Hello can i get a little help giveing 20 points to who ever help and bralyles so yeh help

Hello Can I Get A Little Help Giveing 20 Points To Who Ever Help And Bralyles So Yeh Help

Answers

Answer 1

Answer:

a) n less than or equal to 21

b) n greater than or equal to 5

c) n > 3/5

Step-by-step explanation:

i hope this helps!!

Answer 2

Answer:

A.) n ≤ 21

B.) n  ≥ 5

C.) n > 3/5

Step-by-step explanation:

For the first question it says that the number is no more than 21, so it could be equal to or less than 21

For the second question, it says that the number is at least 5, so it could be equal to or greater than 5

Finally, for the last question it says that the number is more than 3/5, so greater than would be the correct inequality symbol to use


Related Questions

In the figure to the right, AE + DC = 1 1/5 cm, AB = 1 3/4 cm, DE = 1 1/4 cm, and BC = 1 3/10 cm. Find the perimeter of the figure.
active attachment

Answers

The perimeter of the given composite figure is; 5¹/₂ cm

How to find the perimeter of the composite figure?

To get the perimeter of the given composite figure, what we will do is to dd up the given segment side lengths and we are given the following;

AE + DC = 1¹/₅ cm

AB = 1 ³/₄ cm

DE = 1 ¹/₄ cm

BC = 1 ³/₁₀ cm.

 

Thus, we can say that the Perimeter is;

Perimeter = AE + DE + DC + BC + AB

Perimeter  = (AE + DC) + DE + BC + AB

= 1¹/₅ + 1 ¹/₄ + 1 ³/₁₀ + 1 ³/₄

= (1²/₁₀ + 1³/₁₀) +(1¹/₄ + 1³/₄)

= 2⁵/₁₀ + 3

= 5¹/₂ cm

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Pete was building a doghouse for his dog, Chip. He made the door 36 inches tall. The height of the door was twice the height of the window in the doghouse.

Write an equation to determine the height of the window.

36 = 2h
36 = 2 + h
36 = h − 2
36 equals h over 2

Answers

Answer:

36 = 2h

Step-by-step explanation:

Here h represents the heigh

We know that the height of the door was twice the height of the window so that the equation will be

36 = 2h

what is the entire surd for 8 root 2

what is the entire surd of 5 root 9

what is the entire surd of 6 root 5

what is the entire surd of 3 root 13
help its urgent!!

Answers

The entire surds are √128, √225,√180, √117 respectively

What is an entire surd?

An entire surd is a surd in which the entire number is under the root sign.

Given here are 8√2,5√9,6√5,3√13

thus their entire roots are  8√2 =√2×64

                                                   = √128

again, 5√9 = √9×25

                   = √225

          6√5=√5×36

                 = √180

Similarly 3√13= √117

Hence, the respective entire surds are √128, √225,√180, √117

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Find u•v where theta is the angle between u and v

Answers

Answer:

88√2 = 124.5 (nearest tenth)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}[/tex]

Given:

[tex]|u| = 8[/tex][tex]|v| = 22[/tex][tex]\theta =\dfrac{\pi}{4}[/tex]

Substitute the given values into the dot product formula:

[tex]\begin{aligned}\implies u \cdot v &=|u||v| \cos \theta\\\\&=8 \cdot 22 \cdot \cos \left(\dfrac{\pi}{4}\right)\\\\&=176 \cdot \dfrac{\sqrt{2}}{2}\right)\\\\&=88\sqrt{2}\\\\&=124.5\; \sf (nearest\;tenth)\end{aligned}[/tex]

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D is bounded by y = 1 − x2 and y = 0; rho(x, y) = 7ky

Answers

The mass and center of mass of the lamina is [tex]\frac{8}{15} k, (0, \frac{4}{7} )[/tex]

The mass of a homogenous lamina is given by [tex]$m=\iint_R \delta(x, y) d A$[/tex]

We can rewrite the equation using the limits of integration as [tex]$$m=\int_a^b \int_c^d \delta(x, y) d y d x$,[/tex] where a ≤ x ≤ b and c ≤ y ≤ d.

The objective is to find the mass and center of mass of the lamina that occupies the region D.

From the given equations, we get the limits of integration as -1 ≤ x ≤ 1 and  0 ≤ x ≤ 1-[tex]x^{2}[/tex]. Substitute the known values in the equation.

[tex]$$\begin{aligned}& m=\int_{-1}^1 \int_0^{1-x^2} k y d y d x \\& =\int_{-1}^1 \frac{1}{2} k\left(1-x^2\right)^2 d x \\& =\frac{1}{2} k \int_{-1}^1\left(1+x^4-2 x^2\right) d x \\& =\frac{k}{2}\left[x+\frac{x^5}{5}-2 \frac{x^3}{3}\right]_{-1}^1 \\\\\end{aligned}$$[/tex]

[tex]& =\frac{k}{2}\left[1+\frac{1}{5}-\frac{2}{3}+1+\frac{1}{5}-\frac{2}{3}\right] \\\\& =\frac{k}{2}\left[\frac{16}{15}\right] \\\\& =\frac{8}{15} k[/tex]

Hence, the mass of the lamina as [tex]\frac{8}{15} k[/tex].

The center of mass of the lamina is given by[tex]$(\bar{x}, \bar{y})$[/tex], where [tex]$$\begin{gathered}\bar{x}=\frac{1}{m} \iint_R x \delta(x, y) d A \text { and } \\\bar{y}=\frac{1}{m} \iint_R y \delta(x, y) d A .\end{gathered}$$[/tex]

First, find [tex]$\bar{x}$[/tex] as follows:

[tex]$$\begin{aligned}\bar{x} & =\frac{1}{\frac{8}{15} \mathrm{k}} \int_{-1}^1 \int_0^{1-x^2} k x y d y d x \\& =\frac{1}{\frac{8}{15} \mathrm{k}} \int_{-1}^1 \frac{1}{2} k x\left(1-x^2\right)^2 d x \\= & \frac{15}{8 k} \cdot \frac{k}{2} \int_{-1}^1 x\left(1+x^4-2 x^2\right) d x \\= & \frac{15}{16}\left[\frac{x^2}{2}+\frac{x^6}{6}-2 \frac{x^4}{4}\right]_{-1}^1 \\= & 0\end{aligned}$$[/tex]

Thus, the  [tex]$\bar{x}$[/tex]-coordinate of the center of gravity as 0 .

Now, evaluate [tex]$\bar{y}$[/tex].

[tex]& \bar{y}=\frac{1}{\frac{8}{15}} \int_{-1}^1 \int_0^{1-x^2} k y^2 d y d x \\\\& =\frac{1}{\frac{8}{15}} \int_{-1}^1 \frac{1}{3} k\left(1-x^2\right)^3 d x \\\\& =\frac{15}{8 k} \cdot \frac{k}{3} \int_{-1}^1\left(1-x^6-3 x^2+3 x^4\right) d x \\\\& =\frac{15}{24}\left[x-\frac{x^7}{7}-3 \frac{x^3}{3}+3 \frac{x^5}{5}\right]_{-1}^1 \\\\& =\frac{15}{24} \times \frac{32}{35} \\\\& =\frac{4}{7}[/tex]

Hence, the center of gravity of the lamina is ([tex]0, \frac{4}{7}[/tex]).

Therefore,  the mass and center of mass of the lamina that occupies the region D is [tex]\frac{8}{15} k[/tex], [tex](0, \frac{4}{7} )[/tex]

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Noel old 4 carved wooden block at a local fair, earning a total profit of $26. He plan to ell 22 block during the fair. If he ell all the block, how much profit can Noel expect to earn? $

Answers

Noel can expect to earn a total profit of $572 if he sells all 22 blocks at the fair. Profit is an important measure of the financial performance of a business.

Profit is the amount of money that is gained from a business activity after all expenses have been paid. It is calculated by subtracting the costs of producing or acquiring a product or service from the revenue generated by selling that product or service.

To find the total profit that Noel can expect to earn from selling all 22 blocks, we need to multiply the profit from each block by the number of blocks he plans to sell.

We can use the following equation to calculate the total profit:

Total profit = Profit per block x Number of blocks

Plugging in the values we know, we get:

Total profit = $26 x 22 = $<<26*22=572>>572

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natalie is the creator of better brain, a new mindfulness app for teens. the app currently has 1,262 downloads, and natalie has set a goal of doubling the downloads every month. write an exponential equation in the form y

Answers

Answer:

1262(2)^x

Step-by-step explanation:

Planes Q and R are parallel planes. Plane Q contains line a. Plane R contains line b.

Planes Q and R are parallel. Plane Q contains line a and plane R contains line b. Both lines are going the same direction.
If a third plane could be drawn which contains both lines a and b, then

lines a and b must be parallel.
lines a and b cannot be parallel.
lines a and b must be skew.
lines a and b must be perpendicular.

Answers

Answer:

lines a and b must be parallel

Answer:(A)

Step-by-step explanation:edge

The area of the square in the figure below is 16 square inches. Solve for "s", the length of one side. Explain
the solution.

▪️▪️▪️▪️
▪️▪️▪️▪️
▪️▪️▪️▪️
▪️▪️▪️▪️

Area = 16 in²
A=S²
A=16
s²=16

Answers

Answer:

4

Step-by-step explanation:

[tex]\sqrt{16}[/tex] = 4

The side lengths of the square is 4.

Area = Length times width

Area = 4 x 4

Are = 16

all the sides of a triangle are integers, and the perimeter is 12. how many different possible triangles are there

Answers

3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).

Given that,

The perimeter of a triangle 12cm.if the lengths of the three sides are all integers (in cm).

We have to find how many such difference triangle are possible.

We know that,

Perimeter of the triangle is 12cm.

p=12

a+b+c=12

a+b≥c

b+c≥a

So,

a+b+c≥2c

12≥2c

c≤6

So,

a≤6,b≤6,c≤6

We get,

a=6,b=3,c=3

a=5,b=4,c=3

a=4,b=4,c=4

Therefore, 3 such difference triangle are possible when the perimeter of a triangle 12cm. if the lengths of the three sides are all integers (in cm).

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Write y+4=2(x-7) in standard form

Answers

Answer:

[tex] \Large{\boxed{\sf 2x - y = 18}} [/tex]

[tex] \\ [/tex]

Explanation:

We will try to write the given linear equation in standard form.

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Standard \ Form \ of \ a \ linear \ equation \text{:}} \\ ~ \\ \tt Ax + By = C \end{array} \right] } [/tex]

Where:

A is a positive integer. (A ≠ 0)B and C are integers. (B ≠ 0)

[tex] \\ [/tex]

Given linear equation:

[tex] \sf y + 4 = 2(x - 7) [/tex]

[tex] \\ [/tex]

First, expand the right side of the equation:

[tex] \sf y + 4 = 2 \cdot x + 2 \cdot (-7) \\ \\ \sf y + 4 = 2x - 14 [/tex]

[tex] \\ [/tex]

Subtract 2x from both sides of the equation:

[tex] \sf y + 4 - 2x = 2x - 14 - 2x \\ \\ \sf -2x + y + 4 = -14 [/tex]

[tex] \\ [/tex]

Subtract 4 from both sides of the equation:

[tex] \sf -2x + y + 4 - 4 = -14 - 4 \\ \\ \sf -2x + y = -18 [/tex]

[tex] \\ [/tex]

Since the coefficient of x (-2) has to be positive, multiply both sides of the equation by -1:

[tex] \sf -1 \cdot (-2x + y) = -1 \cdot (-18) \\ \\ \sf -1 \cdot (-2x) + (-1) \cdot y = 18 \\ \\ \boxed{\boxed{\sf 2x - y = 18 }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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which of the following is a constant in a mathematical model? a) decision variable. b) parameter. c) objective function. d) constraint. e) none of the answer choices are correct.

Answers

Answer:

b). parameter

Step-by-step explanation:

A parameter is a fixed value in the model that is not a decision variable and is not changed during the optimization process. It is used to represent known quantities that are used in the model but are not being optimized. For example, in a linear programming model, the cost of a product may be represented by a parameter, as the cost is not a decision variable and is fixed.

Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 33 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?

Answers

Answer:330

Step-by-step explanation:

Set up cross multiplication:

33/x    10/100

Cross multiply

10*x   100*33

Divide sums

3,300/10x

Answer:

330 total cards

please help will give brainliest

Answers

The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.

Given that, the polygon IJKL if IJ≅KL, JK≅LI, IJ⊥JK, JK⊥KL, KL⊥LI and LI⊥IJ.

What is a rectangle?

A rectangle is a closed two-dimensional figure with four sides. The opposite sides of a rectangle are equal and parallel to each other and all the angles of a rectangle are equal to 90°.

Here, the opposite sides IJ and KL are equal and the opposite sides JK and LI are equal.

Since, all the sides are perpendicular to each other makes an angle 90°

The given polygon IJKL is a rectangle. Therefore, option C is the correct answer.

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What is the domain of this function?
f(x) = ²x - 3| + 1 ?

Answers

Answer: A.

Step-by-step explanation:

Most of the function f(x) has a domain (- infinity, positive infinity), and the function in the picture is the same. So, the answer is A

Chri want to order DVD over the internet. Each DVD cot $15. 99 and hipping the entire order cot $9. 99. If he can pend no more than $100 , how many DVD could be buy?

Answers

Chris can only buy a maximum of 5 DVDs.

What is a division?

The division is a mathematical operation that involves dividing one number (the dividend) by another number (the divisor) to find the quotient. It is represented by the symbol "/" or "÷".

To determine how many DVDs Chris can buy, we need to subtract the cost of shipping from the total amount of money Chris has available and then divide the remaining amount by the cost of each DVD.

First, we subtract the cost of shipping from the total amount of money Chris has available:

$100 - $9.99 = $90.01

Then, we divide the remaining amount by the cost of each DVD:

$90.01 / $15.99 = 5.63

Chris can buy 5 DVDs.

Hence, Chris can only buy a maximum of 5 DVDs.

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the margin of error of a confidence interval is the error from biased sampling methods. t or f

Answers

False. The margin of error only accounts for sampling variability (the fact that my sample will be different that many other people's and therefore provide different statistics.

What are statistics and their various forms?

Statistics is a technique for interpreting, analyzing, and summarizing data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as through graphs, bar graphs, or tables.

What are the two primary statistical methods?

Inferential statistics, which draws conclusions from information using statistical tests like the student's t-test, is one of the two main statistical methods used in data analysis. Descriptive statistics presents data using indices like mean and median.

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Jayden’s family has completed 90% percent of the trip. They have traveled 75 miles. How far is the trip?

Answers

Answer:

[tex]83\frac{1}{3} miles[/tex]

Step-by-step explanation:

90/100=75/x

90x=100(75)

90x=7500

/90.  /90

x=83 1/3 miles

Hopes this helps

the figure(figure 1) shows the acceleration graph for a particle that starts from rest at t = 0s.

Answers

a) The velocity of particle at t=2s is 5m/s

b) The velocity of particle at t=4s is 20m/s

To obtain the function of velocity from the graph we need to find the equation of accleration- time graph

so the equation of accleration is :

a= [tex]\frac{10-0}{4-0}[/tex]t

a= 5/2t

and we know that :

a= [tex]\frac{dv}{dt}[/tex]

=> dv= adt

=> dv= [tex]\frac{5}{2}[/tex] t dt

integrating both side we get:

v= [tex]\frac{5}{4}[/tex][tex]t^2[/tex]  +c

where c is constant

it is given that at t=0s it starts from rest so

v=0 at t=0

=> 0 = 0+c

=>c=0

so v=[tex]\frac{5}{4}t^2[/tex] ---- (i)

a) as we have got the equation of velocity with respect to time

 we have to find velocity at t=2s

putting t=2s we get

 v = 5/4 *4

 so velocity of particle at t=2s is 5m/s

b) as we have got the equation of velocity with respect to time

 we have to find velocity at t=4s

putting t=4s we get

 v = 5/4 *16

 so velocity of particle at t=2s is 20m/s

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equation of simple straight line

Complete question:

the figure shows the acceleration graph for a particle given that particle starts from rest at t=0.

determine the velocity of partice at

a)2s

b)4s

Please help me respond these two questions!!

Answers

The score of the 60th percentile on the test is 84.

What is a percentile?

The definition of percentile is the percentage that a certain percentage falls beneath. Ben is the fourth-tallest child in a group of 20 kids, whereas 80% of the kids are shorter than you.

Given:

58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

Calculate the percentile of score 71 as shown below,

[tex]Percentile = n / N \times 100[/tex]

Here, n is the number of scores below the score of 60th percentile and N is the total number of scores,

60 = n / 15 × 100

n / 15 = 60 / 100

n = 0.6 ×  15

n = 9

Thus, the 9th term = 84  is the score of the 60th percentile,

Therefore, the score of the 60th percentile on the test is 84.

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Wyatt' Ga Mileage
\text{Gallon (\(x\))}Gallon (x) \text{Mile (\(y\))}Mile (y)
55 153153
77 214. 2214. 2
1010 306306
1414 428. 4428. 4
How much farther can Camden' car travel on one gallon of ga than Wyatt' car?

Answers

Both automobiles' lines have the equation "y = 3x," and their respective gas mileage is 3 miles per gallon. Wyatt's automobile gets more miles per gallon of gas than Camden's vehicle does.

We must compute the mileage (the distance driven per gallon of fuel) for each automobile using the provided information to determine the difference between the ranges of travel for Camden's and Wyatt's vehicles.

We can determine the miles for Wyatt's automobile using the data points (5, 15) and (7, 21). The equation for the slope of the line connecting these two locations is

(y2 - y1) / (x2 - x1) = (21 - 15) / (7 - 5) = 6/2 = 3

"Y = mx + b" is the equation for the line connecting these two points, where m denotes the line's slope and b its y-intercept. We may determine the equation of the line by adding the values of m as well as the dimensions of one of the endpoints into this equation:

y = 3x + b

15 = 3(5) + b

15 = 15 + b

0 = b

"Y = 3x" is the equation for the line passing thru the points (5, 15) and (7, 21).

We can determine the miles for Camden's automobile using the data points (10, 30) and (14, 42). The equation for the slope of the line connecting these two locations is

(y2 - y1) / (x2 - x1) = (42 - 30) / (14 - 10) = 12/4 = 3

"Y = mx + b" is the equation for the line connecting these two points, where m denotes the line's slope and b its y-intercept. We may determine the equation of the line by incorporating the values of m as well as the dimensions of one of the endpoints into this equation:

y = 3x + b

30 = 3(10) + b

30 = 30 + b

0 = b

"Y = 3x" is the equation for the line passing through the points (10, 30) & (14, 42).

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The question is -

Computes the miles per gallon of your car via the miles traveled and the number of gallons used. Also, if you enter the cost per gallon and how many miles you drive a day, it will estimate your monthly and yearly gas expenses with data points (5, 15) and (7, 21).

A bag of marbles contains only yellow and purple marbles. The number of yellow marbles is five times as the purple marbles. The bag contains 138 total marbles. develop a system of equations to represent the situation, determine how many of each color of marble is in the bag
show how you checked your answers ​

Answers

First create a system of equations:
y = number of yellow marbles
p = number of purple marbles
y = 5p
y + p = 138
Now since we already have one of the variables (y) by itself in the first equation, we can substitute that into the second equation so we only have one variable (p) and it’s easier to solve.
(5p) + p = 138
Combine like terms
6p = 138
Divide both sides by 6
p = 23
Now that we have p, we can substitute it in the first equation so we only have one variable (y) and it’s easier to solve.
y = 5(23)
y = 115
So there’s are 23 purple marbles and 116 yellow marbles.
To check our answers, add together the purple and yellow marble numbers that we got to see if it equals 138 to see if they fit into the equations.
23 + 115 = 138
138 = 138
Also, we can check if there are 5 times as many yellow marbles as purple marbles.
115 = 5 x 23
115 = 115
Since we got a valid equation, the answers are correct.

Answer:

23 purple marbles

115 yellow marbles

Step-by-step explanation:

Let y represent the yellow marble

Let p represent the purple marbles

So, we have the equations

y = 5p

Therefore, y + p = 138

5p + p = 138

6p = 138

p = 23 marbles

Now let's put 23 in for the p in the equation to find the number of yellow marbles

y = 5(23)

y = 115 marbles

How do I find the missing side of a triangle ?

Answers

Answer: 1. Given two sides

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

(6)/(a^(2))+(5a^(-2))/(3^(-3))

Answers

Answer:

[tex]\frac{141}{a^{2} }[/tex]

Step-by-step explanation:

[tex]\frac{6}{a^{2} } + \frac{5a^{-2} }{3^{-3} }[/tex]

[tex]\frac{141}{a^{2} }[/tex]

sum of two numbers is -11/12 ,one of them is 9/2, find the other





pls answer fasttttttt!!!!
plssssssssssssssssssssssssssssss.
step by step

Answers

Answer:

- [tex]\frac{65}{12}[/tex]

Step-by-step explanation:

let the number to be found be n , then

n + [tex]\frac{9}{2}[/tex] = - [tex]\frac{11}{12}[/tex]

multiply through by 12 ( the LCM of 2 and 12 ) to clear rhe fractions

12n + 54 = - 11 ( subtract 54 from both sides )

12n = - 65 ( divide both sides by 12 )

n = - [tex]\frac{65}{12}[/tex]

Find the value of x. A B D E C i an irregular pentagon with parallel ide A B and C E. Angle A B D meaure 104 degree. Angle C E D meaure 28 degree. Angle B D E meaure x degree

Answers

Angle B D E measure 228 degrees in the irregular pentagon A B D E C.

Polygons that lack equal sides and angles are referred to as irregular polygons. Polygons that are irregular are not regular, in other words. Closed two-dimensional shapes known as polygons are created by connecting three or more line segments. Regular and irregular polygons are two different forms of polygons.

As we know, the Sum of the interior angles of an irregular polygon =

(n − 2) × 180°

{ 'n' = the number of sides of a polygon.}

As given, A B D E C is a pentagon, so

n= 5

The sum of interior angles=

3 X \180= 540

As AB and CE are parallel to each other:

angle BAC=y

angleECA= 180-y

=>the sum of interior angles:

104+x+28+180-y+y= 540

104+x+28+180=540

x+312=540

=> x=228

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This equation has one solution. 5(x – 1) 3x = 7(x 1) what is the solution?

Answers

Answer:

send the complete question . there are some missing signs .

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

Answers

The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.

Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point

[tex]r(x) = f(g(x))[/tex]therefore the derivative of r is given by [tex]r'(x) = f'g(x)\times g'(x)[/tex]

[tex]r'(1) = f'(g(1))\times g'(1)[/tex] from the graphs

r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0

Similarly s'(1) = g'(f(1))\times f'(1) from the graphs

 f(1)=1.5, f'(1)

=\dfrac{ (3-0)}{(0-2)}

= -3/2 , g'(3/2) = 0

s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0

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Complete question:

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

1) The domain of a function can BEST be described as which of the following:
a) The set of all y-coordinates
b) The set of all x-coordinates
d) The x-intercepts of one of the functions
c) Where the graph of the two
functions meet

Answers

Answer: b) The set of all x-coordinates

Step-by-step explanation:

a rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material for the base costs $15 per square meter. material for the sides costs $9 per square meter. let w denote the width of the base.

Answers

The total cost is $245.31.

Given,

Volume = 10[tex]m^{3}[/tex]

Width = w

Length = 2w

Base area = Length x Width = [tex]2w^{2}[/tex]

Cost of base = $15

Cost of sides = $9

Since the volume is 10[tex]m^{3}[/tex],

Volume = Base Area x Height

Height = [tex]\frac{10}{2w^{2} }[/tex] = [tex]\frac{5}{w^{2} }[/tex]

Cost of making such a container:

Cost of base =  [tex]2w^{2}[/tex] x 15 = $[tex]30w^{2}[/tex]

Cost of sides = [(2 x 2w x  [tex]\frac{5}{w^{2} }[/tex]) + (2 x w x  [tex]\frac{5}{w^{2} }[/tex])] x $9 = $[tex]\frac{270}{w}[/tex]

Overall Cost = Cost of Base + Cost of Sides

f(x) = [tex]30w^{2} + \frac{270}{w}[/tex] = [tex]30(w^{2} + \frac{9}{w})[/tex]

To get the minimum cost, we will have to find the derivative of f(x) and equate it to zero.

d(f(x))/dx = 0

[tex]2w - \frac{9}{w^{2} } = 0\\w^{3} = 4.5 \\w = 1.651m[/tex]

Putting the value of w in f(x),

f(x) = $245.31 (after calculations)

Therefore, the final answer is $245.31.

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