In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?

The simplified expression for the difference in the areas of Circle A and Circle B is = 12π/(x+2)²

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. The unit of area is the square unit, for example, [tex]m^2, cm^2, in^2[/tex], etc.

We know that :

The formula of circle's circumference is = 2πr

We have :

Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units

and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex]

Now, First we calculate the area of circle A is:

8π/x+2 = 2πr

r = 8π/x+2 × 1/2π

r = 4/x+2

Area = πr² = (4/x+2)²π

Now, for circle B

4π/x+2 = 2πr

r = 4π/x+2 × 1/2π

r = 2/2x+2

Area =( 2/2x+2)²π

Simplified expression for the difference in the areas of Circle A and Circle B are:

(4/x+2)²π - ( 2/x+2)²π

= π/(x+2)²( 4²-2²)

= π/(x+2)²(16-4)

= 12π/(x+2)²

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The equation for contribution for each student is 185.5/14 = 13.25.

Price of new easel= $129

Set of blank canvases = $ 46

Sales tax = $ 10.50

So, the total amount is

= 129 + 46 + 10.5

= 185.5

Then, each student contribute

= 185.5 / 14

= 13.25

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Correct Option is,

D) Buy, because the expected rate is greater than the required rate.

Now, Based on the information you've provided,

To calculate the required rate of return, we can use the SML formula as;

Required rate of return = risk-free rate + beta x (expected market return - risk-free rate)

Plugging in the numbers, we get:

Required rate of return = 8% + 0.85 x (16% - 8%)

                                   = 14.6%

Since the expected rate of return for Stock S is,

= dividend yield + growth rate

= (1.1 / 22 + 8%),

= 9.4%

which is higher than the required rate of return of 14.6%,

Here, the stock is undervalued and would be a good buy.

Therefore, the answer is, option D) Buy, because the expected rate is greater than the required rate.

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The probability that Mia and Lia place in 1st or 2nd is 99/2450. There are two possible scenarios in which Mia and Lia can place in 1st or 2nd: Mia places 1st and Lia places 2nd, or Mia places 2nd and Lia places 1st. The probability of the first scenario is (1/50) * (1/49) = 1/2450. The probability of the second scenario is also (1/50) * (1/49) = 1/2450. Since these two scenarios are mutually exclusive, we can add their probabilities to find the total probability: 1/2450 + 1/2450 = 2/2450. However, we must also account for the fact that there are 49 other people who could place in 3rd. So the final probability is (2/2450) * 49 = 98/2450. Adding the probability that neither Mia nor Lia place in 3rd (1/2450), we get 98/2450 + 1/2450 = 99/2450.

Received message. The probability that Mia and Lia place in 1st or 2nd is **99/2450**. There are two possible scenarios in which Mia and Lia can place in 1st or 2nd: Mia places 1st and Lia places 2nd, or Mia places 2nd and Lia places 1st. The probability of the first scenario is `(1/50) * (1/49) = 1/2450`. The probability of the second scenario is also `(1/50) * (1/49) = 1/2450`. Since these two scenarios are mutually exclusive, we can add their probabilities to find the total probability: `1/2450 + 1/2450 = 2/2450`. However, we must also account for the fact that there are `49` other people who could place in 3rd. So the final probability is `(2/2450) * 49 = 98/2450`. Adding the probability that neither Mia nor Lia place in 3rd (`1/2450`), we get `98/2450 + 1/2450 = 99/2450`.

The circumference of the lollipop is 12.57 inches.

Circumference is the measurement of the distance around the outer edge of a closed curve, particularly a circle. It is the total length of the curve that makes up the boundary of the circle.

The circumference of the circle is given by the formula;

Circumference = 2 × π × radius

where π (pi) is the mathematical constant approximately equal to 3.14159265359...

Given that the radius of the round lollipop is 2 inches, we can substitute this value into the formula;

Circumference = 2 × π × 2

Using the approximate value of π as 3.14159265359..., we can calculate the circumference;

Circumference = 2 × 3.141592 × 2

Circumference ≈ 12.56

Therefore, the circumference of the lollipop is approximately 12.57 inches.

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Step-by-step explanation:

Let the volume of shape A be V. Since the surface area of shape A is 3/4 times that of shape B, the surface area of shape A is 3/7 times the total surface area of the two shapes combined.

Therefore, the surface area of shape A is:

3/7 (surface area of shape A + surface area of shape B) = 3/7 (4/3 surface area of shape B) = 12/21 surface area of shape B

We know that the volume of shape B is 10 cm³, and we can find the volume of shape A by using the ratio of the volumes to the ratio of the surface areas:

V/10 = 3/4

V = 7.5 cm³ (to 3 significant figures)

Therefore, the volume of shape A is 7.5 cm³.

The answers are (-8, 5) and (-8, -5)

Given that, the point (8, 5) is on the graph of an even function, we need to find the other point must also be on the graph,

A function f(x) is said to be an even function if it satisfies the following equation: f(−x) = f(x)

A function satisfying this equation has a graph that is symmetric about the y-axis.

So, if the point (8, 5) is on the graph of an even function, the (-8, 5) must also be on the graph of the function.

Also, the point (8, 5) is on the graph of an odd function,

The graph of an odd function is symmetrical about the origin. Therefore, an odd function satisfies the following condition:

-f(x) = f(-x),

Therefore,

(8, 5) = (-8, -5)

Hence, the answers are (-8, 5) and (-8, -5)

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The values of x and y are 4 and 2√2

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin(tetha) = opp/hyp

tan(tetha) = opp/adj

cos(tetha) = adj/hyp

In the triangle;

y is the opposite to angle 45 and x is the hypotenuse

cos 45° = 2√2/x

1/√2 = 2√2/x

x = 2√2 ×√2

x = 2 × 2 = 4

since the triangle is isosceles,

y = 2√2

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Answer:

56% Caesar

Step-by-step explanation:

The only salads sold were Caesar and it is majority

The angle of depression at which Beatrice sees the boat is 83.35°.

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Check the attached image for the sketch of triangle ABC.

From the sketch, the angle of depression is represented with x:

tan x = 600/70   (tan = opposite/adjacent)

x = tan⁻¹(600/70)

x = 83.35°

Therefore, the angle of depression at which Beatrice sees the boat is 83.35°.

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The correct step find p and w is -   add the equations to eliminate p. The correct option is the first option

From the question, we are to determine which of the given steps is a correct step to find p and w.

The given system of equations is:

w = p + 30

w = −p + 5

From the above equation, we can easily add the equations to eliminate p

That is,

  w = p + 30

+ w = −p + 5

------------------------

2w = 35

We can then solve for  by dividing both sides by 2

2w / 2 = 35 / 2

w = 17.5

To determine the value of p, we can substitute the value of w into any of the equations

w = p + 30

17.5 = p + 30

p = 30 - 17.5

p = 12.5

Hence,

The correct step is add the equations to eliminate p

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The Function is linear with a common first difference of 2.

We have,

x     y

-3   -2

-2   0

0    4

4    12

For the first set of points

m=(0-(-2))/(-2--3)

m = (0+2)/(-2+3)

m= 2/1 = 2

For the second set of points

m = (4-0)/(0-(-2))

m = 4/(0+2)

m = 4/2 = 2

For the third set of points

m = (12-4)/(4-0)

m = 8/4

m = 2

Thus, the function is linear with a common first difference of 2.

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The maximum likelihood estimate of the probability of getting a green light on a single pass through the traffic signal is 0.63.

To find the maximum likelihood estimate of the probability p of a green light on a single pass, we need to consider the observed frequency of green lights in the given data.

1. We are given that the car passed through the traffic signal 100 times and got a green light 63 times.
2. To find the maximum likelihood estimate (MLE) of the probability p of a green light, we need to divide the number of successful green light events (63) by the total number of passes (100).
3. Calculate the MLE: p = 63/100 = 0.63

The maximum likelihood estimate of the probability p of a green light on a single pass is 0.63.

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The exact values of s in the interval [-2π, π) that satisfy the given condition cot²s = 1 are s = -3π/2, -π/2, π/2, and 3π/2.

The given trigonometric equation is cot²s=1 and the interval is [-2π, π).

The given equation can be rearranged as cot²s = 1, which can be written as cot s = ±1.

Using the inverse cotangent identity cot⁻¹(±1) = ±π/2, we can find the exact values of s in the interval [-2π, π) that satisfy the given condition:

s = ±π/2 + 2kπ, where k is an integer.

Therefore, the exact values of s in the interval [-2π, π) that satisfy the given condition cot²s = 1 are s = -3π/2, -π/2, π/2, and 3π/2.

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Answer:

The surface area of a rectangular prism is given by the formula:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively. We are given that the surface area of the prism is 1,060 cm², and that the base has measurements 8 cm and 10 cm.

Substituting these values into the formula, we get:

1060 = 2(8)(10) + 2(8)h + 2(10)h

Simplifying and solving for h, we get:

1060 = 160 + 16h + 20h

1060 = 160 + 36h

900 = 36h

h = 25

Therefore, the height of the prism is 25 cm.

Step-by-step explanation:

Answer: Part A) 3,141.59 Part B) 75.40

Step-by-step explanation:

Sorry if this is wrong.

The monthly payment will be $618.71

We know that the formula for the loans are:

[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}}[/tex]

where

P₀ is principal

d is monthly payment, annual payment

r is the annual interest rate in decimal form.

k is the number of compounding periods in one year.

and N is the length of the loan, in years.

Here, P₀ =  $32,000

r = 0.06

N = 5

k = 12

Using above formula of loan we need to find value of d.

[tex]P_0=\frac{d(1-(1+\frac{r}{k} )^{-Nk})}{\frac{r}{k}} \\\\32000 =\frac{d(1-(1+\frac{0.06}{12} )^{-60})}{\frac{0.06}{12}}\\\\32,000 =\frac{d(1-(1+0.005)^{-60})}{0.005} \\\\32000\times 0.05=d(1-(1.005)^{-60})\\\\160=d\times (1-0.7414)\\\\d = 160/0.2586\\\\d=618.72[/tex]

Therefore, the monthly payment = $618.71

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The horizontal and vertical translations that map triangle XYZ onto its image, triangle X'Y'Z' include the following: C. right 3; down 5.

In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In order to map the two triangles, we would have to apply a vertical translation to f(x) by 5 units down and a horizontal translation by 3 units right.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Yes, The argument is valid.

Now, We have;

(∀x) (∃y) (p(x, y) ⇒ r(x))

Means that for any integer x, there exists an integer y such that if x is a factor of y, then x is prime.

(∀x)(∀y)(∀z)(¬q(x, y, z)) means that for any integers x, y, and z, the greatest common factor of x and y is not z.

(∃x)(∀y)(p(x, y) ∨ r(x)) means that there exists an integer x such that for any integer y, either x is a factor of y or x is prime.

Therefore, (∀y)(∃z)(∃x)q(x, y, z) means that for any integer y, there exists integers z and x such that the greatest common factor of x and y is z.

To see why this conclusion follows, consider that if (∀y)(∃z)(∃x)q(x, y, z) were false, then there would be some integer y such that for all integers z and x, the greatest common factor of x and y is not z.

However, this would contradict (∀x)(∀y)(∀z)(¬q(x, y, z)), which states that for any integers x, y, and z, the greatest common factor of x and y is not z.

Therefore, the argument is valid.

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Answer: x = 20

Step-by-step explanation:

[tex]\frac{3}{5} x - \frac{1}{4} x = 7\\12x-5x=140\\7x=140\\x=20[/tex]

The amount of frosting in square centimeters it will take to cover the outside of the gingerbread house, pyramidal in shape, is about 12.65 square centimeters.

The surface area of a square pyramid is the sum of the area of the four triangular faces.

The surface area of the gingerbread house can be found as follows;

The height of the pyramid and the square base indicates;

The slant height of a face of the pyramid = √(3² + 1²) = √(10)

The surface area of the pyramid = 4 × (1/2) × 2 × √(10) = 4·√(10)

4·√(10) ≈ 12.65

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The value of the identities are;

1. tan θ = 5/12

2. cot θ = √7/3

To determine the value of the identities, we need to take note of the different identities;

From the information given, we need to take note that;

tan θ = opposite/adjacent

cot θ = inverse of tangent identity

cot θ = adjacent/opposite

then,

1. tan θ =

Opposite = 5

Adjacent = 12

tan θ = 5/12

2. cot θ = 4√7/12 = √7/3

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Complete sentence is,

⇒ ΔAGC ≈ ΔCDF

⇒ ΔCDE ≈ ΔCAB

And, The length of BC is, 51

The length of DE is, 132.7

We have to given that;

⇒ CF = 32

Hence, We get;

tan 24 = CF / DF

0.44 = 32 / DF

DF = 72.7

Thus, ΔAGC ≈ ΔCDF

Here, We have;

⇒ ΔCDE ≈ ΔCAB

In triangle BCG;

BC² = 24² + 45²

BC² = 576 + 2025

BC² = 2601

BC = 51

In triangle CEF;

⇒ EC² = CF² + EF²

⇒ 68² = 32² + EF²

⇒ 4624 = 1024 + EF²

⇒ EF² = 4624 - 1024

⇒ EF² = 3600

⇒ EF = 60

Thus, We get;

DE = DF + EF

DE = 72.7 + 60

DE = 132.7

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Sawyer has 4 cousins given that Hazel has 2 times as many cousins as Sawyer.

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

Using the above as a guide, we have the following:

Hazel = 2 * Sawyer

Let c stand for the number of cousins Sawyer has.

So, we have

Hazel = 2 * c

Substitute the known values in the above equation, so, we have the following representation

2 * c = 8

Divide by 2

c = 4

Hence, the number of cousins Sawyer has is 5

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Answer:

To find the probability of an event occurring, you need to divide the number of ways the event can occur by the total number of possible outcomes. The probability is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

For example, if you want to find the probability of rolling a 3 on a standard six-sided die, there is only one way to roll a 3 and six possible outcomes (1, 2, 3, 4, 5, 6). So, the probability of rolling a 3 is 1/6 or approximately 0.17.

Keep in mind that the probability of an event occurring is not a guarantee that the event will happen. It only indicates the likelihood of the event happening based on the available information.

The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + [tex]i)^n[/tex]

So, PV =  100, 000 / (1+ 5/100[tex])^{10\\[/tex]

PV = 100,000 / (1+ 0.05[tex])^{10\\[/tex]

PV = 100, 000/ (1.05[tex])^{10\\[/tex]

PV = 100,000 / 1.6288946

PV= $6,139.132

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Answer:

x = 3; z = 60°

Step-by-step explanation:

x:

The angles measuring 120° and (8x + 96)° are vertical angles, which means they're congruent and equal.

Thus, we can solve for x by setting the two angles equal to each other and isolate x:

[tex]120=8x+96\\24=8x\\3=x[/tex]

We can check our answer by plugging in 3 for x and ensure that we get 120:

[tex]120=8(3)+96\\120=24+96\\120=120[/tex]

z:

We see that a horizontal straight line separates the angle measuring 120° and z°.  Straight lines create straight angles, which equal 180°.

Thus, we can find the measure of z by adding the 120° angle and the z° and set them equal to 180.  Then, we must isolate z:

[tex]120+z=180\\z=60[/tex]

The value of x in the circle that shows diameter is calculated as:

x = -7

In a circle, the line segment that divides the circle into two halves is the diameter. Half of the circle is a semicircle which has a measure of 180 degrees.

Note: The measure of a central angle is also the same measure with that of the arc it intercepts.

Therefore, we have:

-8x + 9 + 50 + 65 = 180

-8x + 124 = 180

-8x = 180 - 124

-8x = 56

x = 56/-8

x = -7

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Answer:

0.38 degrees.

Step-by-step explanation:

C = 2π(53) = 106π km

The train is traveling at a speed of 44 km/h, which is equivalent to (44/60) km/min since there are 60 minutes in an hour.

d = (44/60) km/min

θ = (d / C) x 360°

θ = [(44/60) / (106π)] x 360°

θ ≈ 0.38°

Therefore, the angle through which the train turns in 1 minute is approximately 0.38 degrees.