1 1/2 + 3 2/3 + 2/3 equals what?

The inverse function f-¹(x) as required to be determined from the given function; f(x) = (x-7)³ is; f¯¹(x) = ³√x + 7.

It follows from the task content that the inverse function of the given function; f(x) = (x-7)³ is to be determined.

Therefore, let f(x) = y; so that we have;

y = (x - 7)³

make x the subject so that we have;

³√y = x - 7

x = ³√y + 7

By switching the variables; we have;

y = ³√x + 7

Therefore, the required inverse function; f-¹ as required is; f¯¹(x) = ³√x + 7.

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Part A:

[tex]B\cap D[/tex] is asking for what the sets B and D have in common:

   [tex]B\cap D = \{4\}[/tex]

since B and D only have 4 in common.

Now [tex](B \cap D)'[/tex] is asking for all of the things in the universal set [tex]U[/tex] that are not in [tex]B\cap D[/tex].  That's what the little tick mark on the right side means.

   [tex](B \cap D)' = \{2, 3, 6, 7\}[/tex]

Part B:

[tex]B' = \{2, 3, 7\}[/tex] since those are the things not in B.

[tex]D=\{3, 4\}[/tex]

[tex]B'\cup D[/tex] is asking for all the things in either [tex]B'[/tex] or [tex]D[/tex].

    [tex]B'\cup D = \{2, 3, 4, 7\}[/tex]

(We don't need to list 3 twice, even though it was in both sets. )

The derivative formula for the division of two functions is equal to d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]², where θ(x) = f(x) / g(x).

In this problem we need to derive the formula for the derivative of the division of two functions, that is, the expression θ(x) = f(x) / g(x). First, we write the definition of the derivative for the given expression:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\theta(x + h) - \theta (x)}{h}[/tex]

Second, substitute and expand the expression by algebra properties:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\frac{f(x + h)}{g(x + h)} - \frac{f(x)}{g(x)} }{h}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x + h)}{h\cdot g(x + h)\cdot g(x)}[/tex]

Third, expand and simplify the expression one more time by algebra properties and limit properties:

[tex]\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x) + g(x) \cdot f(x) -f(x) \cdot g(x + h)}{h \cdot g(x + h) \cdot g(x)}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} g(x) \cdot \frac{f(x + h) - f(x)}{h\cdot g(x+h)\cdot g(x)} - \lim_{h \to 0} f(x) \cdot \frac{g(x + h) - g(x)}{h\cdot g(x+h)\cdot g(x)}[/tex]

[tex]\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{g(x)}{g(x + h) \cdot g(x)} \cdot \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} - \lim_{h \to 0} \frac{f(x)}{g(x+ h) \cdot g(x)} \cdot \lim_{h \to 0} \cdot \frac{g(x + h) - g(x)}{h}[/tex]

Fourth, simplify the resulting expression by evaluating the limits:

d [θ(x)] / dx = [g(x) / [g(x)]²] · f'(x) - [f(x) / [g(x)]²] · g'(x)

d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]²

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7/8 of sixteen times a half of 30 is 210.

What is a PEMDAS rule?

PEMDAS is an acronym that stands for the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

To calculate this, we can follow the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Start with the expression inside the parentheses: half of 30 is 15.

Multiply 16 by 15: 16 times 15 is 240.

Find 7/8 of 240:

7/8 of 240 = (7/8) x 240

                  = 210

Hence, 7/8 of sixteen times a half of 30 is 210.

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Answer:

I honestly don't know I just need points

The required equation of the line representing line CD is y = x + 2. Option C is correct.

The equation of the line passing through two points is given by the equation,

y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)  - - - -- -(1)

Here,
Line CD passes through points (0, 2) and (4, 6)
Let (0, 2) and (4, 6) equal to (x₁, y₁) and (x₂, y₂) respectively.
Substitute this point in equation 1 to get the equation of the line representing CD,

So,
y - 2 = (6 - 2)/(4-0) (x - 0)
y = x + 2

Thus, the required equation of the line representing line CD is y = x + 2. Option C is correct.

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PLEASE GIVE BRAINLIEST
thank you and have a good day :)

Answer:

You figure out the slope

Step-by-step explanation:

Rise/Run is a formula that calculates the slope.  This determines the direction of the line and how steep it is.

Answer:

its a math term yw my boy

Step-by-step explanation:

Since the domain has 4 elements and the range has 2 elements, each element in the domain can be mapped to one of the two elements in the range. Thus, there are a total of [tex]$2^4 = 16$[/tex] functions from the domain to the range.

What is functions ?

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain or range) with the property that each input is related to exactly one output. Functions can be represented in many ways, including algebraic expressions, graphs, tables, or verbal descriptions.

Functions are widely used in various fields of mathematics, science, and engineering to model and analyse real-world phenomena, and to make predictions or decisions based on data.

There are 4 elements in the domain and an empty set in the codomain.

Using two-line notation, the functions are:

There is only one possible image for each element in the domain, which means that there is only one function.

Since there is only one function, it is both surjective and injective. Therefore, there is only one bijective function.

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The required graph has been attached below which represents the given linear equation y = (2/5)x - 4.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

To plot the graph of y = (2/5)x - 4, you can follow these steps:

Choose a range of values for x that you want to plot. For example, you can choose x values from -10 to 10.

Substitute the x values into the equation to find the corresponding y values. For example, if x = -10, then y = (2/5)(-10) - 4 = -8.

Plot the ordered pairs (x, y) on a coordinate plane. For example, if x = -10 and y = -8, plot the point (-10, -8) on the plane.

Repeat this process for several x values to plot additional points.

Connect the points with a straight line to obtain the graph of the equation y = (2/5)x - 4.

Note that the graph should be a straight line with a slope of 2/5 and a y-intercept of -4.

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The question seems incomplete, the correct question would be as:

How to plot the graph of y = (2/5)x — 4?

Answer: ~ 7.72 square miles

Step-by-step explanation:

One square kilometer is equal to around 0.386 miles.

To get to 20 square kilometers, multiply 0.386 times 20.

hope this helps

MM

The distinct points are (1, 15), (2, 14) and (3, 13)

The slope implies that as the length increases by 1, the width decreases by 1

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

2x + 2y = 32

Divide by 2

So, we have the following representation

x + y = 16

Make y the subject

y = 16 - x

Set x = 1, 2 and 3

So, we have

y = 16 - 1 = 15

y = 16 - 2 = 14

y = 16 - 3 = 13

So, the points are (1, 15), (2, 14) and (3, 13)

The slope is calculated as

y = mx + c

Where m = slope

When compared, we have

slope = -1

This means that as x increases, y decreases

The graph is attached

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On solving the provided question, we can say that  The following are the mean and standard deviation of the sample distribution of x: Average: 225 sec. 19 second standard deviation.

Standard deviation is a statistic that expresses the variability οr variance of a grοup of numbers. While a high standard deviation suggests that the values are mοre dispersed, a low standard deviation suggests that the values tend tο be closer to the established mean.

A measure of hοw dispersed the data are frοm the mean is the standard deviation (οr ). When the standard deviation is lοw, the data tend to be grouped around the mean, and when it is large, the data are mοre dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each scοre from the mean.

The median matches the median οf the population.

The pοpulation standard deviation is divided by the square root of the sample size tο produce the standard deviation.

The following are the criteria fοr this issue:

average population of 225 seconds.

60 second population standard deviatiοn.

10 second sample size.

Consequently, the following is the standard deviation fοr the sample distributiοn of x:

19 seconds are equal to 60/√(10).

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Check the picture below.

Make sure your calculator is in Degree mode.

Answer: In each question you have two options, T and F. Then in 6 questions you have 2 options for the first, two for the second, two for the third... At the end you get 2·2·2·2·2·2 = 26 options and 26 = 64.

Step-by-step explanation:

The number of years the interest was compounded quarterly is given by the equation b = 9.098 years

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after b years be A = $ 26,725.00

The number of years be = b

The number of times the interest is applies n = 4 ( quarterly )

Let the principal amount be P = $ 7,000

A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

t = ln ( A/P ) / n [ ln ( 1 + r/n ) ]

t = b = n ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.15/4 ) ] )

On simplifying the equation , we get

b = ln ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.0375 ) ] )

b = ln ( 3.81785714 ) / 4 [ ln ( 1.0375 ) ]

On further simplification , we get

b = 9.098 years

Hence , the number of years the interest was applied is 9 years 1 months

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For the function f(x) = -tan 4x,

Given the function

f(x) = -tan 4x

The domain of the function is the set of all possible inputs of the function

The range is set of all possible outputs of the function

Here the function is

f(x) = -tan 4x

Domain of the function will be

π[(2n+1)/8] < x < π[(2n+3)/8]

The range of the given function is set of all real numbers

The period = π /4

Two vertical asymptotes are π/8 and -π/8

Therefore, the domain, range period and the two vertical asymptotes of the function has been found

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Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)

Answer:

Below

Step-by-step explanation:

1.4 m = .42     divide both sides of the equation by   1.4 to get

 m = .3     Done.

By making the discriminant equal to zero, we can see that the quadratic equation has one real solution only for z = 10.

For a general quadratic equation:

a*x^2 + b*x + c = 0

We define the discriminant as:

D = b^2 - 4ac

The quadratic equation will have only one real solution only if the discriminant is equal to zero.

Here the quadratic is:

(z - 5)*x^2 - z*x + 5 = 0

Then the discriminant is:

(-z)^2 - 4*5*(z - 5)

And that must be equal to zero, then we need to solve:

z^2 - 20*(z - 5) = 0

z^2 - 20z + 100 = 0

Using the quadratic formula we will get:

[tex]z = \frac{20 \pm \sqrt{(-20)^2 - 4*1*100} }{2} \\\\z = \frac{20 \pm 0}{2} \\\\z = 10[/tex]

So the quadratic equation has one real solution only for z = 10.

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The transformation used are:

(a)

This is a translation of one unit to the left and one unit up.

(b)

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The graph from y = h(x) to y = h(-x)  + 1.

This is a translation of one unit to the left and one unit up.

The graph from y = g(x) to y = 2g(x)  - 4.

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

Now,

The graph of y = h(-x)  + 1 is given below.

The graph of y = 2g(x)  - 4 is given below.

Thus,

(a)

This is a translation of one unit to the left and one unit up.

(b)

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

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A pie has 360 degrees, so a pie cut into 5 equal pieces produces 5 slices that each measure 360 / 5 = 72 degrees.

A small slice measures 27 degrees fewer than a large slice, so it measures 72 - 27 = 45 degrees.

To find the number of pieces a pie should be cut into so that each piece is a small slice, we need to determine how many degrees each slice measures. To do this, we divide 360 by the number of pieces:

360 / n = 45

Solving for n, we get:

n = 360 / 45 = 8

So, the Tasty as Pi Bakery should cut a whole pie into 8 equal pieces so that each piece is a small slice.

52s represents the cost for the snowboard times s days.

What is an expression ?

An expression consists of one or more numbers or variables along with one more operation.

Given :

expression : 52s + 10

Since it represents , total cost to rent a snow board for s days plus the fee for the helmet

Therefore , 52 is the cost of the snowboard rental per day.

s represents the day(s) that the equipment is rented out.

Hence , 52s represents the cost for the snowboard times s days.

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Given question is incomplete , the complete question is given below:

At the ski shack customers can rent skis snowboards boots and poles by the day. josh rents a snowboard and a helmet. The expression 52s + 10 represents the toatak cost to rent a snow board for s days plus the fee for the helmet what dose the term 52s represent​

Answer:

Below

Step-by-step explanation:

If you draw this diagram you will see a right triangle with legs = height

    and   10 miles

for the 6 degree angle  ( in the right triangle)

   tan ( 6) = opposite leg / adjacent leg

      tan (6) = height / 10

       or    10 * tan 6 = height     ( in miles)

                      1.05 miles high

It will take 5.189 hours to get doubled the size of Sample.

A relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

Growth rate = 5.8%

The continuous exponential growth model for populations is given by:

P(t)= [tex]P_0 e^{rt[/tex]

So, r= 5.8%

r = 0.058

Now, the time taken to double the sample then P(t) = 2P(0).

So, P(t)= [tex]P_0 e^{0.058t[/tex]

2P(0) = [tex]P_0 e^{0.058t[/tex]

[tex]e^{0.058t[/tex] = 2

Taking log on both side

log [tex]e^{0.058t[/tex] = log 2

0.058 t = 0.301

t= 0.301/ 0.058

t = 5.189

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Answer:

6.89 billion for year 2010

7.15 billion for year 2023

Step-by-step explanation:

f(x) = [tex]a(1 + r) ^{x}[/tex]

f(x) = [tex]6.08(1+ .0126)^{10}[/tex]

f(x) = 6.89 Rounded to 2 places

f(x) = [tex]6.08(1+ .0126)^{13}[/tex]

f(x) = 7.15 Rounded to 2 places

He then constructs a graph to visualize his results,  For a given number of selections, we can use Joseph's graph to find the number of diamonds that he has picked so far is FALSE.

Probability refers to potential. A arbitrary event's circumstance is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to read the liability of colorful events. The degree to which commodity is likely to be is principally what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

We are only interested in finding red card so we can't differentiate between diamond or hearts at any time. Hence,

The false statement is:

For a given number of selections, we can use Josephs graph to find the number of diamonds that he has picked so far.

Option B is correct.

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The side length of the square with the same area as the circle is given as follows:

9.75 cm.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The radius for this problem is of 5.5 cm, hence the area of the circle is given as follows:

A = π x 5.5²

A = 95.03 cm².

For a square of side length s, the area is given by the side length squared, that is:

A = s².

Hence the desired side length is obtained as follows:

s² = 95.03

s = sqrt(95.03)

s = 9.75 cm.

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The stronger one is 4 scoops of coffee for 6 cups of water.

Strong coffee is prepared by employing a greater coffee grounds-to-water ratio. Typically, 2 teaspoons of coffee grinds are used for every 6 ounces of water in a strong cup of coffee. To make a truly strong cup of coffee, use 3 teaspoons of ground coffee for every 6 ounces of water. If you use a French press, you need also increase the steeping time.

In the given question, it is stronger to use 4 scoops of coffee for 6 glasses of water. This is due to the fact that there are more coffee grounds in relation to the amount of water, resulting in a higher concentration of coffee in the combination.

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Oliver's number is bigger than that of Chen.

It is a number equal to 10 times 10.

Given is that Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds, my number must be bigger.

Oliver number can be written as follows -

8 x 10 x 10

Chens number can be written as follows -

3 x 10 x 10

It can be concluded that Oliver's number is bigger than that of Chen.

Therefore, Oliver's number is bigger than that of Chen.

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The original price of the upright bike is $3,600.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentages is %. Percentage is a measure of frequency.

Original price of the upright bike = sales price / percent discount

= $720 / (20/100)

$720 / 0.2

= $3,600

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