Determine the more basic function that has been shifted reflected stretched or compressed what does

Based on the given parameters, the amount of the investment after 2 years is $3123

The given parameters about the compound interest are

Principal Amount, P = $3000

Interest Rate, R = 2%

Time, t = 2

Number of times, n = 4 i.e quarterly

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R/n)^nt - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R/n)^nt - P

Evaluate the like terms

A = P(1 + R/n)^nt

Substitute the known values in the above equation

A = 3000 * (1 + 2%/4)^(2 * 4)

Express 2% as decimal

A = 3000 * (1 + 0.02/4)^(2 * 4)

Evaluate the sum

A = 3000 * (1.005)^8

Evaluate the exponent

A = 3000 * 1.041

Evaluate the product

A = 3123

Hence, the value of the investment is $3123

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The slope of the line that passes through points (10,4) and (7, 3) is 1/3

Here we are dealing with a slope of a line where a slope of a line is the change in the y coordinate with regard to the change in the x coordinate. If P(x1,y1) and Q(x2,y2) are the two points on a straight line, at that point the slope formula is given by:

m = Change in y-coordinates/Change in x-coordinates

m = (y₂– y₁)/(x₂ – x₁)

Since we are given two points (10,4) and (7, 3),  where x₁ and x₂ are 10, 7 whereas y₁ and y₂ are 4, 3

From  the formula we get,

m = (y₂-y₁)/(x₂-x₁)

 = ( 3-4)/(7 - 10)

 = -1/-3

 =1/3

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After evaluating the limit we have came to find that the limit of  [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex] as x approaches ∞- is 1

The value that a function, sequence, or index approaches as an input, or an index, approaches a particular value is known as a limit in mathematics. Limits, which are essential to calculus and mathematical analysis, are required by the definitions of continuity, derivatives, and integrals.

In addition to being closely related to the concepts of limit and direct limit in category theory, the idea of a limit of a sequence is further generalised to encompass the idea of a limit of a topological network.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x +0}[/tex]

⇒ [tex]\lim_{x\rightarrow -\infty }\frac{2x}{2x }[/tex]

Evalue -∞ as x

⇒ [tex]\frac{2(-\infty)}{2(-\infty)} }[/tex]

⇒ 1

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The distance from city C to city D is 5435 miles

The area of mathematics known as algebra aids in the representation of issues or circumstances into mathematical statements. To create a meaningful mathematical expression, it requires variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including coordinate geometry, calculus, and trigonometry. 2x + 4 = 8 is a basic algebraic expression.When operations like addition, subtraction, multiplication, division, etc. are performed on variables and constants, we obtain algebraic expressions as the mathematical statement.

The distance from city A to city B is 3001 miles Let distance from city A to city B x and distance from city C to city D y

The distance from city A to city B is 3001 miles

x= y - 3001....(i)

x+ y = 7869....(ii)

y- 3001 +y = 7869

2y = 10870

y=5435

The distance from city C to city D is 5435

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Explanation

hen a line instersects a pair of paralle lines diverse angles are created

If you copy A of the corresponding angles and you translate it along the transversal, it will coincide with the other corresponding angle (B)

so angles A and B are called

Corresponding angles, those angles are congruents

hence, if the lines in the problem are parellel, is must fit

therefore, the answer is

I hope this helps you

Using mathematical operations we can conclude that the cost per quart of yogurt is $1.29.

So, the cost per quart:

Cost per quart:

Therefore, using mathematical operations we can conclude that the cost per quart of yogurt is $1.29.

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Answer:

Iiiieie I just got off your phone with weee

Step-by-step explanation: why did I get a hold for him or

oh yeah that’s fine I’ll let lol I was thinking of going out to the house for the next few weeks so I’m not good enough for that lol I think it’s so so to do that all day and you can get a hold on you for sure and I can help with your stuff and help me help help you get it

The probability of four coworkers  having different birth months is 0.572 or 55/96

Given there are four coworkers and the condition is they should have different birth months.

As we know probability is the ratio of favorable out comes to the total number of outputs

Favorable outcomes are

For first person 12 months

For second person 11 months

For third person 10 months

For Fourth person 9 months

Total outcomes

For each and every person total outcomes are 12 months which add up to 12 x 12 x 12 x 12 =  [tex]12^{4}[/tex]

Now probability will be

Probability = [tex]\frac{(12)(11)(10)(9)}{12^{4} }[/tex]

Probability = 55/96

Hence the probability of four coworkers having different birth months is 55/96

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the shape of the curved surface is the sphere

So, as a part of the shape is flat

The block may represents a semi sphere

The approximate probability that a randomly selected 10-year-old child will be more than 51.75 inches tall is 0.6915.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. From the information, the heights of 10-year-old children have a normal probability distribution with a mean of 54.6 inches and standard deviation of 5.7 inches.

Based on this, the probability that a randomly selected 10-year old child will be more than 51.75 inches tall will be:

P(X > 51.75)

= P(Z > [(number - mean) / standard deviation)]

= P(Z > [(51.75 - 54.6) / 5.7)]

= P(Z > -0.5)

= 1 - P(Z = -0.5)

This will be looked at in the z table.

= 1 - 0.3805

= 0.6915

Therefore, the probability is 0.6915.

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Answer:

4y + 5 = 2

Step-by-step explanation:

4y + 5 = 2  Subtract 5 from both sides

4y = -3  Divide both sides by 4

y = [tex]\frac{-3}{4}[/tex]

Answer:

4y+5=2

Step-by-step explanation:

First, replace "a number" with "y"
The sentence becomes: "The sum of 4 times y and 5 is 2"
Replace "is" with the equals sign, "="
The sentence becomes: "The sum of 4 times y and 5 = 2"
Replace "times" with the multiply symbol, " * "
The sentence becomes: "The sum of 4 * y and 5 = 2"
Replace "the sum of ___ and ___" with " ___ + ___"

The sentence becomes: "4*y + 5 = 2".
the " * " isn't needed since 4y implies multiplication already, so you can optionally remove the *

Answer:

6, because anything inside | | are positive so -3 will now be 3.

3 minus -3 = 6

Step-by-step explanation:

Hope it helps! =D

Explanation:

In this case we must compare 2 to 4 and 11 to 11/2

1. The first ratio given is 2 to 4

So, the first ratio is 1/2

2. The second ratio given is 11 to 11/2

Finally, since r1 ≠ r2 they are not proportional

ANSWER:

they are not proportional

The diameter of the outer circle = 12.907 ft

The thickness of the circular pipe = 2.983 ft

The diameter of the inner circle = q = The diameter of the outer circle - The thickness of the circular pipe

⇒ The diameter of the inner circle = 12.907 - 2.983 ft

⇒ The diameter of the inner circle = q = 9.924 ft

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Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

Answer:

  (b)  x=80, y=38, z=63

Step-by-step explanation:

You want to know the values of x, y, and z, given they are angle measures in a diagram showing two triangles.

The angles that form a linear pair are supplementary:

  x° +100° = 180°

  x = 80 . . . . . . . . . divide by °, subtract 100

The angle sum theorem tells you that the sum of angles in a triangle is 180°.

  y° +62° +80° = 180°

  y = 38 . . . . . . . . . . . . divide by °, subtract 142

In the other triangle, the same relation holds:

  z° +100° +17° = 180°

  z = 63 . . . . . . . . . . . . divide by °, subtract 117

The values of x, y, and z are ...

  (x, y, z) = (80, 38, 63)

By using the equation to find the slope, we will see that the value of a is -3.

Here we have two points that define a line.

Remember that a linear equation is of the form:

y = m*x + b

Where m is the slope.

And we know that if the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

m = (y₂ -  y₁)/(x₂ - x₁)

In this case, we know that the points are:

(-10, 0) and (a, -6), and the slope is m = -6/7, then we can write the equation:

-6/7 = (-6 - 0)/(a + 10) = -6/(a + 10)

The denominator should be the same in both sides, so we must have:

a + 10 = 7

a = 7 - 10 = -3

Then the two points are (-10, 0) and (-3, -6).

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Answer: Pentagon

Step-by-step explanation:

       A closed figure with 5 straight line segments is called a pentagon. See attached for a visual example.

       A segment is a straight line with two distinct endpoints.

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First, use a calculator to create a table of values for the function:

A table with inputs for x starting at -6.5 reaching the value of 6.5 with steps of 0.5 would be:

Plotting all the points and joining them with a smooth line, we can see that the graph of y=tan(x) is:

As we can see from the graph, the curve has an asymptote at

On the other hand, the graph reaches all the real values over the Y-axis. Then, the range of the function is the set of all real numbers.

herefore, the domain is:

he range is:

nd the asymptotes are:

The value of x that makes m parallel to n is 90 degrees.

The value of x that makes m and n parallel is 15.

How to find the angles in parallel lines?

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.

The value of x that makes the line ma and n parallel can be calculated as follows:

180 - x  = x (alternate exterior angle)

180  = 2x

x = 180 / 2

x = 90 degrees

2.

3x - 15 + 150 = 180(supplementary angles)

3x = 180 - 150 + 15

3x = 45

x = 45 / 3

x = 15

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The parent functions are defined with all coefficients with value 1.

They can be linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent...

Then we can pick a function and transform it in order to include the point (-1,5) in the function definition.

We will use the quadratic parent function:

We will adjust the coefficient a of the quadratic function in order to include (-1,5)

Then, our transformed function is:

In order to use two unit multipliers we will convert from square inches to cm using the following unit multiplier:

and then we will convert from square cm to square feet, using the following unit multiplier:

Answer:

The two numbers are 11, and 5 if the one number is six less than a second number.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

One number is six less than a second number.

Let the number be x and y:

x - 6 =  y

Twice the first is 2 more than 4 times a second.

2x = 2 + 4y

After solving the two linear equations:

2x = 2 + 4(x - 6)

2x = 2 + 4x - 24

2x = 22

x = 11

y = 5

Thus, the two numbers are 11, and 5 if the one number is six less than a second number.

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Answer:

20.99 m

Step-by-step explanation:

To find the volume of the prism we just multiply all the measures

The volume is 24 cm³

If the sugar cubes have 1 cm³ of volume, to find how much sugar cubes fit in the box we must divide the volume of the box by the volume of the sugar cubes

Therefore we can fit 24 sugar cubes

The correct answer is Option B.

The amount of calories in 246.5 gm of Cereal 397.5372 calories

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example,

Ram spends 36 Rs. for a dozen (12) bananas. 12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees. As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas. This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

In 177.4 gm of cereal contain 110 calories.

So, 1 gram cereal contain

= 177.4 / 110

= 1.6127

and, 246.5 gm will contain

=246.5 x 1.6127

= 397.5372 calories.

Hence, 397.5372 calories are in 246.5 grams of this cereal.

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