On a ferris wheel, Sarah observes that it takes 45 seconds for her chair to complete a full revolution. Her chair is 30 feet from the axle of the ferris wheel.
To the nearest hundreth, Sarah's angular velocity is _____ radians per minute.

The APY for the account would be 3.045%.

What is continuous compounding?

The formula for continuous compounding is given by:

A = P\(e^{(rt)}\)

where:

A = final amount

P = principal amount

e = the mathematical constant e (approximately 2.71828)

r = annual interest rate

t = time in years

In this case, P = $1000, r = 0.03 (since APR is given), and t = 1 year.

Using the formula, we have:

A = 1000\(e^{(0.03*1)}\)

A ≈ $1030.45

So the balance in the account after 1 year is approximately $1030.45.

To find the balance after 5 and 20 years, we simply need to plug in the corresponding values for t:

For t = 5:

A = 1000\(e^{(0.03*5)}\)

A ≈ $1160.92

For t = 20:

A = 1000\(e^{(0.03*20)}\)

A ≈ $1806.11

To find the APY, we use the formula:

APY = (1 + r/n)ⁿ- 1

where:

n = number of compounding periods per year

Since this is continuous compounding, we take the limit as n approaches infinity:

APY = eʳ - 1

APY = \(e^{0.03}\) - 1

APY ≈ 0.03045 or 3.045%

Hence, the APY for the account would be 3.045%.

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9514 1404 393

Answer:

  17

Step-by-step explanation:

Let s represent the smaller number. Then the larger is 3s-7 and their sum is ...

  s +(3s -7) = 61

  4s = 68 . . . . . . . add 7

  s = 17 . . . . . . . . . divide by 4

The smaller number is 17.

__

The larger number is 44.

Answer: 4 units

Step-by-step explanation:

Subtract the x- values of the coordinates.   5 - 1  = 4

You can also count the blocks of the grid between the coordinates to verify your answer.

the y values make no difference here. They would if they were different.

Answer:

Step-by-step explanation:

Hiya Friend! Your answer would be in the same quradrant and 4 units

Answer:

(657)

Step-by-step explanation:

Simplify the following:

3 (300 - 70/5 - (3×23 - (8 - 2×3)))

The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:

3 (300 + -14 - (3×23 - (8 - 2×3)))

-2×3 = -6:

3 (300 - 14 - (3×23 - (-6 + 8)))

8 - 6 = 2:

3 (300 - 14 - (3×23 - 2))

3×23 = 69:

3 (300 - 14 - (69 - 2))

| 6 | 9

- | | 2

| 6 | 7:

3 (300 - 14 - 67)

300 - 14 - 67 = 300 - (14 + 67):

3 ((300 - (14 + 67)))

| 1 |

| 6 | 7

+ | 1 | 4

| 8 | 1:

3 (300 - 81)

| | 9 |

| 2 | | 10

| | |

- | | 8 | 1

| 2 | 1 | 9:

3 (219)

3 (219) = (3×219):

(3×219)

3×219 = 657:

Answer: (657)

Answer:

8

Step-by-step explanation:

7+1

Answer:

x = 100 , y = 6

Step-by-step explanation:

\(\frac{x}{5}\) = 20 ( multiply both sides by 5 to clear the fraction )

x = 5 × 20 = 100

----------------------------

8y - 6 = 9y - 12 ( subtract 9y from both sides )

- y - 6 = - 12 ( add 6 to both sides )

- y = - 6 ( multiply both sides by - 1 )

y = 6

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

más bien ya otro día sera

The correct answer is John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

Let's choose the function "Weekly salary is a function of the hourly pay rate and the number of hours worked."Example: John works as a part-time employee at a grocery store. His hourly pay rate is $12, and he worked for 20 hours in a week. We can evaluate the function to find his weekly salary.

Weekly salary = Hourly pay rate * Number of hours worked

Weekly salary = $12/hour * 20 hours

Weekly salary = $240

So, John's weekly salary is $240 based on his hourly pay rate and the number of hours worked.

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Answer: 4x+1 3/4=10

Step-by-step explanation: Took the test. Plus you can check to see if it equals to - 10 = 10 by replacing x with 2 1/16. Example: 4 * 2 1/16 + 1 3/4 =10. So 10 = 10 is a true match.

The given case can be represented as the equation 4x + 13/4 = 10.

A system of linear equations can be defined as a number of equations needed to solve the equations. For n number of variables n number of equations are required.

Given that,

The length of board = 10 feet.

The length of piece that is cut first = 13/4 feet.

Suppose the length of each remaining piece cut into four equal parts is x feet.

Now, the expression for the total length of the board can be given as the sum of the total length of the remaining piece and the the piece that is cut first.

In mathematical form it can be written as,

4x + 13/4 = 10

Hence, the equation for the given case is 4x + 13/4 = 10.

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Answer:

median: 10 <h <13

mean: 12.12

Step-by-step explanation:

Check the picture below.

Answer:

i believe the answer would be option D

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

10 x sqrt64 - 5 x 4

10 x 8 - 5 x 4

80 - 20

60

Answer: x-intercepts: (-3,0), (1,0)

              vertex: (-1,8)

              axis of symmetry: x = -1

Step-by-step explanation:

Answer:

I believe it's 726=740-S

Answer:

s = 740 - 14

Hope it helps u

Answer:

Yes, Elias got his food before reaching the potluck.

Step-by-step explanation:

Elias left home at 7:00 one morning, determined to make the ten-mile trip to Leaders on a bicycle. Soon thereafter, Elias' parent noticed he had forgotten his potluck dish on the kitchen table, got into the family car, and tried to catch up with the forgetful child. Elias had a fifteen-minute head start, and was pedaling at 12 mph, while the parent pursued at 30 mph. Was Elias reunited with his potluck food before reaching Leaders that day? If so, where? If not, at what time was the food delivered?

Let's set x as the time after the parent leaves as x (time after the first 15-minute headstart)

When the two meet, it means that the distance is equal. Remember, distance = time * speed.

Using this, we know that Elias had a 15-minute headstart at 12 mph, which means that he had 0.25 of an hour. Thus, Elias had a 0.25 * 12 mile headstart.

We can write this equation for the distance Elias traveled.

0.25 * 12 + 12 * x

And this equation for the distance his parent traveled.

30 * x

These equations need to be equal so that the two meet.

0.25 * 12 + 12 * x = 30 * x

Simplify.

3 + 12x = 30x

Subtract 12x from both sides.

3 = 18x

Divide both sides by 18.

x = 1/6

So, it took 1/6 of an hour, which is 10 minutes, for the parent and Elias to meet.

If Elias were to get the food before he reached the potluck, the distance he traveled (0.25 * 12 + 12 * x) needs to be less than 12.

Plug 1/6 in for x.

0.25 * 12 + 12 * 1/6 =

3 + 2 = 5

Elias traveled 5 miles before his parent met him.

So, Elias did get his food before reaching Leaders.

Just in case, let's double-check this answer.

Using the distance = speed * time formula, we know that time = distance/speed. Elias's parent had to travel 5 miles at 30 mph, so it would have taken 1/6 of an hour to drive 5 miles.

Elias traveled at 12 mph for 1/6 + 1/4 of an hour, so he traveled:

(1/6 + 1/4) * 12 =

(4/24 + 6/24) * 12 =

10/24 * 12 =

120/24 = 5 miles

Thus, the previous answer is right.

I hope this helps! Feel free to ask any questions!

∵∵∵∵∵∵∵∵∵∵∵∵.........................ω

The average rate of change is given by the rate of change of both variables.

"Rate" refers to a division. We want to divide the change of y, Δy, by the change of x, Δx:

Δy/Δx

("Δ" means "change").

We want to analyze the change over the interval 3 ≤ x ≤ 9.​

The change from x = 3 and x = 9 is

Δx = 9 - 3 = 6

We observe the right column of the table. When x = 3, y = 28 and when x = 9, y = 4.

The change from y = 28 to y = 4 is

Δy = 4 - 28 = -24

Then, the average rate of change is:

Δy/Δx = -24/6 = -4

Answer: -4

Answer:

Step-by-step explanation:

Martin is two years younger than three times his daughter Ada’s age:

The sum of their ages is 54:

Solving this equation for m:

Eliminate m:

Solve for a:

Find m:

Martin is 40 and Ada is 14

The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

Given that,

Finding the expression that can be utilised to find

20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98.

From the Latin word "per centum," which means "by the hundred," the word "percentage" was borrowed. The denominator of percents is 100, making them fractions. In other words, it is the relationship between a part and a whole in which the value of the whole is consistently set to 100.

Take

20% of 92

Multiply 20%×92

=18.4

45% of 76

Multiply 45% ×76

=34.2

50% of 62

Multiply 50%×62

=31

60% of 92

Multiply 60%×92

=55.2

12% of 98

Multiply 12%×98

=11.76

Therefore,

The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.

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The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Answer:

Step-by-step explanation:

Answer:

the difference of m and 5 is graeter than 10

Answer:

29 beads

Step-by-step explanation:

Red beads: 10

Green beads: 10 - 5 = 5

Yellow beads: 10 + 4 = 14

Add, 10 + 5 + 14 = 29

Albert has 29 total beads

Have a wonderful day! :)

Using the shell method, the volume of the solid generated when R is revolved about the y-axis is V= 324π cubic units.

The shell method refers to a method of finding volumes of the solid by decomposing a solid of revolution into cylindrical shells. It is one of the methods to find the volume of the solid. This solid is generated when region R is rotated about an axis or the y-axis. In case it is y-axis then the following formula is used:

V= ∫_a^b▒〖2πx [f(x)-g(x)]dx〗

Where y = f(x), y = g(x), and the interval is considered as [a,b].

The given curves are: y = 11 − x, y = 0, x = 3, x = 9

V= ∫_3^9▒〖2πx [11-x-0]dx〗

V= 2π∫_3^9▒〖(11x-x^2)dx〗

V= 2π[11/2 x^2-  1/3 x^3]

V= 2π[11/2 9^2-  1/3 9^3-  11/2 3^2+  1/3 3^3]

V= 2π[891/2-  729/3-  99/2+  27/3]

V= 2π[729/2-  702/3]

V= 2π[396-234]

V= 2π[162]

V= 324π cubic units

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Answer:

\(3 \sqrt{5} \)

Step-by-step explanation:

\( \sqrt{ {( - 4 - 2)}^{2} + {(2 - ( - 1))}^{2} } = \sqrt{45} = 3 \sqrt{5} \)

Answer:

3rd option: 32/24

Step-by-step explanation:

8/6 = 4/3

1st option: Now let's change the denominator to 24:

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

2nd option: Now let's change the numerator to 24:

4/3 ==> 24/?

4/3 =

4*6 / 3*6 = 24/18, not 24/32

24/32 = 3/4, not 4/3 ==> don't get confused by this

3rd option: 32/24 is correct [Look at the explanation for 1st option]

4/3 ==> ?/24

4/3 =

4*8 / 3*8 = 32/24, not 3/24.

Hence, the 3rd option is correct.

Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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