Find the 9th term of the geometric sequence 5, -25, 125, ...

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

Quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C(12,4), and D(5, 2) is a parallelogram.

a quadrilateral is a four-sided polygon, having four edges and four corners.

The given vertices of a quadrilateral  ABCD are A(-2, 4), B(5, 6), C(12,4), and D(5, 2).

We need to find the name of the quadrilateral.

The distance =√(x₂-x₁)²+(y₂-y₁)²

AB=√(5+2)²+(6-4)²

=√49+4==√53

CD=√(5-12)²+(2-4)²

=√49+4==√53

AB=CD

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length

Hence, the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C(12,4), and D(5, 2) is a parallelogram.

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The approximate surface area of the package is approximately 245.05 square inches.

The best model for the package is a cylinder.

To calculate the approximate surface area of the package, we need to find the lateral surface area of the cylinder and the area of the circular base.

The lateral surface area of a cylinder can be calculated using the formula:

Lateral Surface Area = 2πrh

where r is the radius of the base and h is the height.

The area of the circular base can be calculated using the formula:

Area of Base = \(πr^2\)

Given that the diameter of the bottom is 9 inches, the radius (r) would be half of that, which is 4.5 inches.

Using the given height of 13 inches, we can now calculate the surface area:

Lateral Surface Area = 2πrh = 2π(4.5)(13) ≈ 117.81 square inches

Area of Base = \(πr^2 = π(4.5)^2 ≈ 63.62\) square inches

To find the total surface area, we add the lateral surface area and the area of the base:

Total Surface Area = Lateral Surface Area + 2 × Area of Base = 117.81 + (2 × 63.62) ≈ 245.05 square inches

Therefore, the approximate surface area of the package is approximately 245.05 square inches.

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Answer:

The answer is 646.02 tell me if you need an explaination

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:10 inches

Step-by-step explanation:

The distance between a two-place on a map is 4 inches. Which is actually 12 miles. To solve for the distance of two places on a map that is 30 miles, you need to find the distance of 1 inch. To find the distance of 1 inch you will need to divide 12 by 4. Which are 3 miles per inch. Then to find how many inches is 30 miles, you need to divide 30 by 3. So when you solve for the answer you should get 10 inches for 30 miles.

First: 12 ÷ 4 = 3

3 miles = 1 inch

Second: 30 ÷ 3 = 10

10 inches = 30 miles

Answer: 10 inches

Answer:

(5x-4)(x+1)

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

This triangle is isosceles, same as the little triangle.

If one side of the little triangle is 3x, then the little side with the tick (let's name it a) is also 3x.

That means the longer side, 2a, is 6x

This triangle is isosceles, so 6x = 4x + 20

Now, if we solve that, x = 10

The answer is 10

Hope this helps :)

Have a good day!

Answer:

Step-by-step explanation:

9kg

Answer:

y>= 2/3(x) - 2.5

Step-by-step explanation:

The sign should be "greater than or equal to" but my keyboard doesn't have that. Sorry.

The slope is "up two, over three" found by finding places where the line passes through the grid lines, and counting.

The y-intercept is -2.5. That tells you the "constant" to put in for "b" in the slope intercept form, y=mx+b

The balance sheet attached shows the Total Assets to be $55.968M  and Total Liabilities and Capital to be $252M respectively.

1. Assets:

  a. Cash in Reserves:

The required reserves are 5.4% of checkable deposits.

Therefore, the required reserves amount to 5.4% of $92 million, which is:

(0.054 * $92 million) = $4.968 million.

This amount is considered a liability for the bank, but it is held as an asset in the form of cash reserves.

  b. Loans: The bank made a $28 million commercial loan and a $23 million mortgage loan. Therefore, the total loans amount to:

total loan =  $28 million + $23 million

                 = $51 million.

2. Liabilities:

  a. Checkable Deposits:

The bank received $92 million in checkable deposits.

  b. Required Reserves:

As mentioned above, the required reserves amount to $4.968 million.

3. Capital:

  The bank started with $155 million in capital.

Based on the above information, the bank's balance sheet would look as attached.

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Answer:

1. any order

2. subtract as the opposite is adding

3. combine like terms

4.

5. opposite of a sum

Step-by-step explanation:

i beileve theese are the answers

If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

Time = Distance/speed

Time taken to row upstream:

(30/2) /(9 - x)

15/(9-x)

Time taken to row downstream:

15/(9 + x)

Total time spent is 6 hours hence,

15/(9- x) + 15/(9 + x) = 6

Cross multiplying

15(9 + x) + 15(9 - x) = 6(9+ x)(9 - x)

= 135 + 15x + 135- 15x =6(81 -9x + 9x - x²)

=270 = 6(81 - x²)

270/6 = 81- x²

45 = 81- x²

x² = 81- 45

x²= 36

x =√36

x = 6

Therefore If the total time to travel downstream and return upstream to the starting point is 6 hours. If the total distance downstream and back is 30 miles, the speed of the river (current speed) is 6.

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Answer:

0.40

Step-by-step explanation:

Change the divisor 1.8 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

We then have the equations:

7.2 ÷ 18 = 0.40

and therefore:

0.72 ÷ 1.8 = 0.40

Both calculated to 2 decimal places.

Answer:

C) 7/2 minutes per lap

Step-by-step explanation:

7 laps/ 2minutes. To find how many minutes it takes Beth to swim one lap, which is her in minutes per lap, you have to divide 7/2 to get 3.5 min/1 lap, or 7/2 min/1 lap.

5(2)^2-2(7) = 6

6(7+2)/2 = 27

Therefor the correct answer is the < symbol.

I hope this helps! :)

Solving for CI in terms of the given lengths, we get: \(Cl=\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }\)

Substituting this expression for CI and the given value for CG into the expression for BI, we get:  \(BI=CG-\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }\).

A triangle is a three-sided polygon, which is a closed two-dimensional shape with straight sides. In a triangle, the three sides connect three vertices, or corners, and the angles formed by these sides are called the interior angles of the triangle. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their side lengths and angle measurements. For example, an equilateral triangle has three sides of equal length, and all of its angles are 60 degrees; an isosceles triangle has two sides of equal length, and its base angles are also equal; a scalene triangle has three sides of different lengths, and all of its angles are also different. Triangles are a fundamental shape in mathematics and geometry, and they have numerous applications in fields such as architecture, engineering, physics, and more.

Given by the question.

Based on the given information, we can start by drawing a diagram of triangle ABC and the segments AH, BJ, CI, CJ, and BI as described.

Since CG = BG, we can draw the perpendicular bisector of side AC passing through point G, which will intersect side AB at its midpoint M.

Now, we can see that triangle CGB is isosceles with CG = BG, so the perpendicular bisector of side CB also passes through point G. This means that G is the circumcenter of triangle ABC, and therefore, the distance from G to any vertex of the triangle is equal to the radius of the circumcircle.

Next, we can use the fact that AJ and BJ are congruent to draw the altitude from point J to side AB, which we will call JN. Similarly, we can draw the altitude from point I to side BC, which we will call IM.

Since AJ and BJ are congruent, the altitude JN will also be the perpendicular bisector of side AB, so it will pass through point M. Similarly, the altitude IM will pass through point G, which is the circumcenter of triangle ABC.

Now, we can use the Pythagorean theorem to find the lengths of JN and IM in terms of the given lengths:

\(JN^{2}= AJ^{2} -AN^{2} \\ = ( AH+HN)^{2} - AN^{2} \\=AH^{2} +2AH*HN+HN^{2}-AN^{2} \\\)

\(IM^{2}= CI^{2} -CM^{2} \\=( CG-GM)^{2} -CM^{2} \\CG^{2}-2CG*GM+GM^{2} -CM^{2}\)

Since CG = BG and GM = BM (since M is the midpoint of AB), we can simplify the expression for IM^2 as follows:

\(IM^{2}\) = \(BG^{2}\) - 2BG * BM + \(BM^{2}\) - \(CM^{2}\)

= \(BG^{2}\) - \(BM^{2}\) - \(CM^{2}\)

Now, we can use the fact that BJ and CI intersect at point K to find the length of KJ:

KJ = BJ - BJ * (CK/CI)

= BJ * (1 - CK/CI)

= BJ * (1 - BM/CM)

To find BM/CM, we can use the fact that triangle BCI is isosceles with BI = CI, so the altitude IM is also a median of the triangle. This means that CM = 2/3 * BI. Similarly, we can find BJ in terms of JN using the fact that triangle ABJ is isosceles with AJ = BJ:

BJ = 2 * JN

Substituting these expressions into the equation for KJ, we get:

KJ = 2 * JN * (1 - 2/3 * BI/CM)

Now, we just need to find BI/CM in terms of the given lengths. Using the fact that triangle BCI is isosceles with BI = CI, we can find BI in terms of CG:

BI = CG - CI

Substituting this expression into the equation for \(IM^{2}\)and simplifying, we get:

\(IM^{2}\) =\(BG^{2}\) - CG * CI

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Answer:

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

Final Answer: \(x = 5\)

Steps/Reasons:

Hey there!

Step 1: Subtract \(3x\) from both sides.

\(5 = 4x - 3x\)

Step 2: Simplify \(4x - 3x\) to \(x\).

\(5 = x\)

Step 3: Switch Sides.

\(x = 5\)

~I hope I helped you :)!

Answer:

width = 4in

length = 8in

Step-by-step explanation:

A = LxW = 32

L = W + 4

W(W+4) = 32

W² + 4W - 32 = 0

(W + 8)(W - 4) = 0

W ≠ -8 (dimensions cannot be negative)

W = 4in

L = W+4 = 4+4 = 8in

SOLUTION:

Let "x" be the number of degrees needed for the temperature to be increased to reach 0°

So we now have,

For the temperature to be increased to reach 0° Fahrenheit, 37° Fahrenheit is what is needed.

Answer:

B

Step-by-step explanation:

They are between integers so they can't be a whole number nor the integer

~~~Hope this helps~~~

Answer: C

Step-by-step explanation:

The statement that is false is no integers are irrational numbers.

Every single integer is a rational number because they do not go on forever.

The answer to the question is option C. Hope this helps!

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

156 cm²

Step-by-step explanation:

The surface area of a square pyramid is a² + 2al if a = the length of the side of the base of the pyramid and l = the height of each triangle. a would be equal to 6 in this case, since it is the length of the side of the base, and l would be 10 because it is the height of each triangle.

So, here's our expression:

6² + 2(6)(10) =

36 + 12(10) =

36 + 120 =

156

The surface area of the square pyramid is 156 cm². If this process doesn't make sense to you or if you'd like some further clarification, please let me know! :)

Answer:

We need more info to solve this problem.

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

FEJ angle is the large angle and the number in red shows how big it is. Remember the whole thing is 180 degrees.

Answer:

x = 58.03°

Step-by-step explanation:

Given:

Solve for x:

1. \(x=cos^{-1}(\frac{9}{17})=58.03\)

Answer:

So, the measure of angle x is equal to 58.03.