1. Distance in space is often written using a light year. A light year is the distance light travels in
one year. It is equal to about 6,000,000,000,000 miles. Write this measurement in scientific
notation.
A. 6 x 10¹0 miles
B. 6 x 10¹1 miles
C. 6 x 10¹2 miles
D. 6 x 10¹3 miles

For the function f(x) =(4 sin x)/(1+cosx) , then f'(x) = 4/(1+cosx) using quotient rule of differentiation and f'(2) = 2.00

Quotient rule for differentiation states that the differentiation the division of two functions u, v is given as

(u/v)' = (u' v  - u v')/v² , where '  represents first derivative  with respect to independent variable

Given f(x) = (4sinx)/(1+cosx)

let u =4 sin x , v = 1+cos x , u'=4cos x , v' = -sin x

Then f(x) =u / v

Using quotient rule of differentiation:

f'(x) = ( u' v -u v' )/v² = (4cosx(1+cosx) +4sin²x )/(1+cos x)²

f'(x) = = 4(cos x +cos² x +sin² x)/(1+ cos x)² = 4(cos x +1)/(1+ cos x)²  

f'(x) = 4/(1+ cos x)

To find value of f'(x) at x= 2

f'(5) = 4/(1+cos2) = 2.000609= 2.00(rounding off )

Therefore if f(x) = (4x² tan x)/sec x  then f'(x) = 4/(1+cos x) and f'(2) =2.00

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Answer: 2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3

Step-by-step explanation:

f(x)=2x^2-2

g(x)=x^2-3x

(f/g)(x)=

[tex]\frac{2x^2-2}{x^2-3x}[/tex]=

[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=

[tex]\frac{2x^2-6x+6x-2}{x^2-3x}[/tex]=

2+[tex]\frac{6x-2}{x^2-3x}[/tex]=2+[tex]\frac{6x-2}{x(x-3)}[/tex] ==> x[tex]\neq[/tex]0, x[tex]\neq[/tex]3

The unit price of the pairs of padded will be $1.23 per pair. The error is the price of the pairs of pads should have been divided by 12.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

For $44.28 a contractor buys 3 dozen pairs of cushioned work gloves.

The unit price of the pairs of padded will be given as,

⇒ $44.28 / (12 x 3)

⇒ $1.23 per pair

The unit price of the pairs of padded will be $1.23 per pair.

The error is the price of the pairs of pads should have been divided by 12.

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Answer:

(r+21 ) / 4

Step-by-step explanation:

as we can see DF = FM
and DF = 4R ,  FM =r+21

so,
4R = r+21
=> R= (r+21)/4

The amount used in decimal is 1.50

The given parameters are

Cans = 2

Amount used = 6/4

The amount used in decimal is calculated as:

Amount used = 6/4

Divide 6 by 4

So, we have

Amount used = 1.50

Hence, the amount used in decimal is 1.50

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Based on the gross pay to Edie of $927.88, the amount contributed by Edie Social Security was $57.53 and the amount to Medicare was $13.45

The current Social Security tax rate is 6.2% which means that to find the Social Security tax that Edie will contribute will be:

= Social security tax rate x Gross pay of Edie

= 927.88 x 6.2%
= $57.52856

= $57.53

The Medicare tax rate is 1.45%. The Medicare tax can therefore be found by multiplying the gross pay by the Medicare tax rate:

= 927.88 x 1.45%

= $13.45

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Month  Cost at Stack n’ Store   Cost at Smart Storage

1               $325                              $185

2              $475                                 $370

3               $625                                  $555

4               $775                                   $740

5                $925                                 $925

6                $1075                                $1100

The company that offers the better deal is Smart Storage.

After 5 months the cost would be the same at both storage companies.

The equation that represent the total cost of renting at Stack n’ Store is:

Total cost = non refundable deposit + charge per month

Total cost in the first month : $175 x ($150 x 1 ) = $325

Total cost in the second month : $175 x ($150 x 2 ) = $475

Total cost in the third month : $175 x ($150 x 3 ) = $625

Total cost in the fourth month : $175 x ($150 x 4) = $775

Total cost in the fifth month : $175 x ($150 x 5) = $925

Total cost in the sixth month : $175 x ($150 x 6) = $1075

The equation that represent the total cost of renting at Smart Storage is:

Total cost = cost per month x number of months

Total cost in the first month : $185 x 1 = $185

Total cost in the second month : $185 x 2 = $370

Total cost in the third month : $185 x 3 = $555

Total cost in the fourth month : $185 x 4 = $740

Total cost in the fifth month : $185 x 5 = $925

Total cost in the sixth month : $185 x 6 = $1,110

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Answer:

[tex]\sqrt{89}[/tex]units

Step-by-step explanation:

[tex]\sqrt{(7-13)^2+(10-2)^2}[/tex]

(-5)^2+(8)^2=25+64

25+64=89

[tex]\sqrt{89}[/tex]

the answer would be [tex]\sqrt{89}[/tex]

Answer:

X= 1/y

Step-by-step explanation:

[tex]y = 1 - \frac{1}{ \sqrt{1} - \frac{1}{1 - x} } \\ y = 1 - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{1 - \frac{1}{1 - x} } \\ y - 1 = - \frac{1}{ \frac{1 - x - 1}{1 - x} } \\ y - 1 = - \frac{1 - x}{ - x} \\ y - 1 = \frac{1 - x}{x} \\ yx - x = 1 - x \\ yx = 1 \\ x = \frac{1}{y} [/tex]

The value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4

In this question,

we have been given a function f(n) = f(n - 1) - 2

Also, we have been given the value of function f(n) for n = 1

i.e., f(1) = 6

We need to find the value of f(6).

For n = 2,

f(2) = f(2 - 1) - 2

f(2) = f(1) - 2

f(2) = 6 - 2

f(2) = 4

For n = 3,

f(3) = f(3 - 1) - 2

f(3) = f(2) - 2

f(3) = 4 - 2

f(3) = 2

For n = 4,

f(4) = f(4 - 1) - 2

f(4) = f(3) - 2

f(4) = 2 - 2

f(4) = 0

For n = 5,

f(5) = f(5 - 1) - 2

f(5) = f(4) - 2

f(5) = 0 - 2

f(5) = -2

For n = 6,

f(6) = f(6 - 1) - 2

f(6) = f(5) - 2

f(6) = -2 - 2

f(6) = -4

Therefore, the value of function f(n) = f(n - 1) - 2, at n = 6 is f(6) = -4

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The required simplification of the given expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex] is 1.

Given that,
To determine the simplified value of the expression [tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
[tex]=\lim_{x \to \infty} \frac{x^2-4x +4}{x^2-4}[/tex]
[tex]=\lim_{x \to \infty} \frac{x^2(1-4/x +4/x^2)}{x^2(1-4/x^2)}[/tex]
Now put limits, so 1 / x², 1 / x becomes zero so,
= 1

Thus, the required simplification of the given expression is 1.

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Answer:

84 tablets with 6 per day

Answer:

here is the answers

Step-by-step explanation:

sample:

1. 4x = 68

x = 68/4

x = 17

Solution :

1) x + 2x + x = 68

>> 4x = 68

>> x = 68 / 4

>> x = 17

2) x + y + 3y = 45

>> x + 4y = 45

>> 17 + 4y = 45

>> 4y = 45 - 17

>> 4y = 28

>> y = 28 / 4

>> y = 7

3) x + y - 4z = -32

>> 17 + 7 - 4z = -32

>> 24 - 4z = -32

>> -4z = -32 - 24

>> -4z = -56

>> z = 56 / 4

>> z = 14

4) x + y + z = ?

>> 17 + 7 + 14

>> 24 + 14

>> 38

5) -x + 8x = 63

>> 7x = 63

>> x = 63 / 7

>> x = 9

6) 4x + 3x - x = 42

>> 7x - x = 42

>> 6x = 42

>> x = 42 / 6

>> x = 7

Answer:

x=19

Step-by-step explanation:

All of the angles add up to 180 degrees since it is a straight angle. So, the equation is:

3x+7+90+x+7=180

You combine like terms:

4x+104=180

Then you subtract on both sides:

4x=76

Then you divide by 4 on both sides:

x=19

The required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 +  i√3,  -2 -  i√3

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

4x^3 + 16x^2 + 28x = 0

Taking x common we get,

x(4x^2 + 16x + 28) = 0

So, we get

x = 0

And 4x^2 + 16x + 28 = 0

or, x^2 + 4x + 7 = 0

Thus from the above equation is of the form

ax^2 + bx + c = 0

where, a = 1, b = 4 and c = 7

Therefore solution of the above equation is given as,

x = [-b ± √(b^2 - 4ac)] / 2a

Putting the values we get,

x = [-4 ± √(4^2 - 4*1*7)] / 2*1

so, x = [-4 ± √(16 - 28)] / 2

x = [-4 ± √(- 12)] / 2

x = [-4 ± 2√(- 3)] / 2

or, x = [-2 ± √(- 3)]

Since √-1 = i

∴ √(- 3) = i√3

Thus,

x = -2 ±  i√3

So, the required values of x are 0,  -2 +  i√3,  -2 -  i√3.

Thus, the required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 +  i√3,  -2 -  i√3.

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Answer:

Slope of one of the dotted lines:

[tex]y=x[/tex] or [tex]y=x+5[/tex]

Slope of the line of reflection:

[tex]y=-x[/tex]

Step-by-step explanation:

When seeing the dotted lines, both of them have a rise & run of 1, indicating that y = x. However, one of the lines has a y-intercept of 5, making it y = x + 5. So, the slopes for the dotted lines are [tex]y=x[/tex] or [tex]y=x+5[/tex].

The line of reflection has a rise & run of -1, and goes through the origin, indicating that the equation is y = -x.

The correct answer choice as required in the task content is; Choice B; Change 1,000 to Scientific notation and then multiply by (2.3 x 10^6).

To find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).

This is a method of writing or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.

which number is one thousand times larger than 2.3 x 10²

1000 to scientific notation

= 10³

2.3 x 10² × 1000

= 2.3 x 10² × 10³

= 2.3 × 10^5

Furthermore, scientific notation helps us to express numbers in decimal number between 1 and 10 followed by an integer power of 10. It also help us to represent numbers in this pattern.

Therefore, to find which number is one thousand times larger than 2.3 x 10², Change 1,000 to Scientific notation and then multiply by (2.3 x 10²).

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The initial total attendance at a science museum is modeled by the function f(x)=17,371(1.041)x will be 17371.

It should be noted that from the information, the total attendance at a science museum is modeled by the function

In this case, the total attendance when x=0 will be:

f(x) = 17,371(1.041)x.

f(x) = 17,371(1.041^0)

= 17371 × 1

= 17371

Therefore, the total attendance when x = 0 will be 17371.

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The Image of the trapezoid under rigid transformation is given by A'B'C'D'  attached below.

The unique process of changing an existing graph or graphed equation to create a completely different version of the given graph is known as graph transformation.

In the given figure we can see that the Trapezoid ABCD is rotated around a fixed point to get the image of the trapezoid A'B'C'D'.

So the figure gets a rotational transformation.

From the figure we can assume that the figure is rotated about 135° clockwise about a fixed point.

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Answer:

At 65mph the car traveled 195 miles in 3hrs.

So divide 195 miles by 80mph to get 2.4375 hrs

Answer: X = 8.4 Y= 3.5

Step-by-step explanation:

The median is a better measure of center for the male's data, while the mean is a better for the female's data.

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

(a) The IQR of the male's data

From the given male's boxplot, we have the following data elements;

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

Then the IQR is calculated as:

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2

IQR = 12

Hence, the IQR for the given males' data is 12

(b) The difference between the median values can be calculated as;

Median of male's data = 14

Median of female's data = 9

The difference (d) between the median values is;

d = 14 - 9

d = 5

Hence, the difference between the median values of each data set is 5

(c) The distribution of data

It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.

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The median is a better measure of center for the male's data, while the mean is a better for the female's data.

What are quartiles?

When we get data which can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each groups approximately possessing 25% of the data.

(a) The IQR of the male's data

From the given male's boxplot, we have the following data elements;

Upper quartile (Q3) = 14

Lower quartile (Q1) = 2

Then the IQR is calculated as:

IQR = Q3 - Q1

So, we have:

IQR = 14 - 2

IQR = 12

Hence, the IQR for the given males' data is 12

(b) The difference between the median values can be calculated as;

Median of male's data = 14

Median of female's data = 9

The difference (d) between the median values is;

d = 14 - 9

d = 5

Hence, the difference between the median values of each data set is 5

(c) The distribution of data

It is found that the median is a better measure of center for the male's data, while the mean is a better measure of center for the female's data.

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The vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).

Herein we find the expression of a quadratic equation in vertex form, whose definition is shown below:

4 · p · (y - k) = (x - h)²      (1)

Where:

h, k - Coordinates of the vertex.

p - Distance from the vertex to the focus.

Then, the vertex form of the quadratic equation is y + 4 = (x + 3)² and the vertex of the parabola is (h, k) = (- 3, - 4).

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Answer:

f(x) = [tex]{\displaystyle {\sqrt[8]{x}}}[/tex]

Step-by-step explanation:

If we let
[tex]g(x) = x^2 - 3\\\\\rm Then \;f(g(x) \;also \;written\; as\; (f\;\circ \rm \;g) \;is\; f(x^2 - 3)\\\\For\; this \;to \;be\; \sqrt[8]{x^2-3} , \\\\\rm f(x) \;has\;to\;be\;\sqrt[8]{x}[/tex]

The equation of the line in slope intercept form is y = (-4/3)x + 7.

According to the slope intercept form, the equation of a line is given as-

y = mx + c

where m is the slope and c is the y intercept.

Here we are given that an equation passes through the point (9,-5) and has a slope of -4/3.

According to the point slope form, the equation of a line passing through (x1, y1) and slope m is given as-

(y - y1) = m(x - x1)

Here,

x1 = 9, y1 = -5 and m = -4/3

Thus,

(y + 5) = -4/3(x - 9)

3(y + 5) = -4(x - 9)

3y + 15 = -4x + 36

3y = -4x + 21

y = (-4/3)x + 21/3

y = (-4/3)x + 7

This is our equation in slope intercept format as m = -4/3 and c = 7

Thus, the equation of the line in slope intercept form is y = (-4/3)x + 7.

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Answer:

Mathematics shaping the modern world.

Answer:

Step-by-step explanation:

more taking a shower you use almost 3 gallons per a shower

The value of the angle 16°43'27"is approximately 16.724167 degrees.

A plane angle is measured in degrees, with the letter ° typically used to indicate that one full rotation is equal to 360 degrees.

To convert a degree from minutes and seconds to decimal we must know the relation between degree and minutes and seconds.

1 degree=60 minutes.

1 minute = 60 seconds.

The given angle is 16°43'27"

27 seconds = 27 ÷ 60 minutes = 0.45 minutes = 0.45 ÷ 60 degree =0.0075 degree

43 minutes= 43 ÷ 60 degree = 0.71666666..

Total angle in decimal = 16+0.71666666+0.0075 =16.7241666...

Therefore required angle ≈ 16.7241667 degrees.

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