Every Friday, A. and B. go out unless at least one of them feel like staying in, in which case they both stay home. Overall, A. wants to stay in 0.3 of the time. Overall, B. wants to stay in 0.2 of the time. 0.15 of the time, they both want to stay in. How often do they stay home

The graph below models the price of items after 120% markup at a small shop. Based only on the given graph, The function's domain is numbers between 5 and 30.

What is graph?

A graph is a structure that resembles a set of items in discrete mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "connected." The items are represented by mathematical abstractions known as vertices (sometimes known as nodes or points), and each pair of connected vertices is known as an edge (also called link or line).

A graph is typically shown diagrammatically as a collection of dots or circles representing the vertices and lines or curves representing the edges. One of the topics studied in discrete mathematics is graphs.

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Complete Question:

Answer:

c

Step-by-step explanation:

Answer:

They are vertical angles so that would only leave C.

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

20-15 = 5, 2 students passed and did the assignment, 0.4 = 40%

The value of f(1) is the y-value when x=1.

From the graph, we see that y=0 when x=1. Thus, the value of f(1) is 0, which is option A.

Let me know if you need any clarifications, thanks!

Answer: the answer is B

Step-by-step explanation: just took it

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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The gradient of f at (-3, 4) is ∇f(-3, 4) = (-3/5, 4/5). The equation of the tangent plane z = (12/5) - (3/5)x + (4/5)y. The unit vectors u for which the directional derivative Duf = 0 at (-3, 4) are u = (4/5, 3/5) and u = (4/5, -3/5).

(a) To find the gradient of the function f(x, y) at the point (-3, 4), we need to compute the partial derivatives ∂f/∂x and ∂f/∂y. The gradient vector ∇f(x, y) is given by (∂f/∂x, ∂f/∂y).

First, let's find the partial derivatives:

∂f/∂x = (∂/∂x)(4 + √(x^2 + y^2)) = x/√(x^2 + y^2)

∂f/∂y = (∂/∂y)(4 + √(x^2 + y^2)) = y/√(x^2 + y^2)

∂f/∂x = -3/√((-3)^2 + 4^2) = -3/5

∂f/∂y = 4/√((-3)^2 + 4^2) = 4/5

Thus, the gradient of f at (-3, 4) is ∇f(-3, 4) = (-3/5, 4/5).

(b) The equation of the tangent plane at the point (-3, 4) can be expressed as z = f(-3, 4) + (∂f/∂x)(-3, 4)(x + 3) + (∂f/∂y)(-3, 4)(y - 4). Substituting the values, we have z = 4 - (3/5)(x + 3) + (4/5)(y - 4), which simplifies to z = (12/5) - (3/5)x + (4/5)y.

(c) The directional derivative Duf is given by Duf = ∇f · u, where ∇f is the gradient of f and u is a unit vector. To find the unit vectors u for which Duf = 0 at (-3, 4), we need to solve the equation ∇f · u = 0.

Substituting the gradient values, we have (-3/5, 4/5) · u = 0. Multiplying the components, we get (-3/5)u1 + (4/5)u2 = 0.This equation implies that u1 = (4/3)u2. Since u is a unit vector, we have u1^2 + u2^2 = 1. Substituting u1 = (4/3)u2, we get (4/3)u2^2 + u2^2 = 1.

Simplifying, we find (16/9 + 1)u2^2 = 1, or (25/9)u2^2 = 1. Taking the square root of both sides, we have u2 = ±(3/5). Therefore, the unit vectors u for which the directional derivative Duf = 0 at (-3, 4) are u = (4/5, 3/5) and u = (4/5, -3/5).

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Answer:

x=42°

Step-by-step explanation:

All sides of a triangle equals 180. so 56+82= 138. 180-138 equals 42

Answer:

-9

Step-by-step explanation:

the expression are equivalent compound condition for the nested conditionals is (x > 200) and (y < 200).

ii. The equivalent compound condition for the nested conditionals is not (x > 200 and y > 200).

iii. The equivalent compound condition for the nested conditionals is not ((x ≤ 200) or (y ≥ 200)).

The equivalent compound conditions for the given nested conditionals are as follows:

i. The compound condition (x > 200) and (y < 200) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be true for the condition to be satisfied.

ii. The compound condition not (x > 200 and y > 200) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be false for the condition to be satisfied.

iii. The compound condition not ((x ≤ 200) or (y ≥ 200)) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be false for the condition to be satisfied.

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Answer:

there is no unit rate but hers an example of an unit rate using 5.76 NOT THE ANSWER

Step-by-step explanation:

Example: 64 ounces of water in a bottle that costs $5.76. To find the unit rate per ounce, divide the amount it costs ($5.76) by the number of ounces (64). $5.76 ÷ 64 ounces = $0.09 per ounce

Answer:

-8

Step-by-step explanation:

Answer:

Option 4

Step-by-step explanation:

So we know that the area of a square is found by s^2. This means that we can just look for (6r)^2, since 6r is our side length! Let's see...We know that (6r)^2 is equal to 6^2 times r^2 because of the distributive property of exponents. Therefore, option 4 is our right answer. 36 is 6^2 and r^2 is r^2.

Answer:

40 Thank You cards

Step-by-step explanation:

1/5 of an hour is 60 minutes ÷ 5 = 12 minutes, therefore it takes her 12 minutes to write 1 Thank You card.

8 hours converted into minutes is 8 x 60 minutes = 480 minutes

480 minutes (in total) ÷ 12 minutes (time taken for 1 card) = 40 cards

Hope this helps!

Answer:

40

Step-by-step explanation:

Write the information algebraically:

1/5 of an hour = 12 mins (60 mins ÷ 5)

∴ 12 mins = 1 thank you note

8 hours = ?

1. Work out how many mins are in 8 hours: (8 × 60 =) 480

2. Divide 480 by 12 to find the number of thank you notes she wrote

She wrote 40 thank you notes

The probability of getting at least one question wrong on a 7 question multiple-choice test with two answers for each question is 1 - (1/4)^7, which is approximately 99.2%.

The probability of getting one question wrong on a 7 question multiple-choice test with two answers for each question is 1/4. This is because there are two options for each question, and if you choose the wrong one, you get the question wrong. Therefore, the probability of getting all 7 questions wrong is (1/4)^7, or one in 16,384. The probability of getting at least one question wrong on the test is 1 - (1/4)^7, which is equal to 1 - 1/16,384, or approximately 99.2%. To calculate the probability of getting at least one question wrong, you subtract the probability of getting all 7 questions correct from 1. This is because if you do not get all 7 questions correct, then you must have gotten at least one question wrong.

The complete question: On a 7 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong? Give your answer as a fraction

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Answer:

A. No solution

Step-by-step explanation:

Please see attachment for the graph.

Hope this helps!

Please mark as brainliest if correct!

The equation has No Solution.

The points at which the lines representing the intersection of two linear equations are defined as the solution to a linear equation. In other words, the set of all possible values for the variables that satisfy the given linear equation is the solution set for the system of linear equations.

The set of linear equations can be solved in one of three ways

Unique Solution, No Solution and Infinitely Many Solutions.

Given equations

2x + 6y = 12

x   0    6  

y   2    0

6x + 18y = 18

x   0    3  

y   1    0

The graph of equations is attached,

for solution of equation,

we can find it by graph, the graph shows the parallel line for both equation since equations have No Solution.

The system of linear equations does not have a solution if the graphs of the linear equations are parallel. In this instance, there is no point at which lines do not cross.

Hence there is no solution for equations.

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Answer:

common ratio=t2/t1

=6/(-2)

=-3

Answer:

B

Step-by-step explanation:

Open circle means the number is not included.

Hope this helps <3

The graph shows the function

For y = x³- 4 when x = 0, y = -4.

For y = x² + 3 when x = 0, y = 3.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have given the graph from which we can Conclude

The function's y-intercept is below 0 according to the graph.

Hence, the top component is from x² + 3 and the bottom part is from

x³- 4.

A black circle indicates that the bottom portion corresponds to the range of x = 1 to x³- 4.

Thus, For y = x³- 4 when x = 0, y = -4.

For y = x² + 3 when x = 0, y = 3.

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Answer:

My answer is true hope this'll help

A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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Answer:

950

Step-by-step explanation:

A=P*(1/2)^(t/h)

The statement holds for n=k+1.

By mathematical induction, we have proven that 1·1!+2·2!+···+n·n!=(n+1)!−1 for all positive integers n.

What are integers?

Integers are a set of numbers that include whole numbers (positive, negative, or zero) as well as their opposites.

We will use mathematical induction to prove the statement.

Base case: Let n=1. Then the left-hand side of the equation is 1·1!=1 and the right-hand side is (1+1)!=2!-1=1. Therefore, the statement holds for n=1.

Induction hypothesis: Assume that the statement holds for some positive integer k, i.e., 1·1!+2·2!+···+k·k!=(k+1)!−1.

Inductive step: We need to show that the statement also holds for k+1, i.e., 1·1!+2·2!+···+(k+1)·(k+1)!=(k+2)!−1.

We have:

1·1!+2·2!+···+k·k!+(k+1)·(k+1)!=k!+1·1!+2·2!+···+k·k!+(k+1)·(k+1)!=k!+(k+1)!−1+(k+1)·(k+1)!=k!(k+1+1)+(k+2)!−1=(k+1)!(k+2)−1=(k+2)!−1,

where we have used the induction hypothesis in the second step and simplified in the fourth step.

Therefore, the statement holds for n=k+1.

By mathematical induction, we have proven that 1·1!+2·2!+···+n·n!=(n+1)!−1 for all positive integers n.

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For the given system of equations, the x-coordinate is 2.

What is the system of linear equations in two variables?

A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.

For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.

The given equations are

               y = x + 12  ---------(I)

             2x + y = 18  ---------(II)

Put the value of y = x + 12 in equation (II), and we get

            2x + x + 12 = 18

             3x + 12 = 18

              3x = 18 - 12

              3x = 6

                x = 6/3

                x = 2

Hence, for the given system of equations, the x-coordinate is 2.

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(1) One of the six countries sent 41 representatives to the congress --> obviously x6=41x6=41 --> x1+x2+x3+x4+A=34x1+x2+x3+x4+A=34.

Given: x1<x2<x3<x4<A<x6x1<x2<x3<x4<A<x6 and x1+x2+x3+x4+A+x6=75x1+x2+x3+x4+A+x6=75. Q: is A≥10A≥10

Can A≥10A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11 --> sum=34sum=34 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9 --> sum=34sum=34 (answer to the question NO).

(2) Country A sent fewer than 12 representatives to the congress --> A<12A<12.

The same breakdown works here as well:

Can 12>A≥1012>A≥10? Yes. For example: x1=2x1=2, x2=3x2=3, x3=8x3=8, x4=10x4=10, A=11A=11, x6=41x6=41 --> sum=75sum=75 (answer to the question YES);

Can A<10A<10? Yes. For example: x1=4x1=4, x2=6x2=6, x3=7x3=7, x4=8x4=8, A=9A=9, x6=41x6=41 --> sum=75sum=75 (answer to the question NO).

(1)+(2) The given examples fit in both statements and A in one is more than 10 and in another less than 10. Not sufficient.

A line segment known as a perpendicular bisector divides a straight line segment into two congruent or equal pieces. At the exact midway of the line segment, they divide it. A perpendicular bisector turns the line segment it bisects 90 degrees.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

The need for determining the perpendicular line is coordinates and a line equation. Think about a line with the equation axe + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. The slopes should add up to -1 if one line is perpendicular to this one.

The line connecting the points of intersection of these arcs is Perpendicular bisector

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We have that the equation given by the Option A is:

y = 2x + 10

and the Option B equation is:

y = 3x

If we graph them, we will obtain the following figure:

The cost is the same when the two line intercept each other. Their interception at the tenth ride

When this happens the cost is $30

Answer: the total cost of both options is the same at the tenth ride

We have that the cheapest plan is always given by the line below.

Before the tenth ride:

the cheapest plan is the Plan B

After the tenth ride:

the cheapest plan is the Plan A

Since Plan A will be the cheaper in the future after Ride number 10, we can say that the cheapest plan is Plan B

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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Answer:

25

Step-by-step explanation:

j(k + 2)

5(3 + 2)

5(5)

25

Answer:

5:25 ; 1:5

Step-by-step explanation:

there's 5/25 at a table. replace the slash with a colon.

5:25. Then simplify, getting 1:5

40  

because 95/100 x 38/1 = 40

Answer:

Step-by-step explanation:

Set up a proportion

Cross multiply

Divide both sides by 95 to solve for x

95 / 100 = 38/ x

95(x) = 38 x 100

95x = 3800

X = 40 There were 40 questions on the test