5 candy bars with 12 sections split between 3 friends equally

Answers

Answer 1

Answer:

20 sections per friend

Step-by-step explanation:

First find the total number of sections

5 * 12 = 60 sections

Divide by 3 friends

60/3 = 20

20 sections per friend


Related Questions

Suppose you want to have $300,000 for retirement in 25 years. Your account earns 5% interest.
A. How much would you need to deposit in the account each month?
B. How much interest will you earn?

Answers

A) The monthly deposit is $503.77

B) Interest per month ≈0.42

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

Let A be the amount in future.

Monthly deposit= [tex]P= \frac{A \times \frac{r}{n}} {(1 +\frac{r}{n})^{t*n} - 1}[/tex]

n= 12, 12 months in a year

So, monthly deposit= [tex]P= \frac{300000 \times \frac{0.05}{12}} {(1 +\frac{0.05}{12})^{25*12} - 1}[/tex]

                                 = 1250/2.4813

                                 = $503.77

So, monthly deposit= $503.77

To find interest:

Interest per year = 5%

Interest per month = 5/12 = 0.416 ≈0.42

To learn more about compound interest from the link

https://brainly.com/question/24274034

#SPJ1

Answer: $503.77

Interest earned: $148,869

Step-by-step explanation:

Let A be the future amount.

Monthly Deposit= P=A*r/n÷ (1+r/n)^t*n-1

n=12 months in a year

P= (300,000*0.05/12)÷ [(1+0.05/12)^25*12]-1

P=1250/2.4813

P=$ 503.77

Interest earned.

$300,000-(503.77*12*25)

$300,000-151,131= $148,869

A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $80 million after 4 years, as shown in the graph:

There is a graph of a line with Years on the x axis and Profits in millions on the y axis that passes through 1, negative 100 and 4, 80.

Which equation most closely represents the line depicted in the graph?

a. f(x) = 60x − 160
b. f(x) = −60x + 160
c. f(x) = −80x + 4
d. f(x) = 80x − 4

Answers

The equation most closely represents the line depicted in the graph is

f(x) = 60x − 160

What is linear equation?

An equation between two variables that gives a straight line when plotted on a graph.

Given a point (4,80) and a slope, m = 60, these can be used to formulate the equation of the graph. Using the point-slope formula:

y - y1 = m(x - x1)

y - 80 = 60(x - 4)

y - 80 = 60x - 240

y = 60x -160

Taking the x and y-intercepts:

At y = 0

0 = 60x - 160

x = 2.7

At x = 0

y = 60(0) - 160

y = -160

Hence, you could state that there is a graph of a line that has a y intercept that is approximately negative $160 million and an x intercept that is approximately 2.7 years.

For more references on linear equation, click;

https://brainly.com/question/11897796

#SPJ1

North Dakota has 465 campgrounds over 12 counties while West Virginia has 711 campgrounds. If North Dakota was proportional to West Virginia in the number of campgrounds to counties, how many counties would West Virginia be expected to have? Round to the nearest whole number.

Answers

Number of countries would west Virginia be expected to have is  18 countries

The number of campgrounds that North Dakota has = 465 campgrounds

The number of countries = 12 countries

The number of campgrounds that West Virginia has = 711 campgrounds

Given that the North Dakota was proportional to West Virginia in the number of campgrounds to counties.

The proportion will be

465 / 12 = 711 / x

Divide the terms

38.75 = 711 / x

x = 711 / 38.75

Divide the terms

x = 18.4

x ≈ 18 countries

Hence, number of countries would west Virginia be expected to have is  18 countries

Learn more about proportional here

brainly.com/question/7096655

#SPJ1

A total of 96 pints of blood were collected at the blood drive. How many quarts were collected?

Answers

Answer: 48 qt

Step-by-step explanation:

The conversion factor between pints and quarts is two which means there are 2 pints in every quart. divide the number of pints by two to find the number of quarts.

96/2 = 48

EX: 24 pints = 12 quarts

24/2 =12

EX 8 quarts = 16 pints

The same rule works in reverse but instead of dividing you multiply.

8x2 = 16

Given: a ║ b and m<6 is 1/8 of m<4, find m<4 and m<6

Answers

Answer:

∠ 4 = 160° , ∠ 6 = 20°

Step-by-step explanation:

∠ 4 and ∠ 6 are same side interior angles and sum to 180°

given ∠ 6 = [tex]\frac{1}{8}[/tex] ∠ 4 ( multiply both sides by 8 to clear the fraction )

8 ∠ 6 = ∠ 4

then

∠ 4 + ∠ 6 = 180° , that is

8 ∠ 6 + ∠ 6 = 180°

9 ∠ 6 = 180° ( divide both sides by 9 )

∠ 6 = 20°

∠ 4 = 8 × ∠ 6 = 8 × 20° = 160°

8y-2x=-40 put the following equation in slope intercept form simplyifing all fractions

Answers

Answer:

[tex]y = \frac{1}{4} x\\[/tex] [tex]- 5[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Identify the range of y = x² - 2x - 3 if the domain is all real numbers.

Answers

The range of this quadratic function y = x² - 2x - 3 is all real numbers greater than 2.

What is the domain and range of a function?

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

We know a quadratic function y = ax² + bx + c is a graph of a parabola that opens upwards as the coefficient of x² is positive.

Given,  y = x² - 2x - 3.

y = x² - 3x + x - 3.

y = x(x - 3) + 1(x - 3).

y = (x - 3)(x + 1).

Now the x-intercepts are at 3 and -1 so the vertex is located at (3 - 1)/2 = 2.

So the range of this function is all real numbers greater than 2 as the parabola opens upwards.

learn more about the domain and range here :

https://brainly.com/question/28135761

#SPJ1

Jack had received a collection of 30 baseball cards and decided he was going to start collecting. If Jack adds 2 stamps every month, how long will it take to have 50 stamps in his collection?

2. Bella opens a savings account with $100 and the bank pays 1% monthly interest rate. How much money will Bella have after 12 months, if she does not deposit or draw an amount?



If someone answers this question they have to determine which equation is linear and which is nonlinear. Then, write a function that models the linear situation and then write 1 ordered pair that is the solution to the situation.

Answers

1) The amount of time that it will take to have 50 stamps is; 10 months

2) The amount of money that bella will have after 12 months is; $112

How to solve linear equation word problems?

1) We are told that Jack received a collection of 30 baseball cards. Now, he decided to start collecting after that and he adds 2 stamps every month. Thus, let m represent the number of months he collects and so we have the equation as;

2m + 30

Now, we want to find out how long it will take to get 50 stamps. Thus;

2m + 30 = 50

2m = 20

m = 10 months

2) Principal = $100

Interest rate = 1% monthly

Thus;

Interest after 12 months = 100(0.01 * 12) = $12

Thus, amount she now has after 12 months = $100 + $12 = $112

Read more about Linear Equation Word Problems at; https://brainly.com/question/20335698

#SPJ1

When the function f (x) is divided by x +8, the quotient is 3x2 -3x +1 and the remainder is -3. Find the function f(x) and write the result in standard form

Answers

The function f(x) in standard form as described in the task content is; 3x³ + 21x² - 23x + 5.

What is the function f(x) which is as described in the task content?

It follows from the task content that the function, f(x) which is as described is to be determined.

Since the polynomial remainder theorem postulates that;

Polynomial = (quotient × divisor) + remainder.

According to the given task content;

The quotient is; 3x² - 3x + 1.

The divisor is; (x + 8) and the remainder is; -3.

Therefore, the required polynomial is;

f(x) = (3x² - 3x + 1)(x + 8) + (-3)

= 3x³ + 24x² -3x² -24x + x + 8 - 3

= 3x³ + 21x² - 23x + 5.

Therefore, the required function, f(x) is; 3x³ + 21x² - 23x + 5.

Read more on remainder theorem;

https://brainly.com/question/27749132

#SPJ1

Which of the following sentences is true?
O 6.473 is less than 6.453.
O24.358 is less than 24.357.
O 19.861 is greater than 19.851.
O 19.322 is greater than 19.522.​

Answers

Answer:

3

Step-by-step explanation:

19.861>19.851

look at hundreds column

An open box is made from a 40 -cm by 50-cm piece of tin by cutting a square from each corner and folding the edges. The area of the resulting base is 1496cm squared. What is the length of the sides of the squares?

Answers

The length of the sides of the squares is 3 cm.

What is a rectangle?

A rectangle is a quadrilateral with all four interior angles 90°.

Given that, the dimension of the rectangular tin piece is 40 cm by 50 cm.

Let the length of the sides of the square is x.

Then, the dimensions of the resulting rectangular base are (40 - 2x) by

(50 -2x).

Given that, the area of the resulting base is 1496 square cm.

Therefore, it follows:

(40 - 2x)(50 -2x) = 1496

2000 - 80x -100x + 4x² = 1496

4x² - 180x + 2000 -1496 = 0

4x² - 180x + 504 = 0

x² - 45x + 126 = 0

x² - 42x - 3x + 126 = 0

x(x- 42) - 3(x - 42) = 0

(x - 3)(x - 42) = 0

x-3 =0 or x - 42 = 0

x = 3 or x = 42

Note that the dimension of the rectangular tin piece is 40 cm by 50 cm, therefore, x = 42 cm cannot be the length of the square.

Hence, the length of the sides of the squares is 3 cm.

Learn more on rectangles here:

https://brainly.com/question/15019502

#SPJ1

Select ALL expressions that are close to a quotient of 1.

(A) 1900 / 21

(B) 210,000 / 190,000

(C) 19 / 210

(D) 2.1 / 1.9

(E) 190 / 210

(F) 190 / 21

Answers

Answer:

Step-by-step explanation:

C E F or just E and F

Mrs. Smit has a yearly budget of 2.300 for the math club. she spends 36% of the budget for transportation. snacks . and rewards. 70% of the 36% was used for transportation. more money was spent on snacks iban rewards​
complete the table so show possible amounts of money. in dollars Mrs . Smith could have spent this year in each category

Answers

1,858.40

2300-36%=1472

1472-70%=441.60

2300-441.6=1,858.40

Consider the following scenario: P(E) = 0.4, P(F) = 0.5

a. Find P(E or F) if E and F are disjoint

b. Find P(E or F) if E and F are independent

Answers

The probabilities are given as follows:

a. P(E or F) if E and F are disjoint: 0.9 = 90%.

b. P(E or F) if E and F are independent: 0.7 = 70%.

What is a Venn probability?

In a Venn probability, two events are related with each other, as are their probabilities.

The "or probability" is given by:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

Disjoint events are events that cannot happen at the same time, hence P(E and F) = 0, and then the probability is:

P(E or F) = P(E) + P(F) = 0.4 + 0.5 = 0.9 = 90%.

When E and F are independent, we have that:

P(E and F) = P(E)P(F) = 0.4 x 0.5 = 0.2.

Hence the probability in item b is given by:

P(E or F) = P(E) + P(F) - P(E and F) = 0.4 + 0.5 - 0.2 = 0.7 = 70%.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

differentiate [tex] \sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } } [/tex]with respect to x ​

Answers

Step-by-step explanation:

Let [tex]{ \green{ \tt{y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4)}{3 {x}^{2} + 4x + 5}}}}} [/tex]

Take log on both sides

[tex]{ \purple{ \sf{ log_{e}y = log_{e} [\frac{(x - 3)( {x}^{2} + 4}{3 {x}^{2} + 4x + 5}]^{ \frac{1}{2}}}} } { \to}{ \tt{ {eq}^{n} (1)}}[/tex]

This above expression is in the form of

[tex]{ \boxed{ \red {\sf{ {x}^{n} = nx}}}}[/tex]

[tex]{ \boxed{ \red{ \sf{ log( \frac{m}{n} ) = log \: m \: - log \: n}}}}[/tex]

Let's apply these two formulas to eqⁿ (1) then,

[tex]{ \purple{ \sf{ log_{e}y = \frac{1}{2}[log(x - 3) + log( {x}^{2} + 4) - log( {3x}^{2} + 4x + 5) ]}}}[/tex]

differentiate with respect to x.

[tex]{ \blue{ \sf{ \frac{1}{y} \frac{dy}{dx} = \frac{1}{2}[ \frac{1}{x - 3} (1 - 0) + \frac{1}{ {x}^{2} + 4 } (2x - 0) - \frac{1}{3 {x}^{2} - 4x + 5} (6x + 4 + 0)]}}}[/tex]

[tex]{ \blue{ \sf{ \frac{dy}{dx} = y[ \frac{1}{2(x - 3)} + \frac{x}{ {x}^{2} + 4} - \frac{3x + 2}{ {3x}^{2} + 4x + 5 } ]}}}[/tex]

where [tex]{ \boxed{ \purple{ \sf{y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{3 {x}^{2} + 4x + 5}}}}} } [/tex]

Answer:

[tex]let \: \: y = \sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } } \\ \\ y =( {{\frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } }})^{ \frac{1}{2} } \\ \\ taking \: \: logarathim \ \: both \: \: sides \: \: \\ \: we \: \:get ⇒ \: ln(y) = {\frac{1}{2} ln(\frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } }) \\ \\ ⇒2 ln(y) = ln(x - 3) + ln( {x}^{2} + 4) - ln(3 {x}^{2} ) + ln(4x) + ln(5) \\ differeciate \: \: both \: \: the \: \: sides \: \: we \: \: get \: \: \\ ⇒ 2 \times \frac{1}{y} (\frac{dy}{dx} ) = \frac{1}{x - 3} + \frac{1}{ {x}^{2} + 4} .2x - \frac{1}{3 {x}^{2} } .6x + \frac{1}{4x} .4 + 0 \\ \\ ⇒ \frac{2}{y} \times \frac{dy}{dx} = \frac{1}{x - 3} + \frac{2x}{ {x}^{2} + 4} - \frac{2}{x} + \frac{1}{x} \\ \\ ⇒ \frac{dy}{dx} = \frac{y}{2} . (\frac{1}{x - 3} + \frac{2x}{ {x }^{2} + 4} - \frac{1}{x} ) \\ \\ put \: \: the \: \: value \: \: of \: \: y \: \: we \: \: get \: \\ ⇒ \frac{dy}{dx} = \frac{\sqrt{ \frac{(x - 3)( {x}^{2} + 4) }{ {3x}^{2} + 4x + 5 } } \\ }{2} \times (\frac{1}{x - 3} + \frac{2x}{ {x }^{2} + 4} - \frac{1}{x} )[/tex]

Step-by-step explanation:

used formula

[tex] { ln(m) }^{n} = n \: ln \: m \\ \\ ln(mn) = ln(m) + ln(n) \\ \\ ln( \frac{m}{n} ) = ln(m) - ln(n) \\ \\ \frac{d}{dx} ( ln(x) ) = \frac{1}{x} [/tex]

A 16,000-gallon pool is being filled at a rate of 50 gallons per minute. At this rate, how many minutes will it take to fill this pool 3\4 full

Answers

To fill the pool 3/4 full it will take 240 minutes

What is rate?

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in mathematical problems.

3/4 of the volume the pool is 3/4×16000= 12000gallons

it takes 1 minutes to fill 50gallons

therefore to fill 12000 gallons it will take 12000×1/50 =240minutes

therefore the number of minutes it will take to fill 3/4 of the pool is 240minutes

learn more about rate from

https://brainly.com/question/25793394

#SPJ1

Kendra earns $11.60 per hour working at the movie theater. Each week, she donates
1
10
of her earnings to Best Friends Animal Society, her favorite charity. If Kendra worked 8
1
2
hours

Answers

Answer:

Kendra will donate $9.86 to her Best Friend's Animal Society.

Step-by-step explanation:

In order to find this answer, we need to multiply $11.60 by the 8.5 hours:

11.60 x 8.5 = $98.60

Now, if she donates 1/10 every week, we can turn 1/10 into 0.10. And on a calculator set up this equation:

0.10 x 98.60 = $9.86

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Triangle CDE is similar to triangle FGH. Find the measure of side HF. Round your
answer to the nearest tenth if necessary.
E
23
D
19
H
G
59

Answers

Answer:

HF ≈ 71.4

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{HF}{EC}[/tex] = [tex]\frac{FG}{CD}[/tex] ( substitute values )

[tex]\frac{HF}{23}[/tex] = [tex]\frac{59}{19}[/tex] ( cross- multiply )

19 HF = 1357 ( divide both sides by 19 )

HF ≈ 71.4 ( to the nearest tenth )

Let sets A and B be defined as follows:
A= {j, k, l, m, q, r}
B is the set of integers greater than -2 and less than 2

(a) Find the cardinalities of A and B.
n(A) =
n(B)=

(b) Select true or false.
(I've attached a picture below to help other)

Answers

Step-by-step explanation:

(a)

it just means how many members are in a set.

there is no mystery or strange mathematical approach. we simply need to count them.

when there is an interval given, sure, we can calculate the length. but for a short interval counting is still faster.

n(A) = 6

n(B) = 3 {-1, 0, 1}

the calculation would be 2 - -2 - 1 = 4 - 1 = 3.

the "-1" comes from the fact that the end of the interval is not included.

(b)

z is not in A. as we can see : true

l is in A. as we can see again : yes. true.

-1 is in B. as I listed above : yes, true.

7 is in B. no, definitely not. false.

C and D are sets of real numbers defined as follows. Write using interval notation.

Answers

The given sets written in interval notation are

C = (4, ∞), and  = (-∞, 9]

Writing sets in interval notation

From the question, we are to write the given sets using the interval notation

The given sets are

C = {v | v > 4}

D = {v | v ≤ 9}

For set C,

C = {v | v > 4}

The elements of the sets are 5, 6, 7, 8, 9, ...

This can be written in interval notation as (4, ∞)

For set D,

D = {v | v ≤ 9}

The elements of the sets are 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, ...

This can be written in interval notation as (-∞, 9]

Hence, the interval notation form of the sets are

C = (4, ∞)

and

D = (-∞, 9]

Learn more on Writing sets in interval notation here: https://brainly.com/question/28353123

#SPJ1

Find the equation of the tangent line to the graph of the function f(x)=(x^2+6)(x−4) at the point (1,−21) .

im stumped and this is due soon, please help

Answers

The equation of the tangent line of the function is y = x + 20

How to find the equation of the tangent line

f(x)=(x^2+6)(x−4)

expanding the function gives

f(x)=x^3 - 4x^2 + 6x - 24

At a specific point the slope, m is the derivative

finding the derivative of f(x)

f'(x) = 3x^2 - 8x + 6

The derivative at the point (1, -21) is found by substituting the point to the equation

f'(1) = 3 * 1 - 8 * 1 + 6 = 1

the slope, m = 1

equation of the line of slope = 1 passing through point (1, -21) is calculated using the point slope formula which is

(y - y') = m(x - x')

(y - -21) = 1(x - 1)

y + 21 = x - 1

y = x + 20

Learn more about equation of line in point slope form:

https://brainly.com/question/29213103

#SPJ1

Vrite an equation in slope-intercept form of the line that passes through (1, −9) and (-3, -9).

Answers

Answer:

y = -9

Step-by-step explanation:

The slope-intercept form is y = mx + b

From two points we can easily determine the slope, m = (y2-y1)/(x2-x1)

You would put in the values into the equation.

m = (-9-(-9))/(-3-1) = 0/-4 = 0

Using the slope-intercept form, y = 0(x) + b ⇒ y = b

But we don't know what the y-intercept (b) is yet.  Using the point-slope form we can determine b.

Point-slope: (y - y1) = m(x - x1)

(y - (-9)) = 0(x - (-3))

y + 9 = 0

y = -9

So the equation is y = -9.

There are two number cubes (dice) with faces labeled 1, 2, 3, 4, 5 and 6 equally likely. Roll two dice (one at a time) and calculate the sum of the two faces.

a. Display the sample space
b. P(sum of 8) =
c. P(odd sum or sum greater than 9)
d. P(odd sum and sum greater than 9)

Let A = rolling a 3 or a 4 first

Let B = sum of at most 7
Are A and B mutually exclusive? Why or why not?
Are A and B independent? Why or why not?

Answers

a. Please find attached the sample space

b. P(sum of 8) = 5/36

c. P(odd sum or sum greater than 9) = 2/3

d. P(odd sum and sum greater than 9) =  1/12

e. P(A) = 1/3

f. P(B) = 1/6

g. P(A and B) = 1/18

h. A and B are not mutually exclusive because both events can occur at the same time.

i. A and B are not independent because the occurrence of A and lead to the occurrence of B.

What are the probabilities?

P(sum of 8) = number of sample spaces that sum up to 8 / total number of sample spaces

P(sum of 8) = 5/36

P(odd sum or sum greater than 9) = (sample spaces that have an odd sum / total number of sample spaces) + (sample spaces that have a sum greater than 9 / total number of sample spaces)

P(odd sum or sum greater than 9) =(18 / 36) + (6/36) = 24/36 = 2/3

P(odd sum and sum greater than 9) = (sample spaces that have an odd sum / total number of sample spaces)  x (sample spaces that have a sum greater than 9 / total number of sample spaces)

P(odd sum and sum greater than 9) = 18/36 x 6/36 = 1/12

P(A) = (sample spaces that have a 3 first / total number of sample spaces) +  (sample spaces that have a 3 first / total number of sample spaces)

P(A) = 6/36 + 6/36 = 1/3

P(B) = (sample spaces that adds up to 7 / total number of sample spaces)

= 6/36 = 1/6

P(A and B) = 1/3 x 1/6 = 1/18

To learn more about probability, please check: brainly.com/question/13234031

#SPJ1

How many minutes will it take to burn 110 calories

Answers

10 minutes jogging; 5 minutes sprinting = 100 calories hope this helps

The following diagram describes the volume of blue and red paint in a mixture.What is the ratio of blue paint to total paint in the mixture? Choose 1 answer:

Answers

Answer:

C

Step-by-step explanation:

blue volume = 10

red volume = 6

total = 10  6 = 16

ratio of

blue : total

= 10 : 16 ( divide both parts by 2 )

= 5 : 8

Each day, Caleb feeds his horse 2.25 lb of oats. He also feeds it hay. The weight
of the hay is 6.5 times the weight of the oats. What is the combined weight of
the oats and the hay Caleb feeds his horse in one week?

Answers

Answer:

102.375

Step-by-step explanation:

hope it helps :)

multiply 6.5 x 2.25, get 14.625

multiply 14.625 x 7, answer is 102.375

Solve the equation √3 Cosecx-2=0

Answers

Answer:

60

Step-by-step explanation:

[tex] \sqrt{3} cosecx - 2 = 0[/tex]

[tex] \sqrt{3} cosecx = 2[/tex]

[tex]cosec = \frac{2}{ \sqrt{3} } [/tex]

[tex]sinx = \frac{ \sqrt{3} }{2} [/tex]

[tex]x = sin {?}^{ - 1} ( \frac{ \sqrt{3} }{2} )[/tex]

[tex]x = 60[/tex]

Find a polynomial f(x) of degree 4 that has the following zeros.
-3, 4, 0, 8
Leave your answer in factored form.
f(x) = 0

Answers

Polynomial of degree 4 in factored form is x(x+3)(x-4)(x-8) = 0

The Standard form of polynomial with degree 4 is ax⁴ + bx³ + cx² + dx + e

Zeros of the polynomial is the points where the polynomial becomes zero.

According to the question,

The zeros of the polynomial are -3 , 4 , 0 , 8

Let equation of polynomial f(x) be

f(x) = ax⁴ + bx³ + cx² + dx + e ------------------(1)

Sum of zeros = -b/a = -3 + 4 + 0 + 8

= 9

Sum of product of two zeros = c/a =  (-3× 4 ) +(0 × 4) + (0 × 8) + (8× -3)

= -12 + 0 + 0 -24

= -12 - 24

= -36

Sum of product of sum of three zeros = -d/a = ( -3×4×0) + ( 4×0 ×8 ) + (0×8×-3) + (-3×4×8)

= 0 - 96

= -96

Product of all four zeros = e/a = (-3×4×0×8)

= 0

So,  b = -9 , c =-36 , d = 96 and e = 0

Substituting value in equation (1),

Hence , the required polynomial = x⁴ -9x³ -36x²+96x

Factored form ,

x⁴ -9x³ -36x² +96x = 0

=> x(x³ - 9x² - 36x + 96) = 0

=> x(x+3)(x-4)(x-8) = 0

To know more about Polynomial here

https://brainly.com/question/16979077

#SPJ9

The ordering and transportation cost C for the c mponents used in manufacturing a product is c= 100(200/x^2+ x/x+30), x≥1 where C is measured in thousands of dollars and x is the order size in hundreds. Find the rate of change of C with respect to x when (a) x = 10, (b) x = 15, and (c) x = 20. What do these rates of change imply about increasing order size?

Answers

The ordering and transportation cost C for the components used in manufacturing a product is c= 100(200/x^2+ x/x+30), x≥1 where C is measured in thousands of dollars and x is the order size in hundreds.

To find the rate of change of C with respect to x when (a) x = 10, (b) x = 15, and (c) x = 20.

The rate of change of the cost with respect to x is its derivative.

The differentiation rules to apply are

Quotient Rule: [tex]\frac{d}{dx} \left[\frac{f(x)}{g(x)}\right] = \frac{g(x)f^{'}(x)-f(x)g^{'}(x)}{\left[g(x)]^{2} }[/tex]

Constant Multiple Rule: [tex]\frac{d}{dx} \left[cf(x) \right] = cf^{'}(x)[/tex]

Power Rule: [tex]\frac{d}{dx} \left[x^{n} \right] = nx^{n-1}[/tex]

Constant Rule: [tex]\frac{d}{dx} [c] = 0[/tex]

So,

[tex]c^{'}(x) = 100 (\frac{x^{2}(200)^{'}-200(x^{2})^{'}}{(x^{2})^{2} }+\frac{(x+30)(x)^{'}-x(x+30)^{'} }{(x+30)^{2} } )[/tex]

[tex]c^{'}(x) = 100 (\frac{x^{2}(0)-200(2x) }{x^{4} } + \frac{(x+30)(1)-x(1+0)}{(x+30)^{2} })[/tex]

[tex]c^{'}(x) = 100 (\frac{0-400x}{x^{4} } + \frac{x+30-x}{(x+30)^{2} })[/tex]

[tex]c^{'}(x) = 100 (\frac{-400x}{x^{4} } + \frac{30}{(x+30)^{2} })[/tex]

From the above values it appears that the rate of change of the cost increases as the size of the order increases

[tex]a) c^{'}(10) = -38.13\\ \\b) c^{'}(15) = -10.37\\ \\c) c^{'}(20) = -3.8[/tex]

Hence the above values it appears that the rate of change of the cost increases as the size of the order increases

To learn more about rate changes click here https://brainly.com/question/11627203

#SPJ9

The cost C (in dollars) for a company to produce and sell x thousand gadgets is given by C = 1 /30 x^2 − 2x + 2530

(a) What is the company's start-up cost? _____________ $

(b) What is the minimum cost? ______________$

(c) How many gadgets must the company produce and sell in order to incur the least cost? (Be careful with your units!) ______________ gadgets

Answers

The company's start-up cost is equal to $1/2530.

The company's minimum cost is equal to $15/37,949.

The number of gadgets that this company must produce and sell in order to incur the least cost is equal to 1/30 gadgets.

How to determine the company's start-up cost?

From the information provided, the cost C (in dollars) for a company to produce and sell x thousand gadgets is modeled by the following function:

Function, C = 1/(30x² − 2x + 2530)

Mathematically, the start-up cost for this company is equal to the total cost when no sales of its gadget has been made i.e the level of activity is at zero (x = 0). Therefore, we would substitute the value of x in the function with zero (0):

Start-up cost = 1/(30(0)² − 2(0) + 2530)

Start-up cost = $1/2530.

What is the minimum cost?

First of all, we would determine the number of gadgets that this company must produce and sell in order to incur the least cost by differentiating the function for the total cost using the quotient rule:

dC/dx = [(0(30x² − 2x + 2530) - 1(60x - 2))1/(30x² − 2x + 2530)²]

dC/dx = [(0 - 60x + 2)1/(30x² − 2x + 2530)²]

Equating the marginal cost function to zero, we have:

-60x + 2/(30x² − 2x + 2530)² = 0

-60x + 2 = 0

60x = 2

x = 2/60

x = 1/30 gadgets.

Now, we can determine the minimum cost:

Function, C = 1/(30x² − 2x + 2530)

Minimum cost = 1/(30(1/30)² − 2(1/30) + 2530)

Minimum cost = 1/(1/30 - 1/15 + 2530)

Minimum cost = 1/(-1/15 + 2530)

Minimum cost = 1/(37,949/15)

Minimum cost = $15/37,949

Read more on cost here: https://brainly.com/question/27060649

#SPJ1

Other Questions
Does a monopolistically competitive firm tend to have a more elastic or less elastic demand than a monopoly? explain why. what is one surprising fact about the four-year old children used in the marshmallow experiment when at the age of eighteen they took the sat exam for college entrance? Pamela is about to host her first international teleconference meeting with clients from all over the world. She asks her mentor, Trayvon, if he has any advice for her. What is the best advice Trayvon can offer to Pamela concerning cultural differences in communication styles? What should Pamela be culturally aware of during this teleconference? Every year 8.8 million hectares of natural forest are cut down thats an area the size of a football field every second.Based on these figures, calculate what the area of a football field equals.Don't really understand the question, can you guys help please?I'm giving 40 points!!! the deposition of thick beds of oxidized iron in the proterozoic oceans (bifs) is often presented as evidence for: A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study. One hundred subjects replied and were informed that one group would receive the new cream and the other group would receive a cream with no active ingredient. All 100 subjects were exposed to poison ivy. Fifty were then randomly assigned to the group with the new cream, and 50 were randomly assigned to the group with the cream with no active ingredient. After three days, the subjects level of irritation was measured.Which of the following accurately describes the benefit of comparison in the experiment?The overall level of irritation can be compared to see if the new cream had a significant effect.The level of irritation for both groups can be compared to see if the new cream had a significant effect.The level of irritation in the treatment group only can be compared to see if the new cream had a significant effectSince one group received a cream with no active ingredient, the researchers will not be able to determine of the new cream is effective. What is the perimeter and area of shaded region? what was the term utilized for the commercial arrangement by which african slaves were shipped to the americas, sugar and tobacco were carried to europe, and european manufactured goods were transported to africa? One day is 1440 minutes long. How many minutes are in 30 days?Group of answer choices4320042200322004320 one explanation for why gardner's theory of multiple intelligences has been so widely accepted and implemented in the field of education is that . quinton is fed up with his supervisor, wally binghampton, and decides his health would improve if he retires early. quinton is 63 years old, and his normal social security retirement age is 66. if he retires today, and his normal age retirement pia is $1,500, how much can quinton expect to receive as a monthly retirement benefit? 722 divided by 68 =? What is the acronym is a reminder of the most common types of hazards caused by electricity?. a constant and deliberate effort to stay healthy and achieve the highest potential for well-being is best described as: a. absence of cardiovascular problems b. freedom from disease c. risk management d. wellness The velocity of sound waves is roughly the same for all wavelengths. Suppose that a sound wave has a wavelength of one meter and a frequency of 1000hz. The wavelength of a 250hz sound wave would then be. If it is 2 pm at 30E,what time will it be at 50E Tonya deposited one check for $56.93, a second check for$761.29, and a third check into a savings account for her daughter. She alsodeposited $75.00 in currency and $25.00 in coin. If she withdrew $150.00 incash and their total deposit was $1,785.23, what was the amount of herthird check? Tommy was going to sell all of his Pokemoncards to buy NBA 2K21. After selling half ofthem he changed his mind and bought 17more Pokemon cards. How many did he startwith if he now has 34? "Which of the following results of Thomas hunt Morgan's experiments with white eyed mutant flies was it unexpected and why out of Mendelian genetics?a. Among F2 progeny only males had white eyes. b. All the females had red eye'' Portia was hired as a yoga instructor. Which skill-related component will she most likely use in this role?.