Suppose that the height H of a Ferris wheel can be modeled by the function H(t) = -12cos(πt/45) + 18, where t is the time in seconds. What is the maximum height of a cabin? Use 3. 14 for π. ​

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The speed at which Shola climbed is 5 m/s and the time taken by Shola to reach the edge is 6 seconds.

According to the question

Given:

The total distance traveled by Shola = 30 meters

He covered a total distance of 22.5 meters  (i.e. 30 meters - 7.5 meters) in 4.5 seconds.

His speed is thus 5 m/s since speed is equal to both distance and time.

Since he has 7.5 meters to cover, the remaining distance,

Therefore, the time it took him to travel the distance was 7.5/5, or 1.5 seconds.

Consequently, the total amount of time needed to go 30 meters,

T=4.5+1.5=6, or one second.

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Answer:

Step-by-step explanation:

Just use a calculator

The least number of seats the manger could order to 270 seats

The information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.

The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.

This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.

Hence the manager will order 270 and heave 3 extra seats

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This problem can be solved used linear equations. Here there are two variables, number of students and number of adults. After calculations we get the number of students attended the play is 50.

Lets consider the number of students is x and number of adults is y.

Total tickets sold = 300

    x + y = 300  ------------ equation 1

The amount of total tickets sold is 3000.

Amount sold to students = 5x

Amount sold to adults = 11y

  So, 5x+11y =3000 ----------- equation 2

Equating the x term for equation 1

 Multiplying both sides with 5

 5 (x+y) = 5 × 300

 5x + 5y = 1500 ---------- equation 3

Subtracting equation 3 from equation 2

   5x + 11y = 3000

-  ( 5x + 5y = 1500)

    6y = 1500

    y = 1500/6 = 250

Number of adult attended = 250

From equation 1, x+y = 300

Substituting the value of y

                x + 250 = 300

                    x    = 300-250 = 50

So number of students attended is 50

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Answer: 50

Step-by-step explanation: i got it right on my quiz

Take care to properly set up your equations. The $3,000 is the sum of total money from student tickets and total money from the adult tickets.

Answer:  1.25 or 1, 1/4

To add or subtract mixed numbers, first add or subtract the integer (whole number) portions of the mixed numbers, then add or subtract the fractional portions of the mixed numbers. Reduce the fractional portion of the answer to its lowest terms and combine it with the integer portion of the answer to get the final answer.

1. To add mixed numbers, first add the integer (whole number) portions of the two mixed numbers together. The result is the integer portion of your answer.

2. Next, add the fractional portions of the two mixed numbers together. If the fractional parts of the two mixed numbers have different denominators, you'll need to convert them to have the same denominator.

3. Reduce the fractional portion of your answer to its lowest terms. This is the fractional portion of your answer.

4. Combine the integer portion of your answer with the fractional portion of your answer to get the final answer.

5. To subtract mixed numbers, first convert the fractional portion of the subtrahend (the number being subtracted) to an equivalent fraction with the same denominator as the minuend (the number being subtracted from).

6. Subtract the integer portions of the two mixed numbers. The result is the integer portion of your answer.

7. Subtract the fractional portions of the two mixed numbers. Reduce the fractional portion of your answer to its lowest terms. This is the fractional portion of your answer.

8. Combine the integer portion of your answer with the fractional portion of your answer to get the final answer.

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The choices that describe an exact number are option b, option c, option d, and option e because they show a definite countable quantity with 100% accuracy.

The following options describe an exact number:

b. The house has four bedrooms.

c. There is one gram of salt in this beaker.

d. You drank one liter of water.

e. The little dog weighs 10 kilograms.

These numbers are exact because they are specific measurements that are not subject to uncertainty. They are countable and defined. While "you ran two miles" or "you drank one liter of water" could be approximate measurements.

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The probability of choosing a perfect cube is [tex]\frac{7}{502}[/tex] .

According to the question,

Suppose a number is chosen at random from the set {0,1,2,3,...,501}.

Cube of 1=1

Cube of 2=8

Cube of 3=27

Cube of 4=64

Cube of 5=125

Cube of 6 = 216

Cube of 7 = 343

Cube of 8 = 512

So in a set of members {0,1,2,3,... 501}, only 7 numbers are a cube of a natural number: 1,8,27,64,125,216,343.

The probability of selecting cubes in a set of members {0,1,2,3,... 501} is

= [tex]\frac{7}{502}[/tex]

So, the probability is [tex]\frac{7}{502}[/tex] .

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Answer:

a. The population is 100 college students.

b. The population is finite.

c. Two parameters and their values:

The total population size: 100

The sample size: 10

d. The sample is a group of 10 college students chosen from the population of 100.

e. Two corresponding statistics and their values:

The sample proportion: This is the proportion of individuals in the sample who have a certain characteristic (e.g. majoring in a certain subject). It is calculated by taking the number of individuals with the characteristic and dividing by the sample size. Its value would be different for each sample of size 10 taken.

The sample mean: This is the average of the measurements for the individuals in the sample. It is calculated by summing up the measurements and dividing by the sample size. Its value would be different for each sample of size 10 taken.

f. When another sample of size 10 is taken, the population and its size remains fixed but sample proportion and sample mean would change.

Step-by-step explanation:

The length of the segment MP is 38 units

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

The triangle

On the triangle, we have

9x - 34 = 3x + 14

Evaluate the like terms

6x = 48

Divide by 6

x = 8

Given that

MP = 9x - 34

We have

MP = 9 * 8 - 34

Evaluate

MP = 38

Hence, the length of MP is 38 units

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Answer: 23,600

Step-by-step explanation: 120x2 = 240, 240x15 = 3600. 20,000 + 3600 = 23,600

For the given stem and leaf plot, the range of data is option C: 25.

What is stem and leaf plot?

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

The stem and leaf plot for data is given.

The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.

From the stem and leaf plot the maximum value obtained is = 35

From the stem and leaf plot the minimum value obtained is = 10

The range is then calculated as -

Range = Maximum value - Minimum value

Range = 35 - 10

Range = 25

Therefore, the range is 25.

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The area in square meters will the oil slick cover is 9.5×10⁶ m².

15 barrels of diesel spilt into the ocean, where each barrel contains 42 gallons. Thereby the total volume of the oil spilt by 15 barrels is calculated as follows:

The total volume of the oil spilt by 15 barrels = 15× 42 gallons.

=630 gallons

1 gallon = 3.78541 liters

Volume in L = 630 gallons × 3.78541 liters/ 1 gallon

= 2384.8083 L

1 L = 10⁻³ m³

2384.8083  L = 2384.8083 × 10⁻³ m³

= 2.3848083 m³

The area covered by the oil spill has to be determined, where the thickness of the oil spill is given to be 2.5×10² nm.

1 nm = 10⁻⁹ m

Thereby, 2.5×10² nm = 2.5×10²×10⁻⁹ m

= 2.5×10⁻⁷ m

Area (m²) = volume (m³)/thickness (m)

= 2.3848083 m³/ 2.5×10⁻⁷ m

= 0.95392×10⁷ m²

= 9.5×10⁶ m²

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Answer:

y=3x+5

Step-by-step explanation:

an equation is always

y= slope*x + intercept so y=3x+5

The translation rule that defines a translation 5 units right and 2 units up is given as follows:

(x,y) -> (x + 5, y + 2).

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

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The linear specific solution of the form [tex]y= mx + b[/tex] where [tex]m + b = 4- 2 = 2[/tex]

Differential equation that cannot be separated:

Non-separable differential equations are those that are incapable of being written as-  [tex]\frac{dy}{dx} = f(x) g(y)[/tex]

In other words, the differential equations that cannot be separated are referred to as non-separable differential equations.Differential equations with non-separable variables are those in which the variables cannot be separated. These equations are difficult to solve and call for techniques that will be covered in upcoming courses, such as numerical or analytical approaches.

Given is the equation,

[tex]\frac{dy}{dx} = 8x - 2y[/tex]

[tex]y = 4x - 2 + ex^{-2x}[/tex]

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The standard error of the mean for these data is 13.14 pounds..

The standard error of the mean (SEM) is a measure of the variability of the sample mean. It is calculated as the standard deviation of the sample divided by the square root of the sample size.

To find the SEM for the given data, we first need to calculate the sample mean:

(160 + 215 + 195) / 3 = 190

Then we need to calculate the deviation of each value from the mean:

160 - 190 = -30

215 - 190 = 25

195 - 190= 5

Next, we need to square these deviations:

(-30)² = 900

25² = 625

5² = 25

Next, we need to calculate the variance:

(900 + 625 + 25) / 3 = 516 2/3

Then we need to calculate the standard deviation:

√(516 2/3) = 22.73

Finally, we can calculate the standard error of the mean:

22.73 / √(3) = 13.14

So, the standard error of the mean for these data is 13.14 pounds.

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Answer:

3 + n = 2n - 5

Step-by-step explanation:

let 'n' equal 'a number'

'more than' implies 'addition', so 3 + n

'is' in math implies 'equals', so 3 + n =

'double the number' means to multiply it by 2

'less than' implies 'subtraction'

So final result is:

3 + n = 2n - 5

The solution is, A. About 257 jars, the employee can complete in 1 hour.

Here, we have,

given that,

Given that it takes an employee about 14 seconds to lift, close, fill, and shelve a jar of peanut butter,

To calculate this, you would take the number of seconds in an hour

(60 seconds/minute * 60 minutes/hour = 3600 seconds)

and divide it by the number of seconds it takes to complete one jar

(14 seconds/jar).

3600 seconds / 14 seconds/jar

= 257 jars/hour.

so, About 257 jars, the employee can complete in 1 hour.

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The solution of the system of equations:

-2x - 10y = -2

-4y = x

is the point (-4, 1).

Here we want to solve the system of equations below:

-2x - 10y = -2

-4y = x

By the substitution method, to do so, we need to isolate one of the variables in one of the equations and then replace that in the other equation.

We can see that x = -4y is already isolated on the second equation, then we can replace this on the first one to get:

-2*(-4y) - 10y = -2

We can solve this for y.

8y - 10y = -2

-2y = -2

y = -2/-2 = 1

And thus, the value of x is:

x = -4y

x = -4*1 = -4

The solution of the system is (-4, 1).

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The perimeter of the rectangle is (29.5t+7)feet

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference.

To find the perimeter of the rectangle we add a the sides together i.e

p = l+l+w+w

p = 2(l+w)

p =2 ( 8.25t - 6.5+ 6.5t + 10)

p = 2( 14.75t + 3.5)

p = (29.5t + 7) feet

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Answer:

D) two solutions

Step-by-step explanation:

because the first one is: x = 5y + 4

and the second one is: -2x+10y=8

and the equals in the first one is just how to get the value of x and it doesn't count as a third solution

Answer:

Inequality Form:

x ≤ −5/12

Interval Notation:

(−∞, −5/12]

Step-by-step explanation:

Answer:

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Step-by-step explanation:

If the distribution of the monthly utility bill for gas or electric energy can be considered mound-shaped and symmetric, we can use the standard normal distribution table to find the percentage of homes that have a monthly utility bill of more than $83.

To use the standard normal distribution table, we need to standardize the variable by subtracting the mean and dividing by the standard deviation:

(83 - 91) / 8 = -0.875

This means that a monthly utility bill of $83 is 0.875 standard deviations below the mean.

Using a standard normal distribution table, we can find that the percentage of homes that have a monthly utility bill of more than $83 is approximately 13.6%.

Sari-sari store must sell 20 pieces of type (a) detergent and 26 pieces of type (b) detergent to raise at least php 180.00.

Determine the number of pieces of type (a) detergent.

9.00 x x = 180.00

Divide both sides by 9.00:

x = 20 pieces

Determine the number of pieces of type (b) detergent.

7.00 x y = 180.00

Divide both sides by 7.00:

y = 25.71

Since we cannot sell partial pieces, the number of pieces of type (b) detergent must be rounded up to 26 pieces.

Therefore, the sari-sari store must sell 20 pieces of type (a) detergent and 26 pieces of type (b) detergent to raise at least php 180.00.

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A statement which best compares the heights of the bars of the bar chart include the following: B. There are 3 times as many people in the Burgers group as in the Pasta group.

In order to better understand and compare number of people who attended her food festival and their favorite food items, we would take note of the following important information;

Based on the information provided above, we can reasonably and logically deduce that the rectangular bar representing Burgers bar with a numerical value of 60 is three times as tall as the rectangular bar representing Pasta bar with a numerical value of 20.

Burgers bar = 20 × 3

Burgers bar = 60 people.

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Answer:  B. There are 3 times as many people in the Burgers group as in the Pasta group.

Step-by-step explanation: <3

The sum of the two given is 7.867.

When expressed in scientific notation, the number of significant figures equals the number of digits. Significant figures are the numbers that give any measurement meaning.

The decimal point is marked by leading zeros. They don't matter much. After the decimal point, a trailing zero is reliably known. It is important. In a whole number, every non-zero number has importance.

You must keep in mind these three guidelines in order to ascertain how many significant figures are present in a number.

If you add 4.667 g and 3.2 g,

the answer has 4 significant figures.

The sum of the two given is 7.867.

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The full question:

If you add 4.667 g and 3.2 g how many significant figures does the answer have

The correct answer for equivalent interest rate and no. of times will the money be compounded is C) 1.5% and 16 times respectively.

The annual interest rate of 6% is equivalent to a quarterly interest rate of 6% / 4 = 1.5%. The money will be compounded quarterly, so it will be compounded 16 times in total over 4 years.

Compound interest is computed as interest on the initial principal plus any accrued interest from prior periods. Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

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Palisade Bakery is a better buy than Union City Bakery.

To determine which bakery has the better buy, we need to calculate the cost per muffin at each bakery. It is determined by dividing the total cost by total number of muffins. Assuming one batch has ten muffin as not mentioned.

Union City Bakery: $10.00 / 3 batches = $3.33 per batch (approx)

= $3.33/ 10

= $0.33 per muffin

Palisade Bakery: $6.25 / 20 muffins = $0.31 per muffin

Based on this calculation, Palisade Bakery has the better buy as each muffin costs $0.31, which is cheaper than the cost per muffin at Union City Bakery, which is approximately $0.33 per muffin.

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Answer:

Okay so the answer would be 8 cups

Step-by-step explanation:

the reason this is is because if you combine the cups its 2 2/3 so then all you have to do is multiply it by 3 and then your answer is 8 cups of sugar