Jack invests £3000 for 2 years at 4% per annum compound interest.
Work out the value of the investment at the end of 2 years.

The apothem is the perpendicular distance from the center of a regular polygon to any one of its sides.

The apothem of a regular polygon is the perpendicular distance from the center of the polygon to any one of its sides because it serves as a measure of the inradius, or the radius of the circle inscribed within the polygon. In a regular polygon, all sides are congruent and all interior angles are equal, so the apothem is the same for all sides.

To see this, imagine drawing radii from the center of the polygon to each vertex, and then drawing the perpendicular bisector of each side. These perpendicular bisectors will all intersect at the same point, which is the center of the polygon. The apothem is the length of the line segment connecting this center point to any one of the sides of the polygon.

The apothem is useful in finding the area of a regular polygon. By using the formula for the area of a regular polygon in terms of the apothem and the number of sides, one can find the area of a regular polygon without having to find the exact shape of the polygon.

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The value of t is obtained, we can substitute it back into the original equation to find the corresponding plasma concentration (Cp).

To determine the plasma concentration when 95% of the administered dose is eliminated, we need to find the time (t) at which 95% of the dose has been eliminated.

Given the equation that describes the plasma concentration-time data:

Cp = 1.3 e^(-0.116t) + 0.4 e^(-0.0067t)

We can set up the equation:

0.95 * 50 mg = 1.3 e^(-0.116t) + 0.4 e^(-0.0067t)

Simplifying further:

47.5 mg = 1.3 e^(-0.116t) + 0.4 e^(-0.0067t)

the time (t), we need to solve this equation numerically or by using numerical methods like iteration or graphing software. It is not possible to find a direct algebraic solution for t in this case.

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Thus, Option B gives a pair of triangles where the cosine of angle B equals the cosine of angle Z, with triangle ABC having side of 8 and 6 and triangle XYZ having the sides of 4 and 3.

The trigonometric variables sine, cosine, tangent, and its inverses make up these trigonometric ratios. Given an angle measurement, so every function represents a distinct ratio in a right triangle.

Trigonometric ratios are crucial in geometry, trigonometry, and all areas of engineering and physical science.

Thus,

cosine = adjacent side / hypotenuse

Option a:

cosine B = AB/CB

CB is found using Pythagorean theorem:

CB² = AB² + AC²

CB² = 4² + 5²

CB² = 16 + 25

CB² = 41

CB = √41

cosine B = 4 /  √41

cosine Z = XZ/YZ

CB is found using Pythagorean theorem:

YZ² = XZ² + Yx²

YZ² = 4² + 3²

YZ² = 16 + 9

YZ² = 25

YZ = 5

cosine Z =  3/5

Thus, cosine B ≠ cosine Z

Similarly for the second case:

Option B:

cosine B = AB/CB

CB is found using Pythagorean theorem:

CB² = AB² + AC²

CB² = 6² + 8²

CB² = 36 + 64

CB² = 100

CB = 10

cosine B = 6 / 10 = 3/5

cosine Z = XZ/YZ

CB is found using Pythagorean theorem:

YZ² = XZ² + Yx²

YZ² = 4² + 3²

YZ² = 16 + 9

YZ² = 25

YZ = 5

cosine Z =  3/5

Thus, cosine B = cosine Z

Thus,

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Answer:

-3, 2, -5, 1, 6

Step-by-step explanation:

The domain would be all the x-values, or in this case, the inputs.

The effect of tripling the sample size while keeping the confidence level the same would be to reduce the margin of error from 0.09 to 0.049, and to narrow the confidence interval from (0.23, 0.41) to (0.263, 0.361).

Assuming that the sample is a simple random sample, we can use the formula for the confidence interval for a proportion:

Confidence interval = sample proportion ± margin of error

where the margin of error is:

Margin of error = z* (standard error)

and z* is the z-score corresponding to the desired level of confidence (in this case, 90%). For a 90% confidence interval, the z* value is 1.645.

The formula for the standard error is:

\(Standard error = \sqrt{[(sample proportion \times (1 - sample proportion)) / sample size]}\)

Using the information given, we can write:

0.23 ≤ sample proportion ≤ 0.41

z = 1.645

We can solve for the sample proportion as follows:

\((sample proportion \times (1 - sample proportion)) / sample size = (1.645 / 2.0)^2\)

Solving this equation gives:

\(sample size = (1.645 / 0.09)^2 \times (0.41 * 0.59)\)

So, tripling the sample size would give us a new sample size of 3 * 50 = 150.

Using the same formula for the confidence interval, but with the new sample size, we get:

\(Margin of error = 1.645 \times \sqrt{ [(sample proportion \times (1 - sample proportion)) / sample size]}\)

Setting the margin of error equal to 0.09 (the margin of error for the original sample), we can solve for the new sample proportion:

0.09 = 1.645 * sqrt [(sample proportion * (1 - sample proportion)) / 150]

Solving for the sample proportion gives:

sample proportion = 0.312

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A translation is a transformation in which all the points of a preimage are moved along the same distance and in the same direction. The translation of the rectangle ABCD to the rectangle A'B'C'D' has been done along the x-axis and the y-axis. The algebraic rule that describes this translation is as follows Translation along the x-axis The preimage of the rectangle ABCD is moved k units to the right to obtain the image rectangle A'B'C'D'.

Therefore, the algebraic rule that describes the translation along the x-axis is Ta(k, 0). Translation along the y-axis The preimage of the rectangle ABCD is moved l units up to obtain the image rectangle A'B'C'D'. Therefore, the algebraic rule that describes the translation along the y-axis is Ta(0, l). Where k and l are the units that the preimage rectangle ABCD has been moved along the x-axis and the y-axis respectively. The algebraic rule that describes the translation along the x-axis is Ta(k, 0), and the algebraic rule that describes the translation along the y-axis is Ta(0, l). Therefore, the algebraic rule that describes the given translation of rectangle ABCD to rectangle A'B'C'D' is Ta(k, l).

Translation is a transformation in which all the points of a preimage are moved along the same distance and in the same direction. The rectangle ABCD has been translated to get the rectangle A'B'C'D' along the x-axis and the y-axis. The amount of units that the rectangle ABCD has been moved along the x-axis and the y-axis are k and l respectively. The algebraic rule that describes the translation along the x-axis is Ta(k, 0).Here, the point A has been moved k units to the right to the point A', while the point B has been moved k units to the right to the point B', and so on. The algebraic rule that describes the translation along the y-axis is Ta(0, l).Here, the point A' has been moved l units up to the point A", while the point B' has been moved l units up to the point B", and so on. Thus, the algebraic rule that describes the given translation of rectangle ABCD to rectangle A'B'C'D' is Ta(k, l). Translation is a transformation in which all the points of a preimage are moved along the same distance and in the same direction. The rectangle ABCD has been translated to get the rectangle A'B'C'D' along the x-axis and the y-axis. The amount of units that the rectangle ABCD has been moved along the x-axis and the y-axis are k and l respectively. The algebraic rule that describes the translation along the x-axis is Ta(k, 0).Here, the point A has been moved k units to the right to the point A', while the point B has been moved k units to the right to the point B', and so on. Therefore, the coordinates of the image rectangle A'B'C'D' will be A'(k + 1, 2), B'(k + 1, 6), C'(k + 3, 6) and D'(k + 3, 2). The algebraic rule that describes the translation along the y-axis is Ta(0, l). Thus, the algebraic rule that describes the given translation of rectangle ABCD to rectangle A'B'C'D' is Ta(k, l).

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Answer:

We are given to find the length of side AB. We know that in a triangle, if two angles have equal measures, then the sides opposite to them are equal in length. Thus, the length of side AB is 6 units.

Hope this helps!!

Answer:

12

Step-by-step explanation:

4x=2×+6

them you use the inverse operation and them the result is and you multiply by 2 the answer is 12

P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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Inequalities are used to represent unequal expressions

The inequality that represents the situation is 12x+56≥200

From the question, we have:

So, the savings after working for x hours is:

Savings = 56 + 12x

The goal is to have at least $200.

So, we have:

12x+56≥200

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The range of possible lengths for the third side be

0 ft < x < 76 ft

0 ft < x < 33 ft

Given, two sides of a triangle

we have to find the range of possible length for the third side of the triangle.

a) 24 ft and 52 ft

given first side of the triangle be, 24 ft

and second side of the triangle be, 52 ft

as we know that the third side should be less than the sum of the remaining two sides of any triangle.

So, let the third side be x

x < 24 + 52

x < 76

Therefore, the third side should be less than 76 ft and obviously greater than 0 ft.

Range of the third side be, 0 ft < x < 76 ft

b) 16 ft and 17 ft

given first side of the triangle be, 16 ft

and second side of the triangle be, 17 ft

as we know that the third side should be less than the sum of the remaining two sides of any triangle.

So, let the third side be x

x < 16 + 17

x < 33

Therefore, the third side should be less than 33 ft and obviously greater than 0 ft.

Range of the third side be, 0 ft < x < 33 ft

Hence, the range of possible lengths for the third side be

0 ft < x < 76 ft

0 ft < x < 33 ft

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Independent variables are the factors that are manipulated or controlled by the researcher in a study. In the context of investigating the impact of a school nutrition program on grade performance of high school students, the independent variable would be the school nutrition program itself.

The researcher would design and implement the program, and this variable would be under their control.

Dependent variables, on the other hand, are the outcomes or variables that are measured in a study and are expected to change as a result of the independent variable. In this case, the dependent variable would be the grade performance of the students. The researcher would collect data on the grades of the students before and after the implementation of the nutrition program, and this would be the variable that is expected to be influenced by the independent variable.

In summary, the independent variable in this research design is the school nutrition program, while the dependent variable is the grade performance of the students. The researcher would manipulate the independent variable (implement the nutrition program) and then measure the dependent variable (student grades) to determine if there is an impact of the program on grade performance.

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Answer:

756

Step-by-step explanation:

42 boxes, each contained 18 flowers, which means

42*18=the total number

Answer:

756 Flowers

Step-by-step explanation:

N.o of boxes: 42

N.o of Flowers in each box= 18

Total n.o of flowers sold= (n.o of boxes * n.o of flowers in each box)

=(42*18)

=756 flowers.

Therefore, the total n.o of flowers sold are 756 flowers.

Hope this helps!

Katy's house is about 8.1 miles from Camilla's house, measured in a straight line.

we apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we have:

H^2 = west distance^2 + north distance^2

H^2 = 4.6^2 + 6.7^2

H^2 = 21.16 + 44.89

He^2 = 66.05

We take the square root of both sides, we get:

hypotenuse = 8.13

We then can say that  Katy's house is about 8.1 miles from Camilla's house, measured in a straight line.

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Therefore the answer is;-18−4x−8x2=(2+x+x2)−2(2−x2)+(5+x+2x2)

Given three functions2+x+x2,-2−x2,5+x+2x2,and a polynomial −18−4x−8x2 that needs to be expressed as a linear combination of these functions

To write the polynomial −18−4x−8x2 in the form of a linear combination of the given functions, we need to find the coefficients a, b, and c, such that

−18−4x−8x2=a(2+x+x2)+b(−2−x2)+c(5+x+2x2)

Using the method of equating coefficients of like powers, we can get the values of a, b, and c

Let's start by equating the coefficients of x2 on both sides−8=c*2... equation (1)

Equating the coefficients of x, we get -4=a+b+2c... equation (2)

And, equating the constants, we get -18=2a-2b+5c... equation (3)

From equation (1), we get c = -4/2=-2From equation (2), we get -4 = a+b+2(-2)=> a+b = 0+4=4From equation (3), we get -18 = 2a-2b+5(-2)=> 2a-2b = -18+10=-8=> a-b = -4=> a = b-4

Replacing the value of a in equation (2), we get -4 = b-4+b+2(-2)=> -4 = 2b-4=> b = 0Therefore, a = -4

Putting values of a, b, and c in the original equation, we get;−18−4x−8x2= (2+x+x2)+ (−2−x2)+ (5+x+2x2)=-2(2-x2)+5+x

Since, we were able to express the polynomial −18−4x−8x2 as a linear combination of the given functions, therefore the answer is;

-18−4x−8x2=(2+x+x2)−2(2−x2)+(5+x+2x2)

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Answer:

8(2x + 5y)

Step-by-step explanation:

You cant fact (take out) 8 from both 16 and 40 since 8 is a factor for both.

Step-by-step explanation:

=16x+40y

=8(2x+5y)

Answer:

15/20 simplified is 3/4

Step-by-step explanation:

So a 3/4 chance or a 75% chance of not drawing a blue marble.

Answer:

4 better inbox

Step-by-step explanation:

The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.

To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.

To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length) + 2(width)

Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:

2x + 2y = 60,000

To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:

60,000 - x = 3x + 2y

The total length of the three sides that are not the front is 3x + 2y.

Now we can calculate how much the builder will pay for each type of fence:

Total cost of the fence = $20x + $30x + $20y = $50x + $20y

To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.

However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:

This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.

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To solve for taxes in equilibrium, we can start by substituting the given equations into the equation for YD:

YD = Y - T

Since C and T are constant, we can write:

YD = (c0 + c1YD) - (t0 + t1Y)

Now, we can rearrange the equation to isolate YD:

YD = c0 + c1YD - t0 - t1Y

Simplifying further:

YD - c1YD = c0 - t0 - t1Y

Factoring out YD:

YD(1 - c1) = c0 - t0 - t1Y

Dividing both sides by (1 - c1):

YD = (c0 - t0 - t1Y) / (1 - c1)

Now, let's analyze the effects of a drop in c0. If c0 decreases, it implies that consumption decreases. As a result, YD will decrease, leading to a decrease in Y. Taxes will also decrease because they are determined by YD.

If the government cuts spending to balance the budget, it will lead to a decrease in G. This decrease in spending will reduce Y and further decrease YD. However, the impact on Y will depend on the magnitude of the cut in spending.

If the cut in spending is significant, it can counteract the decrease in output caused by the drop in c0. On the other hand, if the cut in spending is small, it may reinforce the effect of the drop in c0 on output. The overall effect on Y will depend on the relative magnitudes of the changes in c0 and G.

A drop in c0 will decrease both Y and taxes in equilibrium. If the government cuts spending to balance the budget, the effect on Y will depend on the magnitude of the cut in spending relative to the decrease in c0.

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The cut in spending required to balance the budget counteracts the effect of the drop in c₀ on output (Y).

In equilibrium, taxes can be solved using the given equations:

C = c₀ + c₁YD

T = t₀+ t₁Y

YD = Y – T

To find taxes in equilibrium, we need to substitute the value of YD into the equation for taxes:

T = t₀ + t₁YD

Now, let's analyze the impact of a drop in c₀ on output (Y) and taxes (T).

When c₀ decreases, it means that the intercept of the consumption function (C) decreases.

This results in a decrease in consumption at every level of income. As a result, the aggregate demand decreases, leading to a decrease in output (Y).

The decrease in output (Y) leads to a decrease in income and, consequently, a decrease in disposable income (YD).

Since taxes (T) depend on disposable income, a decrease in YD will lead to a decrease in taxes (T).

Next, let's consider the effect of a government spending cut to balance the budget.

When the government cuts spending to balance the budget, it reduces its expenditure (G) without changing its tax revenue (T).

This reduction in government spending decreases aggregate demand, which in turn reduces output (Y).

However, since the government is keeping the budget balanced, the decrease in government spending is offset by the decrease in taxes (T) that occurs as a result of the decrease in output (Y).

Therefore, the cut in spending required to balance the budget counteracts the effect of the drop in c₀ on output (Y).

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If Clayton has 5 gal 3qt of moto oil to be recycled, Clayton and Ernie are recycling a total of 26.5 quarts of motor oil.

To determine the total amount of motor oil that is being recycled, we first need to convert all the given measurements to the same unit. We can choose to convert everything to quarts, which is a common unit of volume measurement.

5 gallons 3 quarts can be expressed as (5 x 4) + 3 = 23 quarts, since there are 4 quarts in a gallon. Similarly, 7 pints can be expressed as 3.5 quarts, since there are 2 pints in a quart.

So, the total amount of motor oil being recycled is:

23 quarts + 3.5 quarts = 26.5 quarts

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Answer:

Just as the square root is a number that, when squared, gives the radicand, the cube root is a number that, when cubed, gives the radicand. Cubing a number is the same as taking it to the third power: 23 is 2 cubed, so the cube root of 23 is 2.

Step-by-step explanation:

there i hope you understood

The graphs of Square root function only continues in one direction forever whereas the cube root function continues in two directions forever.

"The principal square root function \(f(x) = \sqrt{x}\) (usually just referred to as the "square root function") is a function that maps the set of non negative real numbers onto itself."

"The cube root function \(f(x) = \sqrt[3]{x}\)  is a continuous function, with no start or end point. Its domain is all real numbers."

The similarities  in the graphs of square root function and cube root function are positive function (0,∞), x-intercept: intersects x-axis at (0, 0)

y-intercept: intersects y-axis at (0, 0).

The square root function only utilizes the positive square root. If both positive and negative square root values were used, it would not be a function. The cube root function can process  both positive and negative values.

Hence, the graphs of Square root function only continues in one direction forever whereas the cube root function continues in two directions forever.

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The critical value of the correlation coefficient for a two-tailed test at alpha = 0.05 with a sample size of n = 23 is approximately plus/minus 0.497.

To understand why this is the case, we need to consider the distribution of the correlation coefficient, which follows a t-distribution. In a two-tailed test, we divide the significance level (alpha) equally between the two tails of the distribution. Since alpha = 0.05, we allocate 0.025 to each tail.

With a sample size of n = 23, we need to find the critical t-value that corresponds to a cumulative probability of 0.025 in both tails. Using a t-distribution table or statistical software, we find that the critical t-value is approximately 2.069.

Since the correlation coefficient is a standardized measure, we divide the critical t-value by the square root of the degrees of freedom, which is n - 2. In this case, n - 2 = 23 - 2 = 21.

Hence, the critical value of the correlation coefficient is approximately 2.069 / √21 ≈ 0.497.

Therefore, the correct answer is A. Plus/minus 0.497.

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Answer:

Step-by-step explanation:

Original question is attached

As we see the second option is cheaper so we should hire the Master Remodeling

Answer:

1) At least one (the 11th) student is 23 (years old), Must be true

2) Some students are younger than 15 Could be true

Step-by-step explanation:

1) The given parameters are;

The number of student in the class = 21

The median age of the student = 23

The age of the oldest student = 29

Therefore, given that the median age = The age of the (n + 1)/2 th student

Where;

n = The number of student in the class = 21

∴ The median age = The age of the (21 + 1)/2 th = 11 th student, when the age of the students are arranged in increasing order, therefore, we have;

At least one (the 11th) student is 23 (years old), Must be true

2) Given that there are 10 students with ages equal to or lower than the  median age, and the difference between the median age and the age of the oldest student = 29 - 23 = 6 years, we have;

Some students are younger than 15 Could be true

Answer:

42cm²

Step-by-step explanation:

because if the perimeter of the rectangle is 28 then the length is 5, 5 - 11 = 6, the formula for finding the trapezium is to add the 2 parallel sides, half them, then times them with the length so your sum will look like this, 5+9=14, (i knew the other side was 9 as the length of AB is the same as the length of FC, which is the one of the parallel sides of the trapezium) then we do 14÷2=7, finally we times 7 by 6 which is 42cm²

well, we had a cylinder with 7mL of water, in the rock goes and kaboom the volume for the cylinder and its contents is 9 mL, well, the displaced water from the rock is equivalent to its volume, as Archimedes would properly point out, so since it was 7mL and now is 9mL well, the extra 2mL is the volume of the rock :).

sidenote:  Archimedes is Da Bomb!!!!

now, we know the rock weights 24 grams, and we also know its volume is 2mL, so its density is simply g/mL, or \(\cfrac{24g}{2mL}\implies 12~\frac{g}{mL}\)

Answer:

This is amazing and funny but I would rather not give a stranger my phone number but i would if I wasnt such protective

Step-by-step explanation:

Answer:

cool

Step -by-step explanation:

brain list me please

Answer:

-49/15

Step-by-step explanation:

To determine the position of point A on the number line, we need to subtract the length of segment AB from the position of point B.

Given that the position of point B is 2/5, we can subtract the length of AB, which is 3 2/3, from 2/5.

To subtract fractions, we need to find a common denominator. The least common denominator for 3/3 and 5 is 15.

Converting 3 2/3 to an improper fraction:

3 2/3 = (3 * 3 + 2)/3 = 11/3

Subtracting the fractions:

2/5 - 11/3 = (2 * 3 - 11 * 5)/(5 * 3) = (6 - 55)/15 = -49/15

The position of point A is -49/15 on the number line.

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Answer:

40 years

Step-by-step explanation:

I think 1 score is 20 years

so 2 scores = 2 x 20 = 40 years

I may be wrong so someone check

-Chetan K

Answer:

Living room: 4 x 5

Kitchen: 2 x 2

Office: 4 x 2

Bedroom: 5 x 2

Bedroom: 2 x 2

Bathroom: 3.5 x 3

Step-by-step explanation:

Just divide all the top ones by 4 to get the bottom ones.