begin{gathered} \frac{1}{4}(7)+\frac{1}{4}(13)+\frac{1}{4}(4)+\frac{1}{4}(3) \\ \\ =6.75 \end{gathered}[/tex]Therefore, the fair price to play this game is 6.75.
A buoy oscillates in simple harmonic motion as waves go past. At a given time it is noted that the buoy moves a total of 3.9 feet from its low point to its high point, and that it returns to its high point every 16 seconds
Answers
Concept
What is a simple harmonic motion ?Repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side. The time interval of each complete vibration is the same
a) y= 1.95ftcos(π/2)
b) v(t)= -0.76sin(π/5t)
Part aSince the buoy oscillates in simple harmonic motion the equation to model this is given by: y= A cos(ωt+θ)
For this case from the info given we know that:
2A= 3.9 , A= 3.9/2= 1.95ft
It returns to its high point every 16 seconds. That means period = 16 , and the angular frequency can be founded like this:
ω=2π/16
= π/8
Assuming that the value for the phase is (θ=0°) our model equation is given by
y= 1.95ftcos(π/2)
Part bFrom definition we can obtain the velocity with the derivate of the position function and if w calculate the derivate we got this,
dy/dt= v(t)= -1.95ft(π/8)sin(π/8t)
v(t)= -0.76sin(π/8t)
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It goes from -1 to 1 on the x axis.
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ANSWER :
EXPLANATION :
determine whether the given by binomial is a factor of the polynomial p(x) . If so, find the remaining factors of p(x).
Answers
The given binomial is a factor of the polynomial p(x) with remaining factors of (x + 1)(x - 1).
What is termed as the factors of polynomial?Factorisation is the process of determining the factors of a given value as well as mathematical expression. Factors are integers which are multiplied together to create the original number.For the given question.
The polynomial is given as; x³ + 2x² -x - 2.
The binomial is given as; (x +2).
The, to get the remainder, divide the polynomial with the binomial.
= (x³ + 2x² - x - 2)/ (x +2)
Taking x² common from the first two terms of the numerator and (-1) from the last two terms.
= x²(x + 2) - (x + 2)/ (x +2)
Taking (x + 2) common from two terms.
= (x + 2)(x² - 1)/(x + 2)
Cancel (x + 2) from both.
= (x² - 1)
Now use the identity to open the square.
(a² + b² ) = (a + b) (a - b)
= (x + 1)(x - 1).
Thus, the given binomial is a factor of the polynomial p(x) with remaining factors of (x + 1)(x - 1).
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The correct question is-
Determine whether the given binomial is a factor of the polynomial p(x).
If so, find the remaining factors of p(x).
p(x) = x³ + 2x² -x - 2 ; (x +2)
Answer:
a
Step-by-step explanation:
Real numbersA stock lost 8 and 3/8 on Monday, 1 and 5/8 points on Tuesday. On Wednesday, it gained 13 points. What was the net gain or loss of the stocks for these three days?
Answers
Answer: The net gain was 3 stocks for these three days.
Explanation
Given
• Monday: lost 8 and 3/8.
,• Tuesday: lost 1 and 5/8 points.
,• Wednesday: gained 13 points.
Procedure
To calculate the net gain, we have to add all the values we are giving, considering that the stock lost will have a negative sign:
[tex]\text{Net gain}=Gains-losses[/tex]0. Calculating the losses
We have to mixed numbers, for which we can add the whole numbers and the fractions separately.
• Whole numbers
[tex]-8-1=-9[/tex]• Fractions
[tex]-\frac{3}{8}-\frac{5}{8}=-\frac{8}{8}=-1[/tex]At last, we add both results and we get the losses:
[tex]losses=-9-1=-10[/tex]2. Calculating the gains
As we only have one quantity, there is no need for calculations:
[tex]Gains=13[/tex]3. Calculating net gain
Finally, we put both quantities in the formula:
[tex]\text{Net gain}=13-10=3[/tex]I really need help solving thisIt’s from my trig prep bookIt asks to answer (a) and (b)
Answers
The sum in summation notation is:
[tex]\sum ^4_{r\mathop{=}0}(-1)^r(4Crx^{4-r}y^r)[/tex]The expansion is:
[tex]81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12}[/tex]Explanation:Given the expression:
[tex](3x^5-\frac{1}{9}x^3)^4[/tex]In summation notation, this can be written as:
[tex]\sum ^4_{r\mathop=0}(-1)^r(4Crx^{4-r}y^r)[/tex]The simplified terms of the expression is:
[tex]\begin{gathered} 4C0(3x^5)^{\mleft\{4-0\mright\}}(\frac{1}{9}y^3)^0-4C1(3x^5)^{\mleft\{4-1\mright\}}(\frac{1}{9}y^3)^1+4C2(3x^5)^{\mleft\{4-2\mright\}}(\frac{1}{9}y^3)^2-4C3(3x^5)^{\mleft\{4-3\mright\}}(\frac{1}{9}y^3)^3+4C4(3x^5)^{\mleft\{4-4\mright\}}(\frac{1}{9}y^3)^4 \\ \\ =(3x^5)^4-4(3x^5)^3(\frac{1}{9}y^3)+6(3x^5)^2(\frac{1}{9}y^3)^2-4(3x^5)^{}(\frac{1}{9}y^3)^3+(\frac{1}{9}y^3)^4 \\ \\ =81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12} \end{gathered}[/tex]Four friends had dinner at a restaurant. The bill was $45.40, and they added a 20% tip. The 4 friends shared the total cost equally. How much money did each person pay?
Answers
Answer:
$13.62
Step-by-step explanation:
To find the tip of 20%, multiply 45.40 by 0.20, and you get 54.48.
Now, since there are 4 friends, divide the amount by 4.
54.48/4=13.62
So each person would pay $13.62.
Hope this helps! :D
The area (in square inches) of a rectangle is given by the polynomial function A(b)=b^2 +9b+18. If the width of the rectangle is (b+3) inches what is the length?
Answers
As given by the question
There are given that area of rectangle and width of a rectangle
[tex]\begin{gathered} \text{Area}=A(b)=b^2+9b+18 \\ \text{Width}=(b+3) \end{gathered}[/tex]Now,
From the formula of area of a rectangle:
[tex]\text{Area}=\text{length}\times width[/tex]Then,
Put the value of an area and width into the above formula
So,
[tex]\begin{gathered} \text{Area}=\text{length}\times width \\ b^2+9b+18=length\times(b+3) \end{gathered}[/tex]Then,
[tex]\begin{gathered} b^2+9b+18=length\times(b+3) \\ (b+3)(b+6)=\text{length}\times(b+3) \\ \text{length}=\frac{(b+3)(b+6)}{(b+3)} \\ \text{length}=(b+6) \end{gathered}[/tex]Hence, the value of length is ( b + 6 ).
I need help to know how to solve graphing a system of inequalities2x - 3y > -12x + y ≥ -2
Answers
Answer
2x - 3y > -12 (in red ink)
x + y ≥ -2 (in black ink)
The solution region is the region that the two shaded regions have in common.
Explanation
When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.
If the inequality sign is (< or >), then the line drawn will be a broken line.
If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.
Step 1
For this question, we easily see that the first inequality will have a broken line and the second one will have an unbroken line.
To plot each of the lines, we will use intercepts to obtain the coordinates of two points on each line
Recall, we will first plot the lines like they are equations of a straight line.
To plot the graph
2x - 3y = -12
when x = 0,
2(0) - 3y = -12
-3y = -12
Divide both sides by -3
(-3y/-3) = (-12/-3)
y = 4
First point on the line is (0, 4)
when y = 0
2x - 3(0) = -12
2x = -12
Divide both sides by 2
(2x/2) = (-12/2)
x = -6
Second point on the line is (-6, 0)
For the second line,
To plot the graph,
x + y = -2
when x = 0
0 + y = -2
y = -2
First point on the line is (0, -2)
when y = 0
x + 0 = -2
x = -2
Second point on the line is (-2, 0)
So, for the plotting, we connect the two points for each of the lines.
Step 2
The shaded region now depends on whether the inequality sign is facing y or not.
If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.
If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.
2x - 3y > -12
Can be rewritten as
-3y > -2x - 12
Divide through by -3 (this changes the inequality sign)
y < (2x/3) + 4
Here, we see that the inequality sign is not facing y, hence the numbers below the broken line plotted are the shaded region (in red ink)
x + y ≥ -2
We can rewrite this as
y ≥ -x - 2
Here, we see that the the inequality sign is facing y, hence, the numbers above the unbroken line plotted are the shaded region (in black ink)
The graph of this system of inequalities is presented above under 'Answer'
Hope this Helps!!!
Andy spent 1/3 of his money on pastries and 3/4 of his remaining money on 2 pies. Each pie costs 6 times as much as each pastry. if all pastries cost the same how many did he buy
Answers
This means he originally had enough money to buy 4 pies or 24 pastries
1/3 of his money would buy 8 pastries