jack is paid £1800 a month. he spends half his money on rent. he spends the rest on food, bills and savings in the ratio 4:3:2 how much does he spend on bills?

Answer:

-32 or 4x -8

Step-by-step explanation:

-2 ( -3x + 2 ) : 6x - 4

= 6x -4 - 2 ( x + 2 )

- 2 ( x + 2 ) : - 2x -4

=6x - 4 - 2x - 4

= 6x -2x - 4 - 4

= 6x - 2x - 8

= 4x - 8

= -32  

( Im not really sure what is the answer )

( the "x" is alphabet, not "times" )

Answer:

97.336 (unit)³

Step-by-step explanation:

V=a³=(4.6)³=97.336 (unit)³

Answer:

h-2

Step-by-step explanation:

-2x5=-10

8-10=-2

=h-2

Market researchers want to know what factors influence customers to spend more time in a shop. They have estimated the probability density function of the time spent in the shop to be f(x) = { sin(πx/40)/20, 0 ≤ x ≤ 40}. Using the symmetry of f(x), the expected value of time spent in the shop can be calculated to be 20 minutes.

The market researchers are interested in understanding what makes customers stay longer in the shop. To do this, they have estimated the probability density function of the time spent in the shop to be f(x) = { sin(πx/40)/20, 0 ≤ x ≤ 40}.

The expected value of time spent in the shop can be calculated by finding the mean of the probability density function. As the function is symmetric around x = 20, we can use the symmetry to simplify the computation. This gives us:

E(T) = ∫₀⁴₀ x f(x) dx = 2 ∫₀²₀ x f(x) dx

= 2 ∫₀²₀ x sin(πx/40)/20 dx

= (1/π) ∫₀⁴₀ 40t sin(t) dt (where t = πx/40)

= (1/π) [40 sin(t) - 40t cos(t)] from t = 0 to t = π

= (1/π) [40 sin(π) - 40(π) cos(π) - 40 sin(0) + 40(0) cos(0)]

= 20

Therefore, the expected value of time spent in the shop is 20 minutes.

The researchers plan on interviewing customers who spend more than one standard deviation longer or shorter than the expected value of time spent in the shop. The standard deviation can be calculated using the formula:

σ = √[∫₀⁴₀ (x - 20)² f(x) dx]

= √[2 ∫₀²₀ (x - 20)² f(x) dx]

= √[2 ∫₀²₀ (x² - 40x + 400) sin(πx/40)/800 dx]

= √[(1/π²) ∫₀⁴₀ (t² - 80t + 1600) sin(t) dt] (where t = πx/40)

= √[(1/π²) (π/2)]

= √(2/π)

≈ 0.7979

Therefore, the researchers will ask a customer for an interview if they spend more than 20 + 0.7979 × 1 = 20.7979 minutes or less than 20 - 0.7979 × 1 = 19.2021 minutes in the shop.

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There will be $21,935.05 in retirement account on the day of retirement.

To calculate the amount of money you will have in your retirement account on the day you retire:

The annual contribution to your retirement account is $4,500.

The interest rate is 9.5% per year.

You plan to retire in 43 years.

To calculate the amount of money in your retirement account, we can use the following formula:

retirement fund = annual contribution * (1 + interest rate)**number of years

Plugging in the values for the annual contribution, interest rate, and number of years, we get:

retirement fund = 4500 * (1 + 0.095)**43 = 21935.05

Therefore, you will have $21,935.05 in your retirement account on the day you retire.

Correct Question:

You are trying to decide how much to save for retirement. Assume you plan to save $4,500 per year with the first investment made one year from now. You think you can earn 9.5​% per year on your investments and you plan to retire in 43 ​years, immediately after making your last $4,500 investment. How much will you have in your retirement account on the day you​ retire?

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x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

The curve of intersection between the cylinder x^2 + y^2 = 1 and the plane y + z = 2 is a circle lying on the plane y + z = 2. The parametric equations for this curve are x = cos(θ), y = sin(θ), and z = 2 - sin(θ), where θ is the parameter representing points on the circle.

To find the parametric equations for the curve of intersection between the cylinder and the plane, we can start by parameterizing the cylinder using the angle θ. Since the equation x^2 + y^2 = 1 represents a circle in the x-y plane with radius 1, we can use θ as a parameter to represent points on this circle.

The parametric equations for the cylinder are:

x = cos(θ)

y = sin(θ)

z = 2 - y

Next, we substitute these equations into the plane equation y + z = 2 to determine the intersection points. By substituting y and z, we have sin(θ) + 2 - sin(θ) = 2, which simplifies to sin(θ) - sin(θ) = 0. This implies that the plane equation is satisfied for any value of θ.

Therefore, the intersection between the cylinder and the plane is the entire cylinder itself, lying on the plane y + z = 2. The parametric equations for the curve of intersection are x = cos(θ), y = sin(θ), and z = 2 - sin(θ).

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The probability that for the second​ sample, the mean number of hours worked will be greater than 15.2​ is 0.567.

What is probability?

The probability of an event can be determined using probability. Only the likelihood that an event will occur can be estimated using it. A scale from 0 to 1, where 0 represents impossibility and 1 represents a specific occurrence.

We are given that among a random sample of 250 college​ students, the mean number of hours worked per week at​ non-college related jobs is 15.2 and that this mean lies 1.5 standard​ deviation(s) above the mean of the sampling distribution.

So, here Z = 1.5

Therefore,

⇒ P (X > 15.2) = 1 - P (X < 15.2)

⇒ P (X > 15.2) = 1 - 0.433

⇒ P (X > 15.2) = 0.567

Hence, the probability that for the second​ sample, the mean number of hours worked will be greater than 15.2​ is 0.567.

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The acceleration of the mass at time t=1 is approximately -19.42 inches/second^2.

To find the velocity and acceleration of the mass attached to a vertical spring at time t=1, we need to differentiate the position function with respect to time.

First, we can find the velocity function v(t) by taking the derivative of the position function s(t) with respect to time t:

v(t) = s'(t) = 5cos(2t) * 2 = 10cos(2t)

Plugging in t=1, we get:

v(1) = 10cos(2) ≈ -3.42 inches/second

Therefore, the velocity of the mass at time t=1 is approximately -3.42 inches/second.

Next, we can find the acceleration function a(t) by taking the derivative of the velocity function v(t) with respect to time t:

a(t) = v'(t) = -20sin(2t)

Plugging in t=1, we get:

a(1) = -20sin(2) ≈ -19.42 inches/second^2

Therefore, the acceleration of the mass at time t=1 is approximately -19.42 inches/second^2.

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Answer:

The teacher has 6 candies left.

Step-by-step explanation:

do 12 times 18, then divide that by 30. The remainder is your answer.

The first four-term of the sequence is found by the given equation \(a_{n-1} = 4a_n\) is given as 144, 36, 9, and 9/4.

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

The given equation will be

\(\rm a_n = \dfrac{a_{n-1}}{4} \\\\a_{n-1} = 4a_n\)

And

\(a_4 = 2 \dfrac{1}{4} = \dfrac{9}{4}\)

For n = 4, we have

\(\rm a_{4-1} = 4a_4\\\\a_3 \ \ \ = 4*\dfrac{9}{4} \\\\ a_3 \ \ \ = 9\)

For n = 3, we have

\(\rm a_{3-1} = 4a_3\\\\a_2 \ \ \ = 4*9 \\\\ a_2 \ \ \ = 36\)

For n = 2, we have

\(\rm a_{2-1} = 4a_2\\\\a_1 \ \ \ = 4*36 \\\\ a_1 \ \ \ = 144\)

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Answer:

144

36

9

Step-by-step explanat

The distance between the 3rd lamppost and 8 th lamppost is 100 meters.

EXPLANATION:

If the distance between 2 lampposts is 40 meters, you would divide the neters by 2. This would give you the answer of 20, meaning the distance between lampposts is 20 meters. So multiply 20 * 5 to get the distance between the third lampost and eight lamppost.

Answer:

$16

Step-by-step explanation:

Given data

Total amount= $132,624

Cost of each hard drive=  $112

Total number of hard drive=1184

Cost of all the hard drives=  112*1184

Cost of all the hard drives=$132608

Balance will be= 132,624-132608

Balance will be= $16

A- The average rate of change of g(x) over the interval [-2, 2] is 4, B- the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.

A) To find the average rate of change of the function g(x) over the interval [-2, 2], we need to compute the difference quotient:

average rate of change = [g(2) - g(-2)] / [2 - (-2)]

First, we find the values of the function at the endpoints of the interval:

g(-2) = \(-2^{3}\) - 6 = -14

g(2) = \(2^{3}\) - 6 = 2

Substituting these values into the

average rate of change = (2 - (-14)) / (2 - (-2)) = 16 / 4 = 4

Therefore, the average rate of change of g(x) over the interval [-2, 2] is 4.

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivatives of the function at x=-2 and x=2 using the power rule of differentiation:

g'(x) = 3\(x^{2}\)

g'(-2) = 3\(-2^{2}\) = 12

g'(2)  = 12

The instantaneous rate of change at x=-2 is 12, and the instantaneous rate of change at x=2 is also 12. These values are equal to the average rate of change over the interval [-2, 2], which is 4.

This means that the function g(x) is not a linear function over the interval [-2, 2], and the instantaneous rates of change at the endpoints are different from the average rate of change over the interval.

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The amount of each semi-annual interest payment on the bond is $5,100 (second option)

A bond is a debt instrument that is used by companies or the government to raise capital needed for its operation. A person who buys a bond is known as a bondholder.

A bondholder is entitled to regular interest payment. The interest paid to the bondholder is a function of the par value of the bond and the market interest rate. At the maturity of the bond, the bondholder is paid back the par value of the bond.

Interest payment = par value of the bond x interest rate x (1.number of times the interest is paid)

Interest payment = $170,000 x 0.06 x 1/2

Interest payment = $5,100

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The probability that no two teams win the same number of games, P ≈ 2.084 × 10⁻⁴⁵³

The reason for arriving at the above probability is as follows:

The given parameters are;

The number of teams in the tournament, n = 60

The chance of a team winning a game = 50% = 0.5

The number of ties = No ties

The required parameter:

The probability that no two teams win the same number of games

Method:

Calculate the number of ways no two teams win the same number of games, and divide the result by the total number of possible outcomes

Solution:

The number of matches played, n = \(\dbinom {60} {2}\) = 1,770

The possible outcomes = 2; Winning or losing

The total number of possible outcomes, \(n_p\) = 2¹⁷⁷⁰

The number of games won by each team is between 0 and 59

The ways in which no two teams won the same number of games is given by the games won by the teams to be 0, 1, 2,..., 57, 58, 59

Therefore, the number of ways no two teams won the same number of games, the required outcomes, \(n_k\) = 59!

\(Probability = \dfrac{Number \ of \ possible \ outcomes}{Number \ of \ required\ outcomes}\)

The probability that no two teams win the same number of games is given as follows;

\(\mathbf{P(No \ two \ teams \ won \ the \ same \ number \ of \ games)} = \dfrac{n_k}{n_p}\)

Therefore;

\(P(No \ two \ teams \ won \ the \ same \ number \ of \ games) = \dfrac{59!}{2^{1,770}} \approx \mathbf{2.084 \times 10^{-453}}\)

The probability that no two teams win the same number of games, P ≈ 2.084 × 10⁻⁴⁵³

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Answer:

A

Step-by-step explanation:

A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

After that, we need to substitute the values of x's and y's into the coordinate geometry.

If we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.

In all options, there is a scale factor so it will change area but in option C

A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.

Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".

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To find the line of best fit we follow this steps:

1. Calculate the mean of the x -values and the mean of the y -values

2. The following formula gives the slope of the line of best fit:

In our case, such computation will yield as a result:

The values of a and b are a = 4 and b = -1. Substituting these values into the equation y = ax^2 + bx, we get the parabola y = 4x^2 - x

To find the parabola with equation y = ax^2 + bx whose tangent line at (1, 3) has the equation y = 7x - 4, we need to determine the values of a and b.

The tangent line has the same slope as the derivative of the parabola at the point (1, 3). So, let's find the derivative of the parabola and evaluate it at x = 1.

y = ax^2 + bx

Differentiating both sides with respect to x:

dy/dx = 2ax + b

Now, evaluate dy/dx at x = 1:

7 = 2a(1) + b [Since the derivative is equal to the slope of the tangent line, which is 7]

Simplifying the equation:

2a + b = 7 ----(1)

Next, substitute the coordinates (x, y) = (1, 3) into the equation of the parabola:

3 = a(1)^2 + b(1)
3 = a + b ----(2)

We now have a system of two equations (equations (1) and (2)) with two unknowns (a and b). We can solve this system of equations to find the values of a and b.

From equation (2), we can express b in terms of a:

b = 3 - a

Substitute this value of b into equation (1):

2a + (3 - a) = 7

Simplifying:

2a + 3 - a = 7
a + 3 = 7
a = 7 - 3
a = 4

Now substitute the value of a back into equation (2) to find b:

b = 3 - a
b = 3 - 4
b = -1

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Answer:

The sequence 100, 50, 10, 5, 1, ... is NOT a geometric sequence because there is no single constant ratio that multiplies each term to get the next one.

Answer:

they arrive at the same time

Step-by-step explanation:

the triangle is like the Pythagorean theorm

both the purple lines equal a^2+b^2

and the green line equals c^2

a^2+b^2=c^2

Using mathematical operations to evaluate the equations, the only equation that fits is m/10 + 4.7 = 3.7

An expression is an algebraic statement that is made up of constant, variables etc. An equation on the other hand is two equal expression often times, there's are unknown variables which the values makes them equal to one another.

In this problem, we have to plug the value of m = 10 in all equations and see which fits, or we can simply just solve for m

a) 5m + 5 = -40

5m = -40 - 5

5m = -45

m = -9

This does not fit

b) m/10 + 4.7 = 3.7

multiply through by 10

m + 47 = 37

m = 37 - 47

m = -10

The equation is true.

c)  m / 2 + 21 = 15

collect like terms

m / 2 = 15 - 21

m / 2 = -6

m = -12

This is false

d)

-49 + 3m = 72

3m = 72 + 49

3m = 121

m = 40.3

This is not true

Only m /10 + 4.7 = 3.7 is true for m = -10

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Let's begin by identifying key information given to us:

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

Answer:

The answer is y^6/x^2

Step-by-step explanation:

If you can earn 8 percent on your money, the prize worth to you is: $76,812.50. To calculate the present value of the prize, we need to determine the current worth of receiving $1000 per month for 9 years, given an 8 percent annual interest rate.

This situation can be evaluated using the concept of the present value of an annuity. The present value of an annuity formula is used to find the current value of a series of future cash flows. In this case, the future cash flows are the $1000 monthly payments for 9 years. By applying the formula, which involves discounting each cash flow back to its present value using the interest rate, we find that the present value of the prize is $76,812.50.

This means that if you were to receive $1000 per month for 9 years and could earn an 8 percent return on your money, the equivalent present value of that prize, received upfront, would be $76,812.50.

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