SUppose the total cost C(x) to manufacture a quantity x of insecticide (in hundreds of liters) is given by
C(x) = x^3-27x^2+240x+850.
a. Where is C(x) decreasing?
b. Where is C(x) increases?

190,000 because the 4 in 194... is lower than 5

Answer:

Step-by-step explanation:

To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:

(24/18) * (2/17) * (34/3)

First, we can simplify the fractions by reducing any common factors in the numerators and denominators:

24/18 = (212)/(29) = 12/9 = 4/3

2/17 = 2/17

34/3 = (2*17)/3 = 34/3

Now we can multiply the simplified fractions:

(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153

The product of the given fractions in lowest terms is 272/153.

The teacher will use 3 rolls only to have perfect measurements.

1 yard = 3 feet

4 large bulletin boards are there each needing 9 yards of border.
That means 4 large bulletin boards in total need

9×4 yards of border

= 36 yards of border

= 108 feet of border

Also, there is a small bulletin board that only needs 12 feet border

Hence, in total there is a need for

108 + 12 = 120 feet border.

The border is sold in 40-foot rolls.
Hence, there is a need for 120/40 rolls

i.e. 3 rolls

Hence, the teacher will use 3 rolls only.  

Learn more about measurements here-

brainly.com/question/15658113

#SPJ10

Answer:

The answer is 3

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

this is because 24 divided by 16 equals 1.5

Answer:

7 bars

Step-by-step explanation:

Answer:

a=10/30

Step-by-step explanation:

because you can simplify it to 2/15

City Bank paid more interest than First National Bank over the 5-year period.

What is compound interest?

Compound interest is the interest earned on both the principal amount and the accumulated interest from previous periods.

We can use the formula for compound interest to calculate the amounts of interest earned by the two banks over 5 years:

Amount of interest with First National Bank = \($P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$\)

where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the number of years.

Amount of interest with First National Bank

=\($500\left(1 + \frac{0.085}{1}\right)^{1\times 5} - 500$\)

= $235.15 (rounded to two decimal places)

Amount of interest with City Bank =\($P\left(1 + \frac{r}{n}\right)^{n\cdot t} - P$\)

where P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year (365 in this case, since interest is compounded daily), and t is the number of years.

Amount of interest with City Bank

=\($500\left(1 + \frac{0.0825}{365}\right)^{365\times 5} - 500$\)

= $240.45 (rounded to two decimal places)

The difference in the amounts of interest paid by the two banks is:

$240.45 - $235.15 = $5.30

Therefore, City Bank paid more interest than First National Bank over the 5-year period.

To know more about compound interest visit:

brainly.com/question/20406888

#SPJ1

Answer:

1/9

Step-by-step explanation:

Tom and Carol ran a total of 3/2 miles altogether, which is equivalent to 1 1/2 miles.

A mile is a unit of measurement that is standardised as exactly 1609.344 metres by the International agreement in 1959. A mile is exactly equivalent to 5280 feet, or 1760 yards. It is the biggest measurement that is frequently used to calculate the separation between distant locations.

To show how many more miles Tom ran than Carol using fraction strips, we can represent Tom's distance as 1 whole and Carol's distance as 1/2. Then, we can subtract 1/2 from 1 to find the difference:

1 - 1/2 = 1/2

Therefore, Tom ran 1/2 mile more than Carol.

To show the total number of miles that Tom and Carol ran altogether, we can add their distances as fractions:

1 + 1/2 = 2/2 + 1/2 = 3/2

Therefore, Tom and Carol ran a total of 3/2 miles altogether, which is equivalent to 1 1/2 miles.

Learn more about mile on:

https://brainly.com/question/28466635

#SPJ9

The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

Read more about percentage Problems at; https://brainly.com/question/843074

#SPJ1

A graph that represents the solution set of the compound inequality is: graph D.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given compound inequality by making x the subject of formula as follows;

x + 3 < 1/2(4x - 12) < 20

Multiplying all through by 2, we have the following:

2x + 6 < 4x - 12 < 40

Next, we would solve the compound inequality in parts:

2x + 6 < 4x - 12

4x - 2x < 12 + 6

2x < 18

x < 18/2

x < 9.

4x - 12 < 40

4x < 40 + 12

4x < 52

x < 52/4

x < 13.

In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).

Read more on inequality here: brainly.com/question/27976143

#SPJ1

Answer:

Paul had £40 originally.

Step-by-step explanation:

Given

Let d be the money Dan has and p be the money Paul has

Then according to the given situation,

\(\frac{d}{p} = \frac{9}{5}\\d = \frac{9p}{5}\ \ \ Equation\ 1\)

Now from the statement, "Dan decides this is unfair so he gives Paul £32 of his share to make the ratio 1:1"

\(\frac{d-32}{p} = 1\)     Eqn 2

From 2

\(d - 32 = p\\\)

Putting d = 9p/5

\(\frac{9p}{5} - 32 = p\\9p - 160 = 5p\\9p-5p = 160\\4p = 160\\\frac{4p}{4} = \frac{160}{4}\\p = 40\)

Checking

\(d = \frac{9(40)}{5} = \frac{360}{5} = 72\\\frac{d}{p} = \frac{72}{40} = \frac{9}{5}\)

Hence,

Paul had £40 originally.

The amount that you need to save per month to fund the emergency fund would be $ 861. 58.

The discretionary money left per month would be $ 585. 88.

The gross income for the month :

= 17. 50 x 40 per week x 4 weeks a month

= $ 2, 800

The amount left which is realized funds for the month is:

= Gross income - FICA + Federal tax withholding + State tax withholding

= 2, 800 x ( 1 - 26. 15 %)

= $ 2, 067. 80

Five months of realized income for the emergency fund is:

= 2, 067. 80 x 5

= $ 10, 339

The amount to save per month is:

= 10, 339 / 12

= $ 861. 58

The amount left per month for discretionary expenses ;

= 2, 067. 80 - 861. 58 - 620. 24 rent

= $ 585. 88

Find out more on emergency fund at https://brainly.com/question/16166117

#SPJ1

Answer:

(a) y intercept is approximately 4.3

(b) \(y = 1.5x+4.5\)

Step-by-step explanation:

Given

See attachment for graph

Solving (a) The y intercept

This is the point where \(x =0\)

From the attached graph; By observation

\(y \approx 4.3\) when \(x =0\)

So, the y intercept is approximately 4.3

Solving (b): The equation of best fit.

First, calculate the slope of the line using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Where

\((x_1,y_1) = (9,18)\)

\((x_2,y_2) = (8,16.5)\)

So:

\(m = \frac{16.5- 18}{8 - 9}\)

\(m = \frac{-1.5}{- 1}\)

\(m = 1.5\)

The equation is then calculated using:

\(y =m(x - x_1) + y_1\)

Where: \(m = 1.5\) and \((x_1,y_1) = (9,18)\)

\(y = 1.5(x - 9) + 18\)

\(y = 1.5x - 9*1.5 + 18\)

\(y = 1.5x - 13.5 + 18\)

\(y = 1.5x+4.5\)

Answer:

No

Step-by-step explanation:

10 is not less than 6, so 10 < r when r=6 is not true.

Answer:

The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.

Step-by-step explanation:

We assume that goose is flying at constant velocity. After reading carefully the statement of the problem, we create the following geometrical diagram, which is included at the end of this explanation and represents the following Pythagorean identity:

\(x^{2}+y^{2} = r^{2}\) (Eq. 1)

Where:

\(x\) - Horizontal distance of the goose from pond, measured in feet.

\(y\) - Vertical distance of the goose from pond, measured in feet.

\(r\) - Resultant distance of the goose from pond, measured in feet.

We find the rate of change in time at which resultant distance is increasing by differentiating on (Eq. 1):

\(2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y = 2\cdot r \cdot \dot r\)

\(x\cdot \dot x + y\cdot \dot y = r\cdot \dot r\)

\(\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}\) (Eq. 2)

Where:

\(\dot x\) - Rate of change of horizontal distance, measured in feet per second.

\(\dot y\) - Rate of change of vertical distance, measured in feet per second.

\(\dot r\) - Rate of change of resulting distance, measured in feet per second.

If we know that \(x = 500\,ft\), \(y = 300\,ft\), \(\dot x = 50\,\frac{ft}{s}\) and \(\dot y = 0\,\frac{ft}{s}\), the rate at which the distance from the goose to the pond is increasing is:

\(\dot r = \frac{(500\,ft)\cdot \left(50\,\frac{ft}{s}\right)+(300\,ft)\cdot \left(0\,\frac{ft}{s} \right) }{\sqrt{(500\,ft)^{2}+(300\,ft)^{2}}}\)

\(\dot r \approx 42.875\,\frac{ft}{s}\)

The rate at which the distance from the goose to the pond is increasing is approximately 42.875 feet per second.

====================================================

Explanation:

s = 32 = sample standard deviation

n = 40 = sample size

Despite not knowing the population standard deviation (sigma), we can still use the Z distribution because n > 30. When n is this large, the student T distribution is approximately the same (more or less) compared to the standard Z distribution. The Z distribution is nicer to work with.

At 90% confidence, the z critical value is roughly z = 1.645. This can be found using either a Z table or a calculator.

------------------

We have these values:

Plug these values into the margin of error formula.

\(E = z*\frac{s}{\sqrt{n}}\\\\E \approx 1.645*\frac{32}{\sqrt{40}}\\\\E \approx 8.32311480156318\\\\E \approx 8.323\\\\\)

The margin of error is roughly 8.323

I rounded to 3 decimal places because z = 1.645 is rounded to 3 decimal places. If your teacher wants some other level of precision, then be sure to follow those instructions.

3a. An equation in slope-point for this line is y + 2 = 1/2(x - 0).

3b. The equation in slope-intercept form is y = 1/2(x) - 2.

4a. An equation in slope-point form to represent this function is y - 3875 = -1/695(x - 19375).

4b. The cost of operating a car that has been driven 31250 km is $3892.086.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Part 3.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 2)/(4 - 0)

Slope (m) = 1/2

At data point (0, -2) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 1/2(x - 0)

y = 1/2(x) - 2

Part 4a.

Based on the information provided about Jay's business, we would determine the slope of the line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3900 - 3875)/(2000 - 19375)

Slope (m) = 25/-17375

Slope (m) = -1/695

At data point (19375, 3875) and a slope of -1/695, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3875 = -1/695(x - 19375)

Part 4b.

For the cost when x = 31250 km, we have:

y - 3875 = -1/695(31250 - 19375)

y = 17.086 + 3875

y = $3892.086.

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

Answer:

7.18421051

Step-by-step explanation:

76 ÷ 6 = 12.6666667

91 ÷ 12.6666667 = 7.18421051

https://brainly.com/question/12073326#

The graph of the feasible region is attached

From the question, we have the following parameters that can be used in our computation:

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

Read more about feasible region at

https://brainly.com/question/29084868

#SPJ1

It crosses the y axis at 4... it is 4 :)

Answer:

a. (0, 4)

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, the line crosses the y-axis at y = 4. Therefore, our y-intercept is 4. Writing it in coordinate point would be (0, 4), as definition of the y-int.

Answer:

1) Surface area is: \(A_{Prism}=276\: in^{2}\)

2) Volume is: \(V_{Prism}=280\: in^{3}\)

Step-by-step explanation:

1)

If we multiply 10 in times 22 in we could find the area of prims without the tops and down parts.

\(A_{1}=10*22=220\: in^{2}\)

Now, the area of the up surface is:

\(A_{up}=7*(14-10)=28 \: in^{2}\)

The down surface is equal to the up one, so we total area of the prism will be:

\(A_{Prism}=A_{1}+A_{up}+A_{down}=220+28+28=276\: in^{2}\)

2)

The volume of a prism is the product of length times width and times height.

\(V_{prism}=10*7*4=280\: in^{3}\)

I hope it helps you!

let the nisha be x and nishan be y

Step-by-step explanation:

ATQ

your statement is x=2y

Answer:

√x³=√(x²·x)=x√x

√xy³z=√(x·y²·y·z)=y√xyz

√18x²y=√(3²·2·x²·y)=3x√2y

√32x⁴y²=√(2⁴·2·x⁴·y²)=2²x²y√2=4x²y√2

2√16x⁷y³z⁴=2√(2⁴·x⁶·x·y²·y·z⁴)=2³x³yz²√xy=8x³yz²√xy

-3√180x⁵y=-3√(3²·2²·5·x⁴·x·y)=-3(3)(2)x²√5xy=-18x²√5xy

5√108xyz²=5√(2²·3²·3·x·y·z²)=5(2)(3)z√3xy=30z√3xy

3x√xy¹⁰z⁷=3x√x·y¹⁰·z⁶·z)=3xy⁵z³√xz

x²√x³y²=x²√(x²·x·y²)=x²·x·y√x=x³y√x

Answer:

k(-4) = 12

Step-by-step explanation:

The most simple definition of a function is a set of inputs that have a given set of outputs.

Functions are often written as f(x) = "an expression"

Where "x" is the input and "the expression" results in an output. Whatever the input is you plug into "x" and replace all "x"s with the input

Here, we are given the function k(x) = 8 - x and we want to find k(-4)

This can be rewritten as k(-4) = 8 - x

==> replace all x's with -4

k(-4) = 8 - (-4)

==> remove parenthesis

k(-4) = 8 + 4

==> add 8 and 4

k(-4) = 12

Answer:

6.75 miles per 0.5 hours.

Step-by-step explanation:

The ratio 27/2 is equal to the ratio of 6.75/0.5. This can be shown by dividing the 2 in the denominator by 4, getting you 0.5, and dividing the numerator, 27, by 4 also, which gets you 6.75. Hope this helps!

Answer:

x=19

Step-by-step explanation:

2x - 8 = 30

get x by itself by adding 8 to both sides

2x=38

divide by 2

x=19

Answer:

350 F

Step-by-step explanation:

All the data ordered would be:

150, 300, 325, 350, 350, 400, 400, 450, 450

The median is the middle value when a data set is ordered from least to greatest. Therefore, if there are 9 data, the middle value would be in the position 4.5 as 9 is an odd number.

The rule says that when the amount of data is odd you need to calculate the average between the two middle values.

So, the median would be the mean between 350 and 350.

(350 +350)/2 = 350

Solving a system of equations we can see that each pound of trail mix costs $3.50, and each pound of jelly beans costs $1.50

Let's define the variables:

Then we can write a system of equations so we will get:

5x + 3y = 22

2x + 12y = 25

To solve this, we can subtract 4 times the first equation fom the second one:

2x + 12y - 4(5x + 3y) = 25 - 4*22

2x + 12y - 20x - 12y = -63

-18x = -63

x = -63/-18

x = 3.5

That is the cost of each pound of trail mix, and replacing that in one of the equations:

2*3.5 + 12y = 25

y = (25 - 2*3.5)/12

y = 1.5

Learn more about systems of equations at:

https://brainly.com/question/13729904

#SPJ1