The correct option is (B) yes because all the elements of set R are in set A.
What is an element?In mathematics, an element (or member) of a set is any of the distinct things that belong to that set.Given sets:
U = {x | x is a real number}A = {x | x is an odd integer}R = {x | x = 3, 7, 11, 27}So,
A = 1, 3, 5, 7, 9, 11... are the elements of set A.R ⊂ A can be understood as R being a subset of A, i.e. all of R's elements can be found in A.Because all of the elements of R are odd integers and can be found in A, R ⊂ A is TRUE.Therefore, the correct option is (B) yes because all the elements of set R are in set A.
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The complete question is given below:
Consider the sets below. U = {x | x is a real number} A = {x | x is an odd integer} R = {x | x = 3, 7, 11, 27} Is R ⊂ A?
(A) yes, because all the elements of set A are in set R
(B) yes, because all the elements of set R are in set A
(C) no because each element in set A is not represented in set R
(D) no, because each element in set R is not represented in set A
1
2. Rotate Rectangle ABCD 90° counterclockwise.
Then, translate it along the vector (3,4).
A
D
B
C
-4 -2
4
2
АУ
O
-2.
-4
2
4
X
A'(
B'(
C'(
D'(
A"(
B"(
C"(
D"(
)
)
)
)
HELP ME PLS
Rotating 90 degrees counterclockwise: [tex](x,y) \longrightarrow (-y,x)[/tex]
[tex]A(-4,4) \longrightarrow A'(-4, -4)\\\\B(-3, 4) \longrightarrow B'(-4, -3)\\\\C(-3, 1) \longrightarrow C'(-1, -3)\\\\D(-4, 1) \longrightarrow D'(-1, -4)[/tex]
Translate along [tex]\langle 3, 4 \rangle[/tex]: [tex](x,y) \longrightarrow (x+3, y+4)[/tex]
[tex]A'(-4, -4) \longrightarrow A''(-1, 0)\\\\B'(-4, -3) \longrightarrow B''(-1, 1)\\\\C'(-1, -3) \longrightarrow C''(2, 1)\\\\D'(-1, -4) \longrightarrow D''(2, 0)[/tex]
Can someone PLEASE ANSWER BOTH THESE QUESTIONS!!!!!!!!
Answer:
52º, 128º
Step-by-step explanation:
8. Because ∠6 is an opposite angle to ∠5, ∠6=∠5=52º;
9. Because line a//line b, ∠6=∠4=52º, so ∠7=180º–52º=128º
Hello and Good Morning/Afternoon
Let's take this problem step-by-step:
What does this problem give us:
a || b ⇒ a is parallel to bc ⇒ is a transversalm∠5 ⇒ 52°What does this problem want us to find:
measure of ∠6measure of ∠7Let's solve:
∠6⇒ by the vertical angle theorem is equal in measure to ∠5
⇒ ∠6 = 52°
∠7⇒ lines a and b are parallel
⇒ the corresponding angles on both lines formed by the
transversal are equal
i.e. m∠2 = m∠3, m∠7 = m∠8
⇒ ∠8 is on a straight line with ∠6
[tex]\hookrightarrow angle8 +angle6 = 180\\\hookrightarrow angle8 + 52 = 180\\\hookrightarrow angle8 =128[/tex]
⇒ since m∠8 is equal to m∠7
⇒ m∠7 = 128
Definitions
Vertical Angle Theorem: two opposite angles formed by intersecting lines are equalAnswer:
∠6 = 52°∠7 = 128°Hope that helps!
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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x 3y=108
For given f(x, y) the extremum: (12, 24) which is the minimum.
For given question,
We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108
We use the constraint to build the constraint function,
g(x, y) = 3x + 3y
We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:
[tex]f_x=8x[/tex]
[tex]f_y=4y[/tex]
[tex]g_x=3[/tex]
[tex]g_y=3[/tex]
Setting up the Lagrange multiplier equations:
[tex]f_x=\lambda g_x[/tex]
⇒ 8x = 3λ .....................(1)
[tex]f_y=\lambda g_y[/tex]
⇒ 4y = 3λ ......................(2)
constraint: 3x + 3y = 108 .......................(3)
Taking (1) / (2), (assuming λ ≠ 0)
⇒ 8x/4y = 1
⇒ 2x = y
Substitute this value of y in equation (3),
⇒ 3x + 3y = 108
⇒ 3x + 3(2x) = 108
⇒ 3x + 6x = 108
⇒ 9x = 108
⇒ x = 12
⇒ y = 2 × 12
⇒ y = 24
So, the saddle point (critical point) is (12, 24)
Now we find the value of f(12, 24)
⇒ f(12, 24) = 4(12)² + 2(24)²
⇒ f(12, 24) = 576 + 1152
⇒ f(12, 24) = 1728 ................(1)
Consider point (18,18)
At this point the value of function f(x, y) is,
⇒ f(18, 18) = 4(18)² + 2(18)²
⇒ f(18, 18) = 1296 + 648
⇒ f(18, 18) = 1944 ..............(2)
From (1) and (2),
1728 < 1944
This means, given extremum (12, 24) is minimum.
Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.
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the mean change after 5 days is -0.01 inch what is the change on the fifth day? days: -0.05, 0.09, -0.04, and -0.08
Answer:
.06
Step-by-step explanation:
add all the 4 values listed, plus the .06
divide by 5
you get -.01
:)
One number is 4 more than another and their sum is 60.
If x = the larger number and y = the smaller number, then which of the following is the value of the smaller number?
28
26
32
The smaller number is 28.
Answer:
Solution Given:
let the smaller number be a.
and larger number be a+4.
By question
a+(a+4)=60
a+a+4=60
2a=60-4
2a=56
a=[tex] \frac{56}{2} [/tex]
a=28
Answer:
y = 28
Step-by-step explanation:
Given variables:
x = the larger numbery = the smaller numberCreate two equations with the given information.
Equation 1
If one number is 4 more than another, then:
⇒ x = y + 4
(Remembering that x is the larger number and y is the smaller number).
Equation 2
If their sum is 60, then:
⇒ x + y = 60
Substitute Equation 1 into Equation 2 and solve for y:
⇒ (y + 4) + y = 60
⇒ 2y + 4 = 60
⇒ 2y + 4 -4 = 60 - 4
⇒ 2y ÷ 2 = 56 ÷ 2
⇒ y = 28
Therefore, the value of the smaller number (y) is 28.
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PLEASE HELP IM STUCK
Answer:
Step-by-step explanation:
As per the same approach I answered in a similar problem:
The slope is the Rise/Run between the two points. The change in y for every change in x. Take the two points and calculate theRise/Run:
RISE = (-11 - 9) = -20
RUN = (3 - (-2)) = 5
Rise/Run, or slope, is = -20/5 or -4
I graphed this line and the two points (attached).
Answer:
-20/5 or -4
Step-by-step explanation:
Answer:
Step-by-step explanation:
As per the same approach I answered in a similar problem:
The slope is the Rise/Run between the two points. The change in y for every change in x. Take the two points and calculate theRise/Run:
RISE = (-11 - 9) = -20
RUN = (3 - (-2)) = 5
Rise/Run, or slope, is = -20/5 or -4
LOTS OF POINTS!!!! look at pic
Answer:
2x+6-(x^2+6x+9)*pi
Step-by-step explanation:
2*(x+3) - (x+3)^2*pi
2x+6-(x^2+6x+9)*pi
um I think there are answer choices so I don't know if I have to keep going but that should be right
K
Consider a study conducted in 2018 to estimate the percentage of people from a certain region who do not use the
Internet. Complete parts (a) through (c) below.
a. If a 99% confidence level is used, how many people should be included in the survey if the researchers wanted to
have a margin of error of 7%?
There should be people included in the survey.
(Round up to the nearest person as needed.)
rred
The number of people who must be included in the survey, that is, the sample size should be 340.
We assume the sample size to be n.
The confidence interval required is 99%.
The Z-score corresponding to the 99% confidence interval is (Z) 2.58.
The true proportion (p) of the sample is not given, so we assume it to be 50% or 0.5.
The margin of error for the sample (E) is given to be 7% or 0.07.
By the formula of margin of error, we know that:
E = Z√[{p(1 - p)}/n].
Putting in the values, we have, we get:
0.07 = 2.58√[{0.5*0.5}/n],
or, (0.07/2.58)² = 0.25/n,
or, n = 0.25/{(0.07/2.58)²} = 339.6122449 ≈ 340.
Thus, the number of people who must be included in the survey, that is, the sample size should be 340.
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Drag the factors to the correct locations on the image.
Each factor can be used more than once, but not all factors will be used. What is the factored form of this expression? x3 - 6x2 - 9x + 54
Tiles go here
( )( )( )
Tile options:
x - 6
x - 9
x + 9
x - 3
x + 3
x + 6
Answer: x-6, x+3, x-3
Step-by-step explanation;
Split the equation into two.
x2(x-6)-9(x-6)
(x-6) is seen as one of the tiles. Now work on x2-9
x2-9 is a difference of squares meaning the last two are (x+3) and (x-3).
In right triangle ABC, m angle C equals 90 degree. If sinB = 7/25 which function also equals 7/25
Hi :)
We'll use sohcahtoa to solve this problem
———————————[tex]\large\boxed{\boxed{\begin{tabular} {c|1} \sf{ Sohcahtoa} & \sf{Formulas} \\\cline{1-2} \\\ \sf{Soh} & \sf{Opp/hyp} \\\sf{Cah} & \sf{Adj/hyp} \\\sf{Toa} & \sf{Opp/adj} \end{tabular}}}}[/tex]
Thus
The function that equals [tex]\sf{\dfrac{7}{25}}[/tex] besides [tex]\sin B[/tex] is :
Option (A) | [tex]\underline{\cos A}[/tex]Option (B) | [tex]\sin A[/tex]Option (C) | [tex]\tan A[/tex]Option (D) | [tex]\cos B[/tex][tex]\tt{Learn\:More;Work\;Harder}[/tex]
:)
What is the measure of z?
X
4
y
Z
Z
9
= [?]√
Answer:
z = [tex]3\sqrt{13}[/tex]
Step-by-step explanation:
To find the measure of z we can use the Euclidian Theorem:
[tex]z^{2}[/tex] = 9(9+4) do the multiplication
[tex]z^{2}[/tex] = 117 find the root of both sides
z = [tex]3\sqrt{13}[/tex]
Show how 60/90 becomes 2/3
60 ÷ 30 = 2
and
90 ÷ 30 = 3
---> 60/90 = 2/3
❄ Hi there,
the way 60/90 becomes 2/3 is this:
The fraction's numerator & denominator are both divided by 30:[tex]\sf{\dfrac{60\div30}{90\div30}=\dfrac{2}{3}}[/tex]
That's it!
❄
Given the function f(x) = -5x²-x+ 20, find f(3).
O-28
O-13
O62
O64
Answer: [tex]\Large\boxed{First~Choice.~-28}[/tex]
Step-by-step explanation:
Given function expression
f(x) = -5x² - x + 20
Requirement of the question
Find the value of f(3)
Substitute the values into the function
f(x) = -5x² - x + 20
f(3) = -5(3)² - (3) + 20
Simplify the exponents
f(3) = -5(9) - 3 + 20
Simplify by multiplication
f(3) = -45 - 3 + 20
Simplify by subtraction and addition
f(3) = -48 + 20
[tex]\Large\boxed{f(3)=-28}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The number of patients treated at Dr. Frank's dentist office each day was recorded for ten days: 13, 9, 7, 8, 2, 4, 22, 12, 5, 0. Using the given data, find the mean for this sample.
The mean of the sample from number of patients treated at Dr. Frank's dentist office each day for ten days is 8.2
MeanGiven data:
13, 9, 7, 8, 2, 4, 22, 12, 5, 0.
Mean of the sample = Total number of patients treated / number of days
= (13 + 9 + 7 + 8 + 2 + 4 + 22 + 12 + 5 + 0) / 10
= 82/10
= 8.2
Therefore, the mean of the sample is 8.2
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The probability of event a is x, and the probability of event b is y. if the two events are independent, which condition must be true?
Condition (A) P(B/A) = y is true.
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true.To find the true condition:
If two events are independent, then:
Use formulas for conditional probabilities:
Pr(A/B) = Pr(A∩B) / Pr(B)Pr(B/A) = Pr(B∩A) / Pr(A)For independent events these formulas will be:
Pr(A/B) = Pr(A∩B) / Pr(B) = Pr(A) . Pr(B) / Pr(B) = Pr(A)Pr(B/A) = Pr(B∩A) / Pr(A) = Pr(B) . Pr(A) / Pr(A) = Pr(B)Now in your case, Pr(A) = x and Pr(B) = y.
Pr(A/B) = x, Pr(B/A) = y, Pr(A∩B) = x.yTherefore, condition (A) P(B/A) = y is true.
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The complete question is given below:
The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditions must be true?
a. P(B|A) = y
b. P(A|B) = y
c. P(B|A) = x
d. P(A and B) = x + y
e. P(A and B) = x/y
In c = 2a 3b, the entry represented by c24 is . in d = 3a − 2b, the entry represented by d13 is .
The element value c₂₄ = -12 and d₁₃ = 14 if C = 2A + 3B and A and B are the matrix.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns.To find the element:
As we have given two matrices A and B:
C = 2A + 3Bc₂₄ = 2(3) + 3(-6)c₂₄ = -12d₁₃ = 3(0) - 2(-7)d₁₃ = 14Therefore, the element value c₂₄ = -12 and d₁₃ = 14 if C = 2A + 3B and A and B are the matrix.
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Brianna walks around a triangular park, daily. The longest side of the park measures 75 yards
and the shortest side measures 45 yards. If she walks 3 full laps around the park, how far does she
walk in one day?
She walks 540 yards for 3 full laps around the park per day.
How to determine the distanceFrom the information given;
The longest part of the triangular park = 75 yards
The shortest part = 45 yards
Let's find the other part, using Pythagorean theorem;
a² = b² + c²
75² = 45² + c²
c² = 75² - 45²
Find the squares
c² = 5625 - 2025
c² = 3600
Make 'c' the subject
c = √3600
c = 60 yards
If she walks
75 + 60 + 45 yards per lap
180 yards per lap
For three laps, she walks
= 3 × 180
= 540 yards
Thus, she walks 540 yards for 3 full laps around the park per day.
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Jude Enjoys Eating Potato Chips. He likes to place 3 chips together in a stack to make interesting flavours. If he only has one flavour of chip, for example, original, then he will only have one way to stack the chips: original, original, original, which can be written as O,O,O
The order in which the chips are stacked does not matter. For example, Jude has two different flavours: original and pizza. Stacking them as original, orginal, pizza (O,O, P) would be the same as stacking them as original, pizza, orignal (O,P,O.). In both stacks, he had two original-flavor chips and one pizza-flavor chip.
If Jude has four flavours, Original (O), pizza (P), and chicken (C) and BQQ (B), how many different stacks can he make
Using the combination formula, it is found that he can make 4 different stacks.
The order in which the balls are selected is not important, as stated in the problem. hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, he has four flavors, and will choose three of them for the stacks, hence the number of different stacks is given as follows:
[tex]C_{4,3} = \frac{4!}{3!1!} = 4[/tex]
He can make 4 different stacks.
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There are 8 players on a tennis team. The team is planning to play in a doubles tournament. How many different groups of players of 2 players can the coach make, if the position does not matter?
28
64
20,160
40,320
Using the arrangements formula, it is found that there are 20,160 different groups of players of 2 players that the coach can make.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, all 8 players will play, hence considering the order, the number of ways is:
[tex]A_8 = 8! = 40320[/tex]
However, the position does not matter, as for example, João and Elisa would form the same pair as Elisa and João, hence the removing the order, the number of groups is:
40,320/2 = 20,160.
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Answer:
The answer is 28!!!
Step-by-step explanation:
Use the combinations formula:
[tex]C = \frac{n!}{r!(n-r)!}[/tex]
n = 8
r = 2
[tex]C = \frac{8!}{2!~*~6! } = 28\\[/tex]
I got it right! Look at the pic for proof.
Hope this helps!! :)
Which linear inequality will not have a shared solution set with the graphed linear inequality? y < five-thirdsx – 2 y < negative five-thirdsx 1 y > five-thirdsx 2 y > negative five-thirdsx 2
The inequality will not have a shared solution set with the graphed linear inequality is y > five-thirds x + 2.
Linear inequalities are inequalities that involves at least one linear algebraic expression, that is, a polynomial of degree 1.Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.
y < five-thirds x – 2. The inequality will have a shared solution set with the graphed linear inequality. y < negative five-thirds x - 1. The inequality will have a shared solution set with the graphed linear inequality.y > five-thirds x + 2. The inequality will not have a shared solution set with the graphed linear inequality. y > negative five-thirds x + 2. The inequality will have a shared solution set with the graphed linear inequalityHence, the inequality will not have a shared solution set with the graphed linear inequality is y > five-thirds x + 2.
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Answer:
C
Step-by-step explanation:
answer is C
An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26
Answer:
12.5< × < 18.9
Step-by-step explanation:
because you would use the pythagoras theorem which a² + b² = c² in this case c is the third side the unknown so to work this out do square root of ( 10² + 16²) which is 100 + 256 = 356 and the square root of 356 is 18.86 which rounds to 18.9 so the second answer is correct :)
i hope this helps pls ask if you need any more help :)
what is the answer for 82= $14.00
Answer:
There is no answer
Step-by-step explanation:
82 can not equal $14.00, however if you mean 82x=14.00, the answer will be 0.17 (7/41), and if you mean 82=14x, the answer will be 5.86 (41/7)
find the slope of (2,2), (-1,-2)
Answer:
4/3
Step-by-step explanation:
The slope is the change in y over the change in x.
Your y's from the point given is -2, and 2.
Your x's from the point given is -1, and 2. Since we want to know how much they have changed, we subtract these numbers to find the change.
Change in y's? -2 - 2 or -4
Change in x's -1 - 2 or -3
This gives me a slope of -4/-3 and a negative divided by a positive is a positive.
I could have found the change by going the opposite direction
Change in y's ? 2 - (-2) or 4
Change in x's? 2 - (-1) or 3
This gives me the same slope 4/3
solve for x in x²+8x+15=0 in factorisation method
Answer: [tex]x=-5, -3[/tex]
Step-by-step explanation:
[tex]x^2 +8x+15=0\\\\(x+5)(x+3)=0\\\\x=-5, -3[/tex]
Algebra Find the value of each variable.
13.
X
"i see that your new product is available for $412.50 on the website. how much is it if i buy it in the store?" employee: "buying through the website gets you a 25% discount. if you buy the product in the store, it will cost you __________."
The cost of new product on the website is $309.375.
Given that, the cost of product = $412.50 and discount percentage = 25%.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Discount = 25% of 412.50
= 25/100 × 412.50
= 0.25 × 412.50
= 103.125
So, cost = 412.50-103.125
= $309.375
Therefore, the cost of new product on the website is $309.375.
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What is the equation of the line that passes through (4, -1) and (-2, 3)?
a.) 2 x + 3 y - 5 = 0
b.) -2 x + 3 y - 5 = 0
c.) 2 x - 3 y - 5 = 0
Answer:
a
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 1 ) and (x₂, y₂ ) = (- 2, 3 )
m = [tex]\frac{3-(-1)}{-2-4}[/tex] = [tex]\frac{3+1}{-6}[/tex] = [tex]\frac{4}{-6}[/tex] = - [tex]\frac{2}{3}[/tex] , then
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 2, 3 ) , then
3 = [tex]\frac{4}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{4}{3}[/tex] = [tex]\frac{5}{3}[/tex]
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← in slope- intercept form
multiply through by 3 to clear the fractions
3y = - 2x + 5 ( subtract - 2x + 5 from both sides )
2x + 3y - 5 = 0 ← in general form
How many 5-letter words can be made using exactly 5 of the letters from
TEXAS and MEXICO? Letters may only be used as many times as they appear. (For
example, XETEX is allowed. However, MATEA is not allowed, since the A appears twice
in MATEA but only once in the given words.)
Step-by-step explanation:
for TEXAS using permutation formula
we have:5!/1!1!1!1!1!=5!=120
for MEXICO using permutation formula
we have:6!/1!1!1!1!1!1!=6!=720
what is the parent function of g(x) = 3cos (x + 180°) + 1
The parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
What are parent functions?Parent functions are the basic function that represents the entire family of that function family
How to determine the parent function?The function is given as;
g(x) = 3cos (x + 180°) + 1
As a general rule, the parent function of any function is the basic equation of the function family
The basic equation of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
Hence, the parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
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Which line most accurately represents the line of best fit for the scatter plot?
A graph shows numbers from 0 to 14 on the x axis at increments of 2 and the numbers 0 to 28 on the y axis at increments of 4. Scatter plot shows ordered pairs 2, 5 and 5, 6 and 6, 8 and 8, 10 and 9, 12 and 10, 12 and 11, 14 and 12, 16 and 13, 20. A line labeled A joins ordered pair 0, 0 and 4, 28. A line labeled B joins the ordered pairs 0, 0 and 8, 28. A line labeled C joins the ordered pairs 0, 0 and 13, 28. A line labeled D joins the ordered pairs 0, 0 and 14, 18
Line A
Line B
Line C
Line D
Answer: Line D
Step-by-step explanation:
The points in the scatterplot are closest to line D.