PLEASE HELP!! Thank you in advance.
The formula for the lateral surface area of a cylinder is S=2πrh , where r is the radius of the bases and h is the height.

Solve for h.

Answer:

$595.34

Step-by-step explanation:

Step one

given data

interest rate of 2.5%= 0.025

final amount= $690

time = 6 years

Required

Principal P

Step two

The compound interest formula is

\(A= P(1+r)^t\)

substitute

\(690=P(1+0.025)^6\\\\690=P(1.025)^6\\\\690=P1.159\\\\\)

divide both sides by 1.159

P=690/1.159

P= $595.34

Answer:

590

Step-by-step explanation:

Answer from delta math

Answer:

13.5

Step-by-step explanation:

first let's subtract 6.00 from 6.00 and 26.25

26.25-6=20.25

1.50(m)=20.25

so we need to get rid of the 1.50

so 1.50m divided by 1.50=m

20.25÷1.50=13.5

m=13.5 hope this helps

\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

Given:

Teddy has two sisters. One of them is 3 years younger than Teddy, the other one is 7 years younger than her only brother.

To find:

The age of older sister at the time when the younger sister was born.

Solution:

Let the age of Teddy be x.

One sister is 3 years younger than Teddy.

Age of one sister = x-3 years

The other one is 7 years younger than her only brother. It means other sister is 7 years younger than Teddy.

Age of other sister = x-7 years

Clearly (x-3) > (x-7). So, difference between the ages of sisters is

\(Difference=(x-3)-(x-7)\)

\(=x-3-x+7\)

\(=4\)

Therefore, the age of older sister is 4 years when the younger sister was born.

Answer:

d

Step-by-step explanation:

Answer:

3.2 × 10^-13

Step-by-step explanation:

Answer:

UMAMI I think may be the answer to your question

Answer:

A

Step-by-step explanation:

Use rise over run. The graph rises by 9 units between the 2 points and runs 3 units on the x axis.

Rise/ run = \(\frac{9}{3}\), which can be simplified to 3.

The slope is 3.

Answer:

3(A)

Step-by-step explanation:

To find the slope, you have to find the difference of the two y values divided by the difference of the two x values. The equation for that would be y₁ - y₂ divided by x₁ - x₂. Let's say for this problem (x₁, y₁) is (3,3) and (x₂, y₂) is (0, -6). (It has a subscript just to show that they are different x and y values)

We can then substitute these values into the equation.

y₁ - y₂ divided by x₁ - x₂ would be 3 - (-6) divided by 3-0

This would then be simplified into

3+6 (2 negatives make a positive) divided by 3

This equals 9/3 which equals 3 as the slope.

we need to find the positive even integers less than k that satisfy the condition nx divided by x leaves a remainder of 2.

To solve this problem, we need to use the information given and work step by step. Let's break it down:

1. The number of toy cars that Ray has is a multiple of x. This means the number of cars can be represented as nx, where n is a positive integer.

2. When Ray loses two cars, the number of cars he has left is a multiple of x. This means (nx - 2) is also a multiple of x.

3. If x is a positive even integer less than k, we need to find the possible values for x.

Now, let's analyze the conditions:

Condition 1: nx - 2 is a multiple of x.
To satisfy this condition, nx - 2 should be divisible by x without a remainder. This means nx divided by x should leave a remainder of 2.

Condition 2: x is a positive even integer less than k.
Since x is even, it can be represented as 2m, where m is a positive integer. We can rewrite the condition as 2m < k.

To find the possible values for x, we need to find the positive even integers less than k that satisfy the condition nx divided by x leaves a remainder of 2. The number of possible values for x depends on the value of k. However, without knowing the value of k, we cannot determine the exact number of possible values for x.

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Answer:

m∠B = 70.0° (nearest tenth)

Step-by-step explanation:

Sine Rule for Angles

\(\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Given:

Substituting the given values into the formula to find m∠C:

\(\implies \sf \dfrac{\sin 40^{\circ}}{13}=\dfrac{\sin C}{19}\)

\(\implies \sf \sin C=\dfrac{19\sin 40^{\circ}}{13}\)

\(\implies \sf C=\sin^{-1}\left(\dfrac{19\sin 40^{\circ}}{13}\right)\)

\(\implies \sf m \angle C=69.96086904^{\circ}\)

Interior angles of a triangle sum to 180°

\(\implies \sf m \angle A+ m \angle B+m \angle C=180^{\circ}\)

\(\implies \sf 40^{\circ} + m \angle B+69.960...^{\circ}=180^{\circ}\)

\(\implies \sf m \angle B=70.03913...^{\circ}\)

Therefore, m∠B = 70.0° (nearest tenth)

Answer:

14.4

Step-by-step explanation:

Cross multiply.

5x = 8 * 9

5x = 72

x = 14.4

Answer:

x= 14.4

Step-by-step explanation:

1. cross multiply

5*x and 8*9

5x=72

2. divide 72 by 5

x= 14.4

Answer:

Step-by-step explanation:

jill has 4 one dollar bills, and Mark has 3 one dollar bills so 3 of them would cancel out, so jill would have one more dollar. And then we also know that Jill has 4 dimes, and Mark also has 4 dimes. So they cancel out. And Jill has 3 pennies, and Mark has 2, so Mark has one more penny than Mark. And lastly we know that Jill has 3 quarters. So know we add it all up Jill has 1 dollar, 3 quarters and 1 penny. Which is $1.76.

Answer:

Step-by-step explanation:

Jill's money:

4 one dollar bills- 4 x 1 = 4

3 quarters: 3 x 0.25 = 0.75

4 dimes: 4 x 0.10 = 0.4

3 pennies: 3 x 0.01 = 0.03

4 + 0.75 + 0.4 + 0.03 = $5.18

Jill has $5.18

Mark's Money:

3 one dollar bills: 3 x 1 = 3

4 dimes: 4 x 0.10 = 0.4

2 pennies: 2 x 0.01 = 0.02

3 + 0.4 + 0.02 = $3.42

Mark has $3.42

To find the difference between these values, we subtract.

5.18 - 3.42 = $1.72

The difference between Jill's money and Mark's money is $1.72

$1.72 is your answer.

A regular octagon is formed by cutting an isosceles right triangle from each of the corners of a square. To find the length of the side of the octagon, we can use the Pythagorean theorem to calculate the length of the hypotenuse of the isosceles right triangle.

In an isosceles right triangle, the two legs have the same length and the hypotenuse is the side opposite the right angle. Since the square has sides of length 2000, half of the side of the square is the leg of the isosceles right triangle.

So the leg of the isosceles right triangle is 2000/2 = 1000.

Applying the Pythagorean theorem to find the hypotenuse of the isosceles right triangle:

c^2 = a^2 + b^2

c = sqrt(a^2 + b^2)

c = sqrt(1000^2 + 1000^2)

c = sqrt(1000000)

c = 1000*sqrt(2)

So the length of each side of the octagon is 1000sqrt(2)

Answer:

540 feet 5 feet

Step-by-step explanation:

they're both feet, it cant be a rate.

Answer:

Step-by-step explanation:

The matching of exponential functions to table values involves matching both initial values and rate of growth. The value of a geometric series can be calculated from its formula, or can be shown by a calculator or spreadsheet.

The starting values of the two sequences are different, as are all of the starting values of the answer choices. Matching starting values is sufficient to identify which sum goes with which player.

The series ...

  \(\displaystyle S=\sum_{k=1}^n{AB^{k-1}}\)

gives the sum of a geometric sequence with first term A and common ratio B.

The first term of Erica's series is A=30. The ratio is B=42/30 = 1.4.

The first term of Marquis's series is 50. The ratio is B=75/50 = 1.5.

Using these values in the series formula, the total score after n rounds will be ...

  \(\displaystyle \text{Erica:}\quad \sum_{k=1}^n{30(1.4)^{k-1}}\qquad\text{matches Row 3}\\\\\text{Marquis:}\quad \sum_{k=1}^n{50(1.5)^{k-1}}\qquad\text{matches Row 2}\)

The explicit expression for these sums is ...

  \(S=A\dfrac{B^n-1}{B-1}\)

Then the total scores after 6 rounds are ...

  Erica: 30(1.4^6 -1)/0.4 = 489.7152

  Marquis: 50(1.5^6 -1)/0.5 = 1039.0625 . . . . . matches row 4

Then the required table gets filled in ...

__

Additional comment

The values in the attached table are total scores after each round. One must subtract the previous round's total to find the points scored in a given round.

The purpose of showing totals is to permit matching the value seen in Row 4 of the table.

Answer:

A

Step-by-step explanation:

6 (2) - 4 (3)

12 - 12

0

hope this helps you

Answer:

x = -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

-9x + 1 = -x + 17

Step 2: Solve for x

Answer:

4739 CDs

Step-by-step explanation:

Given the function that models the rate at which the disc is sold expressed as;

R(t)=20,000e^−0.12t

t is the number of weeks since the CD was first released

We are to look for the number of CDs that are expected to be sold during the first 12 weeks after the release. To do this, you will simply substitute t = 12 into the modeled function and get R(12) as shown;

R(t)=20,000e^−0.12t

R(12)=20,000e^−0.12(12)

R(12)=20,000e^−1.44

R(12)=20,000(0.2369)

R(12) = 4738.56

Hence the total number of CDs expected to be sold to nearest thousand is 4739 CDs

Answer:

127,000

Step-by-step explanation:

you take the integral from 0 to 12 of R(t)

Answer:

LOL i belive its 200 because i did this exact same thing yesterday for homework and got it right so yeah i guess it is?

Step-by-step explanation:

The probability of P(3 < X ≤ 6) is approximately 0.6575.

The study of probabilities, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.

To find P(3 < X ≤ 6), where X represents the number of times heads is tossed when a fair coin is tossed 10 times, we need to calculate the probability of obtaining more than 3 but less than or equal to 6 heads.

Since the coin is fair, the probability of getting heads on any single toss is 0.5, and the probability of getting tails is also 0.5.

We can use the binomial probability formula to calculate the probability for a specific number of heads in a given number of coin tosses:

P(X = k) = (n choose k) * \(p^k\) *\((1-p)^{(n-k)\),

where n is the number of trials, k is the number of successful outcomes, p is the probability of success on each trial, and (n choose k) is the binomial coefficient.

In this case, n = 10 (10 coin tosses), p = 0.5 (probability of heads), and we want to calculate the probability for 4, 5, and 6 heads.

P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6)

Using the binomial probability formula, we can calculate these probabilities:

P(X = 4) = (10 choose 4) * \((0.5^4) * (0.5^6)\) = 210 * 0.0625 * 0.015625 = 0.2063

P(X = 5) = (10 choose 5) * \((0.5^5) * (0.5^5)\) = 252 * 0.03125 * 0.03125 = 0.2461

P(X = 6) = (10 choose 6) * \((0.5^6) * (0.5^4)\) = 210 * 0.015625 * 0.0625 = 0.2051

Finally, we can calculate the desired probability:

P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2063 + 0.2461 + 0.2051 = 0.6575

Therefore, P(3 < X ≤ 6) is approximately 0.6575.

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Answer:

(n + 4)(n+ 22)

Step-by-step explanation:

One way to determine which factored expression is accurate is by asking the question: "Which two numbers multiply to 88, but add to 26?" If you are having difficulty using this method, you can always try the guess-and-check method with a multiple choice question. This way involves multiplying the terms inside one set of parentheses with the terms inside the other set of parentheses.

Step #1: Multiply the first terms

(n + 4)(n + 22) ----> n x n = n²

Step #2: Multiply the inside terms

(n + 4)(n + 22) -----> 4 x n = 4n

Step #3: Multiply the outside terms

(n + 4)(n + 22) -----> n x 22 = 22n

Step #4: Multiply the last terms

(n + 4)(n + 22) -----> 4 x 22 = 88

Step #5: Write the new expanded equation and simplify

(n + 4)(n + 22) -----> n² + 4n + 22n + 88 -----> n² + 26n + 88

Answer:

V≈47.12cm³

Step-by-step explanation:

i really hope this helps

To find an unbiased estimate for lambda s, we can use the sample mean as an estimate for the parameter. The sample mean is calculated by adding up all the observed values of X and dividing by the number of observations.

In this case, we have:

Sample mean = (8+5+0+10+0+3+1+12+2+7+9+6)/12 = 5.5

Therefore, an unbiased estimate for lambda s is 5.5.

To find an unbiased estimate for the average number of flaws per square yard, we simply use the same estimate as above since lambda s represents the average number of flaws per square yard.

Thus, an unbiased estimate for the average number of flaws per square yard is also 5.5.

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Answer: 8.54701% difference

Step-by-step explanation: (61-56)/[(61+56)/2] x 100= 8.55%

Answer:

Step-by-step explanation:

To find the cost of the least expensive fence, we need to determine the dimensions of the rectangular area that minimize the cost. Let's assume the length of the rectangle is L and the width is W.

The area of a rectangle is given by the formula: A = length × width.

In this case, we have A = 20,000 ft².

So, L × W = 20,000.

To minimize the cost, we need to minimize the perimeter of the rectangle since that's where the cost of the fence lies.

The perimeter of a rectangle is given by the formula: P = 2(length + width).

In this case, we have P = 2(L + W).

To find the least expensive fence, we need to minimize the cost, which is the sum of the costs of the four sides of the fence.

Cost = (2 sides × $4/ft) + (2 sides × $8/ft)

Cost = 8(L + W) + 16(L + W)

Cost = 24(L + W)

Now we can substitute L × W = 20,000 into the cost equation:

Cost = 24(L + W)

Cost = 24(20000/W + W)

To minimize the cost, we need to find the value of W that minimizes the equation. We can do this by finding the derivative of the cost equation with respect to W and setting it equal to zero. However, this calculation is beyond the scope of this text-based interface.

So, we can solve this problem by trial and error or using mathematical software to find the values of L and W that minimize the cost.

Once we have the values of L and W, we can calculate the cost using the equation:

Cost = 24(L + W).

Without knowing the specific values of L and W, we cannot calculate the exact cost of the least expensive fence.

Answer:

B) 131°

Step-by-step explanation:

-4a + 139 = 4a + 123 because they are vertical angles

-4a + 139 = 4a + 123

reduce:

8a = 16

a = 2

4(2) + 123 = 131°

The given integral ∫(4x^2 + 4x + 2) dx can be evaluated to obtain an expression in the form P arctan(ax + b) + c, where P, a, b, and c are constants. The common divisor of P and q is 1, and the value of P is 9.

In the given expression, the integral of 4x^2 is (4/3)x^3, the integral of 4x is 2x^2, and the integral of 2 is 2x. Summing up these integrals, we get (4/3)x^3 + 2x^2 + 2x + C, where C is the constant of integration.

To express this in the form P arctan(ax + b) + c, we need to manipulate the expression further. We can rewrite (4/3)x^3 + 2x^2 + 2x as (4/3)x^3 + (6/3)x^2 + (6/3)x, which simplifies to (4/3)x^3 + (6/3)(x^2 + x).

Comparing this with the form arctan(ax + b), we can see that a = √(6/3) and b = 1. Therefore, the expression becomes 9 arctans (√(6/3)x + 1) + C, where C is the constant of integration.

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Answer:

Step-by-step explanation:

\(a^{m}*a^{n} =a^{m+n}\\\\\\2^{3}*2^{5} = 2^{3+5} =2^{8}\\\\\\3^{2}*3^{4}=3^{2+4} = 3^{6}\\\\\\a^{2}*a^{5}=a^{2+5}=a^{7}\)