Will and Ben win £1000 in a raffle
they give a fifth of it to charity and share what's left in the ratio 1:3.
How much is bens share

Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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a) If the student misses his alarm, the probability that he is not late to school is 0.25.

b) The probability that the student is late to school is 0.65.

c) One day, the student shows up to school on time. The probability that he missed his alarm is 0.59.

For A,

Let A be the event that the student wakes up on time, and B be the event that the student is late to school. We want to find P(B).

By definition,

P(B) = 1 - P(A)

where A is the event that the student misses his alarm.

Therefore,

P(B) = 1 - P(A)

= 1  -0.75

We are given that P(A') = 0.75, so

P(B) =0.25

For B,

To calculate the probability that the student is late to school, we will use the following formula:

P(X = x) = n!/(x!(n-x)!) * p^x * (1-p)^(n-x)

where:

P(X = x) is the probability that the student is late to school

n is the number of trials

x is the number of events

p is the probability of an event occurring

For this problem, we will let n = 1 and x = 1.

Now that we have our formula, we can plug in our values to solve for P(X = x).

P(X = x) = 1!/(1!(1-1)!) * 0.65^1 * (1-0.65)^(1-1)

P(X = x) = 0.65

We can interpret this answer as follows: there is a 0.65 probability that the student is late to school.

For C,

We first need to find the probability that the student did not miss his alarm, which is 1 - 0.59 = 0.41. We then need to find the probability that the student showed up to school on time given that he did not miss his alarm, which is 1 - 0.41 = 0.59.

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The answer should be 10

She will be able to make the recipe approximately 4 times with 500g of butter. Each recipe requires 125g of butter, so dividing 500g by 125g gives a result of 4.

Since the recipe requires 125g of butter and she buys 500g, dividing the total amount of butter (500g) by the required amount per recipe (125g) gives the number of times she can make the recipe (4).

Sure! To calculate the number of times Kaylin can make the recipe with 500g of butter, we need to divide the total amount of butter she has by the amount of butter required per recipe.

The recipe calls for 125 grams of butter. If Kaylin buys 500 grams of butter, we divide 500 by 125: 500g / 125g = 4.

So, she will be able to make the recipe approximately 4 times with 500g of butter. Each time she makes the recipe, she will use 125g of butter, and since she has 500g in total, she can repeat the process 4 times.

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The polygon has 10 sides.

Each side of the polygon has a measure of 8 cm.

Therefore, the required perimeter is given by:

Therefore, the required perimeter is 80 cm

Answer:

f(1) - 1 = -3

Step-by-step explanation:

Step 1: Find f(1)

f(1) = -3(1) + 1

f(1) = -3 + 1

f(1) = -2

Step 2: Find f(1) - 1

f(1) - 1 = -2 - 1

f(1) - 1 = -3

After one year, Nick will have approximately 135,168 clients.

To calculate the number of clients Nick will have after one year, we need to determine the number of months in one year and apply the doubling rate each month.

There are 12 months in one year.

Starting with 33 clients, we can calculate the number of clients after each month:

Month 1: 33 clients * 2 = 66 clients

Month 2: 66 clients * 2 = 132 clients

Month 3: 132 clients * 2 = 264 clients

...

Month 12: (previous month's clients) * 2 = final number of clients after one year

We can continue this pattern until reaching Month 12:

Month 4: 264 clients * 2 = 528 clients

Month 5: 528 clients * 2 = 1056 clients

Month 6: 1056 clients * 2 = 2112 clients

Month 7: 2112 clients * 2 = 4224 clients

Month 8: 4224 clients * 2 = 8448 clients

Month 9: 8448 clients * 2 = 16896 clients

Month 10: 16896 clients * 2 = 33792 clients

Month 11: 33792 clients * 2 = 67584 clients

Month 12: 67584 clients * 2 = 135,168 clients

Therefore, after one year, Nick will have approximately 135,168 clients.

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Answer:

B / 3 = 6 < 3

hope I helped.

The initial value that I might consider with that slope is the y-intercept. The y-intercept is the point where the line crosses the y-axis, and it is the value of y when x is 0. So, if the slope is 2, then the y-intercept might be 1. This would give us the following linear equation:

y = 2x + 1

This equation represents a line that has a slope of 2 and a y-intercept of 1.

(-4m-2)+(2y+5.5m)+(5+6.7y)

-4m + 5.5m = 1.5m

-2+5 = 3

2y+6.7y = 8.7y

Answer : 1.5m + 3 + 8.7y

Answer:

15 weeks

Step-by-step explanation:

Answer:

Step-by-step explanation:

6.15/5=1.23

The answer is B.

Answer:

C (6*2)

Step-by-step explanation:

Answer:

6 times 2

Step-by-step explanation:

Im not completely confident though so check other answers

The functions f(x) and f^-1(x) are inverse functions

The functions are given as

f(x) = (2x + 9)/(x + 2) and f^-1(x) = (2x - 9)/(2 - x)

To determine that they are inverse functions, we make use of the following:

using the above as a guide, we have the following:

f(f^-1(x)) = f((2x - 9)/(2 - x)) = (2((2x - 9)/(2 - x)) + 9)/(((2x - 9)/(2 - x)) + 2) = x

and

f^-1(f(x)) = f^-1((2x + 9)/(x + 2)) = (2((2x + 9)/(x + 2)) - 9)/(2 - (2x + 9)/(x + 2)) = x

Hence, f(x) and f^-1(x) are inverse functions.

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Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.  After simplifying the expression the answer is 4.

In the phrase \(4m + 5\), for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

simplify the expression \((√5-1)(√5+4)\), you can use the difference of squares formula, which states that \((a-b)(a+b)\) is equal to \(a^2 - b^2.\)

In this case, a is \(√5\) and b is 1.

Applying the formula, we get \((√5)^2 - (1)^2\), which simplifies to 5 - 1. Therefore, the answer is 4.

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Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.   The simplified form of (√5-1)(√5+4) is 4.

To simplify the expression (√5-1)(√5+4), we can use the difference of squares formula, which states that \(a^2 - b^2\) can be factored as (a+b)(a-b).

First, let's simplify the expression inside the parentheses:
√5 - 1 can be written as (√5 - 1)(√5 + 1) because (√5 + 1) is the conjugate of (√5 - 1).

Now, let's apply the difference of squares formula:
\((√5 - 1)(√5 + 1) = (√5)^2 - (1)^2 = 5 - 1 = 4\)

Next, we can simplify the expression (√5 + 4):
There are no like terms to combine, so (√5 + 4) cannot be further simplified.

Therefore, the simplified form of (√5-1)(√5+4) is 4.

In conclusion, the expression (√5-1)(√5+4) simplifies to 4.

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To evaluate the limit of the function f(x) = 4x^3 + 3x^2 + 2x - 2 as x approaches 1, we can substitute x = 1 into the function and calculate the resulting value.

When we substitute x = 1 into the function, we get f(1) = 4(1)^3 + 3(1)^2 + 2(1) - 2 = 4 + 3 + 2 - 2 = 7. This means that as x approaches 1, the function f(x) approaches the value of 7. In other words, the limit of f(x) as x approaches 1 is equal to 7.

Geometrically, we can interpret this result as follows. The function f(x) is a polynomial function of degree 3, which means that it is a cubic function. When we plot the graph of f(x), we get a curve that has a specific shape.

As x approaches 1 from both sides, we can see that the curve gets closer and closer to the horizontal line y = 7. This indicates that the limit of f(x) as x approaches 1 is indeed equal to 7.

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The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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Answer:

\(m=-3\)

Step-by-step explanation:

\(10=7-m\\\\7-m=10\\\\7-7-m=10-7\\\\-m=3\\\\\frac{-m=3}{-1}\\\\ \boxed{m=-3}\)

Hope this helps.

In rectangle pqrs, pq = 18, ps = 14, and pr = 22.8. diagonals and intersect at point t. The length of diagonal from the intersection point p is correct option is c. 22.8

We have given rectangle PQRS

Side PQ =18 .

Side PS = 14 .

Diagonal PR = 22.8  .

Properties of rectangle :

Opposite sides of the rectangle are equals.

Diagonals of the rectangle are equal .

Diagonals of rectangles bisect each other.

Then by second property :

Diagonal PR =QS

QS = 22.8

By the Third property

TQ = 1/2× QS

TQ = 1/2 × 22.8

TQ = 11.4

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Answer:

Step-by-step explanation:

c. 11.4

The maximum number of electrons in the 3d orbital, which is 10.

The quantum numbers for the 3d orbital are:

- Principal quantum number (n) = 3
- Angular momentum quantum number (l) = 2 (d orbital)
- Magnetic quantum number (m) = -2, -1, 0, 1, 2 (five possible values for the d orbital)
- Spin quantum number (s) = -1/2, 1/2 (two possible values for electrons)

The maximum number of electrons in the entire 3d shell is 10. This is because the d orbital can hold a maximum of 5 pairs of electrons (2 electrons per pair), and there are 5 possible values for the magnetic quantum number (m) in the d orbital.

In general, the maximum number of electrons in an entire shell is given by the formula 2n^2, where n is the principal quantum number. For the 3d orbital, the principal quantum number is 3, so the maximum number of electrons in the entire shell is 2(3^2) = 18. However, the question specifically asks for the maximum number of electrons in the 3d orbital, which is 10.

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Answer:

Geoffrey incorrectly found the margin of error because he used the wrong sample size.

Please give me brainliest, I really need it.

The probability of an x that is at least 2 is 0.70.

The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%.

P(E) means the probability of an event to occur.

P(E) is that of at least 2 means P(E) is greater than equals to 2, so we will take value greater than and equal to 2 i.e., 2,3,4

P(E) = P (X \(\geq\) 2)

      = P(X=2) + P(X=3) + P(X=4)

      = 0.35 + 0.25 + 0.10

      = 0.70

Therefore, the required probability is 0.70.

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Answer:

Step-by-step explanation:

The triple integral that evaluates the volume below the plane \(3x + 4y + 2z = 12\) is given by \(\iiint_V dV\), where \(V\) represents the region below the plane. The integral evaluates to a specific value based on the limits of integration.

To set up the triple integral, we need to determine the limits of integration for each variable. Since the region is defined by the plane \(3x + 4y + 2z = 12\), we can express \(z\) in terms of \(x\) and \(y\):

\[z = \frac{12 - 3x - 4y}{2}.\]

The limits for \(x\) and \(y\) can be determined by the intersection points of the plane with the coordinate axes. When \(x = 0\), we have \(y = 0\) and \(z = 6\). When \(y = 0\), we have \(x = 4\) and \(z = 6\). When \(z = 0\), we have \(3x + 4y = 12\), which yields \(x = 4\) and \(y = 3\).

Now we can set up the triple integral as follows:

\[\iiint_V dV = \int_{0}^{4} \int_{0}^{3} \int_{0}^{\frac{12 - 3x - 4y}{2}} dz\, dy\, dx.\]

To evaluate the triple integral \(\iiint_V dV\), we integrate with respect to \(z\), \(y\), and \(x\) using the limits determined earlier:

\[\int_{0}^{4} \int_{0}^{3} \int_{0}^{\frac{12 - 3x - 4y}{2}} dz\, dy\, dx.\]

First, we integrate with respect to \(z\):

\[\int_{0}^{4} \int_{0}^{3} \left[z\right]_{0}^{\frac{12 - 3x - 4y}{2}} dy\, dx.\]

Simplifying the expression, we get:

\[\int_{0}^{4} \int_{0}^{3} \frac{12 - 3x - 4y}{2} dy\, dx.\]

Next, we integrate with respect to \(y\):

\[\int_{0}^{4} \left[\frac{12y - 2xy - 2y^2}{2}\right]_{0}^{3} dx.\]

Simplifying further, we obtain:

\[\int_{0}^{4} (6 - 3x - 3x + 6) dx.\]

Now, integrating with respect to \(x\), we have:

\[\left[6x - \frac{3x^2}{2} + 6x\right]_{0}^{4}.\]

Evaluating this expression, we find:

\[\frac{72}{5}.\]

Therefore, the volume below the plane \(3x + 4y + 2z = 12\) is \(\frac{72}{5}\) cubic units.

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The current, i, to the capacitor is given by i = -2e^(-2t)cos(t) Amps.

To find the current, we need to differentiate the charge function q with respect to time, t.

Given q = e^(2t)cos(t), we can use the product rule and chain rule to find the derivative.

Applying the product rule, we have:

dq/dt = d(e^(2t))/dt * cos(t) + e^(2t) * d(cos(t))/dt

Differentiating e^(2t) with respect to t gives:

d(e^(2t))/dt = 2e^(2t)

Differentiating cos(t) with respect to t gives:

d(cos(t))/dt = -sin(t)

Substituting these derivatives back into the equation, we have:

dq/dt = 2e^(2t) * cos(t) - e^(2t) * sin(t)

Simplifying further, we get:

dq/dt = -2e^(2t) * sin(t) + e^(2t) * cos(t)

Finally, rearranging the terms, we have:

i = -2e^(-2t) * sin(t) + e^(-2t) * cos(t)

Therefore, the current to the capacitor is given by i = -2e^(-2t) * sin(t) + e^(-2t) * cos(t) Amps.

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The area of the pentagon is 1,453 squared centimeters.

Given information-

The length of the apothem of a regular pentagon is 20 cm.

The measure of the perimeter of a regular pentagon is 145.3 cm.

The length of the apothem of a rectangular pentagon is 20 cm.

The measure of the perimeter of a rectangular pentagon is 145.3 cm.

Pentagon is the closed shaped polygon which has 5 sides. When these 5 sides are equal in length then the pentagon is called teh regular pentagon. When four of the sides of pentagon make a rectangle then the pentagon is called the rectangular pentagon.

Area of regular pentagon is half of the product of its apothem and perimeter. It can be given as,

\(A=\dfrac{1}{2} \times 20\times 145.3\\A=1453\)

Thus the area of the pentagon is 1,453 squared centimeters.

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Concept testing is the test done before product launch, clients try a sample product and are then surveyed about whether they would buy the product again. So, option D is correct.

In concept testing, the companies will give newly launched products or new ideas or prototype products to the potential customers, to take reactions from them. This feedback is collected and assisted and analyze the feedbacks in order to improve their products sale.

The main aim of this concept testing is to collect information, patron needs, and assertions and can take powerful good decisions. This can gauge the market price and sale of the products through advertising.

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The complete question is:

type of test before product launch, customers try a sample product and are then surveyed about whether they would buy/use the product again. this process is known as:

a. premarket testing

b. alpha testing

c. prelaunch testing

d. concept testing

e. market testing.