David went shopping at Staples for school supplies. He bought binders, pencils, and a book bag that cost $72. For binders, he spent $17 less than he did on pencils. In total, he spent $119. How much did he spend on binders?

EXPLANATION

Given the polynomials in the problem, we can assevere that:

Formula of Perfect Square Trinomial:

(a+b)^2 = a^2 + 2ab + b^2

Difference of Squares formula:

(a^2 - b^2)

Now, we need to find what formula match better.

y^2 + 12y - 36 -----> Neither

Answer:

y = x, y = x^3, y = x^5

Step-by-step explanation:

For it to be symmetrical over the origin, you need to replace x with -x and y with -y AND make sure it equals to the original function. So for example, take y = x^5. Replace the x and y with -c and -y respectively:

-y = -x^5

Both are still negative so if you divide by -1, it is just the original function so it is symmetrical over origin.

If you don't understand something, comment and I will try my best to answer it

Answer:

C

Step-by-step explanation:

Polygon 3 and 5 are congruent cause they have the same length of side

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer:

The orange (fruit) definitely got named first.

In ancient time, people hunt animals with old hunt tools. We can see some examples of old hunting tools.

And if they used bow, then I think they made string from raw materials like tree's branded peels.

Step-by-step explanation:

The area of the tabletop can be found by multiplying 3.14 by the radius of the circle squared. The radius can be determined by dividing the circumference (6π) by 2π. The area of the tabletop is thus 9.42 square feet.

The area of a circle can be found using the formula A =  π\(r^2\) where r is the radius of the circle and A is the area of the circle. In order to determine the radius, we must first determine the circumference of the circle, which is given as 6π. The circumference of a circle is equal to 2πr, so to find the radius we can divide 6π by 2π, giving us r = 3. Therefore, the area of the circle can be found by substituting 3 for r in the formula

A = π\(r^2\), giving us A = \(3.14 * 3^2 = 9.42\) square feet. Therefore, the area of the tabletop is 9.42 square feet.

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Answer: I believe it is A

The point (3, 2) is feasible for the constraint 2x1 + 6x2 ≤ 30. (False)

To determine if a point is feasible for a constraint, we need to substitute the values of the point into the constraint equation and check if the resulting inequality holds true.

In this case, the constraint is 2x1 + 6x2 ≤ 30. Substituting x1 = 3 and x2 = 2 into the equation, we get 2(3) + 6(2) = 6 + 12 = 18. Since 18 is not less than or equal to 30, the inequality is not satisfied.

Therefore, the point (3, 2) is not feasible for the given constraint. Feasible points satisfy the constraint, while infeasible points do not. In this case, any point that lies below the line represented by the constraint equation would be feasible, while points above the line would be infeasible.

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The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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Required value of s(4), s(7), s(5), s(9) are V(4) + C, V(7) + C, V(5) + C, V(9) + C respectively where c is the constant.

To determine the values of s(t) at different time points, we need to integrate the velocity function v(t) with respect to time. Based on the values you provided, it seems like you have already performed the integration correctly. However, since the values you provided are the definite integrals, we need to find the antiderivative or the indefinite integral of the velocity function to determine s(t) explicitly.

Let's assume the indefinite integral of v(t) is V(t). Then, we have:

s(t) = V(t) + C

where C is the constant of integration. To determine the constant C, we can use the initial condition s(0) = -3. Substituting t = 0 into the equation, we get:

s(0) = V(0) + C

-3 = V(0) + C

Since the constant of integration is the only unknown term, we can solve for C:

C = -3 - V(0)

Now, we can find the position function s(t) for different values of t using the indefinite integral and the constant C:

s(4) = V(4) + C

s(7) = V(7) + C

s(5) = V(5) + C

s(9) = V(9) + C

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Step-by-step explanation:

The slope is the coefficient of x, which is -0.4.

Answer:

-2/5

Step-by-step explanation:

y=-2/5x-3

y=mx+b

m is the slope so -2/5 is the slope

Hope this helps :D

They needed a total of 8 weeks to save the same amount of money, and after 8 weeks, everyone would have $200.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Harper and Joe want to buy season passes for Disneyland but neither of them has the $1,300 needed to purchase a pass.

Since Harper decides to get a job that pays $25 a week. She has nothing saved right now. Joe already has $80 and plans to save $15 of her weekly allowance.

To save up for the season pass:

Harper needs = 1300$

Since, She earns 25$ a week

Harper needs total weeks = 1300/25

Harper needs total weeks = 52 weeks

joe also needs 1300 $

Since, joe already has $80 and plans to save $15 of her weekly allowance.

Joe needs total weeks = (1300 -80)/15

Joe needs total weeks = 81.33

To have the same amount of money saved up:

Let "x" be the weeks they required to save the equal money:

25 *x = 80 + 15*x

10*x = 80

x = 8

Everyone will have = 25 * 8

Everyone will have = 200$

Therefore, they required total of 8 weeks to have the same amount of money saved up and everyone will have 200$ after 8 weeks.

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Answer:

8

Step-by-step explanation:

The probability of picking out a certain colour = 12/48 = 1/4

So, this means that every 4 socks you pick out you can be sure of having one of each colour. If you need to find a pair, then you pick out 8.

Hope this helps

a)The equilibrium production level for a firm is then given by q* = Q/N.

b) The equilibrium number of firms in the long run is:

N* = a/(F + 2bc)

a. Equilibrium price determination: The equation of the inverse demand curve is p(Q) = a - bQ.

The total output produced by all N firms is Q. Since the firms are producing an identical product, they all charge the same price, denoted by p. Therefore, the revenue earned by an individual firm is given by:

R(q) = pq.

Each firm wants to maximize its profits.

The profit of the ith firm is:

π(qi) = R(qi) - c(qi) = pqi - (F + cqi) = (p - c)qi - F

Therefore, it maximizes its profits by choosing that production level at which its profit is the highest.

Therefore, we have:MR = MC(p - c) = F.

Nash Equilibrium:All firms have identical costs and therefore they all produce the same amount. Let this amount be denoted by q*. Since there are N firms, the market supply is given by Q = Nq*.

The equilibrium price is then determined using the inverse demand equation. Thus, we have:p = a - b(Nq*)

The equilibrium production level for a firm is then given by q* = Q/N.

b. Long-run equilibrium number of firms in the market:In the long run, firms enter and exit the market until the profit of each firm is zero.

Therefore, if economic profits can be made, new firms will enter the market.

On the other hand, if losses are being made, firms will exit the market.

The profit of the firm is given by:π(q) = R(q) - c(q) = pq - (F + cq)

The necessary condition for the profit to be zero is:R(q) = c(q)

This condition holds when the price is equal to the average cost. Thus, we have:p = c(q) + F/q

If we substitute the inverse demand equation in this, we get:Nq* = (a - F)/(2b)

Therefore, the equilibrium number of firms in the long run is:

N* = a/(F + 2bc)

As N increases, the equilibrium number of firms approaches infinity.

Therefore, in the limit, we have:N* approaches infinity as N increases

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Answer:

\(21f^{2} g^{4} h^{6\)

Step-by-step explanation:

The given expression is 7fgh*3fg^3h^5

We can multiply the numbers together first to get:

21fghfg^3h^5

Keep in mind this rule:

n^a*n^b=n^a+b

That said, we can simplify it fairly easily:

21f^2g^4h^6

Or:

\(21f^{2} g^{4} h^{6\)

Answer:

The height of the rectangular prism

= 1 1/3 inches

Step-by-step explanation:

The volume of a rectangular prism = Length × Width × Height

From the question:

Length of 5/6​​ inch

Width of 3 /5​​ inch.

The volume of the prism is 2 /3​​ cubic inch.

Find the height of the prism.

Hence:

2/3 = 5/6 × 3/5 × Height

2/3 = 1/2 × Height

Divide both sides by 1/2

Height = 2/3 ÷ 1/2

Height = 2/3 × 2

Height = 4/3 inches = 1 1/3 inches

Therefore, the height of the rectangular prism = 1 1/3 inches

Answer:

25,68$

Step-by-step explanation:

7% of $ 24 is:

24 * 0,07 = 1,68

The total price is then:

24$ + 1,68$ = 25,68$

Answer:

b. x=2

Step-by-step explanation:

The axis of symmetry of a parabola gives us a line of symmetry where the parabola appears the same but flipped on either side. It passes through the parabola's vertex, or the minimum/maximum point of the parabola. Here, we can see that the parabola's minimum point occurs when x=2. Therefore, its axis of symmetry is x=2.

I hope this helps!

Answer:

B. 4x+5

Step-by-step explanation:

First, you multiply both sides by 4, then you have x=y-5. You then add 5 to get 4x+5

(in the very beginning, you switch the x and y so you would have to make the equation x= y-5 / 4 if that confused you)

The minimum number of coin tosses required to have more than a 50% chance of getting at least one head is two.

The possible outcomes of flipping a coin:

If the coin is flipped more than once, there are only two possible outcomes: H or T, whereby each outcome has a 50% chance of occurring.

So let us say that the coin is flipped twice, we have four possible outcomes:

In this case, the only outcome that do not have at least one head is TT.

In conclusion,  the probability of getting at least one head is 1 - (1/2 x 1/2) = 3/4, or 75% which is greater than 50%

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Answer:690

Step-by-step explanation:

690

Answer:  $3,261.

Step-by-step explanation:

The answer is $3,261. Jayden would have more money in his account than Camden because his account pays a higher interest rate and is compounded continuously, which allows more frequent compounding of interest. This means that Jayden's account accumulates more interest than Camden's account over time.

Answer:

f=2

Step-by-step explanation:

The volume of the solid, obtained by revolving the region bounded by xy = 1, y = 0, x = 1, and x = 2, using the washer method, is: a) π/2 cubic units when revolved about the axis x = -1 and b) 7π/6 cubic units when revolved about the x-axis.

What is washer method?

The washer method is a technique used to calculate the volume of a solid of revolution. It involves integrating the cross-sectional area of the solid, which is obtained by subtracting the inner area from the outer area of a "washer" or "annulus" shape.

a) To find the volume when revolved about the axis x = -1, we consider the slices perpendicular to the x-axis. Each slice will have a radius equal to the distance from the axis of revolution to the curve, which is x + 1. The differential thickness of the slice is dx.

Thus, the volume of each washer-shaped slice is π(radius_outer² - radius_inner²)dx. Integrating this expression from x = 1 to x = 2, we get the volume as π/2 cubic units.

b) When revolved about the x-axis, we consider the slices perpendicular to the y-axis. The radius of each slice is y, and the differential thickness is dy. The limits of integration are y = 1 and y = 2. Using the washer method and integrating π(radius_outer² - radius_inner²)dy, we find the volume to be 7π/6 cubic units.

Therefore, the volume of the solid when revolved about the axis x = -1 is π/2 cubic units, and when revolved about the x-axis is 7π/6 cubic units.

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Answer:

Step-by-step explanation:5

As the angle increases from 0 to π/2, the value of sine increases, and the value of cosine decreases.

Trigonometry is a branch of mathematics that deals with the relationships between angles and sides of triangles.

Let us first understand the concept of sine and cosine. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle and the length of the hypotenuse. Similarly, the cosine of an angle is defined as the ratio of the length of the adjacent side and the length of the hypotenuse.

As the angle θ increases from 0 to π/2, the length of the opposite side (the numerator in sine) of the triangle increases, and the length of the hypotenuse (the denominator in sine) remains the same. Therefore, the value of sine increases as θ increases.

On the other hand, as the angle θ increases from 0 to π/2, the length of the adjacent side (the numerator in cosine) decreases and the length of the hypotenuse (the denominator in cosine) remains the same. Therefore, the value of cosine decreases as θ increases.

This behavior is consistent with the fact that sine is an increasing function, while cosine is a decreasing function within this range of angles.

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Complete Question:

If 0< θ <π/2, as Theta increases, the value of

cos(θ) [Decreases/Increases/Remains The Same]

and the value of sin(θ) [Decreases/Increases Remains The Same]​

The correct answer is option C. A sampling plan refers to a detailed strategy for obtaining a sample from a population for the purpose of data collection.

It describes the precise procedures needed to choose the sample, determine the members of the sample, and gather the data.

The sampling strategy should take into account the type of sampling design, sample size, sampling process, and the methods to be employed for data collecting.

The strategy for implementing sampling should be outlined in the plan, along with instructions on how to make sure the sample is representative of the population, how to prevent bias in the sampling process, and how to make sure the data gathered is of high quality.

A good sampling plan should provide a clear and consistent method for gathering data and be founded on basic statistical concepts.

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The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

Compared to the graph of y = x graph y = -x/3 is a negative slope

Compared to the graph of y = x graph y = -x/3 intersects the y axis at same point

Compared to the graph of y = x graph y = x - 2 is a parallel line

Compared to the graph of y = x graph y = x - 2 intersects the y axis at 2 units down

The two graphs compared are linear function graphs

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

y = x

slope = 1

c = 0

y = -x/3

slope = -1/3

c = 0

y = x - 2

slope = 1

equal slopes means the lines are parallel

c = -2 (down 2 units)

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Answer:

Step-by-step explanation: