A government study found that people buy more gasoline when the price per gallon decreases. What can we determine?

Answer:

5

Step-by-step explanation:

if -17 +5 are in value they should equal 12

The shape of the graph changes qualitatively at k = ± 2 and

\(k=\sqrt{(2)\).

The given function is f(x,y) = y-x²+y²+kxy.

The critical points of the function are found by taking the partial derivatives and equating them to zero:

∂f/∂x = -2x + ky = 0

y = 2x/k

∂f/∂y = 2y + kx = 0

y = -kx/2

Substituting y from the first equation into the second equation gives

x = k²x/4, so k² = 4 and k = ± 2.

Therefore, the critical points are (0,0), (2,4), and (-2,4)

We will now examine the critical points to see when the shape of the graph changes qualitatively.

There are two cases to consider:

Case 1: (0,0)At (0,0), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2 0;0 2].

The determinant of the Hessian matrix is -4, which is negative.

Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.

Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is

H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]

=[ -2k 2k;2k 2].

The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).

Therefore, the critical points (2,4) and (-2,4) are local minima when

k > √(2).

Thus, the shape of the graph changes qualitatively at k = ± 2 and

k = √(2).

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Answer:

24.95-6.95= 18

18 divided by 8 = 2.25

So each tube of paint cost 2.25 dollars

Step-by-step explanation:

for the first equation we are subtracting the cost of the canvas from the total cost to find the cost of 8 tubes of paint and we get that 8 tubes of paint cost 18 dollars. Next we divide 18 by 8 to get the cost of a single tube of paint and we get 2.25.

Answer: \((x+10)(x-10)\)

Step-by-step explanation: Difference of squares is an important element in understanding square functions. In order to identify difference of squares, the equation should be given in the form a^2-b^2. You can factor it completely when b^2 can be square rooted perfectly and write the factored expression as (a-b)(a+b) as I have done above.

If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,

Rs 30 = 45 book

Rs 30 = 45

Rs 1 = 45 / 30

Rs 24 = 3/2 × 24

Rs 24 = 34 books

Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

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Answer:

fishy camera

Step-by-step explanation:

most distance in feet from surface

The fish camera is furthest from the surface of the water.

Answer:If r(x) = 3x – 1 and s(x) = 2x + 1, r/s (6) is equivalent to 17/13. Let's understand the solution in detail. Explanation: In this problem, first we perform the division operation on the given functions and find r(x) / s(x).

Your welcome :|

The probability that two children selected at random from Mrs. Attaway's first-grade class are girls and one is a boy is 0.120.

To find the probability that two children selected at random from Mrs. Attaway's class are girls and one is a boy, we need to calculate the number of favorable outcomes (selecting two girls and one boy) and divide it by the total number of possible outcomes.

The total number of children in the class is 5 girls + 16 boys = 21 children.

To calculate the probability, we need to determine the number of ways to select two girls from the five available girls and one boy from the 16 available boys. This can be done using combinations.

The number of ways to select two girls from five is given by the combination formula:

C(5, 2) = 5! / (2! * (5 - 2)!)

= 5! / (2! * 3!)

= (5 * 4) / (2 * 1)

= 10

Similarly, the number of ways to select one boy from 16 is given by the combination formula:

C(16, 1) = 16

The total number of favorable outcomes is the product of these two combinations: 10 * 16 = 160.

Now, let's calculate the total number of possible outcomes when selecting three children from the class:

C(21, 3) = 21! / (3! * (21 - 3)!)

= 21! / (3! * 18!)

= (21 * 20 * 19) / (3 * 2 * 1)

= 1330

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = favorable outcomes / total outcomes

= 160 / 1330

≈ 0.120 (rounded to three decimal places)

Therefore, the probability that two children selected at random from Mrs. Attaway's first-grade class are girls and one is a boy is 0.120.

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Figure (c) is a dilation of figure ABCD.

By drawing rays from point Q to each of the vertices of figure ABCD and extending them to intersect with a new figure, we may determine the dilation since figure ABCD is dilated from point Q.

Looking at the possible answers, we can see that only figure (c), with all angles and side lengths proportional to those in ABCD, has the same form as ABCD. Figure (c) shows a dilatation of Figure ABCD as a result.

As figure (c) exceeds ABCD, the dilation has a scale factor higher than 1. In other words, the ratio of the corresponding side lengths is the same for all sides, and each side length and angle in figure (c) are larger than the corresponding side length and angle in ABCD.

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The table of values that represents exponential decay is (c)

From the question, we have the following parameters that can be used in our computation:

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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Answer:

24 x y

Step-by-step explanation:

Simplify the following:

3×4×2 x y

Hint: | Multiply 3 and 4 together.

3×4 = 12:

12×2 x y

Hint: | Multiply 12 and 2 together.

12×2 = 24:

Answer: 24 x y

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

To solve the inequality y + 7 ≤ -1, we need to isolate the variable y on one side of the inequality sign.

Starting with the given inequality:

y + 7 ≤ -1

We can begin by subtracting 7 from both sides of the inequality:

y + 7 - 7 ≤ -1 - 7

y ≤ -8

The solution to the inequality is y ≤ -8. This means that any value of y that is less than or equal to -8 will satisfy the original inequality.

In the context of a number line, all values to the left of -8, including -8 itself, will make the inequality true. For example, -10, -9, -8, -8.5, and any other value less than -8 will satisfy the inequality. However, any value greater than -8 will not satisfy the inequality.

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The following question may be like this:

What is a solution of the inequality shown below? y+7≤-1

Expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16

What do you mean by One-to-One Correspondence?

the capability of relating one object to another. For each number spoken aloud, the learner should be able to count or move one object while saying "1,2,3,4". She has not learned one-to-one correspondence if she accidentally counts an object twice or skips one of the things while counting. Before starting Giggle Facts, students must be able to match one object to each number counted.

Remind your kids that a double fact is a mathematical expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16. Give children the chance to practise combining groups of the same number using manipulatives or other classroom supplies.

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Answer:

A double expression

Step-by-step explanation:

The sum in summation notation of the expression (a) 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is ΣX from 1 to 4. In other words, it represents the summation of X over the range 1 to 4.

In summation notation, the expression (a) 1 + 2 + 3 + 4 + X5 can be written as ΣX, where X takes the values from 1 to 4. The capital sigma (Σ) represents the summation operator, and the variable X is summed over the range 1 to 4. This means that we need to substitute X with each value from 1 to 4 and add them together.

When we evaluate the expression, we have:

ΣX = 1 + 2 + 3 + 4 = 10

However, the expression also includes X5, indicating that X takes the value 5 as well. Therefore, we add 5 to the sum:

ΣX = 10 + 5 = 15

So, the sum of 1 + 2 + 3 + 4 + X5, where X takes the values 1-4, is equal to 15.

Moving on to expression (b) y2 + y3 + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, we can express it in summation notation as ΣY from 1 to 3. This represents the summation of Y over the range 1 to 3.

Since Y has a different value for each term, we simply substitute Y with each value from 1 to 3 and add them together:

ΣY = y₁ + y₂ + y₃ = -1 + (-0.5) + 0 = -1.5

Hence, the sum of y₂ + y₃ + Y, where Y takes the values y₁ = -1, y₂ = -0.5, y₃ = 0, y₄ = 1.35, is equal to -1.5.

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Answer:

7in, 7in, and 15 in

Step-by-step explanation:

Based on the Triangle Inequality Theorem that states that the sum of any 2 sides of a triangle must be greater than the measure of the third side, we can find what set of lengths cannot form a triangle.

The only set that does not follow the theorem is the set with lengths 7in, 7in, and 15in. It does not follow the theorem because...

7 + 7 < 15 (which should not be true based on the theorem)

1.9 × 10^3  is 215 times smaller than 4.085 × 10^5.

The basic formula for the area of ​​a rectangle is length x width, but the basic formula for volume is length x width x height. The calculation does not change depending on how you refer to different measurements. For example, you can use depth instead of height.

Every 3D object occupies a certain space. This space is measured by its volume. Volume is defined as the space occupied within the bounds of an object in three-dimensional space. Also called the capacity of the object. The volume of an object is the amount of space it fills. Large capacity is measured in cubic meters m3. Smaller volumes are measured in cubic centimeters cm3 or cubic millimeters mm3.

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Answer:

741.63km

Step-by-step explanation:

From the above question, we know the following things:

Diameter of the Earth = 12756000m

Diameter of the new planet = 5/86 of the Diameter of the Earth

Diameter of the new planet =

5/86 × 12756000m

= 741627.90698m

The diameter of the new planet = 741627.90698m

We were asked to find the diameter of the new planet in km, hence we convert from meters to kilometers

1m = 0.001km

741627.90698m =

741627.90698 × 0.001km

= 741.62790698km

Approximately = 741.63km

Therefore, the diameter of the new planet = 741.63km

Answer:

A≈380.13 m²

Step-by-step explanation:

looked it up

Answer:

A= 380.13 m²

Step-by-step explanation:

A=\(\pi r^{2}\)

A= \(\pi\)x\(11^{2}\)

A= 380.13

If the power of the polynomial is 1. Then the degree of the polynomial is one.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The linear polynomial is given below.

⇒ (7/4)x + 3

The power of the polynomial is 1.

Then the degree of the polynomial is 1.

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Using a system of equations, we have:

Parker family’s sprinkler 15 L per hour

Wood family’s sprinkler 20 L per hour

Let's represent the water output rate for the Parker family's sprinkler as "P" and the water output rate for the Wood family's sprinkler as "W".

We know that the Parker family used their sprinkler for 30 hours, so they released a total of 30P liters of water. Similarly, the Wood family released a total of 15W liters of water.

The combined total output of both sprinklers is given as 750 L of water:

30P + 15W = 750

We also know that the sum of the two rates is 35 L per hour:

P + W = 35

Now we have two equations with two unknowns. We can solve for P and W by using substitution or elimination. Here, we will use substitution. Solving the second equation for P, we get:

P = 35 - W

Substituting this expression for P into the first equation, we get:

30(35 - W) + 15W = 750

Expanding and simplifying, we get:

1050 - 30W + 15W = 750

-15W = -300

W = 20

Now that we know W, we can use the second equation to find P:

P + 20 = 35

P = 15

Therefore, the water output rate for the Parker family's sprinkler was 15 L per hour, and the water output rate for the Wood family's sprinkler was 20 L per hour.

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Answer:

its equivalents can be 3/5*2 =6/10 = > 6:103/5×2=6/10=>6:10

second equivalent is 3/5*3=9/15= > 9:153/5×3=9/15=>9:15

Answer:

30/50, 6/10, 15/25, 300/500

actually as a ratio it should be:

30:50 , 6 : 10, 15:25, 300:500

Step-by-step explanation:

The probability that the flight will not be delayed is 0.79.

If the probability that a flight will be delayed is 0.21, then the probability that it will not be delayed must be:

Understand that the total probability of an event is always 1. In this case, there are only two possible outcomes: the flight is delayed, or it is not delayed.
Subtract the probability of the flight being delayed (0.21) from the total probability (1).

1 - 0.21 = 0.79

The probability that the flight will not be delayed is 0.79.

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Answer:

Step-by-step explanation:

x=0

Answer:

There is 1 tree per 1.6 acre.

Step-by-step explanation:

Divide the number of trees from the number of acres. This will tell you how many acres are between each tree.

Answer:

0.6 acres.

Step-by-step explanation:

You divide the total population of the willow tree (30) by the areas they occupy (50 acres). Therefore, 30/50=0.6 population per acre.

John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.

To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.

The present value of an annuity formula is given by:

P = A * [(1 - (1 + r)^(-n)) / r],

where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:

196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].

Simplifying the expression inside the brackets:

196,000 = A * (1 - 0.469091).

196,000 = A * 0.530909.

Dividing both sides by 0.530909:

A = 196,000 / 0.530909.

A ≈ 369,238.68.

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The statement is false. A counterexample can be found by considering the real number x = 1.5. In this case, ⌊x^2⌋ = ⌊1.5^2⌋ = ⌊2.25⌋ = 2, while ⌊x⌋^2 = ⌊1.5⌋^2 = 1^2 = 1. Therefore, the equation ⌊x^2⌋ = ⌊x⌋^2 does not hold for all real numbers x.

In the counterexample x = 1.5, we can see that ⌊x^2⌋ is equal to the greatest integer less than or equal to x^2, which is 2. On the other hand, ⌊x⌋^2 is equal to the greatest integer less than or equal to x, squared. In this case, ⌊1.5⌋^2 is equal to 1^2, which is 1.

Since 1 is not equal to 2, we can conclude that the statement ⌊x^2⌋ = ⌊x⌋^2 is false for the counterexample x = 1.5. Therefore, the original statement is false.

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In graph theory, a "sparse" graph is a graph that has relatively few edges compared to the maximum possible number of edges for that graph.

Specifically, a graph with n vertices can have at most n(n-1)/2 edges, which is the maximum number of possible edges in a complete graph. A sparse graph has many fewer edges than this maximum.

An implementation technique for graphs that is inefficient for sparse graphs is the use of an adjacency matrix to represent the graph. An adjacency matrix is a two-dimensional array where the value in each cell represents the weight of the edge between two vertices. For a sparse graph, most of the cells in the adjacency matrix are empty, since there are relatively few edges in the graph. This means that a lot of memory is wasted on storing zeros, and operations such as finding all adjacent vertices or iterating over all edges are slow and inefficient.

For sparse graphs, a better implementation technique is to use an adjacency list. An adjacency list is a collection of lists or arrays, where each list corresponds to a vertex in the graph and contains the vertices that are adjacent to it. Since there are only a few edges in a sparse graph, the adjacency lists are much shorter than the adjacency matrix would be, and operations such as finding adjacent vertices or iterating over edges are much faster. Additionally, an adjacency list uses less memory than an adjacency matrix, making it more efficient for sparse graphs.

In summary, using an adjacency matrix to represent a sparse graph is inefficient because it wastes memory on storing zeros and is slow for operations such as finding adjacent vertices or iterating over edges. An adjacency list is a more efficient implementation technique for sparse graphs because it uses less memory and is faster for these operations.

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