a) There are 2^6 = 64 subsets total.
b) There are 2^3 = 8 subsets total
c) There are 2^5 = 32 subsets total
d) There are 32^4 = 48 subsets total
e) There are (6 choose 4) = 15 subsets total
f) There are 32 = 6 subsets total
g) There are is (6 choose 4) - (3 choose 4) = 15 - 0 = 15 subsets total
h) There are (3 choose 1) * (3 choose 3) = 3 subsets total
a) There are 2^6 = 64 subsets total.
b) Since we need to include elements 2, 3, and 5 in a subset, we have 3 elements fixed, and we need to choose 1, 2, or 3 elements from the remaining 3 elements (1, 4, and 6). Therefore, there are 2^3 = 8 subsets that contain the elements 2, 3, and 5.
c) There are 2^5 = 32 subsets that contain at least one odd number. This can be seen by noticing that if a subset does not contain any odd numbers, then it must be {2,4,6}, which is not a valid subset since it does not satisfy the condition that it be a subset of S.
d) There are 32^4 = 48 subsets that contain exactly one even number. To see why, notice that there are 3 choices for which even number to include (2, 4, or 6), and then there are 2^4 = 16 choices for which of the remaining 4 odd numbers to include in the subset.
e) There are (6 choose 4) = 15 subsets of cardinality 4. This is the number of ways to choose 4 elements from a set of 6.
f) Since we need to include elements 2, 3, and 5 in a subset of cardinality 4, we have 3 elements fixed, and we need to choose 1 element from the remaining 3 even elements, and 1 element from the remaining 2 odd elements. Therefore, there are 32 = 6 subsets of cardinality 4 that contain the elements 2, 3, and 5.
g) The number of subsets of cardinality 4 that contain at least one odd number is equal to the total number of subsets of cardinality 4 minus the number of subsets of cardinality 4 that contain only even numbers. This is (6 choose 4) - (3 choose 4) = 15 - 0 = 15.
h) The number of subsets of cardinality 4 that contain exactly one even number is equal to the number of ways to choose 1 even number out of 3, and then the number of ways to choose 3 odd numbers out of 3. This is (3 choose 1) * (3 choose 3) = 3.
To learn more about subsets:
https://brainly.com/question/2280091
#SPJ4
A supermarket normally sells 20 eggs for £2.60. In a sale, the cost of the eggs is reduced by 30%. Work out how much 180 eggs cost in the sale. Give your answer in pounds (£).
Answer:
£16.38
Step-by-step explanation:
To calculate the cost of 180 eggs during the sale, we first need to determine the cost of a single egg and then apply the 30% discount.
The initial cost of 20 eggs is £2.60. To find the cost of a single egg, we divide the total cost by the number of eggs:
[tex]\frac{\£2.60}{20} = 0.13[/tex]Now, we need to apply the 30% discount to the cost of a single egg:
[tex]\£0.13 \times (1 - 0.30) = \£0.13 \times 0.70 = \£0.091[/tex]The cost of a single egg during the sale is £0.091. To find the cost of 180 eggs, we multiply the cost of a single egg by the number of eggs:
[tex]\£0.091 \times 180 = \£16.38[/tex]Therefore, the cost of 180 eggs during the sale is £16.38.
________________________________________________________
sam needs a 20% acid solution, but she has only an 18% solution and a 25% solution. she decides to use 100 ml of the 18% solution, and she needs to know how much of the 25% solution she should add.
which equation represents this situation? let x represent the number of milliliters she should add.
let x represent the number of milliliters she should add and the equation represents this situation is 0.18(100) + 0.25x = 0.2(100 + x).
Acid makes up number 0.18(100) = 18 cc of the 18% solution.
Let's suppose Sam needs to blend x millilitres of the 25% fluid.
0.25x times as much acid is present in x millilitres of the 25% solution.
Acid should make up 0.2(100 Plus x) of the entire mixture.
Therefore, 0.18(100) + 0.25x = 0.2(100 + x) represents this scenario mathematically.
Acid makes up 0.18(100) = 18 cc of the 18% solution. Let's suppose Sam needs to blend x millilitres of the 25% fluid. 0.25x times as much acid is present in x millilitres of the 25% solution. Acid should make up 0.2(100 Plus x) of the entire mixture. As a result, 0.18(100) + 0.25x = 0.2(100 + x) represents this scenario mathematically.
Learn more about number here:
https://brainly.com/question/17429689
#SPJ4
Every diagonal of a trapezoid divides it into two congruent triangles
true or false
The statement that every diagonal of a trapezoid divides it into two congruent triangles is false.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
A trapezoid is a quadrilateral which has at least one pair of parallel sides.
The sides may or may not be equal.
Consider an isosceles trapezium, ABCD, given below which has two parallel opposite sides and the other pair of sides are equal.
If we draw a diagonal, AC, we have two triangles ABC and ADC.
AC = AC (common side)
AD = BC (given)
But AB ≠ CD
Hence the triangles cannot be congruent.
Hence the given statement is false.
Learn more about Trapezoids here :
https://brainly.com/question/8643562
#SPJ1
in 1960 the average price of a new car was $2752. Between 1960 and 2022 car prices have nereased by an average of 4.6% per year. How much is the average price of a new car in 2022
The depreciated price of the car in the year 2022 is $148.47
What is depreciation?Depreciation in economics is a measure of the amount of value an asset loses from influential factors affecting its market value.
Given that, in 1960 the average price of a new car was $2752. Between 1960 and 2022 car prices have decreased by an average of 4.6% per year.
We need to calculate the average price of a new car in 2022
The question is depreciated price of the car,
Depreciated price =
A = P(1-r)ⁿ
A = final amount
P = initial amount
r = 4.6%
n = time
Here, the time = 2022 - 1960 = 62 years
Therefore,
A = 2752(1-0.046)⁶²
A = 2752(0.954)⁶²
A = 148.47
Hence, the depreciated price of the car in the year 2022 is $148.47
Learn more about depreciation, click;
https://brainly.com/question/15085226
#SPJ9
D is the midpoint of AC, ∠AED ≅ ∠CFD and ∠EDA ≅ ∠FDC. Prove ΔAED ≅ ΔCFD
To prove that ΔAED ≅ ΔCFD, we will use the two given angle equalities and the fact that D is the midpoint of AC:
Given: D is the midpoint of AC, ∠AED ≅ ∠CFD, and ∠EDA ≅ ∠FDC
To prove: ΔAED ≅ ΔCFD
Proof:
Since D is the midpoint of AC, we know that AD = DC and CF = FA.Since ∠AED ≅ ∠CFD and ∠EDA ≅ ∠FDC, we have two pairs of corresponding angles that are equal.Therefore, by the Angle-Angle (AA) similarity postulate, we can conclude that ΔAED ≅ ΔCFD.Additionally, using the fact that AD = DC and CF = FA, we can conclude that ΔAED is congruent to ΔFAC by the Side-Angle-Side (SAS) similarity postulate.Thus, we have ΔAED ≅ ΔCFD and ΔAED ≅ ΔFAC.By the Transitive Property of Congruence, we can conclude that ΔCFD ≅ ΔFAC.Finally, using the fact that CF = FA, we can conclude that ΔCFD is congruent to ΔFAC by the Side-Side-Side (SSS) congruence postulate.Therefore, we have ΔAED ≅ ΔCFD ≅ ΔFAC.Thus, we have proved that ΔAED ≅ ΔCFD.
use the combined gas law equation to determine the final volume of a system initially of 2 liters if the pressure is tripled and the temperature is tripled.
The final volume of a system with initially of 2 liters if the pressure is tripled and the temperature is tripled, is 11.57 liters.
The combined gas law equation relates the initial and final conditions of a system of gas by considering the effect of changes in pressure, volume, and temperature:
P1 * V1 / T1 = P2 * V2 / T2
Given the initial conditions of the system:
V1 = 2 liters
P1 = 1 atm
T1 = 273 K (room temperature)
And the changes in pressure and temperature:
P2 = 3 * P1 = 3 atm
T2 = 3 * T1 = 819 K
We can calculate the final volume of the system:
V2 = (P1 * V1 / T1) * (T2 / P2) = (1 atm * 2 liters / 273 K) * (819 K / 3 atm) = approximately 11.57 liters
So the final volume of the system would be approximately 11.57 liters if the pressure is tripled and the temperature is tripled from the initial conditions.
To learn more about gas law click on,
https://brainly.com/question/29419458
#SPJ4
You spin the spinner and flip a coin. Find the probability of the compound event.
5
4
3
2
1
The probability of not spinning a 5 and flipping heads is
Answer:
20%
Step-by-step explanation:
What is the value of the expression (12)3
?
Responses
19
1 9
18
1 8
16
1 6
32
The value of the expression (1/2)^3 include the following: D. 1/8.
What is an exponent?In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as;
bⁿ
Where:
the variables b and n represent numerical values or an algebraic expression.
From the information provided, we can logically deduce the following as the only true statement:
Expression = (1/2)^3
Expression = 1/2 × 1/2 × 1/2
Expression = 1/8
In conclusion, the numerical value 3 represents the power of the given expression.
Read more on exponent here: brainly.com/question/9524319
#SPJ1
Complete Question:
What is the value of the expression (1/2)^3?
Responses
19
1/9
18
1/8
16
1/6
32
The region between the graphs of y = x2 and y = 2x is rotated around the line y = 4. Find the volume of the resulting solid.
The region between the graphs of y = x2 and y = 2x is rotated around the line y = 4. The volume of the resulting solid is 31π/15 cubic units.
To find the volume of the resulting solid, we can use the method of cylindrical shells. First, we need to determine the limits of integration.
The graphs of y = x^2 and y = 2x intersect at x = 0 and x = 2. Therefore, we will integrate with respect to x from 0 to 2.
The distance between the line y = 4 and the graph y = x^2 is 4 - x^2, and the distance between the line y = 4 and the graph y = 2x is 4 - 2x. Thus, the radius of the cylindrical shell at x is (4 - x^2) - (4 - 2x) = 2x - x^2.
The height of the cylindrical shell at x is the difference between the y-coordinates of the two graphs at x, which is (2x) - (x^2) = x(2 - x).
Therefore, the volume of the resulting solid is:
V = [tex]\int\limits^2_0 \, 2\pi(x(2 - x))(2x - x^2) dx[/tex]
= [tex]\int\limits^2_0 \, 4\pi x^3 - 2\pi x^4 - 2\pi x^2 + \pi x^3 dx[/tex]
= [tex]\int\limits^2_0 \, 5\pi x^3 - 2\pi x^4 - 2\pi x^2 dx[/tex]
= π(5/4 - 2/5 - 2/3)
= 31π/15
To learn more about volume click on,
https://brainly.com/question/17515923
#SPJ4
Last season Emily soccer team how to win loss ratio of 9 to 12 and Grant soccer team how to win loss ratio of 10 to 15 who’s team has a higher ratio of wins to losses use complete sentences to explain your reasoning
The Emily soccer team has the higher ratio of wins to losses.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
The ratio of a and b is denoted as a : b.
Given that,
Ratio of win to loss of Emily soccer team = 9 : 12
Ratio of win to loss of Grant soccer team = 10 : 15
9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60
10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60
If 60 games are losses, then 45 games are wins for Emily soccer team.
If 60 games are losses, then 40 games are wins for Grant soccer team.
Higher ratio is for Emily soccer team.
Hence higher ratio of wins to losses is for Emily soccer team.
Learn more about Ratios here :
https://brainly.com/question/1706633
#SPJ9
in a brand recognition study, 1036 consumers knew of costco, and 40 did not. use these results to estimate the probability that a randomly selected consumer will recognize costco. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol. prob =
The percentage probability that a random selected consumer will recognize Costco will be 96.3%.
Given, the total number of consumers who recognized the brand was 1036. And the total number of consumers who didn't recognize the brand was 40. Therefore, the total number of our sample will be :
⇒1036 + 40
⇒1076
Now, we know that probability(P) of an event = f/n
where f is the number of favorable outcomes and n is the number of total outcomes. Here, number of favorable outcome is 1036.
Now, the probability that a random selected consumer will recognize the brand will be:
⇒ P = f/n
⇒ P = 1036/1076
⇒P = 0.96282
Therefore, the percentage of probability of consumers recognizing the brand rounded to one decimal place accuracy will be 96.3%.
Learn more about Probability here,
https://brainly.com/question/30034780
#SPJ4
Oht
Find the length
of the diagonal
4 in
11 in
The length of the diagonal of the rectangle is 11.70 in.
What is a diagonal?A diagonal of a polygon is a line segment that joins two vertices of the polygon which are not already joined by an edge of the polygon.
Since, there is no information about which polygon's diagonal length we are asked to find, so let us consider that the given side lengths are of a rectangle,
Now, please refer to the figure attached in the solution,
We know that, the diagonal of a rectangle divides it into two right triangles,
Here our rectangle is ABCD and the diagonal AC divides it into rt. Δ ABC and rt. Δ ADC,
Considering the rt. Δ ABC,
The diagonal AC is acting as the hypotenuse of rt. Δ ABC,
So, using Pythagoras theorem,
AC² = AB² + BC²
AC = √4²+11²
AC = √121+16
AC = 11.70
Since, the diagonals of a rectangle are congruent so, AC = BD = 11.70
Hence, the length of the diagonals of the rectangle is 11.70 in.
Learn more about diagonals, click;
https://brainly.com/question/12274248
#SPJ9
what is a divided by 6 -11=25
You can solve this by using the addition and multiplication properties of equality
the original equation is:
a divided by 6 - 11 = 25
then you can add 11 to both sides to get rid of it (addition property of equality)
a divided by 6 = 36
then you use the multiplication property of equality
a = 216
to find the length of the curve defined by from the point (-3,2136) to the point (3,2238), you'd have to compute
The length of the curve defined by from the point (-3, 2136) and (3, 2238), by use of distance formula is approximately 102.17 units.
The formula for the distance between two points (x1, y1) and (x2, y2) is given by:
[tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]
In this case, we have:
x1 = -3, y1 = 2136
x2 = 3, y2 = 2238
Substituting these values into the formula, we get:
[tex]d = \sqrt{((3 - (-3))^2 + (2238 - 2136)^2)[/tex]
[tex]= \sqrt{(6^2 + 102^2)[/tex]
= [tex]\sqrt{(10440)[/tex]
≈ 102.17
Therefore, the length of the curve defined by the points (-3, 2136) and (3, 2238) is approximately 102.17 units.
To more about distance formula:
https://brainly.com/question/28956738
#SPJ4
_____The given question is incorrect, the correct question is given below:
To find the length of the curve defined by from the point (-3,2136) to the point (3,2238), you'd have to compute by using distance formula.
Given that h(x)=x2, find (h•h)(x)
If Θ1 and Θ2 are independent unbiased estimators of a given parameter Θ and var Θ1 = 3.var Θ2 find the constants a1 and a2 such that a1Θ1 + a2Θ2 is an unbiased estimator with minimum variance for such a linear combination.
The unbiased estimator with minimum variance is: (2/3)Θ1 + (1/3)Θ2. Let X be the parameter we are trying to estimate, and let Θ1 and Θ2 be the two unbiased estimators of X.
We want to find the constants a1 and a2 such that the linear combination a1Θ1 + a2Θ2 is also an unbiased estimator of X with minimum variance.
Since Θ1 and Θ2 are unbiased estimators of X, we have: E(Θ1) = E(X) and E(Θ2) = E(X)
We want to find a1 and a2 such that: E(a1Θ1 + a2Θ2) = E(X)
Using linearity of expectation, we can simplify this to: a1E(Θ1) + a2E(Θ2) = E(X)
Substituting in the expressions for E(Θ1) and E(Θ2), we have: a1E(X) + a2E(X) = E(X), (a1 + a2)E(X) = E(X), a1 + a2 = 1
So, any linear combination of Θ1 and Θ2 with coefficients a1 and a2 such that a1 + a2 = 1 will be an unbiased estimator of X.
Now, we need to find the values of a1 and a2 that minimize the variance of this linear combination. The variance of a1Θ1 + a2Θ2 is given by:
Var(a1Θ1 + a2Θ2) = a1^2Var(Θ1) + a2^2Var(Θ2) + 2a1a2Cov(Θ1,Θ2)
Since Θ1 and Θ2 are independent, their covariance is zero, so the above equation simplifies to: Var(a1Θ1 + a2Θ2) = a1^2Var(Θ1) + a2^2Var(Θ2)
We are given that Var(Θ1) = 3Var(Θ2), so we can write: Var(a1Θ1 + a2Θ2) = a1^2(3Var(Θ2)) + a2^2Var(Θ2), = (3a1^2 + a2^2)Var(Θ2)
To minimize this variance, we need to find the values of a1 and a2 that minimize 3a1^2 + a2^2 subject to the constraint that a1 + a2 = 1.
We can use Lagrange multipliers to solve this optimization problem. We want to minimize the function: L(a1,a2,λ) = 3a1^2 + a2^2 + λ(1 - a1 - a2)
Taking partial derivatives with respect to a1, a2, and λ, we have: dL/da1 = 6a1 - λ, dL/da2 = 2a2 - λ, dL/dλ = 1 - a1 - a2
Setting each of these partial derivatives to zero, we get: 6a1 - λ = 0,
2a2 - λ = 0, 1 - a1 - a2 = 0
Solving these equations, we get: a1 = 2/3, a2 = 1/3
So, the unbiased estimator with minimum variance is: (2/3)Θ1 + (1/3)Θ2
You can read more about independent unbiased estimators at https://brainly.com/question/17083771
#SPJ4
Question 2 of 10
On a piece of paper, graph y<-x+1. Then determine which answer choice
matches the graph you drew.
A
((0, 1)
OA. Graph A
OB. Graph B
OC. Graph C
OD. Graph D
PREVIOUS
B
(0, 1)
D
(0.1)
The shaded region represents the solution set of the given inequality.
What is inequality?An inequality is used to make comparisons between the numbers or expressions. For example -
2x + 4 > 5
4x + 6 > 2
Given is the linear inequality as given below -
y < - x + 1
The graph of the inequality is attached. The shaded region represents the solution set of the given inequality. This means that all the coordinate points on the shaded graph satisfy the inequality -
y < - x + 1
Therefore, the shaded region represents the solution set of the given inequality.
To solve more questions on graphing inequalities, visit the link below -
https://brainly.com/question/29061217
#SPJ9
If the cost, C(x), for manufacturing x units of a certain product is given by
C(x) = x² - 9x + 30
find the number of units manufactured at a cost of $8200.
The number of units manufactured at the cost of $8200 will be 95.
A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the cost, C(x), for manufacturing x units of a certain product is
C(x) = x² - 9x + 30.
The number of units will be calculated as:-
C(x) = x² - 9x + 30
8200 = x² - 9x + 30
x² - 9x - 8170 = 0
Solve the equation as below,
x² - 9x - 8170 = 0
x² - 95x + 86x - 8170 = 0
x ( x - 95 ) + 86 ( x - 95 ) = 0
( x - 95 ) ( x + 86 ) = 0
x = 95 units
Therefore, the number of units manufactured at the cost of $8200 will be 95.
To know more about quadratic equations follow
https://brainly.com/question/1214333
#SPJ1
A box contains two coins: a regular coin and one two-headed coin. I choose a coin at random and toss it twice. Define the following events.
A= First toss results in a H
B= Second toss results in a H
C= Regular coin has been selected
Are A and B independent? Are A and B conditionally independent given C? Find P(A|C), P(B|C), P(A∩B|C), P(A), P(B), and P(A∩B), and use them to answer the question.
A and B are not independent since the result of one toss affects the second toss. Specifically, if the first toss result is a head (A), then the second toss will be more likely to result in a head (B).
A and B are conditionally independent given C since the probability of getting head(A) for the first toss does not depend on the type of coin selected (C).
P(A|C) = 1/2, P(B|C) = 1/2, P(A∩B|C) = 1/4, P(A) = 1/2, P(B) = 3/4, and P(A∩B) = 1/4. Therefore, given the information that a regular coin has been selected (C), the probability of A and B occurring independently is 1/4. This suggests that A and B are conditionally independent given C.
To learn more about independent probability:
https://brainly.com/question/27665211
#SPJ4
A car drove 249.48 miles on 12.6 gallons of gas. How far could the car drive on a full tank of 14.8 gallons of gas? Drag and drop a number to correctly complete the statement. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The car could drive Response area miles on a full tank of gas. I REAALY NEED HEEEEELP PLEASE HELP ME I WILL GIVE FIVE STARS AND HEART TO WHOEVER ANSWERS IT!!!!!!!!!!!!!!!!!!!!!!!!!
The car could drive approximately 293.04 miles on a full tank of gas. Drag and drop the number "293.04" into the response area to complete the statement.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent mathematical relationships and can be used to solve equations and perform calculations.
We can use the given information to find the car's fuel efficiency in miles per gallon (mpg) as follows:
mpg = miles driven / gallons of gas used
mpg = 249.48 miles / 12.6 gallons
mpg ≈ 19.8
This means that the car can travel approximately 19.8 miles on one gallon of gas. To find out how far the car could drive on a full tank of 14.8 gallons of gas, we can multiply the tank capacity by the car's fuel efficiency:
miles on full tank = mpg * gallons in full tank
miles on full tank = 19.8 mpg * 14.8 gallons
miles on full tank ≈ 293.04 miles
Therefore, the car could drive approximately 293.04 miles on a full tank of gas. Drag and drop the number "293.04" into the response area to complete the statement.
To learn more about Algebraic expression from given link.
brainly.com/question/953809
#SPJ1
Can someone please help me for 50 points and brainliest and also show your work on paper and upload the picture
wrong answer such as guessing, or even putting random answers will be reported !
answer only even numbers
A probability experiment is conducted in which the sample space of the experiment is S={3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}. Let event E={4, 5, 6, 7, 8}Assume each outcome is equally likely.a. List the outcomes in E^c (Use a comma to separate answers as needed.)b. Find P(E^c)..
The probability of the complement of event E[tex](E^c)[/tex] is 7/12.
a. Outcomes in [tex]E^c[/tex] = {3, 9, 10, 11, 12, 13, 14}
b. The probability of the complement of event E[tex](E^c)[/tex] is the probability of all outcomes in S that are not in E. P[tex](E^c)[/tex] = 1 - P(E).
The probability of E is calculated by counting the number of elements in E and dividing by the total number of elements in the sample space S.
P(E) = 5/12
Therefore, P[tex](E^c)[/tex] = 1 - P(E) = 1 - (5/12) = 7/12
The probability of the complement of event E [tex](E^c)[/tex] is 7/12.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ4
Find one point on the plane y=-3 and two non-parallel vectors that are parallel to the plane y=-3.
The required one point and two non-parallel vectors are (0, -3, 0) and (1, 0, 0), (0, 0, 1).
What is Vectors?A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
According to question:One point on the plane y=-3 is (0, -3, 0).
Two non-parallel vectors that are parallel to the plane y=-3 can be obtained by taking any two vectors whose y-coordinate is 0,
since any vector with a y-coordinate of 0 lies in the x-z plane, which is parallel to the y=-3 plane.
For example, the vectors (1, 0, 0) and (0, 0, 1) are non-parallel vectors that are parallel to the plane y=-3.
To know more about Vector visit:
brainly.com/question/30202103
#SPJ1
Please help me solve this
The solution of the inequality is x > -2 and x < 7.
Inequality Notation: -2 < x < 7.
The graph is attached.
How to solve and graph inequality?An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4.
-5x - 7 < 3
-5x < 3 + 7
-5x < 10
x > 10/(-5)
x > -2
-5x - 7 > -42
-5x > -42 + 7
-5x > -35
x < -35/(-5)
x < 7
We have x > -2 and x < 7.
x > -2 can be written as -2 < x.
Inequality Notation: -2 < x < 7
This implies that x is in the range of -2 and 7. The graph is attached.
Learn more about inequality on:
brainly.com/question/25275758
#SPJ1
Consider the following equation.
6y=48
Find the x- and y-intercepts, if possible.
Answer: the only y-intercept is 8
Step-by-step explanation:
One way I remembered equations when I was doing algebra with only an x or a y was HOY VUX.
H - horizontal
O = slope
Y = the variable in the line equation
V =vertical
U = undefined slope
X = the variable in the line equation
As we can see this is a horizontal line so there will be no x-intercepts.
6y = 48
y = 8
the only y-intercept is 8
Please help I can’t figure it out
Answer:
um
Step-by-step explanation:
Answer:69.51
Step-by-step explanation:
915-------100%
636-------x%
x=636*100/915=69.51
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.)
f(x) = −x2 + 2x, [0, 2]
Yes, Rolle's Theorem can be applied.
No, because f is not continuous on the closed interval [a, b].
No, because f is not differentiable in the open interval (a, b).
No, because f(a) ≠ f(b).
Answer:
A) Yes, Rolle's Theorem can be applied!
Step-by-step explanation:
Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
Here, for our continuous function [tex]f(x)=-x^2+2x[/tex] over the closed interval [tex][0,2][/tex], we can tell that the function is clearly differentiable over the interval [tex](0,2)[/tex] as [tex]f'(x)=-2x+2[/tex], so we'll need to check if [tex]f(0)=f(2)[/tex]:
[tex]f(0)=-0^2+2(0)=0\\f(2)=-(2)^2+2(2)=-4+4=0[/tex]
Next, we'll need to check if f'(x) = 0 for some x within the closed interval:
[tex]f'(x)=-2x+2=0\\-2x+2=0\\-2x=-2\\x=1[/tex]
As x=1 is contained in [0,2] and the previous conditions were met, Rolle's Theorem can be applied!
show that the cross product of two vectors v and w, explicitly defined as ijkv jwk , transform as a dual vector under rotation. note that the levi-civita symbol is a symbol here and does not transform under rotation. hint: remember that for any matrix mi j , we have `mn det(m)
The cross product of two vectors v and w is explicitly defined as ijkv jwk and also transformed as a dual vector under rotation.
The cross product of two vectors v and w is defined as:
v × w = (v2w3 - v3w2)i - (v1w3 - v3w1)j + (v1w2 - v2w1)k
To show that this cross product transforms as a dual vector under rotation, consider a rotation matrix R that transforms a vector u to u'. The transformation of u can be written as:
u' = Ru
We can write the cross product of v and w in terms of their components as:
v × w = (v1, v2, v3) × (w1, w2, w3) = (v2w3 - v3w2, -(v1w3 - v3w1), v1w2 - v2w1)
To see how this changes under rotation, we can use the matrix-vector product to transform v × w:
(v × w)' = R(v × w) = (Rv × Rw)
Rotation matrix R in terms of its components:
R = (r11, r12, r13; r21, r22, r23; r31, r32, r33)
(v × w)' = (r11r12r13r21r22r23r31r32r33(v2w3 - v3w2) - (v1w3 - v3w1) + (v1w2 - v2w1))
Since the Levi-Civita symbol is a symbol and does not transform under rotation, we have:
(v × w)' = det(R)(v × w)
This shows that the cross product of two vectors v and w transforms as a dual vector under rotation, and that the transformation is proportional to the determinant of the rotation matrix R.
To know more about cross product:
https://brainly.com/question/16522525
#SPJ4
Use the graph below to determine the number of solutions the system has. X=4. Y=x+3
The system of linear equations x = 4 and y = -x -1 has a unique solution.
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
Given is a graph of lines,
We need to find the number of solutions do the lines x = 4 and y = -x-1 have,
In the graph of the lines x = 4 and y = -x -1, intersecting at a point, we know that the lines which intersects at a single point will have only one solution.
Also,
The system of equation has the solution at the point where the line intersects,
By observing the graph it can be concluded that the graph of x = 4 and y = - x - 1 intersect only at one point i.e (4, -5).
Therefore, the solution of the given system of equations is (4, -5)
Hence, the system of linear equations x = 4 and y = -x -1 has a unique solution.
Learn more about linear equations, click;
https://brainly.com/question/29739212
#SPJ9
The length of the sides of two squares differ by 3cm and the sum of their areas is 317cm^2 find the length of the sides of the two squares.
The side lengths of the given squares are 11 cm and 14 cm
What is a square?A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
Given that, the sides of two squares differ by 3cm and the sum of their areas is 317cm², we need to find the length of the sides of the two squares.
Let the sides of the squares be x and y, we know that the area of a square is their side's square.
Therefore, establishing the system of equations,
x-y = 3
x = y+3.......(i)
x²+y² = 317....(ii)
Put eq(i) in eq(ii)
(y+3)²+y² = 317
y²+9+6y+y² = 317
2y²+6y-308 = 0
On factorizing, we get,
y = 11 and y = -14
Since, the length can not be negative so, ignore -14
Put y = 11 in eq(i)
x = 11+3
x = 14
Therefore, the side lengths of the given squares are 11 cm and 14 cm
Learn more about squares, click;
https://brainly.com/question/14198272
#SPJ1