DUE FRIDAY WELL WRITTEN ANSWERS ONLY PLEASE HELP!!!
The height in feet of a seat on a Ferris wheel is given by the function h(t)=50sin(2πt/10) + 60. Time t is measured in minutes since the Ferris wheel started. What is the diameter of the Ferris wheel? How high is the center of the Ferris wheel?
Answers
Diameter is 100 feet
Center is 60ft high
Explanation:
The given function for the height of a seat on a Ferris wheel is:
h(t) = 50sin(2πt/10) + 60
Here, the amplitude of the sine function is 50, which corresponds to the radius of the Ferris wheel. The diameter of the Ferris wheel is twice the radius. Thus, the diameter is:
Diameter = 2 * radius = 2 * 50 = 100 feet
The vertical shift of the sine function is 60, which represents the height of the center of the Ferris wheel above the ground. So, the center of the Ferris wheel is 60 feet high.
Related Questions
What is the total area of the figure?
Answers
Answer: 130.5
Step-by-step explanation:
Divide the object into 2 separate shapes and find areas
(Forget about the cutout for now, imagine a part of original figure)
rectangle:
Area (A)= base (b) x Height (h)
A=bh
Plug-in
A= (18)x8 (because both are 9 add them)
A= 144
Triangle:
A=1/2bh
A=1/2 9(5)
A= 22.5
incomplete total: 166.5
cutout:
A=bh
A = 9x4 (because the opp. is 8 and the known is 4, subtract: 8-4)
A= 36
Subtract incomplete total from cutout
166.5-36=130.5
The formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl; where 'P' is the perimeter of the base and 'l' is the slant height.
a. true
b. false
Answers
The formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl; is true
What is the Surface Area of a Pyramid?
The total area of a pyramid's faces is referred to as the pyramid's surface area. In other terms, a pyramid's surface area is the whole area that the pyramid's surface occupies. Typically, it is measured in square units like m2, cm2, in2, and so forth.
The pyramid's two types of surface areas are:
A pyramid's lateral surface area (LSA) is the sum of its side faces' surface areas.LSA of the pyramid plus the base's area equals the pyramid's total surface area (TSA).Regular Pyramid Lateral Surface Area = (1/2) Pl Square Units
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True, the formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl.
What is the Surface Area of a Pyramid?The total area of a pyramid's faces is referred to as the pyramid's surface area. In other terms, a pyramid's surface area is the whole area that the pyramid's surface occupies. Typically, it is measured in square units like m², cm², in², and so forth.
The pyramid's two types of surface areas are:
A pyramid's lateral surface area (LSA) is the sum of its side faces' surface areas.LSA of the pyramid plus the base's area equals the pyramid's total surface area (TSA).Refer to the attachment.
The base area of the pyramid is, B = a2
The base perimeter of the pyramid is, P = 4a
The area of each of the side faces = (1/2) × base × height = (1/2) × (a) × l
Therefore, the sum of all side faces = 4 [(1/2) × (a) × l] = (1/2) × (4a) × l
= (1/2) Pl.
Regular Pyramid Lateral Surface Area = (1/2) Pl Square Units
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what is the slope of 3y = 9 – 4x
Answers
Answer:
The slope is -4/3
I hope this helps :)
Wrealized loss of $40,000. Realized loss of $10,000. Unrealized gain of $30,000. A. Moving to another question will save this response
Answers
To calculate the net gain or loss, we need to consider both the realized and unrealized components. Therefore, the net gain/loss is -$20,000. This indicates a net loss of $20,000.
The net gain or loss is calculated by adding the realized gains or losses and the unrealized gains or losses:
Net Gain/Loss = (Realized Gain/Loss) + (Unrealized Gain/Loss)
Given the information provided:
Realized Loss = $40,000
Realized Loss = $10,000
Unrealized Gain = $30,000
Net Gain/Loss = (-$40,000) + (-$10,000) + $30,000
Net Gain/Loss = -$50,000 + $30,000
Net Gain/Loss = -$20,000
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-5, _____, _____, 7, 11
Answers
Answer:
the missing numbers are -1, 3,
Step-by-step explanation:
11-7=4
sooo
-5+4= -1
-1+4=3
given f(x)=x-5 and g(x)=4x^2+2 find (fof)(x)
Answers
Answer:
\((fof) = x - 5 - 5 \\ = x - 10\)
identify the vertex of the parabola given by f(x) = (x + 2)^2 – 4
Answers
Answer:
The vertex is ( -2, -4)
Step-by-step explanation:
The vertex form is
y = a( x-h) ^2 +k
where ( h,k) is the vertex
f(x) = (x + 2)^2 – 4
Rewriting
f(x) = (x - -2)^2 – 4
The vertex is ( -2, -4)
If a= 4, b=6, and c=2, evaluate the expression ab-c
Answers
Write 13 divided by 4/7 as a multiplication expression
Answers
Answer:
13/1*7/4
Step-by-step explanation:
The way you get this is by using the Keep, Change, Flip Method. 13 as a fraction would be 13/1, and this is the keep phase. The change phase is where you change division to multiplication. The flip phase is when we flip the numerator and denominator. Remember, this only works when dividing fractions.
Round the decimal equivalent of 856 1/6 to the nearest hundredth. What number is in the hundredth place PLEASE HELP
Answers
Answer:
The answer is 856.17.
Step-by-step explanation:
If you made the fraction into a decimal, you would get 856.166666666. If you round it to the nearest hundredth, you would get 856.17.
7
You are comparing 3 different cell phone plans to see which is the cheapest:
Plan A costs a basic fee of $30 per month and $10 for every GB of data used
Try writing each plan as an
equation in y = mx + b form where
Plan B costs a basic fee of $80 per month with unlimited data
=GBs used and y total cost.
Plan C costs a basic fee of $50 per month and $5 for every GB of data used
You're looking to replace the m and
b in the equation. For Plan A, where
a) Write an equation for each plan that calculates the total cost (y) in terms of GB of data used (x) would the $30 go? Where would
the
Plan A:
Plan B:
Plan C:
$10 go?
b) Graph each plan on the following set of axes.
Cell Phone Plan Costs
Cost
100
c) When does Plan A cost the same as
Plan C?
80
60
d) Which plan is best if you only use 0-
4 GBs of data a month?
40:
20.
GBs of
8 10 data used
4
6
e) When does Plan B become the best
deal?
Answers
Answer:
Plan A equation: y = 10x + 30
Plan B equation: y = x + 80
Plan C equation: y = 5x + 50
Plan A costs the same as Plan C in 4 months
Plan A is the better option if you use 0 - 4 GBs of data each month
Plan B becomes the better deal when 8 months pass
Step-by-step explanation:
When does Plan A cost the same as Plan C?
Set the equations equal to each other (the cost) and solve for x (time in months)
10x + 30 = 5x + 50
5x = 20
x = 4 months
Which plan is best if you only use 0-4 GBs of data a month?
Test the maximum and minimum values to check which plan costs less
At 0 GBs of data used per month
Plan A: y = 0 + $ 30 = $30 total
Plan B: y = 0 +$80 = $80 total
Plan C: y = 0 + $50 = $50 total
At 4 GBs of data used per month
Plan A: y = $ 40 + $ 30 = $ 70
Plan B: y = $ 4 + $ 80 = $ 84
Plan C: y = $ 20 + $ 50 = $ 70
Comparing the plans at maximum and minimum amount of GBs used, only one plan has the lowest cost overall. Even though Plan C is the same price at 4 GBs as Plan A, when you use 0 GBs you will end up paying more in Plan C than Plan A. Therefore, Plan A is the better option
When does Plan B become the best deal?
When you plot the different Plans on a graph, the slope intercept of x = 7.5 (rounded up to 8) yields the lowest cost for plan B
Fill in the blank. When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a _____ . When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a ____.
Answers
When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a Z-Score.
In statistics, each mathematical formula and each element has an internationally recognised name. This is to ensure that everyone in the world understands what every researcher has to say in every letter. A statistic that tells the number of standard deviations a data value is above or below the mean is called a z-score. And its formula is, Z = (X − μ)/σ
where, μ--> population mean,
σ --> population standard deviation and
x --> the raw-score.
Hence, when a data value is converted to a standardized scale, new value, Z-Score is representing the number of standard deviations the data value lies from the mean.
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a bin contains 21 balls, numbered 1 through 21. how many ways are there to pick a set of six balls from the bin in which at least one ball has an odd number?
Answers
To find the number of ways to pick a set of six balls from the bin in which at least one ball has an odd number, we can use the principle of inclusion-exclusion.
First, we find the total number of ways to pick a set of six balls from the bin, which is 21 choose 6 (written as C(21,6)) = 54264.
Next, we find the number of ways to pick a set of six balls from the bin in which all the balls have even numbers. There are only 10 even-numbered balls in the bin, so the number of ways to pick a set of six even-numbered balls is 10 choose 6 (written as C(10,6)) = 210.
Therefore, the number of ways to pick a set of six balls from the bin in which at least one ball has an odd number is:
C(21,6) - C(10,6) = 54264 - 210 = 54054.
So there are 54054 ways to pick a set of six balls from the bin in which at least one ball has an odd number.e
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the diameter of a sphere is measured to be 4.52 in. (a) find the radius of the sphere in centimeters. 5.74 correct: your answer is correct. cm (b) find the surface area of the sphere in square centimeters. 414.03 correct: your answer is correct. cm2 (c) find the volume of the sphere in cubic centimeters. 792.18 correct: your answer is correct. cm3
Answers
a) The radius of the sphere is 5.74 cm.
b) The surface area of the sphere is 414.03 cm².
c) The volume of the sphere is 792.18 cm³.
In the first paragraph, we summarize the answers: the radius of the sphere is 5.74 cm, the surface area is 414.03 cm², and the volume is 792.18 cm³. In the second paragraph, we explain how these values are calculated. The diameter of the sphere is given as 4.52 inches. To find the radius, we divide the diameter by 2, which gives us 4.52/2 = 2.26 inches. To convert inches to centimeters, we multiply by the conversion factor 2.54 cm/inch, resulting in a radius of 5.74 cm.
To calculate the surface area of the sphere, we use the formula A = 4πr², where r is the radius. Plugging in the value of the radius, we get A = 4π(5.74)² = 414.03 cm².
Finally, to find the volume of the sphere, we use the formula V = (4/3)πr³. Substituting the radius into the equation, we have V = (4/3)π(5.74)³ = 792.18 cm³.
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Find m Of the function
Answers
Answer:
m=1
Step-by-step explanation:
slope formula is y=mx-b
whenever a variable is by itself, the coefficient is always 1
Lorenzo Neal is a teacher assistant. He earns $15.50 per hour. He is allowed a flexible hours. Lorenzo was only able to work 32.25 hours last week. How much money did he earn?
Answers
Answer:
15.50 x 32.25=499.875
The beta for the DAK Corporation is 1.25. The yield on 30-year T-bonds is 5.65 percent, and the long-term average return on the S&P 500 is-11 percent. Calculate the required rate of return for DAK Corporation. I
Answers
The required rate of return for DAK Corporation is 12.34%.
What is the required rate?
The minimal profit (return) an investor will seek or expect in exchange for taking on the risk of investing in a stock or other type of security is known as the required rate of return (RRR). RRR can also be used to determine a project's potential profitability in relation to its funding costs.
Here, we have
Given Information
Beta = 1.25
The yield on 30-year T bonds (rf)= 5.65%
Return on S&P (rM) = 11%
Required Return for DAK = rf + Beta*(rM - rf)
= 5.65% + 1.25*(11% - 5.65%)
= 12.34%
Hence, the required rate of return for DAK Corporation is 12.34%.
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The 99% confidence interval for the mean length of frog jumps is (12.64 cm, 14.44 cm).Which of the following statements is a correct interpretation of the 99% confidence?a. If we were to repeat this sampling many times, 99% of the confidence intervals we could construct would contain the true population mean.b. 99% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.c. There is a 99% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm.d. Of the total number of frogs in your area of the country, 99% can jump between 12.64 cm and 14.44 cm.
Answers
The correct interpretation of the 99% confidence interval for the mean length of frog jumps, (12.64 cm, 14.44 cm), is:
a. If we were to repeat this sampling many times, 99% of the confidence intervals we could construct would contain the true population mean.
This interpretation correctly captures the concept of a confidence interval. It means that if we were to take multiple samples from the population and construct 99% confidence intervals using the same method, approximately 99% of those intervals would contain the true population mean. It provides a measure of confidence in the accuracy of the interval estimation.
Option b is incorrect because it describes the specific values of the given confidence interval, rather than the general behavior of constructing intervals.
Option c is incorrect because it implies a probability for individual frogs, which is not what the confidence interval represents. Confidence intervals are about the population parameter, not the probability of individual observations.
Option d is incorrect because it makes a claim about the characteristics of all frogs in the area, which is beyond the scope of the confidence interval. The interval only provides information about the mean length of frog jumps, not individual frogs.
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What is the perimeter of the parallelogram? 12 cm 6 cm 5 cm 7 cm
Answers
You need to have only 2
For ex: 4 cm and 7 cm
So, P=2• (a•b)
2•(4•7)
P=56cm
Answer:
12
Step-by-step explanation:
3. Consider the following function. f(x) = x^2+ 4.
Part A: Write a function that shifts f(x) up 5 units.
Part B: Write a function that shifts f(x) down 8 units.
Part D: Write a function that vertically stretches f(x) by 6 units.
Part E: Write a function that reflects f(x) about the x-axis.
Answers
Part A: To shift f(x) up 5 units, we need to add 5 to the output of f(x). Therefore, the new function g(x) that shifts f(x) up 5 units is:
g(x) = f(x) + 5 = x^2 + 4 + 5 = x^2 + 9
Part B: To shift f(x) down 8 units, we need to subtract 8 from the output of f(x). Therefore, the new function h(x) that shifts f(x) down 8 units is:
h(x) = f(x) - 8 = x^2 + 4 - 8 = x^2 - 4
Part C: To horizontally stretch f(x) by 6 units, we need to multiply the input of f(x) by 6. Therefore, the new function j(x) that stretches f(x) horizontally by 6 units is:
j(x) = f(6x) = (6x)^2 + 4 = 36x^2 + 4
Part D: To reflect f(x) about the x-axis, we need to multiply the output of f(x) by -1. Therefore, the new function k(x) that reflects f(x) about the x-axis is:
k(x) = -f(x) = -(x^2 + 4) = -x^2 - 4
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2. Write the following in order from least
to greatest:
0.7, 0.84, 4/5, 82%, 71/100
Answers
Answer:
0.7, 71/100, 4/5, 82%, 0.84
the larger circle has center $o$ and passes through $d$. the smaller circle has diameter $od$. what percent of the larger circle's area is gray?
Answers
25% is the larger circle area is gray.
Area of a Circle: The area of a circle is pi times the radius squared.
To calculate the area of the circle we have the formula:
A = π r²-----(1)
where
A=area
r=radius.
First, we have to analyze the given data, the large circle center o passes through d, so
Gray circle area=π*(radius)^2----(2)
The radius of the smaller circle = OD/2 substitute in (2)
Gray circle area=π*(OD/2)^2
Gray circle area=π*OD^2/4
Larger circle area=π*(radius)2
radius of the larger circle = OD
larger circle area=π*OD^2
To know the percentage of a large circle we have a small formula:
gray circle area/large circle area--------(3)
=π*OD^2/4/π*OD^2
=π*OD^2/4*1/π*OD^2=1/4
=25/100
=25%
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how many trace lines can be drawn for the plane 2x + 4z = 5
Answers
There are infinitely many trace lines that can be drawn for the plane 2x + 4z = 5.
The equation of the plane is given as 2x + 4z = 5. To visualize the trace lines, we can rewrite the equation in slope-intercept form:
2x + 4z = 5
4z = -2x + 5
z = (-1/2)x + (5/4)
Now we can see that the equation represents a plane in three-dimensional space. Each point (x, y, z) on the plane satisfies the equation. Since there are infinitely many values of x and z that satisfy the equation, there are infinitely many points on the plane.
Therefore, there are infinitely many trace lines that can be drawn for the plane 2x + 4z = 5, as each line can be represented by different combinations of x and z that satisfy the equation.
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Calvin took his friends to a movie for his birthday. The movie tickets cost $12 per person. He spent less than $180.
If x is the number of friends he took along, then the inequality that represents the situation is
.
Calvin took at most
friends to the movie.
Answers
Answer:
Answer: Your answer would have to be 12x<180
He took 14 friends.
Step-by-step explanation:
hope this helps and have a great rest of your day!
5 2/5 divided by 9/10
Answers
Answer:
Step-by-step explanation:
5 2/5 = [(5*5)]+2 / 5 = (25+2) / 5 = 27/5
(27/5)/(9/10) = 27/5 * 10/9
cross cancel 27 becomes 3 and 9 becomes 1, 5 becomes 1 and 10 becomes 2
= 3/1 * 2/1 = 6/1 = 6
One hundred and five students see a play. Each ticket costs $45. What is the total amount the students spend for tickets? Use mental math.
Answers
Answer:
4725
Step-by-step explanation:
105 students
think of 100 students
100 × 45 = 4500
now the remaining 5 students
cost for 10 students will be
45 × 10 = 450
divide 450 by 2 to find out for 5 students
it is 225
4500 + 225 = 4725
g+1/4Ua=b
solve for A.
Answers
Answer:
a=4b/u-4g/u
Step-by-step explanation:
You got this!
Solve for X please! I'll give a lot of points
Answers
Answer: \(x=6\)
Step-by-step explanation: Since the triangles are similar, line them up so that the equivalent angle is in the same spot on both triangles. In triangle JKL the 12 represents the same side on QRS being 20. This means that triangle QRS's sides are 5/3 greater than the other triangle. To solve for x, set up the equation based on the similar sides and it is,
\(7x-2 = 5/3(24)\)
which means that
\(7x-2 = 40\)
then
\(7x=42\)
lastly,
\(x=6\)
What is the volume of the figure?
Answers
Answer:
341.25
Step-by-step explanation:
You first split the figure into 2 pieces the triangular prism and the rectangular prism now that we know the dimensions of each figure we can create an expression, we will start with the triangular prism. the expression will be 3/2 x 5/2 x 10.5. Then we solve the rectangular prism. 5 x 5 x 10.5.
Now that we have acquired all the math that we need we can continue to simplify. 3 x 2 x 5/2 was derived from (3 x 5)/2 and we physically drew it out with properties of algebra (a later topic to study) anyways we get 15/2=7.5 and we multiply that by 10.5 giving us 78.75. the triangular prism is easier we just do 25 x 10.5 giving us 262.5. Now that we have succumbed both figures we can combine the to get the volume which is 341.25 (78.75 + 262.5).
By trial and error find examples of 2 by 2 matrices such that (a) A² = -I, A having only real entries. (b) B² = 0, although B ≠ 0. (c) CD = -DC, not allowing the case CD = 0. (d) EF = 0, although no entries of E or F are zero.
Answers
A: (a) A = [0 1; -1 0]. This matrix has only real entries and when we square it, we get A² = [-1 0; 0 -1], which is equal to -I.
(b) B = [0 1; 0 0]. This matrix is not 0, but when we square it, we get B² = [0 0; 0 0], which is equal to 0.
(c) C = [0 1; -1 0] and D = [1 0; 0 -1]. When we multiply these two matrices, we get CD = [-1 0; 0 1] and DC = [0 -1; 1 0], which are opposite matrices.
(d) E = [1 1; 1 1] and F = [-1 1; 1 -1]. When we multiply these two matrices, we get EF = [0 0; 0 0], which is equal to 0, although no entries of E or F are zero.
Here is explanation -
(a) A = [[0, -1], [1, 0]] is a 2x2 matrix with real entries that satisfies A^2 = -I. To see this, we can simply calculate the square of the matrix A:
A^2 = [[0, -1], [1, 0]] * [[0, -1], [1, 0]]
= [[00 + -11, 0*-1 + -10], [10 + 01, 1-1 + 0*0]]
= [[-1, 0], [0, -1]]
As we can see, A^2 = -I, where I is the 2x2 identity matrix.
(b) B = [[0, 1], [0, 0]] is a 2x2 matrix with real entries that satisfies B^2 = 0, although B ≠ 0. To see this, we can calculate the square of the matrix B:
B^2 = [[0, 1], [0, 0]] * [[0, 1], [0, 0]]
= [[00 + 10, 01 + 10], [00 + 00, 01 + 00]]
= [[0, 0], [0, 0]]
As we can see, B^2 = 0, although B ≠ 0.
(c) C = [[0, 1], [-1, 0]] and D = [[0, -1], [1, 0]] are 2x2 matrices with real entries that satisfy CD = -DC. To see this, we can calculate the product of matrices C and D:
CD = [[0, 1], [-1, 0]] * [[0, -1], [1, 0]]
= [[00 + 10, 0*-1 + 11], [-10 + 01, -1-1 + 0*0]]
= [[0, 1], [1, 1]]
DC = [[0, -1], [1, 0]] * [[0, 1], [-1, 0]]
= [[00 - 11, 01 + -10], [10 - 0-1, 11 + 00]]
= [[-1, 0], [1, 1]]
As we can see, CD ≠ -DC, so C and D do not satisfy the condition CD = -DC, not allowing the case CD = 0.
(d) E = [[1, 1], [0, 1]] and F = [[1, 0], [1, 1]] are 2x2 matrices with real entries that satisfy EF = 0, although no entries of E or F are zero. To see this, we can calculate the product of matrices E and F:
EF = [[1, 1], [0, 1]] * [[1, 0], [1, 1]]
= [[11 + 10, 11 + 11], [01 + 10, 01 + 11]]
= [[1, 2], [0, 1]]
As we can see, EF = 0, although no entries of E or F are zero.
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