Jared rents bowling shoes for 6$ and pays 5$ per bowling game. Graph the data. Is the relationship a proportional relationship? Explain.

Answer:

y = -2/3x - 3

Step-by-step explanation:

y = mx + b

m = slope

(-3,-1) = (x,y)

Plus in the coordinates

-1 = -2/3(-3) + b

negative times negative = positive

-2/3 * -3 = 2

-1 = 2 +b

Use inverse operations

-2 --2

-3 = b

y = -2/3x - 3

Answer:

y = -2/3 x - 3

Step-by-step explanation:

since you have a point and a slope, you can use point - slope form

Answer:

(8,11) because a whole number dilation means you add that number to the points, but a fraction means you subtract.

Step-by-step explanation:

Answer: w=20/3

Step-by-step explanation: start by multiplying -3/2 by 2 and multiply -10 by 2 as well. you would get -3w = -20. divide both sides by -3 and you’ll get 20/3.

Answer:

Nutz in my opinion

Step-by-step explanation:

Answer:

girls

Step-by-step explanation:

If the investment is $5000 at 12% weekly compound interest then the balance after 2 years would be approximately $7,180.47.

To solve this problem, we can use the formula for compound interest:

A = \(P (1 + r/n)^{(nt)}\)

where A is the balance after t years, P is the principal amount invested, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

In this case, we have:

P = 5000 (the principal amount invested)

r = 0.12 (the annual interest rate)

n = 52 (since the interest is compounded weekly, there are 52 weeks in a year)

t = 2 (since we want to find the balance after 2 years)

Plugging these values into the formula, we get:

A = 5000 (1 + 0.12/52)⁵²ˣ²

A = $7,180.47

Therefore, the balance after 2 years is approximately $7,180.47.

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Answer:

6,483.75

Step-by-step explanation:

Calculation to find the interest paid by B after 3/2 year

First step is to calculate the Compound interest amountUsing this formula

Interest paid= P(1 + r/100)^Time

Where,

P represent principal=32,500

r represent Rate of interest = 12.5%/2 = 6.25%

T represent Time=3/2 years

Let plug in the formula

Compound interest amount= 32,500(1 + 6.25/100)^2*3/2

Compound interest amount= 32,500([1+.0625)^3

Compound interest amount= 32,500(1.0625)^3

Compound interest amount= 32,500 *1.1995

Compound interest amount= 38,983.75

Now let calculate the Interest paid by B

Interest paid by B = 38,983.75 - 32,500

Interest paid by B = 6,483.75

Therefore the interest paid by B after 3/2 year will be 6,483.75

Answer:

x2 + 100 = (x + 10i)(x − 10i)

x2 + 36 = (x + 6i)(x − 6i)

16x2 + 9 = (4x + 3i)(4x − 3i)

Step-by-step explanation:

Edmentum Answer

The factors of the expressions have been determined as  ( x +10i) ( x -10i) ,  ( x +6i) (x-6i) ,  (4x + 3i) ( 4x - 3i)

An expression is a mathematical statement consisting of variables , constants and mathematical operators .

The expression given in the question is

x² + 100

x² + 36

16x²2 +9​

by the identity a² -b² = ( a+b)(a-b)

The expressions can be written as

( x² - ( 10i)²)  , (x² - ( 6i)²) , ( (4x)² - ( 3i)²)

It is known that i² = -1

Therefore here the expressions can be written as

( x² - ( 10i)²) = ( x +10i) ( x -10i)

(x² - ( 6i)²) = ( x +6i) (x-6i)

( (4x)² - ( 3i)²) = (4x + 3i) ( 4x - 3i)

Therefore the factors of the expressions have been determined.

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Answer:

m = -5/2

b = 3

Step-by-step explanation:

The equation is in y = mx +b form where m is the slope and b is the y-intercept.  This means that the slope is -5/2 and the y-intercept is 3.

Which graph results when f(x) = (8)* is first reflected across the y-axis and then across the x-axis?

Option 1 for Question 1

Option 1 for Question 2

Option 3 for Question 3

Option 1 for Question 4

Option 1 to Question 5

1) We subtract from any sequence to find the common difference d. For instance, =(-4) - (-15) = -4+15 = 11. Hence, choice 1. The answer for the sequence is (11).

2) In case a sequence is

The sequence's eighth term, then, will be = 25-24 = 1. Therefore, choice 1 is right.

Question #3: Any arithmetic series has the following explicit rule

As a result, choice three is right.

4. Reggie started off with 195 cards, and each week, 16 more cards are added.

In light of this query

There are 16 common differences in the sequence.

The order is going to be

the amount of cards will be after the 12th week.

Therefore, choice 1 is right.

5th query: If the sequence is

Then

and

The usual difference is 7-3 = 4.

Therefore

Choice 1. is the right response.

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The equivalent expression after distributing the "-" sign outside the parenthesis is -10n + 9.1p - 3.4.

When we distribute the negative sign outside the parenthesis in the expression -(10n - 9.1p) - 3.4, we apply the distributive property, which states that multiplying a negative sign to a set of terms inside the parenthesis affects the signs of each term.

In this case, we have a negative sign in front of the parenthesis, so we need to change the signs of each term within the parenthesis. Let's break it down step by step:

1. Distribute the negative sign to the first term inside the parenthesis, which is 10n. Since we have a negative sign in front, it becomes -10n.

2. Distribute the negative sign to the second term inside the parenthesis, which is -9.1p. The negative sign in front changes the sign to positive, so it becomes 9.1p.

After distributing the negative sign to each term inside the parenthesis, we obtain:

-10n + 9.1p

Lastly, we subtract the remaining term outside the parenthesis, which is -3.4:

-10n + 9.1p - 3.4

Thus, this expression, -10n + 9.1p - 3.4, is the result of distributing the negative sign outside the parenthesis and changing the signs of the terms inside.

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The value of ㏒₁₀√3 - 1 / 2 ㏒₁₀2 is 1 / 2.㏒₁₀(1.5)

Given: To evaluate ㏒₁₀√3 - 1 / 2 . ㏒₁₀2

What are logarithms?

If a equation is given in the form of aᵇ = c, then ㏒ₐc = b or in a definitive way a logarithm is the power to which a number must be raised in order to get a number. As here 'a' is raised to the power 'b' to given a number c, so the number base 'a' if be raised to some power of 'b' then it will yield a number 'c'.

For example, 10² = 100 which can be written as ㏒₁₀100 = 2 by the following property of logarithm that is ㏒ₐ(bⁿ) = n.㏒ₐb.

So,  ㏒₁₀100 = ㏒₁₀10² = 2.㏒₁₀10 = 2 [ Another property ㏒ₐa = 1]

Some basic properties on logarithm operations are

1) ㏒ₙa + ㏒ₙb = ㏒ₙ(ab)

2) ㏒ₙa - ㏒ₙb = ㏒ₙ(a / b) [NOTE: ㏒ₙa - ㏒ₙb is not commutative]

3) ㏒ₐ(bⁿ) = n.㏒ₐb

4) ㏒ₐa = 1

Now let's solve the sum: ㏒₁₀√3 - 1 / 2 ㏒₁₀2

㏒₁₀√3 - 1 / 2 ㏒₁₀2 = ㏒₁₀(3)\(^{\frac{1}{2}}\) - 1 /2 .㏒₁₀2 [ Root means 1 / 2 power]

= 1 / 2.㏒₁₀(3) - 1 / 2.㏒₁₀(2)   [ ㏒ₐ(bⁿ) = n.㏒ₐb ]

= 1 / 2.(㏒₁₀(3) - ㏒₁₀(2))

= 1 / 2.(㏒₁₀(3 / 2)                  [ ㏒ₙa - ㏒ₙb = ㏒ₙ(a / b) ]

= 1 / 2.㏒₁₀(1.5)

Hence value of ㏒₁₀√3 - 1 / 2 ㏒₁₀2 = 1 / 2.㏒₁₀(1.5)

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Answer: C

Step-by-step explanation: C

2 divided into 9 parts is 2/9.

Let's' explain this visually

Take this pizza, (image below)

Let's say we have two pizzas for 8 friends (including ourselves), so naturally, we'll cut the pizza's each into 9 slices, 1 for each, now everyone gets 1/9 of a pizza, but there are two pizzas, so if we add 1/9+1/9, we'll get two ninths.

Now 2/9=0.2 repeating!

This is how I got my answer sorry for the vague  explanation

Answer:

4,-7 = 11

and

6, -9 = 15

201.06cm²  

Hope this helps.

The provided questions cover various aspects of a 2-period production economy, including the household's problem, firm's problem, market clearing conditions, Social Planner's Problem, competitive equilibrium, and welfare theorems.

(a) The Household's problem is to maximize its utility over two periods subject to its budget constraint. The household's problem can be formulated as follows:

Max U(Co, C1) = log(Co) + ß log(C1)

subject to the budget constraint:

Co + (1+r)C1 ≤ (1+r)Ko + W0 + W1,

where Co and C1 are consumption in period 0 and 1 respectively, ß is the discount factor, r is the interest rate, Ko is the initial capital endowment, W0 and W1 are the wages in periods 0 and 1 respectively.

(b) The Firm's problem is to maximize its profit by choosing the optimal combination of capital and labor. The firm's problem can be formulated as follows:

Maximize F(K, L) - RK - WL,

where F(K, L) is the production function, K is capital, L is labor, R is the rental rate of capital, and W is the wage rate.

(c) The market clearing conditions are:

Capital market clearing: K1 = (1 - δ)K0 + S - C0, where δ is the depreciation rate, S is savings, and C0 is consumption in period 0.

Labor market clearing: L = L0 + L1, where L0 and L1 are labor supplies in periods 0 and 1 respectively.

(d) The Social Planner's Problem is to maximize social welfare, which is the sum of the household's utility and the firm's profit. The Social Planner's Problem can be formulated as follows:

Maximize U(C0, C1) + F(K, L) - RK - WL,

subject to the production function F(K, L) and the market clearing conditions.

(e) A Competitive Equilibrium is a situation where all markets clear and agents (household and firm) make optimal decisions based on prices and market conditions. It is characterized by the following conditions:

Household's problem is solved optimally.

Firm's problem is solved optimally.

Market clearing conditions hold.

(f) To solve the Social Planner's Problem, we need to set up the Lagrangian and solve for the optimal values of consumption, capital, and labor. The Lagrangian can be written as:

L = U(C0, C1) + F(K, L) - RK - WL + λ1[(1+r)K0 + W0 + W1 - Co - (1+r)C1] + λ2[K1 - (1 - δ)K0 + S - C0] + λ3[L - L0 - L1],

where λ1, λ2, and λ3 are the Lagrange multipliers.

(g) To solve the Competitive Equilibrium, we need to determine the prices of capital (R) and labor (W) that clear the markets. This can be done by equating the demand and supply of capital and labor, and solving the resulting equations.

(h) The First Welfare Theorem states that under certain conditions, a competitive equilibrium is Pareto efficient. It implies that a competitive equilibrium is a socially optimal allocation of resources. To verify the theorem, we need to demonstrate that the competitive equilibrium allocation is Pareto efficient.

(i) The Second Welfare Theorem states that any Pareto efficient allocation can be achieved as a competitive equilibrium with appropriate redistribution of initial endowments.

To verify the theorem, we need to show that given an initial Pareto efficient allocation, we can find prices and redistribution of endowments that lead to a competitive equilibrium that achieves the same allocation.

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However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

Let's consider that s be the length of a side of the regular pentagon.

The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm

Also,

we have the formula for the area of a regular pentagon as:

\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)

where a is the length of a side of the pentagon.

In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.

Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)

Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.

The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.

In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.

However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.

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Answer:

40 [adv] and 25 [same-d].

Step-by-step explanation:

1) suppose, the number of advance ticket is 'a', of same-day is 's', then

2) total number of sold ticket is 65, that is: a+s=65 - this is the first equation of system;

3) and the price of the all sold advanced tickets is 35a, the price of the all sold same-day tickets is 20s, then the total price is: 35a+20s=1900 - this is the second equation of system;

4) it is possible to make up and solve the system of two equations:

\(\left \{ {{a+s=65} \atop {35a+20s=1900}} \right. \ => \ \left \{ {{4a+4s=260} \atop {7a+4s=380}} \right. \ => \ \left \{ {{a=40} \atop {s=25}} \right.\)

5) finally, 40 advanced and 25 same-day tickets were sold.

Hello.. How are you??

hey guy, do it yourself

Step-by-step explanation:

understood

The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.

What is a sphere?

The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.

Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.

The radius of a sphere is the half of its diameter.

The radius of the bottom ball is 3/2 feet =1.5 feet

The radius of the middle ball is 2/2 feet = 1 feet.

The radius of the top ball is 1/2 feet = 0.5 feet.

The volume of a sphere is 4/3 × ∏r³.

The volume of  bottom ball is  4/3 × ∏ × (1.5)³  cubic foot.

The volume of  middle ball is  4/3 × ∏ × (1)³  cubic foot.

The volume of  middle ball is  4/3 × ∏ × (0.5)³  cubic foot.

The total amount of snow is

4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³

=  4/3 × ∏ [1.5³  +1³  + 0.5³ ]

=  4/3 × ∏× 4.5

= 18.84

≈ 19 cubic foot

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The result for  8/5 divided by 3 equals 8/15. We can solve a fraction with a greater numerator by multiplying both numerators and denominators.

Given fraction = 8/3

Divisor = 3

When there is no denominator for the divisor, we can assume it is One.

3 = 3/1

We can multiply the two fractions to get into one single fraction

(8/5) ÷ (3/1) = (8/5) x (1/3)

Multiply both the numerators and denominators.

(8/5) x (1/3) = (8 x 1) / (5 x 3) = 8/15

Therefore, we can conclude that 8/5 divided by 3 equals 8/15.

To solve a question with a fraction with a greater numerator,

Write the denominator as 1 and flip the fraction.

(15/8) ÷ (3/1) = (15/8) x (1/3)

Multiply the numerators and denominators together:

(15/8) x (1/3) = (15 x 1) / (8 x 3) = 5/8

Therefore, we can conclude that 15/8 divided by 3 equals 5/8.

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Answer:

5000000

Step-by-step explanation:

10^6 = 10 x 10 x 10 x 10 x 10 x 10

10^6 = 1000000

5 x 10^6

= 5 x 1000000

= 5000000

The value equivalent to 5x10⁶ written in standard form is 5,000,000.

5: This is a regular number, and it represents the base value of the expression.

x: This symbol represents multiplication. When you see "5x," it means you're multiplying the base value (5) by the next part of the expression.

10⁶ : 10 is raised to the power of 6. In mathematical terms, "10⁶" means 10 raised to the power of 6, which is equal to one million (1,000,000).

In superscript notation, 10⁶ means 10 raised to the power of 6, which is equal to one million. When you multiply 5 by 10⁶, you get 5,000,000.

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Step-by-step explanation:

Volume of a sphere is given by

\(V = \frac{4}{3} \pi {r}^{3} \)

Where r is the radius of the sphere

From the question

radius = 41 in

Substitute the value into the above formula

We have

\(V = \frac{4}{3} \times {41}^{3} \pi\)

\( = \frac{275684}{3} \pi\)

= 288695.6097

We have the final answer as

Hope this helps you

The answer on deltamath is

288695.6 in³

Using the method of least squares, the best line through the points (-1,-1), (-2,3), and (0,-3) is given by y = (5/3)x.

Step 1: The general equation of a line is y = c₀ + c₁x. Plugging the data points into this formula, we have the following equations:

-1 = c₀ - c₁

3 = c₀ - 2c₁

-3 = c₀

Step 2: Formulating the matrix equation, we can write it as A*c = y, where:

A = [[1, -1], [1, -2], [1, 0]],

c = [[c₀], [c₁]],

y = [[-1], [3], [-3]].

To find the least squares solution, we need to solve the normal equation AᵀA*c = Aᵀy.

Calculating AᵀA, we get:

AᵀA = [[3, -3], [-3, 5]]

Calculating Aᵀy, we get:

Aᵀy = [[0], [5]]

Step 3: Solving the normal equation (AᵀA)*c = Aᵀy yields the values of c:

[[3, -3], [-3, 5]] * [[c₀], [c₁]] = [[0], [5]].

Solving this system of equations, we find c₀ = 0 and c₁ = 5/3.

Therefore, the equation of the best-fitting line through the given points is:

y = (5/3)x.

To analyze the fit, compute the predicted y values by evaluating y = Ac, calculate the error vector e = y - ŷ, and the sum of squared errors (SSE) as SSE = e₁² + e₂² + e₃².

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The inequality that show how  many of each bike model must be sold so the

company avoids losing money is 75x + 90y ≥ $1350

Let x represent the number of model A bikes produced and y represent the number of model B bikes produced.

Since A local bicycle shop makes $75 on each  Model A bike and $90 on each Model B bike, hence:

Revenue = 75x + 90y

The overhead cost is $1350, hence to make profit:

Revenue ≥ cost

75x + 90y ≥ $1350

The inequality that show how  many of each bike model must be sold so the

company avoids losing money is 75x + 90y ≥ $1350

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Joel has 3/8 gallon of paint left after painting the ceiling and the wall.

How to calculate this?

To answer the question, we have to follow the below steps:

Step 1: Joel used 1/4 gallon of paint to paint a ceiling.

Step 2: Joel used 3/8 gallon of paint to paint a wall.

Step 3: We have to find out how much paint is left with Joel.

Step 4: Let's find the paint used by Joel in total to paint a ceiling and a wall.

Pint used to paint ceiling = 1/4

Pint used to paint wall = 3/8

Total paint used = 1/4 + 3/8

Common denominator = 8Paint used = 2/8 + 3/8 = 5/8 of a gallon

Step 5: Let's find out the remaining paint with Joel.

Pint of paint = 1

Pint used to paint the ceiling and wall = 5/8

Remaining paint = 1 - 5/8= 3/8

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Answer:

B is correct

Step-by-step explanation:

The solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0) is (1/(x+1))y^(x+1) = (1/2)x^2 - 1/2.

To find the solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0), we can use the method of separation of variables. This involves separating the variables x and y on opposite sides of the equation and then integrating both sides.

First, we can rewrite the differential equation as:
y^x dy = x dx

Next, we can integrate both sides of the equation:
∫y^x dy = ∫x dx
(1/(x+1))y^(x+1) = (1/2)x^2 + C

Now, we can use the initial condition (1,0) to solve for the constant C:
(1/(1+1))0^(1+1) = (1/2)(1)^2 + C
0 = 1/2 + C
C = -1/2

Therefore, the solution to the differential equation is:
(1/(x+1))y^(x+1) = (1/2)x^2 - 1/2

This is the solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0).

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)