If a circle has an area of 12π cm² and a diameter of line AB, what is the length of arc AB?

The surface area obtained by rotating about the y -axis is 168.159.

In mathematics, integration is a technique for combining or adding the parts to arrive at the total. It is a form of differentiation in reverse where we break down functions into their component elements. This technique is employed to determine the summation on a sizable scale.

We have the function y=1+5x² from x=0 to x=2 about the y -axis.

So, the Surface are is

S = 2π ∫ R(x) √ (1+ f'(x)²}

Then, f'(x) = 10x

Then, S = 2π ∫ R(x) √ (1+ f'(x)²}

= 2π ∫ (1+5x²) √ (1+100x²)

= 1/150 (401 (√401-1)) π

= 168.159

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Answer:

39,580

Step-by-step explanation:

It means to multiply 9895 4 times.

Hope this helps.

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

The given function is f(x) = (3x + 6)/(x + 4.5)The domain of the function f(x) = (3x + 6)/(x + 4.5) is given as{-3, -1, 2, 4, 5 .The range of a function is defined as the set of all possible values that the function can take.

 we can put some arbitrary values of x and then find the corresponding values of f(x).Let's take x = -3.Substituting the value of x = -3 in the given function, we get f(x) = (3x + 6)/(x + 4.5) = (3(-3) + 6)/(-3 + 4.5) = -3Putting x = -1Substituting the value of x = -1 in the given function, we get f(x) = (3x + 6)/(x + 4.5) = (3(-1) + 6)/(-1 + 4.5) = 0.67Putting x = 2Substituting the value of x = 2 in the given function, we get f(x) = (3x + 6)/(x + 4.5) = (3(2) + 6)/(2 + 4.5) = 1Putting x = 4Substituting the value of x = 4 in the given function . Hence, the range of the given function is {-3, 0.67, 1, 2, 3}.

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Given:

Total number of students = 40

In the school ECA club, 3/8 of the students chose chess.

Of the students who chose chess, 4/5 also chose painting.

To find:

The number of student who chose both chess and painting.

Solution:

Total number of students = 40

3/8 of the students chose chess. So, number of students who chose chess is

\(\dfrac{3}{8}\times 40=15\)

Of the students who chose chess, 4/5 also chose painting. So, number of students who chose both chess and painting is

\(\dfrac{4}{5}\times 15=12\)

Therefore, 12 students chose both chess and painting.

Answer:

v=Bh

B=6×4.5

v=27×9

v=243ft³

The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.

The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.

The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.

Where:

A = future value

P = Present value of investment

i = interest rate

n = number of periods.

The future value of the investment can also be determined using an online finance calculator, as follows.

Then the interest is the difference between the future value and the present value.

Initial deposit = $8,241.78

Interest rate = 5.5% compounded daily

Investment period = 31 days

N (# of periods) = 31 days

I/Y (Interest per year) = 5.5%

PV (Present Value) = $8,241.78

PMT (Periodic Payment) = $0

Results:

FV = $8,280.37

Total Interest $38.59 ($8,280.37 - $8,241.78)

Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.

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The position of the center of mass of the weighted wheel is 5.11 cm out from the center. The moment of inertia about an axis through its CM, perpendicular to its face is roughly 26357 kg cm².

(a) We must take into account the masses and their various distances from the center in order to determine the location of the weighted wheel's center of mass (CM).

Let's use the symbol x to represent how far the CM is from the wheel's centre. Without a weight, the centre of the wheel, or CM, will be at a distance of 0 cm from the centre.

We can formulate the equation using the center of mass principle:

(m₁ × x₁ + m₂ × x₂)/(m₁ + m₂) = x

where m₁ is the weight's mass (2.0 kg), x₂ is the weight's distance from the center (23 cm), and m₁ is the mass of the wheel (7.0 kg), with x₁ being the distance from the wheel's center (0 cm).

Inserting the values:

(7.0 kg × 0 cm + 2.0 kg × 23 cm) / (7.0 kg + 2.0 kg) = x

(46.0 kg cm)/9.0 kg = x

x ≈ 5.11 cm

As a result, the weighted wheel's centre of mass is located 5.11 cm out from the centre.

(b) The parallel-axis theorem can be used to determine the weighted wheel's moment of inertia around an axis that passes through its CM and is perpendicular to its face. The following equation gives the wheel's moment of inertia about its own axis (via the center):

I(wheel) = (1/2) × m(wheel) × r²

where r is the wheel's radius (38 cm) and m(wheel) is the wheel's mass (7.0 kg).

Calculations for the weight's moment of inertia around the same axis are as follows:

I(weight) = m(weight) × d²

where d is the weight's distance from the axis (which is equal to the weight's distance from the center, 23 cm), and m(weight) is the weight's mass (2.0 kg).

By summing the inertial moments of the wheel and the weight, one may get the moment of inertia of the weighted wheel about the axis through its CM:

I(total) = I(wheel) + I(weight)

I(total) = (1/2) × m(wheel) × r² + m(weight) × d²

I(total) = (1/2) × 7.0 kg × (38 cm)² + 2.0 kg × (23 cm)²

I(total) ≈ 26357 kg cm²

Consequently, the weighted wheel's moment of inertia along an axis through its CM that is perpendicular to its face is roughly 26357 kg cm².

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Answer:

Each hour the water will rise 10 in. After 4 hours the water will be 40 in deep. It will take 8 hours for the water to reach a depth of 80 in.

The probability that Akira will choose apple pie and Paula will choose strawberry cheesecake for dessert is; B: 0.028

We are told that;

There are 6 dessert options menu.

Now, Akira and Paula like all of the choices equally. Thus, probability of selecting any of the 6 menus will be; P(select 1 menu) = 1/6

Thus, probability that they select the preferred menu written in the question is; P(both select 1 menu) = 1/6 * 1/6 = 0.028

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Answer:

None of the given points satisfy the inequality 2x - 3y < 1.

Step-by-step explanation:

To determine which points satisfy the inequality 2x - 3y < 1, we can substitute the coordinates of each point into the inequality and check if the inequality holds true.

Let's consider the given points:

Point A: (1, 0)

2(1) - 3(0) < 1

2 - 0 < 1

2 < 1 (False)

Point B: (-1, -1)

2(-1) - 3(-1) < 1

-2 + 3 < 1

1 < 1 (False)

Point C: (3, -2)

2(3) - 3(-2) < 1

6 + 6 < 1

12 < 1 (False)

None of the given points satisfy the inequality 2x - 3y < 1.

Therefore, none of the points A, B, or C satisfy the inequality.

Step-by-step explanation:

1 pound = 5 cups

3 pounds = 5 ×3

= 15 cups

Answer:

2.50 + 2.65x = y

Step-by-step explanation:

The 2.50 fee won't change but the price per mile will, each mile will cost $2.65 more. And since we don't know how many miles the plot is taking, $2.65x. Then the total cost is y

Answer:

Step-by-step explanation: if the 2.50 is staying the same, then the answer is y=2.50x + 2.65

Answer:

i have the same question

Step-by-step explanation:

i have the same question

Answer: 17 minutes and 30 seconds

Step-by-step explanation:

You would do 35,000 ÷ 2,000 = 17.5 therefore it's 17 minutes and 30 seconds until the airplane will reach the ground

Answer:

96 ft/s toward home plate

Step-by-step explanation:

because I Know this because I actually teached a class about this

The velocity of the ball is 96.031 ft/second if a pitcher throws a baseball to home plate from a distance of 60.5 ft the ball reaches home plate in 0.63 seconds.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

A pitcher throws a baseball to home plate from a distance of 60.5 ft the ball reaches home plate in 0.63 seconds.

The distance baseball traveled = 60.5 ft

Time it takes = 0.63 seconds

As we know, the distance-time relationship:

u = d/t

Here, u is the velocity

d is the distance

t is the time

u = 60.5/0.63

u = 96.031 ft/second

Thus, the velocity of the ball is 96.031 ft/second if a pitcher throws a baseball to home plate from a distance of 60.5 ft the ball reaches home plate in 0.63 seconds.

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The answers are:

A. Toy car is being pushed across the floor by a child.

D. A ball is kicked around the room.

E. A weight is raised over the head of the lifter.

When a force is applied to an object and the object is moved in the direction of the force, mechanical work takes place. In other words, when a force acts on an object to induce a displacement, work is being done. The force's magnitude times the distance it acts on equals the quantity of work that is completed. if the force applies in a straight line and is constant

The following three examples of mechanical work are

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Answer:

-34 (?)

Step-by-step explanation:

I think it's -34. I'm making a reasonable guess. I'm in fifth grade, so I think it's -34. Sorry if I'm wrong..

Answer:

82 square feet

Step-by-step explanation:

The surface area of this pyramid:

\(5(4) + 2(\frac{1}{2} (4)(7) + \frac{1}{2} (5)(6.8))\)

\(20 + 2(14 + 17)\)

\(20 + 2(31) = 20 + 62 = 82\)

Answer:

\(V(x)=3(x-6)(x-6)\)

Step-by-step explanation:

Polynomial Factoring

The volume of a cardboard box is expressed as:

\(V(x)=3x^2-36x+108\)

It's required to factor that expression.

First, factor out 3:

\(V(x)=3(x^2-12x+36)\)

The expression in parentheses is a perfect square:

\(\boxed{V(x)=3(x-6)(x-6)}\)

The probability is approximately 0.6915, or 69.15%..

Given that the mean (μ) of VO₂MAX scores for men aged 20 to 29 is 42 ml/min/kg and the standard deviation (σ) is 6 ml/min/kg, we can standardize the value of 45 ml/min/kg to calculate the probability using the z-score formula: z = (x - μ) / σ.

Substituting the values into the formula,

z = (45 - 42) / 6 = 0.5

Using a standard normal distribution table or calculator, we find the probability corresponding to a z-score of 0.5 is approximately 0.3085.

To find the probability of a score greater than 45 ml/min/kg, we subtract the obtained probability from 1:

1 - 0.3085 = 0.6915

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Answer:

the correct anwser is b b cause they both are positive y intercepts

a. The value of the annuity is $326,450 and b. the interest is $99,451.

Periodic Deposit = $2000

Rate = 5.25% compounded quarterly

Time = 8 years

Since the deposits are made at the end of every three months, there are 8 * 4 / 3 = 10.6667 compounding periods.

Applying the formula to calculate the future value of an annuity:

FV = PMT x [((1 + r / n)^(n*t) - 1) / (r/n)]

where FV = Future Value of Annuity, PMT = Periodic Deposit, r = Interest Rate per compounding period, t = Time in years and n = Number of compounding periods

Therefore, the Future Value of Annuity is:

FV = $2000 x [((1 + 0.0525 / 4)^(4*10.6667) - 1) / (0.0525/4)] ≈ $326,449.56

Rounded to the nearest dollar, the future value is $326,450.

To find the interest, we subtract the sum of all deposits from the Future Value of Annuity, which is:

Interest = $326,449.56 - ($2000 x 4 x 8)≈ $99,450.56

Rounded to the nearest dollar, the interest is $99,451.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

The account starts at 2000$

2000$×0.06(same as 6%)= 120$

The account gains 120$ yearly

A. After 4yrs that would be 480$ interest

120$×4= 480$

2000$+480$= 2480$ after 4yrs

B. Aftee 16yrs that would be 1920$ interest

120$×16= 1920$

1920$+2000$= 3920$

C. 2500$-2000$= 500$

500$÷120$= 4.16yrs

It will take about 4.2 years for the account to reach 2500$

D. 3000$-2000$= 1000$

1000$÷120$= 8.33yrs

It will take about 8.3yrs for the account to reach 3000$

The given table represents the counts from three independent random samples taken from three major cities regarding whether teenagers consumed a soft drink in the past week.

By summing up the counts of teenagers who consumed a soft drink from all three cities and dividing it by the total number of teenagers surveyed, we can calculate the overall proportion. Dividing this proportion by the total number of teenagers and multiplying by 100 will give us the percentage of teenagers who consumed a soft drink.

For example, if the first city had a count of 150 teenagers who consumed a soft drink out of a total of 300 surveyed, the second city had 200 out of 400, and the third city had 180 out of 350, the overall proportion would be (150 + 200 + 180) / (300 + 400 + 350) = 530 / 1050. Multiplying this by 100, we find that approximately 50.48% of teenagers consumed a soft drink in the past week based on the combined sample.

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A research center conducted a national survey about teenage behavior. Teens were asked whether they had consumed a soft drink in the past week. The following table shows the counts for three independent random samples from major cities. Baltimore Yes 727 Detroit 1,232 431 1,663 San Diego 1,482 798 2,280 Total 3,441 1,406 4,847 No 177 904 Total (a) Suppose one teen is randomly selected from each city's sample. A researcher claims that the likelihood of selecting a teen from Baltimore who consumed a soft drink in the past week is less than the likelihood of selecting a teen from either one of the other cities who consumed a soft drink in the past week because Baltimore has the least number of teens who consumed a soft drink. Is the researcher's claim correct? Explain your answer. (b) Consider the values in the table. (i) Baltimore Detroit San Diego 0 0.1 0.9 1.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Relative Frequency of Response (ii) Which city had the smallest proportion of teens who consumed a soft drink in the previous week? Determine the value of the proportion. (c) Consider the inference procedure that is appropriate for investigating whether there is a difference among the three cities in the proportion of all teens who consumed a soft drink in the past week. (i) Identify the appropriate inference procedure. (ii) Identify the hypotheses of the test.

Answer:

The value of x in given question will be \(x=\frac{k+c}{7}\)

Step-by-step explanation:

Given data:

7x-c=k

Now,

7x-c=K

7x=K+c

\(x=\frac{k+c}{7}\)

Therefore,

The value of x in given question will be : k+c/7

Answer:

75 percent

Step-by-step explanation:

Answer:

\(p = 7 \\ p \times 9 \\ \\ 7 \times 9 \\ \\ = 63\)

if P= 7

then,

p×9 = 7×9

=63.