Emily borrows £580 from a bank at an interest rate of 896 per year.
She will give the money back after 4 years.
How much money will Emily have to pay back?

Step-by-step explanation:

The photo above is the Venn diagram

Now, the number of persons that are both managers and engineers= n

Since, Total number of persons is 50

Therefore, 50= M+n+E

M only = 36-n

E only = 24-n

Therefore, 50= 36 - n + n + 24 - n

50 = 36+24-n

50 = 60 - n

60 - n = 50

-n = 50 - 60

-n = - 10

Therefore, n = 10

Therefore, the number of persons that are both Managers and Engineers is 10persons.

Answer:

vr

Step-by-step explanation:

konho bi  m

9514 1404 393

Answer:

  r = 18

Step-by-step explanation:

Let d represent the number of districts. The given information lets us write two equations:

  3d = 27 . . . . . the number of state senators

  d +r = 27 . . . . the number of representatives

The first equation tells us ...

  d = 27/3 = 9

The the second equation tells us ...

  r = 27 -d = 27 -9 = 18

The number of at-large representatives is r = 18.

The length of the curve (and thus the total distance traveled by the particle along the curve) is

[tex]\displaystyle\int_0^{3\pi}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt[/tex]

We have

x(t) = 3 sin²(t )   ==>   x'(t) = 6 sin(t ) cos(t ) = 3 sin(2t )

y(t) = 3 cos²(t )   ==>   y'(t) = -6 cos(t ) sin(t ) = -3 sin(2t )

Then

√(x'(t) ² + y'(t) ²) = √(18 sin²(2t )) = 18 |sin(2t )|

and the arc length is

[tex]\displaystyle 18 \int_0^{3\pi} |\sin(2t)| \,\mathrm dt[/tex]

Recall the definition of absolute value: |x| = x if x ≥ 0, and |x| = -x if x < 0.

Now,

• sin(2t ) ≥ 0 for t ∈ (0, π/2) U (π, 3π/2) U (2π, 5π/2)

• sin(2t ) < 0 for t ∈ (π/2, π) U (3π/2, 2π) U (5π/2, 3π)

so we split up the integral as

[tex]\displaystyle 18 \left(\int_0^{\pi/2} \sin(2t) \,\mathrm dt - \int_{\pi/2}^\pi \sin(2t) \,\mathrm dt + \cdots - \int_{5\pi/2}^{3\pi} \sin(2t) \,\mathrm dt\right)[/tex]

which evaluates to 18 × (1 - (-1) + 1 - (-1) + 1 - (-1)) = 18 × 6 = 108.

This is a question that asks about the advantages of a systematic random sampling. Thus, we first take a look at the types of sampling, and then we see the advantage of systematic random sampling.

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

Systematic:

One of the bigger advantages is that the systematic sampling eliminate clusters, which means that the last option is wrong.

Inadvertently missing patterns is a problem in systematic sampling, and not an advantage, thus the third option is also wrong.

It also does not reduce sampling variability, thus the first option is wrong.

From this, it can be concluded that the correct option is:

Systematic random sampling does not require a finite population size.

For another example of systematic random sampling, you can check https://brainly.com/question/21100042

Solution :

Given :

There are five cities in a network and the cost of [tex]\text{building}[/tex] a road directly between [tex]i[/tex] and [tex]j[/tex]  is the entry [tex]a_{i,j}[/tex]

[tex]a_{i,j}[/tex]  refers to the matrix.

Road cannot be built because there is a mountain.

The given matrix :

[tex]\begin{bmatrix}0 & 3 & 5 & 11 & 9\\ 3 & 0 & 3 & 9 & 8\\ 5 & 3 & 0 & \infty & 10\\ 11 & 9 & \infty & 0 & 7\\ 9 & 8 & 10 & 7 & 0\end{bmatrix}[/tex]

The matrix on the left above corresponds to the weighted graph on the right.

Using the [tex]\text{Kruskal's algorithm}[/tex] we can select the cheapest edge that is not creating a cycle.

Starting with 2 edges of weight 3 and the edge of weight 5 is forbidden but the edge is 7  is available.

The edge of the weight 8 completes a minimum spanning tree and total weight 21.

If the edge of weight 8 had weight 10 then either of the edges of weight 9 could be chosen the complete the tree and in this case there could be 2 spanning trees with minimum value.

Answer:

the average number of cars waiting in line L[tex]q[/tex] is 0.45

Step-by-step explanation:

Given the data in the question;

Cars arrive at an automatic car wash system every 10 minutes on average.

Car arrival rate λ = 1 per 10 min = [ 1/10 × 60 ]per hrs = 6 cars per hour

Washing time for each is 6 minutes per car

Car service rate μ = 6min per car = [ 1/6 × 60 ] per hrs = 10 cars per hour

so

P = λ/μ = 6 / 10 = 0.6

Using the length of queue in M/D/1 system since there is only one service bay;

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ P² / ( 1 - P ) ]

so we substitute

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ (0.6)² / ( 1 - 0.6 ) ]

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.36 / 0.4 ]

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.9 ]

L[tex]q[/tex] = 0.45

Therefore, the average number of cars waiting in line L[tex]q[/tex] is 0.45

Answer:

The answer is 21.98. I just took area of the whole circle and subtracted it with the area of two circles in it

Answer:

21. 99

Step-by-step explanation:

[tex]s = \pi \times {r}^{2} \\ s1 = 3.14 \times 9 = 28.27 \\ s2 = 3.14 \times 1 = 3.14 \\ a = 28.27 - (3.14 \times 2) = 28.27 - 6.28 = 21.99[/tex]

Answer:

f

Step-by-step explanation:

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

Answer:

The Poisson's ratio for the material is 0.0134.

Step-by-step explanation:

The Poisson's ratio ([tex]\nu[/tex]), no unit, is the ratio of transversal strain ([tex]\epsilon_{t}[/tex]), in inches, to axial strain ([tex]\epsilon_{a}[/tex]), in inches:

[tex]\nu = -\frac{\epsilon_{t}}{\epsilon_{a}}[/tex] (1)

[tex]\epsilon_{a} = l_{a,f}-l_{a,o}[/tex] (2)

[tex]\epsilon_{t} = l_{t,f}-l_{t,o}[/tex] (3)

Where:

[tex]l_{a,o}[/tex] - Initial axial length, in inches.

[tex]l_{a,f}[/tex] - Final axial length, in inches.

[tex]l_{t,o}[/tex] - Initial transversal length, in inches.

[tex]l_{t,f}[/tex] - Final transversal length, in inches.

If we know that [tex]l_{a,o} = 61.2\,in[/tex], [tex]l_{a,f} = 61.235\,in[/tex], [tex]l_{t,o} = 2.7\,in[/tex] and [tex]l_{t,f} = 2.69953\,in[/tex], then the Poisson's ratio is:

[tex]\epsilon_{a} = 61.235\,in - 61.2\,in[/tex]

[tex]\epsilon_{a} = 0.035\,in[/tex]

[tex]\epsilon_{t} = 2.69953\,in - 2.7\,in[/tex]

[tex]\epsilon_{t} = -4.7\times 10^{-4}\,in[/tex]

[tex]\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}[/tex]

[tex]\nu = 0.0134[/tex]

The Poisson's ratio for the material is 0.0134.

First check the characteristic solution. The characteristic equation to this DE is

r ² - r = r (r - 1) = 0

with roots r = 0 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(0x) + C₂ exp(1x)

y (char.) = C₁ + C₂ exp(x)

For the particular solution, we try the ansatz

y (part.) = (ax + b) exp(x)

but exp(x) is already accounted for in the second term of y (char.), so we multiply each term here by x :

y (part.) = (ax ² + bx) exp(x)

Differentiate this twice and substitute the derivatives into the DE.

y' (part.) = (2ax + b) exp(x) + (ax ² + bx) exp(x)

… = (ax ² + (2a + b)x + b) exp(x)

y'' (part.) = (2ax + 2a + b) exp(x) + (ax ² + (2a + b)x + b) exp(x)

… = (ax ² + (4a + b)x + 2a + 2b) exp(x)

(ax ² + (4a + b)x + 2a + 2b) exp(x) - (ax ² + (2a + b)x + b) exp(x)

= x exp(x)

The factor of exp(x) on both sides is never zero, so we can cancel them:

(ax ² + (4a + b)x + 2a + 2b) - (ax ² + (2a + b)x + b) = x

Collect all the terms on the left side to reduce it to

2ax + 2a + b = x

Matching coefficients gives the system

2a = 1

2a + b = 0

and solving this yields

a = 1/2, b = -1

Then the general solution to this DE is

y(x) = C₁ + C₂ exp(x) + (1/2 x ² - x) exp(x)

For the given initial conditions, we have

y (0) = C₁ + C₂ = 6

y' (0) = C₂ - 1 = 5

and solving for the constants here gives

C₁ = 0, C₂ = 6

so that the particular solution to the IVP is

y(x) = 6 exp(x) + (1/2 x ² - x) exp(x)

Answer:

1100 and 130 (km/h)

Step-by-step explanation:

1. if the velocity of the wind is 'w' and the velocity of the plane in still air is 'p', then

2. it is possible to make up two equations:

the fly against the wind: (p-w)*8=7760;

the fly with the wind: (p+w)*3=3690.

3. if to solve the system made up, then:

[tex]\left \{ {{3(p+w)=3690} \atop {8(p-w)=7760}} \right. \ => \ \left \{ {{p+w=1230} \atop {p-w=970}} \right. \ => \ \left \{ {{p=1100} \atop {w=130}} \right.[/tex]

4. the required rate of the plane in still air is p=1100 km/h; the rate of the wind is w=130 km/h.

Answer:

y=x216–6x16+4116

Step-by-step explanation:

plato :)

The equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.

It is defined as the graph of a quadratic function that has something bowl-shaped.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

The equation of a parabola that has a vertical axis, passes through the point (–1, 3)

The vertex of the parabola is at (3, 2)

As we know, in the standard form of the parabola (h, k) represents the vertex of the parabola.

h = 3

k = 2

Plug the above point in the equation:

[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]

x = 3

y = 2

[tex]\rm 2\ =\ \dfrac{3^{2}}{16}-\dfrac{6(3)}{16}+\dfrac{41}{16}[/tex]

= 9/16 - 18/16 + 41/16

= (9-18+41)/16

= 32/16

2 = 2 ( true)

The equation of the parabola is:

[tex]\rm y\ =\ \dfrac{x^{2}}{16}-\dfrac{6x}{16}+\dfrac{41}{16}[/tex]

Thus, the equation of the parabola is in option (C) if the parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2) option (C) is correct.

Learn more about the parabola here:

brainly.com/question/8708520

#SPJ2

Answer:

5 is the answer to your question

Step-by-step explanation:

the numbers are increasing by +5

Answer:

y=-4x+2

Step-by-step explanation:

Hi there!

We want to find out which equation represents a line with a slope of -4 and a y intercept of (0,2)

The most common way to write the equation of the line is in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

We have everything we need to plug into the equation, let's just label the values to avoid confusion

m=-4

b=2 (when you substitute the y intercept as b, b is the value of y in the point)

Now substitute into the equation

y=-4x+2

Hope this helps!

Answer:

The FitnessGram™ Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. [beep] A single lap should be completed each time you hear this sound. [ding] Remember to run in a straight line, and run as long as possible. The second time you fail to complete a lap before the sound, your test is over.ep explanation:

Answer:

The height of the spanning tree is one by the breadth-first search at the central vertex of Wn.

Step-by-step explanation:

The graph is connected and has a spanning tree where the tree can build using a depth-first search of the graph. Start with chosen vertex, the graph as the root, and root add vertices and edges such as each new edge is incident with vertex and vertices are not in path. If all vertices are included, it will do otherwise, move back to the next level vertex and start passing. It is for depth-first search. For breadth-first search, start with chosen vertex add all edges incident to a vertex. The new vertex is added and becomes the vertices at level 1 in the spanning tree, and each vertex at level 1 adds each edge incident to vertex and other vertex connected to the edge of the tree as long as it does not produce.

Answer:

Easy, all you ha

Step-by-step explanation:

Answer:

B) 32

Step-by-step explanation:

(sin 74) / 10 = (sin c) / 10

c = 74

180 - 74 -74

= 32

1) I think 15 choose (d)

2) The choose (C) -4fg+4g

3) The choose (d) 3xy/2

4) The choose (a) ab/6

5) The choose (C) 2p+4q-6

6)

[tex]\pi {r}^{2} h = 3.14 \times {3}^{2} \times 1.5 = 42.39 {m}^{3} = 42.390 {m}^{3} [/tex]

Point 6 I think there is an error because the unit m must be m³ because it is r² (m²) and h(m) becomes m³.

I hope I helped you^_^

Step-by-step explanation:

Step 1:  Factor the equation

[tex]f(x) = -16x^{2} + 22x + 3\\f(x) = -(8x + 1)(2x - 3)[/tex]

Step 2:  Find the x-intercepts of the graph of f(x)

[tex]-8x - 1 + 1 = 0 + 1\\-8x / -8 = 1 / -8\\x = -1/8[/tex]

[tex]2x - 3 + 3 = 0 + 3\\2x / 2 = 3 / 2\\x = 3/2[/tex]

Step 3:  Describe the end behavior of the graph of f(x)

Since the function is to the power of 2, that means that it is a parabola.  And since the leading coefficient is negative, means that the arrows will be pointing down therefore, the end behavior of this graph is as x goes to infinity, f(x) goes to negative infinity and as x goes to negative infinity, f(x) goes to negative infinity.

Step 4:  What are the steps you would use to graph f(x)

The first step that I would do is factor the equation.  Then I would find the x-intercepts of the graph and plot them on the graph.  I would then plug in 0 for all of the x values to get the y intercept.  After doing that I would get the vertex using the vertex formula plotting it on the graph.  Finally, I would connect all of the dots together to form the graph of the equation.

Answer:

The person above me is correct!

9514 1404 393

Answer:

  x = 7

Step-by-step explanation:

10.5 maps to x with a scale factor of 2/3:

  x = 10.5 × 2/3

  x = 7

1st rectangle:

width: 2.48cm

length: 4.96

2nd rectangle:

width: 4.96 (equals to the length of the 1st rectangle)

area: 9.92

length: 9.92/4.96 = 2

Answer:

Sorry, i dont know

Step-by-step explanation:

I dont know the answer to this question.....

Answer:

90in2

Step-by-step explanation:

3x5x6=90

Answer:

C.90

Step-by-step explanation:

first multiply 3 and 5 which is 15 then times it with 6 which equals 90

Answer:

A

Step-by-step explanation:

(2x-3)=4x, x=-3/2 which isn't possible as x>3/2

-(2x-3)=4x, x=1/2.

Hence the answer is x=1/2

(a) We have ⌊x⌋ = 5 if 5 ≤ x < 6, and similarly ⌊x/3⌋ = 5 if

5 ≤ x/3 < 6   ==>   15 ≤ x < 18

(b) ⌊x⌋ = -2 if -2 ≤ x < -1, so ⌊x/3⌋ = -2 if

-2 ≤ x/3 < -1   ==>   -6 ≤ x < -3

In general, ⌊x⌋ = n if n ≤ x < n + 1, where n is any integer.

I do not understand what is being asked in (c) and (d), so you'll have to clarify...