Speed and time are _________ variable.​

\(\huge\text{Hey there!}\)

\(\mathsf{\dfrac{1}{5}\ of\ \dfrac{5}{6}}\)

\(\bullet \large\textsf{ FUN FACT: The word \underline{of} in mathematics means \underline{multiply}}\)

\(\large\text{So, your new \underline{EQUATION} is}\downarrow\)

\(\mathsf{=\dfrac{1}{5}\times\dfrac{5}{6}}\)

\(\mathsf{= \dfrac{1\times5}{5 \times6}}\)

\(\mathsf{1\times5=\bf 5\leftarrow}\large\text{ NUMERATOR}\)

\(\mathsf{5\times6= \bf 30\leftarrow }\large\text{ DENOMINATOR}\)

\(\mathsf{= \dfrac{5}{30}}\)

\(\mathsf{= \dfrac{5\div5}{30\div5}}\)

\(\mathsf{5\div5=\bf 1\leftarrow}\large\text{ NUMERATOR}\)

\(\mathsf{30\div5=\bf 6\leftarrow}\large\text{ DENOMINATOR}\)

\(\mathsf{=\bf \dfrac{1}{6}}\)

\(\boxed{\boxed{\large\text{ANSWER: }\mathsf{\bf \dfrac{1}{6}}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

Step-by-step explanation:

We know:

Convert cm to km:

The nth term of the sequence -3, 0, 5, 10, 25, 5, 47 can be represented by the piecewise function:

nth term =

-3 + (n - 1) * 5, if n mod 5 ≤ 5

5 + (n - 1) * 15, if n mod 5 > 5

To find the nth term of a sequence, we need to identify the pattern or rule that governs the sequence. Upon analyzing the given sequence -3, 0, 5, 10, 25, 5, 47, we can observe the following:

The sequence starts with -3 and increases by 5 each time, except for the 5th term, where it increases by 15 (from 10 to 25). After the 5th term, the sequence starts again with 5 and continues to increase by 15 each time.

Based on this pattern, we can divide the sequence into two parts:

Part 1: -3, 0, 5, 10, 25 (increasing by 5 each time)

Part 2: 5, 20, 35, 50, 65 (increasing by 15 each time)

Now, to determine the nth term, we can consider the formula for arithmetic sequences:

nth term = first term + (n - 1) * common difference

For Part 1, the first term is -3 and the common difference is 5. Thus, the nth term for Part 1 is given by:

nth term = -3 + (n - 1) * 5

For Part 2, the first term is 5 and the common difference is 15. Therefore, the nth term for Part 2 can be expressed as:

nth term = 5 + (n - 1) * 15

However, since the sequence alternates between Part 1 and Part 2, we need to determine which part the nth term falls into. For that, we can use modular arithmetic:

If n mod 5 is less than or equal to 5, then the nth term is from Part 1.

If n mod 5 is greater than 5, then the nth term is from Part 2.

Let's calculate a few terms to illustrate this:

For n = 1, the sequence starts with -3, so the 1st term is -3.

For n = 2, we are still in Part 1, so the 2nd term is 0.

For n = 3, Part 1 continues, so the 3rd term is 5.

For n = 4, we are still in Part 1, so the 4th term is 10.

For n = 5, Part 1 ends, and the 5th term is 25.

For n = 6, the sequence starts with 5 in Part 2, so the 6th term is 5.

For n = 7, Part 2 continues, so the 7th term is 20.

For n = 8, we are still in Part 2, so the 8th term is 35.

Based on this analysis, we can conclude that the nth term for the given sequence is:

If n mod 5 ≤ 5:

nth term = -3 + (n - 1) * 5

If n mod 5 > 5:

nth term = 5 + (n - 1) * 15

Therefore, depending on the value of n and the remainder when divided by 5, we can use the appropriate formula to calculate the nth term.

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Answer:

\(\displaystyle f^{-1}(x)=\frac{1+x}{3x}\)

Step-by-step explanation:

The Inverse of a Function

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

\(\displaystyle y=\frac{1}{3x-1}\)

* Solve the equation for x.

Multiply by 3x-1

\(y(3x-1)=1\)

Divide by y:

\(\displaystyle 3x-1=\frac{1}{y}\)

Sum 1:

\(\displaystyle 3x=\frac{1}{y}+1\)

Operate the right side:

\(\displaystyle 3x=\frac{1+y}{y}\)

Divide by 3:

\(\displaystyle x=\frac{1+y}{3y}\)

* Swap the variables:

\(\displaystyle y=\frac{1+x}{3x}\)

Write back into function form:

\(\boxed{\displaystyle f^{-1}(x)=\frac{1+x}{3x}}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}\)

The perimeter of a figure is the sum of lengths of the sides.

For the given rectangle the perimeter is:

Use the equation above to solve z:

Use the vlue of z to find the length of AD:

The equivalent expression is -1

The surface area of given triangular prism = 24 ft².

For the given triangular prism

Base = 2 ft

height = 3 ft

side = 3ft

We know that,

Surface area of triangular prism

= side x base + 3x base x height

=  3 x 2  + 3x2x3

= 6 + 18

= 24 ft²

Thus,

Surface area = 24 ft²

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Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Answer:

1 (a) x = 12

1 (b) x = 4

2 (a) x = 24

2 (b) x = 20

3 (a) x = 4

3 (b) x = 17.5

Step-by-step explanation:

1 (a)

2x/3 = 8

2x = 8 × 3

2x = 24

x = 24 ÷ 2

x = 12

1 (b)

3x/2 = 6

3x = 6 × 2

3x = 12

x = 12 ÷ 3

x = 4

2 (a)

x/3 - 2 = 6

x/3 = 6 + 2

x/3 = 8

x = 8 × 3

x = 24

2 (b)

x/5 + 1 = 5

x/5 = 5 - 1

x/5 = 4

x = 4 × 5

x = 20

3 (a)

5x/2 + 1 = 11

5x/2 = 11 - 1

5x/2 = 10

5x = 10 × 2

5x = 20

x = 20 ÷ 5

x = 4

3 (b)

2x/7 - 3 = 2

2x/7 = 2 + 3

2x/7 = 5

2x = 5 × 7

2x = 35

x = 35 ÷ 2

x = 17.5

Answer:

ITS 24%

Step-by-step explanation:

To rephrase this problem: 120 is what percent of 500.

Let's call the percent we are looking for  

p

. Then we can say:

p

of 500 = 120 or

p × 500 = 120

Solving for  

p  

while keeping the equation balanced gives:

p × 500

500 = 120

500  p = 0.24  or

24 %

Answer:

q=8/3

Step-by-step explanation:

First, add 5/6 to both sides to get rid of -5/6 to get q=16/6 then simplify to q=8/3.

Answer:

\(q=2\frac{2}{3}\)

Step-by-step explanation:

The given equation consists of a fraction and a mixed number.

First, convert the mixed number into an improper fraction by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:

\(q-\dfrac{5}{6}=1 \frac{5}{6}\)

\(q-\dfrac{5}{6}=\dfrac{1 \cdot 6+5}{6}\)

\(q-\dfrac{5}{6}=\dfrac{11}{6}\)

Now, add 5/6 to both sides of the equation to isolate q:

\(q-\dfrac{5}{6}+\dfrac{5}{6}=\dfrac{11}{6}+\dfrac{5}{6}\)

\(q=\dfrac{11}{6}+\dfrac{5}{6}\)

As the fractions have the same denominator, we can carry out the addition by simply adding the numerators:

\(q=\dfrac{11+5}{6}\)

\(q=\dfrac{16}{6}\)

Reduce the improper fraction to its simplest form by dividing the numerator and denominator by the greatest common factor (GCF).  

The GCF of 16 and 6 is 2, therefore:

\(q=\dfrac{16\div 2}{6 \div 2}\)

\(q=\dfrac{8}{3}\)

Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:

\(q=2 \; \textsf{remainder}\;2\)

The mixed number answer is the whole number and the remainder divided by the denominator:

\(q=2\frac{2}{3}\)

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

The sign is positive.

Step-by-step explanation:

(-5)(-3)

= 15 (double negative)

15(-8)

=-120 (positive negative)

(-120)(-6)

= 720 (negative negative)

Therefore, the sign of the answer is positive.

Hope this helped!

Answer:

The sign is postive

Step-by-step explanation:

(-5)(-3)

= 15 (double negative)

15(-8)

=-120 (positive negative)

(-120)(-6)

= 720 (negative negative)

The volume of the first aquarium is 1404 inches = 2 minutes

14784/1404=10.5299145299

10.5299145299*2=21.0598290598

The volume of the second aquarium is 14784 inches = 21.05 minutes

i think its B ......

The difference of the polynomials (5x3 + 4x2) – (6x2 – 2x – 9) is 5x3 – 2x2 + 2x + 9.

A polynomial is an expression consisting of variables and coefficients,

5x3 + 4x2 - (6x2 - 2x - 9)

= 5x3 + 4x2 - 6x2 + 2x + 9

= 5x3 - 2x2 + 2x +

Answer:

The speed in miles per hour

Step-by-step explanation:

Distance = (speed)(time)

We already have time, t, so 65 must represent the speed (which is in miles per hour).

The point is on the 4th quadrant

The point falls on the negative y-axis and positive x-axis

Given:

Point: (6, -6)

To find:

The quadrant where the point lies and specify the axis

To determine the location, we will plot the point on a coordinate plane

The point is on the 4th quadrant

The point falls on the negative y-axis and positive x-axis

Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

Answer:

(A) 89 (B) 91 (C) 92 (D) 95 4.If |x−2| = p, where x < 2, then x+1 equals (A) −2 (B) 3− p (C) |2p−2| (D) 2p−2 5.A

Step-by-step explanation:

Following are the calculation to the find the value of x:

Given:

Please find the question.

To find:

x=?

Solution:

\(\frac{71}{7} <\frac{x}{9} < \frac{113}{11}\\\\10 <\frac{71}{7} < 11 \\\\10< \frac{113}{11}<11\\\\\frac{x}{9} >10\\\\x>90\\\\\text{When}\ x=91 \\\\\frac{71}{7} > \frac{91}{9}\\\\x=92\\\\ \frac{71}{7}< \frac{92}{9} <\frac{113}{11}\\\\\)

so, x= 92 \\\\

by compare score value x= 92

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Math in many areas is used to create models, mathematical systems the describe real-world situations.

During the pandemic, a model called exponential model was used to predict the how many people will get infected given certain parameters, such as infection rate, average age of population, ...

We picked this particular model because viruses spread at an exponential rate, just like for example bacteria division would be modeled with something like \(2^t\) where t is day number. After 1 day there are 2, after 2 days there are \(4, 8, 16, 32, \dots\) which is known as exponential behaviour -- viruses spread that way, first person gets infected, aka patient 0, then that person likely infects others and others likely infect more people.

In particularly \(R_0\) also known as basic reproduction number was used as a base, that is, \(R_0^t\).

You can see if, \(R_0\lt 1\) then we have a reciprocating behaviour, less and less infected with time passing, this is ideal and it means the pandemic is waning.

However if, like in case with current pandemic, \(R_0\gt 1\) then the behaviour is exactly the opposite, more and more get infected with time. The current pandemic had a highest \(R_0\) of 6.49 with a mean of 3.28 and a median of 2.76.

That means at its heighest, 1 new infected person meant potentially 6 new infected people which meant 36 because each of them would probably infect which means \(216,1296,7776,46656,\dots\).

So the main goal is to prevent \(R_0\) from getting larger ie. minimization, that is why vaccination, masks, good hygiene.

Of course the model is much much more complex and parameterized.

The exponential model took a lot into account and came up with various prediction graphs of for example the next week.

The graphs served to the states to decide what to do next.

So in all, everything that you are witnessing was at some point just, math.

Hope this helps :)

Answer:

it was online math cause of the pandemic

Step-by-step explanation:

Answer:

The answer is below

Step-by-step explanation:

12 inches = 1 ft.

6 inches = 6 inches * (1 ft./12 inches) = 0.5 ft.

Therefore the diameter of the cast iron (D) = 6 inches = 0.5 ft.

The area of cast iron (A) = πD²/4 = π(0.5)²/4 = 0.196 ft²

The velocity (V) = 6 ft./s, the acceleration due to gravity (g) = 32.2 ft./s²

ε/D = 0.0004 ft./ 0.5 ft. = 0.0008

Using the moody chart, find the line ε/D = 0.0008 and determine the point of intersection with the vertical line R = 2.7 * 10⁵. Hence we get f = 0.02.

The head loss (h) is:

\(h_f=f*\frac{L}{d}* \frac{V^2}{2g}=0.02*\frac{200\ ft}{0.5\ ft} *\frac{(6\ ft/s)^2}{2*32.2\ ft/s^2}=4.5\ ft\)

The pressure drop (Δp) is:

Δp = ρg\(h_f\) = \((62.4\ lbf/ft^3)(4.5\ ft)= 280\ lbf/ft^2\)

Using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

A probability is a numerical representation of the likelihood or chance that a specific occurrence will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Simply put, probability is the likelihood that something will occur.

When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes.

So, we have the chart:

Penny = 2/5 = 0.4

Nickel = 1/5 = 0.2

Dime = 1/4 = 0.25

Then, the probability of getting a value of at least $0.10

P(E) = 3/3

P(E) = 1

Therefore, using probability we know that we have full probability or 1 that we will draw a coin that will have ethe value of at least $0.10.

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The equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.

What is equation?

In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

The equation has the form y = Ax² + Bx + C

Since (3,0), (-1,0), (1,-16) are points on the graph, we get the following system of equations:

9A + 3B + C = 0

A - B + C = 0

A + B + C = -16

Subtracting the first 2 equations and subtracting the 3rd equation from the first, we obtain:

8A - 4B = 0

8A + 2B = 16

Since 8A - 4B = 0, 8A = 4B.  So, A = 1/2B.

Therefore, 8A + 2B = 16

6B = 16  So , B = 8/3  and A = 8/6

Since A + B + C = -16 and A = 8/6 , B = 8/3, we have 4 + C = -16.  So, C = -20.

An equation of the parabola is y = 4/3x² + 8/3x - 20

Hence , the equation for a parabola with x-intercept is y = 4/3x² + 8/3x - 20.

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Answer:

12

Step-by-step explanation:

10x - 20 + 6x + 8 = 180

Supplementary angles

Answer:

x = 12

Step-by-step explanation:

The two given angles create a straight line (Definition of Straight Line). This means that:

\((10x - 20) + (6x + 8) = 180\)

First, combine like terms. Like terms are terms that share the same amount of the same variables:

\((10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\\)

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 12 to both sides of the equation:

\(16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192\)

Next, divide 16 from both sides of the equation:

\(\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12\)

12 is your answer.

~

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Answer:

FCB, I think.

Step-by-step explanation:

2 angles are supplementary when they add up to 180°

Answer:

It's C.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

just put the x and y values into the equations and see which equation stays true.

for example, point (4, 68) rules out A and C even without detailed calculation, because these 2 expressions can produce for positive x only negative y (and 68 is clearly a positive y).

so, when using this point in B :

68 = 4×4² + 2×4 - 4 = 4×16 + 8 - 4 = 64 + 8 - 4 = 68

correct.

and it is correct also for the other points.

so, B is the right answer.

Answer: 0.166666667 yards OR 0.1524 meters OR 0.5 feet

Step-by-step explanation:

1 / 6 = 0.166666667 yards

1 yard = 0.9144 meters

0.9144 / 6 = 0.1524 meters

1 yard = 3 feet

3 / 6 = 0.5 feet