Ella invests £7000 for 2 years in an account paying compound interest.

In the first year, the rate of interest is 3%
In the second year, the rate of interest is 1.5%

Work out the value of Ella's investment at the end of 2 years.

Answer:

[tex]\frac{x}{x+(x-2)}[/tex] = [tex]\frac{10}{16}[/tex]

[tex]\frac{x}{2x-2}[/tex] = [tex]\frac{5}{8}[/tex]

5(2x-2) = 8x

10x - 10 = 8x

2x = 10

x = 5

Answer:

[tex] \sin( \alpha ) = \frac{16}{ \sqrt{281} } [/tex]

Step-by-step explanation:

Greetings!!!

Firstly, remember the sin trigonometric equation

[tex] \sin( \alpha ) = \frac{opposite}{hypotenuse} [/tex]

Assuming the image as this question and solve

If you have any questions or unclear ideas tag on comments

Hope it helps!!!

The value of the indicated trigonometric ratio sin( α ) is (16√281 )/281.

The figure in the image is a right triangle.

To find sin(α), we use trigonometric ratio.

Sine = Opposite / Hypotenuse

Plug in the values

sin( α ) = 16/√281

To simplify further, we rationalize the denominator

Multiply both the numerator and denominator by √281

sin( α ) = (16 × √281 ) /(√281 × √281 )

sin( α ) = (16 × √281 ) / 281

sin( α ) = (16√281 )/281

Therefore, the value of sin( α ) is (16√281 )/281.

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Answer:

n = 12

Step-by-step explanation:

Solve for n

3 ( n -5 ) = 21

Divide each side by 3.

3/3 ( n -5 ) = 21/3

n-5 = 7

Add 5 to each side.

n-5+5 = 7+5

n = 12

Answer:

1) 2/5

2) 4/13

3) 1/8

4) 25/4 or 6 + 1/4

Step-by-step explanation:

1) 5/2 * x = 1

x = 1 / (5/2)

x = 2/5

2) (3 + 1/4) * x = 1

13/4 * x = 1

x = 1 / (13/4)

x = 4/13

3) 8 * x = 1

x = 1/8

4) (2/5)^2 * x = 1

2^2 / 5^2 * x = 1

4/25 * x = 1

x = 1 / (4/25)

x = 25/4

x = 6 + 1/4

The length of one edge of the cube is 8 cm and the radius of the sphere is 9 cm.

What is the cube root?

The cube root of a number is a value that when multiplied by itself thrice or three times produces the original value. For example, the cube root of 27, denoted as 3√27, is 3, because when we multiply 3 by itself three times we get 3 x 3 x 3 = 27 = 33.

The surface area of a cube is given by the formula:

A = 6 * a^2

where A is the surface area and a is the length of one edge of the cube.

So, in this case:

384 = 6 * a²

Dividing both sides by 6:

64 = a²

Taking the square root of both sides:

a = 8 cm

So the length of one edge of the cube is 8 cm.

The formula for the volume of a sphere is:

V = (4/3) * π * r³

where V is the volume, π is Pi (approximately equal to 3.14), and r is the radius of the sphere.

So, in this case:

729 = (4/3) * π * r³

Dividing both sides by (4/3) * π:

729 / (4/3) * π = r³

Taking the cube root of both sides:

r = pow(729 / (4/3) * π, 1/3) = 9 cm

So the radius of the sphere is 9 cm.

The cube root of 729 is 9.

Hence, the length of one edge of the cube is 8 cm and the radius of the sphere is 9 cm.

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Answer:

Step-by-step explanation:

In a triangle, the sides have a ratio of 3:7:10. If the perimeter is 210 feet, what is the length of the longest side in feet? (A) * 10.5 (B) 31.5 (C) (D) 105​

[210 : (3 + 7 + 10)] x 10 = 105 ft (your answer)

Step-by-step explanation:

the ratio tells us into how many units the total amount is split and then distributed among the different parts or members of the ratio.

3:7:10 means there are 3+7+10 = 20 units of length.

210 ft is the total of all lengths.

this is now split into these 20 units.

that means one unit of length for the ratio is

210/20 = 10.5 ft

the longest side is clearly the one with 10 units in the ratio.

so, it has

10×10.5 = 105 ft

Answer: 60

Step-by-step explanation:

(42/70) * 100

42/70 = 0.6

0.6 * 100 = 60

Answer :  70 - 42 = 28

then find out using percentage formula then will get answer  =

60%

Lines are not perpendicular .

What makes a line parallel?

Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane.

                               Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes are reciprocals with a negative sign.

  2x - 5y = -20

       5y = 2x + 20

      y = 2/5x + 20/5

      y = 2/5x + 4

    m₁ = 2/5

y = 2/5x - 1

 m₂ = 2/5

The product of the slopes of the two lines is

             2/5 * 2/5 = -1

                   4/25  =  -1

   the lines are not perpendicular .

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Answer:

width=71km, length=177.5km

Step-by-step explanation:

Let x be the width of the farm.

Then the length of the farm will be 2.5x.

perimeter of farm in terms of x=2.5x+2.5x+x+x=7x

perimeter of farm in terms of x=perimeter of farm

7x=497

x=71

width=71km

length=71×2.5=177.5

Arithmetic overflow error converting numeric to data type numeric can be solved by increasing the precision and the scale, storing number in different data type or use user-defined datatype.

An "arithmetic overflow error converting numeric to data type numeric" error occurs when you try to store a number in a numeric column that is too large to be represented by the specified precision and scale. To resolve this error, you have a few options:

Increase the precision and scale of the numeric column, you can increase the precision and scale of the numeric column so that it can store larger numbers.

If you don't need the precision and scale of a numeric column, you can store the number in a different data type, such as float or big int.

 If the number is too large to be represented in the numeric column, you can round it to a smaller value before inserting it into the database.

 If the number is still too large to be represented in a numeric column or a different data type, you can create a custom data type in SQL Server to store the number.

It's important to choose the right solution based on your requirements and the specific use case. You may also need to consider the performance implications of each solution, especially if the data being stored is very large or complex.

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Work Shown:

If cos(x) = 8/17, then sin(x) = 15/17. Use the identity [tex]\sin^2(\text{x}) + \cos^2(\text{x}) = 1[/tex] to determine this.

If cos(y) = 3/5, then sin(y) = 4/5 using that same identity.

So,

sin(x-y) = sin(x)cos(y) - cos(x)sin(y)

sin(x-y) = (15/17)*(3/5) - (8/17)*(4/5)

sin(x-y) = 45/85 - 32/85

sin(x-y) = (45 - 32)/85

sin(x-y) = 13/85

Answer:

0.0002

Step-by-step explanation:

She divides by 10.

The monthly payment is  $86.55. The result is obtained by using the formula for simple interest.

The simple interest of an amount of money can be counted by the following formula.

I = P × r × t

Where

A motocross company offers a loan to buy an ATV for $4,000. Loan Offer 9.3% Simple Interest.

If it is for 6 years, find the monthly payment!

We have

It is not mentioned that the simple interest apply per year or per month. We assume the simple interest is per year. It will be

I = P × r × t

I = $4,000 × 9.3% × 6

I = $2,232

The total money to be paid will be

A = P + I

A = $4,000 + $2,232

A = $6,232

The monthly payment is

MP = A/t

MP = $6,232/(6 × 12)

MP = $6,232/72

MP = $86.55

Hence, the person who borrows for $4,000 to buy an ATV should pay $86.55 each month for 6 years.

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A wheel of cheese has a radius of 7 inches and a height of 3 inches

The approximate surface area of this wheel of cheese is 458.4 square inches.

To get the surface area of a cylinder,  we have to calculate the area of the lateral surface and add the areas of the two circular end faces.

The lateral surface area of a cylinder is calculated as 2 * pi * r * h, where r is the radius and h is the height.

So the lateral surface area in this scenario would be: 2 * 3.14 * 7 * 3 = 150.52 square inches.

The area of the two end faces must then be calculated. we know, Pi * r^2, where r is the radius, gives the area of a circle.

So the area of each end face in this situation would be 3.14 * 7^2 = 153.94 square inches.

Total surface area= lateral surface area + end face area

=150.52 + 153.94 + 153.94 = 458.4 square inches (approximately)

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The highest number obtainable by multiplying the numbers 1-9 is 40,320. To obtain this result, you need to arrange the numbers in a specific order.

The problem is to find the highest number that can be obtained by multiplying the numbers 1-9, where each number can only be used once. To obtain the highest possible number, it's important to arrange the numbers in a specific order. One possible arrangement is 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. This arrangement results in the highest product of 40,320. It's worth mentioning that different arrangements of the numbers may result in different products, but the arrangement mentioned above gives the highest possible product. Understanding the order of operations and how to manipulate the numbers is key to solving this problem and finding the highest number.

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5- Perimeter of the new rectangle is 48 cm.

6- Area of the new triangle is 9 cm².

5- A rectangle that has a perimeter of 16 cm has been dilated with a scale factor of 3. To find the perimeter of the new shape, we need to multiply the original perimeter by the scale factor:

16 cm * 3 = 48 cm

So the perimeter of the new shape is 48 cm.

6- A triangle that has an area of 36 squared cm has been dilated with a scale factor of 0.5. To find the area of the new triangle, we need to multiply the original area by the square of the scale factor:

36 cm² * (0.5)²

= 36 cm² * 0.25

= 9 cm²

So the area of the new triangle is 9 cm².

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Answer:

  (a)  -1/2x +3 = 3x -4

Step-by-step explanation:

Given a graph of two lines, you want to know which equation it is showing the solution for.

The blue line has a slope of -3/6 = -1/2, and a y-intercept of +3, so its slope-intercept equation is ...

  y = -1/2x +3

This expression is seen on the left side of the equal sign for the first choice, and is not seen anywhere else.

By way of confirmation, the red line has slope 3/1 = 3 and a y-intercept that is a negative value less than -2. It is reasonable to say its slope-intercept equation is ...

  y = 3x -4

This expression matches the right side of the equal sign for the first choice.

The solution to the system of these two equations might reasonably be found by equating the expressions for y:

  -1/2x +3 = 3x -4

Answer: A = 5/12, B = 5/6

Step-by-step explanation:

The sample space of rolling two dice has 36 possible outcomes.  Remember that the "sample space" is a set which contains all possible outcomes.  

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

The probability of rolling a 2 is 1/36.

The probability of rolling a 3 is 2/36.

The probability of rolling a 4 is 3/36.

The probability of rolling a 5 is 4/36.

The probability of rolling a 6 is 5/36.

The probability of rolling a 7 is 6/36.

The probability of rolling an 8 is 5/36.

The probability of rolling a 9 is 4/36.

The probability of rolling a 10 is 3/36.

The probability of rolling an 11 is 2/36.

The probability of rolling a 12 is 1/36.

Using these probabilities, you can answer your questions:

Probability of rolling a number bigger than 7 is the sum of the probabilities of rolling an 8, 9, 10, 11, and 12.

5/36 + 4/36 + 3/36 + 2/36 + 1/36 = 15/36 which reduces to 5/12

The probability of rolling a number not divisible by 6 is from the combinations 1,5 : 2,4 : 3,3 : 4,2 : 5,1 : and 6,6.

1 - 6/36 of possible combinations, which reduces to 1 - 1/6, which is reduced to 5/6.

Hope this helps, and you understand

Answer:

Probability of rolling a number bigger than 7 is 5/12The probability of rolling a number not divisible by 6 is reduced to 5/6.

Step-by-step explanation: (answer from 2800818, he was the one who gave the answer)

The result is obtained by using the formula for a triangle.

Simply we count the number of grids representing a certain unit.

We have a flag in coordinate system can be seen in the picture.

Each grid represents a foot. Kenna will make five flags.

The flag is a triangle with the base at y-axis.

The base length is 3 ft and the height is 2. The area of the triangle is

Area of a flag = ½ bh

Area of a flag = ½(3)(2)

Area of a flag = 3 ft²

Area of five flags = 5(3 ft)

Area of five flags = 15 ft²

Hence, Kenna will need the material of 3 ft² for one flag and 15 ft² for five flags.

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Answer:

Nov 27 at 14:24 hours

Step-by-step explanation:

57.6 days equates to 57 days, 14 hours, 24 minutes (using a calculator)

Adding to Oct 1 at 12:00:00 we get this as Nov 27 at 14:24 hours

Answer:

20 liters of white paint, 12 liters of red paint

Step-by-step explanation:

Let w = liters of red paint and r = liters of red paint

[tex] \frac{w}{r} = \frac{5}{3} [/tex]

[tex]w = \frac{5}{3} r[/tex]

[tex]w + r = 32[/tex]

[tex] \frac{5}{3} r + r = 32[/tex]

[tex] \frac{8}{3} r = 32[/tex]

[tex]r = 12[/tex]

[tex]w = 20[/tex]

Answer:

Below

Step-by-step explanation:

y varies directly with  x  means

y = k x

now with y = -93 and x = -3

   -93  =  k (-3)      shows k =  30

so   y = 30 x

now with x = -2

    y = 30 (-2) = -60

Answer: The expression that represents the amount of money John has collected is:

5 * m

This expression calculates the amount of money John collects by multiplying the number of members (m) by the amount of money collected per member ($5).

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to know which functions have 5 in their domain, and what the function value is at x=5.

It is more convenient to do the second part first, as that tells you the answer to the first part:

f(5) = 5² -3·5 = 25 -15 = 10 . . . . 5 is in the domain

g(5) = (5 -5)/5 = 0/5 = 0 . . . . 5 is in the domain

h(5) = √(5 -10) = √(-5) . . . . UNDEFINED; 5 is not in the domain

Answer:

Step-by-step explanation:

The Pythagorean Theorem will be applied:

[tex]c^{2} = a^{2} + b^{2}[/tex]

Substituting the values provided in the question:

[tex]7^{2} = 6^{2} + b^{2}[/tex]

[tex]= 49 = 36 + b^{2}[/tex]

[tex]= 49 - 36 = b^{2}[/tex]

[tex]= b^{2} = 13[/tex]

Taking the square root on both sides to get rid of the square:
[tex]= \sqrt{b^{2}} = \sqrt{13}[/tex]

[tex]= b = \sqrt{13}[/tex] yards

= b = 3.6 yards (Rounded to the nearest tenth)

The standard form of the equation for the given p value and theta is equal to -x + y = 26√2.

Standard form of the equation is :

x cosθ + y sinθ = p

Here p = 26 and theta 'θ' = 3π /4

Substitute the value in the standard form we get,

x cos (3π/4 ) + y sin( 3π /4 ) = 26

⇒ x cos ( π - π/4 ) + y sin ( π - π/4 ) = 26

⇒ - x cosπ/4 + y sinπ/4 = 26

Substitute the value of cosπ/4 and sinπ/4 is equal to 1/√2 we get,

⇒ -x /√2 + y / √2 = 26

⇒ -x + y = 26√2

Therefore, the standard form of the equation is equal to -x + y = 26√2.

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Answer:

Step-by-step explanation:

Let's start by defining a variable to represent the minimum number of points that Jose must score on the remaining tests:

n = minimum number of points Jose must score on the remaining tests

To get an A for the semester, Jose must score at least 660 points. We know that he has already scored 570 points, so the total number of points he needs to score is:

660 - 570 = 90

Therefore, we can write the following inequality to find the minimum number of points Jose must score on the remaining tests:

n ≥ 90

This means that Jose must score at least 90 points on the remaining tests to get an A for the semester.