Answer:
x = 14
Step-by-step explanation:
Extend line AB so that it intersects ray CE at point G. Then angles BGC and BAD are "alternate interior angles", hence congruent.
The angle at B is exterior to triangle BCG, and is equal to the sum of the interior angles at C and G:
138 = (376 -23x) +(x^2 -8x)
Subtracting 138 and collecting terms we have ...
x^2 -31x +238 = 0
For your calculator, a=1, b=-31, c=238.
__
Additional comment
You will find that the solutions to this are x = {14, 17}. You will also find that angle BCE will have corresponding values of 54° and -15°. That is, the solution x=17 is "extraneous." It is a solution to the equation, but not to the problem.
For x=14, the marked angles are A = 84°, C = 54°.
Peter walks at 5 kilometers per hour. Complete the table.
Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
Step-by-step explanation:
The tree is .0564 meters
Answer:
Step-by-step explanation:
de chill de chill
A new cylindrical can with a diameter of 4 cm is being designed by a local company The surface area of the can is 130 square centimeters What is the height of the can? Estimate using 3 14 for x and
round to the nearest hundredth Apply the formula for surface area of a cylinder SA-28+ Ph
The height of the can is approximately 9.74 centimeter.
Define surface area of cylinderThe surface area of a cylinder is the total area of the curved and flat surfaces that make up the cylinder. It can be calculated using the formula:
SA = 2πr² + 2πrh
where r is the radius of the cylinder and h is its height.
In this case, we are given that the diameter of the can is 4 cm, which means the radius is 2 cm.
We are also given that the surface area is 130 square centimeters. Substituting these values into the formula, we get:
130 = 2π(2)² + 2π(2)h
Simplifying this equation, we get:
130 = 8π + 4πh
Subtracting 8π from both sides, we get:
122 = 4πh
Dividing both sides by 4π, we get:
h = 122/(4π) ≈ 9.74 cm (rounded to the nearest hundredth using 3.14 for π)
Therefore, the height of the can is approximately 9.74 cm.
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is a fraction a term? If it's not a term, why is it that we can apply the distributive property to it? the distributive property only works for either terms, or addition and subtraction. a fraction is technically division, so why does it work? Please help!!!!!
No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.
A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.
The distributive property states that for any real numbers a, b, and c:
a × (b + c) = (a × b) + (a × c).
When working with fractions, we can apply the distributive property as follows:
Let's consider the expression: a × (b/c).
We can rewrite this as: (a × b)/c.
Now, let's distribute the 'a' to 'b' and 'c':
(a × b)/c = (a/c) × b.
In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.
Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.
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A certain type of novelty coin is manufac- tured so that 80% of the coins are fair while the rest have a .75 chance of landing heads. Let 0 denote the probability of heads for a novelty coin randomly selected from this population. a. Express the given information as a prior distribution for the parameter 0. b. Five tosses of the randomly selected coin result in the sequence HHHTH. Use this data to determine the posterior distribution of 0.
(a) a random variable coming from a normal distribution and p ( x < 5.3 ) = 0.79 , then p ( x > 5.3 ) = 0.21 .
(B) the posterior distribution will likely place more weight on values of 0 closer to 0.75, as the observed sequence is more likely to come from a biased coin than a fair coin.
In this problem, we are dealing with a population of novelty coins, where 80% of the coins are fair (with a 50% chance of landing heads) and the remaining 20% of the coins have a 75% chance of landing heads. We need to determine the prior distribution for the parameter 0, which represents the probability of heads for a randomly selected coin. The prior distribution can be expressed as a weighted combination of a random variable coming from a normal distribution and p ( x < 5.3 ) = 0.79 , then p ( x > 5.3 ) = 0.21 .
Given the sequence of tosses HHHTH from a randomly selected coin, we can use this data to calculate the posterior distribution of 0. The posterior distribution represents the updated probabilities for the parameter 0 after taking into account the observed data. In this case, the posterior distribution will be a combination of the prior distribution and the likelihood of observing the given sequence of tosses. By applying Bayesian inference, we can calculate the updated probabilities for 0 based on the data and the prior distribution.
To summarize, the prior distribution for the parameter 0 is a weighted combination of the probabilities of heads for fair coins and biased coins in the population. The posterior distribution is obtained by updating the prior distribution with the observed data, reflecting the updated probabilities for 0 based on the sequence of tosses HHHTH.
Now, let's explain the process of determining the posterior distribution of 0. We start with the prior distribution, which is a combination of 0.8 for fair coins and 0.75 for biased coins. After observing the sequence HHHTH, we calculate the likelihood of obtaining this sequence for each possible value of 0, considering the probabilities associated with fair and biased coins. For example, for a fair coin (0.5), the likelihood of observing HHHTH is (0.5)^4 * (1-0.5) = 0.03125, while for a biased coin (0.75), the likelihood is (0.75)^4 * (1-0.75) = 0.0703125.
To obtain the posterior distribution, we multiply the prior distribution by the corresponding likelihoods for each value of 0 and normalize the result to ensure it sums to 1. The normalized values represent the updated probabilities for 0, given the observed data. In this case, the posterior distribution will likely place more weight on values of 0 closer to 0.75, as the observed sequence is more likely to come from a biased coin than a fair coin.
In conclusion, the process of determining the posterior distribution involves updating the prior distribution with the observed data, considering the likelihood of obtaining the sequence of tosses. By applying Bayesian inference, we can calculate the updated probabilities for the parameter 0, reflecting our updated beliefs about the probability of heads for the randomly selected coin.
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Solve this equation
y= -3x +3
Answer:
What do you want me to do? It is already solved
Step-by-step explanation:
Peter says, "If you subtract 17 from my number and multiply the difference by - 2, the result is - 26."
What is Peter's number?
Peter's number is
Answer:
4 is the number
Step-by-step explanation:
(17-x)(-2)=-26
-34+2x=-26
2x=-26+34
2x=8
x=8/2
=4
f(x, m, s) = 1 √278² exp (-2/2 (x-m) ²) 28² Write a function in the form of gauss(x, m=0, s=1) for computing the Gaussian density. Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. Give the name of question5b (c) x-0, m-2, s-1. Give the name of question5e (d) x=0, m=2, s=2. Give the name of question5d (e) x=3, m-3, s-3.
Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.
To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.
First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:
Principal = $1,000
Rate of interest per period = 8% / 4 = 2% per quarter
Number of periods = 12 quarters
Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)
= $1,000 * (1 + 0.02)^12
≈ $1,166.41
Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):
Principal = $1,000
Rate of interest per period = 2% per quarter
Number of periods = 8 quarters
Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)
= $1,000 * (1 + 0.02)^8
≈ $1,165.16
Finally, we add the two values to find the total value of the account on January 1, 2021:
Total value = Value after three years + Value after two years
≈ $1,166.41 + $1,165.16
≈ $2,331.57
Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.
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Find the function f, if: f'(x)=2/(x^3) + 4e^x + 5, f(-1)=1, f(1)=-1 (Note: Consider the domain and write the answer in ascending order of the variable).
Answer:
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)
Step-by-step explanation:
We can find the function f(x) by integrating f'(x) with respect to x:
â«f'(x) dx = â«(2/(x^3) + 4e^x + 5) dx
f(x) = -1/x^2 + 4e^x + 5x + C
To find the constant C, we can use the given initial conditions:
f(-1) = 1 = -1/(-1)^2 + 4e^(-1) - 5 + C
C = 1 + 1/1 - 4e^(-1)
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)
Therefore, the function f(x) is:
f(x) = -1/x^2 + 4e^x + 5x + 1 + 1/x - 4e^(-1)
If RS = 17, ST = x + 6, and RT = 3x - 5, What is ST.
Answer:
ST = 20
Step-by-step explanation:
Line segment RS and segment ST must add up to line segment RT
Step 1: Define
RS = 17
ST = x + 6
RT = 3x - 5
Step 2: Set up equation
mRS + mST = mRT
17 + x + 6 = 3x - 5
Step 3: Solve for x
x + 23 = 3x - 5
23 = 2x - 5
28 = 2x
x = 14
Step 3: Find mST
ST = x + 6
ST = 14 + 6
ST = 20
Hello can someone help me plz
Answer:
A is 3 b is 2 C is 8 D is 9 hope it helps
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
2nd one
Emergency plz help me plz
Answer:
its c
Step-by-step explanation:
Answer:
-3/4
Step-by-step explanation:
the slope is rise/run
Solve the following systems of equation for x and y. Show your work on
how you solved for x and y
1. −4x − 2y = −12
4x + 8y = −24
2. x − y = 11
2x + y = 19
3. 5x + y = 9
10x − 7y = −18
4. −3x + 7y = −16
−9x + 5y = 16
5. −7x + y = −19
−2x + 3y = −19
6. 5x + 4y = −30
3x − 9y = −18
7. −4x + y = 6
−5x − y = 21
Add
2
y
to both sides of the equation.
−
4
x
=
−
12
+
2
ySolve for
x
in the first equation.
Tap for fewer steps...
Add
2
y
to both sides of the equation.
−
4
x
=
−
12
+
2
y
4
x
+
8
y
=
−
24
Divide each term by
−
4
and simplify.
Tap for fewer steps...
Divide each term in
−
4
x
=
−
12
+
2
y
by
−
4
.
−
4
x
−
4
=
−
12
−
4
+
2
y
−
4
4
x
+
8
y
=
−
24
Cancel the common factor of
−
4
.
Tap for more steps...
x
=
−
12
−
4
+
2
y
−
4
4
x
+
8
y
=
−
24
Simplify each term.
Tap for more steps...
x
=
3
−
y
2
4
x
+
8
y
=
−
24
Replace all occurrences of
x
with
3
−
y
2
in each equation.
Tap for more steps...
12
+
6
y
=
−
24
x
=
3
−
y
2
Solve for
y
in the first equation.
Tap for more steps...
y
=
−
6
x
=
3
−
y
2
Replace all occurrences of
y
with
−
6
in each equation.
Tap for more steps...
x
=
6
y
=
−
6
The solution to the system is the complete set of ordered pairs that are valid solutions.
(
6
,
−
6
)
The result can be shown in multiple forms.
Point Form:
(
6
,
−
6
)
Equation Form:
x
=
6
,
y
=
−
6
4
x
+
8
y
=
−
24 Answer: The answer to your ? is A
Answer:
-1, 1
Step-by-step explanation:
Khan Academy
The distance from building 1 to building 2 is 2,000 feet. The distance between building 2 and building 3 is 5,000 feet. The distance between building 1 and 3 is 1,000 feet. Do the building form a right triangle? Why or why not
Answer:
The angle between building 1 and building 3 at building 2 is not a right angle, and hence, the buildings do not form a right triangle.
Step-by-step explanation:
Given the function f(x)=5x−6 find f(4).
Answer:
f(4)=14
Step-by-step explanation:
f(x)=5x-6
f(4)=5(4)-6
f(4)=20-6
f(4)=14
Answer:
f(4) = 14
Step-by-step explanation:
f(x) = 5x -6
f(4) = 5(4) - 6
f(4) = 20 - 6
f(4) = 14
Igor, whose eye height is 4. 5 ft. , wishes to find the height of an oak tree out in front of his castle. He places a mirror on the ground between himself and the tree. He is now 5. 5 feet away from the center of the mirror and the mirrors is 70 feet from the tree. What is the height of the oak tree in front of Igor´s castle?
The height of the oak tree in front of Igor's castle is approximately 57.27 ft. To find the height of the oak tree, we can use the principle of similar triangles.
The height of the tree can be determined by comparing the ratio of the height of Igor to the distance between Igor and the mirror with the ratio of the height of the tree to the distance between the mirror and the tree.
Let's represent the height of the oak tree as 'h'. According to the problem, Igor's eye height is 4.5 ft, and he is 5.5 ft away from the center of the mirror. The mirror is placed 70 ft from the tree.
Using the similar triangles concept, we can set up the following proportion:
(height of Igor) / (distance between Igor and mirror) = (height of tree) / (distance between mirror and tree)
Plugging in the given values, we have:
4.5 ft / 5.5 ft = h / 70 ft
Solving this proportion, we find:
(4.5 ft * 70 ft) / 5.5 ft = h.
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The diagram shows a triangle.
3t
2t–50°
2t–50°
What is the value of t?
t =
An orthogonal rotation of factors identified in a factor analysis produces a communality of .30 for one of the tests included in the analysis. This means that ____% of variability in scores on that test is explained by the factor analysis.A. 9B. 49C. 30D. 70
Vertical angles are always adjacent. True False
Answer:
False
Step-by-step explanation:
Vertical angles are not always adjacent, but they are always congruent.
Hope that helps!
Answer:
False
Step-by-step explanation:
Hope it will help you*
Students in AP classes tend to increase their time studying in the weeks before the test. The
histograms show the distributions of studying times for a group of female students and a group of
male students during the week prior to their AP tests. Compare the distributions using their shapes
and appropriate measures of center and variation.
According to the information, we can infer that the histograms indicate that female students tend to have a higher frequency of studying times compared to male students during the week prior to their AP tests.
How to compare the distributions of each graph?By comparing the histograms, we can observe that the frequency of studying times for female students is generally higher across all time intervals compared to male students. Female students have a higher frequency in each category, indicating that they spend more time studying than male students during the week before the AP tests.
To further analyze the distributions, we can also consider the measures of center and variation. The measures of center, such as the mean or median, would provide insights into the typical studying time for each group. Additionally, measures of variation, such as the standard deviation or interquartile range, would indicate the spread or variability of studying times within each group.
Accoding to the above, based on the provided frequency distributions, it can be concluded that female students tend to dedicate more time to studying during the week prior to their AP tests compared to male students.
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use the chain rule to find dz/dt. z = tan−1(y/x), x = et, y = 9 − e−t
The rate of change of z with respect to t is given by [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2).
To use the chain rule to find dz/dt, we first need to find the partial derivatives of z with respect to x and y.
∂z/∂x = 1/(1 + (y/x)^2) * (y/x^2) = y/(x^2 + y^2)
∂z/∂y = -1/(1 + (y/x)^2) * (1/x) = -x/(x^2 + y^2)
Now we can apply the chain rule:
dz/dt = ∂z/∂x * dx/dt + ∂z/∂y * dy/dt
Substituting in the given values:
dx/dt = e^t
dy/dt = e^(-t)
x = e^t
y = 9 - e^(-t)
∂z/∂x = y/(x^2 + y^2) = (9 - e^(-t)) / (e^(2t) + (9 - e^(-t))^2)
∂z/∂y = -x/(x^2 + y^2) = -e^t / (e^(2t) + (9 - e^(-t))^2)
Substituting these into the chain rule formula:
dz/dt = [(9 - e^(-t)) / (e^(2t) + (9 - e^(-t))^2)] * e^t + [-e^t / (e^(2t) + (9 - e^(-t))^2)] * e^(-t)
Simplifying:
dz/dt = [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2)
Therefore, the rate of change of z with respect to t is given by [9e^t - e^(2t) - e^(-t)] / (e^(2t) + (9 - e^(-t))^2).
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jack needs 22 pirates for every 2 ships he manages
2.
To paint a house, a painting company charges a flat rate of $500 for supplies, plus $50 for
each hour of labor.
y (dollars)
4,000
3,000
2,000
1,000
10
20
30 40 50
x (hours)
1. How much would the painting company charge to paint a house that needs
20 hours of labor? A house that needs 50 hours?
Scom
60
2. Draw a line representing the relationship between x, the number of hours it
takes the painting company to finish the house, and y, the total cost of
painting the house. Label the two points from the earlier question on your
graph.
3. Find the slope of the line. What is the meaning of the slope in this context?
Using a linear function, it is found that:
1. The company would charge $1,500 for 20 hours of labor and $3,000 for 50 hours of labor.
2. The graph is given at the end of the answer.
3. The slope of 50 means that the cost of each additional hour of labor is of $50.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The flat rate is the intercept.The cost per hour is the slope.Hence the charge for x hours of labor is given by the following function:
C(x) = 50x + 500.
Then:
C(20) = 50(20) + 500 = $1500.C(50) = 50(50) + 500 = $3000.The company would charge $1,500 for 20 hours of labor and $3,000 for 50 hours of labor.
The slope of 50 means that the cost of each additional hour of labor is of $50.
The graph with the two points from item a labeled is given at the end of the answer.
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Please help me with this ASAP!!!!!
Answer:
Volume = 1099 cm³
Step-by-step explanation:
Volume = πr²h = 3.14(5²)(14) = 1099 cm³
sarah is trying to decide what combination of cups and plates to buy. her budget is $18. plates cost $6 each and cups cost $3 each. the numbers in the table represent total utility. given her budget, which combination will maximize total utility?
Answer:- Hence, the combination will maximize total utility is \(12.\)
Step-By-Step-Explanation:-
What is cost?
Cost is the amount of money you spent to make the product or service. Price is what you will charge for it.
Here given that,
The cups and plates budget is \($18 (3 plates x $6 each + 6 cups x $3 each)\)
Then the utility for the combination is \(12 (3 plates x 4 utility each + 6 cups x 2 utility each).\)
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Can anyone get the answer with an explanation i dont understand it
Answer:
\(d=\frac{2w(c-2)}{5} \)
Step-by-step explanation:
The given formula is:
c=5d+4w/2w
We need to find d.
Multiply 2w on both sides, we get
c x 2w= 5d+4w/2w x 2w
2cw=5d+4w
Adding -4w on both sides, we get
2cw-4w=5d+4w-4w.
2cw-4w=5d
2w(c-2)=5d
Dividing by 5, we get
2w(c-2)/5 = 5d/5
2w(c-2)/5 = d
Hence the required formula with subject d is
\(d=\frac{2w(c-2)}{5} \)
Please SHOW WORK, will mark brainlist if correct
The correct option is :
C. 18 cm
solution is in attachment !! :)
THIS IS VERY CONFUSING PLEASE HELP BRAINLIEST IF CORRECT 60 POINTS DONT ANSWER IF YOU DONT KNOW THE ANSWER OR REPORTED PLEASE DO NOT
which statement is correct?
A.29 > | -29 |
B.| -22 | 22
D. | -29 | < | 0 |
Answer:
see below
Step-by-step explanation:
A.29 > | -29 |
Absolute value means take the non negative value
A.29 > 29
This is not true
B.| -22 | 22
Absolute value means take the non negative value
22 You do not have an inequality so we cannot solve this
D. | -29 | < | 0 |
Absolute value means take the non negative value
29 < 0
This is not true
Since A and D are not true, B must be true
a(n) ____ is a mathematical representation of an object created by a special software
A(n) MODEL is a mathematical representation of an object created by a special software.
In computer science, a model is a mathematical abstraction of a system, process, or phenomenon that is intended to be simulated or executed on a computer system. A model is used to represent a system or process as a set of mathematical equations or logical rules in order to simulate or analyze it with a computer program.
It can be a physical object, such as a car or building, or an abstract concept, such as an economic system or a social network. In general, a model can be a simple or complex representation of a real-world object or process, and it can be used for a variety of purposes, such as predicting future outcomes, testing hypotheses, or designing new systems.
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