what is the formula of cylinder​

Answer:

d

Step-by-step explanation:

The functions that are exponential are f(x) = 4(1/4)ˣ , g(x) = 14(4)ˣ and k(x) = 6(5.49)ˣ , the options that are correct are (a) , (b) and (e) .

In the question ,

five function are given ,

we need to select the functions that are exponential ,

We know that , Exponential function is a function whose value is a constant raised to power of a variable ,

For Example , f(x) = cˣ, where c is any constant value and x is a variable.

Part(a) ,

f(x) = 4(1/4)ˣ

Since , x is in the exponent , hence it is an exponential function .

Part(b) ,

g(x) = 14(4)ˣ

Since , x is in the exponent , hence it is an exponential function .

Part(c) ,

h(x) = 10x⁵

Since , x is present in the base , hence , it is not an exponential function .

Part(d) ,

j(x) = −9x⁴

Since , x is present in the base , hence ,it is not an exponential function .

Part(e) ,

k(x) = 6(5.49)ˣ

Since , x is in the exponent , hence it is an exponential function .

Therefore , The exponential functions are (a) f(x) = 4(1/4)ˣ  , (b) g(x) = 14(4)ˣ   and  (e) k(x) = 6(5.49)ˣ  .

The given question is incomplete , the complete question is

which of the following are exponential functions? select all correct answers.

(a) f(x) = 4(1/4)ˣ

(b) g(x) = 14(4)ˣ

(c) h(x) = 10x⁵

(d) j(x) = −9x⁴

(e) k(x) = 6(5.49)ˣ

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Answer:

Step-by-step explanation:

Permutations and combinations are mathematical concepts that deal with counting the number of different arrangements or selections of objects from a set.

Permutations:

A permutation is an arrangement of objects in a specific order. For example, consider a set of three letters: A, B, and C. There are 3! = 6 possible permutations of these letters, which are ABC, ACB, BAC, BCA, CAB, and CBA. The notation "3!" is the factorial notation, which means 3 × 2 × 1.

Combinations:

A combination is a selection of objects, where the order does not matter. For example, consider a set of three letters: A, B, and C. There are 3 C 2 = 3 possible combinations of two letters from this set, which are AB, AC, and BC. The notation "3 C 2" is the combination notation, which means the number of ways to choose k objects from a set of n objects.

In summary, permutations deal with the arrangement of objects in a specific order, while combinations deal with the selection of objects without regard to the order.

Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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Answer:

the slope of the diagonal of triangle DEF is equal to the slope of the diagonal of triangle GHI

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

Given a line parallel to a side of the triangle and it intersects the other 2 sides then it divides those sides proportionally, that is

\(\frac{x}{24}\) = \(\frac{5}{10}\) ( cross- multiply )

10x = 120 ( divide both sides by 10 )

x = 12

Answer:

B

Step-by-step explanation:

The square root of a negative number does not exist, no real number solution.

The constant of proportionality in table four is -1/3

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

In each of the table, we can check if proportionality exists.

In the first table, there's no proportionality.

In the second table, there's no proportionality

In the third table, there's no proportionality

In the fourth table, proportionality exist here which we can find the constant of proportionality.

When x = 6, y = -2

y = ax

a = constant of proportionality

-2 = a(6)

a = -1/3

The constant of proportionality is -1/3

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The number of children and adult that were there are 117 aand 178 respectively.

Two hundred ninety-five people go to the public swimming pool on a hot summer day. The daily prices are 1.75 for children and 2.00 for adults. The recipients admission total of 560.75 dollars.

The number of children and adult can be calculated as follows;

Using equations,

let

x = number of children

y = number of adult

Therefore,

x + y = 295

1.75x + 2y = 560.75

multiply equation(i) by 2

2x + 2y = 590

1.75x + 2y = 560.75

subtract the equation

0.25 x = 29.25

x = 29.25 / 0.25

x = 117

Hence,

y = 295 - 117

y = 178

Therefore,

number of children = 117

number of adult = 178

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The slope of the line is 25 and Ingrid saves each week is $25.

What is a proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. where the constant of proportionality is also known as slope.

Given, a proportional relationship that can be represented by the equation   y=25x

In the above equation, the constant of proportional = 25

So, by the above definition,

the slope of the line = 25

Ingrid saves each week = 25

Hence, the slope of the line is 25 and Ingrid saves each week is $25.

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Answer: Im pretty sure you do

Step-by-step explanation: your welcome

Answer:

Kindly check explanation

Step-by-step explanation:

Given the question :

A shop sells matching hats and scarves. The scarves cost 1.5 times as much as the hats. Write 2 patterns that could represent the cost of 1,2,3,4,and5 hats and scarves list the first 5 terms of each pattern then write the cost of 6 hats and scarves using the patterns you wrote

Let cost of hats = h

Cost of scarves (s) = 1.5h

Hence of hat = $4 ; Scarve = 1.5 * 4 = 6

___________1__2___3___4___5

Cost of hat__ 4__8___12__16__20

Scarve cost__6__12__18__24__30

cost price * quantity sold

Cost of hat = 6 * $4 = $24

Cost of 6 Scarve = 6 * $6 = $36

Answer:

d

Step-by-step explanation:

Trust

The  determinant of the matrix cannot be uniquely determined from the information given.

The characteristic polynomial of a 2x2 matrix A is given by:

p(λ) = det(A - λI) = λ^2 - tr(A)λ + det(A)

where tr(A) is the trace of A and det(A) is the determinant of A.

In this case, the characteristic polynomial of the matrix is given by:

p(λ) = λ^2 - 5λ + 6

Comparing this to the general form of the characteristic polynomial, we can see that:

- tr(A) = 5
- det(A) = 6

Since the determinant of a 2x2 matrix A is given by:

det(A) = a11*a22 - a12*a21

where aij denotes the entry in the ith row and jth column of A, we can use the fact that det(A) = 6 to solve for the determinant of the matrix. Specifically, we have:

det(A) = a11*a22 - a12*a21 = 6

We don't have enough information to determine the specific values of a11, a12, a21, and a22. However, we do know that their product is 6. For example, we could have:

a11 = 2, a12 = 3, a21 = 1, a22 = 4

which gives det(A) = 2*4 - 3*1 = 5.

Alternatively, we could have:

a11 = 6, a12 = 0, a21 = -1, a22 = -1

which also gives det(A) = 6.

Therefore, the determinant of the matrix cannot be uniquely determined from the information given.

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The amended model is given by:

 h = -9 + (9 - 6d) sin (πt/12) + 12 cos (πt/12) + dt (t = (2 k + 1)/5)

where a = -9, b = 9 - 6d, c = 12 and d is a constant.

Given:The height of a car on a big wheel is modeled by the equation where h is the height of the car above ground in meters, t is time after the ride starts, in seconds, and a, b, c and d are real constants.The initial height of the car is h = 3 m.The maximum height reached on the ride is

h = 12 m, which occurs 6 seconds after the start of the ride.The car completes four full revolutions, and the ride ends with the car in its initial position after 3 minutes.

To Find:

The fairground operator decides to increase the speed of the wheel so that it completes five full revolutions in 2 minutes. Amend the model to reflect this change.

For 4 revolutions, the time period is 60 × 3/4 = 45 seconds

So, for 1 revolution, the time period = 45/4 = 11.25 seconds

We know that, f = 1/T

Now, for 5 revolutions, time period = 2 × 60/5 = 24 seconds

So, frequency, f = 1/24

Therefore, time period,

T = 1/f

=1/(1/24)

= 24 sec

We know that, time period T = 2π/ω

So, angular frequency,

ω = 2π/T

= 2π/24

= π/12

New model:

Height, h = a + b sin (ωt) + c cos (ωt) + d t

Where a, b, c and d are constants.

For h = 3, t = 0

=> 3 = a + c

=> a + c = 3 ……(1)

For h = 12, t = 6

=> 12 = a + b sin (π/2) + c cos (π/2) + 6 d

=> a + c = 3,

b + 6 d = 9

=> b + 6d = 9 ……(2)

For h = 3, the car completes 4 full revolutions

=> (2π/ω) × 4 = 45

=> ω = π/5

=> 5 π t/4 + π/2 = π/2 + kπ

=> t = (2 k + 1)/5 ……(3)

From (2), b + 6d = 9

=> b = 9 - 6d

Putting this value of b in (2), we get,

a = -9 and c = 12

So, the amended model is:

h = -9 + (9 - 6d) sin (πt/12) + 12 cos (πt/12) + dt (t = (2 k + 1)/5)

Hence, the amended model is given by:

 h = -9 + (9 - 6d) sin (πt/12) + 12 cos (πt/12) + dt (t = (2 k + 1)/5)

where a = -9, b = 9 - 6d, c = 12 and d is a constant.

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The cost of each bottle of juice is $0.51.

The tape diagram can be used to illustrate the relationship between the numbers that are given.

Let the cost of each bottle of juice be x.

In this case, she bought a bag of oranges for $2.19 and a 12-pack of juice bottles and the total cost before tax was $8.31.

This will be:.

2.19 + 12x = 8.31

Collect like terms

12x = 8.31 - 2.19

12x = 6.12

Divide

x = 6.12 / 12

x = 0.51

The cost is solved. Note that the tape diagrams weren't given but the.coat is solved accordingly.

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Answer:

The relative frequency is found by dividing the class frequencies by the total number of observations

Step-by-step explanation:

Relative frequency measures how often a value appears relative to the sum of the total values.

An example of how relative frequency is calculated

Here are the scores and frequency of students in a maths test

Scores (classes)              Frequency                Relative frequency

0 - 20                                10                               10 / 50 = 0.2

21 - 40                               15                               15 / 50 = 0.3

41 - 60                               10                               10 / 50 = 0.2

61 - 80                                5                                 5 / 50  = 0.1

81 - 100                             10                                10 / 50 = 0.2

                                          50                                               1

From the above example, it can be seen that :

The constant of proportionality is y divided x so in this case will be:

Answer is C) y = 7x

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Answer:

An expression that is equal to 97/33 is 97 ÷ 33.  

Step-by-step explanation:

Answer: The fraction 97/33 is equivalent 1 to 2 31/33.

Step-by-step explanation:

Answer:

like:-

1/9x20 = 2 2/9

1/9-20 = 19 8/9

Step-by-step explanation:

Answer: The constant rate change would be \(\frac{1}{9}\).

Step-by-step explanation: The general rate of change can be found by using the difference quotient formula. To find the average rate of change over an interval, enter a function with an interval: f (x) = \(x^{2}\) , [2,3]

Write y = \(\frac{1}{9}\)x - 20 as a function which is f (x) = \(\frac{1}{9}\)x - 20

Consider the difference quotient formula which is \(\frac{f (x +h) - f (x) }{h}\).

Find the components of the definition. \(\frac{f (x+h) = \frac{h}{9} + \frac{x}{9} - 20}\)simplify then it would be \(\frac{f (x) = \frac{x}{9} - 20 }\).

Lastly plug in all the components.

\(\frac{f (x + h) - f (x)}{h} = \frac{\frac{h}{9} +\frac{x}{9} - 20 - (\frac{x}{9} - 20) }{h}\)

After solving all this the answer would be \(\frac{1}{9}\)

The absolute extrema of y = x³ - 12x + 23 on the interval [-5, 3] are the minimum value of 14 at x = 3 and the maximum value of 39 at x = -2.

To find the absolute extrema of y = x³ - 12x + 23 on the interval [-5, 3], follow these steps:

1. Find the critical points by taking the derivative of the function y'(x) and setting it equal to zero:
y'(x) = 3x² - 12
3x² - 12 = 0
x² = 4
x = ±2

2. Check the endpoints of the interval and the critical points to find the maximum and minimum values of the function:
y(-5) = (-5)³ - 12(-5) + 23 = -125 + 60 + 23 = -42
y(3) = (3)³ - 12(3) + 23 = 27 - 36 + 23 = 14
y(-2) = (-2)³ - 12(-2) + 23 = -8 + 24 + 23 = 39
y(2) = (2)³ - 12(2) + 23 = 8 - 24 + 23 = 7

3. Compare the values of y at the critical points and endpoints to find the absolute extrema:
Minimum: y(3) = 14
Maximum: y(-2) = 39

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Answer:

16 hours

Step-by-step explanation:

200 divided by 10 is 20.

320 divided by 20 is 16.

So, 16 hours.

Hope that helps :D.

To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

The way we can do a translation and a rotation to be used to map ΔHJK to ΔLMN is:

Option C: translate K to N and rotate about K until HK lies on the line containing LN.

There are different types of transformation such as:

Translation

Rotation

Reflection

Dilation

We want to find how a translation and a rotation be used to map ΔHJK to ΔLMN.

This is the concept of the transformation, ΔHJK=ΔLMN, from the diagram:

∠H=∠L

∠K=∠N

∠M=∠J

In order to map ΔHJK to ΔLMN, we need to translate K to N and rotate about K until HK lies on the same line containing LN.

Thus, the way we can do a translation and a rotation to be used to map ΔHJK to ΔLMN is:

Option C: translate K to N and rotate about K until HK lies on the line containing LN.

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A square pyramid's volume and base area allow figuring out its height simple. H = 3 * V / (A_b).

How to determine a square pyramid's height

H = 3 * V / (A_b)

Where:

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Answer:

x=8

Step-by-step explanation:

x/4=12/6

x=12×4/6

x=48

x=8

Answer:

0

x

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

\(\frac{10}{x}\) = \(\frac{x}{40}\)

We cross-multiply and get

400 = \(x^{2}\)

\(\sqrt{400}\) = \(\sqrt{x^{2} }\)

x = 20

So, the answer is x = 20