Part (a)
A = {prime numbers between 10 and 16}
A = {11, 13}
B = {multiples of 3 between 10 and 16}
B = {12, 15}
A U B = union of set A with set B
A U B = {set of stuff from A or B or both}
A U B = {11, 12, 13, 15}
=================================================
Part (b)
I'm assuming that you meant to write [tex]A \cap B[/tex]
If so, then this is the set of values inside set A and set B at the same time.
Since there is no common overlap between the sets A and B, we say that the answer is the empty set. We write the empty set as a pair of curly braces with nothing inside. Not even zero is a member of the empty set.
[tex]A \cap B = \{ \ \}[/tex]
we could also write the empty set using the symbol [tex]\varnothing[/tex]
So,
[tex]A \cap B = \varnothing[/tex]
=================================================
Part (c)
Answer: FalseReason:
The weird looking E symbol in this context means "is inside" or "is part of"
In other words, a statement like [tex]11 \in B[/tex] translates to "11 is part of set B", which is a false statement. Recall that B = {12, 15}
If we said [tex]11 \in A[/tex], then it would be true since A = {11, 13} which shows 11 as one of the values of set A.
Suppose that kellogg believes that the average weight for a box of frosted flakes is 18 ounces. As part of a quality control effort, they sample 30 boxes and find that the mean of those 30 boxes is 18. 2 ounces. Historical records show that the standard deviation of the filling process is 0. 32 ounces. How likely is it for the sample mean to have been 18. 2 ounces or larger if the actual mean is 18 ounces and the standard deviation of the filling process is 0. 32 ounces? round your answer to four decimal places.
If the actual mean is 18 ounces, there is a 0.0003 chance that the sample mean was 18.2 ounces or more.
Given that 18 ounces are what Kellogg estimates to be the typical weight of a box of Frosted Flaked. The average weight of the 30 cartons they sampled was 18.2 ounces. According to past data, the filling procedure's standard deviation is 0.32 ounces.
Let Y be a box weights random variable.
μ = 18 ounces
SD = 0.32 ounces
The sample size and mean are provided as,
Sample size (n) = 30
Sample mean (y) = 18.2
Y then follows roughly the standard deviation N(μ = 18, SD = 0.32)
Z score appears as:
[tex]z = \frac{\sqrt{n}(y-u)} {SD}[/tex]
where z is a normal standard variable having a mean of 0 and a standard deviation of 1.
Since sample size n is 30 and the standard deviation is given. y follows approximately Normal distribution
If the actual mean is 18 ounces, the likelihood that the sample mean will have been 18.2 ounces or more is given as,
[tex]P[Y \geq 18.2] = P [\frac{\sqrt{n(y - u)} }{SD} \geq \frac{\sqrt{30}(18.2- 18) }{0.32}\\ \\ =P [z\geq \frac{\sqrt{30}* 0.2 }{0.32}]\\ \\= P [z\geq \frac{1.0954}{0.32}]\\ \\=P [z\geq 3.4233]\\\\= 0.0003[/tex]
Therefore, if the actual mean is 18 ounces, there is a 0.0003 chance that the sample mean was 18.2 ounces or more.
To know more about probability, refer to this link:
https://brainly.com/question/12629667
#SPJ9
work out (5 times 10^3) x (9 times 10^7) Give your answer in standard form
The standard form of (5 times 10^3) x (9 times 10^7) is 45x10^10
(5 times 10^3) x (9 times 10^7)
=5x10^3 x 5x10^7
=5x9 x 10^(3+7)
=45x10^10
The answer can also be written in the Decimal Point format,
=4.5x10^11
This answer can be elaborated by using the Product of Powers rule of exponents. In this rule, we add exponents when multiplying powers with the same base.
Exponent = The number of multiplications by itself. It is represented as written above and to the right of a number.
For example:
10^7, where 10 is the base and 7 is an exponent.
Product of Powers rule of Exponents:
a^b x a^c = a^(b+c)
To know more about standard form here
https://brainly.com/question/17264364
#SPJ1
Estimate the quotient of 35 ÷ 0.7.
3.5
5
50
70
Answer:
your answer would be 50.
Step-by-step explanation:
Answer: 3.5
Step-by-step explanation: 0.7 rounds to 10, and 35 divided by 10 is 3.5
The distance between Town A and Town
B on a map is 15.6 cm. If the scale is 1 cm =
12 miles, what is the actual distance
between towns?
Answer:
187.2
Step-by-step explanation:
if the scale is 1:12 then you would need to multiply 12 by the 15.6 which gets you 187.2 miles.
Determine if the given lines are parallel, perpendicular or neither. line a: 6x - 12y = -24 line b: 3y = 2x + 18
Answer: n = 1/2; m = 2/3
Step-by-step explanation:
A ⇒ 12 y = 6x + 24
[tex]y=\frac{n}{2}+2[/tex]
[tex]n=\frac{1}{2}[/tex]
B ⇒ 3y = 2x + 18
[tex]y=\frac{2}{3}n+6[/tex]
[tex]m=\frac{2}{3}[/tex]
∴ Lines are neither because slop diff.
Find the derivative of the following function:
The derivative of the function [tex]f(x) = \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}[/tex] will be given below.
[tex]f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(1.5x^3 + 4x^2 + 2x + 2)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}[/tex]
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decrease.
The equation of the function will be given as,
[tex]f(x) = \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}[/tex]
The derivative of the function will be given as,
[tex]f'(x) = \dfrac{d}{dx} \ \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} \\\\\\f'(x) = \dfrac{2 + 2(x^2 + 1)(0.5x^2 + 2x + 1) \cdot (x + 2) + (0.5x^2 + 2x + 1)^2 \cdot 2x}{2\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} }\\\\\\f'(x) = \dfrac{2 + (0.5x^2 + 2x + 1)[2(x^2 + 1)(x + 2) + (0.5x^2 + 2x + 1) \cdot 2x]}{2\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} }\\[/tex]
Solve the equation further, then we have
[tex]f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)[(x^2 + 1)(x + 2) + (0.5x^2 + 2x + 1) \cdot x}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}\\\\\\f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(x^3 + 2x^2 + x + 2 + 0.5x^3 + 2x^2 + x)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}\\\\\\f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(1.5x^3 + 4x^2 + 2x + 2)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}[/tex]
More about the differentiation link is given below.
https://brainly.com/question/24062595
#SPJ1
Please answer the question in the photo (will mark Brainliest if correct)
Answer:
z = 54
Step-by-step explanation:
The sum of all interior angles in a polygon is given by the formula :
(n-2) × 180 (Where n is the number of sides) .
There are 5 sides so the sum of all interior angles will be :
(5-2) × 180 = 540°
So :
108 + 130 + 140 + 2z + z = 540
Simplify :
378 + 3z = 540
Subtract 378 from both sides :
3z = 540 - 378
3z = 162
Divide both sides by 3 :
z = 162 ÷ 3
z = 54
Hope this helped and have a good day
A given line passes through the points
(
−
2
,
15
)
and
(
6
,
−
5
)
. What is the equation of a line that is perpendicular to the given line that passes through the point
(
5
,
−
5
)
? Write your answer in slope-intercept form.
Answer:
hggssssssssssssssssssss
40 POINTS
The table shows the distance, y, a greyhound dog can travel (in feet) in x seconds.
Time, x (seconds) Distance, y (feet)
0 0
5 220
10 440
15 660
Based on the information in the table, which equation can be used to represent the relationship between time and the distance a greyhound dog can travel?
The equation that can be used to represent the proportional relationship between time and the distance a greyhound dog can travel is:
y = 44x.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality, as follows:
y = kx.
In which k is the constant of proportionality, also representing the rate between the output and the input for any pair of (input, output) except (0,0).
From the table of distances and time given in this problem, the constant is found as follows:
k = 220/5 = 440/10 = 660/15 = 44.
Hence the constant is of 44 and the relation is given by:
y = 44x.
More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
Samuel was preparing for the triathlon. HE did 3 activities every morning:
ran for 30 minutes covering 4.5 miles
swam for 20 minutes,covering 2/3mile
biked for 45 minutes, covering 9 miles
What was Samuels average speed during his morning routine?
Giving brainliest
Samuel's average speed during his morning routine is 24.3 miles per hour.
What is the average speed?
Average speed measures how fast an object or a person is travelling with respect to time. Average speed is the ratio of total distance travelled and total time travelled.
Average speed = total distance / total time
Total distance = 4.5 + 2/3 + 9
= 4.5 + 9 + 0.67 = 14.2 miles
Total time = 30 + 20 + 45 = 95 minutes = 1 hour 35 minutes = 1 7/12 hours = 1.6 hours
Average speed = 14.2 / 1.6 = 24.3 miles per hour
To learn more about average speed, please check: https://brainly.com/question/21734785
#SPJ1
Enter the equation of the parabola passing through the points (3, 9), (30, -9), (0,1).
The equation of the parabola is y=
Equation is y = 2x² + 4x + 1.
What is parabola?A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Given Data
Standard form of quadratic equation
Y = ax² +bx + c
Given points
(3,9), (30,-9). (0,1)
Equating points in formula
9= a(3)² + b(3) + c
9 = 9a + 3b +c
-9 = a(30)² + 3(30) + c
-9 = 900a + 90 + c
1 = a(0)² + b(0) + c
c = 1
Equating c in the equation
9 = 9a + 3b +1
8 = 9a + 3b
-9 = 900a + 90b +1
-10 = 900a + 90b
Multiplying both sides by 100
800 = 900a + 300b
-10 = 900a + 90b
--------------------------
790 = 210b
b = 4 (rounding off)
Putting values of b into equation
8 = 9a + 3(4)
20 = 9a
a = 2 (rounding off)
Equation is y = 2x² + 4x + 1.
To learn more about parabola, visit:
https://brainly.com/question/21685473
#SPJ9
What is 80000*60/70[64+87)/6
Answer: 1725714.28571
Answer:
12080000/7 or 1725714.28571
Step-by-step explanation:
A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
How many people will 10 cups of rice serve?
How many cups of rice are needed to serve 45 people?
A recipe says that 6 spring rolls will serve 3 people. Complete the table
Answer:
1a. 10 cups of dry rice will serve 30 people.
1b. 15 cups of dry rice will serve 45 people.
2. 30 spring rolls = 15 people
40 spring rolls = 20 people
56 spring rolls = 28 people
Step-by-step explanation:
1a. To find a constant, the equation is y/x. When 6 is divided by 2, you get 3 and from there the input increases by 3. So, you multiply 10 by 3 to find how many people it can serve.
1b. To find this answer, you divide 45 by 3 to get 15. So 15 cups will serve 45 people.
2. Any number in the second column is divided by .5 to get the number in the first column. Any number in the first column is multiplied by .5 to get the number in the second column.
I hope that helps :)
Which equation has no solution
4(x+1)=2x+4 or 9-5x+2=4-5x
the answer:
9-5x+2=4-5x
Step-by-step explanation:
as there is -5X in the two sides
Solve for v.
v²-2v-8=0
Answer:
v=4,−2
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
Answer:
[tex]{ \sf{ {v}^{2} - 2v - 8 = 0}} \\ { \sf{(x + 2)(x - 4) = 0}} \\ { \tt{x = - 2 \: \: or \: \: 4}}[/tex]
Write an algebraic expression for the word phrase.
4 less than the product of y and 12
a) 12y + 4
b) 4 − 12y
c) 12y − 4
d) 12y − 4y
Answer:
c
Step-by-step explanation:
the product (multiply ) of y and 12 is 12y and 4 less than 12y is
12y - 4
Answer:
12y - 4.
Step-by-step explanation:
The product is 12y and we subtract 4 from it.
I need help pleaseee
Answer: Degree of Polynomial: 12
Step-by-step explanation:
Use algebra tiles to show the expressions are equivalent.
1) y + 10y and 11y
2) -2(x + 8) and -2x + (-16)
3) x + 2(y - 5x) and 2y - 9x
Hey you man what are you doing here go to there
Each marble bag sold by alan's marble company contains 6 orange marbles for every 5 yellow marbles. if a bag has 40 yellow marbles, how many orange marbles does it contain?
Answer:
48 orange marbles
Step-by-step explanation:
[tex] \frac{6}{5} = \frac{x}{40} [/tex]
[tex]5x = 240[/tex]
[tex]x = 48[/tex]
What is 10+10? I’ll give brainliest
Answer:
Step-by-step explanation:
20
Order the values from least to greatest:
9/4 , 160%, 1.8, 16/5 , 220%, and 2.1
The values from the least to greatest is 160%, 1.8, 2.1, 220%, 16/5 .
In the question ,
it is given that
the values 9/4 , 160%, 1.8, 16/5 , 220%, and 2.1
to arrange the values , we first need to simplify all the values .
(i) the value 9/4 = 2.25
(ii) 160% = 160/100 = 1.60
(iii)the value 1.80
(iv) Simplifying 16/5 , we get 3.20
(v) Simplifying 220% = 220/100 = 2.20
(vi) the value 2.10
the least value is 1.60 which is 160%.
the greatest value is 3.20 which is 16/5 .
Therefore ,the values from the least to greatest is 160%,1.8,2.1,220%,16/5 .
Learn more about Arrangements here
https://brainly.com/question/3844889
#SPJ1
Solve for k.
2k 3k +4
k=
Answer:
incomplete question
Directions: Solve each problem. Show all of your work.
1) Maribel has seven piles of three slices of pizza and seven slices left over. Bruno has four
groups of five slices of pizza and two slices left over. Who has more pizza? Write an
expression. Draw a diagram and then solve.
A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction.
Maribel has :
total slice of pizza left = 3 x7 +7 = 28 slice.
Bruno has :
total slice of pizza left = 4x 5 + 2 = 22 slice.
Since Maribel has More Pizza .
What is a fraction ?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator.Fractions are an important foundation for learning more advanced mathematics. As a student's first introduction to abstraction in mathematics, fractions provide the best introduction to algebra in elementary and middle school.To learn more about : Fraction
Ref : https://brainly.com/question/20323470
#SPJ13
Roxanne claims that all linear equations represent proportional relationships. Which statement explains whether Roxanne is correct?
A Yes, because all linear equations have graphs that are straight lines.
B No, because not all linear equations have graphs that pass through the origin.
C Yes, because all proportional relationships can be expressed as linear equations.
D No, because not all proportional relationships can be expressed as linear equations.
Roxanne claims that all linear equations represent proportional relationships. So, this statement "Yes, because all linear equations have graphs that are straight lines." makes him correct.
When there is a proportionate relationship between two variables, the other variable changes at a consistent pace regardless of how the first variable changes, grows or shrinks. A constant ratio between the two variables can be thought of as the constant rate.
Equations, graphs, and tables that use proportions can be used to show proportional relationships. A broad structure is followed by the proportional relationship equation, which will be taught in this session. Straight lines are used to illustrate the graphs. The tables are sets of numbers that are always paired in the same ratio.
Hence the correct option is A
To know more about Proportional relationship here
https://brainly.com/question/12917806
#SPJ1
PLEASE HELP i only have 20 points...
Answer:
I would say corresponding angles are converse
Step-by-step explanation:
I'm not that sure though, but I'm looking at my notes and it's kind of similar to the fact that it's corresponding
Analyze the definition below and complete the instructions that follow.
A calf is a young cow.
Identify the p and q statements from the given definition.
A.
p: A cow is young ↔ q: A cow is not a calf
B.
p: A young cow is a calf ↔ q: A calf is a cow
C.
p: A cow is a young calf ↔ q: A calf is a young cow
D.
p: A cow is a calf ↔ q: A cow is young
Answer: B
Step-by-step explanation:
Assuming we mean biconditional statements. A biconditional must always be true. B is the only answer choice were both p and q are true. A young cow is a calf, and calfs are cows. Hope this helps!
Which of the following is equivalent to 57x + 19y + 5x?
57x + 24xy
57x + 5x + 19y
57x(19y + 5x)
5x(57x + 19y)
HELP PLS ASAP
Answer:
57x + 5x + 19y by the commutative property for addition.
Please help and thanks!!! :))
Step-by-step explanation:
the same scale factor has to apply to all sides.
we see for the left vertical side that for C it is 3 units long, for D it is 2 units long.
so, the scale factor is
3/2 = 1.5
to go from D to C we have to multiply all lengths by 1.5.
dang this hard, i need some help
Hello!
Part (A)
[tex]\text{Mean} = \dfrac{\text{sum of all salaries}}{\text{number of workers}} =\dfrac{13500 + 27500+13750 + 79000+ 19250 + 29000+21000}{7} \\\\\text{Mean}= 29000 \text{ dollars}[/tex]
Part (B)
==> The mean of other six worker's salary
[tex]\text{Mean}= \dfrac{\text{sum of the 6 worker's salary}}{\text{number of workers} }=\dfrac{13500+27500+13750+19250+29000 + 21000}{6} \\\\ \text{Mean}= \dfrac{124000}{6}=20,666.67 \text{ dollars}[/tex]
Hope that helps!
find the image of the point A(2,3) rotating about the point (0,0) through plus 90 degree
Answer:
3,-2
Step-by-step explanation:
3,-2