A dressmaker measures a length of fabric as 600m correct to the nearest 5 meters.
He cuts this into dress lengths of 9cm correct to the nearest meter.

Calculate the largest number of completer dress lengths he could cut.

Answer:

B

Step-by-step explanation:

Answer:

B

I copied the answer above me tbh

Answer:

Convergent

Step-by-step explanation:

One method to determine if  \(\displaystyle \sum^\infty_{k=1}ke^{-k^2}\)is convergent or divergent is the Integral Test.

Suppose that the function we use is \(f(x)=xe^{-x^2}\). Over the interval \([1,\infty)\), the function is always positive and continuous, but we also need to make sure it is decreasing before we can proceed with the Integral Test.

The derivative of this function is \(f'(x) = e^{-x^2}(1-2x^2)\), so our critical points will be \(\displaystyle x=\pm\frac{1}{\sqrt{2}}\), but we can drop the negative critical point as we are starting at \(k=1\). Using some test points, we can see that the function increases on the interval \(\bigr[0,\frac{1}{\sqrt{2}}\bigr]\) and decreases on the interval \(\bigr[\frac{1}{\sqrt{2}},\infty\bigr)\). Since the function will eventually decrease, we can go ahead with the Integral Test:

\(\displaystyle \int_{{\,1}}^{{\,\infty }}{{x{{{e}}^{ - {x^2}}}\,dx}} & = \mathop {\lim }\limits_{t \to \infty } \int_{{\,1}}^{{\,t}}{{x{{{e}}^{ - {x^2}}}\,dx}}\hspace{0.5in}u = - {x^2}\\ & = \mathop {\lim }\limits_{t \to \infty } \left. {\left( { - \frac{1}{2}{{{e}}^{ - {x^2}}}} \right)} \right|_1^t\\ & = \mathop {\lim }\limits_{t \to \infty } \left( {-\frac{1}{2}{{e}}^{ - {t^2}}-\biggr(-\frac{1}{2e}\biggr)}} \right) = \frac{1}{2e}\)

Therefore, since the integral is convergent, the series must also be convergent by the Integral Test.

a) The initial amount of flyers is given as follows: 62 flyers.

b) The statement that best describes the relation is given as follows:

As time increases, the number of flyers that Andre has increases at a rate of 3 flyers per minute.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by 5, y increases by 15, hence the slope m is given as follows:

m = 15/5

m = 3.

Hence:

y = 3x + b.

When x = 10,  y = 92, hence the intercept b, representing the initial amount, is obtained as follows:

92 = 30 + b

b = 62.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

Answer:

Step-by-step explanation:

it is a

Answer: 540 tiles are needed to tile a floor that is 36 feet by 15 feet.

Step-by-step explanation: You need to find the area of the floor. 36x15 is 540.

Answer: inverse of 2,48 there is none and the inverse of 56,2130 there is none

Step-by-step explanation: hope this helps

The unpaid balance is $94.32, the finance charge is approximately $1.18, and the new balance is approximately $212.92.

To calculate the unpaid balance, finance charge, and new balance using the unpaid balance method, we need to follow these steps:

1. Calculate the unpaid balance: Subtract the payments/credits from the previous balance.

2. Calculate the finance charge: Multiply the unpaid balance by the monthly interest rate.

3. Calculate the new balance: Add the unpaid balance, finance charge, and any new purchases.

Given the information:

Previous balance: $179.32

Payments/credits: $85.00

Unpaid balance: $ (to be calculated)

Monthly rate: 1.25%

Finance charge: $ (to be calculated)

New purchases: $117.42

New balance: $ (to be calculated)

Let's calculate each step:

1. Unpaid balance = Previous balance - Payments/credits

Unpaid balance = $179.32 - $85.00

Unpaid balance = $94.32

2. Finance charge = Unpaid balance * Monthly rate

Finance charge = $94.32 * (1.25 / 100)

Finance charge ≈ $1.18

3. New balance = Unpaid balance + Finance charge + New purchases

New balance = $94.32 + $1.18 + $117.42

New balance ≈ $212.92

Therefore, the unpaid balance is $94.32, the finance charge is approximately $1.18, and the new balance is approximately $212.92.

To know more about unpaid balance, refer here:

https://brainly.com/question/18917426

#SPJ4

Answer:

A

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

oeoddododdkfkfkdkkkdkdk

Answer:

He was 11

Step-by-step explanation:

if Camila was 4 years younger than her brother and she was seven. That means he is 4 years older than her. so 7+4=11

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

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

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

The Laplace transform of a bt + ct^2 for some constants a, b, and c can be found using the linearity property of the Laplace transform. The Laplace transform of a linear combination of functions is equal to the linear combination of their Laplace transforms. Therefore, the Laplace transform of a bt + ct^2 is equal to the Laplace transform of at + the Laplace transform of bt^2.

The Laplace transform of at is a/s, and the Laplace transform of bt^2 is 2b/s^3. Therefore, the Laplace transform of a bt + ct^2 is:

a/s + 2b/s^3

This is the direct answer to the problem.

In more detail, the Laplace transform is a mathematical tool that allows us to convert a function of time into a function of complex frequency. It is defined as the integral of the function multiplied by the exponential function e^(-st), where s is the complex frequency parameter. The Laplace transform has many applications in engineering, physics, and mathematics, particularly in the analysis of linear time-invariant systems.

In this problem, we used the linearity property of the Laplace transform to find the Laplace transform of a bt + ct^2. This property states that the Laplace transform of a linear combination of functions is equal to the linear combination of their Laplace transforms. We first found the Laplace transform of at and bt^2 separately using the Laplace transform formulas. Then, we added them together to obtain the Laplace transform of a bt + ct^2.

Learn more about Laplace Transform:

https://brainly.com/question/30401252

#SPJ11

The Laplace transform of a bt + ct^2 for some constants a, b, and c can be found using the linearity property of the Laplace transform. The Laplace transform of a linear combination of functions is equal to the linear combination of their Laplace transforms. Therefore, the Laplace transform of a bt + ct^2 is equal to the Laplace transform of at + the Laplace transform of bt^2.

The Laplace transform of at is a/s, and the Laplace transform of bt^2 is 2b/s^3. Therefore, the Laplace transform of a bt + ct^2 is:

a/s + 2b/s^3

This is the direct answer to the problem.

In more detail, the Laplace transform is a mathematical tool that allows us to convert a function of time into a function of complex frequency. It is defined as the integral of the function multiplied by the exponential function e^(-st), where s is the complex frequency parameter. The Laplace transform has many applications in engineering, physics, and mathematics, particularly in the analysis of linear time-invariant systems.

In this problem, we used the linearity property of the Laplace transform to find the Laplace transform of a bt + ct^2. This property states that the Laplace transform of a linear combination of functions is equal to the linear combination of their Laplace transforms. We first found the Laplace transform of at and bt^2 separately using the Laplace transform formulas. Then, we added them together to obtain the Laplace transform of a bt + ct^2.

Learn more about Laplace Transform:

https://brainly.com/question/30401252

#SPJ11

To find the line integral ∫C sin(2z) dz, where C is the curve given by z(t) = 2cost + i(2sint) for t in the interval [0, π/2], we can parametrize the curve and then evaluate the integral using the given parametrization.

We start by parameterizing the curve C with respect to t: z(t) = 2cost + i(2sint), where t varies from 0 to π/2. Differentiating z(t) with respect to t, we get dz = -2sint dt + 2cost dt. Now we substitute the parameterization and dz into the line integral: ∫C sin(2z) dz = ∫[0,π/2] sin(2(2cost + i(2sint))) (-2sint dt + 2cost dt). Simplifying the integral, we have: ∫[0,π/2] sin(4cost + 4isint) (-2sint dt + 2cost dt). Expanding the sine function using the angle sum formula, we get: ∫[0,π/2] sin(4t) (-2sint dt + 2cost dt). Evaluating this integral gives the final result.

To know more about line integrals here: brainly.com/question/30763905

#SPJ11

She should dock her boat at 5.81 kilometers.

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is traveling along a route.

Given:

Distance and rate to get to her grandmother's house, little red riding hood first rows a bot along a river at a speed of 10 km/hr and then walks through the woods at 4 km/hr.

If she starts from a point that is 7 km south and 12 km west of grandma's house,

then the distance is  d + √{(7−d)²+12²}.

The total time it takes her to reach her grandmother's house is:

d/10 + √{(7−d)²+12²}/4.

To find the value of d that makes the total time exactly 3 hours,

d/10 + √{(7−d)²+12²}/4 = 3.

2d + 5√(7−d)²+12² = 60

4d²+ 100d+25(7−d)² + 25(12²) = 3,600

d ≈ 9.19 or 5.81

Therefore, the only valid solution is d ≈ 5.81 kilometers.

To learn more about the speed;

https://brainly.com/question/7359669

#SPJ1

Answer:

x= 52

y= 25

z= 90

pls mark me as BRAINLIAST

Answer:

351 ccm

Step-by-step explanation:

Let's split the prism in a rectangular prism and a triangular prism:

- the volume of the rectangular prism is 6 * 5 * 9 = 270 ccm

- the volume of the triangular prism is base of the surface x height:
   (3 * 6)/2 * 9 = 81 ccm

Total volume is 270 + 81 = 351 ccm

Step-by-step explanation:

As we observe on the prism we have the

. slant height of 9cm

. height of base of 6cm

. long side of the base of 8cm

. short side of the base which is 5 cm

So as we know the volume of the prism is A=(BA(base area)* slant Height)  /2      

So the area of the trapezium is A=((B(long base side)+b (short base side ))*h)/2

it's A=((8+5)*6)/2=39 square centimeters

So the volume is=(39*9)/2=175.5 cubic centimeters

The rate at which the water level is rising when it is 5 meters high is approximately 0.477 m/min

The volume of a conical tank:
V = (1/3)πr^2h
where V is the volume of the tank, r is the radius, and h is the height.
Differentiating both sides with respect to time, we get:
dV/dt = (1/3)π(2rh dr/dt + r^2 dh/dt)
Where dV/dt is the rate at which the volume is changing (in m^3/min), and dr/dt and dh/dt are the rates at which the radius and height are changing, respectively.
We know that water is pouring into the tank at a rate of 6m^3/min, so we can substitute this value for dV/dt. We also know that the height of the water level is rising, so dh/dt is what we need to find. Finally, we know that when the water level is 5 meters high, the radius of the water surface can be found using similar triangles:
r/h = 4/10
r = (4/10)h = 0.4h
Now we can substitute all of these values into the formula and solve for dh/dt:
6 = (1/3)π(2(0.4h)(dh/dt) + (0.4h)^2 dh/dt)
6 = (1/3)π(0.8h + 0.16h^2) dh/dt
dh/dt = 6 / [(1/3)π(0.8h + 0.16h^2)]
When the water level is 5 meters high, h = 5, so:

dh/dt = 6 / [(1/3)π(0.8(5) + 0.16(5)^2)]

dh/dt = 0.477m/min

Therefore, the rate at which the water level rises when it is 5 meters high is approximately 0.477 m/min.

Learn more about volume

https://brainly.com/question/29218467

#SPJ11

In Algebra 2, students typically use a scientific calculator.

A scientific calculator has advanced functions beyond basic arithmetic operations.

Some of the functions commonly used in Algebra 2 include logarithms, exponents, trigonometric functions, and statistical calculations. Therefore, a scientific calculator with these functions would be most useful for Algebra 2.

Examples of calculators that are often used in Algebra 2 include the TI-84 Plus , the TI-Nspire CX, the Casio fx-9750GII, and the HP Prime Graphing Calculator.

Know more about scientific calculator here:

https://brainly.com/question/2059390

#SPJ11

Answer:

what are the answers?

Step-by-step explanation:

Otherwise it isn't answerable

The association between lung function (FEV) and age can be observed through the analysis of the provided output from R.

The output from R likely includes statistical measures such as correlation coefficients or regression analysis results to determine the relationship between FEV and age. These calculations can help quantify the association between the two variables. For example, a correlation coefficient can indicate the strength and direction of the relationship, where a positive value suggests a positive association between FEV and age.

Based on the provided output from R, it can be concluded that there is an association between lung function (FEV) and age. However, without the actual output or specific statistical measures, it is challenging to provide further details or draw more precise conclusions. It is important to consider that the association between FEV and age may not necessarily imply causation, as other factors such as lifestyle, health conditions, and genetics can also impact lung function. Further analysis and additional data would be necessary to fully understand the nature and significance of this association.

Overall, it is reasonable to conjecture that lung function (FEV) changes with age, but a comprehensive analysis of the provided output and additional research would be required to establish the precise relationship between the two variables.

To know more about statistical measures, visit;
https://brainly.com/question/32611082
#SPJ11

Answer:

y <= 40

Step-by-step explanation:

Let's call the number of people traveling by van "x", and the number of people buying train tickets "y". We know that the total number of people in the group is 40, so we can write the equation:

x + y = 40

And we also know that the van can hold up to 12 people, so we can write the inequality:

0 <= x <= 12

Now, to find the number of train tickets, we just need to substitute

x = 40 - y into the second inequality:

0 <= 40 - y <= 12

Expanding and solving for y, we get:

0 <= 40 - y <= 12

-40 <= -y <= -28

y >= 28

y <= 40

So the number of train tickets needed (y) is equal to or greater than 28 and equal to or less than 40.

Answer:

Inequality:    12 + x ≤ 40

Solution:   x ≤ 28

Step-by-step explanation:

Let x be the number of train tickets that the group will need.

As the van holds 12 people and the rest will buy train tickets, an expression for the total number of people is:

If the group is up to 40 people then 12 + x will be less than or equal to 40:

Therefore, the inequality that can be used to find the number of train tickets that the group will need is:

To solve the inequality, subtract 12 from both sides:

⇒ 12 + x - 12 ≤ 40 - 12

⇒ x ≤ 28

Therefore the number of train tickets that the group will need is less than or equal to 28 tickets.

The area of the part of the plane 3x 2y z = 6 that lies in the first octant  is  mathematically given as

A=3 √(4) units ^2

Generally, the equation for is  mathematically given as

The Figure is the x-y plane triangle formed by the shading. The formula for the surface area of a z=f(x, y) surface is as follows:

\(A=\iint_{R_{x y}} \sqrt{f_{x}^{2}+f_{y}^{2}+1} d x d y(1)\)

The partial derivatives of a function are f x and f y.

\(\begin{aligned}&Z=f(x)=6-3 x-2 y \\&=\frac{\partial f(x)}{\partial x}=-3 \\&=\frac{\partial f(y)}{\partial y}=-2\end{aligned}\)

When these numbers are plugged into equation (1) and the integrals are given bounds, we get:

\(&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{(-3)^{2}+(-2)^2+1dxdy} \\\\&=\int_{0}^{2} \int_{0}^{3-\frac{3}{2} x} \sqrt{14} d x d y \\\\&=\sqrt{14} \int_{0}^{2}[y]_{0}^{3-\frac{3}{2} x} d x d y \\\\&=\sqrt{14} \int_{0}^{2}\left[3-\frac{3}{2} x\right] d x \\\\\)

\(&=\sqrt{14}\left[3 x-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3-\frac{3}{2} \cdot \frac{1}{2} \cdot x^{2}\right]_{0}^{2} \\\\&=\sqrt{14}\left[3.2-\frac{3}{2} \cdot \frac{1}{2} \cdot 3^{2}\right] \\\\&=3 \sqrt{14} \text { units }{ }^{2}\)

In conclusion,  the area is

A=3 √4 units ^2

Read more about the plane

https://brainly.com/question/1962726

#SPJ4

Answer: x < 25

Step-by-step explanation:

2/3(x+2)-1/2(x-4)>1/4(x+5)

2/3x+4/3-1/2x+2>1/4x+5/4

Multiply both sides by 12

8x+40-6x>3x+15

2x+40>3x+15

2x-3x>15-40

-x > -25

x<25

Answer:

{x:x=[[3,4,5,6...]}

Step-by-step explanation:

x∈W

\(\frac{2}{3}(x+2)-\frac{1}{2}(x-4)>\frac{1}{4}(x+5)\\\frac{2x+4}{3}-\frac{x+4}{2}>\frac{x+5}{4} \\\frac{2(2x+4)-3(x+4)}{2*3}>\frac{x+5}{4} \\\frac{4x+8+3x-12}{6}>\frac{x+5}{4} \\\frac{x}{y} \frac{x-4}{6}>\frac{x+5}{4}\\ 4(x-4)>6(x+5)\\ 4x-16>6x+30\\ 4x-6x>30+16\\ -2x>46\\ x<-23\\x= no solution\)

Answer:

"+"

Step-by-step explanation:

Multiply 5 through out the bracket

5/2 q + 15r - 9r - 20s

5/2q + 6r - 20s

Answer:

the system has no solutions

Step-by-step explanation:

the systems are shaded in different directions with no part of them intersecting

this means that there are no solutions