For how many minutes did Lynn run at a greater speed than kael

In order to determine which annuity option would be best, we need to calculate the accumulated value for each option. The accumulated value can be found using the continuous compounding formula:

A = P * e^(rt)

Where A is the accumulated value, P is the annuity payment per year, r is the annual interest rate, and t is the number of years.

For option #5, with an annuity of $500 per year, compounded continuously at 8% for 6 years, the accumulated value can be calculated as:

A5 = $500 * e^(0.08 * 6)

For option #6, with an annuity of $650 per year, compounded continuously at 8% for 4 years, the accumulated value is:

A6 = $650 * e^(0.08 * 4)

Similarly, we can calculate the accumulated values for options #7 and #8 using their respective parameters.

After calculating the accumulated values for each option, we can compare them to determine which option will earn the most money.

To answer question #10, comparing options #5 and #6, we need to compare their accumulated values. If the accumulated values are the same, then it doesn't matter whether you invest less money for a longer period of time or more money for a shorter period of time, as long as the total amount invested is the same.

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Answer:

\(3-[-(-1)]=2\)

Step-by-step explanation:

\(3-(-(-1))=3-1\\\)

\(3-1=2\)

\(=2\) ← Our Solution

Hope this helps!

no

Step-by-step explanation:

because it's a prime number

The volume of empty space in the box will be 220cm³

The diameter of the candle is equal to the width of the box (the length of the side of the square base of the box), and the height of the box is equal to the height of the candle, assuming that the candle fits tightly inside the box without wasting any room.

You may compute the prism's volume by multiplying it by the square base's area (height).

The area of the circular base can be used to compute the volume of the candle's cylinder (height).

The square box base's side measures 8 cm long, hence its area is equal to that measurement= 8cm²=64cm²

The candle's diameter is two times its radius, hence the radius is 8cm/2=4cm

area of the circular base thus Equals (A = π r²).

=πx4²

=16π²

Since the height of the candle and of the box is 16cm, the difference in volume is 1024-256π

=220cm³

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Answer:

Step-by-step explanation:

The distributive property of multiplication over addition tells us that the product of a value and a sum will be the same as the sum of products of the value and the sum's addends. This property can be used to add or remove parentheses from an arithmetic expression.

  a(b +c) = ab +ac . . . . expression of the distributive property

__

When applying the distributive property to a sum, the first step is to look for a factor common to the terms of the sum. That factor need not be the greatest common factor, though it is often useful if it is.

Below, we have written each expression using two different common factors.

  27x +24x = x(27 +24) = 3x(9 +8)

__

  0.5n +2.5 = 0.5(n +5) = 2.5(n/5 +1)

_____

Additional comment

Finding a common factor can make use of knowledge of multiplication tables, rules of exponents, and identities involving various functions used in algebraic expressions. It is sometimes useful to list the prime factors of each of the terms as an aid to finding a common one. Where fractions are involved, it is sometimes helpful to express them all using a common denominator.

The Euclidean Algorithm can also be useful for finding common factors.

Answer:

-3,8

Step-by-step explanation:

The request is to download a document and complete the proof of the Triangle Sum Theorem. After finishing the proof, the completed file should be saved for upload on a webpage.

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees. To complete the proof, it is necessary to provide a logical and coherent argument that supports this theorem. The document provided likely contains a partially completed proof, and the task is to finish it.

The proof of the Triangle Sum Theorem typically involves using the properties of parallel lines and alternate interior angles. By extending one side of the triangle, parallel lines can be created that intersect with the other sides. This forms interior and exterior angles that can be related to the interior angles of the triangle. Through geometric reasoning and the use of angle relationships, the proof should demonstrate that the sum of the interior angles of a triangle equals 180 degrees.

Once the proof is completed, the document should be saved for upload on the webpage specified, most likely for evaluation or further review. It is important to follow any instructions provided regarding the file format or naming conventions for the upload.

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Answer:

10x - 40 = 100, x = 14

Step-by-step explanation:

At a flower shop, there are 10 bouquets with the same amount of flowers in each of them. In total, 40 flowers were purchased. Now, there are 100 flowers left in the shop. How many flowers are in a bouquet?

This situation can be represented by

10x

- 40

= 100

Answer: The slope of the line passing through the points (1,-1) and (4,3) is 4/3

Explanation:

The two points marked on the green line are (1,-1) and (4,3)

Let's use the slope formula.

\((x_1,y_1) = (1,-1) \text{ and } (x_2,y_2) = (4,3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{3 - (-1)}{4 - 1}\\\\m = \frac{3 + 1}{4 - 1}\\\\m = \frac{4}{3}\\\\\)

The slope is 4/3

slope = rise/run = 4/3

rise = 4

run = 3

It means "go up 4 and to the right 3" so we can move from (1,-1) to (4,3).

4th term of an AP = 10

11th term exceeds 4th term by 1.

the sum of 20 terms ​

⟹ 11th term = 10 + 11 = 11.

We know that,

nth term of an AP (an) = a + (n - 1)d

Hence,

⟹ a₄ = a + (4 - 1)d

⟹ a + 3d = 10

⟹ a = 10 - 3d -- equation (1)

⟹ a₁₁ = a + (11 - 1)d

Substitute the value of a from equation (1).

⟹ 10 - 3d + 10d = 11

⟹ 7d = 11 - 10

⟹ 7d = 1

⟹ d = 1/7

Substitute the value of d in equation (1).

⟹ a = 10 - 3(1/7)

⟹ a = (70 - 3)/7

⟹ a = 67/7

Now,

Sum of first n terms of an AP (Sn) = n/2 * [ 2a + (n - 1)d ]

⟹ S₂₀ = 20/2 * [ 2(67/7) + (20 - 1)(1/7) ]

⟹ S₂₀ = 10 (134 + 19)/7

⟹ S₂₀ = 1530/7

∴ Sum of first 20 terms of the given AP is 1530/7.

I hope it will help you.

Regards.

Answer:

→ 11(2 + y) + 11y

→ 22 + 11y + 11y = 154

→ 22y + 22 = 154

→ 22y = 154 - 22

→ 22y = 132

→ y = 132/22

→ y = 6

Step-by-step explanation:

The correct answer is c. 6 ft³.To calculate the volume of the sculpture, we need to find the volume of one pyramid and then multiply it by four.

The volume of a pyramid can be calculated using the formula V = (1/3) * base area * height. In this case, the base area of the pyramid is a square with side length 2 feet, so the area is 2 * 2 = 4 square feet. The height of the pyramid is 6 feet. Plugging these values into the formula, we get V = (1/3) * 4 ft² * 6 ft = 8 ft³ for one pyramid. Since there are four identical pyramids, the total volume of the sculpture is 8 ft³ * 4 = 32 ft³.

However, the question asks for the volume of sculpting material needed, so we need to subtract the volume of the hollow space inside the sculpture if there is any. Without additional information, we assume the sculpture is solid, so the volume of material needed is equal to the volume of the sculpture, which is 32 ft³. Therefore, the correct answer is c. 6 ft³.

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The first function represents the graph of a function provided in the picture option first is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function shown in the picture.

\(\rm f\left(x\right)\ =\ -\sqrt{\left(x-3\right)}\ +\ 2\)

x - 3 ≥ 0

x ≥ 3

Plug x = 3

f(x) = 2

Thus, the first function represents the graph of a function provided in the picture option first is correct.

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Answer:

Since it is area, it is most defined as base times height, so the larger rectangle would be 9x14 which is 126 and the smaller rectangle is 6x8 which is 48, and since they are together in one shape, you can add both areas which would give you an answer of 174

Step-by-step explanation:

Answer:

D.  1.8c

Step-by-step explanation:

Step 1:

c - 0.2c

Answer:

1.8c

Hope This Helps :)

The number of ounces in an imperial quart is 40

An imperial quart is a unit of volume measurement used in the British system of units, primarily in the United Kingdom and its former colonies.

Here we have to convert imperial quarts to the ounces

It is equal to 1/4 of an imperial gallon, which is approximately 1.201 US liquid quarts. Therefore, an imperial quart is equal to 40 fluid ounces.

This means that if you have an imperial quart of liquid, you have 40 ounces of that liquid. The imperial quart is not commonly used in the United States, where the US customary system of units is used, and the quart is defined as 32 fluid ounces.

Therefore, there are 40 ounces in an imperial quarts

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Answer:6.28

Step-by-step explanation:

you multaply 2 feet by 3.14 because diameter is cercumfrence times pie

Answer: y = 60

the value of y will be 60 when the value of x is 1.

Solution set = (1 , 60)

hope that helps...

To find a linear function h(x) given two points, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Where m is the slope, (x1, y1) and (x2, y2) are the two points.

In this case, the two points are (-3, -4) and (-9, -5). Plugging in the values into the formula, we get:
m = (-5 - (-4)) / (-9 - (-3))
m = (-1) / (-6)
m = 1/6
Now that we have the slope, we can use the point-slope form of a linear equation to find the function h(x):
y - y1 = m(x - x1)
Plugging in the slope and one of the points, we get:
y - (-4) = (1/6)(x - (-3))
y + 4 = (1/6)(x + 3)
y = (1/6)x + 3/6 - 4
y = (1/6)x - 21/6

Simplifying the equation, we get:
y = (1/6)x - 7/2

Therefore, the linear function h(x) is:
h(x) = (1/6)x - 7/2

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Answer:

a) subtracting '8' on both sides, we get

                                      - 5 x² + 8-8 = 133-8

                                        - 5 x²  = 125

b) The solution is x = 5 i

Step-by-step explanation:

Explanation:-

Step (i):-

Given quadratic equation  - 5 x² + 8 = 133

subtracting '8' on both sides, we get

                                      - 5 x² + 8-8 = 133-8

                                       - 5 x²  = 125

Step(ii):-

dividing '-5' on both sides, we get

          \(\frac{-5 x^2}{-5} = \frac{125}{-5}\)

            x²  = -25

            \(x = \sqrt{-25}\)

            x = 5 i

Answer:

its b

Step-by-step explanation:

Answer: Its is 1

Step-by-step explanation:

Answer:

The answer should be 17.15!

Hope this helps(:

Step-by-step explanation:

Answer:

17.15$ I just need to get those 20 letters

Answer:

It would be -5 + -6 = 65

Step-by-step explanation:

Add it up to together by removing the -

The ounces of food eaten by Becca is 29 ounces.

This is a question of linear equation in one variable.

Given that:-

Total amount of food eaten by Liz and Becca = 152 ounces

Also, Liz ate seven more ounces that 4 times the amount Becca ate.

We have to find the ounces of food eaten by Becca.

Let the ounces of food eaten by Becca be x.

Hence, we can write,

Food eaten by Liz = (4x + 7) ounces

Total food eaten = 152 ounces = x + (4x + 7) = 5x + 7

Hence,

152 = 5x + 7

5x = 152 - 7

5x = 145

x = 145/5 = 29 ounces.

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y in equation 1

-28=3 is false, therefore the system of equations has no solution

Answer:

Step-by-step explanation:

The angle defines the slope,

there for slope=tan6π/7

To find an equivalent vector XY with initial point X and terminal point Y for the vector v=<-3,-4>, we need to add the coordinates of the initial point X to the coordinates of the vector v to get the coordinates of the terminal point Y.

So, let's choose an initial point X with coordinates (x,y) and add the coordinates of the vector v to get the coordinates of the terminal point Y, which will be (x + (-3), y + (-4)). Simplifying this expression, we get (x - 3, y - 4). Therefore, an equivalent vector XY with initial point X and terminal point Y for the vector v=<-3,-4> is given by XY=.

Now, let's find an equivalent vector RS with initial point R and terminal point S for the given vector v. Again, we need to add the coordinates of the initial point R to the coordinates of the vector v to get the coordinates of the terminal point S.

So, let's choose an initial point R with coordinates (a,b) and add the coordinates of the vector v to get the coordinates of the terminal point S, which will be (a + (-3), b + (-4)). Simplifying this expression, we get (a - 3, b - 4). Therefore, an equivalent vector RS with initial point R and terminal point S for the vector v is given by RS=.

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