A pendulum on a grandfather clock is swinging back and forth and it keeps time. A device measures the height of the pendulum above the floor as it swings back and forth. At the beginning of the measurements, the pendulum is at its highest point, 36 cm above the floor. After 4 seconds, it is at its lowest point, 12 cm above the floor. At 8 seconds, the pendulum is back at its greatest height from the floor. Assume that the graph of the distance above the floor varies sinusoidally as time. A table of values is given below.

b. Write an equation of the form H(t)=A cos (Bt) +D for your graph above.

c. What is the distance (to the nearest tenth) from the floor when t=6.5 seconds?

Answer:

23,850 cubic inches

Step-by-step explanation:

I think I know your dad officer Chau he works at my middle school in Navarre. this was also kind of a basic and easy question I would recommend trying to figure it out yourself before turning to the internet.

The transformed fuction shifted 4 units to the right of the parent function is g(x)= x + 2

From the question, we have the following parameters that can be used in our computation:

Parent function, f(x)= x+6,

Transformation: shifted 4 units to the right

The rule of the above transformation is

g(x) = f(x - 4)

Substitute the known values in the above equation, so, we have the following representation

g(x)= x - 4 + 6,

Evaluate the terms

g(x)= x + 2

Hence, the transformed fuction is g(x)= x + 2

Read more about Transformation at

https://brainly.com/question/27224272

#SPJ1

Note that the table of budget is attached accordingly, and steps 1-4 have been completed. See the table.

4) Since the emergency fund for that month was $200, it means that they are in the short for $105. They can only affod it if they take from their savings.

5) they had a balance of $800 for the month. This is miscellaneous funds. They can make use of this for the trip to NASA. This way, they won't have to touch the savings or entertainment.

Learn more about emergency:
https://brainly.com/question/20411681
#SPJ1

Full Question:
See attached image.

Reflect

4. Analyze Relationships One month, the family must make an

emergency car repair for $305. Are they able to pay for it out of the

fixed emergency fund for that month? If not, how can they afford it?

5. The family wants to make a trip to Houston to visit the NASA Space

Center. What are some ways they can save without using all of the

allotted $160 for entertainment

Answer:1,000

Step-by-step explanation:

So we add 25 million to 5 million which is 30 million. Then we divide 30 million to 30 thousand and get 1 thousand.

Answer:

The list represents the ages of students in a gymnastics class.

-------

8, 8, 8, 9, 9, 10, 10, 10, 11, 12

If another student of age 10 joins the class, how is the mean affected?

The mean will remain the same at 10.

The mean will increase to about 10.2.

The mean will decrease to about 9.

-------

8 + 8 + 8 + 9 + 9 + 10 + 10+ 10 + 11 + 12

= 95

95 ÷ 10

=9.5

8 + 8 + 8 + 9 + 9 + 10 + 10 + 10+ 10 + 11 + 12

= 105

105 ÷ 11

= 9.54.....

The ordered pair that would represent the coordinates of vertex D' is given as follows:

D'(4u, -3u).

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor for this problem is given as follows:

k = u.

The coordinates of each vertex are multiplied by y, hence the ordered pair that would represent the coordinates of vertex D' is given as follows:

D'(4u, -3u).

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).

To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results

x² - 4 = 0

Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

x² = -4

Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.

3x² + 12 = 0

Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.

4x² = 16

Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

2(x - 2)² = 0

Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.

Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).

To know more about substitution:

https://brainly.com/question/30284922

#SPJ1

Answer:

Step-by-step explanation:

I’m sorry but I don’t know how I can solve you question

The table can be complete based on the function given by substituting as:

When s = 0, M(s) = -3

When s = 4, M(s) = 7

When s = 9, M(s) = 12

Given a function,

M(s) = 5√s - 3

Substitute each of the value of s to find the corresponding value of M(s).

When s = 0,

M(s) = 5√0 - 3 = 0 - 3 = -3

When s = 4,

M(s) = 5√4 - 3 = 10 - 3 = 7

When s = 9,

M(s) = 5√9 - 3 = 15 - 3 = 12

Hence the blank spaces are -3, 7 and 12.

Learn more about Functions here :

https://brainly.com/question/7975626

#SPJ1

There are 24 ways to pick two green marbles first and one red marble last.

The probability of picking a green marble on the first draw is 4/10, and then 3/9 on the second draw since there are only 3 green marbles left out of 9 total marbles remaining.

The probability of picking a red marble on the third draw is 4/8 since there are 4 red marbles left out of 8 total marbles remaining.

So the probability of picking two green marbles first and one red marble last is (4/10) x (3/9) x (4/8) = 2/45.

To calculate the number of ways to pick two green marbles first and one red marble last, we need to use combinations.

There are [tex]^4C_2[/tex] = 6 ways to choose two green marbles from four, and there are 4 ways to choose one red marble from four.

So there are 6 x 4 = 24 ways to pick two green marbles first and one red marble last.

To learn more on Combinations click:

https://brainly.com/question/19692242

#SPJ1

The solution is, the simplification of the expression is:

{16 - 9x^2 + 14x}

Here, we have,

given that,

the expression:

{√49 + [√81 - x (9x - 14)]}

now, we have to simplify this expression:

{√49 + [√81 - x (9x - 14)]}

={7 + [9 - x (9x - 14)]}

={7 + [9 - 9x^2 + 14x]}

={7 +9 - 9x^2 + 14x}

={16 - 9x^2 + 14x}

Hence, The solution is, the simplification of the expression is:

{16 - 9x^2 + 14x}

To know more about expression follow

brainly.com/question/723406

#SPJ1

The expression 7/12x - y/6x² in its simplest form is (7x - 2y)/(12x²).

We have,

To simplify the expression 7/12x - y/6x², we need to find a common denominator for the two terms.

The common denominator is 12x^2.

Multiplying the first term by x/x and the second term by 2/2, we get:

(7x)/(12x²) - (2y)/(12x²)

Combining the two terms, we get:

(7x - 2y)/(12x²)

Therefore,

7/12x - y/6x² in its simplest form is (7x - 2y)/(12x^2).

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The difference in volumes for the two cylinders is given as follows:

A. 61π mm³.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

For Cylinder 1, the parameters are given as follows:

r = 0.5 x 8 = 4 mm, h = 10 mm.

Hence the volume is given as follows:

V = π x 4² x 10

V = 160π mm³.

For Cylinder 2, the parameters are given as follows:

r = 0.5 x 6 = 3 mm, h = 11 mm.

Hence the volume is given as follows:

V = π x 9² x 11

V = 99π mm³.

Hence the difference is given as follows:

160π mm³ - 99π mm³ = 61π mm³.

More can be learned about the volume of a cylinder at brainly.com/question/9554871

#SPJ1

The solution of the expression is 3.659

First, we will start with the expression inside the brackets, i.e., [(3 1/3 * 1.9) + (19.5 / (4 1/2)]. Here, we have two operations - multiplication and division. According to PEMDAS, we need to perform multiplication before division.

To simplify this expression, we will first convert 3 1/3 to an improper fraction. 3 1/3 is the same as 10/3. Therefore, the expression inside the brackets becomes

=> [(10/3 * 1.9) + (19.5 / (9/2)].

Next, we will simplify the multiplication first -

=> 10/3 * 1.9 = 19/3.

Now, let's simplify the division operation

=>  19.5 / (9/2) = 4.33

Therefore, the expression inside the brackets becomes

=>  [(19/3) + 4.33] = 8.99

Moving on to the denominator of the given expression

=> [62/75 - 0.16]. Here, we need to perform subtraction first as it comes before division in PEMDAS.

62/75 =  0.8266

Therefore, the denominator of the given expression becomes

=> [0.8266 - 0.16] = 0.6666

Now, let's simplify the numerator of the given expression. We have

=> [(3.5 + 4 2/3 + 2 2/15) / (0.5 * (1 1/20 + 4.1))].

Let's first convert all the mixed fractions to improper fractions.

3.5 can be written as 7/2, 4 2/3 can be written as 14/3, and 2 2/15 can be written as 32/15.

Therefore, the numerator becomes

=>  [(7/2 + 14/3 + 32/15) / (0.5 * (21/20 + 4.1))].

Let's first simplify the expression inside the brackets

=>  21/20 + 4.1 = 5.15.

Therefore, the numerator becomes

=>  [(7/2 + 14/3 + 32/15) / (0.5 * 5.15)].

Now, let's simplify the addition operation in the numerator. We need to find a common denominator to add the fractions.

The common denominator for 2, 3, and 15 is 30.

Therefore, (7/2 + 14/3 + 32/15) can be written as

=> (105/30 + 140/30 + 64/30).

Adding the fractions, we get (309/30).

Therefore, the numerator becomes [(309// (0.5 * 5.15)].

Next, let's simplify the expression inside the brackets - 0.5 * 5.15 = 2.575.

Therefore, the numerator becomes

[(309/30) / 2.575] = 3.68

Now that we have simplified the numerator and denominator of the given expression separately, we can simplify the entire expression.

[(8.99) / (0.6666)] / [3.68]

Let's first simplify the expression inside the first set of brackets.

(8.99) / (0.6666) = 13.486

Therefore, the given expression becomes 13.486 / 3.68 = 3.659

To know more about expression here

https://brainly.com/question/14083225

#SPJ1

Answer:

We can use the binomial probability formula to find the probability of getting exactly 3 blue marbles in two draws:

P(X=3) = (2 choose 3) * (0.6)^3 * (0.4)^(-1) = 0.288

However, since we are asked for the probability of the random variable having an outcome of 3 (i.e. getting exactly 3 blue marbles), we can simply use this probability:

P(X=3) = 28.8%

Therefore, the answer is (a) 24%.

The acceleration of the car at that time was 3 m/s².

We have,

From the kinematic equation to find the acceleration:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Initial velocity u = 15 m/s

Final velocity v = 45 m/s,

Time t = 10 s

We can rearrange the equation to solve for acceleration:

a = (v - u) / t

Substituting the values, we get:

a = (45 m/s - 15 m/s) / 10 s

a = 3 m/s^2

Therefore,

The acceleration of the car at that time was 3 m/s².

Learn more about accelerations here:

https://brainly.com/question/30581474

#SPJ1

The complete question in English.

A car moving on a straight track increases its speed from 15 m/s to 45 m/s using a po of 10 seconds.

Assuming that the acceleration was uniform, calculate:

acceleration at that time.

Answer:

Option 2 is correct. The function is increasing on the set of all positive real numbers.

The value of c in the given diagram would be 10. 83.

From the diagram we see that when C is subtracted by 5 and then multiplied with this value 6 times, we get the value of 35.

In other words:

6 ( C - 5 ) = 35

Showing that when C - 5 is multiplied by 6, we get the value of 35.

Therefore, solving gives:

6 C - 30 = 35

6 C = 35 + 30

6 C = 65

C = 65 / 6

C = 10. 83

In conclusion, the value of C is 10. 83.

Find out more on values at https://brainly.com/question/14996939

#SPJ1

The possible sum of Kiran adding 4.7x10 √4 and 1.2 x 10 √5 is 94 + 1.2 x 10 √5

From the question, we have the following parameters that can be used in our computation:

Kiran added 4.7x10 √4 and 1.2 x 10 √5

This means that we have

4.7 * 10√4 + 1.2 x 10 √5

Evaluate the square root of 4

So, we have

4.7 * 10 * 2 + 1.2 x 10 √5

When the products are evaluated, we have

94 + 1.2 x 10 √5

Hence, the possible result of the summation is 94 + 1.2 x 10 √5

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

The total cost of the meal is $65.50, with tip included.

Here, in this question we need to find the percentage Value, to find the total cost of the meal plus the tip, Carter needs to multiply the cost of the meal by a factor of 1 + the tip percentage, which is 1 + 31% = 1.31.

So, the number Carter should multiply the cost of the meal by to find the total plus tip in one step is 1.31.

For example, if the cost of the meal was $50, then the total cost including the tip would be addition of cost of meal and tip.

Total cost = Cost of meal + Tip

Total cost = $50 + 31% of $50

Total cost = $50 + $15.50

Total cost = $65.50

To know more about Percentage:

https://brainly.com/question/29630127

#SPJ1

There is no solution from the given matrix equation.

In a two by two matrix equation system, two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. It implies that the first matrix is 2×2 and the second matrix is 2×1.

Given that:

[tex]\left[\begin{array}{cc}6&4\\9&6\end{array}\right] \left[\begin{array}{c}x\\y \end{array}\right] = \left[\begin{array}{c}1 \\ 3 \end{array}\right][/tex]

We multiply each row in the first matrix by each column in the second matrix, so we get:

[tex]\left[\begin{array}{c}6x+4y\\9x+6y\end{array}\right] = \left[\begin{array}{c}1 \\ 3 \end{array}\right][/tex]

Then, we can express it as a system of linear equations:

6x + 4y = 1 --- (1)

9x + 6y = 3 --- (2)

Here, we decided to use the substitution method to solve the system of equations.

From equation (1)

x = 1/6 - 2y/3

Replace the value of x into equation (2) and solve for y, we get:

9(1/6 - 2y/3) + 6y = 3

By solving it, we get:

3/2 = 3

Thus, since 3/2 = 3 is not a true solution, then we can conclude that there is no solution.

Learn more about solving matrix equations here:

https://brainly.com/question/27929071

#SPJ1

Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

The volume of the cylinder of radius 3 m and height 8 m is given as follows:

V = 72π cubic meters.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

The parameters for this problem are given as follows:

r = 3 m and h = 8 m.

Hence the volume of the cylinder is obtained as follows:

V = π x 3² x 8

V = 72π cubic meters.

More can be learned about the volume of a cylinder at brainly.com/question/9554871

#SPJ1

The domain of this relation is [0, 5].

The range of this relation is [-4, 3].

No, this relation is not a function.

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graphs shown in the image attached above, we can reasonably and logically deduce the following domain and range for graph 4:

Domain = [0, 5].

Range = [-4, 3].

Read more on domain here: brainly.com/question/9765637

#SPJ1

The solution is, the measure of angle C is 52.

Here, we have,

If AC = BC

and, given that,

.A =(8x-40)

B =(5x - 1)

so, we have,

AC = BC i.e. ABC  is isosceles triangle.

so, the angle A & B are equal .

so, we get,

(8x-40)  = (5x - 1)

or, x = 39/3

        = 13

so, angle A = angle B = 64

so, m<C = 180 - 2*64

              = 52

Hence, The solution is, the measure of angle C is 52.

To learn more on angle click:

brainly.com/question/28451077

#SPJ1

Answer:1.112,121, 124,137,147,156,173,189

2.the median is 242

Step-by-step explanation:

Don would take 1500 minutes to fill the 1000-gallon water tank using the 2-gallon bucket.

If the capacity of the water tank is 1000 gallons and Don uses a bucket that can hold 2 gallons to fill the tank, we can calculate the number of buckets Don needs to fill the tank.

Let's assume the number of buckets Don needs to fill the tank is represented by 'n'.

Capacity of the tank = 1000 gallons

Capacity of each bucket = 2 gallons

Number of buckets needed to fill the tank, n = Capacity of the tank / Capacity of each bucket

n = 1000 gallons / 2 gallons

n = 500

So, Don needs 500 buckets, each holding 2 gallons, to fill the 1000-gallon water tank.

Given that it takes Don 3 minutes to fill the bucket with water and pour it into the tank, the total time taken by Don to fill the tank would be the product of the number of buckets (500) and the time taken to fill each bucket (3 minutes).

Total time taken to fill the tank = Number of buckets × Time taken to fill each bucket

Total time taken = 500 × 3 minutes

Total time taken = 1500 minutes

To know more about gallon here

https://brainly.com/question/31702678

#SPJ1

If Farmer Johnson's minimum AVC is, for example, $1.50 per dozen eggs, then any price below $1.50 would result in losses that he could not sustain in the long run.

To determine the lowest price a dozen eggs could reach before Farmer Johnson would be forced to shut down in the short run, we need to know his minimum average variable cost (AVC) of producing eggs.

The average variable cost is the variable cost per unit of output, and it includes costs that vary with the level of production, such as labour, feed, and utilities.

If the price of a dozen eggs falls below the minimum AVC, Farmer Johnson will not be able to cover his variable costs and will incur losses. In the short run, he may continue to produce as long as he can cover his variable costs, but he will eventually be forced to shut down if he cannot cover his fixed costs as well.

Without information on Farmer Johnson's specific costs, we cannot determine the exact minimum AVC or the lowest price at which he would shut down. However, we can say that the lowest price a dozen eggs could reach before he would be forced to shut down is equal to his minimum AVC.

If Farmer Johnson's minimum AVC is, for example, $1.50 per dozen eggs, then any price below $1.50 would result in losses that he could not sustain in the long run.

To know more about an expression follow

https://brainly.com/question/24000826

#SPJ1