Solve 170 = 134 + 65sin(pi/6)t
Answers
The solution is t = 0.5538.
To solve for t, we need to isolate the sin term on one side of the equation:
170 = 134 + 65sin(pi/6)t
Subtract 134 from both sides:
36 = 65sin(pi/6)t
Divide both sides by 65:
36/65 = sin(pi/6)t
Now we can solve for t by dividing both sides by sin(pi/6):
t = (36/65) / sin(pi/6)
Using a calculator, we can simplify sin(pi/6) to 0.5:
t = (36/65) / 0.5
t = 0.5538
To solve the equation 170 = 134 + 65sin(pi/6)t, follow these steps:
1. Subtract 134 from both sides:
36 = 65sin(pi/6)t
2. Divide both sides by 65:
36/65 = sin(pi/6)t
3. Calculate the inverse sine (arcsin) of both sides:
arcsin(36/65) = (pi/6)t
4. Multiply both sides by 6/pi to solve for t:
t = 6(arcsin(36/65))/pi
Now you can use a calculator to find the numerical value of t if needed.
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Related Questions
Jane is a new engineer at a factory, and part of her job is lowering the number of defective
parts produced. In her first month, there were 1,280 defective parts. In her second month,
there were 1,088 defective parts.
Write an exponential equation in the form y = a(b)* that can model the monthly number of
defective parts, y, x months after Jane was hired.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y = 1.8( )*
How many months after Jane was hired will the monthly number of defective parts be less
than 500?
Submit
months
Answers
The exponential function is \(y = 1505.88(0.85)^x\).
The monthly number of defective parts will be less than 500 about 7 months after Jane was hired.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
To model the monthly number of defective parts, we can use an exponential equation of the form:
\(y=a(b)^x\)
Where y is the number of defective parts, x is the number of months after Jane was hired, a is the initial number of defective parts, and b is the common ratio between consecutive months.
To find the values of a and b, use the two data points given -
In the first month, there were 1,280 defective parts, which means that y = 1280 when x = 1.
In the second month, there were 1,088 defective parts, which means that y = 1088 when x = 2.
Substituting these values into the exponential equation -
1280 = a(b)
1088 = a(b)²
Dividing the second equation by the first equation -
1088/1280 = (a(b)²)/(a(b))
0.85 = b
Substituting b = 0.85 into the first equation -
1280 = a(0.85)
1280 = 0.85a
a = 1505.88 (rounded to two decimal places)
So the exponential equation that models the monthly number of defective parts is -
\(y = 1505.88(0.85)^x\)
To find when the monthly number of defective parts will be less than 500, we can set y = 500 and solve for x -
\(500 = 1505.88(0.85)^x\)
Dividing both sides by 1505.88 -
\(0.332 = (0.85)^x\)
Taking the logarithm of both sides (with any base) -
log(0.332) = x log(0.85)
Dividing both sides by log(0.85) -
x = log(0.332) / log(0.85)
x ≈ 6.87
Therefore, the monthly number of defective parts will be less than 500 about 7 months after Jane was hired.
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how do we find the values of x and y.
Answers
We are given the following equation in vector form:
\(\begin{bmatrix}{5x} & {} \\ {20} & {}\end{bmatrix}=\begin{bmatrix}{3} & {} \\ {5y} & {}\end{bmatrix}\)To solve the equation we need to remember that two vectors are equal of the corresponding elements are equal. Therefore, we set equal the first elements:
\(5x=3\)Now, we divide both sides by 5:
\(x=\frac{3}{5}\)Now, we set equal the second elements:
\(20=5y\)Now, we divide both sides by 5:
\(\begin{gathered} \frac{20}{5}=y \\ \\ 4=y \end{gathered}\)Therefore, "x = 3/5" and "y = 4".
If a position on the ocean floor is 12 kilometers below the sea level, which value describes the elevation of the ocean floor
Answers
Answer:
- 12
Step-by-step explanation:
The sea level serves as a reference point and may be used to describe objacetsvir positions above or below it. Therefore, the sea level is regarded as a zero point or level. Hence, objects below are describes to be at a negative distance while those above are assigned the positive sign. Hence, for a position which is 12 km below sea level, then the object is said to be at a distance of - 12 km (below sea level takes the negative sign.)
Please help me i am confused :)
Answers
Answer:
A
Step-by-step explanation:
A herd of cows is stricken by an outbreak of cold cow disease. The disease lowers a cow's body temperature from normal levels, and a cow will die if its temperature goes below 90 degrees F. The disease epidemic is so intense that it lowered the average temperature of the herd to 85 degrees. Body temperatures as low as 70 degrees, but no lower, were actually found in the herd. - Use Markov's Theorem to prove that at most 3/4 of the cows could survive. [15 marks] - Suppose there are 400 cows in the herd. Show that the bound from the previous part is the best possible by giving an example set of temperatures for the cows so that the average herd temperature is 85 and 3/4 of the cows will have a high enough temperature to survive.
Answers
Using Markov's Theorem, it can be proven that at most 3/4 of the cows in a herd can survive an outbreak of cold cow disease. This is demonstrated by showing an example set of temperatures for a herd of 400 cows where the average temperature is 85 degrees and 3/4 of the cows have a temperature high enough to survive.
Markov's Theorem states that for any set of temperatures in a herd of cows, the probability that a cow's temperature is below a certain threshold is less than or equal to the ratio of the average temperature to the threshold temperature. In this case, the threshold temperature is 90 degrees, which is the minimum temperature for survival.
To prove that at most 3/4 of the cows can survive, we assume that all cows with temperatures below 90 degrees will die. Since the average temperature of the herd is 85 degrees, we can use Markov's Theorem to show that the probability of a cow having a temperature below 90 degrees is 85/90 = 17/18.
Now, let's consider a herd of 400 cows. If we assume that the probability of a cow having a temperature below 90 degrees is 17/18, then the expected number of cows with temperatures below 90 degrees would be (17/18) * 400 = 377.78. Since we cannot have a fraction of a cow, the maximum number of cows with temperatures below 90 degrees is 377.
Therefore, the maximum number of cows that can survive the outbreak is 400 - 377 = 23. This means that at most 23/400 = 3/4 of the cows can survive.
To demonstrate that this bound is the best possible, we can construct an example set of temperatures where 3/4 of the cows survive. Let's say 300 cows have a temperature of 90 degrees and 100 cows have a temperature of 70 degrees. The average temperature of the herd would be (300 * 90 + 100 * 70) / 400 = 85 degrees. In this scenario, 3/4 of the cows (300) have a high enough temperature to survive, which matches the bound from Markov's Theorem.
Thus, by applying Markov's Theorem and providing an example, it is proven that at most 3/4 of the cows in a herd can survive an outbreak of cold cow disease.
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Use the graph to evaluate the function.
f(-5) =
y
-8 -6
Answers
Answer:
-4
Step-by-step explanation:
Go to x value of -5 and go down until you touch line.
What is the area of a circle with a radius of 12 feet?
Answers
Answer:
\(144 \times \pi = 452.38\)
Answer:
144π ft² or approximately 452.16 ft²
Step-by-step explanation:
The area of a circle is \(\pi r^2\), where r = radius. We're given the radius as 12 feet. For pi, we can solve area in terms of pi or approximate pi to 3.14.
Approximation of Pi:
\(3.14 *12^2\) \(3.14*144\) \(452.16\) 452.16 ft²In terms of Pi:
\(\pi *12^2\) \(\pi *144\) \(144\pi\) 144π ft²a rectangular patio is 9 ft by 6 ft. when the length and width are increased by the same amount, the area becomes 88 sq ft. ginger is using the zero product property to solve the equation (6 x)(9 x)
Answers
Solving the equation (6x)(9x) using the zero product property we get the solution is x = 2.
To find the solution to the equation, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. In this case, the product of (6x) and (9x) is given as 88 square feet. So, we have the equation (6x)(9x) = 88.
To solve this equation, we can first simplify it by multiplying the terms inside the parentheses. (6x)(9x) becomes 54x^2. Now our equation is 54x^2 = 88.
To isolate x, we divide both sides of the equation by 54. This gives us x^2 = 88/54. Simplifying further, we have x^2 = 22/27.
Taking the square root of both sides of the equation, we get x=±√(22/27). However, since the length and width of the rectangular patio are increased, we are only interested in the positive value of x.
Approximating the value of √(22/27), we find that x ≈ 0.832. This value represents the amount by which both the length and width of the patio should be increased to obtain an area of 88 square feet.
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Frito-Lay Fiery Mix Variety Pack (20 Count) are assembled by a process at a Frito-Lay facility that produces an overall normally distributed weight with mean of 556.8g and standard deviation of 1.2g. If a recent order from Walmart demands that the overall weight must be no less than 556g and no more than 558g, what is the chance that Walmart's quality standard will be satisfied by the average weight of a random sample of 10 bags of Fiery Mix pack? (Enter the probability as a decimal number with as many digits after the decimal point as you can enter, e.g. 0.1234. DO NOT ENTER as 12.34% or 12.34) You might get different values every time you answer this question.
Answers
The probability that Walmart's quality standard will be satisfied by average weight of a random sample of 10 bags of the Frito-Lay Fiery Mix Variety Pack is calculated using the properties of normal distribution.
The average weight of a random sample of 10 bags from the Frito-Lay Fiery Mix Variety Pack follows a normal distribution with the same mean as the individual bags (556.8g) but with a standard deviation equal to the original standard deviation divided by the square root of the sample size \(\(\frac{{1.2g}}{{\sqrt{10}}}\)\). To find the probability that the average weight falls within Walmart's demanded range (556g to 558g), we need to calculate the area under the normal curve between these two values.
To do this, we can standardize the values by subtracting the mean from each limit and dividing by the standard deviation of the sample mean. This will give us the z-scores for each limit. Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities for each z-score. The probability between these two limits represents the chance that Walmart's quality standard will be satisfied.
Please note that the specific decimal value for the probability may vary depending on the z-table or calculator used, but it will typically be a small probability since the demanded range is relatively narrow.
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The temperature in the morning was -4 F. At night the temperature dropped to -12.8 F. How can the temperature drop from the morning to the night be represented?
A. 16.8 F
B. 8.4 F
C. -8.8 F
D. -16.8 F
Answers
Answer:
C. -8.8 F is the answer!
Step-by-step explanation:
did the question
I kinda got stuck on this
Answers
Answer:
220 yards
Step-by-step explanation:
15*1760 = 26,400
26,400/120 = 220
Suppose M is a point in the interior of ZJKL.
If mZMKL = 42 and mZJKL = 84, what is mZJKM?
Answers
\(\angle JKL=\angle JKM+\angle MKL \\ \\ 84^{\circ}=\angle JKM+42^{\circ} \\ \\ \boxed{\angle JKM=42^{\circ}}\)
Which expression is equivalent to -3[4*-0.50]?
–12x – 1.50
–12x + 1.50
–12x – 2.50
–12x – 3.50
Answers
In given expressions no one is equivalent to the expression -3 [4 × -0.50]
Given,
The expression : -3 [4 × -0.50]
We have to find the expression equivalent to the above expression from the given options.
Solve the expression:
-3 [4 × -0.50] = -3 × -2 = 6
Now we can solve the expressions given in the options:
1) -12 × -1.50 = 18
Not equal to the given expression
2) -12 × 1.50 = -18
Not equal to the given expression
3) -12 × -2.50 = 30
Not equal to the given expression
4) -12 × -3.50 = 42
Not equal to the given expression
So, we can conclude that, there is no equivalent expression in the options for the expression -3 [4 × -0.50]
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PLEASE ANSWER! I WILL GIVE 25 POINTS! NEED IT IN 10 AND WILL GIVE U MAKE U BRAINLIEST!
Answers
Answer: here you go this should do the trick.
Answer: the slope is -1/2 and the y-intercept is (0,4)
The parallelogram shown below has an area of 84 units2.
6
h
Find the missing height.
h=
units
Answers
Answer:
h = 14 units
Step-by-step explanation:
area of a parallelogram = b*h
where:
area = 84 sq. units
b = 6 units
h = ? units
plugin values into the formula:
84 = 6 (h)
h = 84 / 6
h = 14 units
determine an equation of the tangent line to the curve y^2-x^2y=3-2y
Answers
This is the equation y = [(x₀y₀ - 2y₀) / (2y₀ - x₀²)](x - x₀) + y₀ of the tangent line to the curve y² - x²y = 3 - 2y at the point (x₀, y₀).
To find the equation of the tangent line to the curve y² - x²y = 3 - 2y at a point (x₀, y₀), we need to follow these steps
Find the slope of the tangent line at the point (x₀, y₀) by taking the derivative of the curve with respect to x and evaluating it at that point.
Use the point-slope form of the equation of a line to write the equation of the tangent line, using the slope and the point (x₀, y₀).
Let's do these steps one by one
Finding the slope of the tangent line:
We start by taking the derivative of the curve with respect to x
2y(dy/dx) - x²(dy/dx) - xy + x²(dy/dx) = 0
Simplifying and solving for dy/dx, we get
dy/dx = (xy - 2y) / (2y - x₂)
Now, we evaluate this expression at the point (x₀, y₀).
dy/dx = (x₀y₀ - 2y₀) / (2y₀ - x₀²)
This gives us the slope of the tangent line at the point (x₀, y₀).
Writing the equation of the tangent line
Using the point-slope form of the equation of a line, we can write the equation of the tangent line
y - y₀ = m(x - x₀)
where m is the slope we found in step 1, and (x₀, y₀) is the point of tangency.
Plugging in the values we found, we get
y - y₀ = [(x₀y₀ - 2y₀) / (2y₀ - x₀²)](x - x₀)
Finally, we can simplify this equation by rearranging it
y = [(x₀y₀ - 2y₀) / (2y₀ - x₀²)](x - x₀) + y₀
This is the equation of the tangent line to the curve at the point (x₀, y₀).
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Can someone please tell me how to solve this and this type of questions?
Answers
P is (4,0) R is (-6,-4)
Then you can plug it into this formula: (x1-x2)^2 + (y1-y2)^2
Using P and R coordinates that’s:
(4- -6)^2 + (0- -4)^2
10^2 + 4^2
100 + 16=
116
Then you are going to find the square root
So 116 square root is 10.8 rounding to the nearest tenth
Hope this helps!
find all solutions of the equation in the interval (0 2π) : 2sinθ 1=0
Answers
The solutions of the equation 2sinθ - 1 = 0 in the interval (0, 2π) are θ = π/6 and θ = 13π/6.
To find all solutions of the equation 2sinθ - 1 = 0 in the interval (0, 2π), we can solve for θ by isolating the sine term and then using inverse sine (arcsin) to find the angles.
Start with the equation: 2sinθ - 1 = 0.
Add 1 to both sides of the equation: 2sinθ = 1.
Divide both sides by 2: sinθ = 1/2.
Take the inverse sine (arcsin) of both sides: θ = arcsin(1/2).
The inverse sine (arcsin) of 1/2 is π/6, so we have one solution θ = π/6.
However, we need to find all solutions in the interval (0, 2π). Since the sine function has a periodicity of 2π, we can add 2π to the solution to find additional solutions.
Adding 2π to π/6, we get θ = π/6 + 2π = π/6, 13π/6.
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Help please due asappp
Suppose that the functions f and g are defined as follows
Answers
x and x⁴-16x²+56 are the resulting composite functions respectively.
Solving composite functionsGiven the following functions below
f(x) = 7/x
g(x) = x² - 8
We need to determine the composite functions (fof)(x) and (gog)(x)
(fof)(x) = f(f(x))
f(f(x)) = f(7/x)
Replace x with 7/x
f(7/x) = 7/(7/x)
f(7/x) = 7 * x/7
f(7/x) = x
Similarly:
(gog)(x) = g(g(x))
g(g(x)) = (x² - 8)² - 8
g(g(x)) = x⁴-16x²+64 - 8
g(g(x)) = = x⁴-16x²+56
Hence the resulting composite functions of f(f(x) and g(g(x)) are x and x⁴-16x²+56
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Kieran and Louise each think of a number.
4 less than Kieran's number is equal to 2 lots of Louise's
number.
3 lots of Kieran's number added to Louise's number is 68.
Using the information above, write and solve two
simultaneous equations to work out Kieran and Louise's
numbers.
Answers
Using simultaneous equations, Kieran and Louise's numbers are 20 and 8 respectively.
How to represent situation with system of equation?Kieran and Louise each think of a number. 4 less than Kieran's number is equal to 2 lots of Louise's number.
let's
x = Kieran's number
y = Louise's number.
x - 4 = 2y
x - 2y = 4
3 lots of Kieran's number added to Louise's number is 68.
Hence,
3x + y = 68
Hence, let's combine the system of equation.
x - 2y = 4
3x + y = 68
multiply equation(i) by 3
3x - 6y = 12
3x + y = 68
-7y = -56
y = -56 / -7
y = 8
Therefore, let's find x
x = 4 + 2y
x = 4 + 2(8)
x = 4 + 16
x = 20
Hence,
Kieran number = 20
Louise number = 8
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what does the observed score represent in classical test theory?
2.) compare test-retest and alternate forms reliabilities. what are the strengths and weaknesses of each approach?
please please respond to questions 1 and 2 well done! i posted it before and it was completely wrong and confusing, it is for my applied research methods class! please be detailed and specific. i want to see questions 1 & 2, i would really appreciate it. i really need it. its simple.
Answers
The observed score in classical test theory represents an individual's raw score on a test or assessment without any adjustments or corrections.
What is the concept of observed score in classical test theory?In classical test theory, the observed score refers to the raw score obtained by an individual on a test or assessment.
It is a straightforward representation of the number of correct responses or points earned by the test taker.
The observed score does not take into account any measurement errors or variations that might have occurred during the testing process. It is a simple and direct reflection of the test taker's performance on the specific test at a given point in time.
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Select true or false for each statement.
True
False
Surface area and volume both measure the amount of space
occupled by a solid figure.
A
B
True
False
Surface area and volume are measured using the same unit.
A
B
True
False
Surface area and volume are both attributes of solid figures.
A
B
Answers
Answer:
1 is false
2 is false
3 is true
Step-by-step explanation:
8p-6=2p
how do you solve this
Answers
Step-by-step explanation:
you want to get p by itself
8p-6=2p
subtract 8p from both sides
-6=-6p
then you divide both sides by -6
p= 1
which of the following expressions are equivalent to -5/8-(-1/8-1/8
Answers
The expression that is equivalent to -5/8-(-1/8-1/8) will be C. - 3/8.
How to illustrate the expression?Arithmetical statements that have at least two terms connected by an operator and containing either numbers, variables, or both are regarded to as expressions. Mathematical operations involve addition, subtraction, multiplication, and division. The expression x + y, for example, consists of the terms x and y with an addition operator in between them.
The expressions are equivalent to -5/8-(-1/8-1/8) will be:
= -5/8 - (-1/8 - 1/8)
= -5/8 - (2/8)
= - 5/8 + 2/8
= - 3/8
Therefore, the correct option is C.
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which of the following expressions are equivalent to -5/8-(-1/8-1/8)
-7/8
-5/8
-3/8
-1/2
Ernesto brings his dog to training classes. The equation -60x + 2y - 120 =0 relates y, the total cost of a pets training and x, the number of classes taken Ernesto states that the y-intercept of the line represented by the equation is 30. is he correct?
Answers
The y-intercept of the line represented by the equation is; 60.
What is the y-intercept of the line represented by the equation?It follows from the task content that the y-intercept of the line represented by the equation is to be determined.
On this note, we must recall that the y-intercept of an equation is the value of y when x = 0.
Therefore, we have;
-60 (0) + 2y - 120 = 0
2y = 120
y = 60.
Hence, the y-intercept of the line represented by the equation is; 60.
Consequently, it can be inferred that the Ernesto is wrong in his evaluation of the y-intercept as 30.
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BC =
Round your answer to the nearest hundredth.
B
50°
7
Answers
Answer:
BC = 5.87
Step-by-step explanation:
Reference angle = 50°
Side Opposite to reference angle = 7
Adjacent side = BC = ?
Apply trigonometric function, TOA, thus:
Tan 50 = Opp/Adj
Tan 50 = 7/BC
BC × Tan 50 = 7
BC = 7/Tan 50
BC = 5.87369742 ≈ 5.87 (nearest hundredth)
Answer:
5.87
Step-by-step explanation:
khan said it was correct.
SIMPLE CONGRUENCE QUESTION!!! LOTS OF POINTS!
Answers
Answer:
A. Side-Angle-Side (SAS).
Step-by-step explanation:
Sides go first. Side.
Angle next. Angle.
Side again. Side.
You got Side angle side.
If quadrilateral be ABCD
There are two traingles∆ABC and ∆ADC
Now
AD=BC<DAC=<ACB<BAC=<DCAHence
Angle Angle side is correct
In isosceles ABC, AB=AC. if B=55,calculate A
Answers
Answer:
Two base angles of an isosceles triangles are equal.
55 + 55 + a = 180
110 + a = 180
a = 180-110
a = 70
Any help on this please?
Answers
Answer:
18
Step-by-step explanation:
1:14
x:252
252/14= 18
The question is: You and your second favorite pet moose each start a new job. After w weeks, you have (10w +120) dollars in your bank account and your pet moose has (45w + 25) dollars in their account. How much money do you have after 5 weeks? How much money does your pet moose have after the same 5 weeks?
Answers
Money after w weeks in my account :
\(M_m=10w+20\)
Money after w weeks in pet moose account :
\(M_p=45w+25\)
Now,
Money I have after 5 weeks, \(M_m=10w+20=(10\times 5)+20=\$70\)
Money pet have after 5 weeks, \(M_p=(45\times 5)+25=\$250\)
Hence, this is the required solution.