a gymnast practices 6 days each week.She practices the same number of ours each day.If she practices 120 hours in a 4 week period how many hours each day does she practice?

The required derivative of the given function g(z) = ln√(16- z² / 16+z²) is

[tex]g'(z) =-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]

The outside-inside rule, the composite function rule, and the function of a function rule are all synonyms for this chain rule in differentiation. It is exclusively used to calculate the derivatives of composite functions.

The chain rule formula as shown below

d/dx ( f(g(x) ) = f' (g(x)) · g' (x)

The function is given in the question

g(z) = ln√(16- z² / 16+z²)

We have to differentiate g(z) = ln√(16- z² / 16+z²)

Differentiation with respect to z in the given function,

[tex]\frac{d}{dz}\left(\ln \left(\sqrt{\left(\left(\frac{16-z^2}{16+z^2}\right)\right)}\right)\right)[/tex]

We have to apply the chain rule of differentiation for finding derivatives,

[tex]\dfrac{1}{\sqrt{\dfrac{16-z^2}{16+z^2}}}\dfrac{d}{dz}\left(\sqrt{\dfrac{16-z^2}{16+z^2}}\right)[/tex]

[tex]-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]

Therefore, the required derivative of the given function g(z) = ln√(16- z² / 16+z²) is

[tex]g'(z) =-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}[/tex]

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Using the multiplication, 192 unique keys will result from the distribution.

In the given question we have to find the number of unique keys will result from the distribution.

As given that a package contains 12 electrical locks, each with a unique key.  A package is delivered to 16 job site superintendents.

So 1 package have 12 electrical locks with a unique key.

Package delivered to 16 job site.

We can find the total number of unique keys y multiplying the total number of electrical locks with a unique key in a pckage to the total number of site of package delivery.

So total keys=12×16

Total keys=192

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After 5 years, Offer A will offer a higher total salary.

The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

Given

a)  that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:

b) Offer A -> Arithmetic

=>55000 x 1.05 ^ 5 = X

=>55000 x 1.2762 = X

70,195.48 = X

Offer B -> Geometric

=>56000 + (5 x 2000) = X

=>56000 + 10000 = X

66,000 = X

c) Hence comparing the above 2, Offer A will provide a greater total income after 5 years.

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5x - 3x = 2x

2x = 40

x = 20

x * 8 = 160

Answer:

  y = -3x +7

Step-by-step explanation:

You want the equation of the median line through point A, given that the vertices of the triangle are A(2, 1), B(-2, 3) and C(4, 5).

The median will go through the midpoint of the segment opposite vertex A. That midpoint is ...

  D = (B +C)/2

  D = ((-2, 3) +(4, 5))/2 = (-2+4, 3+5)/2 = (2, 8)/2 = (1, 4)

The slope of the line is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

Then the slope of AD is ...

  m = (4 -1)/(1 -2) = 3/-1 = -3

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

The equation of the line with slope -3 through point A(2, 1) is ...

  y -1 = -3(x -2) . . . . . equation of the median line

This can be simplified to slope-intercept form:

  y = -3x +6 +1 . . . . . eliminate parentheses, add 1

  y = -3x +7 . . . . . slope-intercept equation of the median line

These lines y = 12x + 1 and y = 2x + 4 intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given are two equations y = 12x + 1 and y = 2x + 4.

Now by graphing we conclude that these lines intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.

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Answer:

25.12

Step-by-step explanation:

C = [tex]\pi[/tex]d  The d is the diameter.  This is the distance across the ha that goes through  the middle of the circle.

C 3.14(8)  The c stands for the circumference or the distance around the circle.  We generally use 3.14 for [tex]\pi[/tex]

C= 25.12

Answer:

1170 teenagers would have corrective devices

Step-by-step explanation:

hope this helps :)

The slope equation form is :

m = - 7/5

Slope Solution

To calculate the slope use the slope formula.

m = (y2- y1)/(x2- x1)

Where (x1,y1) and (x2,y2) are 2 coordinate points.

Here the 2 points are (0,-3) and (-5,4)

let (x1,y1) = (0,-3) and (x2,y2) = (-5,4)

m = (4 - (-3))/((-5) - 0)

m = 7/((-5) )

m = - 7/5

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In given order puzzle Aya's bag is the heaviest bag .

What is order puzzle?

 A puzzle is a thing that is difficult to understand or explain. The term also refers to a game, toy, or problem designed to test ingenuity or knowledge. Math puzzles are problems that require mathematical logic and calculation. These types of puzzles carry recreational as well as educational value for the pupils.

Here the given statements ,

=> Alex bag > Hisham bag

And Hisham bag < Aya bag and Irene bag

Now ,

=> Aya bag > Alex bag and Irene bag

Then combine the given ,

=> Aya bag> Alex bag>Irene bag>Hisham bag.

Therefore Aya's bag is the heaviest bag.

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Answer:

(x,y)=(0,4)

Step-by-step explanation:

write as systems as equations, multiply both sides of the equation by -1, sum the equations vertically to eliminate at least one variable, divide both sides of the equation by -19, substitute the given value of x into the equation 5x+y=4, The possible solution of the system is the ordered pairs (x,y) =(0,4), then you're done. whew. ;)

Answer:

y = 2(x + 4)(x - 3)

Step-by-step explanation:

Knowing the x-intercepts, we can set up the equation:

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

However, we are unaware of whether there is a dilation applied to it, so we input a point on the parabola. "a = dilation"

-12 = a(2 + 4)(2 - 3)

-12 = a(6)(-1)

-12 = -6a

2 = a

Now, we can write the equation for the parabola:

y = 2(x + 4)(x - 3)

Answer: 8÷2 or 8/2 and also just in case, the answer is 4

Step-by-step explanation: Ok, 8 markers split equally between 2 students, this means that for each marker that student one takes, student two also takes one. they repeat this until there are no more markers left. This ends up with the two students each having four markers. Now, what is 8 divided by 2? Why yes, the answer is 4, just like the word problems answer. So the word problem "Two students share 8 markers equally" translates to 8÷2.

Hope this helps!

Answer:

1 intersection point at (11,96)

Step-by-step explanation:

Comment

The best way to solve this is to start with a graph. Then you can work out the actual intersection points.

The graph shows that there is only 1 intersect point. Let's try and find it.

Givens

y = (x - 5)(x + 5) = x^2 - 25

y = (x +1)(x - 3) = x^2 -2x - 3

If the intersect points are what you want, then the y value for both equations must be equal.

Solution

x^2 - 25 = x^2 - 2x - 3                     Subtract x^2 from both sides

x^2 - x^2 - 25 = x^2 - 2x - 3            Combine

- 25 = - 2x - 3                                   Add 3 to both sides

-25+3 = -2x - 3 + 3                           Combine

-22 = - 2x                                         Divide by - 2

 -22/-2 = x

x = 11

y = x^2 - 25

y = 11^2 - 25

y = 121 - 25

y  = 96

Answer:

you multiply the numbers to find the area so W*H with times hight so the answer would be 6,250

Answer:

Estimation and Confidence Intervals

Step-by-step explanation:

Just found it on a math website basically.

The five consecutive odd integers are 11, 13, 15, 17 and 19.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Odd numbers are whole numbers that cannot be divided exactly into pairs.

Therefore, odd integers are integers that cannot be divided exactly into pairs.

Hence, let's find five consecutive odd integers if the sum of the first three integer is 3 more than the sum of the last 2.

let

the first odd integer = x

x + x + 2 + x + 4 = x + 6 + x + 8 + 3

3x + 6 = 2x + 17

3x - 2x = 17 - 6

x = 11

Therefore, the consecutive odd integers are 11, 13, 15, 17 and 19.

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The cost of covering the felt with glitter is $3,317.60.

The cost of the outdoor carpeting to cover the patio is $240.

The first step is to determine the area of the parallelogram. A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length

Area = base x height

52 x 58 = 3,016 in²

Cost of covering the felt = cost of the glitter per feet  are of the felt

$1.10 x 3,016 = $3,317.60

A trapezoid is a shape that has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Area of a trapezoid =   1/2 x (sum of the lengths of the parallel sides) x height

Area of a trapezoid =   1/2 x (19 + 13) x 10

Area of a trapezoid =  1/2 x 32 x 10 = 160 ft²

Cost of the outdoor carpeting =cost per square feet x area of the patio

$1.50 x 160 = $240

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The correct statement will be  "Neither ordered pair is a solution".

What are ordered pairs?

Given equation is:  6x = 14

For ordered pair (-9, 3) ,  the values of x=-9 and y=3

Plugging these values into the given equation

6(-9) = 14

-54 = 14 (False)

Now for ordered pair (2, -4) ,  the values of x=2 and y=-4

Plugging these values into the given equation

6(2) = 14

12 = 14 (False)

The correct statement will be  "Neither ordered pair is a solution".

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Answer:

Step-by-step explanation:

Solving word problems is always hard.  even w/o any learning challenges.  I'm kind of good at word problems but what I notice is that people have ways to ask word problem questions that can be very much about their own thought process, not really about the math.  Often it matters who is asking the word problem more than what the question is about for understanding the problem.   I don't think Josie will stand a chance with some peoples questions, like she'll solve it .01% of the time.  Not 85% of the time.  Just my perspective. :)

Answer:

5.92

Step-by-step explanation:

Line in standard form

-6x + y - 7 = 0

distance = |-6 * 6 + 1 * 7 - 7|/([tex]\sqrt{(-6^2)+ 1^2)}[/tex]

|-36 +7 - 7| = √37

|-36|/√37

36/√37

5.918363 = 5.92

Answer:

Step-by-step explanation:

Hi,  Danna,  these are tough to figure out...

so,  first check to see if the 3 known angles add up to 180°,  they don't I checked, so, it tells us that the one angle 96° up at the top,  does not include ∠2 , which is good, b/c we now know 2 of the angles in that inner triangle.. and we know that a triangle adds up to 180° , so just find that last angle... the one opposite to ∠1 .... nice, if we get the ∠1' angle we can then also figure out ∠1

180-96-30=54

∠1' =54°

so ∠1= 180-54 =126°

we now know ∠1

use that , and that the next smaller triangle also adds up to 180

to find ∠2

∠2= 180-28-126=26°

∠1=126°

∠2 = 26°

:)  it's tough to think all of that through.  don't worry.  just keep working these , they will get easier.

If a 40-foot rope is cut into 2 pieces.  the length of the longer rope piece x  is 23ft.

Seven less than 4 times = 4x-7

4x-7=5(40-x)

4x-7=200-5x

Collect like terms

9x=207

Divide both side by 9x

x = 207 /9

x=23 ft  (longer part of the rope)

Shorter part of the rope

40-x where x is 23

40 -23

= 17ft

Therefore the longer part is 23ft.

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Answer:

It looks just fine! Well done!

It looks just fine! Well done!A bit more simply,

It looks just fine! Well done!A bit more simply,(A+C)(AD+AD)+AC+C=(A+C)AD+AC+C=AAD+CAD+AC+C=AD+(AD+A+1)C=AD+C

Step-by-step explanation:

Hope this helped

The probability of getting a total that is a factor of 21 is 2/9

Tom rolls 2 fair dice and adds the results from each

Total number of outcomes = 6 × 6

= 36

The probability = Number  of favorable outcomes / Total number of outcomes

The factors of 21 = 1, 3, 7, 21

The possible outcomes = {(1,2), (2,1), (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

Number of possible outcomes = 8

The probability = Number  of favorable outcomes / Total number of outcomes

Substitute the values in the equation

= 8 / 36

= 2/9

Hence, the probability of getting a total that is a factor of 21 is 2/9

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The expressions which have only one constant are:

A. 18+5r³

B. 90(h-4)

Given: we have a set of equations.

an equation is  a combination of variables and constants.

In the given set of equations we have a single variable with a single constant.

those are:

→ 18+5r³

→  90(h-4)

In the other equations we don't have constants.

A constant is defined as an object whose value is fixed regardless of changes in its usage.

Even after the expression is changed, these values stay the same.

Natural numbers, whole numbers, real numbers, integers, and decimal numbers are examples of constants in mathematics.

A variable is a thing whose value changes depending on how it's used and isn't fixed.

Hence we get the required answer.

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Answer:

t = 1/9

Step-by-step explanation:

Combine multiplied terms into a single fraction

-3/2 (t) + 1/3 = 2/4

3t/2+ 1/3 = 2/4

Find common denominator

3 x 3t/6 + 2/6 = 2/4

Combine fractions with common denominator

3 x 3t/6 + 2/6 = 2/4

3x3t + 2

/ 6= 2/4

Multiply the numbers

9t+2

/6 = 2/4

Divide the numbers

9t+2 divided by 6 is 1/2

Multiply all terms by the same value to eliminate fraction denominators

6 x 9t+2 divided by 6 = 6 x 1/2

Cancel multiplied terms that are in the denominator

9t+2=3

Subtract 2 from both sides

9t+2-2=3-2

Simplify

9t=1

Divide both sides by the same factor

9t/9+=1/9

Simplify

t= 1/9

The error that Bianka made in the algebraic expression is that; when 15 was distributed it should be '45 - 15y' rather than '45 + 15y'

An algebraic expression is defined as an expression that is made up of variables and constants, as well as algebraic operations such as multiplication, addition, division, subtraction, etc.

Now, the steps that Bianka took to solve the algebraic expression are;

12 + 15(3 - y) - 10y

12 + 45 + 15y - 10y

57 + 5y

Now, the first step according to the rule PEMDAS is to expand the bracket and when positive and negative are multiplied, the sign is negative and as such step 2 should have been 12 + 45 - 15y - 10y.

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The equation to represent the total number of students taking the yoga classes is s = 13c.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the number of students = s

Let the number of classes = c

Therefore the total students will be:

s = 13 × c

s = 13c

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