In a roll of 50 pennies, there are 12 dated 1977. If a penny is drawn at random, what is the probability that it is dated 1977?

The relationship between the lines are they have same slope and they are parallel.

What is slope?

If [tex](x_1,y_1) \: and \: (x_2,y_2) [/tex] are two points on line then slope of the line will be [tex]m= \frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

To determine the relationship between the two lines, we need to find out if they are parallel, perpendicular, or neither.

First, we can find the slope of the line passing through (7,1) and (10,5) using the slope formula:

[tex]m_1 = \frac{(y_2 - y_1)}{(x_2 - x_1)} \\ m_1 = \frac{ (5 - 1)}{(10 - 7)} \\ m_1 = \frac{4}{3} [/tex]

Similarly, we can find the slope of the line passing through (-8,5) and (-5,9):

[tex]m_2 = \frac{ (y_2 - y_1) }{ (x_2 - x_1)} \\ m_2 = \frac{(9 - 5) }{(-5 - (-8))} \\ m_2 = \frac{4}{3} [/tex]

Since both lines have the same slope of 4/3, they are parallel to each other.

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Answer:

Step-by-step explanation:

In (b) you may be more used to the formula for arc length: [tex]P=\frac{\theta }{180} \times \pi r[/tex].

The result is the same.

We can conclude after answering the presented question that As a probability result, the likelihood of discovering a package that deviates from the target weight by more than 12 grammes is around 0.4014.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

The mean of the box's overall weight is:

n * mu X = mu Y

With a mean weight of 500/n grammes for each chocolate, we get:

mu Y =n * (500/n) = 500

The standard deviation of the box's total weight is:

sqrt(n) * sigma X = sigma Y

When we substitute the provided values, we get:

= 2 * P(Z > 0.8485)

= 2 * (1 - P(Z < 0.8485))

= 2 * (1 - 0.7993) (1 - 0.7993)

= 0.4014 (rounded to four decimal places) (rounded to four decimal places)

As a result, the likelihood of discovering a package that deviates from the target weight by more than 12 grammes is around 0.4014.

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Answer:

C, D

Step-by-step explanation:

Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.

C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left

D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4

The average rate of change of the function is 3.

The average rate of change of a function is given by the formula:

average of change = (f(b) - f(a)) / (b - a)

Where [a, b] is the interval of the function

f(x) = x³ + 2x;  [-1, 1]

average rate of  change = ([ 1³ + 2(1)] - [ (-1)³ + 2(-1)]) / (1 - (-1))

average rate of change = (3 - (-3))/(1 + 1)

average rate of change = 6/2

average rate of change = 3

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Answer:

[tex]2 {x}^{2} + 10x - 48[/tex]

[tex]2( {x}^{2} + 5x - 24)[/tex]

[tex]2(x + 8)(x - 3)[/tex]

So C is correct.

Answer:

4550

Step-by-step explanation:

Answer:

4,550

Step-by-step explanation:

4,550 x 2% = 91

What is a rectangular prism?

A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.

The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.

How do I find the volume of a rectangular prism?

The rectangular prism volume formula is:

volume = h × w × l,

where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:

Find the box length. For example, it can be equal to 18 in.

Determine its width. Let's say you measured 12 in.

Find out the rectangular prism height. Assume it's 15 in.

Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.

How do I find the area of a rectangular prism?

The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is prism height, w is its width, and l is its length.

Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:

Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².

Or save yourself some time and use our rectangular prism calculator.

Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.

How do I calculate the diagonal of a rectangular prism?

To determine the diagonal of a rectangular prism, apply the formula:

diagonal = √(l² + h² + w²)

where h is prism height, w is its width, and l is its length.

Do you have the feeling that you saw the formula before? Yes, that's possible because this equation resembles the famous one from the Pythagorean theorem.

Suzie must pay $27,864 on delivery for the new truck. To determine how much Suzie must pay on delivery, we need to add the extra charges to the base price of the truck and subtract the down payment she already made.

Let's first list the extra charges:

Freight and PDI: $1,650

Air Tax: $100

Tire Tax: $20

GST (Goods and Services Tax): 5%

To calculate the extra charges, we can use the following formula:

Extra charges = Freight and PDI + Air Tax + Tire Tax + (GST x Base Price)

Substituting the given values, we get:

Extra charges = 1650 + 100 + 20 + (0.05 x 27280)

Extra charges = 1650 + 100 + 20 + 1364

Extra charges = 3134

Therefore, the total cost of the truck, including extra charges, is:

Total cost = Base price + Extra charges - Down payment

Total cost = 27280 + 3134 - 2450

Total cost = 27864

Thus, Suzie must pay $27,864 on delivery for the new truck.

It's important to note that the amount Suzie will actually pay will depend on the financing and payment options available to her. She may be able to spread out the payments over a longer period of time or negotiate a different down payment amount. It's always a good idea to research and compare different financing options before making a major purchase like a new vehicle.

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Answer:

4000/3 * π

Step-by-step explanation:

The formula for the volume of a sphere is;

V = (4/3) * π * r^3

Where;

r = the radius of the sphere

Substituting the given value, we get;

r = 10

V = (4/3) * π * (10)^3

= (4/3) * π * 1000

= 4000/3 * π

Therefore the volume of the sphere is (4000/3)π cubic units.

Answer:

d

Step-by-step explanation:

trust me bro im a math teacher

Ruth will have the principal is approximately $5,534.04 in 1 year at earns 12% interest compounded annually.

What is principal?

To find how much Ruth will have in 1 year, we can use the formula for compound interest:

A = [tex]P(1 + r/n)^{n*t}[/tex]

where A is the amount after t years, P is the principal (initial amount), r is the annual interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the number of years.

Plugging in the given values, we get:

A =  [tex]$4,942(1 + 0.12/1)^{1*1}[/tex]

A = $4,942(1.12)

A = $5,534.04

Therefore, Ruth will have approximately $5,534.04 in 1 year.

What is an interest?

Interest is the amount of money charged by a lender to a borrower for the use of money over a period of time. It is typically calculated as a percentage of the amount borrowed or invested, and is often expressed as an annual percentage rate (APR). Interest can be simple or compound, depending on whether it is calculated only on the principal amount or on both the principal and accumulated interest. Interest is an important concept in finance and economics, and is used in a wide range of financial transactions, including loans, investments, and savings accounts.

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The final answer for linearizing the function f(x) = cos^5(x) around a = 0 is:

f(x) ≈ 1.

Linearizing a function is the process of approximating the behavior of a function by a linear function (i.e., a function of the form y = mx + b) in a certain region around a specific point.

Linearization is useful because linear functions are easy to work with mathematically, and they can provide a good approximation of the original function near the point of interest. By linearizing a function, we can simplify calculations and make predictions about the behavior of the function in the vicinity of the point of interest.

In the given question,

To linearize the function f(x) = cos^5(x) around a point a, we can use the first two terms of the Taylor series expansion:

f(x) ≈ f(a) + f'(a)(x - a)

where f'(a) is the first derivative of f evaluated at x = a.

In this case, we want to linearize around a = 0, so we have:

f(x) ≈ f(0) + f'(0)(x - 0)

To find f(0) and f'(0), we need to evaluate the function and its derivative at x = 0:

f(x) = cos^5(x)

f(0) = cos^5(0) = 1

f'(x) = 5cos^4(x)(-sin(x))

f'(0) = 5cos^4(0)(-sin(0)) = 0

Therefore, the linearization of f(x) = cos^5(x) around a = 0 is:

f(x) ≈ 1 + 0(x - 0) = 1

So the linearization is simply the constant function f(x) = 1. This means that for small values of x, the function cos^5(x) can be approximated by the constant function 1. The accuracy of this approximation depends on how small x is and how far away x is from 0.

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Answer: We can simplify the expression by using the identity for the tangent of half an angle:

tan(x/2) = sin(x) / (1 + cos(x))

where x is the angle in radians. We can use this identity by setting x = 56° since 2*28°= 56°.

So, we have:

sin(28°) / (1 + cos(28°)) = tan(56°/2)

We know that 56°/2 = 28°, so we have:

tan(28°)

Therefore, the expression simplifies to a single trigonometric function:

tan(28°)

Step-by-step explanation:

The coordinate of the complex numbers are plotted on a graph below

i) Z₁ + Z₂ = (2+j4) + (3-j) = (2+3) + (j4-j) = 5 + j3

ii) Z₁ - Z₂ = (2+j4) - (3-j) = (2-3) + (j4+j) = -1 + j5

iii) Z₂ - Z₁ = (3-j) - (2+j4) = (3-2) + (-j-4j) = 1 - j5

iv) To represent these complex numbers on an Argand diagram, we plot the real part on the x-axis and the imaginary part on the y-axis.

Z₁ = 2 + j4 can be represented as a point in the complex plane with coordinates (2,4).

Z₂ = 3 - j can be represented as a point in the complex plane with coordinates (3,-1).

Using these coordinates, we can plot the results from parts (i) to (iii) as follows:

(i) Z₁ + Z₂ = 5 + j3 can be represented as a point in the complex plane with coordinates (5,3).

(ii) Z₁ - Z₂ = -1 + j5 can be represented as a point in the complex plane with coordinates (-1,5).

(iii) Z₂ - Z₁ = 1 - j5 can be represented as a point in the complex plane with coordinates (1,-5).

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Answer: 3.625 or 3 5/8

Step-by-step explanation:

So I personally would turn everything into decimals and subtract.

21.250 -17.625

And using our handy calculator, you get

3.625

The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

What is meant by budget?

In general, a budget is a financial plan or estimate that outlines the expected income and expenses over a specific period.

The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

In scenario 1, Carlos chose a more expensive cereal because he recognized it from a TV commercial, which may have influenced his perception of its quality or desirability.

In scenario 2, Evelyn decided not to purchase a plane ticket because the prices were too high for her budget, despite there being multiple airlines offering flights to London.

Therefore,The purchasing decisions in both scenarios were affected by the prices of the products/services being considered.

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Answer:

true

Step-by-step explanation:

Answer:

  [tex]\frac{20}{19}[/tex] or ≈ 1.053

Step-by-step explanation:

We Know

220 responded 'yes', and 209 responded 'no'

Find the probability that if a person is chosen at random, they had run a red light in the last year.

The probability is: [tex]\frac{220}{209}[/tex] = [tex]\frac{20}{19}[/tex] ≈ 1.053

So, the answer is [tex]\frac{20}{19}[/tex] or ≈ 1.053

Answer: To obtain triangle A'B'C' from triangle ABC by reflection over the line y = 2, we reflect each point of the triangle over the line. This gives us:

A' = (A_x, 4 - A_y)

B' = (B_x, 4 - B_y)

C' = (C_x, 4 - C_y)

To obtain triangle A"B"C" from triangle A'B'C' by translation by the directed line segment from (0,0) to (3,2), we add the vector (3,2) to each point of the triangle. This gives us:

A" = (A'_x + 3, A'_y + 2) = (A_x + 3, 6 - A_y)

B" = (B'_x + 3, B'_y + 2) = (B_x + 3, 6 - B_y)

C" = (C'_x + 3, C'_y + 2) = (C_x + 3, 6 - C_y)

Therefore, the vertices of triangle A"B"C" are (A_x + 3, 6 - A_y), (B_x + 3, 6 - B_y), and (C_x + 3, 6 - C_y).

Step-by-step explanation:

Answer:

(x - 4)(x - 7)

Step-by-step explanation:

x² - 11x + 28

consider the factors of the constant term (+ 28) which sum to give the coefficient of the x- term (- 11)

the factors are - 4 and - 7 , since

- 4 × - 7 = + 28 and - 4 - 7 = - 11

then

x² - 11x + 28 = (x - 4)(x - 7) ← factored form

Answer:

linear function

Step-by-step explanation:

straight line then add up

Answer:

Step-by-step explanation:

Answer:

the first car drove 30 miles and the second drove 35

Step-by-step explanation:

1. add how many mile they can travel together.

15+20=35

2. subtract 35 from 65 and whats left is how youll determine which car drove how many the lower number goes to the lower miled vehicle.

Answer:     change in y divided by change in x

Step-by-step explanation:    The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run"

The flux density is 3000 uT.

Flux density (B) is a measure οf the strength οf a magnetic field in a given regiοn.

It is defined as the amοunt οf magnetic flux () that passes thrοugh a unit area (A) perpendicular tο the magnetic field's directiοn.

The flux density (B) can be calculated using the fοrmula:

B = Φ / A

where 'Φ' is -> flux and A is the -> crοss-sectiοnal area.

Plugging in the values given, we get:

B = 1500 uWb / 0.5 m²

B = 3000 uT (micrοtesla)

Therefοre, the flux density is 3000 uT.

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Answer: Not true

Step-by-step explanation:

This isn't true.

There is no way to manipulate the number 20 to get the number 5908 by subtraction or any other arithmetic operation.

Therefore, "20-4=5908" is false.

Answer:

Step-by-step explanation:

99+988

If inversion be defined on K as a physical act of turning a member of K upside down. Then it will be the upside-down triangle.

consider the set K = (triangle, upside-down triangle, square, rectangle). Inversion is defined on K as the act of turning a member of K upside down.

To determine which shape is the triangle, follow these steps:
1. Identify the properties of each shape in set K:
  - Triangle: 3 sides and 3 angles
  - Upside-down triangle: same properties as a triangle, but inverted
  - Square: 4 sides, all equal in length, and 4 right angles
  - Rectangle: 4 sides, opposite sides equal in length, and 4 right angles
2. Analyze the effect of inversion on each shape:
  - Triangle: Inverting a triangle results in an upside-down triangle.
  - Upside-down triangle: Inverting an upside-down triangle results in a regular triangle.
  - Square: Inverting a square does not change its appearance.
  - Rectangle: Inverting a rectangle does not change its appearance.
3. Identify the shape that becomes a triangle after inversion:
  - The upside-down triangle becomes a regular triangle after inversion.
So, the shape in set K that corresponds to the triangle after applying inversion is the upside-down triangle.

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