Sam is collecting pennies. On the first day of the month, Samnis given 16 pennies. Each day after that he gets 4 more pennies. Which of the following equations defines how many pennies he has after the nth day?

A. an = 16n + 4
B. an = 4n + 16
C. an = 4n + 16
D. an = 64n - 64​

Answer:

d)

Step-by-step explanation:

So we have an equation for the sales based on the year.

Sales are y and the year is x, we can therefore plug in x into the equation (2008) and extrapolate what the sales are in millions.

y=7.36(2008)- 14 354.33= 424.55 million

To write this in numerical form we times it by one million (1 000 000)

424.45 x 1 000 000= 424 550 000

Using implicit differentiation, we found that dy/dx = [tex](18x) / (5y^4)[/tex]. When solving the equation explicitly for y, we obtained y =[tex](9x^2)^(1/5) - 2^(1/5)[/tex], and differentiating this expression gave dy/dx = [tex](18/5) * x^(-2/5) * (9x^2)^(1/5)[/tex].

A) To find y' by implicit differentiation, we differentiate both sides of the equation with respect to x using the chain rule and product rule:

d/dx (9x^2) - d/dx (y^5) = d/dx (2)

Simplifying, we get:

18x - 5y^4 * (dy/dx) = 0

Rearranging the equation and solving for dy/dx, we have:

dy/dx = (18x) / (5y^4)

B) To solve the equation explicitly for y, we isolate y:

9x^2 - y^5 = 2

9x^2 = y^5 + 2

Taking the fifth root of both sides, we get:

[tex](9x^2)^(^1^/^5^) = (y^5 + 2)^(1^/^5^)y = (9x^2)^(^1^/^5^) - 2^(^1^/^5^)[/tex]

Now, we differentiate y with respect to x using the power rule:

dy/dx = [tex](1/5) * (9x^2)^(-4/5) * (18x)[/tex]

Simplifying further:

dy/dx =[tex](18/5) * x^(-2/5) * (9x^2)^(1/5)[/tex]

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By differentiating the given equation implicitly and then solving for y', we get y' = (18x) / (5y^4). Alternatively, if we first solve for y and then differentiate, we get the same expression for y'.

The given equation is [tex]9x^2 - y^5 = 2[/tex]. We will differentiate it implicitly and solve for y' for part A, and solve for y first and then differentiate to find y' for part B.

Differentiating with respect to x gives 18x - 5y'^4y = 0. Solving this equation for y', we get, [tex]y' = (18x) / (5y^4).[/tex]

First, solve the equation for y to give y = [(9x^2 −2 )]^(1/5). Differentiating this with respect to x, we find [tex]y' = 2/5*9x * [(9x^2 -2 )]^(-4/5)[/tex] which simplifies to [tex]y' = (18x) / (5y^4).[/tex]

Therefore, whether we use implicit differentiation (Part A) or solve for y and differentiate (Part B), we get the same expression for y' in terms of x.

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a) The inflation rate at t = 1 is 0 and the output gap at t = 1 is 0.1.

b) So, 7₁ > 0 and To > 0 (As given, all parameters are > 0)

c) It is possible to stabilize inflation after only one period at B/p = (r - 7₁)/0.1

d) a higher ratio of on/oy is beneficial for inflation stabilization.

(a) Given,

Inflation target (π) = 0

Nominal interest rate (i) = F + t + t

Natural real interest rate (r) = 7 > 0

Output gap (y) = ỹt

Aggregate demand equation is t = -(rt-1- F) + πt-1 + ε

Aggregate supply equation is ỹt = ỹt-1+0t + e

Inflation rate (πt) = 0 for all t.

Nominal interest rate i = r + πt + ỹt

By Fisher identity, rt = it - πt

Now, for t = 0

Before the shock, i = r, π = 0 and y = 0

Given,

shock = 0.1

So, for t = 0,

output gap is given by

ỹt = ỹt-1+0t + e

= 0 + 0.1 + 0

= 0.1

Now, i = r + πt + ỹt

= r + 0 + 0.1

= r + 0.1

So, at t = 0, inflation rate π = 0 and output gap ỹ0 = 0.1

At t = 1

Inflation rate π1 = 0 (As given in the question)

Nominal interest rate i1 = r + π1 + ỹ1

So, we need to find ỹ1.

Now, putting the value of inflation rate and nominal interest rate in the Fisher identity, we get

rt-1 = i1 - π0

= r + ỹ1

Therefore, from the aggregate supply equation we ge

tỹ1 = ỹ0+0(ỹ1) +

e= 0.1 + e

Putting the value of ỹ1 in the nominal interest rate equation we get

i1 = r + π1 + ỹ1

= r + 0 + 0.1 + e

= r + 0.1 + e

(b) Given,o, B, p,

y < 1

Let ỹ0 = α

Then ỹ1 = 0.1 + e ≤ 1 (As given)

So, 0 ≤ ỹ1 ≤ 1

Now, from the aggregate supply equation we have,

ỹt = ỹt-1+0(ỹt) + e

As it is an increasing function of e and 0 < ỹ1 ≤ 1, we get ỹ2 < ỹ1 and 0 ≤ ỹ2 ≤ 1

So, 0 ≤ ỹt ≤ 1 for all t.

Hence, yo ≥ 0

Now, ỹ1 = α + 0.1 + e ≤ 1

So, α ≤ 0.9

So, 0 ≤ α ≤ 0.9

Now, let's calculate 7₁ and

π1.7₁ = rt-1

= i1 - π0

= r + ỹ1 - 0

= r + 0.1

So, 7₁ > 0 and To > 0 (As given, all parameters are > 0)

(c) Given, > 1

At time t = 0, the output gap is given by ỹ0 = α

Then, ỹ1 = 0.1 + e, and ỹ2 = 0.1 + 0 = 0.1

As ỹ2 is constant, it is clear that inflation will be stabilized after only one period.

To check this explicitly, let's calculate π1

Now, 7₁ = r + 0.1So, i1 = 7₁ + π1

By Fisher identity, i0 - π0 = rt-1

= r

Therefore, i0 = r + π0

So, the shock is given bye = ỹ1 - ỹ0-0(7₁)

= 0.1 - α

From the aggregate demand equation, we get

t = -(rt-1- F) + πt-1 + ε

= -(r - F) + 0 + ε

= -r + F + ε

Now, we can calculate inflation at t = 1 as

π1 = π0 + (1-B)(α - ỹ0) + B(π0 + o + y ỹ1) - p(7₁ - r)

π1 = 0 + (1-B)(α - α) + B(0 + o + y 0.1) - p(7₁ - r)

π1 = 0.1B - p(7₁ - r)

We want π1 = 0

So, 0.1B - p(7₁ - r) = 0

Thus, B/p = (r - 7₁)/0.1

Let B/p = ζ, then ζ = (r - 7₁)/0.1

Thus, it is possible to stabilize inflation after only one period at B/p = (r - 7₁)/0.1

(d) As we saw in part (c), a higher value of the ratio B/p results in the stabilization of inflation after only one period. Therefore, a higher ratio of on/oy is beneficial for inflation stabilization.

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To calculate the cost of shortage (Cs), we need to find the area under the normal distribution curve to the left of the optimal service level. The cost of shortage is the difference between the selling price and the Monday price, multiplied by the probability of shortage.

To calculate the cost of excess (Ce), we find the area under the normal distribution curve to the right of the optimal service level. The cost of excess is the difference between the cost of making the cake and the selling price, multiplied by the probability of excess. The optimal service level is determined by minimizing the total cost, which is the sum of the cost of shortage and the cost of excess. We can find the corresponding z value for the optimal service level using the standard normal distribution table. Once we have the optimal service level (z value), we can find the corresponding demand value. Since demand is normally distributed, we can calculate the optimal number of birthday cakes to make for the weekend by subtracting the expected demand from the optimal service level demand. However, without specific information on the desired service level or target level of shortage/excess, it is not possible to provide numerical answers to the questions. The optimal service level, corresponding z value, and the optimal number of cakes will depend on the specific parameters and objectives of the supermarket bakery.

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Answer:

1) C

2) C

Step-by-step explanation:

Question 1)

We want a parabola that has the vertex (-8, -7) and also passes through the point (-7, -4).

So, we can use the vertex form. Remember that the vertex form is:

[tex]y=a(x-h)^2+k[/tex]

Where a is our leading co-efficient and (h, k) is our vertex.

We know that our vertex is (-8, -7). So, substitute this into the equation:

[tex]y=a(x-(-8))^2+(-7)[/tex]

Simplify:

[tex]y=a(x+8)^2-7[/tex]

Now, we need to determine the value of our a. To do so, we can use the point the problem had given us. We know that the graph passes through (-7, -4).

So, when x is -7, y is -4. Substitute -7 for x and -4 for y:

[tex](-4)=a((-7)+8)^2-7[/tex]

Solve for a. Add within the parentheses:

[tex]-4=a(1)^2-7[/tex]

Square:

[tex]-4=a-7[/tex]

Add 7 to both sides. Therefore, the value of a is:

[tex]a=3[/tex]

So, our entire equation in vertex form is:

[tex]y=3(x+8)^2-7[/tex]

Our answer is C.

Question 2)

We are given a graph and are asked to find the equation of the graph.

Again, let's use the vertex form. From the graph, we can see that the vertex is at (-2, 2). Let's substitute this into our vertex equation:

[tex]y=a(x-(-2))^2+2[/tex]

Simplify:

[tex]y=a(x+2)^2+2[/tex]

Again, we need to find the value of a.

Notice that the graph crosses the point (-1, 5).

So, let's substitute -1 for x and 5 for y. This yields:

[tex]5=a((-1)+2)^2+2[/tex]

Solve for a. Add within the parentheses.

[tex]5=a(1)^2+2[/tex]

Square:

[tex]5=a+2[/tex]

Subtract 2 from both sides. So, the value of a is:

[tex]a=3[/tex]

Therefore, our entire equation is:

[tex]y=3(x+2)^2-2[/tex]

Our answer is C.

And we're done!

Answer:

Top left

Step-by-step explanation:

Step-by-step explanation:

let the two angles be x and x

since the sum of complementary angles is equal to 90 degree therefore according to question sum of x and x is equal to 90 degree

so the equation is

x + x =90

2x = 90

x= 90 /2

x= 45

Given :

Natalie is going mountain biking. She can buy a bike for $250 or she can rent a bike for $30 an hour.

In both cases, she must also rent a helmet for $5 an hour.

To Find :

Which inequality shows the number of hours Natalie must bike for the cost of buying a bike to be less than renting a bike.

Solution :

Let, after t hours total money required is ( if she rent bike ).

T = 30t.

Money required to purchase bike , M = $250.

For cost of buying a bike to be less than renting a bike :

[tex]30t>250\\\\t > \dfrac{25}{3}\ hours\\\\t>8\dfrac{1}{3}\ hours\\\\t>8\ hours \ 20 \ minutes[/tex]

Hence, this is the required solution.

Answer:

(-2, 1)

Step-by-step explanation:

TRUE A natural number is another name for the counting number.

Natural numbers are those in mathematics that are utilized for counting and ordering.

Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering.

The term "counting numbers" refers to all natural numbers. These are always positive whole numbers, such as 1, 2, 3, 4, 5, and 6.

Mathematical number systems depend heavily on the infinite counting numbers, which can be counted.

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Answer:

what

Step-by-step explanation:

Answer:

C. 3a + 6

Step-by-step explanation:

The expression that describes the verbal expression is 3a + 6.

Now let us approach this step wisely;

  Triple quantity a = 3a

Increased by 6 =  + 6 , an increment is addition to a term.

So, the full algebraic expression is 3a + 6

The solution is 3a + 6. Word problems like this should be approached step wisely.

Answer:

multiply both sides by 3 and do not reverse the inequality symbol

Step-by-step explanation:

Given

[tex]\frac{1}{3}[/tex] m < - 21 ( isolate m by multiplying both sides by 3 )

m < - 63

Multiplication both sides by 3 but not reversing the inequality sign to isolate the variable

Please find the given question.

isolate variable=?

[tex]\to \frac{1}{3} m < - 21[/tex] ( isolating the value of m multiplying both sides with 3 )

[tex]\to m < - 63[/tex]

Therefore, the final answer is "Tyson aims to fix the inequality [tex]\frac{1}{3} m < - 21[/tex]multiplication both sides by 3 but not reversing the inequality sign to isolate the variable".

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Answer:

355

Step-by-step explanation:

We have the sequence:

12, 19, 26, 33...

And we want to find the 50th term.

First, notice that this is an arithmetic sequence. This is because each subsequent term is 7 more than the previous term. So, this is increasing linearly.

Therefore, we can write an explicit formula for our sequence. The standard form for the explicit formula for an arithmetic sequence is:

[tex]x_n=a+d(n-1)[/tex]

Where a is the initial term, d is the common difference, and n is the nth term.

We can see from our sequence that our initial term a is 12.

We also know that d is +7 because each term is 7 more than the previous term.

So, substitute 12 for a and 7 for d. This yields:

[tex]x_n=12+7(n-1)[/tex]

To find the 50th term, let's substitute 50 for n:

[tex]x_{50}=12+7(50-1)[/tex]

Evaluate. Subtract within the parentheses:

[tex]x_{50}=12+7(49)[/tex]

Multiply:

[tex]x_{50}=12+343[/tex]

Add:

[tex]x_{50}=355[/tex]

So, the 50th term is 355.

And we're done!

Answer:

The pattern goes by adding 7 to the previous number to get the result.

12+7 = 19

19+7 = 26

26+7 = 33

The  

Use the formula  [tex]a_{n} = a_{1}+d(n-1)[/tex]

The sequence = 7n-2

Therefore the 50th term

= 7(50)-2

= 350-2

= 348

Answer:

b

Step-by-step explanation:

Answer:

15-5y=20

15-20=5y

-5=5y

y=-1

Answer:

1

Step-by-step explanation:

[tex]swap \: - 5y \: and \: 15[/tex]

working step:

[tex]

15+−5y=20 \\

−5y+15=20 \\

−5y+15−15=20−15 \\

−5y=5 \\

−5y−5=5−5 \\

y=−1

[/tex]

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25.8064

Step-by-step explanation:

when sold is 62$

lost is 100 percentage

nyali sold 46$ lost price is 16$

The lost is _____

16×100/62=25.8064

Answer:

[tex]\huge{\sf{ 25.80 }}[/tex] %

Step-by-step explanation:

Cost price of a bicycle = $ 62

Selling price of a bicycle = $ 46

Since, CP > SP , she made a loss.

Finding loss amount

Loss amount = CP - SP = $ 62 - $ 46 = $ 16

Now finding the loss percentage :

[tex]\sf{\frac{Loss }{CP} * 100 }[/tex]

⇒[tex]\frac{16}{62} * 100[/tex] %

⇒[tex]25.80[/tex] %

Hope I helped!

Best regards!

~ TheAnimeGirl

Answer:

8 + 6x - 10x = 16 - 8x

This is

8 = 4x

So, x = 2 :)

Answer:

[tex]\boxed {x = 2}[/tex]

Step-by-step explanation:

Solve for the value of [tex]x[/tex]:

[tex]8 + 6x - 10x = 16 - 8x[/tex]

-Combine like terms:

[tex]8 + 6x - 10x = 16 - 8x[/tex]

[tex]8 + -4x = 16 - 8x[/tex]

-Take [tex]8x[/tex] and add it to [tex]-4x[/tex]:

[tex]8 + -4x + 8x = 16 - 8x + 8x[/tex]

[tex]8 + 4x = 16[/tex]

-Subtract [tex]8[/tex]to both sides:

[tex]8 - 8 + 4x = 16 - 8[/tex]

[tex]4x = 8[/tex]

-Divide both sides by:

[tex]\frac{4x}{4} = \frac{8}{4}[/tex]

[tex]\boxed {x = 2}[/tex]

So, the value of [tex]x[/tex] is [tex]2[/tex].

Answer:

D

Step-by-step explanation:

Equilateral triangle

An equilateral triangle will always have a perpendicular bisector that is also an angle bisector.

Option D is the correct answer.

We have,

In an equilateral triangle,

All sides are congruent, and all angles are congruent (each measuring 60 degrees).

The perpendicular bisector of any side of an equilateral triangle will also be an angle bisector, since it will pass through the vertex opposite to that side, dividing the angle into two congruent angles.

Thus,

An equilateral triangle will always have a perpendicular bisector that is also an angle bisector.

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The properties of the function are

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

y = x² - 5

The vertex of the above function is

(0, -5)

The axis of symmetry is the x-coordinate of the vertex

So, we have

x = 0

The y-intercept is when x = 0

So, we have

y = -5

Because the leading coefficient is positive, the function has a minimum vertex

From the graph, we have the x-intercepts to be

x = ±2.236

The domain is the set of all real values, and the range is (-5, ∞)

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Answer:

20 days

Step-by-step explanation:

we know: we can represent the number of days 18 scouts did as "x"

15 scouts = 24 days

18 scouts = x days

first you do the number of days times the number of scouts:

15 * 24 = 360, 360 is the number of cookies

then you can do;

360/18 = 20 days

hope this helps :)

Days taken by 18 Scout to sale cookies is 20 days

Given that;

15 Scout sales total cookies = 24 days

Find:

Days taken by 18 Scout to sale cookies

Computation:

Days taken by 18 Scout to sale cookies = [15 × 24] / Number of new scouts

Days taken by 18 Scout to sale cookies = [15 × 24] / 18

Days taken by 18 Scout to sale cookies = 360 / 18

Days taken by 18 Scout to sale cookies = 20 days

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Answer:

The correct options are;

1) The shape maps unto itself after a rotation of 270 degrees

2) The smallest angle of rotational symmetry is 90 degrees

3) The shape maps unto itself after a rotation of 180 degrees

Step-by-step explanation:

We note that the shape of a cross which consists of two equal members (segments) bisecting each other at right angles such that when a member is placed vertically upright, the other member will be horizontal, therefore we have;

After rotation by 90 degrees, the vertical member will become horizontal and vice versa

After rotation by 180 degrees, the vertical member will become horizontal and vice versa again

Similarly, after rotation by 270  degrees, the once vertical member will become horizontal and the horizontal member will become vertical

Answer:

2,3,5 on edge

Step-by-step explanation:

Took test

Answer:

B 4 is the correct answer

Step-by-step explanation:

b - 12 = - 8

b = 12 - 8

b = 4

Answer:

x = -8

Step-by-step explanation:

x- (-10) = 2

Subtracting a negative is like adding

x+10 =2

Subtract 10 from each side

x+10-10 = 2-10

x = -8

Answer:

4

Step-by-step explanation:

[tex]\sqrt[3]{64}[/tex] is 4/ the cube root of 64 is 4

4x4x4

4x4=16

16x4=64

 The total debt of the government at the end of year three is $7.2 billion.

Starting with a total debt of $5.5 billion, the government's deficits of $600 million in year one and $1.5 billion in year two contribute to an increase in the debt. However, in year three, the government runs a surplus of $400 million, which helps reduce the debt.

Thus, the total debt at the end of year three is calculated by adding the initial debt and deficits, and subtracting the surplus. In this case, the total debt at the end of year three is $7.2 billion.

Assuming the government runs a deficit of $200 million in year three, the calculation changes. With the initial debt of $5.5 billion, the deficits of $600 million in year one and $1.5 billion in year two, and the additional deficit of $200 million in year three, the total debt at the end of year three would be $7.8 billion. This demonstrates how the deficit amounts impact the overall debt accumulation.

If a government runs a budget deficit of $5 billion each year for ten years, resulting in a total deficit of $50 billion, followed by a surplus of $2 billion per year for five years, reducing the debt by $10 billion, and then maintaining a balanced budget for another ten years, the government debt would amount to $40 billion. The deficits over the initial ten years lead to a significant accumulation of debt, but the subsequent surpluses help mitigate the debt by reducing the deficit. Finally, the balanced budget in the later years ensures that there is no further increase in debt. Understanding the interplay between deficits, surpluses, and a balanced budget is crucial to grasp the long-term implications on government debt and fiscal stability.

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The period of the voltage signal V(t) = 10 sin(t) is 2π because the sine function has a natural period of 2π and the coefficient of t does not affect the period in this case.

To find the period T of the voltage signal V(t) = 10 sin(t), we can use the properties of the sine function.

The sine function has a period of 2π, which means it repeats itself every 2π units. In the given equation V(t) = 10 sin(t), the coefficient of t is 1, which means the period is affected by the coefficient.

In this case, the voltage function has a coefficient of 1, so the period T can be found by equating 2π to the coefficient multiplied by the period:

2π = 1 * T

Simplifying the equation, we have:

T = 2π

Therefore, the period T of the voltage signal is 2π.

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Complete question

The voltage in an electrical circuit varies with time according to the formula V(t) = 10 sin(t) for t in the interval [0,T]. The numerical value of the mean voltage in the circuit is 6.3662. What is the period T of the voltage signal?

The final answer rounded to 5 decimal places is:`x = 0.57735`

A) Given trigonometric expression is;`sin (π/6) + cos (π/6)`

Using the trigonometric values of π/6 from the trigonometric table, we have:

sin π/6 = 1/2cos π/6 = √3/2.Substituting the trigonometric values into the given expression, we have:

sin π/6 + cos π/6= 1/2 + √3/2= (1 + √3)/2

Therefore, the value of `sin (π/6) + cos (π/6)` is `(1 + √3)/2`.

B) Now, coming to the next part, we need to find the side labeled x.

The value of the tangent of an angle is equal to the ratio of the opposite side and the adjacent side. Thus, we can write:tan θ = Opposite side/Adjacent side

We have the values of the angle and the adjacent side, using that, we can find the opposite side as follows:`

tan 30° = Opposite side/1`Opposite side = `tan 30°`Opposite side = `(1/√3)`

Therefore, the side labeled x is `(1/√3)`.

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Answer:tbh, that's impossible

Step-by-step explanation: