relative maxima and relative minima of the function f(x) = x^5 - 4x^3 + 3x^2 - 8x - 6

The sum of even numbers between 105 and 351 is 28,044 .

An additive or arithmetic sequence is a sequence of numbers such that the difference between  consecutive terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15 ... is an exponent plus the common difference of 2.

even numbers between 105 and 351

the series will start like

106 , 108 , 110 , .................................. , 346 , 348 , 350

this is a arithmetic progression

a = 106 d  = 2 l = 350

we need to find n

350 = 106 + ( n - 1 ) 2

350 - 106 = (n -1 ) 2

244/2 = n -1

n = 123

now sum = 123/2 ( 106 + 350)

               = 28,044

so the sum of even numbers between 105 and 351 is 28,044 .

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The exchange rate if each souvenir costs 200 Jamaican dollars, 38 might be purchased.

The exchange rate refers to the value of one country currency about's currency. It is determined by the foreign currency market, often known as the FOREX market.

Amount needed for vacation = $50 USD = $7,740 JMD

Each souvenir is priced at 200 Jamaican dollars.

One US dollar = 154.8 Jamaican dollars when converted to Jamaican currencies.

50 US dollars = 154.8 × 50

= 7,740 Jamaican dollars

Number of souvenirs you can buy = Amount of money with you for vacation ÷ Cost of each souvenir

= 7,740 Jamaican dollars ÷ 200 Jamaican dollars

= 38.7 souvenirs.

As a result, for 200 Jamaican dollars for each souvenir, about 38 souvenirs may be obtained with 50 US dollars.

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The nearest whole number to the number 5.2 is 5.

Given number:

= 5.2

we can determine the whole number of any decimals using the properties that is,

if decimal part < .5 its nearest whole number is 0.

example = 0.5 whole number is 0.

if decimal part  >  0.5 its nearest whole number is 1.

In this case,

= 5.2

decimal part  = 0.2 < 0

so the nearest whole number is 5.

Therefore the nearest whole number to the number 5.2 is 5.

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The range values for the domain of the functions are as follows

x   y

-2  7

0   3

1     1

3    -3

The domain are the input values of the graph the output values are solved using the given functions

The given function 2x-y=3

rearranging gives

y = 3 - 2x

solving for the range values using the domain values: (-2,0,1,3)

= 3 - 2x = 3 - 2 * -2 = 7

= 3 - 2 * 0 = 3

= 3 - 2 * 1 = 1

= 3 - 2 * 3 = -3

The graph is attached

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Second table represents an exponential function of the form y = b when 0

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered. In addition to many other applications, exponential functions are used to estimate populations, carbon date artefacts, assist coroners in determining the time of death, compute investments, and many more. Three of the most popular applications—population expansion, exponential decay, and compound interest—will be covered in this session.

Given,

Second table represents an exponential function of the form y = b when 0

Function: y = bˣ

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Answer:

190 43/100

Step-by-step explanation:

First, you turn the mixed fractions into improper fractions. 382 3/10 is 3823/10, and 191 87/100 is 19187/100. Then, you need to have a common denominator in order to subtract. This turns 3823/10 into 38230/100. 38230/100 - 9187/100 is 19043/100 since you only subtract the numerators. Finally, you turn it back into a mixed fraction by dividing 19043/100. This equals 190 with a remainder of 43. In conclusion, the answer is 190 43/100. I attached the image where I worked it out to show my thought process a bit more as well. I hope this helped! :D

Answer:

16x² - 18x

Step-by-step explanation:

(25x² + 4 - 30x) - (9x² + 4 - 12x) ← distribute this parenthesis by - 1

= 25x² + 4 - 30x - 9x² - 4 + 12x ← collect like terms

= (25x² - 9x²) + (4 - 4) + (- 30x + 12x)

= 16x² + 0 + (- 18x)

= 16x² - 18x

The solution for r in equation 5 + r = 6 - r,   r =1/2

The solution for z in equation  z - 16 = - 16,  z= 0

The solution for n in equation 7n - 7 = 0 ,    n= 1

(8) 5 + r = 6 - r

Step 1: Rearrange the equation by collecting the like terms

r +r=6-5

Step 2: Simplify r +r=6-5

2r = 1

Step 3: Divide both sides by 2

2r/ 2 =1/2

r =1/2

9) z - 16 = - 16

Step 1; Add 16 to both sides

z-16 +16 = -16 +16

z= 0

10) 7n - 7 = 0

To solve for n

Step 1: Add 7 to both sides

7n - 7 +7 = 0+7

7n =7

Step 2: Divide both side by 7

7n/7 =7/7

n= 1

Therefore, the solution for r in equation 5 + r = 6 - r, r =1/2

The solution for z in equation  z - 16 = - 16,    z= 0

The solution for n in equation 7n - 7 = 0,   n= 1

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Answer:

a = 9 ; b = 26 ; c = 24

Step-by-step explanation:

(x^2+3x+2x+6)(x+4)

(x^2+5x+6)(x+4)

x^3+5x^2+6x+4x^2+20x+24

x^3+9x^2+26x+24

The correct statement regarding the proportional relationship c = 0.8w is given as follows:

The equation c = 0.8w is correctly represented by the graph.

A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.

When the two variables x and y are direct proportional, the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k, as follows:

y = kx.

In this problem, the equation is given as follows:

c = 0.8w.

In which:

For a input of 2, the output is given as follows:

c = 0.8 x 2 = 1.6.

Hence point (1,0.8) is in the graph, along with point (2,1.6).

The statements are given as follows:

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The equation of the given graph is y = (x + 4)² -5.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The vertex form of a parabola is y = (x - h)² + k which is opened upward direction and vertex is (h, k).

From the graph, the vertex of the quadratic equation is (-4, -5)

Thus h = -4 and k = -5.

Putting h = -4 and k = -5 in y = (x - h)² + k

y = (x - (-4))² + (-5)

y = (x + 4)² -5

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Considering the vertex of the quadratic function at point (6,-2), it is found that:

a) The meaning is that the turning point of the function is at point (6,-2).

b) If the parabola is concave down, then the vertex is a maximum. If the parabola is concave up, then it is a minimum.

c) If the parabola is concave down, then f(2) = f(10) < f(6). If the parabola is concave up, then f(2) = f(10) > f(6).

d) f(2) = f(10).

A quadratic equation is defined by the rule presented as follows:

y = ax² + bx + c.

The vertex can represent either a maximum point or a minimum point, depending on the coefficient a, as follows:

The vertex is also the turning point of the graph of the parabola.

In this problem, the coordinates of the vertex are (6,-2), hence:

When two points are equidistant from the vertex, they have the same numeric value, hence:

f(2) = f(6).

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Since Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Then  CG is 6 in.

The area of the square whose side is the hypotenuse (the side across from the right angle) in any right triangle equals the sum of the areas of the squares whose sides are the two legs, according to the Pythagorean theorem.

Note that from the question, A triangle's centroid, G, is located 2/3 of the way down one of its medians. We tend must determine the median C's length in order to find CG.

We require the use of Thale's Theorem to get the median length at C. According to this, a right triangle ABC can be encircled by a semicircle with the hypotenuse acting as the diameter.

Therefore, the median C is a point on the semicircle that connects to the diameter of the hypotenuse AB. Since it is connected to the center, median C is a radius. Half of its length, or 18/2, or 9 inches, makes it.

So:

CG is 2/3 down the median, which is:

9 x 2/3 = 6 inches.

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The probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

In the given probability case we have;

What is the likelihood that, out of a random sample of 500 persons, fewer than 60 will work from home if 15% of adults in a particular country do so?

Let,

P = 15% = 0.15

n = 500

By considering the binomial distribution case the formula is given by

P( X = x ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

P( X ≤ 60 ) = ⁿCₓ * Pˣ * (1 - P)ⁿ⁻ˣ

                 = ⁶⁰∑ₓ=₀ (⁵⁰⁰Cₓ) (0.15)ˣ (1 - 0.15)⁵⁰⁰⁻ˣ

                 = 0.031

                 ≅ 0.03

Hence, the probability that fewer than 60 out of a random sample of 500 adults will work from home is 0.03

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The quotient of the fraction is 0.05 and the fraction in its simplest form is 1/20

The quotient of a fraction is the whole number that is obtained when you simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction

Given: 1/5÷4

1/5÷4 = 1/5 × 1/4            (Note: If ÷ change to ×, 4 will change to 1/4 )

        = 1/20 = 0.05

Therefore, the quotient of the fraction is 0.05 and 1/20 should be filled in the box

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The value of 150/4 to the nearest tenth is 37.50

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. . In a proper fraction, the numerator is less than the denominator. In improper fraction, the denominator is smaller to the numerator.

The value of 150/4 = 75/2= 37 1/2

1/2 in decimal is 0.5

Therefore 150/4= 37+ 0.5= 37.5

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The mixture of 13% disinfectant solution needs to be made with 8 gallons of 11% solution and 4 gallons of 17% solution respectively.

Let

x + y = 12

0.11x + 0.17y = 0.13 × 12

x + y = 12

0.11x + 0.17y = 1.56

From (1)

x = 12 - y

Substitute into (2)

0.11x + 0.17y = 1.56

0.11(12 - y) + 0.17y = 1.56

1.32 - 0.11y + 0.17y = 1.56

- 0.11y + 0.17y = 1.56 - 1.32

0.06y = 0.24

divide both sides by 0.06

y = 0.24/0.06

y = 4

x + y = 12

x + 4 = 12

x = 12 - 4

x = 8

So therefore, the gallons of 11% solution and

gallons of 17% solution needed are 8 and 4 gallons respectively.

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(4i+1)² can be simplified to 8i-15

A complex number is a number of the form a + bi, where a and b are real numbers

Given expression is (4i+1)²

four times of i plus one whole square.

(4i+1)² can be expanded by using algebraic identity

(a+b)²=a²+b²+2ab

(4i+1)²

Now put a as 4i and b as 1

(4i+1)²=16i²+1+2(4i)(1)

Where i²=-1

=-16+1+8i

=8i-15

Hence (4i+1)² can be simplified to 8i-15

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Answer:

Step-by-step explanation:

You have a square with sides labeled (y-4), (3x-8), (2y-12), and you want to know the values of the variables as well as the side length.

All sides of the square are the same length. Equating two different y-expressions, we get ...

  y -4 = 2y -12

We can use the solution to that to find x:

  y -4 = 3x -8

Adding 12-y to the first of these equations gives us ...

  8 = y

Using this value in the second equation, we have ...

  8 -4 = 3x -8

  12 = 3x . . . . . . add 8

  4 = x . . . . . . . . divide by 3

The side length is ...

  y -4 = 8 -4 = 4

The values of the variables are x = 4, y = 8, and the side length of the square is 4.

Answer:

0.02 or 2%

Step-by-step explanation:

$700(x)=$714

$700(0.02)=14

700+14=714

the cost of full coverage insurance in female in her 50s as a percentage of the same insurance in a male in his 30s if female cost $819. 73 and male cost $1192. 64  was $ 68.73

We have the insurance coverage amount for men of 30 years and for women of 50 years. Therefore, to find the percentage that represents the cost of coverage of the 50-year-old woman based on the cost of coverage of the man, we need to perform the following operation:

Xw= Cw/Cm * 100%

Where:

Cw: cost of coverage for a woman of 50 years.

Cm: coverage cost for a 30-year-old man.

Xw= 819.73/1192.64 *100%

    = 68.73

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We will see that the linear equations are:

Parallel line: x = -9

Perpendicular line: y = 3

Here we have the vertical line:

x = -2

A parallel line to this one will also be vertical, of the form:

x = a

And a perpendicular line to this one will be horizontal, of the form:

y = b

We want the parallel line to pass through (-9, 3)

So our line x = a needs to pass through that point, then:

x = -9

Is the parallel line.

And if the perpendicular line y = b needs to pass through that point, then:

y = 3

Is the perpendicular line.

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The dimensions (in m) of the cardboard box with the largest volume is obtained as 2 m length.

Dimensions of piece of cardboard;

Let the corner cut length be 'x',

New dimensions;

Volume = length x width x height

Put the values;

V = ( 8 - 2x ) (4 - 2x) x

Find the solution of the obtained quadratic equation by quadratic formula.

x = 0, 2 and 4.

As, x ≠ 0 and 4.

Thus, x = 2.

Thus, the dimensions (in m) of the box with the largest volume is obtained as 2 m length.

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Answer:

[tex](x+5)^{2}+(y-7)^{2} =16[/tex]

Step-by-step explanation:

The Standard Form of Circle Equation whose Center is at ( h , k) and Radius of r is given by

[tex](x-h)^{2}+(y-k)^{2} =r^{2}[/tex]

So for our Question

we have ( h , k ) = ( -5 , 7 )  and r = 4

By substitution

[tex](x-(-5))^{2}+(y-7)^{2} =4^{2}[/tex]

Simplify [tex](x+5)^{2}+(y-7)^{2} =16[/tex]

Answer: 721 ft

Step-by-step explanation:

formula for area is a=l*w

Given: w=103, length=7

103*7=721

Answer: The answer 721. When you are finding an area of something you must multiply the length and the width so the information given.

103 x 7 = 721 feet long

Here is the real problem:

It's sloppy as long as you understand the concept : )

The artifact was created 11,460 years ago.

Given

that,25% of the carbon-14 found in living trees can be found in a wooden artifact from an ancient tomb and the half-life of carbon-14 is 5730 years Half Time  [tex]t_{1/2}[/tex] = 5730 yearsln 2 / k = 5730k =  5730 / ln 2Let Po = 100P(t) =25 after t yearsP(t) = Po e^ -kt25 = 100 e ^ -(5730t / ln 2)5730t / ln 2 = ln 4

By applying

we get,t = 5730 * log⁴₂t = 11460 years Hence, the artifact was made 11,460 years ago.

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Answer/Step-by-step explanation:

[tex]-\frac{8}{27} a^{15} = (-\frac{2}{3})^{3} * (a^3)^5 = (-\frac{2}{3} a^{5})^3[/tex]

I hope this helps!

Answer: $342.40

Step-by-step explanation:

There are two ways you can solve this problem:

Simply turning the percentage to a decimal and multiplying it to the $320.

In the picture provided the method at the top represents you multiplying $320 x .07, You might be wondering “why .07 instead of 7%?” Well, if you were turning this number from a percent to a decimal you would shift the decimal point over to the left 2 times.

And so multiplying $320 x .07 = 22.4 or 22.40. Either way works but without the zero is the way you should write it. And you would add 22.4 to $320 and get $342.40.

Also in the picture provided I used the method of proportions.

Where the total is $320 in this case which you would put next to 100% as 100% means complete or the total. And you would put 7% above 100%. Then, proceed to cross multiply $320 by 7 and it will give you, 2240. Then, you divide it by 100. When you divide it you get 22.40. Then you would add it to $320 and get 342.40.