A carnival ferris wheel with a radius of 7m rotates once every 16 seconds. The bottom of the wheel is 1m above the ground.
Find the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel.
Please use math tools to state your answer - see hint. Or attach your work as ONE easy to read file.
The equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds is y(t) = 14sin(πt/8) + 1
The equation of the function that gives the height of the ferris wheel
Since the motion of the ferris wheel is periodic,it follows a sinusoidal function form.
So, the general form of a sine function y(t) is
y(t) = Asin(2πt/T) + K where
A = amplitude, T = period, t = time and K = vertical shiftNow since radius of 7m, the maximum value from its lowest point is at y = 2r + 1 = 2 × 7 + 1 = 14 + 1 = 15 at sin(2πt/T) = 1 which is the maximum value for sinФ = 1.
Since the bottom of the wheel is 1m above the ground, its minimum value is y = 1 at t = 0.
Also, it rotates once every 16 seconds, so its period T = 16 s.
So, y(t) = Asin(2πt/T) + K
y(t) = Asin(2πt/16) + K
y(t) = Asin(πt/8) + K
At maximum value
15 = Asin(πt/8) + K
15 = A + K (1)
At minimum value
1 = Asin(πt/8) + K
1 = A(0) + K
1 = 0 + K
K = 1
Substituting K into (1), we have
15 = A + 1
15 - 1 = A
14 = A
A = 14
So, y(t) = Asin(πt/8) + K
y(t) = 14sin(πt/8) + 1
So, the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel is y(t) = 14sin(πt/8) + 1
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In exercises 21 and 22, point B is between A and C on Line AC. Use the information to write an equation in terms of x. Then solve the equation and find AB, BC, and AC. AB= 13+ 2x BC= 12 AC= x+2
The value of x is -23 and the values of AB, BC, and AC are -33, 12 and -21
How to solve the equation and find AB, BC, and AC?The equations are given as
AB = 13 + 2x
BC = 12
AC = x + 2
Point B is between A and C on Line AC.
So, we have
AC = AB + BC
This gives
x + 2 = 13 + 2x + 12
Evaluate the like terms
x - 2x = 13 + 12 - 2
This gives
-x = 23
Divide by -1
x =-23
Substitute x =-23 in AB = 13 + 2x and AC = x + 2
AB = 13 - 2 * 23 = -33
AC = -23 + 2 = -21
Hence, the value of x is -23 and the values of AB, BC, and AC are -33, 12 and -21
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You are loading a rental truck with 78-pound boxes and have
60 boxes to load. If the empty truck weighs 8840 pounds,
then the equation W=78b+8840 gives the total weight of
the truck if it is carrying b boxes.
Suppose the truck is not legally allowed to weigh more than
13,200 pounds.
Will your rental truck be able to legally carry the load of 60
boxes?
Explain why you answered yes or no and show all work.
Answer:
13200 needs to be less than 78*60+8840,
which is false because 13200 < 13520
Step-by-step explanation:
The truck cannot load 60 boxes as it exceeds the weight limit.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
W=78b+8840
So, b= 60
W= 78 x 66 + 8840
W = 5148 +8840
W = 13988 > 13200 ( limit for the weight)
Hence, the truck cannot load 60 boxes as it exceeds the weight limit.
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A Food Marketing Institute found that 29% of households spend more than $125 a week on groceries. Assume the population proportion is 0.29 and a simple random sample of 207 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?
There is a ___ probability that the sample proportion of households spending more than $125 a week is less than 0.31. Round the answer to 4 decimal places.
Using the normal distribution, there is a 0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The estimate and the sample size are:
p = 0.29, n = 207.
Hence the mean and the standard error are given as follows:
[tex]\mu = p = 0.29[/tex].[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.29(0.71)}{207}} = 0.0315[/tex].The probability that the sample proportion of households spending more than $125 a week is less than 0.31 is the p-value of Z when X = 0.31, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.31 - 0.29}{0.0315}[/tex]
Z = 0.63
Z = 0.63 has a p-value of 0.7357.
0.7357 = 73.57% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
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The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than an unknown number of inches.
Suppose the area of this rectangle is less than 12 square inches. Which of the following numbers could be the value of the unknown number? Select all that apply.
Answer:
6,4
Step-by-step explanation:
I'm not sure if 4 is correct but 6 definitely is. I hope this helps
Which represents an exterior angle of triangle ABF?
∠BAD
∠AFE
∠CAD
∠CAB
The angle that represents an exterior angle of the given triangle is: D. ∠CAB.
What is an Exterior Angle of a Triangle?An exterior angle of a triangle is the angle that is located outside a triangle on an extended adjacent side of the triangle.
In the image given, and considering the options we have, ∠CAB is located outside a triangle ABF on an extended adjacent side CF of the triangle.
Therefore, the answer is: D. ∠CAB.
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helpppp meeeeee
Which expression represents the following statement? Add 8 to 6 times the quotient of 21 and 3.
6 x (21 ÷ 3) + 8
6 + 8 − (21 ÷ 3)
21 ÷ 3 − (8 + 6)
6 x (21 + 3) + 8
Answer:
(a) 6 x (21 ÷ 3) + 8
Step-by-step explanation:
The first step in translating English to math is to understand the English.
Parsing itThe quotient of 21 and 3 is written (21 ÷ 3). Six times that quotient is ...
6×(21÷3)
When 8 is added to this, it becomes ...
6 × (21 ÷ 3) + 8
Which choice is a term in this expression? -3x − 7(x + 4)
Answer:
Mate im sorry for replying here but i need points to ask a question.
Which graph shows a negative correlation? A graph with both axes unnumbered. Points show a steady trend. A graph with both axes unnumbered. Points are scattered loosely in the top half of the graph. A graph with both axes unnumbered. Points show a downward trend. A graph with both axes unnumbered. Points are scattered loosely all Over graph.
Answer:
The graph with a downward trend is the negative correlation
Step-by-step explanation:
Answer:
The Downward Slope or 'C' is the answer.
Step-by-step explanation:
Negative Slopes go down
Positive Slopes go up
Random Slopes are random
Scattered Slopes are scattered but together
Which of the following equations is an example of inverse variation between
the variables x and y?
Answer:
we need a whole example not just the variables.
Step-by-step explanation:
− 2 x − 2 > 4 OR − 8 x − 7 ≤ − 23
interval notaton and plot on line graph
The interval notation of the possible values of x according to.the given inequalities is; -3 > x and x>= 2.
What is the interval notation of the inequalities given in the task content?The interval notation of the given inequalities which describes the possible value of x according to the task content are as follows;
For − 2 x − 2 > 4; we have;
− 2 x > 4 +2
-2x > 6
x < -3.
For − 8 x − 7 ≤ − 23; we have;
− 8 x ≤ − 23 +7
-8x ≤ -16
x >= 2.
Consequently, the interval notation of the given inequalities is; -3 > x and x >= 2.
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where are the two variables is part A? Tiya earns $7 an hour mowing her neighbor's lawn.
Part A: Create two variables and determine which is dependent and which is independent for this situation. (4 points)
The two variables are; earnings, y and hours, x in which case, the former is the dependent variable while the latter is the independent variable.
Which is the dependent and which is the independent variable?It follows from the task content that Tiya earns $7 an hour mowing her neighbor's lawn.
On this note, it follows that the amount of money earned by Tiya is a dependent variable which solely depends on the number of hours spent on the job, which is the independent variable.
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Solve the following system of equations
y= -½/x-2
Answer:
Wolfram|Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints.
Step-by-step explanation:
Part 1:
A. Express the new length of the long side of the note card, once the two corners are removed.
B. Express the new width of the short side of the note card, once the two corners are removed.
Part 2:
Write a function A(x) that defines the area of the bottom of the box, once the corners are removed and the sides are folded up.
Part 3:
A. Suppose you want the bottom of your box to cover a total area of 16 in2. Set up an equation in standard form that will help you find the size (x) of the corner you need to cut in order for your box to have this area.
B. Solve this equation and take note of any extraneous solutions. Explain why the answer is extraneous, and clearly state the correct answer
The size of the corner you need to cut in order for your box to have this area is 0.5 inches
Part 1: A. Express the new length of the long side of the note card, once the two corners are removed.The base length is given as:
Length = 7
When the edges are removed, the new length becomes
New length = 7 - x - x
Evaluate
New length = 7 - 2x
Part 1: B. Express the new width of the short side of the note card, once the two corners are removed.The base width is given as:
Width = 4
When the edges are removed, the new length becomes
New width = 4 - x - x
Evaluate
New width = 4 - 2x
Part 2: Write a function A(x) that defines the area of the bottom of the box, once the corners are removed and the sides are folded up.The area of the bottom of the box is calculated as:
Area = New length * New width
This gives
Area = (7 - 2x) * (4 - 2x)
Rewrite as:
A(x) = (7 - 2x) * (4 - 2x)
Part 3: Set up an equation in standard form that will help you find the size (x)The area is given as:
Area = 16
So, we have:
(7 - 2x) * (4 - 2x) = 16
Expand
28 - 14x - 8x + 4x^2 = 16
Rewrite as
4x^2 - 14x - 8x + 28 - 16 = 0
Evaluate the like terms
4x^2 - 22x + 12= 0
Part 3: Solve this equation and take note of any extraneous solutionsWe have:
4x^2 - 22x + 12= 0
Expand the equation
4x^2 - 24x - 2x + 12 = 0
Factorize the equation
4x(x - 6) - 2(x - 6) = 0
Factor out x - 6
(4x - 2)(x - 6) = 0
Solve for x
x = 0.5 or x = 6
The value of x = 6 is too big for the dimensions of the box.
So, x = 6 is an extraneous solution for the equation
Hence, the size of the corner you need to cut in order for your box to have this area is 0.5 inches
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will give brainliest
ax² + bx + c = 0
discriminant = b² - 4ac
----> x² + 7x + 12
---> Discriminant of this equation = 7² - 12.1.4 = 49 - 48 = 1 (Positive discriminant)
x = (-7 + 1)/(2.1) = -6/2 = -3
or
x = (-7 - 1)/(2.1) = -8/2 = -4
Therefore, this equation has two real solutions and has a positive discriminant.
The correct answer is B
Time: ~15 minutes
Materials: pencil/paper or whiteboard/marker
Task: Two men and two women want to take a rowboat to an island. The boat has a maximum capacity of one man or two women. Someone must always be in the boat when it’s moving. How can all four of them get to the island?
The four of them can get to the island if the two women begins the journey first. Detail below:
How can the four of them get to the island?From the question given, we were told that:
The boat has a maximum capacity of one man or two women.Someone must always be in the boat when it’s moving.With the above information in mind, we can determine how the four of them can get to the island by following the steps listed below:
The two women will take the boat to the island.One of the women will return with the boat to meet with the other two men leaving the other woman on the island.One of them men will then take the boat to the island to meet the other women on the island.The woman on the island will return with the boat to meet the other man and woman.The two women will take the boat to meet the other man on the island.One of the women will return with the boat to meet with the other man.The last man will take the boat to meat the other man and woman on the island.The woman on the island will return with the boat to meet the last woman.Finally, the two women will take the boat to meet the two men on the islandLearn more about riddles:
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Find the indicated side of the
right triangle.
60°
30°
X
x = 3√√√/[?]
3
Answer:
[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
The given is a special right triangle with angle measures 30-60-90
The measure of side lengths for this special right triangle are represented with
a-a[tex]\sqrt{3}[/tex]-2a respectively
Now, since the side length that sees angle measure 30 is given as 3 (represented with a) then the measure of the side length that sees angle measure 60 would be [tex]3\sqrt{3}[/tex]
Please tell me fast on a time crunch
Answer:
x ≥ -6
Step-by-step explanation:
x - 4 ≤ 3x + 8
Add 4 to both sides.
x ≤ 3x + 12
Subtract 3x from both sides.
-2x ≤ 12
Divide both sides by -2. Remember to change the direction of the inequality sign since you are dividing by a negative number.
x ≥ -6
Answer:
[tex]x \geqslant - 6[/tex]
Step-by-step explanation:
[tex]x - 4 \leqslant 3x + 8 = = > \\ - 12 \leqslant 2x = = = > \\ x \geqslant - 6[/tex]
Find the area. This is a trapezoid, with bases that measure 5 feet and 10 feet, and a height of 4 feet.
Answer:
A = 30 ft²
Step-by-step explanation:
the area (A) of a trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases , then
A = [tex]\frac{1}{2}[/tex] × 4 × (5 + 10) = 2 × 15 = 30 ft²
Find the measure of a
Answer:
112°
Step-by-step explanation:
Angles on a line add to 180°.
What kind of transformation is illustrated in this figure?
The transformation illustrated in the figure is translation.
What is Translation?Translation is a Transformation process in which the size or shape of a figure is not changed rather it only changes the coordinates of the vertices that make up that shape by moving them from one point to another.
Analysis:
Both shapes are congruent, since all the vertices remain in their respective positions even though they were moved and no change in the shape or size, then the transformation process is Translation.
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you deposit 2000 in an account earning 3% interest compounded monthly.
a. how much will you have in the account in 20 years
b. how much interest will you earn
Answer:
a. 3641.51
b. 1641.51
Step-by-step explanation:
The future value formula will tell you the amount in the account in 20 years.
FormulaFV = P(1 +r/n)^(nt)
Principal P is compounded n times per year at annual rate r for t years.
ApplicationThe future value of the account with P=2000, r=0.03, n=12, and t=20 will be ...
FV = 2000(1 +0.03/12)^(12·20) = 2000(1.0025^240) ≈ 3641.50999
a.The account value in 20 years will be 3641.51.
b.The first 2000 of account value is the principal, so the interest is ...
interest = 3641.51 -2000
interest = 1641.51
__
Additional comment
Many calculators and all spreadsheets have built-in capability for making this calculation.
the sum of two numbers is 55 and the difference is 15 what are the numbers
[tex]x + y = 55 \\ x - y = 15 \\ \\ 2x = 70 \: \: \: \: \: \: x = 35 \\ y = 55 - x = 55 - 35 = 20[/tex]
True or False - All whole numbers are integers but not all integers are whole numbers
Answer:
false
correct me if i'm wrong :]
Answer:
True
Step-by-step explanation:
the picture is the explanation and pretty much sus everything up about integers
A model house has a scale of 1 in : 2 ft. if the real house is 26 ft wide then how wide is the model house.
Answer: 13 in.
Step-by-step explanation:
All you need to do is divide 26 by 2 in this case.
Which graph is the result of reflecting f(x) = (8)* across the y-axis and then across the x-axis? O 8- 6- 8 7
I assume you meant [tex]f(x)=8^x[/tex].
Reflecting across the x-axis would give [tex]y=-8^x[/tex].
Reflecting across the y-axis would give [tex]y=8^{-x}[/tex].
The function f(X) =7^x + 1 is transformed to function g through a horizontal compression by a factor of 1/3
The equation of the function g(x) is g(x) = 7^(3x) + 1
How to determine the function g(x)The function f(x) is given as:
f(x) = 7^x 1
When compressed horizontally by a factor of 1/3.
We have:
g(x) = f(3x)
This implies that:
g(x) = 7^(3x) + 1
Hence, the equation of the function g(x) is g(x) = 7^(3x) + 1
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find x and y
plssss help
90 + 6x = 180
-90
6x = 90
÷6
x = 15
5y + 4y + 90 + (6x15) =360
9y + 90 + 90 = 360
9y + 180 = 360
- 180
9y = 180
÷9
y = 20
Hope this helps!
please help asap
thank you very much
Answer:
x=30 , y=165 & z=10happy to help { bts army girl }Answer:
Step-by-step explanation:
Comment
You must solve x and then y in that order. The reason for that is there are 2 x values and they can be equated to each other. The you can go after the y value, since they are supplement with the value you get from the first operation.
Equations
x + 45 = 2x+ 8
<3 + y + 30 = 180
Solution
<1 and <3 are equal Two vertically opposite angles are always =.
x + 45 = 2x + 8 Subtract x from both sides
x-x + 45 = 2x - x + 8 Combine
45 = x + 8 Subtract 8 from both sides
45 - 8 = x + 8 - 8 Combine
37 = x
<1 + <2 = 180 These two angles sit on the same straight line and have a side in common
x + 45 + y + 30 = 180 Substitute for x
37 + 45 + y + 30 = 180 Combine
112 + y = 180 Subtract 112 from both sides
112-112 + y = 180 - 112 Combine
y = 68
Need help with this math question
The correlation coefficient is -0.87; strong correlation
How to determine the correlation coefficient?The given parameters are:
x = Time spent working out
y = lbs Overweight
Next, we enter the table of values in a graphing tool.
From the graphing tool, we have the following summary:
X Values
∑ = 27.1Mean = 2.71∑(X - Mx)2 = SSx = 22.569Y Values
∑ = 89Mean = 8.9∑(Y - My)2 = SSy = 778.9X and Y Combined
N = 10∑(X - Mx)(Y - My) = -114.19R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -114.19 / √((22.569)(778.9))
r = -0.8613
Approximate
r = -0.87
This means that the correlation coefficient is -0.87
Also, the correlation coefficient is a strong correlation, because it is closer to -1 than it is to 0
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