Declan invested an amount of money in a savings account that pays compound interest at a rate of 8% per annum.
After 14 years there is £14,685.97 in the savings account (rounded to the nearest 1p).
How much money did Declan initially invest?
Give your answer to the nearest £1.

The formula for the volume of a rectangular prism is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

We know that the volume of Caleigh's jewelry box is 14 cubic inches, and the area of the base is 7 square inches. Since the base of the box is a rectangle, we can use the formula for the area of a rectangle to find the length and width of the base:

A = l x w

7 = l x w

We don't know the exact values of l and w, but we do know that their product is 7.

Now we can use the formula for the volume of a rectangular prism to find the height:

14 = l x w x h

We know that l x w = 7, so we can substitute 7 for l x w:

14 = 7 x h

Dividing both sides by 7 gives:

h = 2

Therefore, the height of Caleigh's jewelry box is 2 inches.

The angle subtended by the arc AB in the circle is 68.75 degrees.

We have,

We know that the circumference of a circle is given by 2πr,

where r is the radius of the circle.

The circumference of the circle with a radius of 6 cm is.

C = 2πr = 2π(6) = 12π cm

Since the arc AB of the circle is 9 cm, we can find the angle subtended by this arc using the formula:

angle = (arc length / circumference) x 360°

Plugging in the values we have:

angle = (9 / 12π) x 360°

angle = 68.75°

Therefore,

The angle subtended by the arc AB is 68.75 degrees.

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Answer:

The answer to your problem is, A. 5/2 and 25/4 

Step-by-step explanation:

In the problem the two similar figures, with side lengths 30 yds and 12 yds.

In order to solve the problem we need to find the ratio of the perimeters and the ratio of the areas of the larger figure to the smaller figure.

Using this information we know the the ratio of the perimeter of similar figure is equal to the scale factor and the ratio of the areas equal to the square of the scale factor.

the scale factor = 30/12 = 5/2

the ratio of the perimeter = 5/2

the ratio of the areas = (5/2)² = 25/4

Thus the answer to your problem is, A. 5/2 and 25/4 

Answer: below

Step-by-step explanation:

The first equation y = x + 5 is the equation of a straight line with slope 1 and y-intercept 5. We can plot this line by starting at the point (0, 5) and then moving up one unit for every one unit to the right.

The second equation y = -(x + 5) is also the equation of a straight line, but with slope -1 and y-intercept -5. We can plot this line by starting at the point (0, -5) and then moving down one unit for every one unit to the right.

The third equation y = |x + 5| is the equation of a V-shaped graph, or an absolute value function, centered at x = -5. We can plot this graph by first plotting the portion of the graph for x < -5, which is given by y = -(x + 5). Then, we can plot the portion of the graph for x > -5, which is given by y = x + 5. Finally, we can connect these two portions of the graph at x = -5 by drawing a vertical line segment from (-5, 0) to (-5, 10).

Answer:

First, let's start with y = x + 5.

To graph this equation, we can use a table of values. We'll choose a few values of x, and then plug them into the equation to find the corresponding values of y.

x | y

--|---

-5 | 0

-4 | 1

-3 | 2

-2 | 3

-1 | 4

0 | 5

1 | 6

2 | 7

3 | 8

4 | 9

5 | 10

Now, we can plot these points on a graph and connect them with a straight line.

```

| *

10|

| *

| *

| *

|*

| -------------

| -5 -4 -3 -2 -1 0 1 2 3 4 5

```

This is the graph of y = x + 5.

Next, let's look at y = -(x + 5).

This equation is similar to the first one, but with a negative sign in front of the parentheses. This means that the graph will be a mirror image of the first one, reflected across the y-axis.

So, we already know some of the points on this graph. If we take the points from the first graph and flip them horizontally (i.e. change the sign of the x-coordinate), we'll get the points for the second graph.

x | y

--|---

5 | 0

4 | -1

3 | -2

2 | -3

1 | -4

0 | -5

-1 | -6

-2 | -7

-3 | -8

-4 | -9

-5 | -10

Plotting these points on a graph and connecting them with a straight line, we get:

```

|*

10| *

| *

| *

| *

| *

| *

| *

|---------------

| -5 -4 -3 -2 -1 0 1 2 3 4 5

```

This is the graph of y = -(x + 5).

Finally, let's look at y = |x + 5|.

This equation involves absolute value, which means that the graph will be "V"-shaped. The vertex of the "V" will be at x = -5.

To find some points on this graph, we can again use a table of values. We'll choose some values of x, and then plug them into the equation, being careful to take the absolute value of the result.

x | y

--|---

-10 | 5

-5 | 0

0 | 5

5 | 10

10 | 15

Now, we can plot these points on a graph and connect them to form a "V" shape.

```

| *

15| *

| *

| *

| *

| *

|-------------

|-10 -5 0 5 10

```

This is the graph of y = |x + 5|.

The requried larger number x is 80 and the smaller number y is 27.

Let's use the given variables:

x be the larger number

y be the smaller number

According to question

The sum of two numbers is 107 is represented by x + y = 107

The difference between the two numbers is 53 is represented by x - y = 53.

Solving the system of equations:

(x + y) + (z - y) = 107 + 53

2x = 160

x = 80

Now, z = 80, substitute this value into one of the original equations to solve for y.

x + y = 107

80 + y = 107

y = 27

Therefore, the requried larger number x is 80 and the smaller number y is 27.

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For a unique solution is: [tex]\frac{10}{a}\neq \frac{5}{b}[/tex]

For an infinitely many solution is: [tex]\frac{10}{a}= \frac{5}{b}=\frac{-20}{c}[/tex]

An equation of the form ax+by+c=0 is called a linear equation where a, b, c∈R

We have the linear equation is:

10x + 5y = 20

Now, we have to find the unique solution and infinitely many solution:

Firstly, For a unique solution, we need an equation ax+by+c=0 such that

[tex]\frac{10}{a}\neq \frac{5}{b}[/tex]

Now, For an infinitely many solutions, we need an equation ax+by+c=0 such that:

[tex]\frac{10}{a}= \frac{5}{b}=\frac{-20}{c}[/tex]

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For, complete question, to see the attachment.

The length of the third side is given as follows:

x = 3√3.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the third side is given as follows:

x² + 3² = 6²

x² + 9 = 36

x² = 27

x = √3³

x = 3√3.

The triangle is given by the image presented at the end of the answer.

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The system of inequalities that represents the graph is

y ≥ x² - 2x + 4 and y < -x² + 4 is the

Option B is the correct answer.

We have,

The inequality y ≥ x² - 2x + 4 represents a parabola that opens upwards and has a vertex at (1,3) as shown below:

The inequality y < -x² + 4 represents an inverted parabola that opens downwards and has a vertex at (0,4) as shown below:

Therefore,

The system of inequalities that represents the graph is

y ≥ x² - 2x + 4 and y < -x² + 4 is the

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There is a statistically significant difference in life expectancy between people who ate fruits and vegetables and people who did not eat fruits and vegetables by hypothesis

State the null hypothesis and the alternative hypothesis.

The null hypothesis (H₀) is that there is no difference in life expectancy between people who ate fruits and vegetables and people who did not eat fruits and vegetables.

The alternative hypothesis (Ha) is that there is a difference in life expectancy between the two groups.

H₀: μ₁ = μ₂

Ha: μ₁ ≠ μ₂

Determine the appropriate test statistic and significance level.

Since we are comparing the means of two independent samples, we can use a two-sample t-test.

We will use a significance level of α = 0.05.

We can use a calculator or statistical software to calculate the test statistic.

t = -2.379

df = 8.98

p-value = 0.042

where t is the test statistic

The p-value is 0.042, which is less than the significance level of 0.05.

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The concentration of copper(II) sulfate in one brand of soluble plant fertilizer is 0.0700% by weight. A 24.0 g sample of this fertilizer is dissolved in 2.00 L of solution. Number of moles of copper ions available in the solution is 8.77×10⁻⁵mole.

In chemistry, a mole, usually spelt mol, is a common scientific measurement unit for significant amounts of very small objects like atoms, molecules, and other predetermined particles. The mole designates 6.02214076 1023 units, which is a very large number. In this the Worldwide System of Units (SI), the mole is defined as this number as of May 20, 2019, per the decisions of the General Conference upon Measurements and Weights. Amount of copper sulfate available in  24.0  grams of the sample =

0.07/100× 24.0 =0.014g

number of moles of copper sulfate=0.014/159.6=8.77×10⁻⁵

Number of moles of copper ions available in the solution=8.77×10⁻⁵mole

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The amount invested at 15% is $2,840 and at 6% is $2,741. The interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 6% by $261.54.

Let's assume that the amount invested at 15% is x, and the amount invested at 6% is y. We know that

x + y = 5,581 (equation 1) (since the total amount invested is $5,581)

We also know that the interest earned from the amount invested at 15% exceeds the interest earned from the amount invested at 6% by $261.54. This can be expressed as

0.15x - 0.06y = 261.54 (equation 2)

(since the interest earned is equal to the amount invested multiplied by the interest rate)

Now, we can use these two equations to solve for x and y.

First, we will isolate y in equation 1

y = 5,581 - x

Next, we will substitute this expression for y into equation 2

0.15x - 0.06(5581 - x) = 261.54

Simplifying this equation gives

0.15x - 334.86 + 0.06x = 261.54

0.21x = 596.40

x = 2,840

Now that we know x, we can use equation 1 to find y

2,840 + y = 5,581

y = 2,741

Therefore, $2,840 is invested at 15%, and $2,741 is invested at 6%.

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The expression a + b cannot be added/evaluated because 2.00x and 1.50y are not like terms

From the question, we have the following parameters that can be used in our computation:

a + b is equal to what ​

The above statement is an addition expression that adds the values of a and b

However, the terms of the expression are not like terms

i.e. a and b are not like terms

This means that the expression cannot be added/evaluated

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In order to decrease the margin of error, the best option in this instance is by decreasing the confidence level would make the interval to be narrower.

The correct option is D.

The margin of error, also known as the confidence interval, provides information on how closely your survey results will likely reflect the opinions of the general community.

The margin of error is a measure of the potential uncertainty in your survey results. It is more likely that the results will deviate from the "true figures" for the entire population the wider the margin of error.

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The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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Answer:

[tex]\Huge \boxed{\bf{x = 33}}[/tex]

Step-by-step explanation:

To solve for x in the equation [tex]3x - 3 = 4(x - 9)[/tex], we will follow these steps:

1. Distribute the 4 on the right-hand side of the equation:

2. To isolate x, subtract 3x from both sides:

3. Lastly, add 36 to both sides of the equation to solve for x:

So, the solution to the equation [tex]3x - 3 = 4(x-9)[/tex] is [tex]x = 33[/tex].

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________________________________________________________

The blanks will be -

(a) Capital Gain = $4000

(b) Percent of Capital Gain = 14.8%

(c) Purchase price per share = $5

(d) Percent of capital gain = 140%

(e) The selling price per share = $35.65

(f) Capital Gain = $3022.5

(g) Purchase price per share = $29

(h) Percent of capital loss = 20.7%

(i) Purchase price per share $54 and selling price per share $62.

The number of shares is 500.

So, Capital Gain = (500*62 - 500*54) = $4000

Percent of Capital Gain = (4000/(500*54))*100% = 14.8% (rounding to nearest tenth)

(ii) Number of shares = 100 and selling price of per share = $12 and capital gross = $700.

Purchase price per share = (12*100 - 700)/100 = 500/100 = $5

So the percent of capital gain = (700/(5*100))*100% = 140%

(iii) Number of shares = 650 and purchasing price per share = $31 and percent of capital gain = 15%

The selling price per share = 31*(100+15)/100 = $35.65

Capital Gain = (31*650)*15% = $3022.5

(iv) Number of shares = 1300 and selling price of per share = $23 and capital loss = - $7800

Purchasing price per share = $ (23*1300+7800)/1300 = $29

Percent of capital loss = (7800/(29*1300))*100% = 20.7% (rounding to nearest tenth)

Hence, (a) $4000; (b) 14.8% (gain); (c) $5; (d) 140% (gain); (e) $35.65; (f) $3022.5; (g) $29; (h) 20.7% (loss).

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The company should invest in 69.06 units of labor and 67.47 units of capital to maximize production output given the budget constraint.

We have,

We want to maximize the production output

P = L^0.8 K^0.2

subject to the constraint 10L + 20K = 2700.

We can solve for K in terms of L from the constraint equation:

10L + 20K = 2700

20K = 2700 - 10L

K = (2700 - 10L) / 20

K = 135 - 0.5L

Substitute this expression for K into the production function:

P = L^0.8 K^0.2

P = L^0.8 (135 - 0.5L)^0.2

We want to maximize P with respect to L.

Taking the derivative of P with respect to L:

dP/dL = 0.8L^-0.2 (135 - 0.5L)^0.2 + 0.2L^0.8 (135 - 0.5L)^-0.8 (-0.5)

dP/dL = 0.16(135 - 0.5L)^0.2 L^-0.2 - 0.1(135 - 0.5L)^-0.8 L^0.8

Setting dP/dL equal to zero and solving for L:

[tex]0.16 (135 - 0.5L)^{0.2} L^{-0.2} - 0.1 (135 - 0.5L)^{-0.8} L^{0.8} = 0[/tex]

0.16(135 - 0.5L)^0.2 = 0.1(135 - 0.5L)^-0.8 L^1

1.6(135 - 0.5L) = (135 - 0.5L)^-0.8 L

1.6 = (135 - 0.5L)^-1.8 L^-1

1.6L = (135 - 0.5L)^1.8

1.6L = (135^1.8 - 0.5L)^1.8

1.6L = 2.24474e+15 - 4.52222e+14 L + 1.22313e+13 L^1.8

1.22313e+13 L^1.8 - 4.52222e+14 L + 2.24474e+15 - 1.6L = 0

This equation can be solved numerically using a solver or a graphing calculator.

The solution is L = 69.06 units of labor.

To find the corresponding value of K, we can use the constraint equation:

10L + 20K = 2700

20K = 2700 - 10L

K = (2700 - 10(69.06)) / 20

K = 67.47 units of capital

Therefore,

The company should invest in 69.06 units of labor and 67.47 units of capital to maximize production output given the budget constraint.

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Answer:

A and D are correct. This is a parallelogram, which is a quadrilateral. B is not correct because not all the sides are congruent. C is not correct. E and F are not correct because this parallelogram does not have any right angles.

The triangle triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

Triangle ∆BCD is not similar to the triangle ∆BTS, BT does not correspond to BC, and BS does not correspond to BD. Also, the angle m∠SBT does not correspond to m∠DBC.

Therefore, the triangle ∆BCD is not similar to the triangle ∆BTS since their sides and angle does not correspond in proportion.

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Hello!

To find the equation of the line that passes through the points (0,-8) and (4,-3), we can use the slope-intercept form of the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

First, find the slope (m) of the line using the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (0,-8) and (x2, y2) = (4,-3).

m = (-3 - (-8))/(4 - 0) = 5/4

Now that we have the slope (m), we can use the point-slope form of the equation to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) = (0,-8) and m = 5/4.

y - (-8) = (5/4)(x - 0)

Simplify the equation to get the slope-intercept form:

y + 8 = (5/4)x

y = (5/4)x - 8

Therefore, the equation of the line that passes through the points (0,-8) and (4,-3) is y = (5/4)x - 8.

The contrapositive statement is option D

If the hypothesis and conclusion of an earlier conditional statement are reversed, a contrapositive statement is produced.

Technically speaking, the contrapositive of a conditional statement that starts with "If p, then q" is "If not q, then not p." The initial assertion and its contrapositive, then, are both true because they are logically equivalent.

Thus the contrapositive statement as shown is the statement ~q ~p

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The solution of "quadratic-equation" , 3x² - 6x + 2 = 0 is (b) x = (3 ± √3)/3.

A "Quadratic-Equation" is defined as a second-degree polynomial equation of the form : ax² + bx + c = 0,

where x = variable, and "a", "b", and "c" are constants, with a ≠ 0.

We use the "quadratic-formula" to solve : which is ⇒ x = (-b ± √(b²-4ac))/(2a),

In the quadratic equation "3x² - 6x + 2 = 0", We get , a = 3, b = -6, and c = 2.

Substituting the values,

we get,

⇒ x = (-(-6) ± √((-6)²-4(3)(2)))/(2×3),

⇒ x = (6 ± √(36-24))/6,

⇒ x = (6 ± √12)/6,

⇒ x = (6 ± 2√3)/6,

⇒ x = (3 ± √3)/3,

So the two roots of the quadratic equation 3x² - 6x + 2 = 0 are : x = (3 + √3)/3 and x = (3 - √3)/3.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Find the solution of the given quadratic equation , 3x² - 6x + 2 = 0.

(a) x = 3 ± 23√3

(b) x = (3 ± √3)/3

(c) x = 6 ± 43√3

(d) x = 6 ± 23

Answer:

Step-by-step explanation:

To complete the job in 12 days, they need 100 workers.

We know that 30 workes can complete 1 job in 40 days, then if each worker works at a rate R, then we can write:

30*R*40 days = 1 job

R = (1/1200) job/day

Then if they need to complete the job in 12 days, the number N of workers needed is:

N*(1/1200)*12 = 1

N = (1200/12) = 100

100 workers are needed.

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Answer: 4.375 Cups and 35 Ounces.

Step-by-step explanation:

The amount of fluid ounces in 1 cup is 8, meanwhile the amount of fluid ounces in an ounce is 1.

Hope that helps

The minimum value of the objective function is 47, which occurs at the point (3,2), and the maximum value is 117, which occurs at the point (0,9).

To solve this linear programming problem, we need to first graph the feasible region defined by the given constraints:

The first constraint, x ≥ 0, represents the non-negative values of x along the x-axis.

The second constraint, 4x + 8y ≥ 32, can be rewritten as y ≥ -(1/2)x + 4, which is a line with a y-intercept of 4 and a slope of -(1/2). The feasible region is above this line.

The third constraint, 10x - y ≤ 30, can be rewritten as y ≥ 10x - 30, which is a line with a y-intercept of -30 and a slope of 10. The feasible region is above this line as well.

The fourth constraint, x + 6y ≤ 54, can be rewritten as y ≤ -(1/6)x + 9, which is a line with a y-intercept of 9 and a slope of -(1/6). The feasible region is below this line.

The feasible region is therefore the polygon bounded by the lines y = -(1/2)x + 4, y = 10x - 30, y = -(1/6)x + 9, and x = 0. To find the minimum and maximum values of the objective function f(x,y) = 11x + 13y, we need to evaluate this function at each corner of the feasible region and compare the results.

The corners of the feasible region are (0,4), (3,2), (5,4), and (0,9). Evaluating the objective function at these corners, we get:

f(0,4) = 52

f(3,2) = 47

f(5,4) = 89

f(0,9) = 117

Therefore, the minimum value of the objective function is 47, which occurs at the point (3,2), and the maximum value is 117, which occurs at the point (0,9).

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The Volume of the box is 12 cubic unit.

We have,

Height = 1 unit

Width = 2 unit

Length = 6 unit

So, Volume of box

= l w h

= 1 x 2 x 6

= 12 cubic unit

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$138.38  you pay per month if you choose to not pay in full

If you pay in full, you get a 10% discount on the six-month policy, which means you would pay:

1,025 - 0.1(1,025) = 922.50

If you choose to not pay in full, you would not get the 10% discount for paying in full.

We get the 10% discount for being a good driver, which would be applied to each monthly payment.

This means that each monthly payment would be:

(1 - 0.1)(922.50) / 6 = 138.38

we get a monthly payment of $138.38.

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