Answers
Answer:
Step-by-step explanation:
A + B= 180°
(5x+20)+(9x-92)=180°
14x-72=180°
14x=252
x=18
A=5(18)+20
A=110
Answer:
x = 18 , ∠ A = 110°
Step-by-step explanation:
∠ A and ∠ B are same- side interior angles and sum to 180° , that is
5x + 20 + 9x - 92 = 180
14x - 72 = 180 ( add 72 to both sides )
14x = 252 ( divide both sides by 14 )
x = 18
Then
∠ A = 5x + 20 = 5(18) + 20 = 90 + 20 = 110°
Related Questions
please help me im in a rush
Answers
Answer:
Step-by-step explanation:
A = 4 ft
B = 10 ft
C = 8 ft
D = 6 ft
b) Area of rectangle = length * width
Area of 2 triangle = base * height
Area of right triangular prism = area of 2 triangles +area of left rectangle + area of middle rectangle + area of right rectangle
= 6 * 8 + 4* 6 + 4 * 10 + 4 * 8
= 48 + 24 + 40 + 32
= 144 ft²
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Formulas:}[/tex]
[tex]\huge\text{Area of rectangle is: }\huge\boxed{\rm{\bold{w}idth \times \bold{h}eight = \bold{a}rea}}[/tex]
[tex]\huge\text{Area of triangle is: }\huge\boxed{\rm{\dfrac{1}{2} \times \bold{b}ase \times \bold{h}eight = \bold{a}rea}}[/tex]
[tex]\huge\textbf{Now, that we have that out of the}\\\\\huge\textbf{way, we can label your given equation:}[/tex]
[tex]\rm{A \rightarrow 4\ \boxed{\rm{ft}}}\\\\\rm{B \rightarrow 10\ \boxed{\rm{ft}}}\\\\\rm{C \rightarrow 8 \ \boxed{\rm{ft}}}\\\\\rm{D \rightarrow 6\ \boxed{\rm{ft}}}[/tex]
[tex]\huge\textbf{What should your equation look like?}[/tex]
[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]
[tex]\huge\textbf{What should it look like when we're}\\\huge\textbf{solving for the answer?}[/tex]
[tex]\rm{6\times 8 + 4\times 6 + 4 \times 10 + 4 \times 8}[/tex]
[tex]\rm{= 48 + 4\times6 + 4\times10 + 4\times8}[/tex]
[tex]\rm{= 48 + 24 + 4 \times 10 + 4\times8}[/tex]
[tex]\rm{= 72 + 4\times 10 + 4\times8}[/tex]
[tex]\rm{= 72 + 40 + 4\times8}[/tex]
[tex]\rm{= 112 + 4\times8}[/tex]
[tex]\rm{= 112 + 32}[/tex]
[tex]\rm{= 144}[/tex]
[tex]\huge\textbf{What is the answer?}[/tex]
[tex]\huge\boxed{\textsf{Answer: }\boxed{\frak{144\ ft^2}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
hy some help me with this I'd appreciate it and also show the work
Answers
[tex] \sqrt{5612} = \frac{5612 + 5625}{2 \sqrt{5625} } = \frac{11237}{2 \times 75} = 74.913333[/tex]
How do i find the value of y?
Answers
Answer: 65
Step-by-step explanation:
We know that from the 65-degree angle, x=130.
So, by the inscribed angle theorem, y=65.
Solve algebraically:
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation a.}[/tex]
[tex]\rm{2x^2 - 162 = 0}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\rm{2x^2 - 162 = 0}[/tex]
[tex]\huge\textbf{Add \boxed{\bf 162} to both sides:}[/tex]
[tex]\rm{2x^2 - 162 + 162 = 0 + 162}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{2x^2 = 0 + 162}[/tex]
[tex]\rm{2x^2 = 162}[/tex]
[tex]\huge\textbf{Divide \boxed{\bf 2} to both sides:}[/tex]
[tex]\rm{\dfrac{2x^2}{2} = \dfrac{162}{2}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x^2 = \dfrac{182}{2}}[/tex]
[tex]\rm{x^2 = 81}[/tex]
[tex]\huge\textbf{Take the square root of \boxed{\bf 81}}[/tex]
[tex]\rm{x = \pm \sqrt{81}}[/tex]
[tex]\rm{x = 9\ or\ x = -9}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{x = } \frak{9\ or } \ \textsf{x = }\frak{-9}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation b.}[/tex]
[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]
[tex]\huge\textbf{Solving for:}[/tex]
[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]
[tex]\huge\textbf{Simplify both sides of your equation:}[/tex]
[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} = -2}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf -2} to both sides:}[/tex]
[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} - (-2) = -2 - (-2)}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{- \dfrac{1}{2}x^2 + 3x - \dfrac{5}{2} = 0}[/tex]
[tex]\huge\textbf{Now, we can convert the equation to:}[/tex]
[tex]\rm{-0.5x^2 + 3x - 2.5 = 0}[/tex]
[tex]\large\text{When we changed the equation entirely, we made it easier to solve}\uparrow[/tex]
[tex]\huge\textbf{Use the quadratic formula to solve.}[/tex]
[tex]\large\textsf{The quadratic formula:}[/tex]
[tex]\mathsf{x= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
[tex]\huge\textbf{Here are your labels:}[/tex]
[tex]\text{a = }\rm{-0.5}\\\\\text{b = }\rm{ 3}\\\\\rm{c = }\rm{\ -2.5}[/tex]
[tex]\huge\textbf{Your new equation:}[/tex]
[tex]\rm{x = \dfrac{-(3) \pm \sqrt{3^2 - 4(-0.5)(-2.5)}}{2(-0.5)}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x = \dfrac{-3 \pm \sqrt{4}}{-1}}[/tex]
[tex]\rm{x = 1\ or \ x = 5}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\textsf{x = }\frak{1}\ \textsf{or x = }\frak{5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex][tex]a)\ x_1=-9,\ x_2=9\\\\b)\ x_1=1,\ x_2=5[/tex]
Step-by-step explanation:Given equations:
[tex]a)\ 2x^2 - 162 = 0\\\\b) -\dfrac{1}{2}(x-3)^2=-2[/tex]
A) 2x² - 162 = 0
Step 1: Divide both sides by 2.
[tex]\\\implies \dfrac{2x^2 - 162}{2} = \dfrac{0}{2}\\\\\implies x^2-81=0\\\\\implies x^2=81[/tex]Step 2: Take the square root of both sides (using both the positive and negative roots).
[tex]\\\implies \sqrt{x^2}=\sqrt{81}\\\\\implies x=\pm\ 9[/tex]
Step 3: Separate into two cases.
[tex]\implies x_1 = -9,\ x_2 =-9[/tex]
----------------------------------------------------------------------------------------------------------------
B) -1/2(x - 3)² = -2
Step 1: Multiply both sides by -2.
[tex]\\\implies -2\left(-\dfrac{1}{2}(x-3)^2\right)=-2(-2)\\\\\implies (x-3)^2=4[/tex]
Step 2: Take the square root of both sides (using both the positive and negative roots).
[tex]\\\implies\sqrt{(x-3)^2}=\sqrt{4}\\\\\implies x-3=\pm\ 2[/tex]
Step 3: Separate into two cases and solve each one.[tex]1)\ x-3=-2\implies x=-2+3\implies \boxed{x=1}\\\\2)\ x-3=2\implies x=2+3\implies \boxed{x=5}[/tex]
Using that income equation, after how many years will the income be $300? Round your answer correct UP TO TWO (2) decimal digits.
Answers
The number of years based on the equation is 24 years.
How to illustrate the information?The information is incomplete. An overview will be given. Let the income equation be represented as I = 60 + 10x where x represents the years taken.
Therefore i = 60 + 10x
60 + 10x = 300
10x = 300 - 60
10x = 240
x = 240/10
x = 24
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Using the defects method, which of these relationships represents the law of cosines if the measure of the included angle between the sides a and b of ∆abc is more than 90°? a. area of square c2 = -area of square a2 − area of squareb2 area of defect1 area of defect2 b. area of square c2 = area of square a2 area of squareb2 area of defect1 − area of defect2 c. area of square c2 = area of square a2 area of squareb2 − area of defect1 − area of defect2 d. area of square c2 = area of square a2 area of squareb2 area of defect1 area of defect2 e. area of square c2 = area of square a2 − area of squareb2 area of defect1 − area of defect2
Answers
The relationship that represents the law of cosines if the measure of the included angle between the sides a and b is D. area of square c² = area of square a² area of squareb² area of defect1 area of defect2
What is the law of cosine?It should be noted that the cosine law is simply used to solving triangles.
The law simply states that c² = a² + b² - 2abcosC.
The correct option that illustrates this is D.
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Answer:
c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2
Step-by-step explanation:
Ben has 3/4 pounds of cherries and ate 2/3 of the cherries. How many pounds of cherries does Ben eat?
Answers
Answer:
1/2 pounds
Step-by-step explanation:
3/4 * 2/3 = 1/2 pounds
A bag contains 50 tokens: 20 pink ,13 blue and 17 purble.if a person selects one token, replaces it,and then selects a second token,what is the probability of selecting 2 of the same colour
Answers
Answer:
Step-by-step explanation:
this is independent
20/50= 2/5= 40% of getting pink, probability of getting 2= 20%
13/50=0.26= 26% of getting blue, probability of getting 2= 13%
17/50=0.34=34% of getting purple, probability of getting 2 = 17%
70%
The write right company manufactures ballpoint pens and has been experiencing a 5% rate of defective pens. modifications are made to the manufacturing process in an attempt to improve quality, and the manager claims that the modified procedure is better, because a test of 50 pens shows that only one is defective. a. assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective. b. assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective. c. what probability value should be used for determining whether the modified process results in a defect rate that is less than 5%? d. what do you conclude about the effectiveness of the modified production process?
Answers
a. The probability that exactly one is defective is 0.2025
b. The probability that none will be defective is 0.0769
c. The probability rate that should be used is 2%
d. The modified production process is better.
The question has to do with binomial probability.
What is binomial probability?Binomial probability is probability in which the event can only have two values or is binary.
Given the binomial probability formula,
P(X = x) = ⁿCₓpˣ(1 - p)ⁿ ⁻ ˣ
where
p = probability of defective = 5% = 0.05 and n = 50a. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, exactly one is defective.For the probability that exactly one is defective, x = 1
So, P(x = 1) = ⁵⁰C₁p¹(1 - p)⁵⁰ ⁻ ¹
= ⁵⁰C₁p(1 - p)⁴⁹
= ⁵⁰C₁(0.05)(1 - 0.05)⁴⁹
= ⁵⁰C₁(0.05)(0.95)⁴⁹
= 50(0.05)(0.95)⁴⁹
= 50(0.05)(0.081)
= 0.2025
So, the probability that exactly one is defective is 0.2025
b. Assuming that the 5% rate of defects has not changed, find the probability that among 50 pens, none are defective.For the probability that exactly one is defective, x = 0
So, P(x = 0) = ⁵⁰C₀p⁰(1 - p)⁵⁰ ⁻ ⁰
= ⁵⁰C₀(1 - p)⁵⁰
= ⁵⁰C₀(1 - 0.05)⁵⁰
= ⁵⁰C₀(0.95)⁵⁰
= 1 × (0.95)⁵⁰
= 0.0769
So, the probability that none will be defective is 0.0769
c. What probability value should be used for determining whether the modified process results in a defect rate that is less than 5%?
Since the modified result results in a defective rate of one out of 50 pens.
The probability rate that should be used is p = number of defective pens/total number of pens = 1/50
= 1/50 × 100 %
= 2%
The probability rate that should be used is 2%
d. What do you conclude about the effectiveness of the modified production?Since the defective rate of the modified production process is 2% which is less than that of the previous production process which is 5%, the modified production process is better.
So, the modified production process is better.
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The probability that a football game will go into overtime is 18%. What is the probability that two of three football games will go to into overtime
Answers
The probability that two of three football games will go to into overtime is 0.08
How to determine the probability that two of three football games will go to into overtime?From the question, we have the following parameters about the probability
Sample size, n = 3
Proportion that goes to overtime, p = 18%
Number that goes into overtime, x = 2
The probability that two of three football games will go to into overtime is calculated using the following binomial probability
P(x) = nCx * p^x * (1 - p)^(n -x)
Substitute the known values in the above equation
P(2) = 3C2 * (18%)^2 * (1 - 18%)^(3 -2)
Express 18% as decimal
P(2) = 3C2 * (0.18)^2 * (1 - 0.18)^(3 -2)
Evaluate the difference
P(2) = 3C2 * (0.18)^2 * (0.82)^1
Evaluate the combination expression
P(2) = 3 * (0.18)^2 * (0.82)^1
Evaluate the exponent
P(2) = 3 * 0.0324 * (0.82)
Evaluate the product
P(2) = 0.079704
Approximate
P(2) = 0.08
Hence, the probability that two of three football games will go to into overtime is 0.08
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On a typical day, brianne uses her computer for 3 hours and her hair dryer for 10 minutes. what is the total cost of using both appliances for 6 days?
Answers
The total cost of using both appliances for 6 days is about 3000-4000 watt.
According to the statement
Brianne uses her computer for 3 hours
Brianne uses hair dryer for 10 minutes
Now we use the formula
C = wtc/1000
substitute the values in it
then
C = 600*6/1000
C = 3.6
and same for hair dryer
So, The total cost of using both appliances for 6 days is about 3000-4000 watt.
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If the farmer isn't present, the fox cannot be left with either the dog or the goose, or both. if need be, the goose can be left with the grain provided the dog is present because the dog will guard the grain and won't eat the goose. help the farmer cross the river.
Answers
Answer:
See below
Step-by-step explanation:
Take fox across
go back to get goose
take goose across
take fox BACK
grab dog.....take dog across
go back get grain and take it across
go back get fox and take it across
33. Companies will likely have autonomous robots delivering packages in the next few years. It has been determined that robots can meet their quotas if they have 4 robots for every 30 square miles of area they cover. If they want to offer service to a city of 75 square miles, how many robots must they have?
A)12 robots
B)10 robots
C)9 robots
D)15 robots
Answers
The number of robots have have for a city of 75 square miles would be 10 robots.
How many robots is needed for a 75 square miles?
The first step is to determine how many robots are needed for 1 square mile: 4/30.
The second step is to multiply this fraction by 75
4/30 x 75 = 10 robots
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1. Which of the statements is NOT true about the illustration?
Angle DME is another name for angle 3.
MDis congruent to AE.
Angle 3 is congruent to angle 5.
MEis parallel to AD.
Answers
Answer: Option (1)
Step-by-step explanation:
[tex]\angle DMA[/tex] is another name for angle 3, but not [tex]\angle DME[/tex].
please help me i need to turn this in soon and i don't understand
Answers
Answer:
(a) C=88pi
A=1936pi
(b) Area
(c) Circumference
Step-by-step explanation:
Circumference formula = 2r(pi)
Area formula = pi(r^2)
Circumference = 2(44)(pi) = 88pi
Area = pi(44^2) = 1936pi
When something is paved it is the whole area not just the border so AREA
The chain will surround the place not fill it up so CIRCUMFERENCE
a rectangle has a lengths and width of twelve and eight units, respectively. Using only multiplication show in a diagram which of the solutions below represent the perimeter of the entire rectangle
96 units
384 units
None of these
20 units
40 units
192 units
Answers
Answer:
40 units
Step-by-step explanation:
lengths:
12+12=24
width:
8+8=16
perimeter:
2l+2w
2(12)+2(8)
24+16=40
ales volume last weekend for four samples, each consisting of five car dealerships, were as follows: Data Point 1 2 3 4 5 Sample 1 37 15 43 25 21 Sample 2 38 31 12 19 28 Sample 3 16 21 45 32 25 Sample 4 19 10 45 37 22 What is the standard deviation of the distribution of sample means
Answers
The sample standard deviation of sample 1 is 11.54, of sample 2 is 10.21, of sample 3 is 11.25, of sample 4 is 14.15.
Given
Data point sample 1 sample 2 sample 3 sample 4
1 37 38 16 19
2 15 31 21 10
3 43 12 45 45
4 25 19 32 37
5 21 28 25 22
We have to find the sample standard deviation of each sample.
We have to first mean of each sample.
Sample mean of 1=141/5=28.2
Sample mean of 2=128/5=25.6
Sample mean of 3=139/5=27.8
Sample mean of 4=133/5=26.6
Sample standard deviation=[tex]\sqrt{}[/tex]∑[tex](x-x bar)^{2}/n-1[/tex]
∑[tex](x-x bar)^{2}[/tex] is calculated in the figure.
Sample standard deviation of sample 1=[tex]\sqrt{532.8/4}[/tex]
=[tex]\sqrt{133.2}[/tex]
=11.54
Sample standard deviation of sample 2=[tex]\sqrt{417.2/4}[/tex]
=[tex]\sqrt{104.3}[/tex]
=10.21
Sample standard deviation of sample 3=[tex]\sqrt{506.8/4}[/tex]
=[tex]\sqrt{126.7}[/tex]
=11.25
Sample standard deviation of sample 4=[tex]\sqrt{801.2/4}[/tex]
=[tex]\sqrt{200.3}[/tex]
=14.15.
Hence the sample standard deviation of sample 1 is 11.54, sample standard deviation of sample 2 is 10.21, sample standard deviation of sample 3 is 11.25, sample standard deviation of sample 4 is 14.15.
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The income statement comparison for rush delivery company shows the income statement for the current and prior year. required: a) determine the operating income (loss) for each year. (2 marks) b) determine the operating income (% of sales) for each year. (2 marks) c) the company made a strategic decision to invest in additional assets in the current year. these amounts are provided. using the total assets amounts as the investment base, calculate the roi. was the decision to invest additional assets in the company successful? explain. (3.5 marks) d) assuming an 8% cost of capital, calculate the ri for each year. explain how this compares to your findings in (c). (3.5 marks)
Answers
Company's average operating assets for last year is $193000, company's margin is 15%, return on investment is 42%, company's residual income for last year is $521000.
Given the balance sheet and income statement of Joel de Paris and we have to calculate company's average operating assets for last year, company's margin,return on investment and company's residual income for last year.
1) Company's average operating assets=
(beginning operating assets+closing operating assets)/2
={(2562000-349000-253000)+(2634000-434000-25000)}/2
=(1910000+1950000)/2
=3860000/2
=$1930000
2)Company's margin= net operating income/ sales
=810000/540400
=15%
3)Turnover=sales/average inventory
=540400/1930000*100
=27.9%
=28%
4) Return on investment=margin* turnover
=15% of 28%
=42%.
Hence company's average operating assets for last year is $193000, company's margin is 15%, return on investment is 42%, company's residual income for last year is $521000.
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The question is incomplete and the information of question is in figure.
The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°.
A) Use the Law of Cosines to find the length of the diagonal.
A) Use the Law of Sines to find the length of the shorter base.
Round your answers to the nearest hundredth.
You must show all of your work to receive credit.
Answers
The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
How to determine the lengthThe cosine rule is given as;
[tex]c = \sqrt{a^2 + b^2 - 2ab cos \alpha }[/tex]
c = length of the diagonal
a = base length = 22 feet
b = 7 feet
[tex]c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}[/tex]
[tex]c = \sqrt{533 - 308 * 0. 7660}[/tex]
[tex]c = \sqrt{533 - 235. 93}[/tex]
[tex]c = \sqrt{297. 072}[/tex]
[tex]c = 17. 24[/tex] feet
Using sine rule
[tex]\frac{a}{sin A } = \frac{c}{sin C}[/tex]
[tex]\frac{a}{sin 70} = \frac{17. 24}{sin 40}[/tex]
Cross multiply
[tex]a[/tex] × [tex]sin 60[/tex] = [tex]c[/tex] × [tex]sin 70[/tex]
[tex]a[/tex] × [tex]0. 8660[/tex] = [tex]17. 24[/tex] × [tex]0. 9397[/tex]
[tex]a = \frac{16. 20}{0. 8660}[/tex]
a = 18. 7 feet long
Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.
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14. Ashley is holding a fair six-sided die and a fair
coin. If Ashley rolls the die once and then flips
the coin, what is the probability that the die will
show a 5 and the coin will come up tails?
Answers
Answer:
1/12
Step-by-step explanation:
Landing on the 5 is a 1/6 chance, landing on tails is a 1/2 chance, multiply, and you get 1/12
The points (1, 5) and (0, –2) fall on a particular line. What is its equation in slope-intercept form?
Answers
The equation of the line in slope intercept form is y = 7x - 2
How to find the equation of a line?The equation of the line can be solved with the following equation.
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = -2 - 5 / 0 - 1 = -7 / -1
m = 7
Hence, using (1, 5)
y = 7x + b
5 = 7(1) + b
5 - 7 = b
b = -2
Therefore,
y = 7x - 2
Hence, the equation of the line in slope intercept form is y = 7x - 2
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Using the image below, identify the type of angle relationship, construct the equation, and find x. Do not include any spaces in your answers.
If you are using a screen-reader, please consult your instructor for assistance.
Type of Angle Relationship:
Angles (You may use spaces in your answer here.)
Equation:
+
=
Solve: x=
Answers
thanks!!
1) Now is your chance to find examples of sinusoids. Come up with some examples of natural or man-made phenomena that repeat at predictable intervals.
Search the Internet to find descriptions, and post the link as well as your analysis of why the behavior is periodic. You do not have to find an equation or write one. Examples already given in the lessons for this unit are off limits, so look for something new.
As you ride a ferris wheel, your distance from the ground varies sinusoidally with time. When the last passenger boards the ferris wheel and the ride starts moving, let your position be modeled by the diagram provided.
2) Let t be the number of seconds that have elapsed since you began moving. It takes you 5 seconds to reach the top of the wheel (38 feet above the ground) and 20 seconds to make a complete revolution. The diameter of the wheel is 30 feet.
Work with your classmates to answer the following questions:
What is the lowest you go as the ferris wheel turns?
Why is this number always greater than zero?
Write the equation of a sinusoid that describes this motion.
Predict your height above the ground when t = 3, t = 8, t = 15, and t = 19.
Answers
The examples of sinusoids include sound and water waves.
How to illustrate the information?Simple harmonic motion such as that of a pendulum or a weight attached to a spring results in a sinusoidal relationship between position and time.
The angle will be formed after t time of the starting of the motion.
θ = wt = 2πt/20 = πt/10
Radius of the wheel = 30/2 = 15 feet
Distance from the ground = (15 - 15cosθ) + 8 = (15 - 15cosπt/10) + 8
= 23 - 15cos(πt/10)
As we know the minimum value of the cos is -1
-1 ≤ cos(πt/10) ≤ 1
8 ≤ 23 - 15cos(πt/10) ≤ 38
The lowest distance = 8 feet
It should be always greater than zero as the lowest point of what should be above the ground.
d = 23 - 15cos(πt/10)
Plug t = 3 in the above equation:
d(3) = 14.18 feet
For t = 8
d(8) = 35.13 feet
For t = 15
d(15) = 23 feet
For t = 19
d(19) = 8.73 feet
Thus, the lowest distance is 8 feet, and the lowest point of what should be above the ground and the equation is d = 23 - 15cos(πt/10).
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help me please guys!!!
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathsf{|-8| + 9 = }[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\textsf{The additive inverse of }\mathsf{|-8|}\textsf{ is positive 8.}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathsf{|-8| + 9}[/tex]
[tex]\mathsf{= \bold 8 + 9}[/tex]
[tex]\mathsf{= 17}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{17}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{|-8 + 9| =}[/tex]
[tex]\huge\textbf{Random note:}[/tex]
[tex]\textsf{We will convert your equation to }\mathsf{-8 + 9}\textsf{ because it can make the equation}\\\textsf{a lot easier to solve.}[/tex]
[tex]\huge\textbf{Solving for the equation:}[/tex]
[tex]\mathsf{|-8 + 9|}[/tex]
[tex]\mathsf{= -8 + 9}[/tex]
[tex]\text{Start at }\rm{-8}\text{ and go \boxed{up} 9 spaces to the right and you have your answer.}[/tex]
[tex]\mathsf{= 1}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A sample of 148 college students at a large university reports getting an average of 6.85 hours of sleep last night with a standard deviation of 2.12 hours.
a.Verify that it is reasonable to use the t-distribution to construct a confidence interval for the average amount of sleep students at this university got last night.
b. Construct a 98% confidence interval for the average amount of sleep students at this university got last night. Use two decimal places in your margin of error.
c.. Provide an interpretation of your interval in the context of this data situation.
d.. Suppose you want to conduct a similar study at your university. Assuming that the standard deviation of this sample is a reasonable estimate of the standard deviation of sleep time at your university, how many students do you need to survey to estimate the mean sleep time of students at your university with 95% confidence and a margin of error of 0.5 hours?
Answers
The solution for the questions is mathematically given as
a)
t-distribution.
b)
the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952, 7.3048 )
c) the value of the [tex]\mu_0[/tex] is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_0; otherwise, reject H _0.
d)
you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.
What is the distribution to use?Generally, the equation for is mathematically given as
a.
In this case, the standard deviation of the population is unknown.
As a result, we make use of the t-distribution.
b)
We wish to generate a confidence interval with a 98 percent likelihood for the mean.
Because of this,
[tex](\bar{X}-t_{n-1,\alpha/2}\frac{s}{\sqrt{n}},\bar{X}+t_{n-1,\alpha/2}\frac{s}{\sqrt{n}})[/tex]
[tex](6.85-t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}},6.85+t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}})[/tex]
[tex](6.85-t_{147,0.01}\frac{2.12}{12.1655},6.85+t_{147,0.01}\frac{2.12}{12.1655})[/tex]
(6.3952,7.3048)
Therefore, the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952 , 7.3048 )
c )
If the value of the mu _0 is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_o; otherwise, reject H_0.
d . Here, we want to determine the sample size
Therefore,
[tex]n=t_{n-1,\alpha/2}^2\frac{s^2}{E^2}[/tex]
[tex]n=t_{148-1,0.05/2}^2\frac{2.12^2}{0.5^2}[/tex]
[tex]n=t_{147,0.025}^2\frac{2.12^2}{0.5^2}[/tex]
[tex]n=2.6097^2\frac{2.12^2}{0.5^2}[/tex]
n=122.4364
In conclusion, you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.
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[tex]27a^3+189a^2b+441ab^2+343b^3[/tex]
Answers
27a³ + 189a²b + 441ab² + 343b³ = (3a + 7b)³
How to simplify an expression?27a³ + 189a²b + 441ab² + 343b³
Therefore,
27a³ = (3a)³
189a²b = 3(3a)²(7b)
441ab² = 3(3a)(7b)²
343b³ = (7b)³
(3a)³ + (7b)³ + 3(3a)²(7b) + 3(3a)(7b)²
a³ + b³ + 3a²b + 3ab² = (a + b)³
Therefore,
27a³ + 189a²b + 441ab² + 343b³ = (3a + 7b)³
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Huan runs a business selling sweets. She is designing a container to hold the sweets. She uses rectangular pieces of cardboard measuring 20 cm by 30 cm. The mass of 1 square metre of the cardboard is 210 grams. She cuts a square from each corner of a piece of cardboard. She then folds the cardboard to make an open box. By changing the size of the square she cuts out, Huan can change the volume of the box.
(a) Work out the mass of the box made when she cuts a square of side 5cm from each corner.
(b) Huan cuts a square of side x from each corner of the cardboard.
(i) Explain why the volume of the box she makes is given by x(20-2x)(30-2x).
(ii) Explain why 0<x<10
(c) Huan wants to make a box with volume of at least 900cm3. She wants the mass of the box to be as small as possible.
By drawing a suitable graph, work out the mass of the box she will make
Answers
Answer:
d33z3 n0ts divided by ur m0m square root that x10 then divide by your d3pression.
Step-by-step explanation:
gotem
A psychologist treats 16 patients and records the number of sessions required to complete a behavioral therapy treatment for each patient. she computes ss = 800. assuming the 16 patients constitute all patients under her care (so the population of her patients), what is the standard deviation for these data?
Answers
Hence, the standard deviation for these data is 7.1 sessions
In statistics, the standard deviation is a measure of the volatility or variance of a set of values. [1] A low standard deviation indicates that the values tend to be close to the mean of the set (also known as the mean), and a high standard deviation indicates that the values are more widely distributed. indicate.
Standard deviation can be abbreviated as SD, and in mathematical texts and equations, it is most commonly represented by the Greek lower σ (sigma) for population standard deviation or the Latin letter s for sample standard deviation. It is a target.
The standard deviation of a random variable, sample, population, dataset, or probability distribution is the square root of its variance. It's algebraically simple, but it's actually less robust than mean absolute deviation. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data.
Expression
\ sigma = {\ sqrt {\ frac {\ sum (x_ {i}-{\ mu}) ^ {2}} {N}}}
\ sigma = Population standard deviation
N = size mother Population
x_i = Arbitrary value from population
\ mu = Population mean
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Do 7 ft, 9 ft, 11 ft form a right triangle
Answers
Answer:
no
Step-by-step explanation:
using the converse of Pythagoras' identity
if the square on the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.
longest side = 11 and 11² = 121
7² + 9² = 49 + 81 = 130
since 121 ≠ 130 then sides do not form a right triangle
I need to find the table of -csc theta
Answers
See below for the table of -csc theta
How to determine the table?The function is given as:
-csc theta
Rewrite properly as:
[tex]-\csc(\theta)[/tex]
This is calculated as:
[tex]-\csc(\theta) = -\frac{1}{\sin(\theta)}[/tex]
Set [tex]\theta[/tex] to 0, 30, 45, 60 and 90
[tex]-\csc(0) = unde fined[/tex]
[tex]-\csc(30) = -2[/tex]
[tex]-\csc(45) = -\sqrt 2[/tex]
[tex]-\csc(60) = -\frac{2\sqrt 3}{3}[/tex]
[tex]-\csc(90) = -1[/tex]
So, the table of -csc theta is
Angle -csc theta
0 undefined
30 -2
45 -√2
60 -2/3 √3
90 -1
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