Mary has some chocolates. If she shares them equally among 4 friends or 5 friends, there are always 2 extra chocolates left. What is the possible number of chocolates Mary could have?

[tex]\stackrel{\textit{reciprocal ident.}}{csc(\theta)=\cfrac{1}{sin(\theta)}} ~\hfill \stackrel{\textit{symmetry ident.}}{sin(-\theta )=-sin(\theta)}~\hfill \begin{array}{llll} \stackrel{\textit{pythagorean ident.}}{sin^2(\theta)+cos^2(\theta)=1}\\ sin^2(\theta)=1-cos^2(\theta)\\ cos^2(\theta)=1-sin^2(\theta) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\cfrac{csc^2(-x)-1}{1-cos^2(-x)}\implies \cfrac{~~\frac{1}{sin^2(-x)}-1~~}{sin^2(-x)}\implies \cfrac{~~ \frac{1-sin^2(-x)}{sin^2(-x)}~~}{\frac{sin^2(-x)}{1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{keeping in mind that}~\hfill }{sin^2(-x)\implies [sin(-x)]^2\implies [-sin(x)]^2\implies [sin(x)]^2\implies sin^2(x)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{~~ \frac{1-sin^2(x)}{sin^2(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{1-sin^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cot^2(x)csc^2(x)~\hfill[/tex]

As a result of the Industrial Revolution, things changed for women in that C. Women gained increased economic independence by working in  factories

The Industrial Revolution:

When women started earning salaries, they did not have to rely on men as much as they could not provide for themselves which led to increased economic independence.

In conclusion, the industrial revolution allowed for the economic independence of women to increase.

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Answer:

D. Compound interest accrues on the interest, as well as the

principal.

Answer:

D. Compound interest accrues on the interest, as well as the

principal.

Step-by-step explanation:

The value of x from the expression is [tex]\frac{ln8-8}{3}[/tex]

Given the exponential function [tex]e^{3x+8}=8[/tex]

Take the natural logarithm of both sides:

[tex]lne^{3x+8}=ln8\\3x +8=ln8[/tex]

Subtract 8 from both sides:

[tex]3x-8+8=ln8-8\\3x=ln8-8[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3} =\frac{ln8-8}{3}\\x= \frac{ln8-8}{3}[/tex]

Hence the value of x from the expression is [tex]\frac{ln8-8}{3}[/tex]

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Answer:

1-2

Step-by-step explanation:

honestly idek what this stuff is I just need points

Given function:-

Degree of the given function is the highest power of the variable.

We have variable x there.

So, we can say:

Degree = 6 ( an even degree)

And leading coefficent is the coefficent of highest power term.

We have highest power term is 2x^6.

So, the leading coefficent is : 2 (Positive number)

For even degree and positive leading coefficent, end behaviour is

x --> ∞  f(x) = +∞

x-->-∞   f(x) = +∞

Answer:

Step-by-step explanation:

$92.43 / 0.74 = $124.91

The total bill is equal to $124.9

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here, the given bill as 74% of the total bill as $92.43

Thus the total bill must be = 92.43×100/74

                                            = $124.9

Hence, The total bill is equal to $124.9

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Answer:

3

Step-by-step explanation:

4x+2=5x-1

4x - 5x = -1 -2

x = 3

[tex]e^{2x} = \ln(y^3)\\\\\implies e^{2x} = 3 \ln y\\\\\implies \dfrac{d}{dx} e^{2x} = 3\dfrac{d}{dx}( \ln y)\\\\\implies 2e^{2x} = 3 \cdot \dfrac 1y \cdot \dfrac{dy}{dx}\\\\\implies 3\dfrac{dy}{dx} = 2ye^{2x}\\\\\implies \dfrac{dy}{dx} = \dfrac{2y}3 e^{2x}[/tex]

Answer:

B. slope

Step-by-step explanation:

Answer:

(0,-3), (1,1)

Step-by-step explanation:

An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is B.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that has a "x" term with a coefficient of 1 is the expression that has positive one in from of the term that has x in the expression.

Now, If all the options are observed, then it can be found that the second option has x term with leading coefficient as 1.

Hence, the correct option is B.

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Answer:

A AND B IS TRUE  C IS FALSE

Step-by-step explanation:

Answer:

It does not, unless [tex]x=0[/tex] or [tex]x=1[/tex]

If you remember how to raise a power to a given power you remember to multiply the exponents (or, if you don't, apply the definition of [tex](x^3)^3=(x^3)(x^3)(x^3)=x^9[/tex]

At this point you're being asked if [tex]x^9=x^6[/tex] and the only two numbers for which this is true are 0 and 1 (side note: if the left hand side was an even function also [tex]-1[/tex] was a possible candidate, but alas 9 is odd).

Answer:

Either one: the two line have a point in common, or infinite: they are the same line.

Explanation:

We multiply the y coordinate by -1/3 because of the notation (-1/3)*f(x). Recall that y = f(x). The x coordinate stays the same.

[tex]\huge\underline\mathtt\colorbox{cyan}{3/8}[/tex]

[tex]\huge\mathsf\colorbox{white}{}[/tex]

Total shared part:

1/4 + 1/8

Taking LCM and adding:

2/8+1/8

Adding gives:

3/8

Answer:

1

Step-by-step explanation:

y2 - y1 / x2 - x1

6 - 4 / 0 - -2

2 / 2 = 1

we need the image to solve the problem

Answer:

53

Step-by-step explanation:

pls give me brainlest

The required equation that represents the graph is y = x + 30

The standard linear equation is given as y = mx + b

Using the coordinates (20, 50) and (40, 70)

Get the slope of the line:

m = 70-50/40-20

m = 20/20

m = 1

Since the line cuts the y-axis at y = 30, hence the y-intercept is 30.

The required equation that represents the graph is y = x + 30

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Answer:

The equation

Step-by-step explanation:

I need the equation so I can answer your question.

If you know how to set up the format for long division, the answer is 9.5 because 4 goes into 3 zero times, and you don't necessarily need to write down the zero on top since it equals nothing in a whole number. then, 4 goes into 38 nine times. (yes 38 because you didn't do anything with the 3 so you just make it 38) 4 × 9 = 36. it doesn't exactly make 38, so you take away 36 from 38 and you are left with a remainder of 2. then to get no remainder, add a zero to the end of 38. so it would look something like 4/380 so you take down the zero next to the 2 so it makes 20, 4 × 5 = 20 and you are left with a remainder of 0 and the answer: 9.5 ( P.S.: added the decimal because it wasn't exactly equal when doing 4 × 9 so we had to add a zero)

Answer:

f(x)=|x+6|

Step-by-step explanation:

it moves 6 to the left!

Answer:

1/4

Step-by-step explanation:

4 skittles and one being green

Answer:

4/5

Step-by-step explanation:

According to the Wrigley's Consumer Care Department, the fruit candies are produced in equal proportions— 20% of each of the five colors (green, red, orange, yellow, and purple). However, although these candies are made in equal proportions, the individual Skittles bags are filled by weight and by machines but on average I'd say 4/5 chance its a green.

Answer:

126 1/3 yards

Step-by-step explanation:

1 foot = 1/3 yard

379 feet = 379/3 yard= 126 1/3 yards

[tex]\text{Given that,}\\\\\\f(x) = \ln(x^4 +e^{2x})\\\\\\f'(x) = \dfrac{1}{x^4 + e^{2x}} \left(4x^3+2e^{2x}\right) = \dfrac{2(2x^3+e^{2x})}{x^4 + e^{2x}}~~~~;[\text{Chain rule}]\\\\\\\text{Note:}\\\\\dfrac{d}{dx} \ln x = \dfrac 1x\\\\\dfrac{d}{dx} x^n = nx^{n-1}\\\\\dfrac{d}{dx} e^{mx} = m e^{mx}[/tex]

After solving the given equation, the value obtained is equal to [tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex].

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. To include terms in an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given data in the question,

f(x) = ln (x⁴ + e²ˣ)

[tex]f'(x)=\frac{1}{x^4+e^2^x}(4x^3+2e^2^x)[/tex]

Now, use the chain rule,

[tex]\frac{2(2x^3+e^2^x)}{x^4+e^2^x}[/tex]

Also, note some points,

d/dx ln (x) = 1/x

[tex]\frac{d}{dx}x^n=nx^n^-^1[/tex]

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Answer: 24

Step-by-step explanation

8-8-16-24-32-40

6-6-12-18-24-30-36

[tex]\left(3+\sqrt{-16} \right) \left(5-\sqrt{-25} \right)\\\\=\left(3+\sqrt{-1} \cdot \sqrt{16} \right) \left(5- \sqrt{-1} \cdot \sqrt{25} \right)\\\\=(3+4i)(5-5i)~~~~~~~~~~~~~~;\left[i=\sqrt{-1} \right]\\\\=15-15i + 20i - 20i^2\\\\=15+5i -20(-1)~~~~~~~~~~~~;[i^2 =-1]\\\\=15+5i +20\\\\=35+5i[/tex]