A ladybug sits on the tip of the minute hand of a clock at 1:00. The minute hand is 6 inches long.
The function () represents the height (inches) of the ladybug from the center of the clock after t minutes.
Fill in the blanks in the table below.
t
0
15
30
45
60
POSSIBLE POINTS: 100
v(t)
Rev
Answers
0 | 0
15 | 6 * sin((2π/60) * 15) = 6 * sin(π/2) = 6 * 1 = 6
30 | 6 * sin((2π/60) * 30) = 6 * sin(π) = 6 * 0 = 0
45 | 6 * sin((2π/60) * 45) = 6 * sin((3π/2)) = 6 * (-1) = -6
60 | 6 * sin((2π/60) * 60) = 6 * sin(2π) = 6 * 0 = 0
To determine the height of the ladybug from the center of the clock after t minutes, we can use trigonometry and the properties of a circle.
The minute hand of the clock is 6 inches long, and it rotates around the center of the clock, which can be considered as the origin (0,0) on a coordinate plane.
As the minute hand moves, it forms an angle with the positive x-axis. The angle formed by the minute hand at any given time can be calculated using the formula:
θ = (2π/60) * t
where θ is the angle in radians and t is the time in minutes.
The height of the ladybug from the center of the clock can be calculated using the trigonometric function sine. The formula for the height is:h(t) = r * sin(θ)
where r is the length of the minute hand.
Let's fill in the table:
t | v(t)
0 | 0
15 | 6 * sin((2π/60) * 15) = 6 * sin(π/2) = 6 * 1 = 6
30 | 6 * sin((2π/60) * 30) = 6 * sin(π) = 6 * 0 = 0
45 | 6 * sin((2π/60) * 45) = 6 * sin((3π/2)) = 6 * (-1) = -6
60 | 6 * sin((2π/60) * 60) = 6 * sin(2π) = 6 * 0 = 0
In the given table, the values of v(t) represent the height of the ladybug from the center of the clock at different times. At 1:00 (t=0), the ladybug is at the center of the clock, so the height is 0. At 1:15 (t=15), the ladybug is 6 inches above the center, and at 1:30 (t=30), the ladybug returns to the center. At 1:45 (t=45), the ladybug is 6 inches below the center, and at 2:00 (t=60), the ladybug returns to the center.
Hence, the table is completed with the corresponding values for v(t).
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Related Questions
The theater group sold adult and student tickets for the play. They sold a total of 560 tickets. Each adult ticket was $8 and each student ticket was $3.50. The group took in a total of $3166. How many of each type of ticket was sold for the play?
Answers
Answer:
268 adult and 292 student tickets sold
Step-by-step explanation:
a = number adult tickets sold
s = number student tickets sold
a + s = 560
8a + 3.50s = 3166
a = 268 adult tickets
s = 292 student tickets
The principal would like to assemble a committee of 7 students from the 13-member
tudent council. How many different committees can be chosen?
Answers
If the committee requires 7 students to be on it, and 7 can only go into 13 once (13 is a prime number), you can only have one committee
Factor the Expression. 121x + 44 *
11(10x + 4)
21x + 4
11(11x + 44)
11(11x + 4)
Answers
i like chicken nuggets
Answer:
what the heck is this
Step-by-step explanation:
i seriously dont know what the answers are for these, can anyone help?
Answers
Answer:
9. x = 5
10. m∠Y = 34°
Step-by-step explanation:
9.
Remember that congruent sides have congruent angles as well. That means 9x + 1 will be shown up in our equation twice. And as always, all angles in a triangle add up to 180.
2(9x + 1) + 88 = 180
18x + 2 + 88 = 180
18x + 90 = 180
18x = 90
x = 5
10.
The same concept applies here in question 10. Congruent angles and sides match each other. Therefore,
Step 1:
6x - 23 = 4x + 9
2x - 23 = 9
2x = 32
x = 16
Step 2:
Now that you have found x, plug it back into the given equations and find the other angle.
6(16) - 23 = 73
4(16) + 9 = 73
180 - (73)(2) = 34
Brian asked a group of people their favourite holiday destination. The results are summarised in the table. Destination=Uk=84, Europe=72, USA=108, Africa=60, Other=156 How many degrees does one person represent? Give your answer as a fraction in its simplest form.
Answers
Answer:
0.4615
Step-by-step explanation:
1/780 x 360 = 0.4615
Answer:
3/4°
Step-by-step explanation:
84+72+108+60+156= 480 people
480*x= 360°
x= 360°/480= 3/4°
the roller coaster at treasure island amusement park consists of 17 cars, each of which can carry up to two passengers. according to a time study, each run takes 5.5 minutes, and the time to unload and load riders is 6.5 minutes. what is the the theoretical capacity of the system in number of passengers per hour? round your answer down to the nearest whole number.
Answers
The theoretical capacity of the roller coaster system in number of passengers per hour at Treasure Island Amusement Park is 170 passengers per hour, based on 17 cars that carry two passengers each, with a run time of 5.5 minutes and load/unload time of 6.5 minutes.
The theoretical capacity of the roller coaster system in number of passengers per hour can be calculated as follows:
There are 17 cars, and each car can carry up to two passengers. So, the total number of passengers per run is 17 x 2 = 34.
Each run takes 5.5 minutes, and the time to unload and load riders is 6.5 minutes, for a total cycle time of 5.5 + 6.5 = 12 minutes.
To calculate the theoretical capacity in passengers per hour, we need to convert the cycle time to hours and then divide by the cycle time. There are 60 minutes in an hour, so the cycle time in hours is 12 / 60 = 0.2 hours.
The theoretical capacity in passengers per hour is then calculated as:
Capacity = (Number of passengers per run) x (Number of runs per hour)
To find the number of runs per hour, we need to divide the total available time per hour (60 minutes) by the cycle time:
Number of runs per hour = 60 / 12 = 5 runs per hour
Now we can calculate the theoretical capacity as:
Capacity = 34 x 5 = 170 passengers per hour
Rounding this down to the nearest whole number, we get the final answer:
The theoretical capacity of the roller coaster system in number of passengers per hour is 170.
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Sydney’s cat is 8% heavier than Greg’s cat, and Jackie’s cat is 25% lighter than Greg’s cat. By what percent is Sydney’s cat heavier than Jackie’s?
PLEASE HELP!!!
Answers
Answer:
look at the attached image
Which algebraic expression below shows
a reflection over the x-axis?
A. (x,y) → (x,-Y)
B. (x,y) → (-XY)
C. (x,y) → (-x, -Y)
D. (x, y) - (y,x)
Answers
Answer:
A
Step-by-step explanation:
When an expression is reflected across the x-axis, the x values stay the same but the y values are now negative.
The same digits are used for the expressions 3^4 and 4^3. Select the symbol that correctly compares the expressions.
Answers
Answer:
3^4 > 4^3
Step-by-step explanation:
3^4 = 3 × 3 × 3 × 3 = 81
4^3 = 4 × 4 × 4 = 64
81 > 64
3^4 > 4^3
Answer:
Answer:
3^4 > 4^3
Step-by-step explanation:
Why? Well, 3^4 is just 3 × 3 × 3 × 3. Which would equal 81. 4^3 is just 4 × 4 × 4. Which equals 64. Of course, 81 > 64. Therefore, 3^4 > 4^3.
if you drive 30,000 miles per year, the total annual expense for this car is
Answers
The total annual Expense for a car that drives 30,000 miles per year would be around $8500 ($2500 + $1000 + $1500 + $3500).
If you drive 30,000 miles per year, the total annual expense for this car would depend on various factors.
take a look at some of the expenses you would need to consider:
Gasoline Cost: The average gasoline cost in the United States is $2.50 per gallon. Therefore, for 30,000 miles per year, you would need approximately 1000 gallons of gasoline. This means your annual gasoline expense would be around $2500.Maintenance Cost: Maintenance is essential to ensure your car runs smoothly and lasts for a long time. The average annual maintenance cost for a car is around $1000. This includes oil changes, tire rotations, brake inspections, and other general maintenance costs. Insurance Cost: The average annual car insurance premium is around $1500. However, this cost can vary depending on various factors such as age, driving history, and location. Therefore, it is important to get an insurance quote specific to your situation. Depreciation Cost: Cars lose value over time due to wear and tear, age, and mileage. The depreciation cost for a car can vary widely depending on the make and model of the car. On average, the depreciation cost for a car is around $3500 per year.Therefore, the total annual expense for a car that drives 30,000 miles per year would be around $8500 ($2500 + $1000 + $1500 + $3500).
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1.33333333333 in a full number
Answers
Answer:
I think it’s 2
Step-by-step explanation:
Evaluate (4)^-4 pls answer!!!
Answers
Answer:
Fraction: 1/256 or
Decimal: 0.00390625 or 0.00391
Step-by-step explanation:
4^-4=1/4^4
4^4=256
=1/256
Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answers
Answer:
B and C
Step-by-step explanation:
vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.
the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.
Liza found a recipe for a fruit smoothie. She wants to know if any ingredients make up an equal amount of the smoothie. What is the whole for the factions in this problem? do all the fractions have the same whole? be precise
Answers
In this problem, the whole for the fractions is the total amount of the fruit smoothie. No specific value or measurement is provided for the whole, as it depends on the quantity of the smoothie being prepared.
To determine if any ingredients make up an equal amount of the smoothie, we need to compare the fractions representing the quantities of each ingredient. The fractions will have the same whole if they all represent the same unit or measurement. For example, if all the fractions are in terms of cups or milliliters, they would have the same whole. However, if the fractions are in different units or measurements, the wholes would not be the same.
Therefore, the specific whole for the fractions in this problem is not provided, as it depends on the overall quantity of the fruit smoothie being prepared. The fractions may or may not have the same whole depending on the unit or measurement they represent.
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irst consider a public good of value to Ann and Bob with the property that the value of the good can be expressed in monetary terms. In this case, the Samuelson condition states that the efficient level of the good is determined by MV +MVP where p is the per A B unit price of the good, and, for example, MV is Ann's marginal value of the good. Now consider a public good of value to Ann and Bob, the value of which CANNOT be expressed in monetary terms. In this case A O a. The Samuleson condition continues to work as in the case where values CAN be expressed in monetary terms. O b. We need more information before we can know how to modify the Samuelson condition. O c. The Samuelson condition is of no use because we cannot compare Ann's utility to Bob's. O d. The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.
Answers
The correct answer is (d) The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution.
When the value of a public good cannot be expressed in monetary terms, the Samuelson condition still holds, but some modifications are required. In this case, the per-unit price (p) used in the Samuelson condition needs to be replaced with a relative price, which represents the trade-off between the public good and other goods or services. Additionally, the marginal values (MV) of the public good need to be replaced with the Marginal Rates of Substitution (MRS), which measure the rate at which one person is willing to substitute the public good for another good.
Therefore, to determine the efficient level of the public good, the modified Samuelson condition uses a relative price and the corresponding Marginal Rates of Substitution.
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Test for relative maxima and minima. Use the second-derivative test, if possible. \[ y=x^{3}-12 x+3 \] Select the correct choice below and, if necessary, fill in the answer box(es) to complete your ch
Answers
In this the correct choice is: D. There are no relative maxima and no relative minima.
The given function is y = \(x^{3}\) - 12x + 3. To find the relative maxima and minima, we need to calculate the first and second derivatives of the function.
First, let's find the first derivative: y' = 3\(x^{2}\) - 12
Now, let's find the second derivative: y'' = 6x
To apply the second-derivative test, we need to determine the critical points by setting the first derivative equal to zero and solving for x:
3\(x^{2}\) - 12 = 0
\(x^{2}\)- 4 = 0
(x - 2)(x + 2) = 0
From this equation, we find that x = 2 and x = -2 are the critical points.
Now, let's evaluate the second derivative at these critical points:
y''(2) = 6(2) = 12
y''(-2) = 6(-2) = -12
Since the second derivative at x = 2 is positive (12 > 0) and the second derivative at x = -2 is negative (-12 < 0), the second-derivative test tells us that there are no relative maxima or minima. Therefore, the correct choice is D. There are no relative maxima and no relative minima for the given function.
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The complete question is:
Test for relative maxima and minima. Use the second-derivative test, if possible. y=x3 - 12x + 3 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The relative maxima occur at x = 2. The relative minima occur at -2. (Type integers or simplified fractions. Use a comma to separate answers as needed.) The relative maxima occur at x=-2. There are no relative minima. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. The relative minima occur at x = 2 . There are no relative maxima. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OD. There are no relative maxima and no relative minima.
The volume of a rectangular box is 1.0 ft3. what is the length if the width is 1.0 ft and the height is 1.5 ft?
Answers
The length of the rectangular box is 0.67 feet
How to determine the length of the box?The given parameters are:
Length = ??
Width = 1.0 ft
Height = 1.5 ft
Volume = 1.0 ft^3
The volume is calculated as:
Volume = Length * Width * Height
Substitute the known values in the above equation
1 = Length * 1 * 1.5
Evaluate the product
1 = Length * 1.5
Divide both sides by 1.5
Length = 0.67
Hence, the length of the rectangular box is 0.67 feet
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question 6 do these data provide convincing evidence that age and body fat percentage are significantly positively associated? why or why not? use quantitative information based on the model output to support your answer, and make sure to note the p-value you use to make this decision. 0 / 1 point yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.000. since the p-value is small we reject the null hypothesis of no relationship. yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. since the p-value is small we reject the null hypothesis of no relationship. yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039 / 2
Answers
The correct answer is b). Yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. Since the p-value is small we reject the null hypothesis of no relationship.
In statistics, the p-value is used to determine the likelihood that the observed relationship between two variables occurred by chance. If the p-value is small, it means that the relationship is statistically significant and unlikely to have occurred by chance. In this case, the p-value of 0.039 indicates that there is a statistically significant positive relationship between age and body fat percentage.
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Heidikae reads 420 pages a week. In the summer, she reads 17% less. Approximately how many pages per week does she read in the summer.
Answers
This is it because she read 420 pages during the summer but then she reads 17% less which is subtracting then get the answer which is 348.6
Automobile repair shops typically recommend that their customers change their oil and oil filter every 2,500 miles. Your automobile user's manual suggests changing your eil every 4,000−5,500 mies. If you drive your car 10,000 miles each year and an oil and filter change costs $27, how much money would you save each year if you had this service performed every 4,000 miles? Your savings will be 1 per year, (Round to the nearest cent.) Focus on the diflerence between feasible alternatives (Principle 2) Insulated concrete forms (iCF) can be used as a substitute for corwentional wood framing in building construction, Heating and cooling bils will be about 50% less than in a similar wood-framed building in upstate New York. An ICF hame will be approximately 10% more expensive to construct than a wood-framed home. For a bpical 2,100 n
2
home costing $150 per n
2
to construct in upstate New York and costing $280 per month to heat and cool, how many months does it take for a 2,100 f
2
iCF home to pay back its extra construction cost? It will take months to pay back the extra iCF construction cost through monthily energy savings. (Round to the nearest whole number.)
Answers
You savings would be $54 per year by having the oil and filter change performed every 4,000 miles.
To calculate the annual savings from changing the oil every 4,000 miles instead of every 2,500 miles, we need to determine the number of oil and filter changes required in each case.
Option 1: Changing the oil every 2,500 miles
For a car driven 10,000 miles per year, you would need 10,000 miles / 2,500 miles per change = 4 oil and filter changes per year.
Option 2: Changing the oil every 4,000 miles
For a car driven 10,000 miles per year, you would need 10,000 miles / 4,000 miles per change = 2.5 oil and filter changes per year. Since you cannot have a fraction of an oil change, we consider this as 2 oil and filter changes per year.
Now, let's calculate the annual savings:
Number of oil and filter changes per year:
Option 1: 4 changes per year
Option 2: 2 changes per year
Cost per oil and filter change: $27
Annual savings = (Number of changes per year in Option 1 - Number of changes per year in Option 2) * Cost per change
Annual savings = (4 - 2) * $27 = $54
Therefore, you would save $54 per year by having the oil and filter change performed every 4,000 miles instead of every 2,500 miles.
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Task 1
Print
1
The Area of a Triangle
Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to
find the area of a triangle if you know only the coordinates of its vertices in this task, you'll find out. Consider ABC, whose
vertices are A (2,1), B (3,3), and C(1,6), let AC represent the base of the triangle.what is the base and height for anchors
Answers
Answer:
Hope it helps!!!Brainliest pls!!!Sorry, I can't write it. it won't let me.
For a fundraiser, the basketball team was selling butter braids for $8.50. If they sold 155 butter braids, how much money did they make?
Answers
Answer:
1,317
Step-by-step explanation:
Question 7 (4 points) Other Stuff Savings Entertainment 11% 4% 4% Retirement 10% Food -12% 7%Insurance Utilities +6% 16% Taxes 10% 20% Transportation Housing The pie graph above shows the distribution of funds for a typical household. What are your observations about the distribution of funds into the categories of this household budget? What do you conclude about the priorities of spending? (write at least 3 sentences.)
Answers
The pie graph represents the distribution of funds for a typical household, with the largest portions being allocated to taxes (20%), housing (19%), and food (12%), followed by savings and transportation (11% each).
The lowest portions go to entertainment (4%), insurance (4%), and retirement (2%). Overall, the budget prioritizes necessities like housing, taxes, and food over discretionary expenses like entertainment and retirement.
The pie chart provides a visual representation of the distribution of funds for a typical household. The largest portion of the budget goes towards taxes (20%), which includes federal, state, and local taxes.
The second-largest allocation is for housing (19%), which covers mortgage or rent payments, utilities, and household maintenance expenses. Food (12%) is the third largest expense, which includes both groceries and dining out.
Savings and transportation receive equal allocations of 11%, with savings covering emergency funds and long-term investments, while transportation includes car payments, gas, and maintenance expenses.
Entertainment and insurance receive the lowest allocations at 4% each, with entertainment including hobbies and leisure activities, and insurance covering health, life, and home insurance premiums. Retirement is the smallest allocation at 2%, which covers contributions to retirement savings plans.
From this budget, we can conclude that the household prioritizes spending on necessities like taxes, housing, and food. The budget also includes allocations for savings and transportation, which are considered important expenses for many households.
However, discretionary expenses like entertainment and retirement receive relatively low allocations, indicating that they are not the top priorities for this household.
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Recycled CDs, Incorporated, offers a choice of 5 used CDs for $29, with each additional CD costing $. Write a cost function for purchasing 5 or more CDs. What will the cost of buying CDs be? Let x represent the number of CDs over 5.
Answers
The cost function will be of the form f(x) = x + 29.
What is a function ?A function have a set of dependent variable for the given or specified independent variable.
According to the given question Recycled CDs, Incorporated, offers a choice of 5 used CDs for 29 dollars with each additional CD costing a dollar.
We have to write a function for purchasing 5 or more CDs where x represents the no. of CDs over 5.
Let f(x) represents the cost of CDs.
∴ f(x) = x + 29.
Here the constant 29 dollars represents the cost of 5 CDs and x represents no. of CD's over 5.Put x = 0 and the cost for 5 CDs will be 29 and for any more value of x we will get our desire result.
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What is the completely factored form of this polynomial? 7x4 14x3 − 168x2
Answers
The completely factored form of the polynomial is 7x² (x + 6) (x - 4)
Given,
The polynomial ; 7x⁴ + 14x³ - 168x²
We have to find the complete factored form of this polynomial;
Polynomial;
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Here,
The polynomial is 7x⁴ + 14x³ - 168x²
Now,
Factorize the polynomial using common factors;
That is,
7x⁴ + 14x³ - 168x²
7x² (x² + 2x - 24)
Solve x² + 2x - 24 using quadratic formula;
That is,
\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2
Now,
Solve
-2 + √-92 / 2 = 3.79 ≈ 4
Solve
-2 - √-92 / 2 = -5.79 ≈ -6
Then,
The factors will be (x - 4) and (x + 6)
So,
7x² (x + 6) (x - 4) will be the factored form of the polynomial.
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What is the equation of the line that goes through
the points (4,6) and (2,12)?
A.y=3x+18
B.y=-3x+18
C.y=-3x+6
D.y=3x
Answers
Answer:
B) y=-3x+18
how do u write y=e^-1.5t into y=ab^x
Answers
Consequently, the exponential function y=e-1.5t can be changed to y=abx. The transcendental number is the most popular exponential-function base.
what is exponential function ?The formula for a mathematical function called an exponential function is f (x) = an x, where x is a variable and an is a fixed quantity known as the function's base. The exponential-function base that is most frequently used is the transcendental number e, or approximately 2.71828. An example of an exponential function is the growth of bacteria. Some bacteria can multiply by two in one hour. There will be twice as many germs around after x hours as there were at the beginning. F(x) = 2x is the formula for this.
given
y=e^-1.5t
f(x) = 2. x
f(x) = 1/ 2x = 2. -x
f(x) = 2. x+3
f(x) = 0.5. x
y=ab^x
Consequently, the exponential function y=e-1.5t can be changed to y=abx. The transcendental number is the most popular exponential-function base.
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Help me please
The question is in the picture above..
Answers
i need help with please
Answers
Answer:
c
Step-by-step explanation:
Solve each equation. Answers should be in simplest fraction form
A) ² = 15
B) = 1/
28
c) - 25
D) -
=
5
W
Answers
Answer:
The answers are in the image attached to this response.
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